File ‹SMT_Examples_CVC.certs›

6a33976868a55be638caf0f290f64cb011c34b04 9 0
unsat
(
(assume a0 (! (not true) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_2)) (not @p_1) false) :rule equiv_pos2)
(step t1 (cl @p_2) :rule evaluate)
(step t2 (cl false) :rule resolution :premises (t0 t1 a0))
(step t3 (cl (not false)) :rule false)
(step t4 (cl) :rule resolution :premises (t2 t3))
)
c67da9daed0375d1fc6c0a90c7c24f255500088b 42 0
unsat
(
(assume a1 (! (= y$ (! (+ x$ 4) :named @p_1)) :named @p_2))
(assume a2 (! (not (! (< 0 (! (- y$ x$) :named @p_3)) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (= (! (>= (! (+ x$ (! (* -1 y$) :named @p_6)) :named @p_7) 0) :named @p_8) false) :named @p_18)) (! (not @p_8) :named @p_10) false) :rule equiv_pos2)
(step t1 (cl (not (! (= @p_2 (! (= x$ (! (+ -4 y$) :named @p_19)) :named @p_24)) :named @p_25)) (not @p_2) @p_24) :rule equiv_pos2)
(step t2 (cl (= @p_1 (! (+ 4 x$) :named @p_26))) :rule poly_simp)
(step t3 (cl (= @p_2 (! (= y$ @p_26) :named @p_27))) :rule cong :premises (t2))
(step t4 (cl (= (* 4 (- y$ @p_26)) (* -4 (- x$ @p_19)))) :rule poly_simp)
(step t5 (cl (= @p_27 @p_24)) :rule poly_simp_rel :premises (t4))
(step t6 (cl @p_25) :rule trans :premises (t3 t5))
(step t7 (cl @p_24) :rule resolution :premises (t1 t6 a1))
(step t8 (cl (= @p_6 @p_6)) :rule refl)
(step t9 (cl (= @p_7 (! (+ @p_19 @p_6) :named @p_20))) :rule cong :premises (t7 t8))
(step t10 (cl (= 0 0)) :rule refl)
(step t11 (cl (= @p_8 (! (>= @p_20 0) :named @p_21))) :rule cong :premises (t9 t10))
(step t12 (cl (= @p_20 (! (+ @p_6 y$ -4) :named @p_23))) :rule poly_simp)
(step t13 (cl (= @p_23 -4)) :rule poly_simp)
(step t14 (cl (= @p_20 -4)) :rule trans :premises (t12 t13))
(step t15 (cl (= @p_21 (! (>= -4 0) :named @p_22))) :rule cong :premises (t14 t10))
(step t16 (cl (= @p_22 false)) :rule evaluate)
(step t17 (cl (= @p_21 false)) :rule trans :premises (t15 t16))
(step t18 (cl @p_18) :rule trans :premises (t11 t17))
(step t19 (cl (not (! (= @p_5 @p_8) :named @p_9)) (not @p_5) @p_8) :rule equiv_pos2)
(step t20 (cl (= @p_4 (! (not (! (>= 0 @p_3) :named @p_12)) :named @p_13))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_3))
(step t21 (cl (= @p_3 (! (+ y$ (! (* -1 x$) :named @p_14)) :named @p_17))) :rule poly_simp)
(step t22 (cl (= @p_17 (! (+ @p_14 y$) :named @p_15))) :rule poly_simp)
(step t23 (cl (= @p_3 @p_15)) :rule trans :premises (t21 t22))
(step t24 (cl (= @p_12 (! (>= 0 @p_15) :named @p_16))) :rule cong :premises (t23))
(step t25 (cl (= (* 1 (- 0 @p_15)) (* 1 (- @p_7 0)))) :rule poly_simp)
(step t26 (cl (= @p_16 @p_8)) :rule poly_simp_rel :premises (t25))
(step t27 (cl (= @p_12 @p_8)) :rule trans :premises (t24 t26))
(step t28 (cl (= @p_13 @p_10)) :rule cong :premises (t27))
(step t29 (cl (= @p_4 @p_10)) :rule trans :premises (t20 t28))
(step t30 (cl (= @p_5 (! (not @p_10) :named @p_11))) :rule cong :premises (t29))
(step t31 (cl (= @p_11 @p_8)) :rule rare_rewrite :args ("bool-double-not-elim" @p_8))
(step t32 (cl @p_9) :rule trans :premises (t30 t31))
(step t33 (cl @p_8) :rule resolution :premises (t19 t32 a2))
(step t34 (cl false) :rule resolution :premises (t0 t18 t33))
(step t35 (cl (not false)) :rule false)
(step t36 (cl) :rule resolution :premises (t34 t35))
)
1ba6ec6538d8c03dbbe235e2b369b94d433e9a7c 19 0
unsat
(
(assume a0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_2)) :named @p_3))
(step t0 (cl (not (! (= @p_3 false) :named @p_4)) (not @p_3) false) :rule equiv_pos2)
(step t1 (cl (! (= p$ @p_1) :named @p_6)) :rule aci_simp)
(step t2 (cl @p_2) :rule symm :premises (t1))
(step t3 (cl (= @p_2 @p_6)) :rule cong :premises (t2 t1))
(step t4 (cl @p_2) :rule symm :premises (t1))
(step t5 (cl (= @p_6 (! (= p$ p$) :named @p_7))) :rule cong :premises (t4))
(step t6 (cl (= @p_7 true)) :rule rare_rewrite :args ("eq-refl" p$))
(step t7 (cl (= @p_6 true)) :rule trans :premises (t5 t6))
(step t8 (cl (= @p_2 true)) :rule trans :premises (t3 t7))
(step t9 (cl (= @p_3 (! (not true) :named @p_5))) :rule cong :premises (t8))
(step t10 (cl (= @p_5 false)) :rule evaluate)
(step t11 (cl @p_4) :rule trans :premises (t9 t10))
(step t12 (cl false) :rule resolution :premises (t0 t11 a0))
(step t13 (cl (not false)) :rule false)
(step t14 (cl) :rule resolution :premises (t12 t13))
)
75dac6089759ea6ef02a54a865f71a1426e6d402 7 0
unsat
(
(assume a0 (! (not (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1)) :named @p_2))
(step t0 (cl @p_1) :rule not_implies1 :premises (a0))
(step t1 (cl (not @p_1)) :rule not_implies2 :premises (a0))
(step t2 (cl) :rule resolution :premises (t0 t1))
)
5ab63980555417b7de4f9399d609940016dba3e7 9 0
unsat
(
(assume a0 (! (not (=> (or (and p1$ p2$) p3$) (! (or (! (=> p1$ (or (and p3$ p2$) (and p1$ p3$))) :named @p_1) p1$) :named @p_2))) :named @p_3))
(step t0 (cl (not @p_2)) :rule not_implies2 :premises (a0))
(step t1 (cl (not @p_1)) :rule not_or :premises (t0) :args (0))
(step t2 (cl p1$) :rule not_implies1 :premises (t1))
(step t3 (cl (not p1$)) :rule not_or :premises (t0) :args (1))
(step t4 (cl) :rule resolution :premises (t2 t3))
)
37084f38567b6e7dfcdc944a26d43e7f17554473 9 0
unsat
(
(assume a0 (! (not (or p$ (! (not p$) :named @p_1))) :named @p_2))
(step t0 (cl (not (! (not @p_1) :named @p_3)) p$) :rule not_not)
(step t1 (cl @p_3) :rule not_or :premises (a0) :args (1))
(step t2 (cl p$) :rule resolution :premises (t0 t1))
(step t3 (cl @p_1) :rule not_or :premises (a0) :args (0))
(step t4 (cl) :rule resolution :premises (t2 t3))
)
a6b36d11a7dec4cdc7523db64e3404e9aa32e67a 11 0
unsat
(
(assume a0 (! (not (=> (! (and (! (or p$ q$) :named @p_2) (! (not p$) :named @p_1)) :named @p_3) q$)) :named @p_4))
(step t0 (cl @p_3) :rule not_implies1 :premises (a0))
(step t1 (cl @p_2) :rule and :premises (t0) :args (0))
(step t2 (cl p$ q$) :rule or :premises (t1))
(step t3 (cl (not q$)) :rule not_implies2 :premises (a0))
(step t4 (cl p$) :rule resolution :premises (t2 t3))
(step t5 (cl @p_1) :rule and :premises (t0) :args (1))
(step t6 (cl) :rule resolution :premises (t4 t5))
)
d49a353f40235dcfff61d5da77087c78df49ce66 45 0
unsat
(
(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_3) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9)) :named @p_10))
(step t0 (cl (not (! (= @p_10 false) :named @p_11)) (not @p_10) false) :rule equiv_pos2)
(step t1 (cl (= @p_9 (! (= p$ @p_8) :named @p_13))) :rule rare_rewrite :args ("eq-symm" @p_8 p$))
(step t2 (cl (= @p_8 (! (= p$ @p_7) :named @p_14))) :rule rare_rewrite :args ("eq-symm" @p_7 p$))
(step t3 (cl (= @p_7 (! (= p$ @p_6) :named @p_16))) :rule rare_rewrite :args ("eq-symm" @p_6 p$))
(step t4 (cl (= @p_6 (! (= p$ @p_5) :named @p_17))) :rule rare_rewrite :args ("eq-symm" @p_5 p$))
(step t5 (cl (= @p_5 (! (= p$ @p_4) :named @p_18))) :rule rare_rewrite :args ("eq-symm" @p_4 p$))
(step t6 (cl (= @p_4 (! (= p$ @p_3) :named @p_19))) :rule rare_rewrite :args ("eq-symm" @p_3 p$))
(step t7 (cl (= @p_3 (! (= p$ @p_2) :named @p_20))) :rule rare_rewrite :args ("eq-symm" @p_2 p$))
(step t8 (cl (= @p_2 (! (= p$ @p_1) :named @p_21))) :rule rare_rewrite :args ("eq-symm" @p_1 p$))
(step t9 (cl (= @p_1 true)) :rule rare_rewrite :args ("eq-refl" p$))
(step t10 (cl (= @p_21 (! (= p$ true) :named @p_15))) :rule cong :premises (t9))
(step t11 (cl (= @p_15 p$)) :rule rare_rewrite :args ("bool-eq-true" p$))
(step t12 (cl (= @p_21 p$)) :rule trans :premises (t10 t11))
(step t13 (cl @p_3) :rule trans :premises (t8 t12))
(step t14 (cl (= @p_20 @p_1)) :rule cong :premises (t13))
(step t15 (cl (= @p_20 true)) :rule trans :premises (t14 t9))
(step t16 (cl (= @p_3 true)) :rule trans :premises (t7 t15))
(step t17 (cl (= @p_19 @p_15)) :rule cong :premises (t16))
(step t18 (cl (= @p_19 p$)) :rule trans :premises (t17 t11))
(step t19 (cl @p_5) :rule trans :premises (t6 t18))
(step t20 (cl (= @p_18 @p_1)) :rule cong :premises (t19))
(step t21 (cl (= @p_18 true)) :rule trans :premises (t20 t9))
(step t22 (cl (= @p_5 true)) :rule trans :premises (t5 t21))
(step t23 (cl (= @p_17 @p_15)) :rule cong :premises (t22))
(step t24 (cl (= @p_17 p$)) :rule trans :premises (t23 t11))
(step t25 (cl @p_7) :rule trans :premises (t4 t24))
(step t26 (cl (= @p_16 @p_1)) :rule cong :premises (t25))
(step t27 (cl (= @p_16 true)) :rule trans :premises (t26 t9))
(step t28 (cl (= @p_7 true)) :rule trans :premises (t3 t27))
(step t29 (cl (= @p_14 @p_15)) :rule cong :premises (t28))
(step t30 (cl (= @p_14 p$)) :rule trans :premises (t29 t11))
(step t31 (cl @p_9) :rule trans :premises (t2 t30))
(step t32 (cl (= @p_13 @p_1)) :rule cong :premises (t31))
(step t33 (cl (= @p_13 true)) :rule trans :premises (t32 t9))
(step t34 (cl (= @p_9 true)) :rule trans :premises (t1 t33))
(step t35 (cl (= @p_10 (! (not true) :named @p_12))) :rule cong :premises (t34))
(step t36 (cl (= @p_12 false)) :rule evaluate)
(step t37 (cl @p_11) :rule trans :premises (t35 t36))
(step t38 (cl false) :rule resolution :premises (t0 t37 a0))
(step t39 (cl (not false)) :rule false)
(step t40 (cl) :rule resolution :premises (t38 t39))
)
501cece397b07a78db382a58f0ab54a65b438f5a 76 0
unsat
(
(assume a0 (! (or a$ (! (or b$ (or c$ d$)) :named @p_1)) :named @p_2))
(assume a2 (! (or (! (not (! (or a$ (! (and c$ (! (not c$) :named @p_3)) :named @p_4)) :named @p_5)) :named @p_6) b$) :named @p_7))
(assume a3 (! (or (! (not (and b$ (! (or x$ (! (not x$) :named @p_8)) :named @p_9))) :named @p_10) c$) :named @p_11))
(assume a4 (! (or (! (not (! (or d$ false) :named @p_12)) :named @p_13) c$) :named @p_14))
(assume a5 (! (not (or c$ (and (not p$) (or p$ (and q$ (not q$)))))) :named @p_15))
(step t0 (cl (not (! (= @p_7 (! (or (! (not a$) :named @p_37) b$) :named @p_38)) :named @p_39)) (not @p_7) @p_38) :rule equiv_pos2)
(step t1 (cl (not (! (= @p_3 (! (= c$ false) :named @p_24)) :named @p_25)) (not @p_3) @p_24) :rule equiv_pos2)
(step t2 (cl (= @p_24 @p_3)) :rule rare_rewrite :args ("bool-eq-false" c$))
(step t3 (cl @p_25) :rule symm :premises (t2))
(step t4 (cl @p_3) :rule not_or :premises (a5) :args (0))
(step t5 (cl @p_24) :rule resolution :premises (t1 t3 t4))
(step t6 (cl (= @p_3 (! (not false) :named @p_40))) :rule cong :premises (t5))
(step t7 (cl (= @p_4 (! (and false @p_40) :named @p_41))) :rule cong :premises (t5 t6))
(step t8 (cl (= @p_5 (! (or a$ @p_41) :named @p_42))) :rule cong :premises (t7))
(step t9 (cl (= @p_6 (! (not @p_42) :named @p_43))) :rule cong :premises (t8))
(step t10 (cl (= b$ b$)) :rule refl)
(step t11 (cl (= @p_7 (! (or @p_43 b$) :named @p_44))) :rule cong :premises (t9 t10))
(step t12 (cl (= @p_41 false)) :rule evaluate)
(step t13 (cl (= @p_42 (! (or a$ false) :named @p_45))) :rule cong :premises (t12))
(step t14 (cl (= @p_45 a$)) :rule aci_simp)
(step t15 (cl (= @p_42 a$)) :rule trans :premises (t13 t14))
(step t16 (cl (= @p_43 @p_37)) :rule cong :premises (t15))
(step t17 (cl (= @p_44 @p_38)) :rule cong :premises (t16 t10))
(step t18 (cl @p_39) :rule trans :premises (t11 t17))
(step t19 (cl @p_38) :rule resolution :premises (t0 t18 a2))
(step t20 (cl @p_37 b$) :rule or :premises (t19))
(step t21 (cl b$ @p_37) :rule reordering :premises (t20))
(step t22 (cl (not (! (= @p_2 (! (or a$ b$) :named @p_26)) :named @p_27)) (not @p_2) @p_26) :rule equiv_pos2)
(step t23 (cl (= @p_1 (! (or b$ c$ d$) :named @p_35))) :rule aci_simp)
(step t24 (cl (= @p_2 (! (or a$ @p_35) :named @p_36))) :rule cong :premises (t23))
(step t25 (cl (= @p_36 (! (or a$ b$ c$ d$) :named @p_28))) :rule aci_simp)
(step t26 (cl (= @p_2 @p_28)) :rule trans :premises (t24 t25))
(step t27 (cl (not (! (= (! (not d$) :named @p_31) (! (= d$ false) :named @p_30)) :named @p_34)) (not @p_31) @p_30) :rule equiv_pos2)
(step t28 (cl (= @p_30 @p_31)) :rule rare_rewrite :args ("bool-eq-false" d$))
(step t29 (cl @p_34) :rule symm :premises (t28))
(step t30 (cl (not (! (= @p_14 (! (or @p_31 c$) :named @p_32)) :named @p_33)) (not @p_14) @p_32) :rule equiv_pos2)
(step t31 (cl (= @p_12 d$)) :rule aci_simp)
(step t32 (cl (= @p_13 @p_31)) :rule cong :premises (t31))
(step t33 (cl (= c$ c$)) :rule refl)
(step t34 (cl @p_33) :rule cong :premises (t32 t33))
(step t35 (cl @p_32) :rule resolution :premises (t30 t34 a4))
(step t36 (cl @p_31 c$) :rule or :premises (t35))
(step t37 (cl @p_31) :rule resolution :premises (t36 t4))
(step t38 (cl @p_30) :rule resolution :premises (t27 t29 t37))
(step t39 (cl (= @p_28 (! (or a$ b$ false false) :named @p_29))) :rule cong :premises (t5 t38))
(step t40 (cl (= @p_29 @p_26)) :rule aci_simp)
(step t41 (cl (= @p_28 @p_26)) :rule trans :premises (t39 t40))
(step t42 (cl @p_27) :rule trans :premises (t26 t41))
(step t43 (cl @p_26) :rule resolution :premises (t22 t42 a0))
(step t44 (cl a$ b$) :rule or :premises (t43))
(step t45 (cl (not (! (= @p_11 @p_10) :named @p_22)) (not @p_11) @p_10) :rule equiv_pos2)
(step t46 (cl (= @p_11 (! (or @p_10 false) :named @p_23))) :rule cong :premises (t5))
(step t47 (cl (= @p_23 @p_10)) :rule aci_simp)
(step t48 (cl @p_22) :rule trans :premises (t46 t47))
(step t49 (cl @p_10) :rule resolution :premises (t45 t48 a3))
(step t50 (cl (! (not b$) :named @p_16) (! (not @p_9) :named @p_20)) :rule not_and :premises (t49))
(step t51 (cl (not (! (= (! (or @p_9 (! (not @p_8) :named @p_18)) :named @p_19) (! (or @p_9 x$) :named @p_17)) :named @p_21)) (not @p_19) @p_17) :rule equiv_pos2)
(step t52 (cl (= @p_18 x$)) :rule rare_rewrite :args ("bool-double-not-elim" x$))
(step t53 (cl @p_21) :rule cong :premises (t52))
(step t54 (cl @p_9 @p_18) :rule or_neg :args (1))
(step t55 (cl @p_19 @p_20) :rule or_neg :args (0))
(step t56 (cl @p_19 (not @p_18)) :rule or_neg :args (1))
(step t57 (cl @p_19 @p_19) :rule resolution :premises (t54 t55 t56))
(step t58 (cl @p_19) :rule contraction :premises (t57))
(step t59 (cl @p_17) :rule resolution :premises (t51 t53 t58))
(step t60 (cl @p_9 x$) :rule or :premises (t59))
(step t61 (cl x$ @p_9) :rule reordering :premises (t60))
(step t62 (cl @p_9 @p_8) :rule or_neg :args (0))
(step t63 (cl @p_8 @p_9) :rule reordering :premises (t62))
(step t64 (cl @p_9) :rule resolution :premises (t61 t63))
(step t65 (cl @p_16) :rule resolution :premises (t50 t64))
(step t66 (cl a$) :rule resolution :premises (t44 t65))
(step t67 (cl) :rule resolution :premises (t21 t66 t65))
)
0e15f8234c640c0d5591744166b381149d9ab3f2 27 0
unsat
(
(assume a0 (forall ((?v0 A$) (?v1 A$)) (= (symm_f$ ?v0 ?v1) (symm_f$ ?v1 ?v0))))
(assume a1 (! (not (! (and (! (= a$ a$) :named @p_2) (! (= (symm_f$ a$ b$) (symm_f$ b$ a$)) :named @p_1)) :named @p_3)) :named @p_4))
(step t0 (cl (! (=> (forall ((?v0 A$) (?v1 A$)) (= (symm_f$ ?v0 ?v1) (symm_f$ ?v1 ?v0))) @p_1) :named @p_9) (forall ((?v0 A$) (?v1 A$)) (= (symm_f$ ?v0 ?v1) (symm_f$ ?v1 ?v0)))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 A$) (?v1 A$)) (= (symm_f$ ?v0 ?v1) (symm_f$ ?v1 ?v0))))
(step t1.t0 (cl (or (! (not (forall ((?v0 A$) (?v1 A$)) (= (symm_f$ ?v0 ?v1) (symm_f$ ?v1 ?v0)))) :named @p_8) @p_1)) :rule forall_inst :args (a$ b$))
(step t1.t1 (cl @p_8 @p_1) :rule or :premises (t1.t0))
(step t1.t2 (cl @p_1) :rule resolution :premises (t1.t1 t1.a0))
(step t1 (cl @p_8 @p_1) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_9 @p_1) :rule resolution :premises (t0 t1))
(step t3 (cl @p_9 (! (not @p_1) :named @p_5)) :rule implies_neg2)
(step t4 (cl @p_9 @p_9) :rule resolution :premises (t2 t3))
(step t5 (cl @p_9) :rule contraction :premises (t4))
(step t6 (cl @p_8 @p_1) :rule implies :premises (t5))
(step t7 (cl @p_1 @p_8) :rule reordering :premises (t6))
(step t8 (cl (not (! (= @p_4 @p_5) :named @p_6)) (not @p_4) @p_5) :rule equiv_pos2)
(step t9 (cl (= @p_2 true)) :rule rare_rewrite :args ("eq-refl" a$))
(step t10 (cl (= @p_1 @p_1)) :rule refl)
(step t11 (cl (= @p_3 (! (and true @p_1) :named @p_7))) :rule cong :premises (t9 t10))
(step t12 (cl (= @p_7 @p_1)) :rule aci_simp)
(step t13 (cl (= @p_3 @p_1)) :rule trans :premises (t11 t12))
(step t14 (cl @p_6) :rule cong :premises (t13))
(step t15 (cl @p_5) :rule resolution :premises (t8 t14 a1))
(step t16 (cl) :rule resolution :premises (t7 t15 a0))
)
2082b5345a2fa38ee2578c9d44390d8bf7a0b1bc 38 0
unsat
(
(assume a0 (! (not (exists ((?v0 Int)) (= (+ ?v0 1) (* ?v0 2)))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_3)) (not @p_1) false) :rule equiv_pos2)
(anchor :step t1 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1.t0 (cl (= (! (+ ?v0 1) :named @p_14) (! (+ 1 ?v0) :named @p_17))) :rule poly_simp)
(step t1.t1 (cl (= (! (* ?v0 2) :named @p_13) (! (* 2 ?v0) :named @p_16))) :rule poly_simp)
(step t1.t2 (cl (= (! (= @p_14 @p_13) :named @p_15) (! (= @p_17 @p_16) :named @p_18))) :rule cong :premises (t1.t0 t1.t1))
(step t1.t3 (cl (= (* -1 (- @p_17 @p_16)) (* 1 (- ?v0 1)))) :rule poly_simp)
(step t1.t4 (cl (= @p_18 (! (= ?v0 1) :named @p_8))) :rule poly_simp_rel :premises (t1.t3))
(step t1.t5 (cl (= @p_15 @p_8)) :rule trans :premises (t1.t2 t1.t4))
(step t1 (cl (= (exists ((?v0 Int)) (= (+ ?v0 1) (* ?v0 2))) (exists ((?v0 Int)) (= ?v0 1)))) :rule bind)
(step t2 (cl (= (exists ((?v0 Int)) (= ?v0 1)) (! (not (forall ((?v0 Int)) (not (= ?v0 1)))) :named @p_5))) :rule connective_def)
(anchor :step t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t3.t0 (cl (= (! (not @p_8) :named @p_9) (! (or @p_9 @p_9) :named @p_10))) :rule aci_simp)
(step t3 (cl (= (forall ((?v0 Int)) (not (= ?v0 1))) (forall ((?v0 Int)) (or (not (= ?v0 1)) (not (= ?v0 1)))))) :rule bind)
(anchor :step t4 :args ((:= (?v0 Int) 1)))
(step t4.t0 (cl (= @p_10 (! (or (! (not (! (= 1 1) :named @p_6)) :named @p_7) @p_7) :named @p_11))) :rule refl)
(step t4.t1 (cl (= @p_11 @p_7)) :rule rare_rewrite :args ("or-not-refl" 1 (rare-list @p_7)))
(step t4.t2 (cl (= @p_10 @p_7)) :rule trans :premises (t4.t0 t4.t1))
(step t4 (cl (= (forall ((?v0 Int)) (or (not (= ?v0 1)) (not (= ?v0 1)))) @p_7)) :rule onepoint)
(step t5 (cl (= (forall ((?v0 Int)) (not (= ?v0 1))) @p_7)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_6 true)) :rule evaluate)
(step t7 (cl (= @p_7 (! (not true) :named @p_4))) :rule cong :premises (t6))
(step t8 (cl (= @p_4 false)) :rule evaluate)
(step t9 (cl (= @p_7 false)) :rule trans :premises (t7 t8))
(step t10 (cl (= (forall ((?v0 Int)) (not (= ?v0 1))) false)) :rule trans :premises (t5 t9))
(step t11 (cl (= @p_5 (! (not false) :named @p_2))) :rule cong :premises (t10))
(step t12 (cl (= @p_2 true)) :rule evaluate)
(step t13 (cl (= @p_5 true)) :rule trans :premises (t11 t12))
(step t14 (cl (= (exists ((?v0 Int)) (= ?v0 1)) true)) :rule trans :premises (t2 t13))
(step t15 (cl (= (exists ((?v0 Int)) (= (+ ?v0 1) (* ?v0 2))) true)) :rule trans :premises (t1 t14))
(step t16 (cl (= @p_1 @p_4)) :rule cong :premises (t15))
(step t17 (cl @p_3) :rule trans :premises (t16 t8))
(step t18 (cl false) :rule resolution :premises (t0 t17 a0))
(step t19 (cl @p_2) :rule false)
(step t20 (cl) :rule resolution :premises (t18 t19))
)
e2187d15d2b6c2744678489c83ca4bcc9d475f84 25 0
unsat
(
(assume a0 (! (not (forall ((?v0 Int)) (=> (p$ ?v0) (forall ((?v1 Int)) (or (p$ ?v0) (p$ ?v1)))))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_2)) (not @p_1) false) :rule equiv_pos2)
(anchor :step t1 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1.t0 (cl (= (forall ((?v1 Int)) (or (p$ ?v0) (p$ ?v1))) (! (or (! (p$ ?v0) :named @p_5) (forall ((?v1 Int)) (p$ ?v1))) :named @p_6))) :rule miniscope_split)
(step t1.t1 (cl (= (=> @p_5 (forall ((?v1 Int)) (or (p$ ?v0) (p$ ?v1)))) (! (=> @p_5 @p_6) :named @p_7))) :rule cong :premises (t1.t0))
(step t1 (cl (= (forall ((?v0 Int)) (=> (p$ ?v0) (forall ((?v1 Int)) (or (p$ ?v0) (p$ ?v1))))) (forall ((?v0 Int)) (=> (p$ ?v0) (or (p$ ?v0) (forall ((?v1 Int)) (p$ ?v1))))))) :rule bind)
(anchor :step t2 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t2.t0 (cl (= @p_7 (! (or (! (not @p_5) :named @p_8) @p_6) :named @p_9))) :rule rare_rewrite :args ("bool-impl-elim" @p_5 @p_6))
(step t2.t1 (cl (= @p_9 (! (or @p_8 @p_5 (forall ((?v1 Int)) (p$ ?v1))) :named @p_10))) :rule aci_simp)
(step t2.t2 (cl (= @p_10 true)) :rule rare_rewrite :args ("bool-or-taut2" rare-list @p_5 rare-list (rare-list (forall ((?v1 Int)) (p$ ?v1)))))
(step t2.t3 (cl (= @p_9 true)) :rule trans :premises (t2.t1 t2.t2))
(step t2.t4 (cl (= @p_7 true)) :rule trans :premises (t2.t0 t2.t3))
(step t2 (cl (= (forall ((?v0 Int)) (=> (p$ ?v0) (or (p$ ?v0) (forall ((?v1 Int)) (p$ ?v1))))) (forall ((?v0 Int)) true))) :rule bind)
(step t3 (cl (= (forall ((?v0 Int)) true) true)) :rule qnt_rm_unused)
(step t4 (cl (= (forall ((?v0 Int)) (=> (p$ ?v0) (or (p$ ?v0) (forall ((?v1 Int)) (p$ ?v1))))) true)) :rule trans :premises (t2 t3))
(step t5 (cl (= (forall ((?v0 Int)) (=> (p$ ?v0) (forall ((?v1 Int)) (or (p$ ?v0) (p$ ?v1))))) true)) :rule trans :premises (t1 t4))
(step t6 (cl (= @p_1 (! (not true) :named @p_3))) :rule cong :premises (t5))
(step t7 (cl (= @p_3 false)) :rule evaluate)
(step t8 (cl @p_2) :rule trans :premises (t6 t7))
(step t9 (cl false) :rule resolution :premises (t0 t8 a0))
(step t10 (cl (not false)) :rule false)
(step t11 (cl) :rule resolution :premises (t9 t10))
)
f57edabba5c71466cf3c4c8aca234a9eb2043820 454 0
unsat
(
(assume a0 (! (not x0$) :named @p_1))
(assume a1 (! (not x30$) :named @p_2))
(assume a2 (! (not x29$) :named @p_3))
(assume a3 (! (not x59$) :named @p_4))
(assume a4 (! (or x1$ (or x31$ x0$)) :named @p_5))
(assume a6 (! (or x3$ (or x33$ x2$)) :named @p_6))
(assume a8 (! (or x35$ x4$) :named @p_7))
(assume a9 (! (or x5$ (or x36$ x30$)) :named @p_8))
(assume a11 (! (or x7$ (! (or x38$ (or x6$ x32$)) :named @p_9)) :named @p_10))
(assume a13 (! (or x9$ (! (or x40$ (or x8$ x34$)) :named @p_11)) :named @p_12))
(assume a16 (! (or x11$ (! (or x43$ (or x10$ x37$)) :named @p_13)) :named @p_14))
(assume a18 (! (or x13$ (! (or x45$ (or x12$ x39$)) :named @p_15)) :named @p_16))
(assume a20 (! (or x47$ (or x14$ x41$)) :named @p_17))
(assume a21 (! (or x15$ (or x48$ x42$)) :named @p_18))
(assume a23 (! (or x17$ (! (or x50$ (or x16$ x44$)) :named @p_19)) :named @p_20))
(assume a25 (! (or x19$ (! (or x52$ (or x18$ x46$)) :named @p_21)) :named @p_22))
(assume a28 (! (or x21$ (! (or x55$ (or x20$ x49$)) :named @p_23)) :named @p_24))
(assume a30 (! (or x23$ (! (or x57$ (or x22$ x51$)) :named @p_25)) :named @p_26))
(assume a32 (! (or x59$ (! (or x24$ x53$) :named @p_27)) :named @p_28))
(assume a33 (! (or x25$ x54$) :named @p_29))
(assume a35 (! (or x27$ (or x26$ x56$)) :named @p_30))
(assume a37 (! (or x29$ (! (or x28$ x58$) :named @p_31)) :named @p_32))
(assume a41 (! (or (! (not x2$) :named @p_34) (! (not x32$) :named @p_33)) :named @p_35))
(assume a42 (! (or @p_34 (! (not x1$) :named @p_36)) :named @p_37))
(assume a43 (! (or @p_33 @p_36) :named @p_38))
(assume a47 (! (or (! (not x4$) :named @p_40) (! (not x34$) :named @p_39)) :named @p_41))
(assume a48 (! (or @p_40 (! (not x3$) :named @p_42)) :named @p_43))
(assume a49 (! (or @p_39 @p_42) :named @p_44))
(assume a54 (! (or (! (not x6$) :named @p_46) (! (not x37$) :named @p_45)) :named @p_47))
(assume a55 (! (or @p_46 (! (not x5$) :named @p_48)) :named @p_49))
(assume a56 (! (or @p_46 (! (not x31$) :named @p_50)) :named @p_51))
(assume a57 (! (or @p_45 @p_48) :named @p_52))
(assume a58 (! (or @p_45 @p_50) :named @p_53))
(assume a59 (! (or @p_48 @p_50) :named @p_54))
(assume a66 (! (or (! (not x8$) :named @p_56) (! (not x39$) :named @p_55)) :named @p_57))
(assume a67 (! (or @p_56 (! (not x7$) :named @p_58)) :named @p_59))
(assume a68 (! (or @p_56 (! (not x33$) :named @p_60)) :named @p_61))
(assume a69 (! (or @p_55 @p_58) :named @p_62))
(assume a70 (! (or @p_55 @p_60) :named @p_63))
(assume a71 (! (or @p_58 @p_60) :named @p_64))
(assume a78 (! (or (! (not x41$) :named @p_66) (! (not x9$) :named @p_65)) :named @p_67))
(assume a79 (! (or @p_66 (! (not x35$) :named @p_68)) :named @p_69))
(assume a80 (! (or @p_65 @p_68) :named @p_70))
(assume a81 (! (or (! (not x10$) :named @p_72) (! (not x42$) :named @p_71)) :named @p_73))
(assume a82 (! (or @p_72 (! (not x36$) :named @p_74)) :named @p_75))
(assume a83 (! (or @p_71 @p_74) :named @p_76))
(assume a90 (! (or (! (not x12$) :named @p_78) (! (not x44$) :named @p_77)) :named @p_79))
(assume a91 (! (or @p_78 (! (not x11$) :named @p_80)) :named @p_81))
(assume a92 (! (or @p_78 (! (not x38$) :named @p_82)) :named @p_83))
(assume a93 (! (or @p_77 @p_80) :named @p_84))
(assume a94 (! (or @p_77 @p_82) :named @p_85))
(assume a95 (! (or @p_80 @p_82) :named @p_86))
(assume a102 (! (or (! (not x14$) :named @p_88) (! (not x46$) :named @p_87)) :named @p_89))
(assume a103 (! (or @p_88 (! (not x13$) :named @p_90)) :named @p_91))
(assume a104 (! (or @p_88 (! (not x40$) :named @p_92)) :named @p_93))
(assume a105 (! (or @p_87 @p_90) :named @p_94))
(assume a106 (! (or @p_87 @p_92) :named @p_95))
(assume a107 (! (or @p_90 @p_92) :named @p_96))
(assume a114 (! (or (! (not x16$) :named @p_98) (! (not x49$) :named @p_97)) :named @p_99))
(assume a115 (! (or @p_98 (! (not x15$) :named @p_100)) :named @p_101))
(assume a116 (! (or @p_98 (! (not x43$) :named @p_102)) :named @p_103))
(assume a118 (! (or @p_97 @p_102) :named @p_104))
(assume a119 (! (or @p_100 @p_102) :named @p_105))
(assume a126 (! (or (! (not x18$) :named @p_107) (! (not x51$) :named @p_106)) :named @p_108))
(assume a127 (! (or @p_107 (! (not x17$) :named @p_109)) :named @p_110))
(assume a128 (! (or @p_107 (! (not x45$) :named @p_111)) :named @p_112))
(assume a129 (! (or @p_106 @p_109) :named @p_113))
(assume a130 (! (or @p_106 @p_111) :named @p_114))
(assume a131 (! (or @p_109 @p_111) :named @p_115))
(assume a138 (! (or (! (not x53$) :named @p_117) (! (not x19$) :named @p_116)) :named @p_118))
(assume a139 (! (or @p_117 (! (not x47$) :named @p_119)) :named @p_120))
(assume a140 (! (or @p_116 @p_119) :named @p_121))
(assume a141 (! (or (! (not x20$) :named @p_123) (! (not x54$) :named @p_122)) :named @p_124))
(assume a142 (! (or @p_123 (! (not x48$) :named @p_125)) :named @p_126))
(assume a143 (! (or @p_122 @p_125) :named @p_127))
(assume a150 (! (or (! (not x22$) :named @p_129) (! (not x56$) :named @p_128)) :named @p_130))
(assume a151 (! (or @p_129 (! (not x21$) :named @p_131)) :named @p_132))
(assume a152 (! (or @p_129 (! (not x50$) :named @p_133)) :named @p_134))
(assume a153 (! (or @p_128 @p_131) :named @p_135))
(assume a155 (! (or @p_131 @p_133) :named @p_136))
(assume a162 (! (or (! (not x24$) :named @p_138) (! (not x58$) :named @p_137)) :named @p_139))
(assume a163 (! (or @p_138 (! (not x23$) :named @p_140)) :named @p_141))
(assume a164 (! (or @p_138 (! (not x52$) :named @p_142)) :named @p_143))
(assume a165 (! (or @p_137 @p_140) :named @p_144))
(assume a166 (! (or @p_137 @p_142) :named @p_145))
(assume a167 (! (or @p_140 @p_142) :named @p_146))
(assume a172 (! (or (! (not x26$) :named @p_148) (! (not x25$) :named @p_147)) :named @p_149))
(assume a173 (! (or @p_148 (! (not x55$) :named @p_150)) :named @p_151))
(assume a174 (! (or @p_147 @p_150) :named @p_152))
(assume a178 (! (or (! (not x28$) :named @p_154) (! (not x27$) :named @p_153)) :named @p_155))
(assume a179 (! (or @p_154 (! (not x57$) :named @p_156)) :named @p_157))
(assume a180 (! (or @p_153 @p_156) :named @p_158))
(step t0 (cl x35$ x4$) :rule or :premises (a8))
(step t1 (cl x4$ x35$) :rule reordering :premises (t0))
(step t2 (cl @p_66 @p_68) :rule or :premises (a79))
(step t3 (cl @p_68 @p_66) :rule reordering :premises (t2))
(step t4 (cl (not (! (= @p_14 (! (or x11$ x43$ x10$ x37$) :named @p_203)) :named @p_204)) (not @p_14) @p_203) :rule equiv_pos2)
(step t5 (cl (= @p_13 (! (or x43$ x10$ x37$) :named @p_205))) :rule aci_simp)
(step t6 (cl (= @p_14 (! (or x11$ @p_205) :named @p_206))) :rule cong :premises (t5))
(step t7 (cl (= @p_206 @p_203)) :rule aci_simp)
(step t8 (cl @p_204) :rule trans :premises (t6 t7))
(step t9 (cl @p_203) :rule resolution :premises (t4 t8 a16))
(step t10 (cl x11$ x43$ x10$ x37$) :rule or :premises (t9))
(step t11 (cl x10$ x11$ x37$ x43$) :rule reordering :premises (t10))
(step t12 (cl @p_88 @p_87) :rule or :premises (a102))
(step t13 (cl (not (! (= @p_22 (! (or x19$ x52$ x18$ x46$) :named @p_175)) :named @p_176)) (not @p_22) @p_175) :rule equiv_pos2)
(step t14 (cl (= @p_21 (! (or x52$ x18$ x46$) :named @p_177))) :rule aci_simp)
(step t15 (cl (= @p_22 (! (or x19$ @p_177) :named @p_178))) :rule cong :premises (t14))
(step t16 (cl (= @p_178 @p_175)) :rule aci_simp)
(step t17 (cl @p_176) :rule trans :premises (t15 t16))
(step t18 (cl @p_175) :rule resolution :premises (t13 t17 a25))
(step t19 (cl x19$ x52$ x18$ x46$) :rule or :premises (t18))
(step t20 (cl x18$ x19$ x46$ x52$) :rule reordering :premises (t19))
(step t21 (cl (not (! (= @p_17 (! (or x47$ x14$ x41$) :named @p_163)) :named @p_164)) (not @p_17) @p_163) :rule equiv_pos2)
(step t22 (cl @p_164) :rule aci_simp)
(step t23 (cl @p_163) :rule resolution :premises (t21 t22 a20))
(step t24 (cl x47$ x14$ x41$) :rule or :premises (t23))
(step t25 (cl x14$ x41$ x47$) :rule reordering :premises (t24))
(step t26 (cl @p_107 @p_106) :rule or :premises (a126))
(step t27 (cl @p_117 @p_119) :rule or :premises (a139))
(step t28 (cl @p_119 @p_117) :rule reordering :premises (t27))
(step t29 (cl @p_117 @p_116) :rule or :premises (a138))
(step t30 (cl @p_116 @p_117) :rule reordering :premises (t29))
(step t31 (cl (not (! (= @p_26 (! (or x23$ x57$ x22$ x51$) :named @p_179)) :named @p_180)) (not @p_26) @p_179) :rule equiv_pos2)
(step t32 (cl (= @p_25 (! (or x57$ x22$ x51$) :named @p_181))) :rule aci_simp)
(step t33 (cl (= @p_26 (! (or x23$ @p_181) :named @p_182))) :rule cong :premises (t32))
(step t34 (cl (= @p_182 @p_179)) :rule aci_simp)
(step t35 (cl @p_180) :rule trans :premises (t33 t34))
(step t36 (cl @p_179) :rule resolution :premises (t31 t35 a30))
(step t37 (cl x23$ x57$ x22$ x51$) :rule or :premises (t36))
(step t38 (cl x22$ x23$ x51$ x57$) :rule reordering :premises (t37))
(step t39 (cl (not (! (= @p_28 @p_27) :named @p_165)) (not @p_28) @p_27) :rule equiv_pos2)
(step t40 (cl (= @p_28 (! (or x59$ x24$ x53$) :named @p_166))) :rule aci_simp)
(step t41 (cl (not (! (= @p_4 (! (= x59$ false) :named @p_168)) :named @p_169)) (not @p_4) @p_168) :rule equiv_pos2)
(step t42 (cl (= @p_168 @p_4)) :rule rare_rewrite :args ("bool-eq-false" x59$))
(step t43 (cl @p_169) :rule symm :premises (t42))
(step t44 (cl @p_168) :rule resolution :premises (t41 t43 a3))
(step t45 (cl (= x24$ x24$)) :rule refl)
(step t46 (cl (= x53$ x53$)) :rule refl)
(step t47 (cl (= @p_166 (! (or false x24$ x53$) :named @p_167))) :rule cong :premises (t44 t45 t46))
(step t48 (cl (= @p_167 @p_27)) :rule aci_simp)
(step t49 (cl (= @p_166 @p_27)) :rule trans :premises (t47 t48))
(step t50 (cl @p_165) :rule trans :premises (t40 t49))
(step t51 (cl @p_27) :rule resolution :premises (t39 t50 a32))
(step t52 (cl x24$ x53$) :rule or :premises (t51))
(step t53 (cl @p_137 @p_142) :rule or :premises (a166))
(step t54 (cl @p_142 @p_137) :rule reordering :premises (t53))
(step t55 (cl @p_137 @p_140) :rule or :premises (a165))
(step t56 (cl @p_140 @p_137) :rule reordering :premises (t55))
(step t57 (cl @p_138 @p_137) :rule or :premises (a162))
(step t58 (cl (not (! (= @p_32 @p_31) :named @p_170)) (not @p_32) @p_31) :rule equiv_pos2)
(step t59 (cl (= @p_32 (! (or x29$ x28$ x58$) :named @p_171))) :rule aci_simp)
(step t60 (cl (not (! (= @p_3 (! (= x29$ false) :named @p_173)) :named @p_174)) (not @p_3) @p_173) :rule equiv_pos2)
(step t61 (cl (= @p_173 @p_3)) :rule rare_rewrite :args ("bool-eq-false" x29$))
(step t62 (cl @p_174) :rule symm :premises (t61))
(step t63 (cl @p_173) :rule resolution :premises (t60 t62 a2))
(step t64 (cl (= x28$ x28$)) :rule refl)
(step t65 (cl (= x58$ x58$)) :rule refl)
(step t66 (cl (= @p_171 (! (or false x28$ x58$) :named @p_172))) :rule cong :premises (t63 t64 t65))
(step t67 (cl (= @p_172 @p_31)) :rule aci_simp)
(step t68 (cl (= @p_171 @p_31)) :rule trans :premises (t66 t67))
(step t69 (cl @p_170) :rule trans :premises (t59 t68))
(step t70 (cl @p_31) :rule resolution :premises (t58 t69 a37))
(step t71 (cl x28$ x58$) :rule or :premises (t70))
(step t72 (cl @p_153 @p_156) :rule or :premises (a180))
(step t73 (cl @p_156 @p_153) :rule reordering :premises (t72))
(step t74 (cl @p_154 @p_153) :rule or :premises (a178))
(step t75 (cl @p_153 @p_154) :rule reordering :premises (t74))
(step t76 (cl (not (! (= @p_30 (! (or x27$ x26$ x56$) :named @p_187)) :named @p_188)) (not @p_30) @p_187) :rule equiv_pos2)
(step t77 (cl @p_188) :rule aci_simp)
(step t78 (cl @p_187) :rule resolution :premises (t76 t77 a35))
(step t79 (cl x27$ x26$ x56$) :rule or :premises (t78))
(step t80 (cl x26$ x27$ x56$) :rule reordering :premises (t79))
(step t81 (cl @p_128 @p_131) :rule or :premises (a153))
(step t82 (cl @p_131 @p_128) :rule reordering :premises (t81))
(step t83 (cl @p_129 @p_131) :rule or :premises (a151))
(step t84 (cl @p_131 @p_129) :rule reordering :premises (t83))
(step t85 (cl (not (! (= @p_24 (! (or x21$ x55$ x20$ x49$) :named @p_193)) :named @p_194)) (not @p_24) @p_193) :rule equiv_pos2)
(step t86 (cl (= @p_23 (! (or x55$ x20$ x49$) :named @p_195))) :rule aci_simp)
(step t87 (cl (= @p_24 (! (or x21$ @p_195) :named @p_196))) :rule cong :premises (t86))
(step t88 (cl (= @p_196 @p_193)) :rule aci_simp)
(step t89 (cl @p_194) :rule trans :premises (t87 t88))
(step t90 (cl @p_193) :rule resolution :premises (t85 t89 a28))
(step t91 (cl x21$ x55$ x20$ x49$) :rule or :premises (t90))
(step t92 (cl x20$ x21$ x49$ x55$) :rule reordering :premises (t91))
(step t93 (cl @p_147 @p_150) :rule or :premises (a174))
(step t94 (cl @p_150 @p_147) :rule reordering :premises (t93))
(step t95 (cl @p_148 @p_147) :rule or :premises (a172))
(step t96 (cl @p_147 @p_148) :rule reordering :premises (t95))
(step t97 (cl x25$ x54$) :rule or :premises (a33))
(step t98 (cl @p_122 @p_125) :rule or :premises (a143))
(step t99 (cl @p_125 @p_122) :rule reordering :premises (t98))
(step t100 (cl @p_123 @p_125) :rule or :premises (a142))
(step t101 (cl @p_125 @p_123) :rule reordering :premises (t100))
(step t102 (cl (not (! (= @p_18 (! (or x15$ x48$ x42$) :named @p_201)) :named @p_202)) (not @p_18) @p_201) :rule equiv_pos2)
(step t103 (cl @p_202) :rule aci_simp)
(step t104 (cl @p_201) :rule resolution :premises (t102 t103 a21))
(step t105 (cl x15$ x48$ x42$) :rule or :premises (t104))
(step t106 (cl x15$ x42$ x48$) :rule reordering :premises (t105))
(step t107 (cl @p_100 @p_102) :rule or :premises (a119))
(step t108 (cl @p_102 @p_100) :rule reordering :premises (t107))
(step t109 (cl @p_97 @p_102) :rule or :premises (a118))
(step t110 (cl @p_102 @p_97) :rule reordering :premises (t109))
(step t111 (cl x41$ x42$ @p_102) :rule resolution :premises (t12 t20 t25 t26 t28 t30 t38 t52 t54 t56 t57 t71 t73 t75 t80 t82 t84 t92 t94 t96 t97 t99 t101 t106 t108 t110))
(step t112 (cl x25$ x54$) :rule or :premises (a33))
(step t113 (cl @p_98 @p_100) :rule or :premises (a115))
(step t114 (cl @p_100 @p_98) :rule reordering :premises (t113))
(step t115 (cl @p_98 @p_97) :rule or :premises (a114))
(step t116 (cl (not (! (= @p_20 (! (or x17$ x50$ x16$ x44$) :named @p_189)) :named @p_190)) (not @p_20) @p_189) :rule equiv_pos2)
(step t117 (cl (= @p_19 (! (or x50$ x16$ x44$) :named @p_191))) :rule aci_simp)
(step t118 (cl (= @p_20 (! (or x17$ @p_191) :named @p_192))) :rule cong :premises (t117))
(step t119 (cl (= @p_192 @p_189)) :rule aci_simp)
(step t120 (cl @p_190) :rule trans :premises (t118 t119))
(step t121 (cl @p_189) :rule resolution :premises (t116 t120 a23))
(step t122 (cl x17$ x50$ x16$ x44$) :rule or :premises (t121))
(step t123 (cl x16$ x17$ x44$ x50$) :rule reordering :premises (t122))
(step t124 (cl @p_129 @p_133) :rule or :premises (a152))
(step t125 (cl @p_133 @p_129) :rule reordering :premises (t124))
(step t126 (cl x17$ x42$ x44$ @p_129) :rule resolution :premises (t94 t112 t92 t99 t101 t106 t114 t115 t123 t125 t84))
(step t127 (cl @p_88 @p_87) :rule or :premises (a102))
(step t128 (cl x24$ x53$) :rule or :premises (t51))
(step t129 (cl @p_154 @p_156) :rule or :premises (a179))
(step t130 (cl @p_156 @p_154) :rule reordering :premises (t129))
(step t131 (cl x28$ x58$) :rule or :premises (t70))
(step t132 (cl @p_140 @p_142) :rule or :premises (a167))
(step t133 (cl @p_142 @p_140) :rule reordering :premises (t132))
(step t134 (cl x24$ x53$) :rule or :premises (t51))
(step t135 (cl x28$ x58$) :rule or :premises (t70))
(step t136 (cl @p_138 @p_140) :rule or :premises (a163))
(step t137 (cl @p_140 @p_138) :rule reordering :premises (t136))
(step t138 (cl @p_138 @p_137) :rule or :premises (a162))
(step t139 (cl x22$ x51$ @p_138) :rule resolution :premises (t130 t38 t135 t137 t138))
(step t140 (cl x18$ x22$ x46$ x51$) :rule resolution :premises (t130 t38 t131 t133 t54 t20 t30 t134 t139))
(step t141 (cl x18$ x22$ x41$ x51$) :rule resolution :premises (t25 t28 t127 t128 t140 t139))
(step t142 (cl @p_109 @p_111) :rule or :premises (a131))
(step t143 (cl @p_111 @p_109) :rule reordering :premises (t142))
(step t144 (cl @p_106 @p_111) :rule or :premises (a130))
(step t145 (cl @p_111 @p_106) :rule reordering :premises (t144))
(step t146 (cl @p_107 @p_111) :rule or :premises (a128))
(step t147 (cl @p_111 @p_107) :rule reordering :premises (t146))
(step t148 (cl (not (! (= @p_16 (! (or x13$ x45$ x12$ x39$) :named @p_183)) :named @p_184)) (not @p_16) @p_183) :rule equiv_pos2)
(step t149 (cl (= @p_15 (! (or x45$ x12$ x39$) :named @p_185))) :rule aci_simp)
(step t150 (cl (= @p_16 (! (or x13$ @p_185) :named @p_186))) :rule cong :premises (t149))
(step t151 (cl (= @p_186 @p_183)) :rule aci_simp)
(step t152 (cl @p_184) :rule trans :premises (t150 t151))
(step t153 (cl @p_183) :rule resolution :premises (t148 t152 a18))
(step t154 (cl x13$ x45$ x12$ x39$) :rule or :premises (t153))
(step t155 (cl x12$ x13$ x39$ x45$) :rule reordering :premises (t154))
(step t156 (cl @p_123 @p_122) :rule or :premises (a141))
(step t157 (cl x25$ x54$) :rule or :premises (a33))
(step t158 (cl @p_98 @p_97) :rule or :premises (a114))
(step t159 (cl @p_148 @p_150) :rule or :premises (a173))
(step t160 (cl @p_150 @p_148) :rule reordering :premises (t159))
(step t161 (cl @p_129 @p_128) :rule or :premises (a150))
(step t162 (cl @p_107 @p_109) :rule or :premises (a127))
(step t163 (cl @p_109 @p_107) :rule reordering :premises (t162))
(step t164 (cl @p_107 @p_106) :rule or :premises (a126))
(step t165 (cl x28$ x58$) :rule or :premises (t70))
(step t166 (cl @p_138 @p_142) :rule or :premises (a164))
(step t167 (cl @p_142 @p_138) :rule reordering :premises (t166))
(step t168 (cl @p_138 @p_137) :rule or :premises (a162))
(step t169 (cl x24$ x53$) :rule or :premises (t51))
(step t170 (cl @p_116 @p_119) :rule or :premises (a140))
(step t171 (cl @p_119 @p_116) :rule reordering :premises (t170))
(step t172 (cl @p_87 @p_90) :rule or :premises (a105))
(step t173 (cl @p_90 @p_87) :rule reordering :premises (t172))
(step t174 (cl @p_88 @p_90) :rule or :premises (a103))
(step t175 (cl @p_90 @p_88) :rule reordering :premises (t174))
(step t176 (cl x41$ x44$ @p_90) :rule resolution :premises (t156 t92 t157 t158 t160 t96 t123 t80 t125 t84 t161 t38 t163 t164 t130 t75 t20 t165 t167 t137 t168 t169 t171 t28 t25 t173 t175))
(step t177 (cl @p_77 @p_80) :rule or :premises (a93))
(step t178 (cl @p_80 @p_77) :rule reordering :premises (t177))
(step t179 (cl @p_78 @p_80) :rule or :premises (a91))
(step t180 (cl @p_80 @p_78) :rule reordering :premises (t179))
(step t181 (cl x39$ x41$ x42$ @p_80) :rule resolution :premises (t126 t141 t143 t145 t147 t155 t176 t178 t180))
(step t182 (cl x10$ x37$ x39$ x41$ x42$) :rule resolution :premises (t11 t111 t181))
(step t183 (cl @p_72 @p_74) :rule or :premises (a82))
(step t184 (cl @p_74 @p_72) :rule reordering :premises (t183))
(step t185 (cl (not (! (= @p_8 (! (or x5$ x36$) :named @p_207)) :named @p_208)) (not @p_8) @p_207) :rule equiv_pos2)
(step t186 (cl (= @p_8 (! (or x5$ x36$ x30$) :named @p_209))) :rule aci_simp)
(step t187 (cl (not (! (= @p_2 (! (= x30$ false) :named @p_211)) :named @p_212)) (not @p_2) @p_211) :rule equiv_pos2)
(step t188 (cl (= @p_211 @p_2)) :rule rare_rewrite :args ("bool-eq-false" x30$))
(step t189 (cl @p_212) :rule symm :premises (t188))
(step t190 (cl @p_211) :rule resolution :premises (t187 t189 a1))
(step t191 (cl (= @p_209 (! (or x5$ x36$ false) :named @p_210))) :rule cong :premises (t190))
(step t192 (cl (= @p_210 @p_207)) :rule aci_simp)
(step t193 (cl (= @p_209 @p_207)) :rule trans :premises (t191 t192))
(step t194 (cl @p_208) :rule trans :premises (t186 t193))
(step t195 (cl @p_207) :rule resolution :premises (t185 t194 a9))
(step t196 (cl x5$ x36$) :rule or :premises (t195))
(step t197 (cl @p_48 @p_50) :rule or :premises (a59))
(step t198 (cl @p_50 @p_48) :rule reordering :premises (t197))
(step t199 (cl (not (! (= @p_5 (! (or x1$ x31$) :named @p_215)) :named @p_216)) (not @p_5) @p_215) :rule equiv_pos2)
(step t200 (cl (= @p_5 (! (or x1$ x31$ x0$) :named @p_217))) :rule aci_simp)
(step t201 (cl (not (! (= @p_1 (! (= x0$ false) :named @p_219)) :named @p_220)) (not @p_1) @p_219) :rule equiv_pos2)
(step t202 (cl (= @p_219 @p_1)) :rule rare_rewrite :args ("bool-eq-false" x0$))
(step t203 (cl @p_220) :rule symm :premises (t202))
(step t204 (cl @p_219) :rule resolution :premises (t201 t203 a0))
(step t205 (cl (= @p_217 (! (or x1$ x31$ false) :named @p_218))) :rule cong :premises (t204))
(step t206 (cl (= @p_218 @p_215)) :rule aci_simp)
(step t207 (cl (= @p_217 @p_215)) :rule trans :premises (t205 t206))
(step t208 (cl @p_216) :rule trans :premises (t200 t207))
(step t209 (cl @p_215) :rule resolution :premises (t199 t208 a4))
(step t210 (cl x1$ x31$) :rule or :premises (t209))
(step t211 (cl x41$ x42$ x44$ @p_111) :rule resolution :premises (t126 t141 t143 t145 t147))
(step t212 (cl x12$ x39$ x41$ x42$ x44$) :rule resolution :premises (t155 t176 t211))
(step t213 (cl @p_77 @p_82) :rule or :premises (a94))
(step t214 (cl @p_82 @p_77) :rule reordering :premises (t213))
(step t215 (cl @p_78 @p_82) :rule or :premises (a92))
(step t216 (cl @p_82 @p_78) :rule reordering :premises (t215))
(step t217 (cl (not (! (= @p_10 (! (or x7$ x38$ x6$ x32$) :named @p_197)) :named @p_198)) (not @p_10) @p_197) :rule equiv_pos2)
(step t218 (cl (= @p_9 (! (or x38$ x6$ x32$) :named @p_199))) :rule aci_simp)
(step t219 (cl (= @p_10 (! (or x7$ @p_199) :named @p_200))) :rule cong :premises (t218))
(step t220 (cl (= @p_200 @p_197)) :rule aci_simp)
(step t221 (cl @p_198) :rule trans :premises (t219 t220))
(step t222 (cl @p_197) :rule resolution :premises (t217 t221 a11))
(step t223 (cl x7$ x38$ x6$ x32$) :rule or :premises (t222))
(step t224 (cl x6$ x7$ x32$ x38$) :rule reordering :premises (t223))
(step t225 (cl @p_46 @p_45) :rule or :premises (a54))
(step t226 (cl @p_71 @p_74) :rule or :premises (a83))
(step t227 (cl @p_74 @p_71) :rule reordering :premises (t226))
(step t228 (cl x5$ x36$) :rule or :premises (t195))
(step t229 (cl @p_98 @p_102) :rule or :premises (a116))
(step t230 (cl @p_102 @p_98) :rule reordering :premises (t229))
(step t231 (cl @p_72 @p_71) :rule or :premises (a81))
(step t232 (cl x11$ x37$ x41$ x44$ @p_111) :rule resolution :premises (t11 t230 t231 t123 t126 t125 t141 t143 t145 t147))
(step t233 (cl x11$ x12$ x37$ x39$ x41$ x44$) :rule resolution :premises (t155 t232 t176))
(step t234 (cl @p_80 @p_82) :rule or :premises (a95))
(step t235 (cl @p_82 @p_80) :rule reordering :premises (t234))
(step t236 (cl @p_45 @p_48) :rule or :premises (a57))
(step t237 (cl @p_48 @p_45) :rule reordering :premises (t236))
(step t238 (cl @p_46 @p_48) :rule or :premises (a55))
(step t239 (cl @p_48 @p_46) :rule reordering :premises (t238))
(step t240 (cl x7$ x32$ x39$ x41$ @p_48) :rule resolution :premises (t233 t235 t214 t216 t224 t237 t239))
(step t241 (cl @p_40 @p_39) :rule or :premises (a47))
(step t242 (cl @p_90 @p_92) :rule or :premises (a107))
(step t243 (cl @p_92 @p_90) :rule reordering :premises (t242))
(step t244 (cl @p_87 @p_92) :rule or :premises (a106))
(step t245 (cl @p_92 @p_87) :rule reordering :premises (t244))
(step t246 (cl (not (! (= @p_12 (! (or x9$ x40$ x8$ x34$) :named @p_159)) :named @p_160)) (not @p_12) @p_159) :rule equiv_pos2)
(step t247 (cl (= @p_11 (! (or x40$ x8$ x34$) :named @p_161))) :rule aci_simp)
(step t248 (cl (= @p_12 (! (or x9$ @p_161) :named @p_162))) :rule cong :premises (t247))
(step t249 (cl (= @p_162 @p_159)) :rule aci_simp)
(step t250 (cl @p_160) :rule trans :premises (t248 t249))
(step t251 (cl @p_159) :rule resolution :premises (t246 t250 a13))
(step t252 (cl x9$ x40$ x8$ x34$) :rule or :premises (t251))
(step t253 (cl x8$ x9$ x34$ x40$) :rule reordering :premises (t252))
(step t254 (cl @p_66 @p_65) :rule or :premises (a78))
(step t255 (cl @p_65 @p_66) :rule reordering :premises (t254))
(step t256 (cl @p_46 @p_45) :rule or :premises (a54))
(step t257 (cl @p_107 @p_106) :rule or :premises (a126))
(step t258 (cl x24$ x53$) :rule or :premises (t51))
(step t259 (cl @p_138 @p_137) :rule or :premises (a162))
(step t260 (cl x28$ x58$) :rule or :premises (t70))
(step t261 (cl x25$ x54$) :rule or :premises (a33))
(step t262 (cl x13$ x39$ x42$ x46$ @p_80) :rule resolution :premises (t126 t140 t143 t145 t147 t155 t178 t180))
(step t263 (cl x8$ x10$ x34$ x37$ x39$ x42$) :rule resolution :premises (t20 t257 t30 t38 t258 t54 t56 t259 t260 t73 t75 t80 t82 t84 t92 t94 t96 t261 t99 t101 t106 t108 t110 t11 t262 t243 t245 t253 t255 t182))
(step t264 (cl x5$ x36$) :rule or :premises (t195))
(step t265 (cl @p_72 @p_71) :rule or :premises (a81))
(step t266 (cl x7$ x8$ x32$ x34$ x39$ @p_48) :rule resolution :premises (t11 t230 t265 t123 t126 t125 t140 t143 t145 t147 t155 t243 t245 t253 t255 t233 t235 t214 t216 t224 t237 t239))
(step t267 (cl x7$ x8$ x32$ x34$ x39$) :rule resolution :premises (t126 t140 t143 t145 t147 t155 t243 t245 t253 t255 t212 t214 t216 t224 t256 t263 t227 t184 t264 t266))
(step t268 (cl @p_58 @p_60) :rule or :premises (a71))
(step t269 (cl @p_60 @p_58) :rule reordering :premises (t268))
(step t270 (cl @p_55 @p_60) :rule or :premises (a70))
(step t271 (cl @p_60 @p_55) :rule reordering :premises (t270))
(step t272 (cl @p_56 @p_60) :rule or :premises (a68))
(step t273 (cl @p_60 @p_56) :rule reordering :premises (t272))
(step t274 (cl (not (! (= @p_6 (! (or x3$ x33$ x2$) :named @p_213)) :named @p_214)) (not @p_6) @p_213) :rule equiv_pos2)
(step t275 (cl @p_214) :rule aci_simp)
(step t276 (cl @p_213) :rule resolution :premises (t274 t275 a6))
(step t277 (cl x3$ x33$ x2$) :rule or :premises (t276))
(step t278 (cl x2$ x3$ x33$) :rule reordering :premises (t277))
(step t279 (cl @p_107 @p_106) :rule or :premises (a126))
(step t280 (cl x28$ x58$) :rule or :premises (t70))
(step t281 (cl @p_138 @p_137) :rule or :premises (a162))
(step t282 (cl x24$ x53$) :rule or :premises (t51))
(step t283 (cl @p_88 @p_92) :rule or :premises (a104))
(step t284 (cl @p_92 @p_88) :rule reordering :premises (t283))
(step t285 (cl @p_56 @p_55) :rule or :premises (a66))
(step t286 (cl @p_46 @p_45) :rule or :premises (a54))
(step t287 (cl @p_107 @p_106) :rule or :premises (a126))
(step t288 (cl x24$ x53$) :rule or :premises (t51))
(step t289 (cl @p_56 @p_55) :rule or :premises (a66))
(step t290 (cl x9$ x34$ x41$ x42$ @p_80) :rule resolution :premises (t126 t139 t163 t287 t20 t167 t288 t171 t28 t25 t245 t284 t253 t289 t181 t178))
(step t291 (cl x5$ x36$) :rule or :premises (t195))
(step t292 (cl @p_72 @p_71) :rule or :premises (a81))
(step t293 (cl @p_107 @p_106) :rule or :premises (a126))
(step t294 (cl x28$ x58$) :rule or :premises (t70))
(step t295 (cl @p_138 @p_137) :rule or :premises (a162))
(step t296 (cl x24$ x53$) :rule or :premises (t51))
(step t297 (cl @p_56 @p_55) :rule or :premises (a66))
(step t298 (cl @p_123 @p_122) :rule or :premises (a141))
(step t299 (cl x25$ x54$) :rule or :premises (a33))
(step t300 (cl @p_98 @p_97) :rule or :premises (a114))
(step t301 (cl @p_78 @p_77) :rule or :premises (a90))
(step t302 (cl @p_129 @p_128) :rule or :premises (a150))
(step t303 (cl @p_107 @p_106) :rule or :premises (a126))
(step t304 (cl x28$ x58$) :rule or :premises (t70))
(step t305 (cl @p_138 @p_137) :rule or :premises (a162))
(step t306 (cl x24$ x53$) :rule or :premises (t51))
(step t307 (cl @p_55 @p_58) :rule or :premises (a69))
(step t308 (cl @p_58 @p_55) :rule reordering :premises (t307))
(step t309 (cl @p_56 @p_58) :rule or :premises (a67))
(step t310 (cl @p_58 @p_56) :rule reordering :premises (t309))
(step t311 (cl x9$ x34$ x41$ @p_58) :rule resolution :premises (t298 t92 t299 t300 t160 t96 t123 t80 t301 t125 t84 t302 t155 t38 t147 t163 t303 t130 t75 t20 t304 t167 t137 t305 t306 t171 t28 t25 t243 t245 t284 t253 t308 t310))
(step t312 (cl x9$ x32$ x34$ x41$ @p_48) :rule resolution :premises (t11 t230 t292 t123 t126 t125 t38 t163 t293 t130 t20 t294 t167 t137 t295 t296 t171 t28 t25 t245 t284 t253 t297 t155 t232 t176 t235 t214 t216 t224 t237 t239 t311))
(step t313 (cl @p_65 @p_68) :rule or :premises (a80))
(step t314 (cl @p_68 @p_65) :rule reordering :premises (t313))
(step t315 (cl @p_39 @p_42) :rule or :premises (a49))
(step t316 (cl @p_42 @p_39) :rule reordering :premises (t315))
(step t317 (cl @p_40 @p_42) :rule or :premises (a48))
(step t318 (cl @p_42 @p_40) :rule reordering :premises (t317))
(step t319 (cl x32$ @p_42) :rule resolution :premises (t126 t38 t163 t279 t130 t20 t280 t167 t137 t281 t282 t171 t28 t25 t245 t284 t253 t285 t155 t211 t176 t214 t216 t224 t286 t11 t290 t111 t227 t184 t291 t312 t311 t314 t3 t1 t316 t318))
(step t320 (cl @p_33 @p_36) :rule or :premises (a43))
(step t321 (cl @p_36 @p_33) :rule reordering :premises (t320))
(step t322 (cl @p_34 @p_36) :rule or :premises (a42))
(step t323 (cl @p_36 @p_34) :rule reordering :premises (t322))
(step t324 (cl @p_36) :rule resolution :premises (t212 t214 t216 t224 t225 t182 t227 t184 t228 t240 t3 t1 t241 t267 t269 t271 t273 t278 t319 t321 t323))
(step t325 (cl x31$) :rule resolution :premises (t210 t324))
(step t326 (cl @p_48) :rule resolution :premises (t198 t325))
(step t327 (cl x36$) :rule resolution :premises (t196 t326))
(step t328 (cl @p_72) :rule resolution :premises (t184 t327))
(step t329 (cl @p_45 @p_50) :rule or :premises (a58))
(step t330 (cl @p_50 @p_45) :rule reordering :premises (t329))
(step t331 (cl @p_45) :rule resolution :premises (t330 t325))
(step t332 (cl @p_34 @p_33) :rule or :premises (a41))
(step t333 (cl @p_46 @p_50) :rule or :premises (a56))
(step t334 (cl @p_50 @p_46) :rule reordering :premises (t333))
(step t335 (cl @p_46) :rule resolution :premises (t334 t325))
(step t336 (cl @p_40 @p_39) :rule or :premises (a47))
(step t337 (cl @p_71) :rule resolution :premises (t227 t327))
(step t338 (cl x34$ @p_58) :rule resolution :premises (t263 t331 t328 t337 t308 t310))
(step t339 (cl @p_58) :rule resolution :premises (t1 t3 t336 t182 t331 t328 t337 t338 t308))
(step t340 (cl x28$ x58$) :rule or :premises (t70))
(step t341 (cl @p_106 @p_109) :rule or :premises (a129))
(step t342 (cl @p_109 @p_106) :rule reordering :premises (t341))
(step t343 (cl @p_131 @p_133) :rule or :premises (a155))
(step t344 (cl @p_133 @p_131) :rule reordering :premises (t343))
(step t345 (cl x25$ x54$) :rule or :premises (a33))
(step t346 (cl @p_82) :rule resolution :premises (t56 t38 t340 t342 t73 t75 t123 t80 t344 t82 t84 t92 t94 t96 t345 t99 t101 t106 t337 t108 t110 t230 t11 t331 t328 t235 t214))
(step t347 (cl x32$) :rule resolution :premises (t224 t335 t339 t346))
(step t348 (cl @p_34) :rule resolution :premises (t332 t347))
(step t349 (cl @p_42) :rule resolution :premises (t11 t331 t328 t111 t337 t290 t337 t314 t3 t1 t316 t318))
(step t350 (cl x33$) :rule resolution :premises (t278 t348 t349))
(step t351 (cl @p_55) :rule resolution :premises (t271 t350))
(step t352 (cl x41$) :rule resolution :premises (t182 t328 t331 t351 t337))
(step t353 (cl @p_68) :rule resolution :premises (t3 t352))
(step t354 (cl @p_40 @p_39) :rule or :premises (a47))
(step t355 (cl @p_56) :rule resolution :premises (t273 t350))
(step t356 (cl x34$) :rule resolution :premises (t263 t355 t328 t331 t351 t337))
(step t357 (cl @p_40) :rule resolution :premises (t354 t356))
(step t358 (cl) :rule resolution :premises (t1 t353 t357))
)
29e98a3de09ff0342128c3737bfe385f6a6c3b4e 39 0
unsat
(
(assume a0 (! (ite (! (p$ x$) :named @p_2) (! (not (exists ((?v0 A$)) (p$ ?v0))) :named @p_1) (forall ((?v0 A$)) (not (p$ ?v0)))) :named @p_3))
(assume a1 (! (not (=> @p_2 (p$ y$))) :named @p_4))
(step t0 (cl (! (=> (forall ((?v0 A$)) (not (p$ ?v0))) (! (not @p_2) :named @p_9)) :named @p_10) (forall ((?v0 A$)) (not (p$ ?v0)))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 A$)) (not (p$ ?v0))))
(step t1.t0 (cl (or (! (not (forall ((?v0 A$)) (not (p$ ?v0)))) :named @p_7) @p_9)) :rule forall_inst :args (x$))
(step t1.t1 (cl @p_7 @p_9) :rule or :premises (t1.t0))
(step t1.t2 (cl (not (! (= @p_3 (forall ((?v0 A$)) (not (p$ ?v0)))) :named @p_5)) (not @p_3) (forall ((?v0 A$)) (not (p$ ?v0)))) :rule equiv_pos2)
(step t1.t3 (cl (= (exists ((?v0 A$)) (p$ ?v0)) @p_7)) :rule connective_def)
(step t1.t4 (cl (= @p_1 (! (not @p_7) :named @p_8))) :rule cong :premises (t1.t3))
(step t1.t5 (cl (= @p_8 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (not (p$ ?v0)))))
(step t1.t6 (cl (= @p_1 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule trans :premises (t1.t4 t1.t5))
(step t1.t7 (cl (= (forall ((?v0 A$)) (not (p$ ?v0))) (forall ((?v0 A$)) (not (p$ ?v0))))) :rule refl)
(step t1.t8 (cl (= @p_3 (! (ite @p_2 (forall ((?v0 A$)) (not (p$ ?v0))) (forall ((?v0 A$)) (not (p$ ?v0)))) :named @p_6))) :rule cong :premises (t1.t6 t1.t7))
(step t1.t9 (cl (= @p_6 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule rare_rewrite :args ("ite-eq-branch" @p_2 (forall ((?v0 A$)) (not (p$ ?v0)))))
(step t1.t10 (cl @p_5) :rule trans :premises (t1.t8 t1.t9))
(step t1.t11 (cl (forall ((?v0 A$)) (not (p$ ?v0)))) :rule resolution :premises (t1.t2 t1.t10 a0))
(step t1.t12 (cl @p_9) :rule resolution :premises (t1.t1 t1.t11))
(step t1 (cl @p_7 @p_9) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_10 @p_9) :rule resolution :premises (t0 t1))
(step t3 (cl @p_10 (not @p_9)) :rule implies_neg2)
(step t4 (cl @p_10 @p_10) :rule resolution :premises (t2 t3))
(step t5 (cl @p_10) :rule contraction :premises (t4))
(step t6 (cl @p_7 @p_9) :rule implies :premises (t5))
(step t7 (cl @p_2) :rule not_implies1 :premises (a1))
(step t8 (cl (not @p_5) (not @p_3) (forall ((?v0 A$)) (not (p$ ?v0)))) :rule equiv_pos2)
(step t9 (cl (= (exists ((?v0 A$)) (p$ ?v0)) @p_7)) :rule connective_def)
(step t10 (cl (= @p_1 @p_8)) :rule cong :premises (t9))
(step t11 (cl (= @p_8 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (not (p$ ?v0)))))
(step t12 (cl (= @p_1 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule trans :premises (t10 t11))
(step t13 (cl (= (forall ((?v0 A$)) (not (p$ ?v0))) (forall ((?v0 A$)) (not (p$ ?v0))))) :rule refl)
(step t14 (cl (= @p_3 @p_6)) :rule cong :premises (t12 t13))
(step t15 (cl (= @p_6 (forall ((?v0 A$)) (not (p$ ?v0))))) :rule rare_rewrite :args ("ite-eq-branch" @p_2 (forall ((?v0 A$)) (not (p$ ?v0)))))
(step t16 (cl @p_5) :rule trans :premises (t14 t15))
(step t17 (cl (forall ((?v0 A$)) (not (p$ ?v0)))) :rule resolution :premises (t8 t16 a0))
(step t18 (cl) :rule resolution :premises (t6 t7 t17))
)
5d01ed63febefd6a5aa8e546bb47d9b1f4c1420a 466 0
unsat
(
(define-fun @quantifiers_skolemize_2 () A$ (choice ((?v0 A$)) (not (not (p$ x$ ?v0)))))
(assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
(assume a2 (! (not (! (= (exists ((?v0 A$)) (p$ x$ ?v0)) (! (p$ x$ c$) :named @p_1)) :named @p_2)) :named @p_3))
(step t0 (cl (not (! (= (! (=> (forall ((?v0 A$)) (not (p$ x$ ?v0))) (! (not @p_1) :named @p_4)) :named @p_99) @p_99) :named @p_100)) (not @p_99) @p_99) :rule equiv_pos2)
(step t1 (cl (= (! (= (! (= x$ x$) :named @p_18) true) :named @p_19) @p_18)) :rule equiv_simplify)
(step t2 (cl (not @p_19) @p_18) :rule equiv1 :premises (t1))
(step t3 (cl @p_18) :rule refl)
(step t4 (cl (= @p_18 @p_18)) :rule cong :premises (t3))
(step t5 (cl @p_19) :rule rare_rewrite :args ("eq-refl" x$))
(step t6 (cl @p_19) :rule trans :premises (t4 t5))
(step t7 (cl @p_18) :rule resolution :premises (t2 t6))
(step t8 (cl (= c$ c$)) :rule refl)
(step t9 (cl (! (= @p_1 @p_1) :named @p_17)) :rule cong :premises (t7 t8))
(step t10 (cl (! (= @p_4 @p_4) :named @p_21)) :rule cong :premises (t9))
(step t11 (cl @p_100) :rule cong :premises (t10))
(step t12 (cl @p_99 (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :rule implies_neg1)
(anchor :step t13)
(assume t13.a0 (forall ((?v0 A$)) (not (p$ x$ ?v0))))
(step t13.t0 (cl (or (! (not (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :named @p_6) @p_4)) :rule forall_inst :args (c$))
(step t13.t1 (cl @p_6 @p_4) :rule or :premises (t13.t0))
(step t13.t2 (cl @p_4) :rule resolution :premises (t13.t1 t13.a0))
(step t13 (cl @p_6 @p_4) :rule subproof :discharge (t13.a0))
(step t14 (cl @p_99 @p_4) :rule resolution :premises (t12 t13))
(step t15 (cl @p_99 (! (not @p_4) :named @p_9)) :rule implies_neg2)
(step t16 (cl @p_99 @p_99) :rule resolution :premises (t14 t15))
(step t17 (cl @p_99) :rule contraction :premises (t16))
(step t18 (cl @p_99) :rule resolution :premises (t0 t11 t17))
(step t19 (cl @p_6 @p_4) :rule implies :premises (t18))
(step t20 (cl (not (! (= @p_3 (! (not (! (= @p_6 @p_1) :named @p_11)) :named @p_12)) :named @p_13)) (not @p_3) @p_12) :rule equiv_pos2)
(step t21 (cl (= (exists ((?v0 A$)) (p$ x$ ?v0)) @p_6)) :rule connective_def)
(step t22 (cl @p_17) :rule refl)
(step t23 (cl (= @p_2 @p_11)) :rule cong :premises (t21 t22))
(step t24 (cl (= @p_11 (! (= @p_1 @p_6) :named @p_14))) :rule rare_rewrite :args ("eq-symm" @p_6 @p_1))
(step t25 (cl (= @p_2 @p_14)) :rule trans :premises (t23 t24))
(step t26 (cl (= @p_3 (! (not @p_14) :named @p_15))) :rule cong :premises (t25))
(step t27 (cl (= @p_6 @p_6)) :rule refl)
(step t28 (cl (= @p_14 @p_14)) :rule cong :premises (t9 t27))
(step t29 (cl (! (= @p_14 @p_11) :named @p_16)) :rule rare_rewrite :args ("eq-symm" @p_1 @p_6))
(step t30 (cl @p_16) :rule trans :premises (t28 t29))
(step t31 (cl (= @p_15 @p_12)) :rule cong :premises (t30))
(step t32 (cl @p_13) :rule trans :premises (t26 t31))
(step t33 (cl @p_12) :rule resolution :premises (t20 t32 a2))
(step t34 (cl @p_6 @p_1) :rule not_equiv1 :premises (t33))
(step t35 (cl (not (! (= (! (or (! (not (! (not x$) :named @p_46)) :named @p_52) (! (not (! (p$ x$ @quantifiers_skolemize_2) :named @p_22)) :named @p_25) (! (not (! (not (! (p$ false @quantifiers_skolemize_2) :named @p_67)) :named @p_68)) :named @p_81) (! (not (! (not false) :named @p_58)) :named @p_80)) :named @p_82) (! (or x$ @p_25 @p_67 false) :named @p_79)) :named @p_98)) (not @p_82) @p_79) :rule equiv_pos2)
(step t36 (cl (= @p_52 x$)) :rule rare_rewrite :args ("bool-double-not-elim" x$))
(step t37 (cl (= @p_25 @p_25)) :rule refl)
(step t38 (cl (= @p_81 @p_67)) :rule rare_rewrite :args ("bool-double-not-elim" @p_67))
(step t39 (cl (= @p_80 false)) :rule rare_rewrite :args ("bool-double-not-elim" false))
(step t40 (cl @p_98) :rule cong :premises (t36 t37 t38 t39))
(step t41 (cl (! (=> (! (and @p_46 @p_22 @p_68 @p_58) :named @p_85) (! (and @p_22 @p_46 @p_58 @p_68) :named @p_87)) :named @p_97) @p_85) :rule implies_neg1)
(anchor :step t42)
(assume t42.a0 @p_46)
(assume t42.a1 @p_22)
(assume t42.a2 @p_68)
(assume t42.a3 @p_58)
(step t42.t0 (cl (not (! (= (! (= false false) :named @p_76) @p_58) :named @p_78)) (not @p_76) @p_58) :rule equiv_pos2)
(step t42.t1 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t42.t2 (cl @p_76) :rule refl)
(step t42.t3 (cl @p_58) :rule resolution :premises (t42.t0 t42.t1 t42.t2))
(step t42.t4 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) @p_68) :named @p_69) @p_69) :named @p_75)) (not @p_69) @p_69) :rule equiv_pos2)
(step t42.t5 (cl (= (! (= @p_76 true) :named @p_77) @p_76)) :rule equiv_simplify)
(step t42.t6 (cl (not @p_77) @p_76) :rule equiv1 :premises (t42.t5))
(step t42.t7 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t42.t8 (cl @p_78) :rule trans :premises (t42.t7 t42.t1))
(step t42.t9 (cl (= @p_58 @p_58)) :rule cong :premises (t42.t2))
(step t42.t10 (cl (= @p_58 true)) :rule evaluate)
(step t42.t11 (cl @p_77) :rule trans :premises (t42.t8 t42.t9 t42.t10))
(step t42.t12 (cl @p_76) :rule resolution :premises (t42.t6 t42.t11))
(step t42.t13 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t42.t14 (cl (= @p_67 @p_67)) :rule cong :premises (t42.t12 t42.t13))
(step t42.t15 (cl (= @p_68 @p_68)) :rule cong :premises (t42.t14))
(step t42.t16 (cl @p_75) :rule cong :premises (t42.t15))
(step t42.t17 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) (! (= false @p_67) :named @p_70)) :named @p_71) @p_69) :named @p_72)) (not @p_71) @p_69) :rule equiv_pos2)
(step t42.t18 (cl (= @p_70 (! (= @p_67 false) :named @p_73))) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t42.t19 (cl (! (= @p_73 @p_68) :named @p_74)) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t42.t20 (cl (= @p_70 @p_68)) :rule trans :premises (t42.t18 t42.t19))
(step t42.t21 (cl @p_72) :rule cong :premises (t42.t20))
(step t42.t22 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t42.t23)
(assume t42.t23.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t42.t23.t0 (cl (or (! (not (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :named @p_36) @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t42.t23.t1 (cl @p_36 @p_70) :rule or :premises (t42.t23.t0))
(step t42.t23.t2 (cl (not (! (= (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :named @p_34)) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t42.t23.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t42.t23.t3.t0 (cl (= (= (! (p$ ?v0 ?v1) :named @p_35) ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t42.t23.t3 (cl @p_34) :rule bind)
(step t42.t23.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t42.t23.t2 t42.t23.t3 a0))
(step t42.t23.t5 (cl @p_70) :rule resolution :premises (t42.t23.t1 t42.t23.t4))
(step t42.t23 (cl @p_36 @p_70) :rule subproof :discharge (t42.t23.a0))
(step t42.t24 (cl @p_71 @p_70) :rule resolution :premises (t42.t22 t42.t23))
(step t42.t25 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t42.t26 (cl @p_71 @p_71) :rule resolution :premises (t42.t24 t42.t25))
(step t42.t27 (cl @p_71) :rule contraction :premises (t42.t26))
(step t42.t28 (cl @p_69) :rule resolution :premises (t42.t17 t42.t21 t42.t27))
(step t42.t29 (cl @p_69) :rule resolution :premises (t42.t4 t42.t16 t42.t28))
(step t42.t30 (cl @p_36 @p_68) :rule implies :premises (t42.t29))
(step t42.t31 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t42.t32 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t42.t32.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t42.t32 (cl @p_34) :rule bind)
(step t42.t33 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t42.t31 t42.t32 a0))
(step t42.t34 (cl @p_68) :rule resolution :premises (t42.t30 t42.t33))
(step t42.t35 (cl @p_87) :rule and_intro :premises (t42.a1 t42.a0 t42.t3 t42.t34))
(step t42 (cl @p_52 @p_25 @p_81 @p_80 @p_87) :rule subproof :discharge (t42.a0 t42.a1 t42.a2 t42.a3))
(step t43 (cl (! (not @p_85) :named @p_86) @p_46) :rule and_pos :args (0))
(step t44 (cl @p_86 @p_22) :rule and_pos :args (1))
(step t45 (cl @p_86 @p_68) :rule and_pos :args (2))
(step t46 (cl @p_86 @p_58) :rule and_pos :args (3))
(step t47 (cl @p_87 @p_86 @p_86 @p_86 @p_86) :rule resolution :premises (t42 t43 t44 t45 t46))
(step t48 (cl @p_86 @p_86 @p_86 @p_86 @p_87) :rule reordering :premises (t47))
(step t49 (cl @p_86 @p_87) :rule contraction :premises (t48))
(step t50 (cl @p_97 @p_87) :rule resolution :premises (t41 t49))
(step t51 (cl @p_97 (! (not @p_87) :named @p_88)) :rule implies_neg2)
(step t52 (cl @p_97 @p_97) :rule resolution :premises (t50 t51))
(step t53 (cl @p_97) :rule contraction :premises (t52))
(step t54 (cl @p_86 @p_87) :rule implies :premises (t53))
(step t55 (cl (! (=> @p_87 false) :named @p_89) @p_87) :rule implies_neg1)
(anchor :step t56)
(assume t56.a0 @p_22)
(assume t56.a1 @p_46)
(assume t56.a2 @p_58)
(assume t56.a3 @p_68)
(step t56.t0 (cl (not (! (= (! (= false true) :named @p_90) false) :named @p_96)) (not @p_90) false) :rule equiv_pos2)
(step t56.t1 (cl @p_96) :rule evaluate)
(step t56.t2 (cl @p_74) :rule equiv_simplify)
(step t56.t3 (cl @p_73 @p_81) :rule equiv2 :premises (t56.t2))
(step t56.t4 (cl (! (not @p_81) :named @p_83) @p_67) :rule not_not)
(step t56.t5 (cl @p_73 @p_67) :rule resolution :premises (t56.t3 t56.t4))
(step t56.t6 (cl (not @p_75) (not @p_69) @p_69) :rule equiv_pos2)
(step t56.t7 (cl (= @p_77 @p_76)) :rule equiv_simplify)
(step t56.t8 (cl (not @p_77) @p_76) :rule equiv1 :premises (t56.t7))
(step t56.t9 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t56.t10 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t56.t11 (cl @p_78) :rule trans :premises (t56.t9 t56.t10))
(step t56.t12 (cl @p_76) :rule refl)
(step t56.t13 (cl (= @p_58 @p_58)) :rule cong :premises (t56.t12))
(step t56.t14 (cl (= @p_58 true)) :rule evaluate)
(step t56.t15 (cl @p_77) :rule trans :premises (t56.t11 t56.t13 t56.t14))
(step t56.t16 (cl @p_76) :rule resolution :premises (t56.t8 t56.t15))
(step t56.t17 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t56.t18 (cl (= @p_67 @p_67)) :rule cong :premises (t56.t16 t56.t17))
(step t56.t19 (cl (= @p_68 @p_68)) :rule cong :premises (t56.t18))
(step t56.t20 (cl @p_75) :rule cong :premises (t56.t19))
(step t56.t21 (cl (not @p_72) (not @p_71) @p_69) :rule equiv_pos2)
(step t56.t22 (cl (= @p_70 @p_73)) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t56.t23 (cl @p_74) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t56.t24 (cl (= @p_70 @p_68)) :rule trans :premises (t56.t22 t56.t23))
(step t56.t25 (cl @p_72) :rule cong :premises (t56.t24))
(step t56.t26 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t56.t27)
(assume t56.t27.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t56.t27.t0 (cl (or @p_36 @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t56.t27.t1 (cl @p_36 @p_70) :rule or :premises (t56.t27.t0))
(step t56.t27.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t56.t27.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t56.t27.t3.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t56.t27.t3 (cl @p_34) :rule bind)
(step t56.t27.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t56.t27.t2 t56.t27.t3 a0))
(step t56.t27.t5 (cl @p_70) :rule resolution :premises (t56.t27.t1 t56.t27.t4))
(step t56.t27 (cl @p_36 @p_70) :rule subproof :discharge (t56.t27.a0))
(step t56.t28 (cl @p_71 @p_70) :rule resolution :premises (t56.t26 t56.t27))
(step t56.t29 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t56.t30 (cl @p_71 @p_71) :rule resolution :premises (t56.t28 t56.t29))
(step t56.t31 (cl @p_71) :rule contraction :premises (t56.t30))
(step t56.t32 (cl @p_69) :rule resolution :premises (t56.t21 t56.t25 t56.t31))
(step t56.t33 (cl @p_69) :rule resolution :premises (t56.t6 t56.t20 t56.t32))
(step t56.t34 (cl @p_36 @p_68) :rule implies :premises (t56.t33))
(step t56.t35 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t56.t36 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t56.t36.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t56.t36 (cl @p_34) :rule bind)
(step t56.t37 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t56.t35 t56.t36 a0))
(step t56.t38 (cl @p_68) :rule resolution :premises (t56.t34 t56.t37))
(step t56.t39 (cl @p_73) :rule resolution :premises (t56.t5 t56.t38))
(step t56.t40 (cl @p_70) :rule symm :premises (t56.t39))
(step t56.t41 (cl (= (! (= x$ false) :named @p_94) @p_46)) :rule equiv_simplify)
(step t56.t42 (cl @p_94 @p_52) :rule equiv2 :premises (t56.t41))
(step t56.t43 (cl (! (not @p_52) :named @p_84) x$) :rule not_not)
(step t56.t44 (cl @p_94 x$) :rule resolution :premises (t56.t42 t56.t43))
(step t56.t45 (cl @p_94) :rule resolution :premises (t56.t44 t56.a1))
(step t56.t46 (cl (! (= false x$) :named @p_93)) :rule symm :premises (t56.t45))
(step t56.t47 (cl @p_93) :rule trans :premises (t56.t12 t56.t46))
(step t56.t48 (cl (= @p_67 @p_22)) :rule cong :premises (t56.t47 t56.t17))
(step t56.t49 (cl (= (! (= @p_22 true) :named @p_91) @p_22)) :rule equiv_simplify)
(step t56.t50 (cl @p_91 @p_25) :rule equiv2 :premises (t56.t49))
(step t56.t51 (cl @p_91) :rule resolution :premises (t56.t50 t56.a0))
(step t56.t52 (cl @p_90) :rule trans :premises (t56.t40 t56.t48 t56.t51))
(step t56.t53 (cl false) :rule resolution :premises (t56.t0 t56.t1 t56.t52))
(step t56 (cl @p_25 @p_52 @p_80 @p_81 false) :rule subproof :discharge (t56.a0 t56.a1 t56.a2 t56.a3))
(step t57 (cl @p_88 @p_22) :rule and_pos :args (0))
(step t58 (cl @p_88 @p_46) :rule and_pos :args (1))
(step t59 (cl @p_88 @p_58) :rule and_pos :args (2))
(step t60 (cl @p_88 @p_68) :rule and_pos :args (3))
(step t61 (cl false @p_88 @p_88 @p_88 @p_88) :rule resolution :premises (t56 t57 t58 t59 t60))
(step t62 (cl @p_88 @p_88 @p_88 @p_88 false) :rule reordering :premises (t61))
(step t63 (cl @p_88 false) :rule contraction :premises (t62))
(step t64 (cl @p_89 false) :rule resolution :premises (t55 t63))
(step t65 (cl @p_89 @p_58) :rule implies_neg2)
(step t66 (cl @p_89 @p_89) :rule resolution :premises (t64 t65))
(step t67 (cl @p_89) :rule contraction :premises (t66))
(step t68 (cl (= @p_89 @p_88)) :rule implies_simplify)
(step t69 (cl (not @p_89) @p_88) :rule equiv1 :premises (t68))
(step t70 (cl @p_88) :rule resolution :premises (t67 t69))
(step t71 (cl @p_86) :rule resolution :premises (t54 t70))
(step t72 (cl @p_52 @p_25 @p_81 @p_80) :rule not_and :premises (t71))
(step t73 (cl @p_82 @p_84) :rule or_neg :args (0))
(step t74 (cl @p_82 (! (not @p_25) :named @p_27)) :rule or_neg :args (1))
(step t75 (cl @p_82 @p_83) :rule or_neg :args (2))
(step t76 (cl @p_82 (not @p_80)) :rule or_neg :args (3))
(step t77 (cl @p_82 @p_82 @p_82 @p_82) :rule resolution :premises (t72 t73 t74 t75 t76))
(step t78 (cl @p_82) :rule contraction :premises (t77))
(step t79 (cl @p_79) :rule resolution :premises (t35 t40 t78))
(step t80 (cl x$ @p_25 @p_67 false) :rule or :premises (t79))
(step t81 (cl x$ @p_25 false @p_67) :rule reordering :premises (t80))
(step t82 (cl (not @p_78) (not @p_76) @p_58) :rule equiv_pos2)
(step t83 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t84 (cl @p_76) :rule refl)
(step t85 (cl @p_58) :rule resolution :premises (t82 t83 t84))
(step t86 (cl (not @p_75) (not @p_69) @p_69) :rule equiv_pos2)
(step t87 (cl (= @p_77 @p_76)) :rule equiv_simplify)
(step t88 (cl (not @p_77) @p_76) :rule equiv1 :premises (t87))
(step t89 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t90 (cl @p_78) :rule trans :premises (t89 t83))
(step t91 (cl (= @p_58 @p_58)) :rule cong :premises (t84))
(step t92 (cl (= @p_58 true)) :rule evaluate)
(step t93 (cl @p_77) :rule trans :premises (t90 t91 t92))
(step t94 (cl @p_76) :rule resolution :premises (t88 t93))
(step t95 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t96 (cl (= @p_67 @p_67)) :rule cong :premises (t94 t95))
(step t97 (cl (= @p_68 @p_68)) :rule cong :premises (t96))
(step t98 (cl @p_75) :rule cong :premises (t97))
(step t99 (cl (not @p_72) (not @p_71) @p_69) :rule equiv_pos2)
(step t100 (cl (= @p_70 @p_73)) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t101 (cl @p_74) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t102 (cl (= @p_70 @p_68)) :rule trans :premises (t100 t101))
(step t103 (cl @p_72) :rule cong :premises (t102))
(step t104 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t105)
(assume t105.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t105.t0 (cl (or @p_36 @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t105.t1 (cl @p_36 @p_70) :rule or :premises (t105.t0))
(step t105.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t105.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t105.t3.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t105.t3 (cl @p_34) :rule bind)
(step t105.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t105.t2 t105.t3 a0))
(step t105.t5 (cl @p_70) :rule resolution :premises (t105.t1 t105.t4))
(step t105 (cl @p_36 @p_70) :rule subproof :discharge (t105.a0))
(step t106 (cl @p_71 @p_70) :rule resolution :premises (t104 t105))
(step t107 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t108 (cl @p_71 @p_71) :rule resolution :premises (t106 t107))
(step t109 (cl @p_71) :rule contraction :premises (t108))
(step t110 (cl @p_69) :rule resolution :premises (t99 t103 t109))
(step t111 (cl @p_69) :rule resolution :premises (t86 t98 t110))
(step t112 (cl @p_36 @p_68) :rule implies :premises (t111))
(step t113 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t114 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t114.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t114 (cl @p_34) :rule bind)
(step t115 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t113 t114 a0))
(step t116 (cl @p_68) :rule resolution :premises (t112 t115))
(step t117 (cl (not (! (= (! (or @p_46 @p_9 (! (not true) :named @p_48) (! (not (! (p$ true c$) :named @p_33)) :named @p_47)) :named @p_50) (! (or @p_46 @p_1 @p_48 @p_47) :named @p_49)) :named @p_66)) (not @p_50) @p_49) :rule equiv_pos2)
(step t118 (cl (= @p_9 @p_1)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1))
(step t119 (cl (= @p_48 @p_48)) :rule refl)
(step t120 (cl (= @p_47 @p_47)) :rule refl)
(step t121 (cl @p_66) :rule cong :premises (t118 t119 t120))
(step t122 (cl (! (=> (! (and x$ @p_4 true @p_33) :named @p_53) (! (and @p_4 x$ true @p_33) :named @p_55)) :named @p_65) @p_53) :rule implies_neg1)
(anchor :step t123)
(assume t123.a0 x$)
(assume t123.a1 @p_4)
(assume t123.a2 true)
(assume t123.a3 @p_33)
(step t123.t0 (cl (not (! (= (! (= true true) :named @p_44) true) :named @p_45)) (not @p_44) true) :rule equiv_pos2)
(step t123.t1 (cl @p_45) :rule rare_rewrite :args ("bool-eq-true" true))
(step t123.t2 (cl @p_44) :rule refl)
(step t123.t3 (cl true) :rule resolution :premises (t123.t0 t123.t1 t123.t2))
(step t123.t4 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) @p_33) :named @p_37) @p_37) :named @p_43)) (not @p_37) @p_37) :rule equiv_pos2)
(step t123.t5 (cl @p_44) :rule symm :premises (t123.t2))
(step t123.t6 (cl (= @p_33 @p_33)) :rule cong :premises (t123.t5 t8))
(step t123.t7 (cl @p_43) :rule cong :premises (t123.t6))
(step t123.t8 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) (! (= true @p_33) :named @p_38)) :named @p_39) @p_37) :named @p_40)) (not @p_39) @p_37) :rule equiv_pos2)
(step t123.t9 (cl (= @p_38 (! (= @p_33 true) :named @p_41))) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t123.t10 (cl (! (= @p_41 @p_33) :named @p_42)) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t123.t11 (cl (= @p_38 @p_33)) :rule trans :premises (t123.t9 t123.t10))
(step t123.t12 (cl @p_40) :rule cong :premises (t123.t11))
(step t123.t13 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t123.t14)
(assume t123.t14.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t123.t14.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t123.t14.t1 (cl @p_36 @p_38) :rule or :premises (t123.t14.t0))
(step t123.t14.t2 (cl @p_38) :rule resolution :premises (t123.t14.t1 t115))
(step t123.t14 (cl @p_36 @p_38) :rule subproof :discharge (t123.t14.a0))
(step t123.t15 (cl @p_39 @p_38) :rule resolution :premises (t123.t13 t123.t14))
(step t123.t16 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t123.t17 (cl @p_39 @p_39) :rule resolution :premises (t123.t15 t123.t16))
(step t123.t18 (cl @p_39) :rule contraction :premises (t123.t17))
(step t123.t19 (cl @p_37) :rule resolution :premises (t123.t8 t123.t12 t123.t18))
(step t123.t20 (cl @p_37) :rule resolution :premises (t123.t4 t123.t7 t123.t19))
(step t123.t21 (cl @p_36 @p_33) :rule implies :premises (t123.t20))
(step t123.t22 (cl @p_33) :rule resolution :premises (t123.t21 t115))
(step t123.t23 (cl @p_55) :rule and_intro :premises (t123.a1 t123.a0 t123.t3 t123.t22))
(step t123 (cl @p_46 @p_9 @p_48 @p_47 @p_55) :rule subproof :discharge (t123.a0 t123.a1 t123.a2 t123.a3))
(step t124 (cl (! (not @p_53) :named @p_54) x$) :rule and_pos :args (0))
(step t125 (cl @p_54 @p_4) :rule and_pos :args (1))
(step t126 (cl @p_54 true) :rule and_pos :args (2))
(step t127 (cl @p_54 @p_33) :rule and_pos :args (3))
(step t128 (cl @p_55 @p_54 @p_54 @p_54 @p_54) :rule resolution :premises (t123 t124 t125 t126 t127))
(step t129 (cl @p_54 @p_54 @p_54 @p_54 @p_55) :rule reordering :premises (t128))
(step t130 (cl @p_54 @p_55) :rule contraction :premises (t129))
(step t131 (cl @p_65 @p_55) :rule resolution :premises (t122 t130))
(step t132 (cl @p_65 (! (not @p_55) :named @p_56)) :rule implies_neg2)
(step t133 (cl @p_65 @p_65) :rule resolution :premises (t131 t132))
(step t134 (cl @p_65) :rule contraction :premises (t133))
(step t135 (cl @p_54 @p_55) :rule implies :premises (t134))
(step t136 (cl (! (=> @p_55 false) :named @p_57) @p_55) :rule implies_neg1)
(anchor :step t137)
(assume t137.a0 @p_4)
(assume t137.a1 x$)
(assume t137.a2 true)
(assume t137.a3 @p_33)
(step t137.t0 (cl (not (! (= (! (= true false) :named @p_59) false) :named @p_64)) (not @p_59) false) :rule equiv_pos2)
(step t137.t1 (cl @p_64) :rule evaluate)
(step t137.t2 (cl @p_42) :rule equiv_simplify)
(step t137.t3 (cl @p_41 @p_47) :rule equiv2 :premises (t137.t2))
(step t137.t4 (cl (not @p_43) (not @p_37) @p_37) :rule equiv_pos2)
(step t137.t5 (cl @p_44) :rule refl)
(step t137.t6 (cl @p_44) :rule symm :premises (t137.t5))
(step t137.t7 (cl (= @p_33 @p_33)) :rule cong :premises (t137.t6 t8))
(step t137.t8 (cl @p_43) :rule cong :premises (t137.t7))
(step t137.t9 (cl (not @p_40) (not @p_39) @p_37) :rule equiv_pos2)
(step t137.t10 (cl (= @p_38 @p_41)) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t137.t11 (cl @p_42) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t137.t12 (cl (= @p_38 @p_33)) :rule trans :premises (t137.t10 t137.t11))
(step t137.t13 (cl @p_40) :rule cong :premises (t137.t12))
(step t137.t14 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t137.t15)
(assume t137.t15.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t137.t15.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t137.t15.t1 (cl @p_36 @p_38) :rule or :premises (t137.t15.t0))
(step t137.t15.t2 (cl @p_38) :rule resolution :premises (t137.t15.t1 t115))
(step t137.t15 (cl @p_36 @p_38) :rule subproof :discharge (t137.t15.a0))
(step t137.t16 (cl @p_39 @p_38) :rule resolution :premises (t137.t14 t137.t15))
(step t137.t17 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t137.t18 (cl @p_39 @p_39) :rule resolution :premises (t137.t16 t137.t17))
(step t137.t19 (cl @p_39) :rule contraction :premises (t137.t18))
(step t137.t20 (cl @p_37) :rule resolution :premises (t137.t9 t137.t13 t137.t19))
(step t137.t21 (cl @p_37) :rule resolution :premises (t137.t4 t137.t8 t137.t20))
(step t137.t22 (cl @p_36 @p_33) :rule implies :premises (t137.t21))
(step t137.t23 (cl @p_33) :rule resolution :premises (t137.t22 t115))
(step t137.t24 (cl @p_41) :rule resolution :premises (t137.t3 t137.t23))
(step t137.t25 (cl @p_38) :rule symm :premises (t137.t24))
(step t137.t26 (cl (= (! (= x$ true) :named @p_63) x$)) :rule equiv_simplify)
(step t137.t27 (cl @p_63 @p_46) :rule equiv2 :premises (t137.t26))
(step t137.t28 (cl @p_63) :rule resolution :premises (t137.t27 t137.a1))
(step t137.t29 (cl (! (= true x$) :named @p_62)) :rule symm :premises (t137.t28))
(step t137.t30 (cl @p_62) :rule trans :premises (t137.t5 t137.t29))
(step t137.t31 (cl (= @p_33 @p_1)) :rule cong :premises (t137.t30 t8))
(step t137.t32 (cl (= (! (= @p_1 false) :named @p_60) @p_4)) :rule equiv_simplify)
(step t137.t33 (cl @p_60 @p_9) :rule equiv2 :premises (t137.t32))
(step t137.t34 (cl (! (not @p_9) :named @p_51) @p_1) :rule not_not)
(step t137.t35 (cl @p_60 @p_1) :rule resolution :premises (t137.t33 t137.t34))
(step t137.t36 (cl @p_60) :rule resolution :premises (t137.t35 t137.a0))
(step t137.t37 (cl @p_59) :rule trans :premises (t137.t25 t137.t31 t137.t36))
(step t137.t38 (cl false) :rule resolution :premises (t137.t0 t137.t1 t137.t37))
(step t137 (cl @p_9 @p_46 @p_48 @p_47 false) :rule subproof :discharge (t137.a0 t137.a1 t137.a2 t137.a3))
(step t138 (cl @p_56 @p_4) :rule and_pos :args (0))
(step t139 (cl @p_56 x$) :rule and_pos :args (1))
(step t140 (cl @p_56 true) :rule and_pos :args (2))
(step t141 (cl @p_56 @p_33) :rule and_pos :args (3))
(step t142 (cl false @p_56 @p_56 @p_56 @p_56) :rule resolution :premises (t137 t138 t139 t140 t141))
(step t143 (cl @p_56 @p_56 @p_56 @p_56 false) :rule reordering :premises (t142))
(step t144 (cl @p_56 false) :rule contraction :premises (t143))
(step t145 (cl @p_57 false) :rule resolution :premises (t136 t144))
(step t146 (cl @p_57 @p_58) :rule implies_neg2)
(step t147 (cl @p_57 @p_57) :rule resolution :premises (t145 t146))
(step t148 (cl @p_57) :rule contraction :premises (t147))
(step t149 (cl (= @p_57 @p_56)) :rule implies_simplify)
(step t150 (cl (not @p_57) @p_56) :rule equiv1 :premises (t149))
(step t151 (cl @p_56) :rule resolution :premises (t148 t150))
(step t152 (cl @p_54) :rule resolution :premises (t135 t151))
(step t153 (cl @p_46 @p_9 @p_48 @p_47) :rule not_and :premises (t152))
(step t154 (cl @p_50 @p_52) :rule or_neg :args (0))
(step t155 (cl @p_50 @p_51) :rule or_neg :args (1))
(step t156 (cl @p_50 (not @p_48)) :rule or_neg :args (2))
(step t157 (cl @p_50 (not @p_47)) :rule or_neg :args (3))
(step t158 (cl @p_50 @p_50 @p_50 @p_50) :rule resolution :premises (t153 t154 t155 t156 t157))
(step t159 (cl @p_50) :rule contraction :premises (t158))
(step t160 (cl @p_49) :rule resolution :premises (t117 t121 t159))
(step t161 (cl @p_46 @p_1 @p_48 @p_47) :rule or :premises (t160))
(step t162 (cl @p_1 @p_46 @p_47 @p_48) :rule reordering :premises (t161))
(step t163 (cl (not @p_45) (not @p_44) true) :rule equiv_pos2)
(step t164 (cl @p_45) :rule rare_rewrite :args ("bool-eq-true" true))
(step t165 (cl @p_44) :rule refl)
(step t166 (cl true) :rule resolution :premises (t163 t164 t165))
(step t167 (cl (not @p_43) (not @p_37) @p_37) :rule equiv_pos2)
(step t168 (cl @p_44) :rule symm :premises (t165))
(step t169 (cl (= @p_33 @p_33)) :rule cong :premises (t168 t8))
(step t170 (cl @p_43) :rule cong :premises (t169))
(step t171 (cl (not @p_40) (not @p_39) @p_37) :rule equiv_pos2)
(step t172 (cl (= @p_38 @p_41)) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t173 (cl @p_42) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t174 (cl (= @p_38 @p_33)) :rule trans :premises (t172 t173))
(step t175 (cl @p_40) :rule cong :premises (t174))
(step t176 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t177)
(assume t177.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t177.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t177.t1 (cl @p_36 @p_38) :rule or :premises (t177.t0))
(step t177.t2 (cl @p_38) :rule resolution :premises (t177.t1 t115))
(step t177 (cl @p_36 @p_38) :rule subproof :discharge (t177.a0))
(step t178 (cl @p_39 @p_38) :rule resolution :premises (t176 t177))
(step t179 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t180 (cl @p_39 @p_39) :rule resolution :premises (t178 t179))
(step t181 (cl @p_39) :rule contraction :premises (t180))
(step t182 (cl @p_37) :rule resolution :premises (t171 t175 t181))
(step t183 (cl @p_37) :rule resolution :premises (t167 t170 t182))
(step t184 (cl @p_36 @p_33) :rule implies :premises (t183))
(step t185 (cl @p_33) :rule resolution :premises (t184 t115))
(step t186 (cl (not (! (= (! (or (! (not @p_6) :named @p_7) @p_22) :named @p_24) (! (or (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_22) :named @p_23)) :named @p_32)) (not @p_24) @p_23) :rule equiv_pos2)
(step t187 (cl (= @p_7 (forall ((?v0 A$)) (not (p$ x$ ?v0))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (not (p$ x$ ?v0)))))
(step t188 (cl (! (= @p_22 @p_22) :named @p_31)) :rule refl)
(step t189 (cl @p_32) :rule cong :premises (t187 t188))
(step t190 (cl (not (! (= (! (=> @p_6 @p_27) :named @p_28) (! (=> @p_6 @p_22) :named @p_26)) :named @p_30)) (not @p_28) @p_26) :rule equiv_pos2)
(step t191 (cl (= @p_27 @p_22)) :rule rare_rewrite :args ("bool-double-not-elim" @p_22))
(step t192 (cl @p_30) :rule cong :premises (t191))
(step t193 (cl @p_31) :rule cong :premises (t7 t95))
(step t194 (cl (= @p_26 @p_26)) :rule cong :premises (t193))
(step t195 (cl @p_30) :rule trans :premises (t192 t194))
(step t196 (cl @p_28 @p_6) :rule implies_neg1)
(anchor :step t197)
(assume t197.a0 @p_6)
(step t197.t0 (cl (not (! (= @p_6 @p_27) :named @p_29)) @p_7 @p_27) :rule equiv_pos2)
(anchor :step t197.t1 :args ((:= (?v0 A$) @quantifiers_skolemize_2)))
(step t197.t1.t0 (cl (= (not (p$ x$ ?v0)) @p_25)) :rule refl)
(step t197.t1 (cl (= (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_25)) :rule sko_forall)
(step t197.t2 (cl @p_29) :rule cong :premises (t197.t1))
(step t197.t3 (cl @p_27) :rule resolution :premises (t197.t0 t197.t2 t197.a0))
(step t197 (cl @p_7 @p_27) :rule subproof :discharge (t197.a0))
(step t198 (cl @p_28 @p_27) :rule resolution :premises (t196 t197))
(step t199 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t200 (cl @p_28 @p_28) :rule resolution :premises (t198 t199))
(step t201 (cl @p_28) :rule contraction :premises (t200))
(step t202 (cl @p_26) :rule resolution :premises (t190 t195 t201))
(step t203 (cl @p_7 @p_22) :rule implies :premises (t202))
(step t204 (cl @p_24 (! (not @p_7) :named @p_10)) :rule or_neg :args (0))
(step t205 (cl @p_24 @p_25) :rule or_neg :args (1))
(step t206 (cl @p_24 @p_24) :rule resolution :premises (t203 t204 t205))
(step t207 (cl @p_24) :rule contraction :premises (t206))
(step t208 (cl @p_23) :rule resolution :premises (t186 t189 t207))
(step t209 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_22) :rule or :premises (t208))
(step t210 (cl (not (! (= (! (or @p_7 @p_4) :named @p_8) (! (or (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_4) :named @p_5)) :named @p_20)) (not @p_8) @p_5) :rule equiv_pos2)
(step t211 (cl @p_21) :rule refl)
(step t212 (cl @p_20) :rule cong :premises (t187 t211))
(step t213 (cl @p_7 @p_4) :rule not_equiv2 :premises (t33))
(step t214 (cl @p_8 @p_10) :rule or_neg :args (0))
(step t215 (cl @p_8 @p_9) :rule or_neg :args (1))
(step t216 (cl @p_8 @p_8) :rule resolution :premises (t213 t214 t215))
(step t217 (cl @p_8) :rule contraction :premises (t216))
(step t218 (cl @p_5) :rule resolution :premises (t210 t212 t217))
(step t219 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_4) :rule or :premises (t218))
(step t220 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :rule resolution :premises (t81 t85 t116 t162 t166 t185 t209 t219))
(step t221 (cl @p_1) :rule resolution :premises (t34 t220))
(step t222 (cl) :rule resolution :premises (t19 t221 t220))
)
1e4383af82f2d8c020d71a0c19f041619f1fdbac 466 0
unsat
(
(define-fun @quantifiers_skolemize_2 () A$ (choice ((?v0 A$)) (not (not (p$ x$ ?v0)))))
(assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
(assume a1 (! (not (! (= (exists ((?v0 A$)) (p$ x$ ?v0)) (! (p$ x$ c$) :named @p_1)) :named @p_2)) :named @p_3))
(step t0 (cl (not (! (= (! (=> (forall ((?v0 A$)) (not (p$ x$ ?v0))) (! (not @p_1) :named @p_4)) :named @p_99) @p_99) :named @p_100)) (not @p_99) @p_99) :rule equiv_pos2)
(step t1 (cl (= (! (= (! (= x$ x$) :named @p_18) true) :named @p_19) @p_18)) :rule equiv_simplify)
(step t2 (cl (not @p_19) @p_18) :rule equiv1 :premises (t1))
(step t3 (cl @p_18) :rule refl)
(step t4 (cl (= @p_18 @p_18)) :rule cong :premises (t3))
(step t5 (cl @p_19) :rule rare_rewrite :args ("eq-refl" x$))
(step t6 (cl @p_19) :rule trans :premises (t4 t5))
(step t7 (cl @p_18) :rule resolution :premises (t2 t6))
(step t8 (cl (= c$ c$)) :rule refl)
(step t9 (cl (! (= @p_1 @p_1) :named @p_17)) :rule cong :premises (t7 t8))
(step t10 (cl (! (= @p_4 @p_4) :named @p_21)) :rule cong :premises (t9))
(step t11 (cl @p_100) :rule cong :premises (t10))
(step t12 (cl @p_99 (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :rule implies_neg1)
(anchor :step t13)
(assume t13.a0 (forall ((?v0 A$)) (not (p$ x$ ?v0))))
(step t13.t0 (cl (or (! (not (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :named @p_6) @p_4)) :rule forall_inst :args (c$))
(step t13.t1 (cl @p_6 @p_4) :rule or :premises (t13.t0))
(step t13.t2 (cl @p_4) :rule resolution :premises (t13.t1 t13.a0))
(step t13 (cl @p_6 @p_4) :rule subproof :discharge (t13.a0))
(step t14 (cl @p_99 @p_4) :rule resolution :premises (t12 t13))
(step t15 (cl @p_99 (! (not @p_4) :named @p_9)) :rule implies_neg2)
(step t16 (cl @p_99 @p_99) :rule resolution :premises (t14 t15))
(step t17 (cl @p_99) :rule contraction :premises (t16))
(step t18 (cl @p_99) :rule resolution :premises (t0 t11 t17))
(step t19 (cl @p_6 @p_4) :rule implies :premises (t18))
(step t20 (cl (not (! (= @p_3 (! (not (! (= @p_6 @p_1) :named @p_11)) :named @p_12)) :named @p_13)) (not @p_3) @p_12) :rule equiv_pos2)
(step t21 (cl (= (exists ((?v0 A$)) (p$ x$ ?v0)) @p_6)) :rule connective_def)
(step t22 (cl @p_17) :rule refl)
(step t23 (cl (= @p_2 @p_11)) :rule cong :premises (t21 t22))
(step t24 (cl (= @p_11 (! (= @p_1 @p_6) :named @p_14))) :rule rare_rewrite :args ("eq-symm" @p_6 @p_1))
(step t25 (cl (= @p_2 @p_14)) :rule trans :premises (t23 t24))
(step t26 (cl (= @p_3 (! (not @p_14) :named @p_15))) :rule cong :premises (t25))
(step t27 (cl (= @p_6 @p_6)) :rule refl)
(step t28 (cl (= @p_14 @p_14)) :rule cong :premises (t9 t27))
(step t29 (cl (! (= @p_14 @p_11) :named @p_16)) :rule rare_rewrite :args ("eq-symm" @p_1 @p_6))
(step t30 (cl @p_16) :rule trans :premises (t28 t29))
(step t31 (cl (= @p_15 @p_12)) :rule cong :premises (t30))
(step t32 (cl @p_13) :rule trans :premises (t26 t31))
(step t33 (cl @p_12) :rule resolution :premises (t20 t32 a1))
(step t34 (cl @p_6 @p_1) :rule not_equiv1 :premises (t33))
(step t35 (cl (not (! (= (! (or (! (not (! (not x$) :named @p_46)) :named @p_52) (! (not (! (p$ x$ @quantifiers_skolemize_2) :named @p_22)) :named @p_25) (! (not (! (not (! (p$ false @quantifiers_skolemize_2) :named @p_67)) :named @p_68)) :named @p_81) (! (not (! (not false) :named @p_58)) :named @p_80)) :named @p_82) (! (or x$ @p_25 @p_67 false) :named @p_79)) :named @p_98)) (not @p_82) @p_79) :rule equiv_pos2)
(step t36 (cl (= @p_52 x$)) :rule rare_rewrite :args ("bool-double-not-elim" x$))
(step t37 (cl (= @p_25 @p_25)) :rule refl)
(step t38 (cl (= @p_81 @p_67)) :rule rare_rewrite :args ("bool-double-not-elim" @p_67))
(step t39 (cl (= @p_80 false)) :rule rare_rewrite :args ("bool-double-not-elim" false))
(step t40 (cl @p_98) :rule cong :premises (t36 t37 t38 t39))
(step t41 (cl (! (=> (! (and @p_46 @p_22 @p_68 @p_58) :named @p_85) (! (and @p_22 @p_46 @p_58 @p_68) :named @p_87)) :named @p_97) @p_85) :rule implies_neg1)
(anchor :step t42)
(assume t42.a0 @p_46)
(assume t42.a1 @p_22)
(assume t42.a2 @p_68)
(assume t42.a3 @p_58)
(step t42.t0 (cl (not (! (= (! (= false false) :named @p_76) @p_58) :named @p_78)) (not @p_76) @p_58) :rule equiv_pos2)
(step t42.t1 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t42.t2 (cl @p_76) :rule refl)
(step t42.t3 (cl @p_58) :rule resolution :premises (t42.t0 t42.t1 t42.t2))
(step t42.t4 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) @p_68) :named @p_69) @p_69) :named @p_75)) (not @p_69) @p_69) :rule equiv_pos2)
(step t42.t5 (cl (= (! (= @p_76 true) :named @p_77) @p_76)) :rule equiv_simplify)
(step t42.t6 (cl (not @p_77) @p_76) :rule equiv1 :premises (t42.t5))
(step t42.t7 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t42.t8 (cl @p_78) :rule trans :premises (t42.t7 t42.t1))
(step t42.t9 (cl (= @p_58 @p_58)) :rule cong :premises (t42.t2))
(step t42.t10 (cl (= @p_58 true)) :rule evaluate)
(step t42.t11 (cl @p_77) :rule trans :premises (t42.t8 t42.t9 t42.t10))
(step t42.t12 (cl @p_76) :rule resolution :premises (t42.t6 t42.t11))
(step t42.t13 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t42.t14 (cl (= @p_67 @p_67)) :rule cong :premises (t42.t12 t42.t13))
(step t42.t15 (cl (= @p_68 @p_68)) :rule cong :premises (t42.t14))
(step t42.t16 (cl @p_75) :rule cong :premises (t42.t15))
(step t42.t17 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) (! (= false @p_67) :named @p_70)) :named @p_71) @p_69) :named @p_72)) (not @p_71) @p_69) :rule equiv_pos2)
(step t42.t18 (cl (= @p_70 (! (= @p_67 false) :named @p_73))) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t42.t19 (cl (! (= @p_73 @p_68) :named @p_74)) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t42.t20 (cl (= @p_70 @p_68)) :rule trans :premises (t42.t18 t42.t19))
(step t42.t21 (cl @p_72) :rule cong :premises (t42.t20))
(step t42.t22 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t42.t23)
(assume t42.t23.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t42.t23.t0 (cl (or (! (not (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :named @p_36) @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t42.t23.t1 (cl @p_36 @p_70) :rule or :premises (t42.t23.t0))
(step t42.t23.t2 (cl (not (! (= (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :named @p_34)) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t42.t23.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t42.t23.t3.t0 (cl (= (= (! (p$ ?v0 ?v1) :named @p_35) ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t42.t23.t3 (cl @p_34) :rule bind)
(step t42.t23.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t42.t23.t2 t42.t23.t3 a0))
(step t42.t23.t5 (cl @p_70) :rule resolution :premises (t42.t23.t1 t42.t23.t4))
(step t42.t23 (cl @p_36 @p_70) :rule subproof :discharge (t42.t23.a0))
(step t42.t24 (cl @p_71 @p_70) :rule resolution :premises (t42.t22 t42.t23))
(step t42.t25 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t42.t26 (cl @p_71 @p_71) :rule resolution :premises (t42.t24 t42.t25))
(step t42.t27 (cl @p_71) :rule contraction :premises (t42.t26))
(step t42.t28 (cl @p_69) :rule resolution :premises (t42.t17 t42.t21 t42.t27))
(step t42.t29 (cl @p_69) :rule resolution :premises (t42.t4 t42.t16 t42.t28))
(step t42.t30 (cl @p_36 @p_68) :rule implies :premises (t42.t29))
(step t42.t31 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t42.t32 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t42.t32.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t42.t32 (cl @p_34) :rule bind)
(step t42.t33 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t42.t31 t42.t32 a0))
(step t42.t34 (cl @p_68) :rule resolution :premises (t42.t30 t42.t33))
(step t42.t35 (cl @p_87) :rule and_intro :premises (t42.a1 t42.a0 t42.t3 t42.t34))
(step t42 (cl @p_52 @p_25 @p_81 @p_80 @p_87) :rule subproof :discharge (t42.a0 t42.a1 t42.a2 t42.a3))
(step t43 (cl (! (not @p_85) :named @p_86) @p_46) :rule and_pos :args (0))
(step t44 (cl @p_86 @p_22) :rule and_pos :args (1))
(step t45 (cl @p_86 @p_68) :rule and_pos :args (2))
(step t46 (cl @p_86 @p_58) :rule and_pos :args (3))
(step t47 (cl @p_87 @p_86 @p_86 @p_86 @p_86) :rule resolution :premises (t42 t43 t44 t45 t46))
(step t48 (cl @p_86 @p_86 @p_86 @p_86 @p_87) :rule reordering :premises (t47))
(step t49 (cl @p_86 @p_87) :rule contraction :premises (t48))
(step t50 (cl @p_97 @p_87) :rule resolution :premises (t41 t49))
(step t51 (cl @p_97 (! (not @p_87) :named @p_88)) :rule implies_neg2)
(step t52 (cl @p_97 @p_97) :rule resolution :premises (t50 t51))
(step t53 (cl @p_97) :rule contraction :premises (t52))
(step t54 (cl @p_86 @p_87) :rule implies :premises (t53))
(step t55 (cl (! (=> @p_87 false) :named @p_89) @p_87) :rule implies_neg1)
(anchor :step t56)
(assume t56.a0 @p_22)
(assume t56.a1 @p_46)
(assume t56.a2 @p_58)
(assume t56.a3 @p_68)
(step t56.t0 (cl (not (! (= (! (= false true) :named @p_90) false) :named @p_96)) (not @p_90) false) :rule equiv_pos2)
(step t56.t1 (cl @p_96) :rule evaluate)
(step t56.t2 (cl @p_74) :rule equiv_simplify)
(step t56.t3 (cl @p_73 @p_81) :rule equiv2 :premises (t56.t2))
(step t56.t4 (cl (! (not @p_81) :named @p_83) @p_67) :rule not_not)
(step t56.t5 (cl @p_73 @p_67) :rule resolution :premises (t56.t3 t56.t4))
(step t56.t6 (cl (not @p_75) (not @p_69) @p_69) :rule equiv_pos2)
(step t56.t7 (cl (= @p_77 @p_76)) :rule equiv_simplify)
(step t56.t8 (cl (not @p_77) @p_76) :rule equiv1 :premises (t56.t7))
(step t56.t9 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t56.t10 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t56.t11 (cl @p_78) :rule trans :premises (t56.t9 t56.t10))
(step t56.t12 (cl @p_76) :rule refl)
(step t56.t13 (cl (= @p_58 @p_58)) :rule cong :premises (t56.t12))
(step t56.t14 (cl (= @p_58 true)) :rule evaluate)
(step t56.t15 (cl @p_77) :rule trans :premises (t56.t11 t56.t13 t56.t14))
(step t56.t16 (cl @p_76) :rule resolution :premises (t56.t8 t56.t15))
(step t56.t17 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t56.t18 (cl (= @p_67 @p_67)) :rule cong :premises (t56.t16 t56.t17))
(step t56.t19 (cl (= @p_68 @p_68)) :rule cong :premises (t56.t18))
(step t56.t20 (cl @p_75) :rule cong :premises (t56.t19))
(step t56.t21 (cl (not @p_72) (not @p_71) @p_69) :rule equiv_pos2)
(step t56.t22 (cl (= @p_70 @p_73)) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t56.t23 (cl @p_74) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t56.t24 (cl (= @p_70 @p_68)) :rule trans :premises (t56.t22 t56.t23))
(step t56.t25 (cl @p_72) :rule cong :premises (t56.t24))
(step t56.t26 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t56.t27)
(assume t56.t27.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t56.t27.t0 (cl (or @p_36 @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t56.t27.t1 (cl @p_36 @p_70) :rule or :premises (t56.t27.t0))
(step t56.t27.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t56.t27.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t56.t27.t3.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t56.t27.t3 (cl @p_34) :rule bind)
(step t56.t27.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t56.t27.t2 t56.t27.t3 a0))
(step t56.t27.t5 (cl @p_70) :rule resolution :premises (t56.t27.t1 t56.t27.t4))
(step t56.t27 (cl @p_36 @p_70) :rule subproof :discharge (t56.t27.a0))
(step t56.t28 (cl @p_71 @p_70) :rule resolution :premises (t56.t26 t56.t27))
(step t56.t29 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t56.t30 (cl @p_71 @p_71) :rule resolution :premises (t56.t28 t56.t29))
(step t56.t31 (cl @p_71) :rule contraction :premises (t56.t30))
(step t56.t32 (cl @p_69) :rule resolution :premises (t56.t21 t56.t25 t56.t31))
(step t56.t33 (cl @p_69) :rule resolution :premises (t56.t6 t56.t20 t56.t32))
(step t56.t34 (cl @p_36 @p_68) :rule implies :premises (t56.t33))
(step t56.t35 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t56.t36 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t56.t36.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t56.t36 (cl @p_34) :rule bind)
(step t56.t37 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t56.t35 t56.t36 a0))
(step t56.t38 (cl @p_68) :rule resolution :premises (t56.t34 t56.t37))
(step t56.t39 (cl @p_73) :rule resolution :premises (t56.t5 t56.t38))
(step t56.t40 (cl @p_70) :rule symm :premises (t56.t39))
(step t56.t41 (cl (= (! (= x$ false) :named @p_94) @p_46)) :rule equiv_simplify)
(step t56.t42 (cl @p_94 @p_52) :rule equiv2 :premises (t56.t41))
(step t56.t43 (cl (! (not @p_52) :named @p_84) x$) :rule not_not)
(step t56.t44 (cl @p_94 x$) :rule resolution :premises (t56.t42 t56.t43))
(step t56.t45 (cl @p_94) :rule resolution :premises (t56.t44 t56.a1))
(step t56.t46 (cl (! (= false x$) :named @p_93)) :rule symm :premises (t56.t45))
(step t56.t47 (cl @p_93) :rule trans :premises (t56.t12 t56.t46))
(step t56.t48 (cl (= @p_67 @p_22)) :rule cong :premises (t56.t47 t56.t17))
(step t56.t49 (cl (= (! (= @p_22 true) :named @p_91) @p_22)) :rule equiv_simplify)
(step t56.t50 (cl @p_91 @p_25) :rule equiv2 :premises (t56.t49))
(step t56.t51 (cl @p_91) :rule resolution :premises (t56.t50 t56.a0))
(step t56.t52 (cl @p_90) :rule trans :premises (t56.t40 t56.t48 t56.t51))
(step t56.t53 (cl false) :rule resolution :premises (t56.t0 t56.t1 t56.t52))
(step t56 (cl @p_25 @p_52 @p_80 @p_81 false) :rule subproof :discharge (t56.a0 t56.a1 t56.a2 t56.a3))
(step t57 (cl @p_88 @p_22) :rule and_pos :args (0))
(step t58 (cl @p_88 @p_46) :rule and_pos :args (1))
(step t59 (cl @p_88 @p_58) :rule and_pos :args (2))
(step t60 (cl @p_88 @p_68) :rule and_pos :args (3))
(step t61 (cl false @p_88 @p_88 @p_88 @p_88) :rule resolution :premises (t56 t57 t58 t59 t60))
(step t62 (cl @p_88 @p_88 @p_88 @p_88 false) :rule reordering :premises (t61))
(step t63 (cl @p_88 false) :rule contraction :premises (t62))
(step t64 (cl @p_89 false) :rule resolution :premises (t55 t63))
(step t65 (cl @p_89 @p_58) :rule implies_neg2)
(step t66 (cl @p_89 @p_89) :rule resolution :premises (t64 t65))
(step t67 (cl @p_89) :rule contraction :premises (t66))
(step t68 (cl (= @p_89 @p_88)) :rule implies_simplify)
(step t69 (cl (not @p_89) @p_88) :rule equiv1 :premises (t68))
(step t70 (cl @p_88) :rule resolution :premises (t67 t69))
(step t71 (cl @p_86) :rule resolution :premises (t54 t70))
(step t72 (cl @p_52 @p_25 @p_81 @p_80) :rule not_and :premises (t71))
(step t73 (cl @p_82 @p_84) :rule or_neg :args (0))
(step t74 (cl @p_82 (! (not @p_25) :named @p_27)) :rule or_neg :args (1))
(step t75 (cl @p_82 @p_83) :rule or_neg :args (2))
(step t76 (cl @p_82 (not @p_80)) :rule or_neg :args (3))
(step t77 (cl @p_82 @p_82 @p_82 @p_82) :rule resolution :premises (t72 t73 t74 t75 t76))
(step t78 (cl @p_82) :rule contraction :premises (t77))
(step t79 (cl @p_79) :rule resolution :premises (t35 t40 t78))
(step t80 (cl x$ @p_25 @p_67 false) :rule or :premises (t79))
(step t81 (cl x$ @p_25 false @p_67) :rule reordering :premises (t80))
(step t82 (cl (not @p_78) (not @p_76) @p_58) :rule equiv_pos2)
(step t83 (cl @p_78) :rule rare_rewrite :args ("bool-eq-false" false))
(step t84 (cl @p_76) :rule refl)
(step t85 (cl @p_58) :rule resolution :premises (t82 t83 t84))
(step t86 (cl (not @p_75) (not @p_69) @p_69) :rule equiv_pos2)
(step t87 (cl (= @p_77 @p_76)) :rule equiv_simplify)
(step t88 (cl (not @p_77) @p_76) :rule equiv1 :premises (t87))
(step t89 (cl (= @p_76 @p_76)) :rule rare_rewrite :args ("eq-symm" false false))
(step t90 (cl @p_78) :rule trans :premises (t89 t83))
(step t91 (cl (= @p_58 @p_58)) :rule cong :premises (t84))
(step t92 (cl (= @p_58 true)) :rule evaluate)
(step t93 (cl @p_77) :rule trans :premises (t90 t91 t92))
(step t94 (cl @p_76) :rule resolution :premises (t88 t93))
(step t95 (cl (= @quantifiers_skolemize_2 @quantifiers_skolemize_2)) :rule refl)
(step t96 (cl (= @p_67 @p_67)) :rule cong :premises (t94 t95))
(step t97 (cl (= @p_68 @p_68)) :rule cong :premises (t96))
(step t98 (cl @p_75) :rule cong :premises (t97))
(step t99 (cl (not @p_72) (not @p_71) @p_69) :rule equiv_pos2)
(step t100 (cl (= @p_70 @p_73)) :rule rare_rewrite :args ("eq-symm" false @p_67))
(step t101 (cl @p_74) :rule rare_rewrite :args ("bool-eq-false" @p_67))
(step t102 (cl (= @p_70 @p_68)) :rule trans :premises (t100 t101))
(step t103 (cl @p_72) :rule cong :premises (t102))
(step t104 (cl @p_71 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t105)
(assume t105.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t105.t0 (cl (or @p_36 @p_70)) :rule forall_inst :args (false @quantifiers_skolemize_2))
(step t105.t1 (cl @p_36 @p_70) :rule or :premises (t105.t0))
(step t105.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t105.t3 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t105.t3.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t105.t3 (cl @p_34) :rule bind)
(step t105.t4 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t105.t2 t105.t3 a0))
(step t105.t5 (cl @p_70) :rule resolution :premises (t105.t1 t105.t4))
(step t105 (cl @p_36 @p_70) :rule subproof :discharge (t105.a0))
(step t106 (cl @p_71 @p_70) :rule resolution :premises (t104 t105))
(step t107 (cl @p_71 (not @p_70)) :rule implies_neg2)
(step t108 (cl @p_71 @p_71) :rule resolution :premises (t106 t107))
(step t109 (cl @p_71) :rule contraction :premises (t108))
(step t110 (cl @p_69) :rule resolution :premises (t99 t103 t109))
(step t111 (cl @p_69) :rule resolution :premises (t86 t98 t110))
(step t112 (cl @p_36 @p_68) :rule implies :premises (t111))
(step t113 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0))) (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t114 :args ((?v0 Bool) (?v1 A$) (:= (?v0 Bool) ?v0) (:= (?v1 A$) ?v1)))
(step t114.t0 (cl (= (= @p_35 ?v0) (= ?v0 @p_35))) :rule rare_rewrite :args ("eq-symm" @p_35 ?v0))
(step t114 (cl @p_34) :rule bind)
(step t115 (cl (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule resolution :premises (t113 t114 a0))
(step t116 (cl @p_68) :rule resolution :premises (t112 t115))
(step t117 (cl (not (! (= (! (or @p_46 @p_9 (! (not true) :named @p_48) (! (not (! (p$ true c$) :named @p_33)) :named @p_47)) :named @p_50) (! (or @p_46 @p_1 @p_48 @p_47) :named @p_49)) :named @p_66)) (not @p_50) @p_49) :rule equiv_pos2)
(step t118 (cl (= @p_9 @p_1)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1))
(step t119 (cl (= @p_48 @p_48)) :rule refl)
(step t120 (cl (= @p_47 @p_47)) :rule refl)
(step t121 (cl @p_66) :rule cong :premises (t118 t119 t120))
(step t122 (cl (! (=> (! (and x$ @p_4 true @p_33) :named @p_53) (! (and @p_4 x$ true @p_33) :named @p_55)) :named @p_65) @p_53) :rule implies_neg1)
(anchor :step t123)
(assume t123.a0 x$)
(assume t123.a1 @p_4)
(assume t123.a2 true)
(assume t123.a3 @p_33)
(step t123.t0 (cl (not (! (= (! (= true true) :named @p_44) true) :named @p_45)) (not @p_44) true) :rule equiv_pos2)
(step t123.t1 (cl @p_45) :rule rare_rewrite :args ("bool-eq-true" true))
(step t123.t2 (cl @p_44) :rule refl)
(step t123.t3 (cl true) :rule resolution :premises (t123.t0 t123.t1 t123.t2))
(step t123.t4 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) @p_33) :named @p_37) @p_37) :named @p_43)) (not @p_37) @p_37) :rule equiv_pos2)
(step t123.t5 (cl @p_44) :rule symm :premises (t123.t2))
(step t123.t6 (cl (= @p_33 @p_33)) :rule cong :premises (t123.t5 t8))
(step t123.t7 (cl @p_43) :rule cong :premises (t123.t6))
(step t123.t8 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))) (! (= true @p_33) :named @p_38)) :named @p_39) @p_37) :named @p_40)) (not @p_39) @p_37) :rule equiv_pos2)
(step t123.t9 (cl (= @p_38 (! (= @p_33 true) :named @p_41))) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t123.t10 (cl (! (= @p_41 @p_33) :named @p_42)) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t123.t11 (cl (= @p_38 @p_33)) :rule trans :premises (t123.t9 t123.t10))
(step t123.t12 (cl @p_40) :rule cong :premises (t123.t11))
(step t123.t13 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t123.t14)
(assume t123.t14.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t123.t14.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t123.t14.t1 (cl @p_36 @p_38) :rule or :premises (t123.t14.t0))
(step t123.t14.t2 (cl @p_38) :rule resolution :premises (t123.t14.t1 t115))
(step t123.t14 (cl @p_36 @p_38) :rule subproof :discharge (t123.t14.a0))
(step t123.t15 (cl @p_39 @p_38) :rule resolution :premises (t123.t13 t123.t14))
(step t123.t16 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t123.t17 (cl @p_39 @p_39) :rule resolution :premises (t123.t15 t123.t16))
(step t123.t18 (cl @p_39) :rule contraction :premises (t123.t17))
(step t123.t19 (cl @p_37) :rule resolution :premises (t123.t8 t123.t12 t123.t18))
(step t123.t20 (cl @p_37) :rule resolution :premises (t123.t4 t123.t7 t123.t19))
(step t123.t21 (cl @p_36 @p_33) :rule implies :premises (t123.t20))
(step t123.t22 (cl @p_33) :rule resolution :premises (t123.t21 t115))
(step t123.t23 (cl @p_55) :rule and_intro :premises (t123.a1 t123.a0 t123.t3 t123.t22))
(step t123 (cl @p_46 @p_9 @p_48 @p_47 @p_55) :rule subproof :discharge (t123.a0 t123.a1 t123.a2 t123.a3))
(step t124 (cl (! (not @p_53) :named @p_54) x$) :rule and_pos :args (0))
(step t125 (cl @p_54 @p_4) :rule and_pos :args (1))
(step t126 (cl @p_54 true) :rule and_pos :args (2))
(step t127 (cl @p_54 @p_33) :rule and_pos :args (3))
(step t128 (cl @p_55 @p_54 @p_54 @p_54 @p_54) :rule resolution :premises (t123 t124 t125 t126 t127))
(step t129 (cl @p_54 @p_54 @p_54 @p_54 @p_55) :rule reordering :premises (t128))
(step t130 (cl @p_54 @p_55) :rule contraction :premises (t129))
(step t131 (cl @p_65 @p_55) :rule resolution :premises (t122 t130))
(step t132 (cl @p_65 (! (not @p_55) :named @p_56)) :rule implies_neg2)
(step t133 (cl @p_65 @p_65) :rule resolution :premises (t131 t132))
(step t134 (cl @p_65) :rule contraction :premises (t133))
(step t135 (cl @p_54 @p_55) :rule implies :premises (t134))
(step t136 (cl (! (=> @p_55 false) :named @p_57) @p_55) :rule implies_neg1)
(anchor :step t137)
(assume t137.a0 @p_4)
(assume t137.a1 x$)
(assume t137.a2 true)
(assume t137.a3 @p_33)
(step t137.t0 (cl (not (! (= (! (= true false) :named @p_59) false) :named @p_64)) (not @p_59) false) :rule equiv_pos2)
(step t137.t1 (cl @p_64) :rule evaluate)
(step t137.t2 (cl @p_42) :rule equiv_simplify)
(step t137.t3 (cl @p_41 @p_47) :rule equiv2 :premises (t137.t2))
(step t137.t4 (cl (not @p_43) (not @p_37) @p_37) :rule equiv_pos2)
(step t137.t5 (cl @p_44) :rule refl)
(step t137.t6 (cl @p_44) :rule symm :premises (t137.t5))
(step t137.t7 (cl (= @p_33 @p_33)) :rule cong :premises (t137.t6 t8))
(step t137.t8 (cl @p_43) :rule cong :premises (t137.t7))
(step t137.t9 (cl (not @p_40) (not @p_39) @p_37) :rule equiv_pos2)
(step t137.t10 (cl (= @p_38 @p_41)) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t137.t11 (cl @p_42) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t137.t12 (cl (= @p_38 @p_33)) :rule trans :premises (t137.t10 t137.t11))
(step t137.t13 (cl @p_40) :rule cong :premises (t137.t12))
(step t137.t14 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t137.t15)
(assume t137.t15.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t137.t15.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t137.t15.t1 (cl @p_36 @p_38) :rule or :premises (t137.t15.t0))
(step t137.t15.t2 (cl @p_38) :rule resolution :premises (t137.t15.t1 t115))
(step t137.t15 (cl @p_36 @p_38) :rule subproof :discharge (t137.t15.a0))
(step t137.t16 (cl @p_39 @p_38) :rule resolution :premises (t137.t14 t137.t15))
(step t137.t17 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t137.t18 (cl @p_39 @p_39) :rule resolution :premises (t137.t16 t137.t17))
(step t137.t19 (cl @p_39) :rule contraction :premises (t137.t18))
(step t137.t20 (cl @p_37) :rule resolution :premises (t137.t9 t137.t13 t137.t19))
(step t137.t21 (cl @p_37) :rule resolution :premises (t137.t4 t137.t8 t137.t20))
(step t137.t22 (cl @p_36 @p_33) :rule implies :premises (t137.t21))
(step t137.t23 (cl @p_33) :rule resolution :premises (t137.t22 t115))
(step t137.t24 (cl @p_41) :rule resolution :premises (t137.t3 t137.t23))
(step t137.t25 (cl @p_38) :rule symm :premises (t137.t24))
(step t137.t26 (cl (= (! (= x$ true) :named @p_63) x$)) :rule equiv_simplify)
(step t137.t27 (cl @p_63 @p_46) :rule equiv2 :premises (t137.t26))
(step t137.t28 (cl @p_63) :rule resolution :premises (t137.t27 t137.a1))
(step t137.t29 (cl (! (= true x$) :named @p_62)) :rule symm :premises (t137.t28))
(step t137.t30 (cl @p_62) :rule trans :premises (t137.t5 t137.t29))
(step t137.t31 (cl (= @p_33 @p_1)) :rule cong :premises (t137.t30 t8))
(step t137.t32 (cl (= (! (= @p_1 false) :named @p_60) @p_4)) :rule equiv_simplify)
(step t137.t33 (cl @p_60 @p_9) :rule equiv2 :premises (t137.t32))
(step t137.t34 (cl (! (not @p_9) :named @p_51) @p_1) :rule not_not)
(step t137.t35 (cl @p_60 @p_1) :rule resolution :premises (t137.t33 t137.t34))
(step t137.t36 (cl @p_60) :rule resolution :premises (t137.t35 t137.a0))
(step t137.t37 (cl @p_59) :rule trans :premises (t137.t25 t137.t31 t137.t36))
(step t137.t38 (cl false) :rule resolution :premises (t137.t0 t137.t1 t137.t37))
(step t137 (cl @p_9 @p_46 @p_48 @p_47 false) :rule subproof :discharge (t137.a0 t137.a1 t137.a2 t137.a3))
(step t138 (cl @p_56 @p_4) :rule and_pos :args (0))
(step t139 (cl @p_56 x$) :rule and_pos :args (1))
(step t140 (cl @p_56 true) :rule and_pos :args (2))
(step t141 (cl @p_56 @p_33) :rule and_pos :args (3))
(step t142 (cl false @p_56 @p_56 @p_56 @p_56) :rule resolution :premises (t137 t138 t139 t140 t141))
(step t143 (cl @p_56 @p_56 @p_56 @p_56 false) :rule reordering :premises (t142))
(step t144 (cl @p_56 false) :rule contraction :premises (t143))
(step t145 (cl @p_57 false) :rule resolution :premises (t136 t144))
(step t146 (cl @p_57 @p_58) :rule implies_neg2)
(step t147 (cl @p_57 @p_57) :rule resolution :premises (t145 t146))
(step t148 (cl @p_57) :rule contraction :premises (t147))
(step t149 (cl (= @p_57 @p_56)) :rule implies_simplify)
(step t150 (cl (not @p_57) @p_56) :rule equiv1 :premises (t149))
(step t151 (cl @p_56) :rule resolution :premises (t148 t150))
(step t152 (cl @p_54) :rule resolution :premises (t135 t151))
(step t153 (cl @p_46 @p_9 @p_48 @p_47) :rule not_and :premises (t152))
(step t154 (cl @p_50 @p_52) :rule or_neg :args (0))
(step t155 (cl @p_50 @p_51) :rule or_neg :args (1))
(step t156 (cl @p_50 (not @p_48)) :rule or_neg :args (2))
(step t157 (cl @p_50 (not @p_47)) :rule or_neg :args (3))
(step t158 (cl @p_50 @p_50 @p_50 @p_50) :rule resolution :premises (t153 t154 t155 t156 t157))
(step t159 (cl @p_50) :rule contraction :premises (t158))
(step t160 (cl @p_49) :rule resolution :premises (t117 t121 t159))
(step t161 (cl @p_46 @p_1 @p_48 @p_47) :rule or :premises (t160))
(step t162 (cl @p_1 @p_46 @p_47 @p_48) :rule reordering :premises (t161))
(step t163 (cl (not @p_45) (not @p_44) true) :rule equiv_pos2)
(step t164 (cl @p_45) :rule rare_rewrite :args ("bool-eq-true" true))
(step t165 (cl @p_44) :rule refl)
(step t166 (cl true) :rule resolution :premises (t163 t164 t165))
(step t167 (cl (not @p_43) (not @p_37) @p_37) :rule equiv_pos2)
(step t168 (cl @p_44) :rule symm :premises (t165))
(step t169 (cl (= @p_33 @p_33)) :rule cong :premises (t168 t8))
(step t170 (cl @p_43) :rule cong :premises (t169))
(step t171 (cl (not @p_40) (not @p_39) @p_37) :rule equiv_pos2)
(step t172 (cl (= @p_38 @p_41)) :rule rare_rewrite :args ("eq-symm" true @p_33))
(step t173 (cl @p_42) :rule rare_rewrite :args ("bool-eq-true" @p_33))
(step t174 (cl (= @p_38 @p_33)) :rule trans :premises (t172 t173))
(step t175 (cl @p_40) :rule cong :premises (t174))
(step t176 (cl @p_39 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1)))) :rule implies_neg1)
(anchor :step t177)
(assume t177.a0 (forall ((?v0 Bool) (?v1 A$)) (= ?v0 (p$ ?v0 ?v1))))
(step t177.t0 (cl (or @p_36 @p_38)) :rule forall_inst :args (true c$))
(step t177.t1 (cl @p_36 @p_38) :rule or :premises (t177.t0))
(step t177.t2 (cl @p_38) :rule resolution :premises (t177.t1 t115))
(step t177 (cl @p_36 @p_38) :rule subproof :discharge (t177.a0))
(step t178 (cl @p_39 @p_38) :rule resolution :premises (t176 t177))
(step t179 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t180 (cl @p_39 @p_39) :rule resolution :premises (t178 t179))
(step t181 (cl @p_39) :rule contraction :premises (t180))
(step t182 (cl @p_37) :rule resolution :premises (t171 t175 t181))
(step t183 (cl @p_37) :rule resolution :premises (t167 t170 t182))
(step t184 (cl @p_36 @p_33) :rule implies :premises (t183))
(step t185 (cl @p_33) :rule resolution :premises (t184 t115))
(step t186 (cl (not (! (= (! (or (! (not @p_6) :named @p_7) @p_22) :named @p_24) (! (or (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_22) :named @p_23)) :named @p_32)) (not @p_24) @p_23) :rule equiv_pos2)
(step t187 (cl (= @p_7 (forall ((?v0 A$)) (not (p$ x$ ?v0))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (not (p$ x$ ?v0)))))
(step t188 (cl (! (= @p_22 @p_22) :named @p_31)) :rule refl)
(step t189 (cl @p_32) :rule cong :premises (t187 t188))
(step t190 (cl (not (! (= (! (=> @p_6 @p_27) :named @p_28) (! (=> @p_6 @p_22) :named @p_26)) :named @p_30)) (not @p_28) @p_26) :rule equiv_pos2)
(step t191 (cl (= @p_27 @p_22)) :rule rare_rewrite :args ("bool-double-not-elim" @p_22))
(step t192 (cl @p_30) :rule cong :premises (t191))
(step t193 (cl @p_31) :rule cong :premises (t7 t95))
(step t194 (cl (= @p_26 @p_26)) :rule cong :premises (t193))
(step t195 (cl @p_30) :rule trans :premises (t192 t194))
(step t196 (cl @p_28 @p_6) :rule implies_neg1)
(anchor :step t197)
(assume t197.a0 @p_6)
(step t197.t0 (cl (not (! (= @p_6 @p_27) :named @p_29)) @p_7 @p_27) :rule equiv_pos2)
(anchor :step t197.t1 :args ((:= (?v0 A$) @quantifiers_skolemize_2)))
(step t197.t1.t0 (cl (= (not (p$ x$ ?v0)) @p_25)) :rule refl)
(step t197.t1 (cl (= (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_25)) :rule sko_forall)
(step t197.t2 (cl @p_29) :rule cong :premises (t197.t1))
(step t197.t3 (cl @p_27) :rule resolution :premises (t197.t0 t197.t2 t197.a0))
(step t197 (cl @p_7 @p_27) :rule subproof :discharge (t197.a0))
(step t198 (cl @p_28 @p_27) :rule resolution :premises (t196 t197))
(step t199 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t200 (cl @p_28 @p_28) :rule resolution :premises (t198 t199))
(step t201 (cl @p_28) :rule contraction :premises (t200))
(step t202 (cl @p_26) :rule resolution :premises (t190 t195 t201))
(step t203 (cl @p_7 @p_22) :rule implies :premises (t202))
(step t204 (cl @p_24 (! (not @p_7) :named @p_10)) :rule or_neg :args (0))
(step t205 (cl @p_24 @p_25) :rule or_neg :args (1))
(step t206 (cl @p_24 @p_24) :rule resolution :premises (t203 t204 t205))
(step t207 (cl @p_24) :rule contraction :premises (t206))
(step t208 (cl @p_23) :rule resolution :premises (t186 t189 t207))
(step t209 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_22) :rule or :premises (t208))
(step t210 (cl (not (! (= (! (or @p_7 @p_4) :named @p_8) (! (or (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_4) :named @p_5)) :named @p_20)) (not @p_8) @p_5) :rule equiv_pos2)
(step t211 (cl @p_21) :rule refl)
(step t212 (cl @p_20) :rule cong :premises (t187 t211))
(step t213 (cl @p_7 @p_4) :rule not_equiv2 :premises (t33))
(step t214 (cl @p_8 @p_10) :rule or_neg :args (0))
(step t215 (cl @p_8 @p_9) :rule or_neg :args (1))
(step t216 (cl @p_8 @p_8) :rule resolution :premises (t213 t214 t215))
(step t217 (cl @p_8) :rule contraction :premises (t216))
(step t218 (cl @p_5) :rule resolution :premises (t210 t212 t217))
(step t219 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0))) @p_4) :rule or :premises (t218))
(step t220 (cl (forall ((?v0 A$)) (not (p$ x$ ?v0)))) :rule resolution :premises (t81 t85 t116 t162 t166 t185 t209 t219))
(step t221 (cl @p_1) :rule resolution :premises (t34 t220))
(step t222 (cl) :rule resolution :premises (t19 t221 t220))
)
5ad0f337026c53ea7777aee7ae489ce98e4d7a40 18 0
unsat
(
(assume a0 (! (not (! (= (! (ite a$ false true) :named @p_2) (! (not a$) :named @p_1)) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 (! (and @p_1 true) :named @p_8))) :rule rare_rewrite :args ("ite-then-false" a$ true))
(step t2 (cl (= @p_8 @p_1)) :rule aci_simp)
(step t3 (cl @p_3) :rule trans :premises (t1 t2))
(step t4 (cl (! (= @p_1 @p_1) :named @p_7)) :rule refl)
(step t5 (cl (= @p_3 @p_7)) :rule cong :premises (t3 t4))
(step t6 (cl (= @p_7 true)) :rule rare_rewrite :args ("eq-refl" @p_1))
(step t7 (cl (= @p_3 true)) :rule trans :premises (t5 t6))
(step t8 (cl (= @p_4 (! (not true) :named @p_6))) :rule cong :premises (t7))
(step t9 (cl (= @p_6 false)) :rule evaluate)
(step t10 (cl @p_5) :rule trans :premises (t8 t9))
(step t11 (cl false) :rule resolution :premises (t0 t10 a0))
(step t12 (cl (not false)) :rule false)
(step t13 (cl) :rule resolution :premises (t11 t12))
)
0c66e55947e82889aee7b2b635169b7d3902a9ea 20 0
unsat
(
(assume a0 (! (not (! (= (! (ite (! (<= 3 5) :named @p_1) 3 5) :named @p_2) 3) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 true)) :rule evaluate)
(step t2 (cl (! (= 3 3) :named @p_7)) :rule refl)
(step t3 (cl (= 5 5)) :rule refl)
(step t4 (cl (= @p_2 (! (ite true 3 5) :named @p_8))) :rule cong :premises (t1 t2 t3))
(step t5 (cl (= @p_8 3)) :rule evaluate)
(step t6 (cl @p_3) :rule trans :premises (t4 t5))
(step t7 (cl (= @p_3 @p_7)) :rule cong :premises (t6 t2))
(step t8 (cl (= @p_7 true)) :rule evaluate)
(step t9 (cl (= @p_3 true)) :rule trans :premises (t7 t8))
(step t10 (cl (= @p_4 (! (not true) :named @p_6))) :rule cong :premises (t9))
(step t11 (cl (= @p_6 false)) :rule evaluate)
(step t12 (cl @p_5) :rule trans :premises (t10 t11))
(step t13 (cl false) :rule resolution :premises (t0 t12 a0))
(step t14 (cl (not false)) :rule false)
(step t15 (cl) :rule resolution :premises (t13 t14))
)
8886ba9d7fe195a561e210f023885261dbdb3a80 15 0
unsat
(
(assume a0 (! (not (! (= (! (+ 3 (! (of_nat$ x$) :named @p_1)) :named @p_3) (! (+ @p_1 3) :named @p_2)) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (= @p_5 false) :named @p_6)) (not @p_5) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 @p_3)) :rule poly_simp)
(step t2 (cl (= @p_4 (! (= @p_3 @p_3) :named @p_8))) :rule cong :premises (t1))
(step t3 (cl (= @p_8 true)) :rule rare_rewrite :args ("eq-refl" @p_3))
(step t4 (cl (= @p_4 true)) :rule trans :premises (t2 t3))
(step t5 (cl (= @p_5 (! (not true) :named @p_7))) :rule cong :premises (t4))
(step t6 (cl (= @p_7 false)) :rule evaluate)
(step t7 (cl @p_6) :rule trans :premises (t5 t6))
(step t8 (cl false) :rule resolution :premises (t0 t7 a0))
(step t9 (cl (not false)) :rule false)
(step t10 (cl) :rule resolution :premises (t8 t9))
)
3bc68011400e4d5821d7f860ffde211d8f60c7da 12 0
unsat
(
(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2))
(step t0 (cl (not (! (= @p_2 false) :named @p_3)) (not @p_2) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 true)) :rule evaluate)
(step t2 (cl (= @p_2 (! (not true) :named @p_4))) :rule cong :premises (t1))
(step t3 (cl (= @p_4 false)) :rule evaluate)
(step t4 (cl @p_3) :rule trans :premises (t2 t3))
(step t5 (cl false) :rule resolution :premises (t0 t4 a0))
(step t6 (cl (not false)) :rule false)
(step t7 (cl) :rule resolution :premises (t5 t6))
)
b87a0e9ca85c1f5854aef1880ecd814d1781df30 12 0
unsat
(
(assume a0 (! (not (! (= 3/1 3/1) :named @p_1)) :named @p_2))
(step t0 (cl (not (! (= @p_2 false) :named @p_3)) (not @p_2) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 true)) :rule evaluate)
(step t2 (cl (= @p_2 (! (not true) :named @p_4))) :rule cong :premises (t1))
(step t3 (cl (= @p_4 false)) :rule evaluate)
(step t4 (cl @p_3) :rule trans :premises (t2 t3))
(step t5 (cl false) :rule resolution :premises (t0 t4 a0))
(step t6 (cl (not false)) :rule false)
(step t7 (cl) :rule resolution :premises (t5 t6))
)
50e621ae43987801c0f0613759ed38cdf45f8019 16 0
unsat
(
(assume a0 (! (not (! (= (+ 3 1) 4) :named @p_1)) :named @p_2))
(step t0 (cl (not (! (= @p_2 false) :named @p_3)) (not @p_2) false) :rule equiv_pos2)
(step t1 (cl @p_1) :rule evaluate)
(step t2 (cl (! (= 4 4) :named @p_5)) :rule refl)
(step t3 (cl (= @p_1 @p_5)) :rule cong :premises (t1 t2))
(step t4 (cl (= @p_5 true)) :rule evaluate)
(step t5 (cl (= @p_1 true)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_2 (! (not true) :named @p_4))) :rule cong :premises (t5))
(step t7 (cl (= @p_4 false)) :rule evaluate)
(step t8 (cl @p_3) :rule trans :premises (t6 t7))
(step t9 (cl false) :rule resolution :premises (t0 t8 a0))
(step t10 (cl (not false)) :rule false)
(step t11 (cl) :rule resolution :premises (t9 t10))
)
47627c896707eec2f51db67b1c74d1ff58204a5d 19 0
unsat
(
(assume a0 (! (not (! (= (! (+ x$ (+ y$ z$)) :named @p_2) (! (+ y$ (+ z$ x$)) :named @p_1)) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 (! (+ z$ y$ x$) :named @p_9))) :rule poly_simp)
(step t2 (cl (= @p_9 (! (+ x$ y$ z$) :named @p_7))) :rule poly_simp)
(step t3 (cl (= @p_2 @p_7)) :rule trans :premises (t1 t2))
(step t4 (cl (= @p_1 @p_9)) :rule poly_simp)
(step t5 (cl (= @p_1 @p_7)) :rule trans :premises (t4 t2))
(step t6 (cl (= @p_3 (! (= @p_7 @p_7) :named @p_8))) :rule cong :premises (t3 t5))
(step t7 (cl (= @p_8 true)) :rule rare_rewrite :args ("eq-refl" @p_7))
(step t8 (cl (= @p_3 true)) :rule trans :premises (t6 t7))
(step t9 (cl (= @p_4 (! (not true) :named @p_6))) :rule cong :premises (t8))
(step t10 (cl (= @p_6 false)) :rule evaluate)
(step t11 (cl @p_5) :rule trans :premises (t9 t10))
(step t12 (cl false) :rule resolution :premises (t0 t11 a0))
(step t13 (cl (not false)) :rule false)
(step t14 (cl) :rule resolution :premises (t12 t13))
)
804584a6ed6488e09126ea20ee3616e0c881021e 28 0
unsat
(
(assume a0 (! (not (! (< 5 (! (ite (! (<= 3 8) :named @p_1) 8 3) :named @p_2)) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_6)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (! (= @p_3 true) :named @p_8)) :rule evaluate)
(step t2 (cl (! (= (! (not (! (>= 5 @p_2) :named @p_9)) :named @p_10) true) :named @p_11)) :rule evaluate)
(step t3 (cl (= true @p_10)) :rule symm :premises (t2))
(step t4 (cl (= @p_3 @p_10)) :rule trans :premises (t1 t3))
(step t5 (cl (= @p_1 true)) :rule evaluate)
(step t6 (cl (= 8 8)) :rule refl)
(step t7 (cl (= 3 3)) :rule refl)
(step t8 (cl (= @p_2 (! (ite true 8 3) :named @p_13))) :rule cong :premises (t5 t6 t7))
(step t9 (cl (= @p_13 8)) :rule evaluate)
(step t10 (cl (= @p_2 8)) :rule trans :premises (t8 t9))
(step t11 (cl (= @p_9 (! (>= 5 8) :named @p_12))) :rule cong :premises (t10))
(step t12 (cl (= @p_12 false)) :rule evaluate)
(step t13 (cl (= @p_9 false)) :rule trans :premises (t11 t12))
(step t14 (cl (= @p_10 (! (not false) :named @p_5))) :rule cong :premises (t13))
(step t15 (cl (= @p_5 true)) :rule evaluate)
(step t16 (cl @p_11) :rule trans :premises (t14 t15))
(step t17 (cl @p_8) :rule trans :premises (t4 t16))
(step t18 (cl (= @p_4 (! (not true) :named @p_7))) :rule cong :premises (t17))
(step t19 (cl (= @p_7 false)) :rule evaluate)
(step t20 (cl @p_6) :rule trans :premises (t18 t19))
(step t21 (cl false) :rule resolution :premises (t0 t20 a0))
(step t22 (cl @p_5) :rule false)
(step t23 (cl) :rule resolution :premises (t21 t22))
)
84b1a4a7656ed6be5662f7912e194ecd57533474 17 0
unsat
(
(assume a0 (! (not (! (= (p$ (! (< 2 3) :named @p_2)) (! (p$ true) :named @p_1)) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 true)) :rule evaluate)
(step t2 (cl @p_3) :rule cong :premises (t1))
(step t3 (cl (! (= @p_1 @p_1) :named @p_7)) :rule refl)
(step t4 (cl (= @p_3 @p_7)) :rule cong :premises (t2 t3))
(step t5 (cl (= @p_7 true)) :rule rare_rewrite :args ("eq-refl" @p_1))
(step t6 (cl (= @p_3 true)) :rule trans :premises (t4 t5))
(step t7 (cl (= @p_4 (! (not true) :named @p_6))) :rule cong :premises (t6))
(step t8 (cl (= @p_6 false)) :rule evaluate)
(step t9 (cl @p_5) :rule trans :premises (t7 t8))
(step t10 (cl false) :rule resolution :premises (t0 t9 a0))
(step t11 (cl (not false)) :rule false)
(step t12 (cl) :rule resolution :premises (t10 t11))
)
f7503c900c526db5945ecadc1f6c9790902b3491 21 0
unsat
(
(assume a0 (! (not (! (or (! (<= 4 (! (+ x$ 3) :named @p_2)) :named @p_3) (! (< x$ 1) :named @p_1)) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (not (! (not (! (>= x$ 1) :named @p_6)) :named @p_7)) :named @p_14)) @p_6) :rule not_not)
(step t1 (cl (not (! (= @p_5 (! (not (! (or @p_6 @p_7) :named @p_8)) :named @p_9)) :named @p_10)) (not @p_5) @p_9) :rule equiv_pos2)
(step t2 (cl (= @p_2 (! (+ 3 x$) :named @p_11))) :rule poly_simp)
(step t3 (cl (= @p_3 (! (<= 4 @p_11) :named @p_12))) :rule cong :premises (t2))
(step t4 (cl (= @p_12 (! (>= @p_11 4) :named @p_13))) :rule rare_rewrite :args ("arith-elim-leq" 4 @p_11))
(step t5 (cl (= (* -1 (- @p_11 4)) (* -1 (- x$ 1)))) :rule poly_simp)
(step t6 (cl (= @p_13 @p_6)) :rule poly_simp_rel :premises (t5))
(step t7 (cl (= @p_12 @p_6)) :rule trans :premises (t4 t6))
(step t8 (cl (= @p_3 @p_6)) :rule trans :premises (t3 t7))
(step t9 (cl (= @p_1 @p_7)) :rule rare_rewrite :args ("arith-elim-lt" x$ 1))
(step t10 (cl (= @p_4 @p_8)) :rule cong :premises (t8 t9))
(step t11 (cl @p_10) :rule cong :premises (t10))
(step t12 (cl @p_9) :rule resolution :premises (t1 t11 a0))
(step t13 (cl @p_14) :rule not_or :premises (t12) :args (1))
(step t14 (cl @p_6) :rule resolution :premises (t0 t13))
(step t15 (cl @p_7) :rule not_or :premises (t12) :args (0))
(step t16 (cl) :rule resolution :premises (t14 t15))
)
5d121e2e02aede1d5efe59c376b2519a904821e9 1426 0
unsat
(
(assume a0 (! (not (! (<= (! (ite (! (< (! (+ x$ y$) :named @p_8) 0/1) :named @p_10) (! (- @p_8) :named @p_9) @p_8) :named @p_11) (! (+ (! (ite (! (< x$ 0/1) :named @p_5) (! (- x$) :named @p_4) x$) :named @p_6) (! (ite (! (< y$ 0/1) :named @p_2) (! (- y$) :named @p_1) y$) :named @p_3)) :named @p_7)) :named @p_12)) :named @p_13))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ (! (ite (! (>= y$ 0/1) :named @p_22) y$ (! (* -1/1 y$) :named @p_14)) :named @p_23) (! (ite (! (>= x$ 0/1) :named @p_20) x$ (! (* -1/1 x$) :named @p_15)) :named @p_21) (! (* -1/1 (! (ite (! (>= @p_8 0/1) :named @p_17) @p_8 (! (+ @p_15 @p_14) :named @p_16)) :named @p_18)) :named @p_19)) :named @p_24) 0/1) :named @p_25)) :named @p_26)) :named @p_128) (! (not (! (= y$ (! (* -1/1 @p_23) :named @p_57)) :named @p_58)) :named @p_262) (! (not (! (= x$ (! (* -1/1 @p_21) :named @p_71)) :named @p_72)) :named @p_184) (! (not (! (= x$ (! (+ @p_14 @p_19) :named @p_113)) :named @p_114)) :named @p_226)) :named @p_355) (! (or @p_25 @p_262 @p_184 @p_226) :named @p_354)) :named @p_370)) (not @p_355) @p_354) :rule equiv_pos2)
(step t1 (cl (= @p_128 @p_25)) :rule rare_rewrite :args ("bool-double-not-elim" @p_25))
(step t2 (cl (= @p_262 @p_262)) :rule refl)
(step t3 (cl (= @p_184 @p_184)) :rule refl)
(step t4 (cl (= @p_226 @p_226)) :rule refl)
(step t5 (cl @p_370) :rule cong :premises (t1 t2 t3 t4))
(step t6 (cl (! (=> (! (and @p_26 @p_58 @p_72 @p_114) :named @p_356) (! (and @p_26 @p_72 @p_58 @p_114) :named @p_358)) :named @p_369) @p_356) :rule implies_neg1)
(anchor :step t7)
(assume t7.a0 @p_26)
(assume t7.a1 @p_58)
(assume t7.a2 @p_72)
(assume t7.a3 @p_114)
(step t7.t0 (cl (not (! (= @p_13 @p_26) :named @p_27)) (not @p_13) @p_26) :rule equiv_pos2)
(step t7.t1 (cl (= @p_10 (! (not @p_17) :named @p_53))) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t7.t2 (cl (= @p_9 (! (* -1/1 @p_8) :named @p_55))) :rule poly_simp)
(step t7.t3 (cl (! (= @p_55 @p_16) :named @p_56)) :rule poly_simp)
(step t7.t4 (cl (= @p_9 @p_16)) :rule trans :premises (t7.t2 t7.t3))
(step t7.t5 (cl (= @p_8 @p_8)) :rule refl)
(step t7.t6 (cl (= @p_11 (! (ite @p_53 @p_16 @p_8) :named @p_54))) :rule cong :premises (t7.t1 t7.t4 t7.t5))
(step t7.t7 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t7.t8 (cl (= @p_11 @p_18)) :rule trans :premises (t7.t6 t7.t7))
(step t7.t9 (cl (! (= @p_5 (! (not @p_20) :named @p_50)) :named @p_52)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t7.t10 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t7.t11 (cl (= x$ x$)) :rule refl)
(step t7.t12 (cl (= @p_6 (! (ite @p_50 @p_15 x$) :named @p_51))) :rule cong :premises (t7.t9 t7.t10 t7.t11))
(step t7.t13 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t7.t14 (cl (= @p_6 @p_21)) :rule trans :premises (t7.t12 t7.t13))
(step t7.t15 (cl (= @p_2 (! (not @p_22) :named @p_48))) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t7.t16 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t7.t17 (cl (= y$ y$)) :rule refl)
(step t7.t18 (cl (= @p_3 (! (ite @p_48 @p_14 y$) :named @p_49))) :rule cong :premises (t7.t15 t7.t16 t7.t17))
(step t7.t19 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t7.t20 (cl (= @p_3 @p_23)) :rule trans :premises (t7.t18 t7.t19))
(step t7.t21 (cl (= @p_7 (! (+ @p_21 @p_23) :named @p_45))) :rule cong :premises (t7.t14 t7.t20))
(step t7.t22 (cl (= @p_12 (! (<= @p_18 @p_45) :named @p_46))) :rule cong :premises (t7.t8 t7.t21))
(step t7.t23 (cl (= @p_46 (! (>= @p_45 @p_18) :named @p_47))) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t7.t24 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- (! (+ @p_19 @p_21 @p_23) :named @p_28) 0/1)))) :rule poly_simp)
(step t7.t25 (cl (= @p_47 (! (>= @p_28 0/1) :named @p_29))) :rule poly_simp_rel :premises (t7.t24))
(step t7.t26 (cl (= @p_46 @p_29)) :rule trans :premises (t7.t23 t7.t25))
(step t7.t27 (cl (= @p_12 @p_29)) :rule trans :premises (t7.t22 t7.t26))
(step t7.t28 (cl (= @p_13 (! (not @p_29) :named @p_30))) :rule cong :premises (t7.t27))
(step t7.t29 (cl (= (! (= (! (= @p_18 @p_18) :named @p_41) true) :named @p_42) @p_41)) :rule equiv_simplify)
(step t7.t30 (cl (not @p_42) @p_41) :rule equiv1 :premises (t7.t29))
(step t7.t31 (cl (= (* -1/1 (! (- @p_18 @p_18) :named @p_44)) (* 1/1 @p_44))) :rule poly_simp)
(step t7.t32 (cl (! (= @p_41 @p_41) :named @p_43)) :rule poly_simp_rel :premises (t7.t31))
(step t7.t33 (cl @p_41) :rule refl)
(step t7.t34 (cl @p_41) :rule refl)
(step t7.t35 (cl @p_43) :rule cong :premises (t7.t33 t7.t34))
(step t7.t36 (cl @p_42) :rule rare_rewrite :args ("eq-refl" @p_18))
(step t7.t37 (cl @p_42) :rule trans :premises (t7.t32 t7.t35 t7.t36))
(step t7.t38 (cl @p_41) :rule resolution :premises (t7.t30 t7.t37))
(step t7.t39 (cl (= @p_19 @p_19)) :rule cong :premises (t7.t38))
(step t7.t40 (cl (= (! (= (! (= @p_21 @p_21) :named @p_37) true) :named @p_38) @p_37)) :rule equiv_simplify)
(step t7.t41 (cl (not @p_38) @p_37) :rule equiv1 :premises (t7.t40))
(step t7.t42 (cl (= (* -1/1 (! (- @p_21 @p_21) :named @p_40)) (* 1/1 @p_40))) :rule poly_simp)
(step t7.t43 (cl (! (= @p_37 @p_37) :named @p_39)) :rule poly_simp_rel :premises (t7.t42))
(step t7.t44 (cl @p_37) :rule refl)
(step t7.t45 (cl @p_37) :rule refl)
(step t7.t46 (cl @p_39) :rule cong :premises (t7.t44 t7.t45))
(step t7.t47 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t7.t48 (cl @p_38) :rule trans :premises (t7.t43 t7.t46 t7.t47))
(step t7.t49 (cl @p_37) :rule resolution :premises (t7.t41 t7.t48))
(step t7.t50 (cl (= (! (= (! (= @p_23 @p_23) :named @p_33) true) :named @p_34) @p_33)) :rule equiv_simplify)
(step t7.t51 (cl (not @p_34) @p_33) :rule equiv1 :premises (t7.t50))
(step t7.t52 (cl (= (* -1/1 (! (- @p_23 @p_23) :named @p_36)) (* 1/1 @p_36))) :rule poly_simp)
(step t7.t53 (cl (! (= @p_33 @p_33) :named @p_35)) :rule poly_simp_rel :premises (t7.t52))
(step t7.t54 (cl @p_33) :rule refl)
(step t7.t55 (cl @p_33) :rule refl)
(step t7.t56 (cl @p_35) :rule cong :premises (t7.t54 t7.t55))
(step t7.t57 (cl @p_34) :rule rare_rewrite :args ("eq-refl" @p_23))
(step t7.t58 (cl @p_34) :rule trans :premises (t7.t53 t7.t56 t7.t57))
(step t7.t59 (cl @p_33) :rule resolution :premises (t7.t51 t7.t58))
(step t7.t60 (cl (= @p_28 @p_28)) :rule cong :premises (t7.t39 t7.t49 t7.t59))
(step t7.t61 (cl (! (= @p_28 @p_24) :named @p_32)) :rule poly_simp)
(step t7.t62 (cl @p_32) :rule trans :premises (t7.t60 t7.t61))
(step t7.t63 (cl (! (= 0/1 0/1) :named @p_31)) :rule refl)
(step t7.t64 (cl (= @p_29 @p_25)) :rule cong :premises (t7.t62 t7.t63))
(step t7.t65 (cl (= @p_30 @p_26)) :rule cong :premises (t7.t64))
(step t7.t66 (cl @p_27) :rule trans :premises (t7.t28 t7.t65))
(step t7.t67 (cl @p_26) :rule resolution :premises (t7.t0 t7.t66 a0))
(step t7.t68 (cl @p_358) :rule and_intro :premises (t7.t67 t7.a2 t7.a1 t7.a3))
(step t7 (cl @p_128 @p_262 @p_184 @p_226 @p_358) :rule subproof :discharge (t7.a0 t7.a1 t7.a2 t7.a3))
(step t8 (cl (! (not @p_356) :named @p_357) @p_26) :rule and_pos :args (0))
(step t9 (cl @p_357 @p_58) :rule and_pos :args (1))
(step t10 (cl @p_357 @p_72) :rule and_pos :args (2))
(step t11 (cl @p_357 @p_114) :rule and_pos :args (3))
(step t12 (cl @p_358 @p_357 @p_357 @p_357 @p_357) :rule resolution :premises (t7 t8 t9 t10 t11))
(step t13 (cl @p_357 @p_357 @p_357 @p_357 @p_358) :rule reordering :premises (t12))
(step t14 (cl @p_357 @p_358) :rule contraction :premises (t13))
(step t15 (cl @p_369 @p_358) :rule resolution :premises (t6 t14))
(step t16 (cl @p_369 (! (not @p_358) :named @p_359)) :rule implies_neg2)
(step t17 (cl @p_369 @p_369) :rule resolution :premises (t15 t16))
(step t18 (cl @p_369) :rule contraction :premises (t17))
(step t19 (cl @p_357 @p_358) :rule implies :premises (t18))
(step t20 (cl (! (=> @p_358 false) :named @p_360) @p_358) :rule implies_neg1)
(anchor :step t21)
(assume t21.a0 @p_26)
(assume t21.a1 @p_72)
(assume t21.a2 @p_58)
(assume t21.a3 @p_114)
(step t21.t0 (cl (! (not (! (= @p_114 (! (= (! (+ x$ y$ @p_18) :named @p_235) 0/1) :named @p_236)) :named @p_258)) :named @p_259) @p_226 @p_236) :rule equiv_pos2)
(step t21.t1 (cl (= (* 1/1 (- @p_235 0/1)) (! (* 1/1 (- x$ @p_113)) :named @p_122))) :rule poly_simp)
(step t21.t2 (cl (= @p_236 @p_114)) :rule poly_simp_rel :premises (t21.t1))
(step t21.t3 (cl @p_258) :rule symm :premises (t21.t2))
(step t21.t4 (cl @p_236) :rule resolution :premises (t21.t0 t21.t3 t21.a3))
(step t21.t5 (cl (! (=> @p_236 false) :named @p_238) @p_236) :rule implies_neg1)
(anchor :step t21.t6)
(assume t21.t6.a0 @p_236)
(step t21.t6.t0 (cl (not (! (= (! (< (! (+ @p_235 (! (* -1/1 (! (+ y$ @p_23) :named @p_274)) :named @p_275) (! (* -1/1 (! (+ x$ @p_21) :named @p_197)) :named @p_198) @p_24) :named @p_362) (! (+ 0/1 (! (* -1/1 0/1) :named @p_91) @p_91 0/1) :named @p_361)) :named @p_363) false) :named @p_364)) (not @p_363) false) :rule equiv_pos2)
(step t21.t6.t1 (cl (= @p_363 (! (not (! (>= @p_362 @p_361) :named @p_365)) :named @p_366))) :rule rare_rewrite :args ("arith-elim-lt" @p_362 @p_361))
(step t21.t6.t2 (cl (= @p_362 (! (+ @p_19 @p_18 (! (* 0/1 @p_21) :named @p_221) (! (* 0/1 @p_23) :named @p_293) (! (* 0/1 y$) :named @p_175) (! (* 0/1 x$) :named @p_174)) :named @p_367))) :rule poly_simp)
(step t21.t6.t3 (cl (= @p_221 0/1)) :rule poly_simp)
(step t21.t6.t4 (cl (= @p_293 0/1)) :rule poly_simp)
(step t21.t6.t5 (cl (= @p_175 0/1)) :rule poly_simp)
(step t21.t6.t6 (cl (= @p_174 0/1)) :rule poly_simp)
(step t21.t6.t7 (cl (= @p_367 (! (+ @p_19 @p_18 0/1 0/1 0/1 0/1) :named @p_368))) :rule cong :premises (t21.t6.t3 t21.t6.t4 t21.t6.t5 t21.t6.t6))
(step t21.t6.t8 (cl (= @p_368 0/1)) :rule poly_simp)
(step t21.t6.t9 (cl (= @p_367 0/1)) :rule trans :premises (t21.t6.t7 t21.t6.t8))
(step t21.t6.t10 (cl (= @p_362 0/1)) :rule trans :premises (t21.t6.t2 t21.t6.t9))
(step t21.t6.t11 (cl (= @p_91 0/1)) :rule evaluate)
(step t21.t6.t12 (cl @p_31) :rule refl)
(step t21.t6.t13 (cl (= @p_361 (! (+ 0/1 0/1 0/1 0/1) :named @p_173))) :rule cong :premises (t21.t6.t11 t21.t6.t11 t21.t6.t12))
(step t21.t6.t14 (cl (= @p_173 0/1)) :rule evaluate)
(step t21.t6.t15 (cl (= @p_361 0/1)) :rule trans :premises (t21.t6.t13 t21.t6.t14))
(step t21.t6.t16 (cl (= @p_365 (! (>= 0/1 0/1) :named @p_107))) :rule cong :premises (t21.t6.t10 t21.t6.t15))
(step t21.t6.t17 (cl (= @p_107 true)) :rule evaluate)
(step t21.t6.t18 (cl (= @p_365 true)) :rule trans :premises (t21.t6.t16 t21.t6.t17))
(step t21.t6.t19 (cl (= @p_366 (! (not true) :named @p_64))) :rule cong :premises (t21.t6.t18))
(step t21.t6.t20 (cl (= @p_64 false)) :rule evaluate)
(step t21.t6.t21 (cl (= @p_366 false)) :rule trans :premises (t21.t6.t19 t21.t6.t20))
(step t21.t6.t22 (cl @p_364) :rule trans :premises (t21.t6.t1 t21.t6.t21))
(step t21.t6.t23 (cl (! (not @p_236) :named @p_237) (! (not (! (= @p_275 @p_91) :named @p_282)) :named @p_289) (! (not (! (= @p_198 @p_91) :named @p_207)) :named @p_215) (! (not (! (< @p_24 0/1) :named @p_159)) :named @p_167) @p_363) :rule la_generic :args (-1/1 -1/1 -1/1 1/1 1/1))
(step t21.t6.t24 (cl (=> (! (and (! (< -1/1 0/1) :named @p_96) (! (= @p_274 0/1) :named @p_283)) :named @p_284) @p_282)) :rule la_mult_neg)
(step t21.t6.t25 (cl (! (not @p_284) :named @p_288) @p_282) :rule implies :premises (t21.t6.t24))
(step t21.t6.t26 (cl (= (! (= @p_96 true) :named @p_98) @p_96)) :rule equiv_simplify)
(step t21.t6.t27 (cl (not @p_98) @p_96) :rule equiv1 :premises (t21.t6.t26))
(step t21.t6.t28 (cl @p_98) :rule evaluate)
(step t21.t6.t29 (cl @p_96) :rule resolution :premises (t21.t6.t27 t21.t6.t28))
(step t21.t6.t30 (cl (! (not (! (= @p_58 @p_283) :named @p_286)) :named @p_287) @p_262 @p_283) :rule equiv_pos2)
(step t21.t6.t31 (cl (= (* 1/1 (- @p_274 0/1)) (! (* 1/1 (- y$ @p_57)) :named @p_68))) :rule poly_simp)
(step t21.t6.t32 (cl (= @p_283 @p_58)) :rule poly_simp_rel :premises (t21.t6.t31))
(step t21.t6.t33 (cl @p_286) :rule symm :premises (t21.t6.t32))
(step t21.t6.t34 (cl @p_283) :rule resolution :premises (t21.t6.t30 t21.t6.t33 t21.a2))
(step t21.t6.t35 (cl @p_284) :rule and_intro :premises (t21.t6.t29 t21.t6.t34))
(step t21.t6.t36 (cl @p_282) :rule resolution :premises (t21.t6.t25 t21.t6.t35))
(step t21.t6.t37 (cl (=> (! (and @p_96 (! (= @p_197 0/1) :named @p_208)) :named @p_209) @p_207)) :rule la_mult_neg)
(step t21.t6.t38 (cl (! (not @p_209) :named @p_214) @p_207) :rule implies :premises (t21.t6.t37))
(step t21.t6.t39 (cl (! (not (! (= @p_72 @p_208) :named @p_212)) :named @p_213) @p_184 @p_208) :rule equiv_pos2)
(step t21.t6.t40 (cl (= (* 1/1 (- @p_197 0/1)) (! (* 1/1 (- x$ @p_71)) :named @p_80))) :rule poly_simp)
(step t21.t6.t41 (cl (= @p_208 @p_72)) :rule poly_simp_rel :premises (t21.t6.t40))
(step t21.t6.t42 (cl @p_212) :rule symm :premises (t21.t6.t41))
(step t21.t6.t43 (cl @p_208) :rule resolution :premises (t21.t6.t39 t21.t6.t42 t21.a1))
(step t21.t6.t44 (cl @p_209) :rule and_intro :premises (t21.t6.t29 t21.t6.t43))
(step t21.t6.t45 (cl @p_207) :rule resolution :premises (t21.t6.t38 t21.t6.t44))
(step t21.t6.t46 (cl (not (! (= @p_26 @p_159) :named @p_160)) @p_128 @p_159) :rule equiv_pos2)
(step t21.t6.t47 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t21.t6.t48 (cl @p_160) :rule symm :premises (t21.t6.t47))
(step t21.t6.t49 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t21.t6.t50 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t21.t6.t51 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t21.t6.t52 (cl @p_56) :rule poly_simp)
(step t21.t6.t53 (cl (= @p_9 @p_16)) :rule trans :premises (t21.t6.t51 t21.t6.t52))
(step t21.t6.t54 (cl (= @p_8 @p_8)) :rule refl)
(step t21.t6.t55 (cl (= @p_11 @p_54)) :rule cong :premises (t21.t6.t50 t21.t6.t53 t21.t6.t54))
(step t21.t6.t56 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t21.t6.t57 (cl (= @p_11 @p_18)) :rule trans :premises (t21.t6.t55 t21.t6.t56))
(step t21.t6.t58 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t21.t6.t59 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t21.t6.t60 (cl (= x$ x$)) :rule refl)
(step t21.t6.t61 (cl (= @p_6 @p_51)) :rule cong :premises (t21.t6.t58 t21.t6.t59 t21.t6.t60))
(step t21.t6.t62 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t21.t6.t63 (cl (= @p_6 @p_21)) :rule trans :premises (t21.t6.t61 t21.t6.t62))
(step t21.t6.t64 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t21.t6.t65 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t21.t6.t66 (cl (= y$ y$)) :rule refl)
(step t21.t6.t67 (cl (= @p_3 @p_49)) :rule cong :premises (t21.t6.t64 t21.t6.t65 t21.t6.t66))
(step t21.t6.t68 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t21.t6.t69 (cl (= @p_3 @p_23)) :rule trans :premises (t21.t6.t67 t21.t6.t68))
(step t21.t6.t70 (cl (= @p_7 @p_45)) :rule cong :premises (t21.t6.t63 t21.t6.t69))
(step t21.t6.t71 (cl (= @p_12 @p_46)) :rule cong :premises (t21.t6.t57 t21.t6.t70))
(step t21.t6.t72 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t21.t6.t73 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t21.t6.t74 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t21.t6.t73))
(step t21.t6.t75 (cl (= @p_46 @p_29)) :rule trans :premises (t21.t6.t72 t21.t6.t74))
(step t21.t6.t76 (cl (= @p_12 @p_29)) :rule trans :premises (t21.t6.t71 t21.t6.t75))
(step t21.t6.t77 (cl (= @p_13 @p_30)) :rule cong :premises (t21.t6.t76))
(step t21.t6.t78 (cl (= @p_42 @p_41)) :rule equiv_simplify)
(step t21.t6.t79 (cl (not @p_42) @p_41) :rule equiv1 :premises (t21.t6.t78))
(step t21.t6.t80 (cl (= (* -1/1 @p_44) (* 1/1 @p_44))) :rule poly_simp)
(step t21.t6.t81 (cl @p_43) :rule poly_simp_rel :premises (t21.t6.t80))
(step t21.t6.t82 (cl @p_41) :rule refl)
(step t21.t6.t83 (cl @p_41) :rule refl)
(step t21.t6.t84 (cl @p_43) :rule cong :premises (t21.t6.t82 t21.t6.t83))
(step t21.t6.t85 (cl @p_42) :rule rare_rewrite :args ("eq-refl" @p_18))
(step t21.t6.t86 (cl @p_42) :rule trans :premises (t21.t6.t81 t21.t6.t84 t21.t6.t85))
(step t21.t6.t87 (cl @p_41) :rule resolution :premises (t21.t6.t79 t21.t6.t86))
(step t21.t6.t88 (cl (= @p_19 @p_19)) :rule cong :premises (t21.t6.t87))
(step t21.t6.t89 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t21.t6.t90 (cl (not @p_38) @p_37) :rule equiv1 :premises (t21.t6.t89))
(step t21.t6.t91 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t21.t6.t92 (cl @p_39) :rule poly_simp_rel :premises (t21.t6.t91))
(step t21.t6.t93 (cl @p_37) :rule refl)
(step t21.t6.t94 (cl @p_37) :rule refl)
(step t21.t6.t95 (cl @p_39) :rule cong :premises (t21.t6.t93 t21.t6.t94))
(step t21.t6.t96 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t21.t6.t97 (cl @p_38) :rule trans :premises (t21.t6.t92 t21.t6.t95 t21.t6.t96))
(step t21.t6.t98 (cl @p_37) :rule resolution :premises (t21.t6.t90 t21.t6.t97))
(step t21.t6.t99 (cl (= @p_34 @p_33)) :rule equiv_simplify)
(step t21.t6.t100 (cl (not @p_34) @p_33) :rule equiv1 :premises (t21.t6.t99))
(step t21.t6.t101 (cl (= (* -1/1 @p_36) (* 1/1 @p_36))) :rule poly_simp)
(step t21.t6.t102 (cl @p_35) :rule poly_simp_rel :premises (t21.t6.t101))
(step t21.t6.t103 (cl @p_33) :rule refl)
(step t21.t6.t104 (cl @p_33) :rule refl)
(step t21.t6.t105 (cl @p_35) :rule cong :premises (t21.t6.t103 t21.t6.t104))
(step t21.t6.t106 (cl @p_34) :rule rare_rewrite :args ("eq-refl" @p_23))
(step t21.t6.t107 (cl @p_34) :rule trans :premises (t21.t6.t102 t21.t6.t105 t21.t6.t106))
(step t21.t6.t108 (cl @p_33) :rule resolution :premises (t21.t6.t100 t21.t6.t107))
(step t21.t6.t109 (cl (= @p_28 @p_28)) :rule cong :premises (t21.t6.t88 t21.t6.t98 t21.t6.t108))
(step t21.t6.t110 (cl @p_32) :rule poly_simp)
(step t21.t6.t111 (cl @p_32) :rule trans :premises (t21.t6.t109 t21.t6.t110))
(step t21.t6.t112 (cl @p_31) :rule refl)
(step t21.t6.t113 (cl (= @p_29 @p_25)) :rule cong :premises (t21.t6.t111 t21.t6.t112))
(step t21.t6.t114 (cl (= @p_30 @p_26)) :rule cong :premises (t21.t6.t113))
(step t21.t6.t115 (cl @p_27) :rule trans :premises (t21.t6.t77 t21.t6.t114))
(step t21.t6.t116 (cl @p_26) :rule resolution :premises (t21.t6.t49 t21.t6.t115 a0))
(step t21.t6.t117 (cl @p_159) :rule resolution :premises (t21.t6.t46 t21.t6.t48 t21.t6.t116))
(step t21.t6.t118 (cl @p_363) :rule resolution :premises (t21.t6.t23 t21.t6.a0 t21.t6.t36 t21.t6.t45 t21.t6.t117))
(step t21.t6.t119 (cl false) :rule resolution :premises (t21.t6.t0 t21.t6.t22 t21.t6.t118))
(step t21.t6 (cl @p_237 false) :rule subproof :discharge (t21.t6.a0))
(step t21.t7 (cl @p_238 false) :rule resolution :premises (t21.t5 t21.t6))
(step t21.t8 (cl @p_238 (! (not false) :named @p_90)) :rule implies_neg2)
(step t21.t9 (cl @p_238 @p_238) :rule resolution :premises (t21.t7 t21.t8))
(step t21.t10 (cl @p_238) :rule contraction :premises (t21.t9))
(step t21.t11 (cl (! (= @p_238 @p_237) :named @p_240)) :rule implies_simplify)
(step t21.t12 (cl (! (not @p_238) :named @p_239) @p_237) :rule equiv1 :premises (t21.t11))
(step t21.t13 (cl @p_237) :rule resolution :premises (t21.t10 t21.t12))
(step t21.t14 (cl) :rule resolution :premises (t21.t4 t21.t13))
(step t21 (cl @p_128 @p_184 @p_262 @p_226 false) :rule subproof :discharge (t21.a0 t21.a1 t21.a2 t21.a3))
(step t22 (cl @p_359 @p_26) :rule and_pos :args (0))
(step t23 (cl @p_359 @p_72) :rule and_pos :args (1))
(step t24 (cl @p_359 @p_58) :rule and_pos :args (2))
(step t25 (cl @p_359 @p_114) :rule and_pos :args (3))
(step t26 (cl false @p_359 @p_359 @p_359 @p_359) :rule resolution :premises (t21 t22 t23 t24 t25))
(step t27 (cl @p_359 @p_359 @p_359 @p_359 false) :rule reordering :premises (t26))
(step t28 (cl @p_359 false) :rule contraction :premises (t27))
(step t29 (cl @p_360 false) :rule resolution :premises (t20 t28))
(step t30 (cl @p_360 @p_90) :rule implies_neg2)
(step t31 (cl @p_360 @p_360) :rule resolution :premises (t29 t30))
(step t32 (cl @p_360) :rule contraction :premises (t31))
(step t33 (cl (= @p_360 @p_359)) :rule implies_simplify)
(step t34 (cl (not @p_360) @p_359) :rule equiv1 :premises (t33))
(step t35 (cl @p_359) :rule resolution :premises (t32 t34))
(step t36 (cl @p_357) :rule resolution :premises (t19 t35))
(step t37 (cl @p_128 @p_262 @p_184 @p_226) :rule not_and :premises (t36))
(step t38 (cl @p_355 (! (not @p_128) :named @p_133)) :rule or_neg :args (0))
(step t39 (cl @p_355 (! (not @p_262) :named @p_265)) :rule or_neg :args (1))
(step t40 (cl @p_355 (! (not @p_184) :named @p_187)) :rule or_neg :args (2))
(step t41 (cl @p_355 (! (not @p_226) :named @p_229)) :rule or_neg :args (3))
(step t42 (cl @p_355 @p_355 @p_355 @p_355) :rule resolution :premises (t37 t38 t39 t40 t41))
(step t43 (cl @p_355) :rule contraction :premises (t42))
(step t44 (cl @p_354) :rule resolution :premises (t0 t5 t43))
(step t45 (cl @p_25 @p_262 @p_184 @p_226) :rule or :premises (t44))
(step t46 (cl (not (! (= (! (ite @p_17 (! (= @p_18 @p_8) :named @p_117) (! (= @p_18 @p_16) :named @p_116)) :named @p_118) (! (ite @p_17 (! (= x$ (! (+ @p_14 @p_18) :named @p_111)) :named @p_112) @p_114) :named @p_115)) :named @p_121)) (! (not @p_118) :named @p_120) @p_115) :rule equiv_pos2)
(step t47 (cl (= (* 1/1 (- @p_18 @p_8)) (* -1/1 (! (- x$ @p_111) :named @p_123)))) :rule poly_simp)
(step t48 (cl (= @p_117 @p_112)) :rule poly_simp_rel :premises (t47))
(step t49 (cl (= (* 1/1 (- @p_18 @p_16)) @p_122)) :rule poly_simp)
(step t50 (cl (= @p_116 @p_114)) :rule poly_simp_rel :premises (t49))
(step t51 (cl @p_121) :rule cong :premises (t48 t50))
(step t52 (cl (not (! (= @p_118 @p_118) :named @p_119)) @p_120 @p_118) :rule equiv_pos2)
(step t53 (cl (= @p_42 @p_41)) :rule equiv_simplify)
(step t54 (cl (not @p_42) @p_41) :rule equiv1 :premises (t53))
(step t55 (cl (= (* -1/1 @p_44) (* 1/1 @p_44))) :rule poly_simp)
(step t56 (cl @p_43) :rule poly_simp_rel :premises (t55))
(step t57 (cl @p_41) :rule refl)
(step t58 (cl @p_41) :rule refl)
(step t59 (cl @p_43) :rule cong :premises (t57 t58))
(step t60 (cl @p_42) :rule rare_rewrite :args ("eq-refl" @p_18))
(step t61 (cl @p_42) :rule trans :premises (t56 t59 t60))
(step t62 (cl @p_41) :rule resolution :premises (t54 t61))
(step t63 (cl (= @p_8 @p_8)) :rule refl)
(step t64 (cl (= @p_117 @p_117)) :rule cong :premises (t62 t63))
(step t65 (cl (= @p_16 @p_16)) :rule refl)
(step t66 (cl (= @p_116 @p_116)) :rule cong :premises (t62 t65))
(step t67 (cl @p_119) :rule cong :premises (t64 t66))
(step t68 (cl (= @p_118 true)) :rule rare_rewrite :args ("ite-eq" @p_17 @p_8 @p_16))
(step t69 (cl @p_118 @p_64) :rule equiv2 :premises (t68))
(step t70 (cl true) :rule true)
(step t71 (cl @p_118) :rule resolution :premises (t69 t70))
(step t72 (cl @p_118) :rule resolution :premises (t52 t67 t71))
(step t73 (cl @p_115) :rule resolution :premises (t46 t51 t72))
(step t74 (cl @p_17 @p_114) :rule ite1 :premises (t73))
(step t75 (cl (not (! (= (! (or (! (not @p_50) :named @p_85) (! (not @p_48) :named @p_86) @p_53) :named @p_340) (! (or @p_20 @p_22 @p_53) :named @p_339)) :named @p_353)) (not @p_340) @p_339) :rule equiv_pos2)
(step t76 (cl (= @p_85 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t77 (cl (= @p_86 @p_22)) :rule rare_rewrite :args ("bool-double-not-elim" @p_22))
(step t78 (cl (= @p_53 @p_53)) :rule refl)
(step t79 (cl @p_353) :rule cong :premises (t76 t77 t78))
(step t80 (cl (! (=> (! (and @p_50 @p_48 @p_17) :named @p_341) false) :named @p_343) @p_341) :rule implies_neg1)
(anchor :step t81)
(assume t81.a0 @p_50)
(assume t81.a1 @p_48)
(assume t81.a2 @p_17)
(step t81.t0 (cl (not (! (= (! (< (! (+ @p_55 x$ y$) :named @p_345) (! (+ @p_91 0/1 0/1) :named @p_344)) :named @p_346) false) :named @p_349)) (not @p_346) false) :rule equiv_pos2)
(step t81.t1 (cl (= @p_346 (! (not (! (>= @p_345 @p_344) :named @p_350)) :named @p_351))) :rule rare_rewrite :args ("arith-elim-lt" @p_345 @p_344))
(step t81.t2 (cl @p_56) :rule poly_simp)
(step t81.t3 (cl (= x$ x$)) :rule refl)
(step t81.t4 (cl (= y$ y$)) :rule refl)
(step t81.t5 (cl (= @p_345 (! (+ @p_16 x$ y$) :named @p_352))) :rule cong :premises (t81.t2 t81.t3 t81.t4))
(step t81.t6 (cl (= @p_352 0/1)) :rule poly_simp)
(step t81.t7 (cl (= @p_345 0/1)) :rule trans :premises (t81.t5 t81.t6))
(step t81.t8 (cl (= @p_91 0/1)) :rule evaluate)
(step t81.t9 (cl @p_31) :rule refl)
(step t81.t10 (cl (= @p_344 (! (+ 0/1 0/1 0/1) :named @p_108))) :rule cong :premises (t81.t8 t81.t9 t81.t9))
(step t81.t11 (cl (= @p_108 0/1)) :rule evaluate)
(step t81.t12 (cl (= @p_344 0/1)) :rule trans :premises (t81.t10 t81.t11))
(step t81.t13 (cl (= @p_350 @p_107)) :rule cong :premises (t81.t7 t81.t12))
(step t81.t14 (cl (= @p_107 true)) :rule evaluate)
(step t81.t15 (cl (= @p_350 true)) :rule trans :premises (t81.t13 t81.t14))
(step t81.t16 (cl (= @p_351 @p_64)) :rule cong :premises (t81.t15))
(step t81.t17 (cl (= @p_64 false)) :rule evaluate)
(step t81.t18 (cl (= @p_351 false)) :rule trans :premises (t81.t16 t81.t17))
(step t81.t19 (cl @p_349) :rule trans :premises (t81.t1 t81.t18))
(step t81.t20 (cl (not (! (<= @p_55 @p_91) :named @p_347)) (! (not @p_5) :named @p_336) (not @p_2) @p_346) :rule la_generic :args (1/1 1/1 1/1 1/1))
(step t81.t21 (cl (=> (! (and @p_96 @p_17) :named @p_348) @p_347)) :rule la_mult_neg)
(step t81.t22 (cl (not @p_348) @p_347) :rule implies :premises (t81.t21))
(step t81.t23 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t81.t24 (cl (not @p_98) @p_96) :rule equiv1 :premises (t81.t23))
(step t81.t25 (cl @p_98) :rule evaluate)
(step t81.t26 (cl @p_96) :rule resolution :premises (t81.t24 t81.t25))
(step t81.t27 (cl @p_348) :rule and_intro :premises (t81.t26 t81.a2))
(step t81.t28 (cl @p_347) :rule resolution :premises (t81.t22 t81.t27))
(step t81.t29 (cl (! (not (! (= @p_50 @p_5) :named @p_204)) :named @p_205) @p_85 @p_5) :rule equiv_pos2)
(step t81.t30 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t81.t31 (cl @p_204) :rule symm :premises (t81.t30))
(step t81.t32 (cl @p_5) :rule resolution :premises (t81.t29 t81.t31 t81.a0))
(step t81.t33 (cl (! (not (! (= @p_48 @p_2) :named @p_280)) :named @p_281) @p_86 @p_2) :rule equiv_pos2)
(step t81.t34 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t81.t35 (cl @p_280) :rule symm :premises (t81.t34))
(step t81.t36 (cl @p_2) :rule resolution :premises (t81.t33 t81.t35 t81.a1))
(step t81.t37 (cl @p_346) :rule resolution :premises (t81.t20 t81.t28 t81.t32 t81.t36))
(step t81.t38 (cl false) :rule resolution :premises (t81.t0 t81.t19 t81.t37))
(step t81 (cl @p_85 @p_86 @p_53 false) :rule subproof :discharge (t81.a0 t81.a1 t81.a2))
(step t82 (cl (! (not @p_341) :named @p_342) @p_50) :rule and_pos :args (0))
(step t83 (cl @p_342 @p_48) :rule and_pos :args (1))
(step t84 (cl @p_342 @p_17) :rule and_pos :args (2))
(step t85 (cl false @p_342 @p_342 @p_342) :rule resolution :premises (t81 t82 t83 t84))
(step t86 (cl @p_342 @p_342 @p_342 false) :rule reordering :premises (t85))
(step t87 (cl @p_342 false) :rule contraction :premises (t86))
(step t88 (cl @p_343 false) :rule resolution :premises (t80 t87))
(step t89 (cl @p_343 @p_90) :rule implies_neg2)
(step t90 (cl @p_343 @p_343) :rule resolution :premises (t88 t89))
(step t91 (cl @p_343) :rule contraction :premises (t90))
(step t92 (cl (= @p_343 @p_342)) :rule implies_simplify)
(step t93 (cl (not @p_343) @p_342) :rule equiv1 :premises (t92))
(step t94 (cl @p_342) :rule resolution :premises (t91 t93))
(step t95 (cl @p_85 @p_86 @p_53) :rule not_and :premises (t94))
(step t96 (cl @p_340 (! (not @p_85) :named @p_188)) :rule or_neg :args (0))
(step t97 (cl @p_340 (! (not @p_86) :named @p_266)) :rule or_neg :args (1))
(step t98 (cl @p_340 (! (not @p_53) :named @p_83)) :rule or_neg :args (2))
(step t99 (cl @p_340 @p_340 @p_340) :rule resolution :premises (t95 t96 t97 t98))
(step t100 (cl @p_340) :rule contraction :premises (t99))
(step t101 (cl @p_339) :rule resolution :premises (t75 t79 t100))
(step t102 (cl @p_20 @p_22 @p_53) :rule or :premises (t101))
(step t103 (cl @p_53 @p_20 @p_22) :rule reordering :premises (t102))
(step t104 (cl (not (! (= (! (or @p_50 @p_128 @p_262 (! (not (! (= x$ @p_21) :named @p_70)) :named @p_125) @p_226) :named @p_299) (! (or @p_50 @p_25 @p_262 @p_125 @p_226) :named @p_298)) :named @p_338)) (not @p_299) @p_298) :rule equiv_pos2)
(step t105 (cl (= @p_125 @p_125)) :rule refl)
(step t106 (cl @p_338) :rule cong :premises (t1 t2 t105 t4))
(step t107 (cl (! (=> (! (and @p_20 @p_26 @p_58 @p_70 @p_114) :named @p_300) (! (and @p_70 @p_114 @p_26 @p_58 @p_20) :named @p_302)) :named @p_337) @p_300) :rule implies_neg1)
(anchor :step t108)
(assume t108.a0 @p_20)
(assume t108.a1 @p_26)
(assume t108.a2 @p_58)
(assume t108.a3 @p_70)
(assume t108.a4 @p_114)
(step t108.t0 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t108.t1 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t108.t2 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t108.t3 (cl @p_56) :rule poly_simp)
(step t108.t4 (cl (= @p_9 @p_16)) :rule trans :premises (t108.t2 t108.t3))
(step t108.t5 (cl (= @p_11 @p_54)) :rule cong :premises (t108.t1 t108.t4 t63))
(step t108.t6 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t108.t7 (cl (= @p_11 @p_18)) :rule trans :premises (t108.t5 t108.t6))
(step t108.t8 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t108.t9 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t108.t10 (cl (= x$ x$)) :rule refl)
(step t108.t11 (cl (= @p_6 @p_51)) :rule cong :premises (t108.t8 t108.t9 t108.t10))
(step t108.t12 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t108.t13 (cl (= @p_6 @p_21)) :rule trans :premises (t108.t11 t108.t12))
(step t108.t14 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t108.t15 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t108.t16 (cl (= y$ y$)) :rule refl)
(step t108.t17 (cl (= @p_3 @p_49)) :rule cong :premises (t108.t14 t108.t15 t108.t16))
(step t108.t18 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t108.t19 (cl (= @p_3 @p_23)) :rule trans :premises (t108.t17 t108.t18))
(step t108.t20 (cl (= @p_7 @p_45)) :rule cong :premises (t108.t13 t108.t19))
(step t108.t21 (cl (= @p_12 @p_46)) :rule cong :premises (t108.t7 t108.t20))
(step t108.t22 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t108.t23 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t108.t24 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t108.t23))
(step t108.t25 (cl (= @p_46 @p_29)) :rule trans :premises (t108.t22 t108.t24))
(step t108.t26 (cl (= @p_12 @p_29)) :rule trans :premises (t108.t21 t108.t25))
(step t108.t27 (cl (= @p_13 @p_30)) :rule cong :premises (t108.t26))
(step t108.t28 (cl (= @p_19 @p_19)) :rule cong :premises (t62))
(step t108.t29 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t108.t30 (cl (not @p_38) @p_37) :rule equiv1 :premises (t108.t29))
(step t108.t31 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t108.t32 (cl @p_39) :rule poly_simp_rel :premises (t108.t31))
(step t108.t33 (cl @p_37) :rule refl)
(step t108.t34 (cl @p_37) :rule refl)
(step t108.t35 (cl @p_39) :rule cong :premises (t108.t33 t108.t34))
(step t108.t36 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t108.t37 (cl @p_38) :rule trans :premises (t108.t32 t108.t35 t108.t36))
(step t108.t38 (cl @p_37) :rule resolution :premises (t108.t30 t108.t37))
(step t108.t39 (cl (= @p_34 @p_33)) :rule equiv_simplify)
(step t108.t40 (cl (not @p_34) @p_33) :rule equiv1 :premises (t108.t39))
(step t108.t41 (cl (= (* -1/1 @p_36) (* 1/1 @p_36))) :rule poly_simp)
(step t108.t42 (cl @p_35) :rule poly_simp_rel :premises (t108.t41))
(step t108.t43 (cl @p_33) :rule refl)
(step t108.t44 (cl @p_33) :rule refl)
(step t108.t45 (cl @p_35) :rule cong :premises (t108.t43 t108.t44))
(step t108.t46 (cl @p_34) :rule rare_rewrite :args ("eq-refl" @p_23))
(step t108.t47 (cl @p_34) :rule trans :premises (t108.t42 t108.t45 t108.t46))
(step t108.t48 (cl @p_33) :rule resolution :premises (t108.t40 t108.t47))
(step t108.t49 (cl (= @p_28 @p_28)) :rule cong :premises (t108.t28 t108.t38 t108.t48))
(step t108.t50 (cl @p_32) :rule poly_simp)
(step t108.t51 (cl @p_32) :rule trans :premises (t108.t49 t108.t50))
(step t108.t52 (cl @p_31) :rule refl)
(step t108.t53 (cl (= @p_29 @p_25)) :rule cong :premises (t108.t51 t108.t52))
(step t108.t54 (cl (= @p_30 @p_26)) :rule cong :premises (t108.t53))
(step t108.t55 (cl @p_27) :rule trans :premises (t108.t27 t108.t54))
(step t108.t56 (cl @p_26) :rule resolution :premises (t108.t0 t108.t55 a0))
(step t108.t57 (cl @p_302) :rule and_intro :premises (t108.a3 t108.a4 t108.t56 t108.a2 t108.a0))
(step t108 (cl @p_50 @p_128 @p_262 @p_125 @p_226 @p_302) :rule subproof :discharge (t108.a0 t108.a1 t108.a2 t108.a3 t108.a4))
(step t109 (cl (! (not @p_300) :named @p_301) @p_20) :rule and_pos :args (0))
(step t110 (cl @p_301 @p_26) :rule and_pos :args (1))
(step t111 (cl @p_301 @p_58) :rule and_pos :args (2))
(step t112 (cl @p_301 @p_70) :rule and_pos :args (3))
(step t113 (cl @p_301 @p_114) :rule and_pos :args (4))
(step t114 (cl @p_302 @p_301 @p_301 @p_301 @p_301 @p_301) :rule resolution :premises (t108 t109 t110 t111 t112 t113))
(step t115 (cl @p_301 @p_301 @p_301 @p_301 @p_301 @p_302) :rule reordering :premises (t114))
(step t116 (cl @p_301 @p_302) :rule contraction :premises (t115))
(step t117 (cl @p_337 @p_302) :rule resolution :premises (t107 t116))
(step t118 (cl @p_337 (! (not @p_302) :named @p_303)) :rule implies_neg2)
(step t119 (cl @p_337 @p_337) :rule resolution :premises (t117 t118))
(step t120 (cl @p_337) :rule contraction :premises (t119))
(step t121 (cl @p_301 @p_302) :rule implies :premises (t120))
(step t122 (cl (! (=> @p_302 false) :named @p_304) @p_302) :rule implies_neg1)
(anchor :step t123)
(assume t123.a0 @p_70)
(assume t123.a1 @p_114)
(assume t123.a2 @p_26)
(assume t123.a3 @p_58)
(assume t123.a4 @p_20)
(step t123.t0 (cl (not @p_52) @p_336 @p_50) :rule equiv_pos2)
(step t123.t1 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t123.t2 (cl @p_205 @p_85 @p_5) :rule equiv_pos2)
(step t123.t3 (cl @p_204) :rule symm :premises (t123.t1))
(step t123.t4 (cl (! (=> @p_20 false) :named @p_305) @p_20) :rule implies_neg1)
(anchor :step t123.t5)
(assume t123.t5.a0 @p_20)
(step t123.t5.t0 (cl (not (! (= (! (< (! (+ @p_15 (! (* -1/2 @p_274) :named @p_312) (! (* 1/2 @p_24) :named @p_311) (! (* 1/2 @p_235) :named @p_310) (! (* 1/2 (! (+ x$ @p_71) :named @p_146)) :named @p_309)) :named @p_313) (! (+ @p_91 (! (* -1/2 0/1) :named @p_307) (! (* 1/2 0/1) :named @p_306) @p_306 @p_306) :named @p_308)) :named @p_314) false) :named @p_327)) (not @p_314) false) :rule equiv_pos2)
(step t123.t5.t1 (cl (= @p_314 (! (not (! (>= @p_313 @p_308) :named @p_328)) :named @p_329))) :rule rare_rewrite :args ("arith-elim-lt" @p_313 @p_308))
(step t123.t5.t2 (cl (= @p_312 (! (+ (* -1/2 y$) (* -1/2 @p_23)) :named @p_334))) :rule poly_simp)
(step t123.t5.t3 (cl (= @p_311 (! (+ (* 1/2 @p_23) (* 1/2 @p_21) (* -1/2 @p_18)) :named @p_333))) :rule poly_simp)
(step t123.t5.t4 (cl (= @p_310 (! (+ (! (* 1/2 x$) :named @p_330) (* 1/2 y$) (* 1/2 @p_18)) :named @p_332))) :rule poly_simp)
(step t123.t5.t5 (cl (= @p_309 (! (+ @p_330 (* -1/2 @p_21)) :named @p_331))) :rule poly_simp)
(step t123.t5.t6 (cl (= @p_313 (! (+ @p_15 @p_334 @p_333 @p_332 @p_331) :named @p_335))) :rule cong :premises (t123.t5.t2 t123.t5.t3 t123.t5.t4 t123.t5.t5))
(step t123.t5.t7 (cl (= @p_335 0/1)) :rule poly_simp)
(step t123.t5.t8 (cl (= @p_313 0/1)) :rule trans :premises (t123.t5.t6 t123.t5.t7))
(step t123.t5.t9 (cl (= @p_91 0/1)) :rule evaluate)
(step t123.t5.t10 (cl (= @p_307 0/1)) :rule evaluate)
(step t123.t5.t11 (cl (= @p_306 0/1)) :rule evaluate)
(step t123.t5.t12 (cl (= @p_308 (! (+ 0/1 0/1 0/1 0/1 0/1) :named @p_219))) :rule cong :premises (t123.t5.t9 t123.t5.t10 t123.t5.t11 t123.t5.t11 t123.t5.t11))
(step t123.t5.t13 (cl (= @p_219 0/1)) :rule evaluate)
(step t123.t5.t14 (cl (= @p_308 0/1)) :rule trans :premises (t123.t5.t12 t123.t5.t13))
(step t123.t5.t15 (cl (= @p_328 @p_107)) :rule cong :premises (t123.t5.t8 t123.t5.t14))
(step t123.t5.t16 (cl (= @p_107 true)) :rule evaluate)
(step t123.t5.t17 (cl (= @p_328 true)) :rule trans :premises (t123.t5.t15 t123.t5.t16))
(step t123.t5.t18 (cl (= @p_329 @p_64)) :rule cong :premises (t123.t5.t17))
(step t123.t5.t19 (cl (= @p_64 false)) :rule evaluate)
(step t123.t5.t20 (cl (= @p_329 false)) :rule trans :premises (t123.t5.t18 t123.t5.t19))
(step t123.t5.t21 (cl @p_327) :rule trans :premises (t123.t5.t1 t123.t5.t20))
(step t123.t5.t22 (cl (! (not (! (<= @p_15 @p_91) :named @p_95)) :named @p_103) (not (! (= @p_312 @p_307) :named @p_323)) (not (! (< @p_311 @p_306) :named @p_321)) (not (! (= @p_310 @p_306) :named @p_319)) (not (! (= @p_309 @p_306) :named @p_315)) @p_314) :rule la_generic :args (1/1 -1/1 1/1 -1/1 -1/1 1/1))
(step t123.t5.t23 (cl (=> (! (and @p_96 @p_20) :named @p_97) @p_95)) :rule la_mult_neg)
(step t123.t5.t24 (cl (! (not @p_97) :named @p_99) @p_95) :rule implies :premises (t123.t5.t23))
(step t123.t5.t25 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t123.t5.t26 (cl (not @p_98) @p_96) :rule equiv1 :premises (t123.t5.t25))
(step t123.t5.t27 (cl @p_98) :rule evaluate)
(step t123.t5.t28 (cl @p_96) :rule resolution :premises (t123.t5.t26 t123.t5.t27))
(step t123.t5.t29 (cl @p_97) :rule and_intro :premises (t123.t5.t28 t123.t5.a0))
(step t123.t5.t30 (cl @p_95) :rule resolution :premises (t123.t5.t24 t123.t5.t29))
(step t123.t5.t31 (cl (=> (! (and (! (< -1/2 0/1) :named @p_324) @p_283) :named @p_325) @p_323)) :rule la_mult_neg)
(step t123.t5.t32 (cl (not @p_325) @p_323) :rule implies :premises (t123.t5.t31))
(step t123.t5.t33 (cl (= (! (= @p_324 true) :named @p_326) @p_324)) :rule equiv_simplify)
(step t123.t5.t34 (cl (not @p_326) @p_324) :rule equiv1 :premises (t123.t5.t33))
(step t123.t5.t35 (cl @p_326) :rule evaluate)
(step t123.t5.t36 (cl @p_324) :rule resolution :premises (t123.t5.t34 t123.t5.t35))
(step t123.t5.t37 (cl @p_287 @p_262 @p_283) :rule equiv_pos2)
(step t123.t5.t38 (cl (= (* 1/1 (- @p_274 0/1)) @p_68)) :rule poly_simp)
(step t123.t5.t39 (cl (= @p_283 @p_58)) :rule poly_simp_rel :premises (t123.t5.t38))
(step t123.t5.t40 (cl @p_286) :rule symm :premises (t123.t5.t39))
(step t123.t5.t41 (cl @p_283) :rule resolution :premises (t123.t5.t37 t123.t5.t40 t123.a3))
(step t123.t5.t42 (cl @p_325) :rule and_intro :premises (t123.t5.t36 t123.t5.t41))
(step t123.t5.t43 (cl @p_323) :rule resolution :premises (t123.t5.t32 t123.t5.t42))
(step t123.t5.t44 (cl (=> (! (and (! (> 1/2 0/1) :named @p_316) @p_159) :named @p_322) @p_321)) :rule la_mult_pos)
(step t123.t5.t45 (cl (not @p_322) @p_321) :rule implies :premises (t123.t5.t44))
(step t123.t5.t46 (cl (= (! (= @p_316 true) :named @p_318) @p_316)) :rule equiv_simplify)
(step t123.t5.t47 (cl (not @p_318) @p_316) :rule equiv1 :premises (t123.t5.t46))
(step t123.t5.t48 (cl @p_318) :rule evaluate)
(step t123.t5.t49 (cl @p_316) :rule resolution :premises (t123.t5.t47 t123.t5.t48))
(step t123.t5.t50 (cl (not @p_160) @p_128 @p_159) :rule equiv_pos2)
(step t123.t5.t51 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t123.t5.t52 (cl @p_160) :rule symm :premises (t123.t5.t51))
(step t123.t5.t53 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t123.t5.t54 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t123.t5.t55 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t123.t5.t56 (cl @p_56) :rule poly_simp)
(step t123.t5.t57 (cl (= @p_9 @p_16)) :rule trans :premises (t123.t5.t55 t123.t5.t56))
(step t123.t5.t58 (cl (= @p_11 @p_54)) :rule cong :premises (t123.t5.t54 t123.t5.t57 t63))
(step t123.t5.t59 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t123.t5.t60 (cl (= @p_11 @p_18)) :rule trans :premises (t123.t5.t58 t123.t5.t59))
(step t123.t5.t61 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t123.t5.t62 (cl (= x$ x$)) :rule refl)
(step t123.t5.t63 (cl (= @p_6 @p_51)) :rule cong :premises (t123.t1 t123.t5.t61 t123.t5.t62))
(step t123.t5.t64 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t123.t5.t65 (cl (= @p_6 @p_21)) :rule trans :premises (t123.t5.t63 t123.t5.t64))
(step t123.t5.t66 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t123.t5.t67 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t123.t5.t68 (cl (= y$ y$)) :rule refl)
(step t123.t5.t69 (cl (= @p_3 @p_49)) :rule cong :premises (t123.t5.t66 t123.t5.t67 t123.t5.t68))
(step t123.t5.t70 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t123.t5.t71 (cl (= @p_3 @p_23)) :rule trans :premises (t123.t5.t69 t123.t5.t70))
(step t123.t5.t72 (cl (= @p_7 @p_45)) :rule cong :premises (t123.t5.t65 t123.t5.t71))
(step t123.t5.t73 (cl (= @p_12 @p_46)) :rule cong :premises (t123.t5.t60 t123.t5.t72))
(step t123.t5.t74 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t123.t5.t75 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t123.t5.t76 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t123.t5.t75))
(step t123.t5.t77 (cl (= @p_46 @p_29)) :rule trans :premises (t123.t5.t74 t123.t5.t76))
(step t123.t5.t78 (cl (= @p_12 @p_29)) :rule trans :premises (t123.t5.t73 t123.t5.t77))
(step t123.t5.t79 (cl (= @p_13 @p_30)) :rule cong :premises (t123.t5.t78))
(step t123.t5.t80 (cl (= @p_19 @p_19)) :rule cong :premises (t62))
(step t123.t5.t81 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t123.t5.t82 (cl (not @p_38) @p_37) :rule equiv1 :premises (t123.t5.t81))
(step t123.t5.t83 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t123.t5.t84 (cl @p_39) :rule poly_simp_rel :premises (t123.t5.t83))
(step t123.t5.t85 (cl @p_37) :rule refl)
(step t123.t5.t86 (cl @p_37) :rule refl)
(step t123.t5.t87 (cl @p_39) :rule cong :premises (t123.t5.t85 t123.t5.t86))
(step t123.t5.t88 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t123.t5.t89 (cl @p_38) :rule trans :premises (t123.t5.t84 t123.t5.t87 t123.t5.t88))
(step t123.t5.t90 (cl @p_37) :rule resolution :premises (t123.t5.t82 t123.t5.t89))
(step t123.t5.t91 (cl (= @p_34 @p_33)) :rule equiv_simplify)
(step t123.t5.t92 (cl (not @p_34) @p_33) :rule equiv1 :premises (t123.t5.t91))
(step t123.t5.t93 (cl (= (* -1/1 @p_36) (* 1/1 @p_36))) :rule poly_simp)
(step t123.t5.t94 (cl @p_35) :rule poly_simp_rel :premises (t123.t5.t93))
(step t123.t5.t95 (cl @p_33) :rule refl)
(step t123.t5.t96 (cl @p_33) :rule refl)
(step t123.t5.t97 (cl @p_35) :rule cong :premises (t123.t5.t95 t123.t5.t96))
(step t123.t5.t98 (cl @p_34) :rule rare_rewrite :args ("eq-refl" @p_23))
(step t123.t5.t99 (cl @p_34) :rule trans :premises (t123.t5.t94 t123.t5.t97 t123.t5.t98))
(step t123.t5.t100 (cl @p_33) :rule resolution :premises (t123.t5.t92 t123.t5.t99))
(step t123.t5.t101 (cl (= @p_28 @p_28)) :rule cong :premises (t123.t5.t80 t123.t5.t90 t123.t5.t100))
(step t123.t5.t102 (cl @p_32) :rule poly_simp)
(step t123.t5.t103 (cl @p_32) :rule trans :premises (t123.t5.t101 t123.t5.t102))
(step t123.t5.t104 (cl @p_31) :rule refl)
(step t123.t5.t105 (cl (= @p_29 @p_25)) :rule cong :premises (t123.t5.t103 t123.t5.t104))
(step t123.t5.t106 (cl (= @p_30 @p_26)) :rule cong :premises (t123.t5.t105))
(step t123.t5.t107 (cl @p_27) :rule trans :premises (t123.t5.t79 t123.t5.t106))
(step t123.t5.t108 (cl @p_26) :rule resolution :premises (t123.t5.t53 t123.t5.t107 a0))
(step t123.t5.t109 (cl @p_159) :rule resolution :premises (t123.t5.t50 t123.t5.t52 t123.t5.t108))
(step t123.t5.t110 (cl @p_322) :rule and_intro :premises (t123.t5.t49 t123.t5.t109))
(step t123.t5.t111 (cl @p_321) :rule resolution :premises (t123.t5.t45 t123.t5.t110))
(step t123.t5.t112 (cl (=> (! (and @p_316 @p_236) :named @p_320) @p_319)) :rule la_mult_pos)
(step t123.t5.t113 (cl (not @p_320) @p_319) :rule implies :premises (t123.t5.t112))
(step t123.t5.t114 (cl @p_259 @p_226 @p_236) :rule equiv_pos2)
(step t123.t5.t115 (cl (= (* 1/1 (- @p_235 0/1)) @p_122)) :rule poly_simp)
(step t123.t5.t116 (cl (= @p_236 @p_114)) :rule poly_simp_rel :premises (t123.t5.t115))
(step t123.t5.t117 (cl @p_258) :rule symm :premises (t123.t5.t116))
(step t123.t5.t118 (cl @p_236) :rule resolution :premises (t123.t5.t114 t123.t5.t117 t123.a1))
(step t123.t5.t119 (cl @p_320) :rule and_intro :premises (t123.t5.t49 t123.t5.t118))
(step t123.t5.t120 (cl @p_319) :rule resolution :premises (t123.t5.t113 t123.t5.t119))
(step t123.t5.t121 (cl (=> (! (and @p_316 (! (= @p_146 0/1) :named @p_151)) :named @p_317) @p_315)) :rule la_mult_pos)
(step t123.t5.t122 (cl (not @p_317) @p_315) :rule implies :premises (t123.t5.t121))
(step t123.t5.t123 (cl (! (not (! (= @p_70 @p_151) :named @p_153)) :named @p_154) @p_125 @p_151) :rule equiv_pos2)
(step t123.t5.t124 (cl (= (* 1/1 (- @p_146 0/1)) (* 1/1 (! (- x$ @p_21) :named @p_81)))) :rule poly_simp)
(step t123.t5.t125 (cl (= @p_151 @p_70)) :rule poly_simp_rel :premises (t123.t5.t124))
(step t123.t5.t126 (cl @p_153) :rule symm :premises (t123.t5.t125))
(step t123.t5.t127 (cl @p_151) :rule resolution :premises (t123.t5.t123 t123.t5.t126 t123.a0))
(step t123.t5.t128 (cl @p_317) :rule and_intro :premises (t123.t5.t49 t123.t5.t127))
(step t123.t5.t129 (cl @p_315) :rule resolution :premises (t123.t5.t122 t123.t5.t128))
(step t123.t5.t130 (cl @p_314) :rule resolution :premises (t123.t5.t22 t123.t5.t30 t123.t5.t43 t123.t5.t111 t123.t5.t120 t123.t5.t129))
(step t123.t5.t131 (cl false) :rule resolution :premises (t123.t5.t0 t123.t5.t21 t123.t5.t130))
(step t123.t5 (cl @p_50 false) :rule subproof :discharge (t123.t5.a0))
(step t123.t6 (cl @p_305 false) :rule resolution :premises (t123.t4 t123.t5))
(step t123.t7 (cl @p_305 @p_90) :rule implies_neg2)
(step t123.t8 (cl @p_305 @p_305) :rule resolution :premises (t123.t6 t123.t7))
(step t123.t9 (cl @p_305) :rule contraction :premises (t123.t8))
(step t123.t10 (cl (= @p_305 @p_50)) :rule implies_simplify)
(step t123.t11 (cl (not @p_305) @p_50) :rule equiv1 :premises (t123.t10))
(step t123.t12 (cl @p_50) :rule resolution :premises (t123.t9 t123.t11))
(step t123.t13 (cl @p_5) :rule resolution :premises (t123.t2 t123.t3 t123.t12))
(step t123.t14 (cl @p_50) :rule resolution :premises (t123.t0 t123.t1 t123.t13))
(step t123.t15 (cl) :rule resolution :premises (t123.a4 t123.t14))
(step t123 (cl @p_125 @p_226 @p_128 @p_262 @p_50 false) :rule subproof :discharge (t123.a0 t123.a1 t123.a2 t123.a3 t123.a4))
(step t124 (cl @p_303 @p_70) :rule and_pos :args (0))
(step t125 (cl @p_303 @p_114) :rule and_pos :args (1))
(step t126 (cl @p_303 @p_26) :rule and_pos :args (2))
(step t127 (cl @p_303 @p_58) :rule and_pos :args (3))
(step t128 (cl @p_303 @p_20) :rule and_pos :args (4))
(step t129 (cl false @p_303 @p_303 @p_303 @p_303 @p_303) :rule resolution :premises (t123 t124 t125 t126 t127 t128))
(step t130 (cl @p_303 @p_303 @p_303 @p_303 @p_303 false) :rule reordering :premises (t129))
(step t131 (cl @p_303 false) :rule contraction :premises (t130))
(step t132 (cl @p_304 false) :rule resolution :premises (t122 t131))
(step t133 (cl @p_304 @p_90) :rule implies_neg2)
(step t134 (cl @p_304 @p_304) :rule resolution :premises (t132 t133))
(step t135 (cl @p_304) :rule contraction :premises (t134))
(step t136 (cl (= @p_304 @p_303)) :rule implies_simplify)
(step t137 (cl (not @p_304) @p_303) :rule equiv1 :premises (t136))
(step t138 (cl @p_303) :rule resolution :premises (t135 t137))
(step t139 (cl @p_301) :rule resolution :premises (t121 t138))
(step t140 (cl @p_50 @p_128 @p_262 @p_125 @p_226) :rule not_and :premises (t139))
(step t141 (cl @p_299 @p_85) :rule or_neg :args (0))
(step t142 (cl @p_299 @p_133) :rule or_neg :args (1))
(step t143 (cl @p_299 @p_265) :rule or_neg :args (2))
(step t144 (cl @p_299 (! (not @p_125) :named @p_131)) :rule or_neg :args (3))
(step t145 (cl @p_299 @p_229) :rule or_neg :args (4))
(step t146 (cl @p_299 @p_299 @p_299 @p_299 @p_299) :rule resolution :premises (t140 t141 t142 t143 t144 t145))
(step t147 (cl @p_299) :rule contraction :premises (t146))
(step t148 (cl @p_298) :rule resolution :premises (t104 t106 t147))
(step t149 (cl @p_50 @p_25 @p_262 @p_125 @p_226) :rule or :premises (t148))
(step t150 (cl (not (! (= (! (ite @p_22 (! (= @p_23 y$) :named @p_62) (! (= @p_23 @p_14) :named @p_61)) :named @p_63) (! (ite @p_22 (! (= y$ @p_23) :named @p_59) @p_58) :named @p_60)) :named @p_67)) (! (not @p_63) :named @p_66) @p_60) :rule equiv_pos2)
(step t151 (cl (= (* 1/1 (- @p_23 y$)) (* -1/1 (! (- y$ @p_23) :named @p_69)))) :rule poly_simp)
(step t152 (cl (= @p_62 @p_59)) :rule poly_simp_rel :premises (t151))
(step t153 (cl (= (* 1/1 (- @p_23 @p_14)) @p_68)) :rule poly_simp)
(step t154 (cl (= @p_61 @p_58)) :rule poly_simp_rel :premises (t153))
(step t155 (cl @p_67) :rule cong :premises (t152 t154))
(step t156 (cl (not (! (= @p_63 @p_63) :named @p_65)) @p_66 @p_63) :rule equiv_pos2)
(step t157 (cl (= @p_34 @p_33)) :rule equiv_simplify)
(step t158 (cl (not @p_34) @p_33) :rule equiv1 :premises (t157))
(step t159 (cl (= (* -1/1 @p_36) (* 1/1 @p_36))) :rule poly_simp)
(step t160 (cl @p_35) :rule poly_simp_rel :premises (t159))
(step t161 (cl @p_33) :rule refl)
(step t162 (cl @p_33) :rule refl)
(step t163 (cl @p_35) :rule cong :premises (t161 t162))
(step t164 (cl @p_34) :rule rare_rewrite :args ("eq-refl" @p_23))
(step t165 (cl @p_34) :rule trans :premises (t160 t163 t164))
(step t166 (cl @p_33) :rule resolution :premises (t158 t165))
(step t167 (cl (= y$ y$)) :rule refl)
(step t168 (cl (= @p_62 @p_62)) :rule cong :premises (t166 t167))
(step t169 (cl (= @p_14 @p_14)) :rule refl)
(step t170 (cl (= @p_61 @p_61)) :rule cong :premises (t166 t169))
(step t171 (cl @p_65) :rule cong :premises (t168 t170))
(step t172 (cl (= @p_63 true)) :rule rare_rewrite :args ("ite-eq" @p_22 y$ @p_14))
(step t173 (cl @p_63 @p_64) :rule equiv2 :premises (t172))
(step t174 (cl true) :rule true)
(step t175 (cl @p_63) :rule resolution :premises (t173 t174))
(step t176 (cl @p_63) :rule resolution :premises (t156 t171 t175))
(step t177 (cl @p_60) :rule resolution :premises (t150 t155 t176))
(step t178 (cl @p_22 @p_58) :rule ite1 :premises (t177))
(step t179 (cl (not (! (= (! (or @p_48 @p_128 (! (not @p_59) :named @p_124) @p_184 @p_226) :named @p_228) (! (or @p_48 @p_25 @p_124 @p_184 @p_226) :named @p_227)) :named @p_261)) (not @p_228) @p_227) :rule equiv_pos2)
(step t180 (cl (= @p_124 @p_124)) :rule refl)
(step t181 (cl @p_261) :rule cong :premises (t1 t180 t3 t4))
(step t182 (cl (! (=> (! (and @p_22 @p_26 @p_59 @p_72 @p_114) :named @p_230) (! (and @p_22 @p_26 @p_72 @p_59 @p_114) :named @p_232)) :named @p_260) @p_230) :rule implies_neg1)
(anchor :step t183)
(assume t183.a0 @p_22)
(assume t183.a1 @p_26)
(assume t183.a2 @p_59)
(assume t183.a3 @p_72)
(assume t183.a4 @p_114)
(step t183.t0 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t183.t1 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t183.t2 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t183.t3 (cl @p_56) :rule poly_simp)
(step t183.t4 (cl (= @p_9 @p_16)) :rule trans :premises (t183.t2 t183.t3))
(step t183.t5 (cl (= @p_11 @p_54)) :rule cong :premises (t183.t1 t183.t4 t63))
(step t183.t6 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t183.t7 (cl (= @p_11 @p_18)) :rule trans :premises (t183.t5 t183.t6))
(step t183.t8 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t183.t9 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t183.t10 (cl (= x$ x$)) :rule refl)
(step t183.t11 (cl (= @p_6 @p_51)) :rule cong :premises (t183.t8 t183.t9 t183.t10))
(step t183.t12 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t183.t13 (cl (= @p_6 @p_21)) :rule trans :premises (t183.t11 t183.t12))
(step t183.t14 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t183.t15 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t183.t16 (cl (= @p_3 @p_49)) :rule cong :premises (t183.t14 t183.t15 t167))
(step t183.t17 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t183.t18 (cl (= @p_3 @p_23)) :rule trans :premises (t183.t16 t183.t17))
(step t183.t19 (cl (= @p_7 @p_45)) :rule cong :premises (t183.t13 t183.t18))
(step t183.t20 (cl (= @p_12 @p_46)) :rule cong :premises (t183.t7 t183.t19))
(step t183.t21 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t183.t22 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t183.t23 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t183.t22))
(step t183.t24 (cl (= @p_46 @p_29)) :rule trans :premises (t183.t21 t183.t23))
(step t183.t25 (cl (= @p_12 @p_29)) :rule trans :premises (t183.t20 t183.t24))
(step t183.t26 (cl (= @p_13 @p_30)) :rule cong :premises (t183.t25))
(step t183.t27 (cl (= @p_19 @p_19)) :rule cong :premises (t62))
(step t183.t28 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t183.t29 (cl (not @p_38) @p_37) :rule equiv1 :premises (t183.t28))
(step t183.t30 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t183.t31 (cl @p_39) :rule poly_simp_rel :premises (t183.t30))
(step t183.t32 (cl @p_37) :rule refl)
(step t183.t33 (cl @p_37) :rule refl)
(step t183.t34 (cl @p_39) :rule cong :premises (t183.t32 t183.t33))
(step t183.t35 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t183.t36 (cl @p_38) :rule trans :premises (t183.t31 t183.t34 t183.t35))
(step t183.t37 (cl @p_37) :rule resolution :premises (t183.t29 t183.t36))
(step t183.t38 (cl (= @p_28 @p_28)) :rule cong :premises (t183.t27 t183.t37 t166))
(step t183.t39 (cl @p_32) :rule poly_simp)
(step t183.t40 (cl @p_32) :rule trans :premises (t183.t38 t183.t39))
(step t183.t41 (cl @p_31) :rule refl)
(step t183.t42 (cl (= @p_29 @p_25)) :rule cong :premises (t183.t40 t183.t41))
(step t183.t43 (cl (= @p_30 @p_26)) :rule cong :premises (t183.t42))
(step t183.t44 (cl @p_27) :rule trans :premises (t183.t26 t183.t43))
(step t183.t45 (cl @p_26) :rule resolution :premises (t183.t0 t183.t44 a0))
(step t183.t46 (cl @p_232) :rule and_intro :premises (t183.a0 t183.t45 t183.a3 t183.a2 t183.a4))
(step t183 (cl @p_48 @p_128 @p_124 @p_184 @p_226 @p_232) :rule subproof :discharge (t183.a0 t183.a1 t183.a2 t183.a3 t183.a4))
(step t184 (cl (! (not @p_230) :named @p_231) @p_22) :rule and_pos :args (0))
(step t185 (cl @p_231 @p_26) :rule and_pos :args (1))
(step t186 (cl @p_231 @p_59) :rule and_pos :args (2))
(step t187 (cl @p_231 @p_72) :rule and_pos :args (3))
(step t188 (cl @p_231 @p_114) :rule and_pos :args (4))
(step t189 (cl @p_232 @p_231 @p_231 @p_231 @p_231 @p_231) :rule resolution :premises (t183 t184 t185 t186 t187 t188))
(step t190 (cl @p_231 @p_231 @p_231 @p_231 @p_231 @p_232) :rule reordering :premises (t189))
(step t191 (cl @p_231 @p_232) :rule contraction :premises (t190))
(step t192 (cl @p_260 @p_232) :rule resolution :premises (t182 t191))
(step t193 (cl @p_260 (! (not @p_232) :named @p_233)) :rule implies_neg2)
(step t194 (cl @p_260 @p_260) :rule resolution :premises (t192 t193))
(step t195 (cl @p_260) :rule contraction :premises (t194))
(step t196 (cl @p_231 @p_232) :rule implies :premises (t195))
(step t197 (cl (! (=> @p_232 false) :named @p_234) @p_232) :rule implies_neg1)
(anchor :step t198)
(assume t198.a0 @p_22)
(assume t198.a1 @p_26)
(assume t198.a2 @p_72)
(assume t198.a3 @p_59)
(assume t198.a4 @p_114)
(step t198.t0 (cl @p_259 @p_226 @p_236) :rule equiv_pos2)
(step t198.t1 (cl (= (* 1/1 (- @p_235 0/1)) @p_122)) :rule poly_simp)
(step t198.t2 (cl (= @p_236 @p_114)) :rule poly_simp_rel :premises (t198.t1))
(step t198.t3 (cl @p_258) :rule symm :premises (t198.t2))
(step t198.t4 (cl @p_236) :rule resolution :premises (t198.t0 t198.t3 t198.a4))
(step t198.t5 (cl @p_238 @p_236) :rule implies_neg1)
(anchor :step t198.t6)
(assume t198.t6.a0 @p_236)
(step t198.t6.t0 (cl (not (! (= (! (< (! (+ @p_235 (! (+ y$ @p_57) :named @p_147) @p_198 @p_24 (! (* -2/1 y$) :named @p_243)) :named @p_244) (! (+ 0/1 0/1 @p_91 0/1 (! (* -2/1 0/1) :named @p_241)) :named @p_242)) :named @p_245) false) :named @p_251)) (not @p_245) false) :rule equiv_pos2)
(step t198.t6.t1 (cl (= @p_245 (! (not (! (>= @p_244 @p_242) :named @p_252)) :named @p_253))) :rule rare_rewrite :args ("arith-elim-lt" @p_244 @p_242))
(step t198.t6.t2 (cl (= @p_244 (! (+ @p_243 @p_57 @p_19 @p_18 @p_221 @p_23 (! (* 2/1 y$) :named @p_254) @p_174) :named @p_255))) :rule poly_simp)
(step t198.t6.t3 (cl (= @p_221 0/1)) :rule poly_simp)
(step t198.t6.t4 (cl @p_33) :rule refl)
(step t198.t6.t5 (cl (= @p_254 @p_254)) :rule refl)
(step t198.t6.t6 (cl (= @p_174 0/1)) :rule poly_simp)
(step t198.t6.t7 (cl (= @p_255 (! (+ @p_243 @p_57 @p_19 @p_18 0/1 @p_23 @p_254 0/1) :named @p_256))) :rule cong :premises (t198.t6.t3 t198.t6.t4 t198.t6.t5 t198.t6.t6))
(step t198.t6.t8 (cl (= @p_256 0/1)) :rule poly_simp)
(step t198.t6.t9 (cl (= @p_255 0/1)) :rule trans :premises (t198.t6.t7 t198.t6.t8))
(step t198.t6.t10 (cl (= @p_244 0/1)) :rule trans :premises (t198.t6.t2 t198.t6.t9))
(step t198.t6.t11 (cl (= @p_91 0/1)) :rule evaluate)
(step t198.t6.t12 (cl @p_31) :rule refl)
(step t198.t6.t13 (cl (= @p_241 0/1)) :rule evaluate)
(step t198.t6.t14 (cl (= @p_242 @p_219)) :rule cong :premises (t198.t6.t11 t198.t6.t12 t198.t6.t13))
(step t198.t6.t15 (cl (= @p_219 0/1)) :rule evaluate)
(step t198.t6.t16 (cl (= @p_242 0/1)) :rule trans :premises (t198.t6.t14 t198.t6.t15))
(step t198.t6.t17 (cl (= @p_252 @p_107)) :rule cong :premises (t198.t6.t10 t198.t6.t16))
(step t198.t6.t18 (cl (= @p_107 true)) :rule evaluate)
(step t198.t6.t19 (cl (= @p_252 true)) :rule trans :premises (t198.t6.t17 t198.t6.t18))
(step t198.t6.t20 (cl (= @p_253 @p_64)) :rule cong :premises (t198.t6.t19))
(step t198.t6.t21 (cl (= @p_64 false)) :rule evaluate)
(step t198.t6.t22 (cl (= @p_253 false)) :rule trans :premises (t198.t6.t20 t198.t6.t21))
(step t198.t6.t23 (cl @p_251) :rule trans :premises (t198.t6.t1 t198.t6.t22))
(step t198.t6.t24 (cl @p_237 (! (not (! (= @p_147 0/1) :named @p_155)) :named @p_168) @p_215 @p_167 (not (! (<= @p_243 @p_241) :named @p_246)) @p_245) :rule la_generic :args (-1/1 -1/1 -1/1 1/1 1/1 1/1))
(step t198.t6.t25 (cl (! (not (! (= @p_59 @p_155) :named @p_157)) :named @p_158) @p_124 @p_155) :rule equiv_pos2)
(step t198.t6.t26 (cl (= (* 1/1 (- @p_147 0/1)) (* 1/1 @p_69))) :rule poly_simp)
(step t198.t6.t27 (cl (= @p_155 @p_59)) :rule poly_simp_rel :premises (t198.t6.t26))
(step t198.t6.t28 (cl @p_157) :rule symm :premises (t198.t6.t27))
(step t198.t6.t29 (cl @p_155) :rule resolution :premises (t198.t6.t25 t198.t6.t28 t198.a3))
(step t198.t6.t30 (cl (=> @p_209 @p_207)) :rule la_mult_neg)
(step t198.t6.t31 (cl @p_214 @p_207) :rule implies :premises (t198.t6.t30))
(step t198.t6.t32 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t198.t6.t33 (cl (not @p_98) @p_96) :rule equiv1 :premises (t198.t6.t32))
(step t198.t6.t34 (cl @p_98) :rule evaluate)
(step t198.t6.t35 (cl @p_96) :rule resolution :premises (t198.t6.t33 t198.t6.t34))
(step t198.t6.t36 (cl @p_213 @p_184 @p_208) :rule equiv_pos2)
(step t198.t6.t37 (cl (= (* 1/1 (- @p_197 0/1)) @p_80)) :rule poly_simp)
(step t198.t6.t38 (cl (= @p_208 @p_72)) :rule poly_simp_rel :premises (t198.t6.t37))
(step t198.t6.t39 (cl @p_212) :rule symm :premises (t198.t6.t38))
(step t198.t6.t40 (cl @p_208) :rule resolution :premises (t198.t6.t36 t198.t6.t39 t198.a2))
(step t198.t6.t41 (cl @p_209) :rule and_intro :premises (t198.t6.t35 t198.t6.t40))
(step t198.t6.t42 (cl @p_207) :rule resolution :premises (t198.t6.t31 t198.t6.t41))
(step t198.t6.t43 (cl (not @p_160) @p_128 @p_159) :rule equiv_pos2)
(step t198.t6.t44 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t198.t6.t45 (cl @p_160) :rule symm :premises (t198.t6.t44))
(step t198.t6.t46 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t198.t6.t47 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t198.t6.t48 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t198.t6.t49 (cl @p_56) :rule poly_simp)
(step t198.t6.t50 (cl (= @p_9 @p_16)) :rule trans :premises (t198.t6.t48 t198.t6.t49))
(step t198.t6.t51 (cl (= @p_11 @p_54)) :rule cong :premises (t198.t6.t47 t198.t6.t50 t63))
(step t198.t6.t52 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t198.t6.t53 (cl (= @p_11 @p_18)) :rule trans :premises (t198.t6.t51 t198.t6.t52))
(step t198.t6.t54 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t198.t6.t55 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t198.t6.t56 (cl (= x$ x$)) :rule refl)
(step t198.t6.t57 (cl (= @p_6 @p_51)) :rule cong :premises (t198.t6.t54 t198.t6.t55 t198.t6.t56))
(step t198.t6.t58 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t198.t6.t59 (cl (= @p_6 @p_21)) :rule trans :premises (t198.t6.t57 t198.t6.t58))
(step t198.t6.t60 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t198.t6.t61 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t198.t6.t62 (cl (= @p_3 @p_49)) :rule cong :premises (t198.t6.t60 t198.t6.t61 t167))
(step t198.t6.t63 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t198.t6.t64 (cl (= @p_3 @p_23)) :rule trans :premises (t198.t6.t62 t198.t6.t63))
(step t198.t6.t65 (cl (= @p_7 @p_45)) :rule cong :premises (t198.t6.t59 t198.t6.t64))
(step t198.t6.t66 (cl (= @p_12 @p_46)) :rule cong :premises (t198.t6.t53 t198.t6.t65))
(step t198.t6.t67 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t198.t6.t68 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t198.t6.t69 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t198.t6.t68))
(step t198.t6.t70 (cl (= @p_46 @p_29)) :rule trans :premises (t198.t6.t67 t198.t6.t69))
(step t198.t6.t71 (cl (= @p_12 @p_29)) :rule trans :premises (t198.t6.t66 t198.t6.t70))
(step t198.t6.t72 (cl (= @p_13 @p_30)) :rule cong :premises (t198.t6.t71))
(step t198.t6.t73 (cl (= @p_19 @p_19)) :rule cong :premises (t62))
(step t198.t6.t74 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t198.t6.t75 (cl (not @p_38) @p_37) :rule equiv1 :premises (t198.t6.t74))
(step t198.t6.t76 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t198.t6.t77 (cl @p_39) :rule poly_simp_rel :premises (t198.t6.t76))
(step t198.t6.t78 (cl @p_37) :rule refl)
(step t198.t6.t79 (cl @p_37) :rule refl)
(step t198.t6.t80 (cl @p_39) :rule cong :premises (t198.t6.t78 t198.t6.t79))
(step t198.t6.t81 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t198.t6.t82 (cl @p_38) :rule trans :premises (t198.t6.t77 t198.t6.t80 t198.t6.t81))
(step t198.t6.t83 (cl @p_37) :rule resolution :premises (t198.t6.t75 t198.t6.t82))
(step t198.t6.t84 (cl (= @p_28 @p_28)) :rule cong :premises (t198.t6.t73 t198.t6.t83 t166))
(step t198.t6.t85 (cl @p_32) :rule poly_simp)
(step t198.t6.t86 (cl @p_32) :rule trans :premises (t198.t6.t84 t198.t6.t85))
(step t198.t6.t87 (cl @p_31) :rule refl)
(step t198.t6.t88 (cl (= @p_29 @p_25)) :rule cong :premises (t198.t6.t86 t198.t6.t87))
(step t198.t6.t89 (cl (= @p_30 @p_26)) :rule cong :premises (t198.t6.t88))
(step t198.t6.t90 (cl @p_27) :rule trans :premises (t198.t6.t72 t198.t6.t89))
(step t198.t6.t91 (cl @p_26) :rule resolution :premises (t198.t6.t46 t198.t6.t90 a0))
(step t198.t6.t92 (cl @p_159) :rule resolution :premises (t198.t6.t43 t198.t6.t45 t198.t6.t91))
(step t198.t6.t93 (cl (=> (! (and (! (< -2/1 0/1) :named @p_247) @p_22) :named @p_248) @p_246)) :rule la_mult_neg)
(step t198.t6.t94 (cl (not @p_248) @p_246) :rule implies :premises (t198.t6.t93))
(step t198.t6.t95 (cl (= (! (= @p_247 true) :named @p_249) @p_247)) :rule equiv_simplify)
(step t198.t6.t96 (cl (not @p_249) @p_247) :rule equiv1 :premises (t198.t6.t95))
(step t198.t6.t97 (cl @p_249) :rule evaluate)
(step t198.t6.t98 (cl @p_247) :rule resolution :premises (t198.t6.t96 t198.t6.t97))
(step t198.t6.t99 (cl @p_248) :rule and_intro :premises (t198.t6.t98 t198.a0))
(step t198.t6.t100 (cl @p_246) :rule resolution :premises (t198.t6.t94 t198.t6.t99))
(step t198.t6.t101 (cl @p_245) :rule resolution :premises (t198.t6.t24 t198.t6.a0 t198.t6.t29 t198.t6.t42 t198.t6.t92 t198.t6.t100))
(step t198.t6.t102 (cl false) :rule resolution :premises (t198.t6.t0 t198.t6.t23 t198.t6.t101))
(step t198.t6 (cl @p_237 false) :rule subproof :discharge (t198.t6.a0))
(step t198.t7 (cl @p_238 false) :rule resolution :premises (t198.t5 t198.t6))
(step t198.t8 (cl @p_238 @p_90) :rule implies_neg2)
(step t198.t9 (cl @p_238 @p_238) :rule resolution :premises (t198.t7 t198.t8))
(step t198.t10 (cl @p_238) :rule contraction :premises (t198.t9))
(step t198.t11 (cl @p_240) :rule implies_simplify)
(step t198.t12 (cl @p_239 @p_237) :rule equiv1 :premises (t198.t11))
(step t198.t13 (cl @p_237) :rule resolution :premises (t198.t10 t198.t12))
(step t198.t14 (cl) :rule resolution :premises (t198.t4 t198.t13))
(step t198 (cl @p_48 @p_128 @p_184 @p_124 @p_226 false) :rule subproof :discharge (t198.a0 t198.a1 t198.a2 t198.a3 t198.a4))
(step t199 (cl @p_233 @p_22) :rule and_pos :args (0))
(step t200 (cl @p_233 @p_26) :rule and_pos :args (1))
(step t201 (cl @p_233 @p_72) :rule and_pos :args (2))
(step t202 (cl @p_233 @p_59) :rule and_pos :args (3))
(step t203 (cl @p_233 @p_114) :rule and_pos :args (4))
(step t204 (cl false @p_233 @p_233 @p_233 @p_233 @p_233) :rule resolution :premises (t198 t199 t200 t201 t202 t203))
(step t205 (cl @p_233 @p_233 @p_233 @p_233 @p_233 false) :rule reordering :premises (t204))
(step t206 (cl @p_233 false) :rule contraction :premises (t205))
(step t207 (cl @p_234 false) :rule resolution :premises (t197 t206))
(step t208 (cl @p_234 @p_90) :rule implies_neg2)
(step t209 (cl @p_234 @p_234) :rule resolution :premises (t207 t208))
(step t210 (cl @p_234) :rule contraction :premises (t209))
(step t211 (cl (= @p_234 @p_233)) :rule implies_simplify)
(step t212 (cl (not @p_234) @p_233) :rule equiv1 :premises (t211))
(step t213 (cl @p_233) :rule resolution :premises (t210 t212))
(step t214 (cl @p_231) :rule resolution :premises (t196 t213))
(step t215 (cl @p_48 @p_128 @p_124 @p_184 @p_226) :rule not_and :premises (t214))
(step t216 (cl @p_228 @p_86) :rule or_neg :args (0))
(step t217 (cl @p_228 @p_133) :rule or_neg :args (1))
(step t218 (cl @p_228 (! (not @p_124) :named @p_132)) :rule or_neg :args (2))
(step t219 (cl @p_228 @p_187) :rule or_neg :args (3))
(step t220 (cl @p_228 @p_229) :rule or_neg :args (4))
(step t221 (cl @p_228 @p_228 @p_228 @p_228 @p_228) :rule resolution :premises (t215 t216 t217 t218 t219 t220))
(step t222 (cl @p_228) :rule contraction :premises (t221))
(step t223 (cl @p_227) :rule resolution :premises (t179 t181 t222))
(step t224 (cl @p_48 @p_25 @p_124 @p_184 @p_226) :rule or :premises (t223))
(step t225 (cl (not @p_27) (not @p_13) @p_26) :rule equiv_pos2)
(step t226 (cl (= @p_10 @p_53)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0/1))
(step t227 (cl (= @p_9 @p_55)) :rule poly_simp)
(step t228 (cl @p_56) :rule poly_simp)
(step t229 (cl (= @p_9 @p_16)) :rule trans :premises (t227 t228))
(step t230 (cl (= @p_11 @p_54)) :rule cong :premises (t226 t229 t63))
(step t231 (cl (= @p_54 @p_18)) :rule rare_rewrite :args ("ite-not-cond" @p_17 @p_16 @p_8))
(step t232 (cl (= @p_11 @p_18)) :rule trans :premises (t230 t231))
(step t233 (cl @p_52) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t234 (cl (= @p_4 @p_15)) :rule poly_simp)
(step t235 (cl (= x$ x$)) :rule refl)
(step t236 (cl (= @p_6 @p_51)) :rule cong :premises (t233 t234 t235))
(step t237 (cl (= @p_51 @p_21)) :rule rare_rewrite :args ("ite-not-cond" @p_20 @p_15 x$))
(step t238 (cl (= @p_6 @p_21)) :rule trans :premises (t236 t237))
(step t239 (cl (= @p_2 @p_48)) :rule rare_rewrite :args ("arith-elim-lt" y$ 0/1))
(step t240 (cl (= @p_1 @p_14)) :rule poly_simp)
(step t241 (cl (= @p_3 @p_49)) :rule cong :premises (t239 t240 t167))
(step t242 (cl (= @p_49 @p_23)) :rule rare_rewrite :args ("ite-not-cond" @p_22 @p_14 y$))
(step t243 (cl (= @p_3 @p_23)) :rule trans :premises (t241 t242))
(step t244 (cl (= @p_7 @p_45)) :rule cong :premises (t238 t243))
(step t245 (cl (= @p_12 @p_46)) :rule cong :premises (t232 t244))
(step t246 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-leq" @p_18 @p_45))
(step t247 (cl (= (* -1/1 (- @p_45 @p_18)) (* -1/1 (- @p_28 0/1)))) :rule poly_simp)
(step t248 (cl (= @p_47 @p_29)) :rule poly_simp_rel :premises (t247))
(step t249 (cl (= @p_46 @p_29)) :rule trans :premises (t246 t248))
(step t250 (cl (= @p_12 @p_29)) :rule trans :premises (t245 t249))
(step t251 (cl (= @p_13 @p_30)) :rule cong :premises (t250))
(step t252 (cl (= @p_19 @p_19)) :rule cong :premises (t62))
(step t253 (cl (= @p_38 @p_37)) :rule equiv_simplify)
(step t254 (cl (not @p_38) @p_37) :rule equiv1 :premises (t253))
(step t255 (cl (= (* -1/1 @p_40) (* 1/1 @p_40))) :rule poly_simp)
(step t256 (cl @p_39) :rule poly_simp_rel :premises (t255))
(step t257 (cl @p_37) :rule refl)
(step t258 (cl @p_37) :rule refl)
(step t259 (cl @p_39) :rule cong :premises (t257 t258))
(step t260 (cl @p_38) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t261 (cl @p_38) :rule trans :premises (t256 t259 t260))
(step t262 (cl @p_37) :rule resolution :premises (t254 t261))
(step t263 (cl (= @p_28 @p_28)) :rule cong :premises (t252 t262 t166))
(step t264 (cl @p_32) :rule poly_simp)
(step t265 (cl @p_32) :rule trans :premises (t263 t264))
(step t266 (cl @p_31) :rule refl)
(step t267 (cl (= @p_29 @p_25)) :rule cong :premises (t265 t266))
(step t268 (cl (= @p_30 @p_26)) :rule cong :premises (t267))
(step t269 (cl @p_27) :rule trans :premises (t251 t268))
(step t270 (cl @p_26) :rule resolution :premises (t225 t269 a0))
(step t271 (cl @p_53 @p_112) :rule ite2 :premises (t73))
(step t272 (cl (not (! (= (! (or @p_85 @p_128 @p_124 @p_184 (! (not @p_112) :named @p_126)) :named @p_186) (! (or @p_20 @p_25 @p_124 @p_184 @p_126) :named @p_185)) :named @p_225)) (not @p_186) @p_185) :rule equiv_pos2)
(step t273 (cl (= @p_126 @p_126)) :rule refl)
(step t274 (cl @p_225) :rule cong :premises (t76 t1 t180 t3 t273))
(step t275 (cl (! (=> (! (and @p_50 @p_26 @p_59 @p_72 @p_112) :named @p_189) (! (and @p_50 @p_59 @p_26 @p_72 @p_112) :named @p_191)) :named @p_224) @p_189) :rule implies_neg1)
(anchor :step t276)
(assume t276.a0 @p_50)
(assume t276.a1 @p_26)
(assume t276.a2 @p_59)
(assume t276.a3 @p_72)
(assume t276.a4 @p_112)
(step t276.t0 (cl @p_191) :rule and_intro :premises (t276.a0 t276.a2 t270 t276.a3 t276.a4))
(step t276 (cl @p_85 @p_128 @p_124 @p_184 @p_126 @p_191) :rule subproof :discharge (t276.a0 t276.a1 t276.a2 t276.a3 t276.a4))
(step t277 (cl (! (not @p_189) :named @p_190) @p_50) :rule and_pos :args (0))
(step t278 (cl @p_190 @p_26) :rule and_pos :args (1))
(step t279 (cl @p_190 @p_59) :rule and_pos :args (2))
(step t280 (cl @p_190 @p_72) :rule and_pos :args (3))
(step t281 (cl @p_190 @p_112) :rule and_pos :args (4))
(step t282 (cl @p_191 @p_190 @p_190 @p_190 @p_190 @p_190) :rule resolution :premises (t276 t277 t278 t279 t280 t281))
(step t283 (cl @p_190 @p_190 @p_190 @p_190 @p_190 @p_191) :rule reordering :premises (t282))
(step t284 (cl @p_190 @p_191) :rule contraction :premises (t283))
(step t285 (cl @p_224 @p_191) :rule resolution :premises (t275 t284))
(step t286 (cl @p_224 (! (not @p_191) :named @p_192)) :rule implies_neg2)
(step t287 (cl @p_224 @p_224) :rule resolution :premises (t285 t286))
(step t288 (cl @p_224) :rule contraction :premises (t287))
(step t289 (cl @p_190 @p_191) :rule implies :premises (t288))
(step t290 (cl (! (=> @p_191 false) :named @p_193) @p_191) :rule implies_neg1)
(anchor :step t291)
(assume t291.a0 @p_50)
(assume t291.a1 @p_59)
(assume t291.a2 @p_26)
(assume t291.a3 @p_72)
(assume t291.a4 @p_112)
(step t291.t0 (cl (! (not (! (= @p_112 (! (= (! (+ x$ y$ @p_19) :named @p_139) 0/1) :named @p_140)) :named @p_180)) :named @p_181) @p_126 @p_140) :rule equiv_pos2)
(step t291.t1 (cl (= (* 1/1 (- @p_139 0/1)) (* 1/1 @p_123))) :rule poly_simp)
(step t291.t2 (cl (= @p_140 @p_112)) :rule poly_simp_rel :premises (t291.t1))
(step t291.t3 (cl @p_180) :rule symm :premises (t291.t2))
(step t291.t4 (cl @p_140) :rule resolution :premises (t291.t0 t291.t3 t291.a4))
(step t291.t5 (cl (! (=> @p_140 false) :named @p_142) @p_140) :rule implies_neg1)
(anchor :step t291.t6)
(assume t291.t6.a0 @p_140)
(step t291.t6.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_139) :named @p_148) @p_198 @p_24 @p_147 (! (* 2/1 x$) :named @p_196)) :named @p_199) (! (+ @p_91 @p_91 0/1 0/1 (! (* 2/1 0/1) :named @p_194)) :named @p_195)) :named @p_200) false) :named @p_216)) (not @p_200) false) :rule equiv_pos2)
(step t291.t6.t1 (cl (= @p_200 (! (not (! (>= @p_199 @p_195) :named @p_217)) :named @p_218))) :rule rare_rewrite :args ("arith-elim-lt" @p_199 @p_195))
(step t291.t6.t2 (cl (= @p_199 (! (+ @p_196 @p_57 (! (* 0/1 @p_18) :named @p_176) @p_221 @p_23 @p_175 (! (* -2/1 x$) :named @p_220)) :named @p_222))) :rule poly_simp)
(step t291.t6.t3 (cl (= @p_176 0/1)) :rule poly_simp)
(step t291.t6.t4 (cl (= @p_221 0/1)) :rule poly_simp)
(step t291.t6.t5 (cl @p_33) :rule refl)
(step t291.t6.t6 (cl (= @p_175 0/1)) :rule poly_simp)
(step t291.t6.t7 (cl (= @p_220 @p_220)) :rule refl)
(step t291.t6.t8 (cl (= @p_222 (! (+ @p_196 @p_57 0/1 0/1 @p_23 0/1 @p_220) :named @p_223))) :rule cong :premises (t291.t6.t3 t291.t6.t4 t291.t6.t5 t291.t6.t6 t291.t6.t7))
(step t291.t6.t9 (cl (= @p_223 0/1)) :rule poly_simp)
(step t291.t6.t10 (cl (= @p_222 0/1)) :rule trans :premises (t291.t6.t8 t291.t6.t9))
(step t291.t6.t11 (cl (= @p_199 0/1)) :rule trans :premises (t291.t6.t2 t291.t6.t10))
(step t291.t6.t12 (cl (= @p_91 0/1)) :rule evaluate)
(step t291.t6.t13 (cl @p_31) :rule refl)
(step t291.t6.t14 (cl (= @p_194 0/1)) :rule evaluate)
(step t291.t6.t15 (cl (= @p_195 @p_219)) :rule cong :premises (t291.t6.t12 t291.t6.t12 t291.t6.t13 t291.t6.t13 t291.t6.t14))
(step t291.t6.t16 (cl (= @p_219 0/1)) :rule evaluate)
(step t291.t6.t17 (cl (= @p_195 0/1)) :rule trans :premises (t291.t6.t15 t291.t6.t16))
(step t291.t6.t18 (cl (= @p_217 @p_107)) :rule cong :premises (t291.t6.t11 t291.t6.t17))
(step t291.t6.t19 (cl (= @p_107 true)) :rule evaluate)
(step t291.t6.t20 (cl (= @p_217 true)) :rule trans :premises (t291.t6.t18 t291.t6.t19))
(step t291.t6.t21 (cl (= @p_218 @p_64)) :rule cong :premises (t291.t6.t20))
(step t291.t6.t22 (cl (= @p_64 false)) :rule evaluate)
(step t291.t6.t23 (cl (= @p_218 false)) :rule trans :premises (t291.t6.t21 t291.t6.t22))
(step t291.t6.t24 (cl @p_216) :rule trans :premises (t291.t6.t1 t291.t6.t23))
(step t291.t6.t25 (cl (! (not (! (= @p_148 @p_91) :named @p_161)) :named @p_166) @p_215 @p_167 @p_168 (not (! (< @p_196 @p_194) :named @p_201)) @p_200) :rule la_generic :args (-1/1 -1/1 1/1 -1/1 1/1 1/1))
(step t291.t6.t26 (cl (=> (! (and @p_96 @p_140) :named @p_162) @p_161)) :rule la_mult_neg)
(step t291.t6.t27 (cl (! (not @p_162) :named @p_165) @p_161) :rule implies :premises (t291.t6.t26))
(step t291.t6.t28 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t291.t6.t29 (cl (not @p_98) @p_96) :rule equiv1 :premises (t291.t6.t28))
(step t291.t6.t30 (cl @p_98) :rule evaluate)
(step t291.t6.t31 (cl @p_96) :rule resolution :premises (t291.t6.t29 t291.t6.t30))
(step t291.t6.t32 (cl @p_162) :rule and_intro :premises (t291.t6.t31 t291.t6.a0))
(step t291.t6.t33 (cl @p_161) :rule resolution :premises (t291.t6.t27 t291.t6.t32))
(step t291.t6.t34 (cl (=> @p_209 @p_207)) :rule la_mult_neg)
(step t291.t6.t35 (cl @p_214 @p_207) :rule implies :premises (t291.t6.t34))
(step t291.t6.t36 (cl @p_213 @p_184 @p_208) :rule equiv_pos2)
(step t291.t6.t37 (cl (= (* 1/1 (- @p_197 0/1)) @p_80)) :rule poly_simp)
(step t291.t6.t38 (cl (= @p_208 @p_72)) :rule poly_simp_rel :premises (t291.t6.t37))
(step t291.t6.t39 (cl @p_212) :rule symm :premises (t291.t6.t38))
(step t291.t6.t40 (cl @p_208) :rule resolution :premises (t291.t6.t36 t291.t6.t39 t291.a3))
(step t291.t6.t41 (cl @p_209) :rule and_intro :premises (t291.t6.t31 t291.t6.t40))
(step t291.t6.t42 (cl @p_207) :rule resolution :premises (t291.t6.t35 t291.t6.t41))
(step t291.t6.t43 (cl (not @p_160) @p_128 @p_159) :rule equiv_pos2)
(step t291.t6.t44 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t291.t6.t45 (cl @p_160) :rule symm :premises (t291.t6.t44))
(step t291.t6.t46 (cl @p_159) :rule resolution :premises (t291.t6.t43 t291.t6.t45 t270))
(step t291.t6.t47 (cl @p_158 @p_124 @p_155) :rule equiv_pos2)
(step t291.t6.t48 (cl (= (* 1/1 (- @p_147 0/1)) (* 1/1 @p_69))) :rule poly_simp)
(step t291.t6.t49 (cl (= @p_155 @p_59)) :rule poly_simp_rel :premises (t291.t6.t48))
(step t291.t6.t50 (cl @p_157) :rule symm :premises (t291.t6.t49))
(step t291.t6.t51 (cl @p_155) :rule resolution :premises (t291.t6.t47 t291.t6.t50 t291.a1))
(step t291.t6.t52 (cl (=> (! (and (! (> 2/1 0/1) :named @p_202) @p_5) :named @p_203) @p_201)) :rule la_mult_pos)
(step t291.t6.t53 (cl (not @p_203) @p_201) :rule implies :premises (t291.t6.t52))
(step t291.t6.t54 (cl (= (! (= @p_202 true) :named @p_206) @p_202)) :rule equiv_simplify)
(step t291.t6.t55 (cl (not @p_206) @p_202) :rule equiv1 :premises (t291.t6.t54))
(step t291.t6.t56 (cl @p_206) :rule evaluate)
(step t291.t6.t57 (cl @p_202) :rule resolution :premises (t291.t6.t55 t291.t6.t56))
(step t291.t6.t58 (cl @p_205 @p_85 @p_5) :rule equiv_pos2)
(step t291.t6.t59 (cl @p_204) :rule symm :premises (t233))
(step t291.t6.t60 (cl @p_5) :rule resolution :premises (t291.t6.t58 t291.t6.t59 t291.a0))
(step t291.t6.t61 (cl @p_203) :rule and_intro :premises (t291.t6.t57 t291.t6.t60))
(step t291.t6.t62 (cl @p_201) :rule resolution :premises (t291.t6.t53 t291.t6.t61))
(step t291.t6.t63 (cl @p_200) :rule resolution :premises (t291.t6.t25 t291.t6.t33 t291.t6.t42 t291.t6.t46 t291.t6.t51 t291.t6.t62))
(step t291.t6.t64 (cl false) :rule resolution :premises (t291.t6.t0 t291.t6.t24 t291.t6.t63))
(step t291.t6 (cl (! (not @p_140) :named @p_141) false) :rule subproof :discharge (t291.t6.a0))
(step t291.t7 (cl @p_142 false) :rule resolution :premises (t291.t5 t291.t6))
(step t291.t8 (cl @p_142 @p_90) :rule implies_neg2)
(step t291.t9 (cl @p_142 @p_142) :rule resolution :premises (t291.t7 t291.t8))
(step t291.t10 (cl @p_142) :rule contraction :premises (t291.t9))
(step t291.t11 (cl (! (= @p_142 @p_141) :named @p_144)) :rule implies_simplify)
(step t291.t12 (cl (! (not @p_142) :named @p_143) @p_141) :rule equiv1 :premises (t291.t11))
(step t291.t13 (cl @p_141) :rule resolution :premises (t291.t10 t291.t12))
(step t291.t14 (cl) :rule resolution :premises (t291.t4 t291.t13))
(step t291 (cl @p_85 @p_124 @p_128 @p_184 @p_126 false) :rule subproof :discharge (t291.a0 t291.a1 t291.a2 t291.a3 t291.a4))
(step t292 (cl @p_192 @p_50) :rule and_pos :args (0))
(step t293 (cl @p_192 @p_59) :rule and_pos :args (1))
(step t294 (cl @p_192 @p_26) :rule and_pos :args (2))
(step t295 (cl @p_192 @p_72) :rule and_pos :args (3))
(step t296 (cl @p_192 @p_112) :rule and_pos :args (4))
(step t297 (cl false @p_192 @p_192 @p_192 @p_192 @p_192) :rule resolution :premises (t291 t292 t293 t294 t295 t296))
(step t298 (cl @p_192 @p_192 @p_192 @p_192 @p_192 false) :rule reordering :premises (t297))
(step t299 (cl @p_192 false) :rule contraction :premises (t298))
(step t300 (cl @p_193 false) :rule resolution :premises (t290 t299))
(step t301 (cl @p_193 @p_90) :rule implies_neg2)
(step t302 (cl @p_193 @p_193) :rule resolution :premises (t300 t301))
(step t303 (cl @p_193) :rule contraction :premises (t302))
(step t304 (cl (= @p_193 @p_192)) :rule implies_simplify)
(step t305 (cl (not @p_193) @p_192) :rule equiv1 :premises (t304))
(step t306 (cl @p_192) :rule resolution :premises (t303 t305))
(step t307 (cl @p_190) :rule resolution :premises (t289 t306))
(step t308 (cl @p_85 @p_128 @p_124 @p_184 @p_126) :rule not_and :premises (t307))
(step t309 (cl @p_186 @p_188) :rule or_neg :args (0))
(step t310 (cl @p_186 @p_133) :rule or_neg :args (1))
(step t311 (cl @p_186 @p_132) :rule or_neg :args (2))
(step t312 (cl @p_186 @p_187) :rule or_neg :args (3))
(step t313 (cl @p_186 (! (not @p_126) :named @p_130)) :rule or_neg :args (4))
(step t314 (cl @p_186 @p_186 @p_186 @p_186 @p_186) :rule resolution :premises (t308 t309 t310 t311 t312 t313))
(step t315 (cl @p_186) :rule contraction :premises (t314))
(step t316 (cl @p_185) :rule resolution :premises (t272 t274 t315))
(step t317 (cl @p_20 @p_25 @p_124 @p_184 @p_126) :rule or :premises (t316))
(step t318 (cl (not (! (= (! (ite @p_20 (! (= @p_21 x$) :named @p_75) (! (= @p_21 @p_15) :named @p_74)) :named @p_76) (! (ite @p_20 @p_70 @p_72) :named @p_73)) :named @p_79)) (! (not @p_76) :named @p_78) @p_73) :rule equiv_pos2)
(step t319 (cl (= (* 1/1 (- @p_21 x$)) (* -1/1 @p_81))) :rule poly_simp)
(step t320 (cl (= @p_75 @p_70)) :rule poly_simp_rel :premises (t319))
(step t321 (cl (= (* 1/1 (- @p_21 @p_15)) @p_80)) :rule poly_simp)
(step t322 (cl (= @p_74 @p_72)) :rule poly_simp_rel :premises (t321))
(step t323 (cl @p_79) :rule cong :premises (t320 t322))
(step t324 (cl (not (! (= @p_76 @p_76) :named @p_77)) @p_78 @p_76) :rule equiv_pos2)
(step t325 (cl (= @p_75 @p_75)) :rule cong :premises (t262 t235))
(step t326 (cl (= @p_15 @p_15)) :rule refl)
(step t327 (cl (= @p_74 @p_74)) :rule cong :premises (t262 t326))
(step t328 (cl @p_77) :rule cong :premises (t325 t327))
(step t329 (cl (= @p_76 true)) :rule rare_rewrite :args ("ite-eq" @p_20 x$ @p_15))
(step t330 (cl @p_76 @p_64) :rule equiv2 :premises (t329))
(step t331 (cl true) :rule true)
(step t332 (cl @p_76) :rule resolution :premises (t330 t331))
(step t333 (cl @p_76) :rule resolution :premises (t324 t328 t332))
(step t334 (cl @p_73) :rule resolution :premises (t318 t323 t333))
(step t335 (cl @p_20 @p_72) :rule ite1 :premises (t334))
(step t336 (cl (not (! (= (! (or @p_128 @p_124 @p_125 @p_126) :named @p_129) (! (or @p_25 @p_124 @p_125 @p_126) :named @p_127)) :named @p_183)) (not @p_129) @p_127) :rule equiv_pos2)
(step t337 (cl @p_183) :rule cong :premises (t1 t180 t105 t273))
(step t338 (cl (! (=> (! (and @p_26 @p_59 @p_70 @p_112) :named @p_134) (! (and @p_70 @p_59 @p_26 @p_112) :named @p_136)) :named @p_182) @p_134) :rule implies_neg1)
(anchor :step t339)
(assume t339.a0 @p_26)
(assume t339.a1 @p_59)
(assume t339.a2 @p_70)
(assume t339.a3 @p_112)
(step t339.t0 (cl @p_136) :rule and_intro :premises (t339.a2 t339.a1 t270 t339.a3))
(step t339 (cl @p_128 @p_124 @p_125 @p_126 @p_136) :rule subproof :discharge (t339.a0 t339.a1 t339.a2 t339.a3))
(step t340 (cl (! (not @p_134) :named @p_135) @p_26) :rule and_pos :args (0))
(step t341 (cl @p_135 @p_59) :rule and_pos :args (1))
(step t342 (cl @p_135 @p_70) :rule and_pos :args (2))
(step t343 (cl @p_135 @p_112) :rule and_pos :args (3))
(step t344 (cl @p_136 @p_135 @p_135 @p_135 @p_135) :rule resolution :premises (t339 t340 t341 t342 t343))
(step t345 (cl @p_135 @p_135 @p_135 @p_135 @p_136) :rule reordering :premises (t344))
(step t346 (cl @p_135 @p_136) :rule contraction :premises (t345))
(step t347 (cl @p_182 @p_136) :rule resolution :premises (t338 t346))
(step t348 (cl @p_182 (! (not @p_136) :named @p_137)) :rule implies_neg2)
(step t349 (cl @p_182 @p_182) :rule resolution :premises (t347 t348))
(step t350 (cl @p_182) :rule contraction :premises (t349))
(step t351 (cl @p_135 @p_136) :rule implies :premises (t350))
(step t352 (cl (! (=> @p_136 false) :named @p_138) @p_136) :rule implies_neg1)
(anchor :step t353)
(assume t353.a0 @p_70)
(assume t353.a1 @p_59)
(assume t353.a2 @p_26)
(assume t353.a3 @p_112)
(step t353.t0 (cl @p_181 @p_126 @p_140) :rule equiv_pos2)
(step t353.t1 (cl (= (* 1/1 (- @p_139 0/1)) (* 1/1 @p_123))) :rule poly_simp)
(step t353.t2 (cl (= @p_140 @p_112)) :rule poly_simp_rel :premises (t353.t1))
(step t353.t3 (cl @p_180) :rule symm :premises (t353.t2))
(step t353.t4 (cl @p_140) :rule resolution :premises (t353.t0 t353.t3 t353.a3))
(step t353.t5 (cl @p_142 @p_140) :rule implies_neg1)
(anchor :step t353.t6)
(assume t353.t6.a0 @p_140)
(step t353.t6.t0 (cl (not (! (= (! (< (! (+ @p_148 @p_24 @p_147 @p_146) :named @p_149) (! (+ @p_91 0/1 0/1 0/1) :named @p_145)) :named @p_150) false) :named @p_170)) (not @p_150) false) :rule equiv_pos2)
(step t353.t6.t1 (cl (= @p_150 (! (not (! (>= @p_149 @p_145) :named @p_171)) :named @p_172))) :rule rare_rewrite :args ("arith-elim-lt" @p_149 @p_145))
(step t353.t6.t2 (cl (= @p_149 (! (+ @p_71 @p_57 @p_176 @p_21 @p_23 @p_175 @p_174) :named @p_177))) :rule poly_simp)
(step t353.t6.t3 (cl (= @p_176 0/1)) :rule poly_simp)
(step t353.t6.t4 (cl @p_37) :rule refl)
(step t353.t6.t5 (cl @p_33) :rule refl)
(step t353.t6.t6 (cl (= @p_175 0/1)) :rule poly_simp)
(step t353.t6.t7 (cl (= @p_174 0/1)) :rule poly_simp)
(step t353.t6.t8 (cl (= @p_177 (! (+ @p_71 @p_57 0/1 @p_21 @p_23 0/1 0/1) :named @p_178))) :rule cong :premises (t353.t6.t3 t353.t6.t4 t353.t6.t5 t353.t6.t6 t353.t6.t7))
(step t353.t6.t9 (cl (= @p_178 0/1)) :rule poly_simp)
(step t353.t6.t10 (cl (= @p_177 0/1)) :rule trans :premises (t353.t6.t8 t353.t6.t9))
(step t353.t6.t11 (cl (= @p_149 0/1)) :rule trans :premises (t353.t6.t2 t353.t6.t10))
(step t353.t6.t12 (cl (= @p_91 0/1)) :rule evaluate)
(step t353.t6.t13 (cl @p_31) :rule refl)
(step t353.t6.t14 (cl (= @p_145 @p_173)) :rule cong :premises (t353.t6.t12 t353.t6.t13 t353.t6.t13 t353.t6.t13))
(step t353.t6.t15 (cl (= @p_173 0/1)) :rule evaluate)
(step t353.t6.t16 (cl (= @p_145 0/1)) :rule trans :premises (t353.t6.t14 t353.t6.t15))
(step t353.t6.t17 (cl (= @p_171 @p_107)) :rule cong :premises (t353.t6.t11 t353.t6.t16))
(step t353.t6.t18 (cl (= @p_107 true)) :rule evaluate)
(step t353.t6.t19 (cl (= @p_171 true)) :rule trans :premises (t353.t6.t17 t353.t6.t18))
(step t353.t6.t20 (cl (= @p_172 @p_64)) :rule cong :premises (t353.t6.t19))
(step t353.t6.t21 (cl (= @p_64 false)) :rule evaluate)
(step t353.t6.t22 (cl (= @p_172 false)) :rule trans :premises (t353.t6.t20 t353.t6.t21))
(step t353.t6.t23 (cl @p_170) :rule trans :premises (t353.t6.t1 t353.t6.t22))
(step t353.t6.t24 (cl @p_166 @p_167 @p_168 (! (not @p_151) :named @p_169) @p_150) :rule la_generic :args (-1/1 1/1 -1/1 -1/1 1/1))
(step t353.t6.t25 (cl (=> @p_162 @p_161)) :rule la_mult_neg)
(step t353.t6.t26 (cl @p_165 @p_161) :rule implies :premises (t353.t6.t25))
(step t353.t6.t27 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t353.t6.t28 (cl (not @p_98) @p_96) :rule equiv1 :premises (t353.t6.t27))
(step t353.t6.t29 (cl @p_98) :rule evaluate)
(step t353.t6.t30 (cl @p_96) :rule resolution :premises (t353.t6.t28 t353.t6.t29))
(step t353.t6.t31 (cl @p_162) :rule and_intro :premises (t353.t6.t30 t353.t6.a0))
(step t353.t6.t32 (cl @p_161) :rule resolution :premises (t353.t6.t26 t353.t6.t31))
(step t353.t6.t33 (cl (not @p_160) @p_128 @p_159) :rule equiv_pos2)
(step t353.t6.t34 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t353.t6.t35 (cl @p_160) :rule symm :premises (t353.t6.t34))
(step t353.t6.t36 (cl @p_159) :rule resolution :premises (t353.t6.t33 t353.t6.t35 t270))
(step t353.t6.t37 (cl @p_158 @p_124 @p_155) :rule equiv_pos2)
(step t353.t6.t38 (cl (= (* 1/1 (- @p_147 0/1)) (* 1/1 @p_69))) :rule poly_simp)
(step t353.t6.t39 (cl (= @p_155 @p_59)) :rule poly_simp_rel :premises (t353.t6.t38))
(step t353.t6.t40 (cl @p_157) :rule symm :premises (t353.t6.t39))
(step t353.t6.t41 (cl @p_155) :rule resolution :premises (t353.t6.t37 t353.t6.t40 t353.a1))
(step t353.t6.t42 (cl @p_154 @p_125 @p_151) :rule equiv_pos2)
(step t353.t6.t43 (cl (= (* 1/1 (- @p_146 0/1)) (* 1/1 @p_81))) :rule poly_simp)
(step t353.t6.t44 (cl (= @p_151 @p_70)) :rule poly_simp_rel :premises (t353.t6.t43))
(step t353.t6.t45 (cl @p_153) :rule symm :premises (t353.t6.t44))
(step t353.t6.t46 (cl @p_151) :rule resolution :premises (t353.t6.t42 t353.t6.t45 t353.a0))
(step t353.t6.t47 (cl @p_150) :rule resolution :premises (t353.t6.t24 t353.t6.t32 t353.t6.t36 t353.t6.t41 t353.t6.t46))
(step t353.t6.t48 (cl false) :rule resolution :premises (t353.t6.t0 t353.t6.t23 t353.t6.t47))
(step t353.t6 (cl @p_141 false) :rule subproof :discharge (t353.t6.a0))
(step t353.t7 (cl @p_142 false) :rule resolution :premises (t353.t5 t353.t6))
(step t353.t8 (cl @p_142 @p_90) :rule implies_neg2)
(step t353.t9 (cl @p_142 @p_142) :rule resolution :premises (t353.t7 t353.t8))
(step t353.t10 (cl @p_142) :rule contraction :premises (t353.t9))
(step t353.t11 (cl @p_144) :rule implies_simplify)
(step t353.t12 (cl @p_143 @p_141) :rule equiv1 :premises (t353.t11))
(step t353.t13 (cl @p_141) :rule resolution :premises (t353.t10 t353.t12))
(step t353.t14 (cl) :rule resolution :premises (t353.t4 t353.t13))
(step t353 (cl @p_125 @p_124 @p_128 @p_126 false) :rule subproof :discharge (t353.a0 t353.a1 t353.a2 t353.a3))
(step t354 (cl @p_137 @p_70) :rule and_pos :args (0))
(step t355 (cl @p_137 @p_59) :rule and_pos :args (1))
(step t356 (cl @p_137 @p_26) :rule and_pos :args (2))
(step t357 (cl @p_137 @p_112) :rule and_pos :args (3))
(step t358 (cl false @p_137 @p_137 @p_137 @p_137) :rule resolution :premises (t353 t354 t355 t356 t357))
(step t359 (cl @p_137 @p_137 @p_137 @p_137 false) :rule reordering :premises (t358))
(step t360 (cl @p_137 false) :rule contraction :premises (t359))
(step t361 (cl @p_138 false) :rule resolution :premises (t352 t360))
(step t362 (cl @p_138 @p_90) :rule implies_neg2)
(step t363 (cl @p_138 @p_138) :rule resolution :premises (t361 t362))
(step t364 (cl @p_138) :rule contraction :premises (t363))
(step t365 (cl (= @p_138 @p_137)) :rule implies_simplify)
(step t366 (cl (not @p_138) @p_137) :rule equiv1 :premises (t365))
(step t367 (cl @p_137) :rule resolution :premises (t364 t366))
(step t368 (cl @p_135) :rule resolution :premises (t351 t367))
(step t369 (cl @p_128 @p_124 @p_125 @p_126) :rule not_and :premises (t368))
(step t370 (cl @p_129 @p_133) :rule or_neg :args (0))
(step t371 (cl @p_129 @p_132) :rule or_neg :args (1))
(step t372 (cl @p_129 @p_131) :rule or_neg :args (2))
(step t373 (cl @p_129 @p_130) :rule or_neg :args (3))
(step t374 (cl @p_129 @p_129 @p_129 @p_129) :rule resolution :premises (t369 t370 t371 t372 t373))
(step t375 (cl @p_129) :rule contraction :premises (t374))
(step t376 (cl @p_127) :rule resolution :premises (t336 t337 t375))
(step t377 (cl @p_25 @p_124 @p_125 @p_126) :rule or :premises (t376))
(step t378 (cl (not (! (= (! (or @p_48 @p_50 @p_83) :named @p_84) (! (or @p_48 @p_50 @p_17) :named @p_82)) :named @p_110)) (not @p_84) @p_82) :rule equiv_pos2)
(step t379 (cl (= @p_83 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t380 (cl @p_110) :rule cong :premises (t379))
(step t381 (cl (! (=> (! (and @p_22 @p_20 @p_53) :named @p_87) false) :named @p_89) @p_87) :rule implies_neg1)
(anchor :step t382)
(assume t382.a0 @p_22)
(assume t382.a1 @p_20)
(assume t382.a2 @p_53)
(step t382.t0 (cl (not (! (= (! (< (! (+ @p_8 @p_14 @p_15) :named @p_93) (! (+ 0/1 @p_91 @p_91) :named @p_92)) :named @p_94) false) :named @p_104)) (not @p_94) false) :rule equiv_pos2)
(step t382.t1 (cl (= @p_94 (! (not (! (>= @p_93 @p_92) :named @p_105)) :named @p_106))) :rule rare_rewrite :args ("arith-elim-lt" @p_93 @p_92))
(step t382.t2 (cl (= @p_93 (! (+ @p_15 @p_14 y$ x$) :named @p_109))) :rule poly_simp)
(step t382.t3 (cl (= @p_109 0/1)) :rule poly_simp)
(step t382.t4 (cl (= @p_93 0/1)) :rule trans :premises (t382.t2 t382.t3))
(step t382.t5 (cl (= @p_91 0/1)) :rule evaluate)
(step t382.t6 (cl (= @p_92 @p_108)) :rule cong :premises (t382.t5 t382.t5))
(step t382.t7 (cl (= @p_108 0/1)) :rule evaluate)
(step t382.t8 (cl (= @p_92 0/1)) :rule trans :premises (t382.t6 t382.t7))
(step t382.t9 (cl (= @p_105 @p_107)) :rule cong :premises (t382.t4 t382.t8))
(step t382.t10 (cl (= @p_107 true)) :rule evaluate)
(step t382.t11 (cl (= @p_105 true)) :rule trans :premises (t382.t9 t382.t10))
(step t382.t12 (cl (= @p_106 @p_64)) :rule cong :premises (t382.t11))
(step t382.t13 (cl (= @p_64 false)) :rule evaluate)
(step t382.t14 (cl (= @p_106 false)) :rule trans :premises (t382.t12 t382.t13))
(step t382.t15 (cl @p_104) :rule trans :premises (t382.t1 t382.t14))
(step t382.t16 (cl (not @p_10) (not (! (<= @p_14 @p_91) :named @p_100)) @p_103 @p_94) :rule la_generic :args (1/1 1/1 1/1 1/1))
(step t382.t17 (cl (not (! (= @p_53 @p_10) :named @p_102)) @p_83 @p_10) :rule equiv_pos2)
(step t382.t18 (cl @p_102) :rule symm :premises (t226))
(step t382.t19 (cl @p_10) :rule resolution :premises (t382.t17 t382.t18 t382.a2))
(step t382.t20 (cl (=> (! (and @p_96 @p_22) :named @p_101) @p_100)) :rule la_mult_neg)
(step t382.t21 (cl (not @p_101) @p_100) :rule implies :premises (t382.t20))
(step t382.t22 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t382.t23 (cl (not @p_98) @p_96) :rule equiv1 :premises (t382.t22))
(step t382.t24 (cl @p_98) :rule evaluate)
(step t382.t25 (cl @p_96) :rule resolution :premises (t382.t23 t382.t24))
(step t382.t26 (cl @p_101) :rule and_intro :premises (t382.t25 t382.a0))
(step t382.t27 (cl @p_100) :rule resolution :premises (t382.t21 t382.t26))
(step t382.t28 (cl (=> @p_97 @p_95)) :rule la_mult_neg)
(step t382.t29 (cl @p_99 @p_95) :rule implies :premises (t382.t28))
(step t382.t30 (cl @p_97) :rule and_intro :premises (t382.t25 t382.a1))
(step t382.t31 (cl @p_95) :rule resolution :premises (t382.t29 t382.t30))
(step t382.t32 (cl @p_94) :rule resolution :premises (t382.t16 t382.t19 t382.t27 t382.t31))
(step t382.t33 (cl false) :rule resolution :premises (t382.t0 t382.t15 t382.t32))
(step t382 (cl @p_48 @p_50 @p_83 false) :rule subproof :discharge (t382.a0 t382.a1 t382.a2))
(step t383 (cl (! (not @p_87) :named @p_88) @p_22) :rule and_pos :args (0))
(step t384 (cl @p_88 @p_20) :rule and_pos :args (1))
(step t385 (cl @p_88 @p_53) :rule and_pos :args (2))
(step t386 (cl false @p_88 @p_88 @p_88) :rule resolution :premises (t382 t383 t384 t385))
(step t387 (cl @p_88 @p_88 @p_88 false) :rule reordering :premises (t386))
(step t388 (cl @p_88 false) :rule contraction :premises (t387))
(step t389 (cl @p_89 false) :rule resolution :premises (t381 t388))
(step t390 (cl @p_89 @p_90) :rule implies_neg2)
(step t391 (cl @p_89 @p_89) :rule resolution :premises (t389 t390))
(step t392 (cl @p_89) :rule contraction :premises (t391))
(step t393 (cl (= @p_89 @p_88)) :rule implies_simplify)
(step t394 (cl (not @p_89) @p_88) :rule equiv1 :premises (t393))
(step t395 (cl @p_88) :rule resolution :premises (t392 t394))
(step t396 (cl @p_48 @p_50 @p_83) :rule not_and :premises (t395))
(step t397 (cl @p_84 @p_86) :rule or_neg :args (0))
(step t398 (cl @p_84 @p_85) :rule or_neg :args (1))
(step t399 (cl @p_84 (not @p_83)) :rule or_neg :args (2))
(step t400 (cl @p_84 @p_84 @p_84) :rule resolution :premises (t396 t397 t398 t399))
(step t401 (cl @p_84) :rule contraction :premises (t400))
(step t402 (cl @p_82) :rule resolution :premises (t378 t380 t401))
(step t403 (cl @p_48 @p_50 @p_17) :rule or :premises (t402))
(step t404 (cl @p_17 @p_50 @p_48) :rule reordering :premises (t403))
(step t405 (cl @p_50 @p_70) :rule ite2 :premises (t334))
(step t406 (cl @p_48 @p_59) :rule ite2 :premises (t177))
(step t407 (cl @p_50 @p_48) :rule resolution :premises (t377 t270 t271 t404 t405 t406))
(step t408 (cl @p_48) :rule resolution :premises (t224 t270 t74 t271 t317 t270 t335 t407 t406))
(step t409 (cl @p_58) :rule resolution :premises (t178 t408))
(step t410 (cl (not (! (= (! (or @p_86 @p_128 @p_262 @p_125 @p_126) :named @p_264) (! (or @p_22 @p_25 @p_262 @p_125 @p_126) :named @p_263)) :named @p_297)) (not @p_264) @p_263) :rule equiv_pos2)
(step t411 (cl @p_297) :rule cong :premises (t77 t1 t2 t105 t273))
(step t412 (cl (! (=> (! (and @p_48 @p_26 @p_58 @p_70 @p_112) :named @p_267) (! (and @p_112 @p_48 @p_58 @p_26 @p_70) :named @p_269)) :named @p_296) @p_267) :rule implies_neg1)
(anchor :step t413)
(assume t413.a0 @p_48)
(assume t413.a1 @p_26)
(assume t413.a2 @p_58)
(assume t413.a3 @p_70)
(assume t413.a4 @p_112)
(step t413.t0 (cl @p_269) :rule and_intro :premises (t413.a4 t413.a0 t413.a2 t270 t413.a3))
(step t413 (cl @p_86 @p_128 @p_262 @p_125 @p_126 @p_269) :rule subproof :discharge (t413.a0 t413.a1 t413.a2 t413.a3 t413.a4))
(step t414 (cl (! (not @p_267) :named @p_268) @p_48) :rule and_pos :args (0))
(step t415 (cl @p_268 @p_26) :rule and_pos :args (1))
(step t416 (cl @p_268 @p_58) :rule and_pos :args (2))
(step t417 (cl @p_268 @p_70) :rule and_pos :args (3))
(step t418 (cl @p_268 @p_112) :rule and_pos :args (4))
(step t419 (cl @p_269 @p_268 @p_268 @p_268 @p_268 @p_268) :rule resolution :premises (t413 t414 t415 t416 t417 t418))
(step t420 (cl @p_268 @p_268 @p_268 @p_268 @p_268 @p_269) :rule reordering :premises (t419))
(step t421 (cl @p_268 @p_269) :rule contraction :premises (t420))
(step t422 (cl @p_296 @p_269) :rule resolution :premises (t412 t421))
(step t423 (cl @p_296 (! (not @p_269) :named @p_270)) :rule implies_neg2)
(step t424 (cl @p_296 @p_296) :rule resolution :premises (t422 t423))
(step t425 (cl @p_296) :rule contraction :premises (t424))
(step t426 (cl @p_268 @p_269) :rule implies :premises (t425))
(step t427 (cl (! (=> @p_269 false) :named @p_271) @p_269) :rule implies_neg1)
(anchor :step t428)
(assume t428.a0 @p_112)
(assume t428.a1 @p_48)
(assume t428.a2 @p_58)
(assume t428.a3 @p_26)
(assume t428.a4 @p_70)
(step t428.t0 (cl @p_154 @p_125 @p_151) :rule equiv_pos2)
(step t428.t1 (cl (= (* 1/1 (- @p_146 0/1)) (* 1/1 @p_81))) :rule poly_simp)
(step t428.t2 (cl (= @p_151 @p_70)) :rule poly_simp_rel :premises (t428.t1))
(step t428.t3 (cl @p_153) :rule symm :premises (t428.t2))
(step t428.t4 (cl @p_151) :rule resolution :premises (t428.t0 t428.t3 t428.a4))
(step t428.t5 (cl (! (=> @p_151 false) :named @p_272) @p_151) :rule implies_neg1)
(anchor :step t428.t6)
(assume t428.t6.a0 @p_151)
(step t428.t6.t0 (cl (not (! (= (! (< (! (+ @p_146 @p_24 @p_275 @p_254 @p_148) :named @p_276) (! (+ 0/1 0/1 @p_91 @p_194 @p_91) :named @p_273)) :named @p_277) false) :named @p_290)) (not @p_277) false) :rule equiv_pos2)
(step t428.t6.t1 (cl (= @p_277 (! (not (! (>= @p_276 @p_273) :named @p_291)) :named @p_292))) :rule rare_rewrite :args ("arith-elim-lt" @p_276 @p_273))
(step t428.t6.t2 (cl (= @p_276 (! (+ @p_254 @p_71 @p_176 @p_21 @p_293 @p_243 @p_174) :named @p_294))) :rule poly_simp)
(step t428.t6.t3 (cl (= @p_176 0/1)) :rule poly_simp)
(step t428.t6.t4 (cl @p_37) :rule refl)
(step t428.t6.t5 (cl (= @p_293 0/1)) :rule poly_simp)
(step t428.t6.t6 (cl (= @p_243 @p_243)) :rule refl)
(step t428.t6.t7 (cl (= @p_174 0/1)) :rule poly_simp)
(step t428.t6.t8 (cl (= @p_294 (! (+ @p_254 @p_71 0/1 @p_21 0/1 @p_243 0/1) :named @p_295))) :rule cong :premises (t428.t6.t3 t428.t6.t4 t428.t6.t5 t428.t6.t6 t428.t6.t7))
(step t428.t6.t9 (cl (= @p_295 0/1)) :rule poly_simp)
(step t428.t6.t10 (cl (= @p_294 0/1)) :rule trans :premises (t428.t6.t8 t428.t6.t9))
(step t428.t6.t11 (cl (= @p_276 0/1)) :rule trans :premises (t428.t6.t2 t428.t6.t10))
(step t428.t6.t12 (cl (= @p_91 0/1)) :rule evaluate)
(step t428.t6.t13 (cl (= @p_194 0/1)) :rule evaluate)
(step t428.t6.t14 (cl (= @p_273 @p_219)) :rule cong :premises (t428.t6.t12 t428.t6.t13 t428.t6.t12))
(step t428.t6.t15 (cl (= @p_219 0/1)) :rule evaluate)
(step t428.t6.t16 (cl (= @p_273 0/1)) :rule trans :premises (t428.t6.t14 t428.t6.t15))
(step t428.t6.t17 (cl (= @p_291 @p_107)) :rule cong :premises (t428.t6.t11 t428.t6.t16))
(step t428.t6.t18 (cl (= @p_107 true)) :rule evaluate)
(step t428.t6.t19 (cl (= @p_291 true)) :rule trans :premises (t428.t6.t17 t428.t6.t18))
(step t428.t6.t20 (cl (= @p_292 @p_64)) :rule cong :premises (t428.t6.t19))
(step t428.t6.t21 (cl (= @p_64 false)) :rule evaluate)
(step t428.t6.t22 (cl (= @p_292 false)) :rule trans :premises (t428.t6.t20 t428.t6.t21))
(step t428.t6.t23 (cl @p_290) :rule trans :premises (t428.t6.t1 t428.t6.t22))
(step t428.t6.t24 (cl @p_169 @p_167 @p_289 (not (! (< @p_254 @p_194) :named @p_278)) @p_166 @p_277) :rule la_generic :args (-1/1 1/1 -1/1 1/1 -1/1 1/1))
(step t428.t6.t25 (cl (not @p_160) @p_128 @p_159) :rule equiv_pos2)
(step t428.t6.t26 (cl (= @p_159 @p_26)) :rule rare_rewrite :args ("arith-elim-lt" @p_24 0/1))
(step t428.t6.t27 (cl @p_160) :rule symm :premises (t428.t6.t26))
(step t428.t6.t28 (cl @p_159) :rule resolution :premises (t428.t6.t25 t428.t6.t27 t270))
(step t428.t6.t29 (cl (=> @p_284 @p_282)) :rule la_mult_neg)
(step t428.t6.t30 (cl @p_288 @p_282) :rule implies :premises (t428.t6.t29))
(step t428.t6.t31 (cl (= @p_98 @p_96)) :rule equiv_simplify)
(step t428.t6.t32 (cl (not @p_98) @p_96) :rule equiv1 :premises (t428.t6.t31))
(step t428.t6.t33 (cl @p_98) :rule evaluate)
(step t428.t6.t34 (cl @p_96) :rule resolution :premises (t428.t6.t32 t428.t6.t33))
(step t428.t6.t35 (cl @p_287 @p_262 @p_283) :rule equiv_pos2)
(step t428.t6.t36 (cl (= (* 1/1 (- @p_274 0/1)) @p_68)) :rule poly_simp)
(step t428.t6.t37 (cl (= @p_283 @p_58)) :rule poly_simp_rel :premises (t428.t6.t36))
(step t428.t6.t38 (cl @p_286) :rule symm :premises (t428.t6.t37))
(step t428.t6.t39 (cl @p_283) :rule resolution :premises (t428.t6.t35 t428.t6.t38 t428.a2))
(step t428.t6.t40 (cl @p_284) :rule and_intro :premises (t428.t6.t34 t428.t6.t39))
(step t428.t6.t41 (cl @p_282) :rule resolution :premises (t428.t6.t30 t428.t6.t40))
(step t428.t6.t42 (cl (=> (! (and @p_202 @p_2) :named @p_279) @p_278)) :rule la_mult_pos)
(step t428.t6.t43 (cl (not @p_279) @p_278) :rule implies :premises (t428.t6.t42))
(step t428.t6.t44 (cl (= @p_206 @p_202)) :rule equiv_simplify)
(step t428.t6.t45 (cl (not @p_206) @p_202) :rule equiv1 :premises (t428.t6.t44))
(step t428.t6.t46 (cl @p_206) :rule evaluate)
(step t428.t6.t47 (cl @p_202) :rule resolution :premises (t428.t6.t45 t428.t6.t46))
(step t428.t6.t48 (cl @p_281 @p_86 @p_2) :rule equiv_pos2)
(step t428.t6.t49 (cl @p_280) :rule symm :premises (t239))
(step t428.t6.t50 (cl @p_2) :rule resolution :premises (t428.t6.t48 t428.t6.t49 t428.a1))
(step t428.t6.t51 (cl @p_279) :rule and_intro :premises (t428.t6.t47 t428.t6.t50))
(step t428.t6.t52 (cl @p_278) :rule resolution :premises (t428.t6.t43 t428.t6.t51))
(step t428.t6.t53 (cl (=> @p_162 @p_161)) :rule la_mult_neg)
(step t428.t6.t54 (cl @p_165 @p_161) :rule implies :premises (t428.t6.t53))
(step t428.t6.t55 (cl @p_181 @p_126 @p_140) :rule equiv_pos2)
(step t428.t6.t56 (cl (= (* 1/1 (- @p_139 0/1)) (* 1/1 @p_123))) :rule poly_simp)
(step t428.t6.t57 (cl (= @p_140 @p_112)) :rule poly_simp_rel :premises (t428.t6.t56))
(step t428.t6.t58 (cl @p_180) :rule symm :premises (t428.t6.t57))
(step t428.t6.t59 (cl @p_140) :rule resolution :premises (t428.t6.t55 t428.t6.t58 t428.a0))
(step t428.t6.t60 (cl @p_162) :rule and_intro :premises (t428.t6.t34 t428.t6.t59))
(step t428.t6.t61 (cl @p_161) :rule resolution :premises (t428.t6.t54 t428.t6.t60))
(step t428.t6.t62 (cl @p_277) :rule resolution :premises (t428.t6.t24 t428.t6.a0 t428.t6.t28 t428.t6.t41 t428.t6.t52 t428.t6.t61))
(step t428.t6.t63 (cl false) :rule resolution :premises (t428.t6.t0 t428.t6.t23 t428.t6.t62))
(step t428.t6 (cl @p_169 false) :rule subproof :discharge (t428.t6.a0))
(step t428.t7 (cl @p_272 false) :rule resolution :premises (t428.t5 t428.t6))
(step t428.t8 (cl @p_272 @p_90) :rule implies_neg2)
(step t428.t9 (cl @p_272 @p_272) :rule resolution :premises (t428.t7 t428.t8))
(step t428.t10 (cl @p_272) :rule contraction :premises (t428.t9))
(step t428.t11 (cl (= @p_272 @p_169)) :rule implies_simplify)
(step t428.t12 (cl (not @p_272) @p_169) :rule equiv1 :premises (t428.t11))
(step t428.t13 (cl @p_169) :rule resolution :premises (t428.t10 t428.t12))
(step t428.t14 (cl) :rule resolution :premises (t428.t4 t428.t13))
(step t428 (cl @p_126 @p_86 @p_262 @p_128 @p_125 false) :rule subproof :discharge (t428.a0 t428.a1 t428.a2 t428.a3 t428.a4))
(step t429 (cl @p_270 @p_112) :rule and_pos :args (0))
(step t430 (cl @p_270 @p_48) :rule and_pos :args (1))
(step t431 (cl @p_270 @p_58) :rule and_pos :args (2))
(step t432 (cl @p_270 @p_26) :rule and_pos :args (3))
(step t433 (cl @p_270 @p_70) :rule and_pos :args (4))
(step t434 (cl false @p_270 @p_270 @p_270 @p_270 @p_270) :rule resolution :premises (t428 t429 t430 t431 t432 t433))
(step t435 (cl @p_270 @p_270 @p_270 @p_270 @p_270 false) :rule reordering :premises (t434))
(step t436 (cl @p_270 false) :rule contraction :premises (t435))
(step t437 (cl @p_271 false) :rule resolution :premises (t427 t436))
(step t438 (cl @p_271 @p_90) :rule implies_neg2)
(step t439 (cl @p_271 @p_271) :rule resolution :premises (t437 t438))
(step t440 (cl @p_271) :rule contraction :premises (t439))
(step t441 (cl (= @p_271 @p_270)) :rule implies_simplify)
(step t442 (cl (not @p_271) @p_270) :rule equiv1 :premises (t441))
(step t443 (cl @p_270) :rule resolution :premises (t440 t442))
(step t444 (cl @p_268) :rule resolution :premises (t426 t443))
(step t445 (cl @p_86 @p_128 @p_262 @p_125 @p_126) :rule not_and :premises (t444))
(step t446 (cl @p_264 @p_266) :rule or_neg :args (0))
(step t447 (cl @p_264 @p_133) :rule or_neg :args (1))
(step t448 (cl @p_264 @p_265) :rule or_neg :args (2))
(step t449 (cl @p_264 @p_131) :rule or_neg :args (3))
(step t450 (cl @p_264 @p_130) :rule or_neg :args (4))
(step t451 (cl @p_264 @p_264 @p_264 @p_264 @p_264) :rule resolution :premises (t445 t446 t447 t448 t449 t450))
(step t452 (cl @p_264) :rule contraction :premises (t451))
(step t453 (cl @p_263) :rule resolution :premises (t410 t411 t452))
(step t454 (cl @p_22 @p_25 @p_262 @p_125 @p_126) :rule or :premises (t453))
(step t455 (cl @p_50) :rule resolution :premises (t149 t409 t270 t74 t271 t454 t409 t408 t270 t405))
(step t456 (cl @p_53) :rule resolution :premises (t103 t455 t408))
(step t457 (cl @p_114) :rule resolution :premises (t74 t456))
(step t458 (cl @p_72) :rule resolution :premises (t335 t455))
(step t459 (cl) :rule resolution :premises (t45 t457 t458 t409 t270))
)
f5e65f83bea94d3f050a1f035e49d9d7018419e8 18 0
unsat
(
(assume a0 (! (not (not (! (= (! (+ 2 2) :named @p_1) 5) :named @p_2))) :named @p_3))
(step t0 (cl (not (! (= @p_3 false) :named @p_4)) (not @p_3) false) :rule equiv_pos2)
(step t1 (cl @p_4) :rule evaluate)
(step t2 (cl (! (= @p_2 false) :named @p_5)) :rule evaluate)
(step t3 (cl (= false @p_2)) :rule symm :premises (t2))
(step t4 (cl (= @p_3 @p_2)) :rule trans :premises (t1 t3))
(step t5 (cl (= @p_1 4)) :rule evaluate)
(step t6 (cl (= 5 5)) :rule refl)
(step t7 (cl (= @p_2 (! (= 4 5) :named @p_6))) :rule cong :premises (t5 t6))
(step t8 (cl (= @p_6 false)) :rule evaluate)
(step t9 (cl @p_5) :rule trans :premises (t7 t8))
(step t10 (cl @p_4) :rule trans :premises (t4 t9))
(step t11 (cl false) :rule resolution :premises (t0 t10 a0))
(step t12 (cl (not false)) :rule false)
(step t13 (cl) :rule resolution :premises (t11 t12))
)
b3d53e63f685256a85e67117f4025b398f421c16 34 0
unsat
(
(assume a0 (! (not (! (= (! (or (! (<= 0 (! (+ y$ (! (* (! (- 1) :named @p_4) x$) :named @p_5)) :named @p_6)) :named @p_7) (or (! (not (! (<= 0 x$) :named @p_2)) :named @p_3) @p_2)) :named @p_8) (! (not false) :named @p_1)) :named @p_9)) :named @p_10))
(step t0 (cl (not (! (not (! (not (! (>= x$ 0) :named @p_11)) :named @p_12)) :named @p_28)) @p_11) :rule not_not)
(step t1 (cl (not (! (= @p_10 (! (not (! (or (! (not (! (>= (! (+ x$ (* -1 y$)) :named @p_13) 1) :named @p_14)) :named @p_15) @p_12 @p_11) :named @p_16)) :named @p_17)) :named @p_18)) (not @p_10) @p_17) :rule equiv_pos2)
(step t2 (cl (= @p_8 (! (or @p_7 @p_3 @p_2) :named @p_20))) :rule aci_simp)
(step t3 (cl (= @p_4 -1)) :rule evaluate)
(step t4 (cl (= x$ x$)) :rule refl)
(step t5 (cl (= @p_5 (! (* -1 x$) :named @p_21))) :rule cong :premises (t3 t4))
(step t6 (cl (= @p_6 (! (+ y$ @p_21) :named @p_27))) :rule cong :premises (t5))
(step t7 (cl (= @p_27 (! (+ @p_21 y$) :named @p_22))) :rule poly_simp)
(step t8 (cl (= @p_6 @p_22)) :rule trans :premises (t6 t7))
(step t9 (cl (= @p_7 (! (<= 0 @p_22) :named @p_23))) :rule cong :premises (t8))
(step t10 (cl (= @p_23 (! (not (! (>= 0 (! (+ @p_22 1) :named @p_24)) :named @p_25)) :named @p_26))) :rule rare_rewrite :args ("arith-leq-norm" 0 @p_22))
(step t11 (cl (= (* -1 (- 0 @p_24)) (* -1 (- @p_13 1)))) :rule poly_simp)
(step t12 (cl (= @p_25 @p_14)) :rule poly_simp_rel :premises (t11))
(step t13 (cl (= @p_26 @p_15)) :rule cong :premises (t12))
(step t14 (cl (= @p_23 @p_15)) :rule trans :premises (t10 t13))
(step t15 (cl (= @p_7 @p_15)) :rule trans :premises (t9 t14))
(step t16 (cl (= @p_2 @p_11)) :rule rare_rewrite :args ("arith-elim-leq" 0 x$))
(step t17 (cl (= @p_3 @p_12)) :rule cong :premises (t16))
(step t18 (cl (= @p_20 @p_16)) :rule cong :premises (t15 t17 t16))
(step t19 (cl (= @p_8 @p_16)) :rule trans :premises (t2 t18))
(step t20 (cl (= @p_1 true)) :rule evaluate)
(step t21 (cl (= @p_9 (! (= @p_16 true) :named @p_19))) :rule cong :premises (t19 t20))
(step t22 (cl (= @p_19 @p_16)) :rule rare_rewrite :args ("bool-eq-true" @p_16))
(step t23 (cl (= @p_9 @p_16)) :rule trans :premises (t21 t22))
(step t24 (cl @p_18) :rule cong :premises (t23))
(step t25 (cl @p_17) :rule resolution :premises (t1 t24 a0))
(step t26 (cl @p_28) :rule not_or :premises (t25) :args (1))
(step t27 (cl @p_11) :rule resolution :premises (t0 t26))
(step t28 (cl @p_12) :rule not_or :premises (t25) :args (2))
(step t29 (cl) :rule resolution :premises (t27 t28))
)
4db39316e8ea9152558a3a347aa9d9a96e924679 220 0
unsat
(
(assume a0 (! (< (! (+ (! (* 3 x$) :named @p_2) (! (* 7 a$) :named @p_1)) :named @p_3) 4) :named @p_4))
(assume a1 (! (< 3 (! (* 2 x$) :named @p_5)) :named @p_6))
(assume a2 (! (not (! (< a$ 0) :named @p_7)) :named @p_8))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ @p_1 @p_2) :named @p_9) 4) :named @p_10)) :named @p_11)) :named @p_36) (! (not (! (>= x$ 2) :named @p_17)) :named @p_21) (! (not (! (>= a$ 0) :named @p_31)) :named @p_33)) :named @p_37) (! (or @p_10 @p_21 @p_33) :named @p_35)) :named @p_74)) (not @p_37) @p_35) :rule equiv_pos2)
(step t1 (cl (= @p_36 @p_10)) :rule rare_rewrite :args ("bool-double-not-elim" @p_10))
(step t2 (cl (= @p_21 @p_21)) :rule refl)
(step t3 (cl (= @p_33 @p_33)) :rule refl)
(step t4 (cl @p_74) :rule cong :premises (t1 t2 t3))
(step t5 (cl (! (=> (! (and @p_11 @p_17 @p_31) :named @p_38) (! (and @p_31 @p_17 @p_11) :named @p_40)) :named @p_73) @p_38) :rule implies_neg1)
(anchor :step t6)
(assume t6.a0 @p_11)
(assume t6.a1 @p_17)
(assume t6.a2 @p_31)
(step t6.t0 (cl (not (! (= @p_8 @p_31) :named @p_32)) (not @p_8) @p_31) :rule equiv_pos2)
(step t6.t1 (cl (= @p_7 @p_33)) :rule rare_rewrite :args ("arith-elim-lt" a$ 0))
(step t6.t2 (cl (= @p_8 (! (not @p_33) :named @p_34))) :rule cong :premises (t6.t1))
(step t6.t3 (cl (= @p_34 @p_31)) :rule rare_rewrite :args ("bool-double-not-elim" @p_31))
(step t6.t4 (cl @p_32) :rule trans :premises (t6.t2 t6.t3))
(step t6.t5 (cl @p_31) :rule resolution :premises (t6.t0 t6.t4 a2))
(step t6.t6 (cl (not (! (= @p_6 @p_17) :named @p_18)) (not @p_6) @p_17) :rule equiv_pos2)
(step t6.t7 (cl (= @p_6 (! (not (! (>= 3 @p_5) :named @p_19)) :named @p_20))) :rule rare_rewrite :args ("arith-elim-lt" 3 @p_5))
(step t6.t8 (cl (= (* 3/2 (to_real (- 3 @p_5))) (* 3/1 (- (! (to_real (! (* -1 x$) :named @p_23)) :named @p_27) -3/2)))) :rule poly_simp)
(step t6.t9 (cl (= @p_19 (! (>= @p_27 -3/2) :named @p_28))) :rule poly_simp_rel :premises (t6.t8))
(step t6.t10 (cl (= (= (to_real (! (to_int -3/2) :named @p_29)) -3/2) false)) :rule evaluate)
(step t6.t11 (cl (= (! (+ @p_29 1) :named @p_30) -1)) :rule evaluate)
(step t6.t12 (cl (= -1 @p_30)) :rule symm :premises (t6.t11))
(step t6.t13 (cl (= @p_28 (! (>= @p_23 -1) :named @p_24))) :rule rare_rewrite :premises (t6.t10 t6.t12) :args ("arith-int-geq-tighten" @p_23 -3/2 -1))
(step t6.t14 (cl (= @p_21 (! (>= 2 (! (+ x$ 1) :named @p_25)) :named @p_26))) :rule rare_rewrite :args ("arith-geq-tighten" x$ 2))
(step t6.t15 (cl (= (* 1 (- 2 @p_25)) (* 1 (- @p_23 -1)))) :rule poly_simp)
(step t6.t16 (cl (= @p_26 @p_24)) :rule poly_simp_rel :premises (t6.t15))
(step t6.t17 (cl (= @p_21 @p_24)) :rule trans :premises (t6.t14 t6.t16))
(step t6.t18 (cl (= @p_24 @p_21)) :rule symm :premises (t6.t17))
(step t6.t19 (cl (= @p_19 @p_21)) :rule trans :premises (t6.t9 t6.t13 t6.t18))
(step t6.t20 (cl (= @p_20 (! (not @p_21) :named @p_22))) :rule cong :premises (t6.t19))
(step t6.t21 (cl (= @p_22 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t6.t22 (cl (= @p_20 @p_17)) :rule trans :premises (t6.t20 t6.t21))
(step t6.t23 (cl @p_18) :rule trans :premises (t6.t7 t6.t22))
(step t6.t24 (cl @p_17) :rule resolution :premises (t6.t6 t6.t23 a1))
(step t6.t25 (cl (! (not (! (= @p_4 @p_11) :named @p_12)) :named @p_15) (! (not @p_4) :named @p_16) @p_11) :rule equiv_pos2)
(step t6.t26 (cl (= @p_4 (! (not (! (>= @p_3 4) :named @p_13)) :named @p_14))) :rule rare_rewrite :args ("arith-elim-lt" @p_3 4))
(step t6.t27 (cl (= @p_3 @p_9)) :rule poly_simp)
(step t6.t28 (cl (= 4 4)) :rule refl)
(step t6.t29 (cl (= @p_13 @p_10)) :rule cong :premises (t6.t27 t6.t28))
(step t6.t30 (cl (= @p_14 @p_11)) :rule cong :premises (t6.t29))
(step t6.t31 (cl @p_12) :rule trans :premises (t6.t26 t6.t30))
(step t6.t32 (cl @p_11) :rule resolution :premises (t6.t25 t6.t31 a0))
(step t6.t33 (cl @p_40) :rule and_intro :premises (t6.t5 t6.t24 t6.t32))
(step t6 (cl @p_36 @p_21 @p_33 @p_40) :rule subproof :discharge (t6.a0 t6.a1 t6.a2))
(step t7 (cl (! (not @p_38) :named @p_39) @p_11) :rule and_pos :args (0))
(step t8 (cl @p_39 @p_17) :rule and_pos :args (1))
(step t9 (cl @p_39 @p_31) :rule and_pos :args (2))
(step t10 (cl @p_40 @p_39 @p_39 @p_39) :rule resolution :premises (t6 t7 t8 t9))
(step t11 (cl @p_39 @p_39 @p_39 @p_40) :rule reordering :premises (t10))
(step t12 (cl @p_39 @p_40) :rule contraction :premises (t11))
(step t13 (cl @p_73 @p_40) :rule resolution :premises (t5 t12))
(step t14 (cl @p_73 (! (not @p_40) :named @p_41)) :rule implies_neg2)
(step t15 (cl @p_73 @p_73) :rule resolution :premises (t13 t14))
(step t16 (cl @p_73) :rule contraction :premises (t15))
(step t17 (cl @p_39 @p_40) :rule implies :premises (t16))
(step t18 (cl (! (=> @p_40 false) :named @p_42) @p_40) :rule implies_neg1)
(anchor :step t19)
(assume t19.a0 @p_31)
(assume t19.a1 @p_17)
(assume t19.a2 @p_11)
(step t19.t0 (cl (! (not (! (= @p_11 (! (< @p_9 4) :named @p_44)) :named @p_62)) :named @p_63) @p_36 @p_44) :rule equiv_pos2)
(step t19.t1 (cl (= @p_44 @p_11)) :rule rare_rewrite :args ("arith-elim-lt" @p_9 4))
(step t19.t2 (cl @p_62) :rule symm :premises (t19.t1))
(step t19.t3 (cl @p_15 @p_16 @p_11) :rule equiv_pos2)
(step t19.t4 (cl (= @p_4 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" @p_3 4))
(step t19.t5 (cl (= @p_3 @p_9)) :rule poly_simp)
(step t19.t6 (cl (= 4 4)) :rule refl)
(step t19.t7 (cl (= @p_13 @p_10)) :rule cong :premises (t19.t5 t19.t6))
(step t19.t8 (cl (= @p_14 @p_11)) :rule cong :premises (t19.t7))
(step t19.t9 (cl @p_12) :rule trans :premises (t19.t4 t19.t8))
(step t19.t10 (cl @p_11) :rule resolution :premises (t19.t3 t19.t9 a0))
(step t19.t11 (cl @p_44) :rule resolution :premises (t19.t0 t19.t2 t19.t10))
(step t19.t12 (cl (not (! (= @p_10 (! (not @p_44) :named @p_45)) :named @p_72)) @p_11 @p_45) :rule equiv_pos2)
(step t19.t13 (cl (= @p_45 @p_36)) :rule cong :premises (t19.t1))
(step t19.t14 (cl (! (= @p_45 @p_10) :named @p_71)) :rule trans :premises (t19.t13 t1))
(step t19.t15 (cl @p_72) :rule symm :premises (t19.t14))
(step t19.t16 (cl (not @p_71) (not @p_45) @p_10) :rule equiv_pos2)
(step t19.t17 (cl (! (=> @p_44 false) :named @p_46) @p_44) :rule implies_neg1)
(anchor :step t19.t18)
(assume t19.t18.a0 @p_44)
(step t19.t18.t0 (cl (not (! (= (! (< (! (+ @p_9 (! (* -3 x$) :named @p_51) (! (* -7 a$) :named @p_50)) :named @p_52) (! (+ 4 (! (* -3 2) :named @p_48) (! (* -7 0) :named @p_47)) :named @p_49)) :named @p_53) false) :named @p_64)) (not @p_53) false) :rule equiv_pos2)
(step t19.t18.t1 (cl (= @p_53 (! (not (! (>= @p_52 @p_49) :named @p_65)) :named @p_66))) :rule rare_rewrite :args ("arith-elim-lt" @p_52 @p_49))
(step t19.t18.t2 (cl (= @p_52 (! (+ @p_50 @p_51 @p_1 @p_2) :named @p_70))) :rule poly_simp)
(step t19.t18.t3 (cl (= @p_70 0)) :rule poly_simp)
(step t19.t18.t4 (cl (= @p_52 0)) :rule trans :premises (t19.t18.t2 t19.t18.t3))
(step t19.t18.t5 (cl (= @p_48 -6)) :rule evaluate)
(step t19.t18.t6 (cl (= @p_47 0)) :rule evaluate)
(step t19.t18.t7 (cl (= @p_49 (! (+ 4 -6 0) :named @p_69))) :rule cong :premises (t19.t18.t5 t19.t18.t6))
(step t19.t18.t8 (cl (= @p_69 -2)) :rule evaluate)
(step t19.t18.t9 (cl (= @p_49 -2)) :rule trans :premises (t19.t18.t7 t19.t18.t8))
(step t19.t18.t10 (cl (= @p_65 (! (>= 0 -2) :named @p_68))) :rule cong :premises (t19.t18.t4 t19.t18.t9))
(step t19.t18.t11 (cl (= @p_68 true)) :rule evaluate)
(step t19.t18.t12 (cl (= @p_65 true)) :rule trans :premises (t19.t18.t10 t19.t18.t11))
(step t19.t18.t13 (cl (= @p_66 (! (not true) :named @p_67))) :rule cong :premises (t19.t18.t12))
(step t19.t18.t14 (cl (= @p_67 false)) :rule evaluate)
(step t19.t18.t15 (cl (= @p_66 false)) :rule trans :premises (t19.t18.t13 t19.t18.t14))
(step t19.t18.t16 (cl @p_64) :rule trans :premises (t19.t18.t1 t19.t18.t15))
(step t19.t18.t17 (cl @p_45 (not (! (<= @p_51 @p_48) :named @p_58)) (not (! (<= @p_50 @p_47) :named @p_54)) @p_53) :rule la_generic :args (1/1 1/1 1/1 1/1))
(step t19.t18.t18 (cl @p_63 @p_36 @p_44) :rule equiv_pos2)
(step t19.t18.t19 (cl @p_15 @p_16 @p_11) :rule equiv_pos2)
(step t19.t18.t20 (cl @p_11) :rule resolution :premises (t19.t18.t19 t19.t9 a0))
(step t19.t18.t21 (cl @p_44) :rule resolution :premises (t19.t18.t18 t19.t2 t19.t18.t20))
(step t19.t18.t22 (cl (=> (! (and (! (< -3 0) :named @p_59) @p_17) :named @p_60) @p_58)) :rule la_mult_neg)
(step t19.t18.t23 (cl (not @p_60) @p_58) :rule implies :premises (t19.t18.t22))
(step t19.t18.t24 (cl (= (! (= @p_59 true) :named @p_61) @p_59)) :rule equiv_simplify)
(step t19.t18.t25 (cl (not @p_61) @p_59) :rule equiv1 :premises (t19.t18.t24))
(step t19.t18.t26 (cl @p_61) :rule evaluate)
(step t19.t18.t27 (cl @p_59) :rule resolution :premises (t19.t18.t25 t19.t18.t26))
(step t19.t18.t28 (cl (not @p_18) (not @p_6) @p_17) :rule equiv_pos2)
(step t19.t18.t29 (cl (= @p_6 @p_20)) :rule rare_rewrite :args ("arith-elim-lt" 3 @p_5))
(step t19.t18.t30 (cl (= (* 3/2 (to_real (- 3 @p_5))) (* 3/1 (- @p_27 -3/2)))) :rule poly_simp)
(step t19.t18.t31 (cl (= @p_19 @p_28)) :rule poly_simp_rel :premises (t19.t18.t30))
(step t19.t18.t32 (cl (= (= (to_real @p_29) -3/2) false)) :rule evaluate)
(step t19.t18.t33 (cl (= @p_30 -1)) :rule evaluate)
(step t19.t18.t34 (cl (= -1 @p_30)) :rule symm :premises (t19.t18.t33))
(step t19.t18.t35 (cl (= @p_28 @p_24)) :rule rare_rewrite :premises (t19.t18.t32 t19.t18.t34) :args ("arith-int-geq-tighten" @p_23 -3/2 -1))
(step t19.t18.t36 (cl (= @p_21 @p_26)) :rule rare_rewrite :args ("arith-geq-tighten" x$ 2))
(step t19.t18.t37 (cl (= (* 1 (- 2 @p_25)) (* 1 (- @p_23 -1)))) :rule poly_simp)
(step t19.t18.t38 (cl (= @p_26 @p_24)) :rule poly_simp_rel :premises (t19.t18.t37))
(step t19.t18.t39 (cl (= @p_21 @p_24)) :rule trans :premises (t19.t18.t36 t19.t18.t38))
(step t19.t18.t40 (cl (= @p_24 @p_21)) :rule symm :premises (t19.t18.t39))
(step t19.t18.t41 (cl (= @p_19 @p_21)) :rule trans :premises (t19.t18.t31 t19.t18.t35 t19.t18.t40))
(step t19.t18.t42 (cl (= @p_20 @p_22)) :rule cong :premises (t19.t18.t41))
(step t19.t18.t43 (cl (= @p_22 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t19.t18.t44 (cl (= @p_20 @p_17)) :rule trans :premises (t19.t18.t42 t19.t18.t43))
(step t19.t18.t45 (cl @p_18) :rule trans :premises (t19.t18.t29 t19.t18.t44))
(step t19.t18.t46 (cl @p_17) :rule resolution :premises (t19.t18.t28 t19.t18.t45 a1))
(step t19.t18.t47 (cl @p_60) :rule and_intro :premises (t19.t18.t27 t19.t18.t46))
(step t19.t18.t48 (cl @p_58) :rule resolution :premises (t19.t18.t23 t19.t18.t47))
(step t19.t18.t49 (cl (=> (! (and (! (< -7 0) :named @p_55) @p_31) :named @p_56) @p_54)) :rule la_mult_neg)
(step t19.t18.t50 (cl (not @p_56) @p_54) :rule implies :premises (t19.t18.t49))
(step t19.t18.t51 (cl (= (! (= @p_55 true) :named @p_57) @p_55)) :rule equiv_simplify)
(step t19.t18.t52 (cl (not @p_57) @p_55) :rule equiv1 :premises (t19.t18.t51))
(step t19.t18.t53 (cl @p_57) :rule evaluate)
(step t19.t18.t54 (cl @p_55) :rule resolution :premises (t19.t18.t52 t19.t18.t53))
(step t19.t18.t55 (cl (not @p_32) (not @p_8) @p_31) :rule equiv_pos2)
(step t19.t18.t56 (cl (= @p_7 @p_33)) :rule rare_rewrite :args ("arith-elim-lt" a$ 0))
(step t19.t18.t57 (cl (= @p_8 @p_34)) :rule cong :premises (t19.t18.t56))
(step t19.t18.t58 (cl (= @p_34 @p_31)) :rule rare_rewrite :args ("bool-double-not-elim" @p_31))
(step t19.t18.t59 (cl @p_32) :rule trans :premises (t19.t18.t57 t19.t18.t58))
(step t19.t18.t60 (cl @p_31) :rule resolution :premises (t19.t18.t55 t19.t18.t59 a2))
(step t19.t18.t61 (cl @p_56) :rule and_intro :premises (t19.t18.t54 t19.t18.t60))
(step t19.t18.t62 (cl @p_54) :rule resolution :premises (t19.t18.t50 t19.t18.t61))
(step t19.t18.t63 (cl @p_53) :rule resolution :premises (t19.t18.t17 t19.t18.t21 t19.t18.t48 t19.t18.t62))
(step t19.t18.t64 (cl false) :rule resolution :premises (t19.t18.t0 t19.t18.t16 t19.t18.t63))
(step t19.t18 (cl @p_45 false) :rule subproof :discharge (t19.t18.a0))
(step t19.t19 (cl @p_46 false) :rule resolution :premises (t19.t17 t19.t18))
(step t19.t20 (cl @p_46 (! (not false) :named @p_43)) :rule implies_neg2)
(step t19.t21 (cl @p_46 @p_46) :rule resolution :premises (t19.t19 t19.t20))
(step t19.t22 (cl @p_46) :rule contraction :premises (t19.t21))
(step t19.t23 (cl (= @p_46 @p_45)) :rule implies_simplify)
(step t19.t24 (cl (not @p_46) @p_45) :rule equiv1 :premises (t19.t23))
(step t19.t25 (cl @p_45) :rule resolution :premises (t19.t22 t19.t24))
(step t19.t26 (cl @p_10) :rule resolution :premises (t19.t16 t19.t14 t19.t25))
(step t19.t27 (cl @p_45) :rule resolution :premises (t19.t12 t19.t15 t19.t26))
(step t19.t28 (cl) :rule resolution :premises (t19.t11 t19.t27))
(step t19 (cl @p_33 @p_21 @p_36 false) :rule subproof :discharge (t19.a0 t19.a1 t19.a2))
(step t20 (cl @p_41 @p_31) :rule and_pos :args (0))
(step t21 (cl @p_41 @p_17) :rule and_pos :args (1))
(step t22 (cl @p_41 @p_11) :rule and_pos :args (2))
(step t23 (cl false @p_41 @p_41 @p_41) :rule resolution :premises (t19 t20 t21 t22))
(step t24 (cl @p_41 @p_41 @p_41 false) :rule reordering :premises (t23))
(step t25 (cl @p_41 false) :rule contraction :premises (t24))
(step t26 (cl @p_42 false) :rule resolution :premises (t18 t25))
(step t27 (cl @p_42 @p_43) :rule implies_neg2)
(step t28 (cl @p_42 @p_42) :rule resolution :premises (t26 t27))
(step t29 (cl @p_42) :rule contraction :premises (t28))
(step t30 (cl (= @p_42 @p_41)) :rule implies_simplify)
(step t31 (cl (not @p_42) @p_41) :rule equiv1 :premises (t30))
(step t32 (cl @p_41) :rule resolution :premises (t29 t31))
(step t33 (cl @p_39) :rule resolution :premises (t17 t32))
(step t34 (cl @p_36 @p_21 @p_33) :rule not_and :premises (t33))
(step t35 (cl @p_37 (not @p_36)) :rule or_neg :args (0))
(step t36 (cl @p_37 @p_22) :rule or_neg :args (1))
(step t37 (cl @p_37 @p_34) :rule or_neg :args (2))
(step t38 (cl @p_37 @p_37 @p_37) :rule resolution :premises (t34 t35 t36 t37))
(step t39 (cl @p_37) :rule contraction :premises (t38))
(step t40 (cl @p_35) :rule resolution :premises (t0 t4 t39))
(step t41 (cl @p_10 @p_21 @p_33) :rule or :premises (t40))
(step t42 (cl (not @p_32) (not @p_8) @p_31) :rule equiv_pos2)
(step t43 (cl (= @p_7 @p_33)) :rule rare_rewrite :args ("arith-elim-lt" a$ 0))
(step t44 (cl (= @p_8 @p_34)) :rule cong :premises (t43))
(step t45 (cl (= @p_34 @p_31)) :rule rare_rewrite :args ("bool-double-not-elim" @p_31))
(step t46 (cl @p_32) :rule trans :premises (t44 t45))
(step t47 (cl @p_31) :rule resolution :premises (t42 t46 a2))
(step t48 (cl (not @p_18) (not @p_6) @p_17) :rule equiv_pos2)
(step t49 (cl (= @p_6 @p_20)) :rule rare_rewrite :args ("arith-elim-lt" 3 @p_5))
(step t50 (cl (= (* 3/2 (to_real (- 3 @p_5))) (* 3/1 (- @p_27 -3/2)))) :rule poly_simp)
(step t51 (cl (= @p_19 @p_28)) :rule poly_simp_rel :premises (t50))
(step t52 (cl (= (= (to_real @p_29) -3/2) false)) :rule evaluate)
(step t53 (cl (= @p_30 -1)) :rule evaluate)
(step t54 (cl (= -1 @p_30)) :rule symm :premises (t53))
(step t55 (cl (= @p_28 @p_24)) :rule rare_rewrite :premises (t52 t54) :args ("arith-int-geq-tighten" @p_23 -3/2 -1))
(step t56 (cl (= @p_21 @p_26)) :rule rare_rewrite :args ("arith-geq-tighten" x$ 2))
(step t57 (cl (= (* 1 (- 2 @p_25)) (* 1 (- @p_23 -1)))) :rule poly_simp)
(step t58 (cl (= @p_26 @p_24)) :rule poly_simp_rel :premises (t57))
(step t59 (cl (= @p_21 @p_24)) :rule trans :premises (t56 t58))
(step t60 (cl (= @p_24 @p_21)) :rule symm :premises (t59))
(step t61 (cl (= @p_19 @p_21)) :rule trans :premises (t51 t55 t60))
(step t62 (cl (= @p_20 @p_22)) :rule cong :premises (t61))
(step t63 (cl (= @p_22 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t64 (cl (= @p_20 @p_17)) :rule trans :premises (t62 t63))
(step t65 (cl @p_18) :rule trans :premises (t49 t64))
(step t66 (cl @p_17) :rule resolution :premises (t48 t65 a1))
(step t67 (cl @p_15 @p_16 @p_11) :rule equiv_pos2)
(step t68 (cl (= @p_4 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" @p_3 4))
(step t69 (cl (= @p_3 @p_9)) :rule poly_simp)
(step t70 (cl (= 4 4)) :rule refl)
(step t71 (cl (= @p_13 @p_10)) :rule cong :premises (t69 t70))
(step t72 (cl (= @p_14 @p_11)) :rule cong :premises (t71))
(step t73 (cl @p_12) :rule trans :premises (t68 t72))
(step t74 (cl @p_11) :rule resolution :premises (t67 t73 a0))
(step t75 (cl) :rule resolution :premises (t41 t47 t66 t74))
)
11a2f0dfa242e06a9ebc0bbf13bb5ee414f58545 474 0
unsat
(
(assume a0 (! (not (! (or (! (and (! (< n$ m$) :named @p_21) (! (< m$ n$a) :named @p_10)) :named @p_41) (! (or (! (and (! (< n$ m$) :named @p_21) (! (= m$ n$a) :named @p_5)) :named @p_39) (! (or (! (and (! (< n$ n$a) :named @p_7) (! (< n$a m$) :named @p_26)) :named @p_37) (! (or (! (and (! (= n$ n$a) :named @p_34) (! (< n$a m$) :named @p_26)) :named @p_35) (! (or (! (and (! (= n$ m$) :named @p_31) (! (< m$ n$a) :named @p_10)) :named @p_32) (! (or (! (and @p_26 (! (< m$ n$) :named @p_14)) :named @p_29) (! (or (! (and @p_26 (! (= m$ n$) :named @p_1)) :named @p_27) (! (or (! (and (! (< n$a n$) :named @p_4) @p_21) :named @p_24) (! (or (! (and (! (= n$a n$) :named @p_13) @p_21) :named @p_22) (! (or (! (and (! (= n$a m$) :named @p_2) (! (< m$ n$) :named @p_14)) :named @p_19) (! (or (! (and @p_14 @p_7) :named @p_17) (! (or (! (and @p_14 @p_13) :named @p_15) (! (or (! (and @p_10 @p_4) :named @p_11) (! (or (! (and @p_1 @p_7) :named @p_8) (or (! (and @p_5 @p_4) :named @p_6) (! (and @p_2 @p_1) :named @p_3))) :named @p_9)) :named @p_12)) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_23)) :named @p_25)) :named @p_28)) :named @p_30)) :named @p_33)) :named @p_36)) :named @p_38)) :named @p_40)) :named @p_42)) :named @p_43))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ n$ (! (* -1 n$a) :named @p_44)) :named @p_60) 0) :named @p_63)) :named @p_64)) :named @p_177) (! (not (! (>= (! (+ m$ @p_44) :named @p_45) 1) :named @p_46)) :named @p_50)) :named @p_243) (! (or @p_63 @p_50) :named @p_242)) :named @p_244)) (not @p_243) @p_242) :rule equiv_pos2)
(step t1 (cl (= @p_177 @p_63)) :rule rare_rewrite :args ("bool-double-not-elim" @p_63))
(step t2 (cl (= @p_50 @p_50)) :rule refl)
(step t3 (cl @p_244) :rule cong :premises (t1 t2))
(step t4 (cl (not (! (= @p_43 (! (not (! (or (! (and (! (>= (! (+ m$ (* -1 n$)) :named @p_48) 1) :named @p_49) (! (not (! (>= @p_45 0) :named @p_47)) :named @p_66)) :named @p_78) (! (and @p_49 @p_5) :named @p_77) (! (and @p_64 @p_46) :named @p_76) (! (and @p_34 @p_46) :named @p_75) (! (and @p_1 @p_66) :named @p_74) (! (and @p_46 (! (not (! (>= @p_48 0) :named @p_51)) :named @p_53)) :named @p_58) (! (and @p_46 @p_1) :named @p_73) (! (and (! (>= @p_60 1) :named @p_61) @p_49) :named @p_72) (! (and @p_34 @p_49) :named @p_71) (! (and @p_5 @p_53) :named @p_70) (! (and @p_53 @p_64) :named @p_69) (! (and @p_53 @p_34) :named @p_68) (! (and @p_66 @p_61) :named @p_67) (! (and @p_1 @p_64) :named @p_65) (! (and @p_5 @p_61) :named @p_62) (! (and @p_5 @p_1) :named @p_59)) :named @p_79)) :named @p_80)) :named @p_81)) (not @p_43) @p_80) :rule equiv_pos2)
(step t5 (cl (= @p_9 (! (or @p_8 @p_6 @p_3) :named @p_141))) :rule aci_simp)
(step t6 (cl (= @p_12 (! (or @p_11 @p_141) :named @p_142))) :rule cong :premises (t5))
(step t7 (cl (= @p_142 (! (or @p_11 @p_8 @p_6 @p_3) :named @p_139))) :rule aci_simp)
(step t8 (cl (= @p_12 @p_139)) :rule trans :premises (t6 t7))
(step t9 (cl (= @p_16 (! (or @p_15 @p_139) :named @p_140))) :rule cong :premises (t8))
(step t10 (cl (= @p_140 (! (or @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_137))) :rule aci_simp)
(step t11 (cl (= @p_16 @p_137)) :rule trans :premises (t9 t10))
(step t12 (cl (= @p_18 (! (or @p_17 @p_137) :named @p_138))) :rule cong :premises (t11))
(step t13 (cl (= @p_138 (! (or @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_135))) :rule aci_simp)
(step t14 (cl (= @p_18 @p_135)) :rule trans :premises (t12 t13))
(step t15 (cl (= @p_20 (! (or @p_19 @p_135) :named @p_136))) :rule cong :premises (t14))
(step t16 (cl (= @p_136 (! (or @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_133))) :rule aci_simp)
(step t17 (cl (= @p_20 @p_133)) :rule trans :premises (t15 t16))
(step t18 (cl (= @p_23 (! (or @p_22 @p_133) :named @p_134))) :rule cong :premises (t17))
(step t19 (cl (= @p_134 (! (or @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_131))) :rule aci_simp)
(step t20 (cl (= @p_23 @p_131)) :rule trans :premises (t18 t19))
(step t21 (cl (= @p_25 (! (or @p_24 @p_131) :named @p_132))) :rule cong :premises (t20))
(step t22 (cl (= @p_132 (! (or @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_129))) :rule aci_simp)
(step t23 (cl (= @p_25 @p_129)) :rule trans :premises (t21 t22))
(step t24 (cl (= @p_28 (! (or @p_27 @p_129) :named @p_130))) :rule cong :premises (t23))
(step t25 (cl (= @p_130 (! (or @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_127))) :rule aci_simp)
(step t26 (cl (= @p_28 @p_127)) :rule trans :premises (t24 t25))
(step t27 (cl (= @p_30 (! (or @p_29 @p_127) :named @p_128))) :rule cong :premises (t26))
(step t28 (cl (= @p_128 (! (or @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_125))) :rule aci_simp)
(step t29 (cl (= @p_30 @p_125)) :rule trans :premises (t27 t28))
(step t30 (cl (= @p_33 (! (or @p_32 @p_125) :named @p_126))) :rule cong :premises (t29))
(step t31 (cl (= @p_126 (! (or @p_32 @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_123))) :rule aci_simp)
(step t32 (cl (= @p_33 @p_123)) :rule trans :premises (t30 t31))
(step t33 (cl (= @p_36 (! (or @p_35 @p_123) :named @p_124))) :rule cong :premises (t32))
(step t34 (cl (= @p_124 (! (or @p_35 @p_32 @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_121))) :rule aci_simp)
(step t35 (cl (= @p_36 @p_121)) :rule trans :premises (t33 t34))
(step t36 (cl (= @p_38 (! (or @p_37 @p_121) :named @p_122))) :rule cong :premises (t35))
(step t37 (cl (= @p_122 (! (or @p_37 @p_35 @p_32 @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_119))) :rule aci_simp)
(step t38 (cl (= @p_38 @p_119)) :rule trans :premises (t36 t37))
(step t39 (cl (= @p_40 (! (or @p_39 @p_119) :named @p_120))) :rule cong :premises (t38))
(step t40 (cl (= @p_120 (! (or @p_39 @p_37 @p_35 @p_32 @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_117))) :rule aci_simp)
(step t41 (cl (= @p_40 @p_117)) :rule trans :premises (t39 t40))
(step t42 (cl (= @p_42 (! (or @p_41 @p_117) :named @p_118))) :rule cong :premises (t41))
(step t43 (cl (= @p_118 (! (or @p_41 @p_39 @p_37 @p_35 @p_32 @p_29 @p_27 @p_24 @p_22 @p_19 @p_17 @p_15 @p_11 @p_8 @p_6 @p_3) :named @p_82))) :rule aci_simp)
(step t44 (cl (= @p_42 @p_82)) :rule trans :premises (t42 t43))
(step t45 (cl (= @p_21 (! (not (! (>= n$ m$) :named @p_106)) :named @p_107))) :rule rare_rewrite :args ("arith-elim-lt" n$ m$))
(step t46 (cl (= (! (not @p_49) :named @p_108) (! (>= 1 (! (+ @p_48 1) :named @p_110)) :named @p_111))) :rule rare_rewrite :args ("arith-geq-tighten" @p_48 1))
(step t47 (cl (= (* -1 (- 1 @p_110)) (* -1 (! (- n$ m$) :named @p_112)))) :rule poly_simp)
(step t48 (cl (= @p_111 @p_106)) :rule poly_simp_rel :premises (t47))
(step t49 (cl (= @p_108 @p_106)) :rule trans :premises (t46 t48))
(step t50 (cl (= @p_106 @p_108)) :rule symm :premises (t49))
(step t51 (cl (= @p_107 (! (not @p_108) :named @p_109))) :rule cong :premises (t50))
(step t52 (cl (= @p_109 @p_49)) :rule rare_rewrite :args ("bool-double-not-elim" @p_49))
(step t53 (cl (= @p_107 @p_49)) :rule trans :premises (t51 t52))
(step t54 (cl (= @p_21 @p_49)) :rule trans :premises (t45 t53))
(step t55 (cl (= @p_10 (! (not (! (>= m$ n$a) :named @p_97)) :named @p_98))) :rule rare_rewrite :args ("arith-elim-lt" m$ n$a))
(step t56 (cl (= (! (* 1 (! (- m$ n$a) :named @p_83)) :named @p_100) (! (* 1 (- @p_45 0)) :named @p_99))) :rule poly_simp)
(step t57 (cl (= @p_97 @p_47)) :rule poly_simp_rel :premises (t56))
(step t58 (cl (= @p_98 @p_66)) :rule cong :premises (t57))
(step t59 (cl (= @p_10 @p_66)) :rule trans :premises (t55 t58))
(step t60 (cl (= @p_41 @p_78)) :rule cong :premises (t54 t59))
(step t61 (cl (= @p_5 @p_5)) :rule refl)
(step t62 (cl (= @p_39 @p_77)) :rule cong :premises (t54 t61))
(step t63 (cl (= @p_7 (! (not (! (>= n$ n$a) :named @p_92)) :named @p_93))) :rule rare_rewrite :args ("arith-elim-lt" n$ n$a))
(step t64 (cl (= (! (* 1 (! (- n$ n$a) :named @p_95)) :named @p_96) (! (* 1 (- @p_60 0)) :named @p_94))) :rule poly_simp)
(step t65 (cl (= @p_92 @p_63)) :rule poly_simp_rel :premises (t64))
(step t66 (cl (= @p_93 @p_64)) :rule cong :premises (t65))
(step t67 (cl (= @p_7 @p_64)) :rule trans :premises (t63 t66))
(step t68 (cl (= @p_26 (! (not (! (>= n$a m$) :named @p_113)) :named @p_114))) :rule rare_rewrite :args ("arith-elim-lt" n$a m$))
(step t69 (cl (= @p_50 (! (>= 1 (! (+ @p_45 1) :named @p_115)) :named @p_116))) :rule rare_rewrite :args ("arith-geq-tighten" @p_45 1))
(step t70 (cl (= (* -1 (- 1 @p_115)) (* -1 (! (- n$a m$) :named @p_84)))) :rule poly_simp)
(step t71 (cl (= @p_116 @p_113)) :rule poly_simp_rel :premises (t70))
(step t72 (cl (= @p_50 @p_113)) :rule trans :premises (t69 t71))
(step t73 (cl (= @p_113 @p_50)) :rule symm :premises (t72))
(step t74 (cl (= @p_114 (! (not @p_50) :named @p_57))) :rule cong :premises (t73))
(step t75 (cl (= @p_57 @p_46)) :rule rare_rewrite :args ("bool-double-not-elim" @p_46))
(step t76 (cl (= @p_114 @p_46)) :rule trans :premises (t74 t75))
(step t77 (cl (= @p_26 @p_46)) :rule trans :premises (t68 t76))
(step t78 (cl (= @p_37 @p_76)) :rule cong :premises (t67 t77))
(step t79 (cl (= @p_35 @p_75)) :rule cong :premises (t77))
(step t80 (cl (= (* 1 @p_112) (* -1 (! (- m$ n$) :named @p_104)))) :rule poly_simp)
(step t81 (cl (= @p_31 @p_1)) :rule poly_simp_rel :premises (t80))
(step t82 (cl (= @p_32 @p_74)) :rule cong :premises (t81 t59))
(step t83 (cl (= @p_14 (! (not (! (>= m$ n$) :named @p_101)) :named @p_102))) :rule rare_rewrite :args ("arith-elim-lt" m$ n$))
(step t84 (cl (= (! (* 1 @p_104) :named @p_105) (! (* 1 (- @p_48 0)) :named @p_103))) :rule poly_simp)
(step t85 (cl (= @p_101 @p_51)) :rule poly_simp_rel :premises (t84))
(step t86 (cl (= @p_102 @p_53)) :rule cong :premises (t85))
(step t87 (cl (= @p_14 @p_53)) :rule trans :premises (t83 t86))
(step t88 (cl (= @p_29 @p_58)) :rule cong :premises (t77 t87))
(step t89 (cl (= @p_1 @p_1)) :rule refl)
(step t90 (cl (= @p_27 @p_73)) :rule cong :premises (t77 t89))
(step t91 (cl (= @p_4 (! (not (! (>= n$a n$) :named @p_85)) :named @p_86))) :rule rare_rewrite :args ("arith-elim-lt" n$a n$))
(step t92 (cl (= (! (not @p_61) :named @p_87) (! (>= 1 (! (+ @p_60 1) :named @p_89)) :named @p_90))) :rule rare_rewrite :args ("arith-geq-tighten" @p_60 1))
(step t93 (cl (= (* -1 (- 1 @p_89)) (* -1 (! (- n$a n$) :named @p_91)))) :rule poly_simp)
(step t94 (cl (= @p_90 @p_85)) :rule poly_simp_rel :premises (t93))
(step t95 (cl (= @p_87 @p_85)) :rule trans :premises (t92 t94))
(step t96 (cl (= @p_85 @p_87)) :rule symm :premises (t95))
(step t97 (cl (= @p_86 (! (not @p_87) :named @p_88))) :rule cong :premises (t96))
(step t98 (cl (= @p_88 @p_61)) :rule rare_rewrite :args ("bool-double-not-elim" @p_61))
(step t99 (cl (= @p_86 @p_61)) :rule trans :premises (t97 t98))
(step t100 (cl (= @p_4 @p_61)) :rule trans :premises (t91 t99))
(step t101 (cl (= @p_24 @p_72)) :rule cong :premises (t100 t54))
(step t102 (cl (= (* 1 @p_91) (* -1 @p_95))) :rule poly_simp)
(step t103 (cl (= @p_13 @p_34)) :rule poly_simp_rel :premises (t102))
(step t104 (cl (= @p_22 @p_71)) :rule cong :premises (t103 t54))
(step t105 (cl (= (* 1 @p_84) (* -1 @p_83))) :rule poly_simp)
(step t106 (cl (= @p_2 @p_5)) :rule poly_simp_rel :premises (t105))
(step t107 (cl (= @p_19 @p_70)) :rule cong :premises (t106 t87))
(step t108 (cl (= @p_17 @p_69)) :rule cong :premises (t87 t67))
(step t109 (cl (= @p_15 @p_68)) :rule cong :premises (t87 t103))
(step t110 (cl (= @p_11 @p_67)) :rule cong :premises (t59 t100))
(step t111 (cl (= @p_8 @p_65)) :rule cong :premises (t67))
(step t112 (cl (= @p_6 @p_62)) :rule cong :premises (t100))
(step t113 (cl (= @p_3 @p_59)) :rule cong :premises (t106 t89))
(step t114 (cl (= @p_82 @p_79)) :rule cong :premises (t60 t62 t78 t79 t82 t88 t90 t101 t104 t107 t108 t109 t110 t111 t112 t113))
(step t115 (cl (= @p_42 @p_79)) :rule trans :premises (t44 t114))
(step t116 (cl @p_81) :rule cong :premises (t115))
(step t117 (cl @p_80) :rule resolution :premises (t4 t116 a0))
(step t118 (cl (not @p_76)) :rule not_or :premises (t117) :args (2))
(step t119 (cl @p_177 @p_50) :rule not_and :premises (t118))
(step t120 (cl @p_243 (! (not @p_177) :named @p_179)) :rule or_neg :args (0))
(step t121 (cl @p_243 @p_57) :rule or_neg :args (1))
(step t122 (cl @p_243 @p_243) :rule resolution :premises (t119 t120 t121))
(step t123 (cl @p_243) :rule contraction :premises (t122))
(step t124 (cl @p_242) :rule resolution :premises (t0 t3 t123))
(step t125 (cl @p_63 @p_50) :rule or :premises (t124))
(step t126 (cl (not (! (= (! (or @p_64 @p_88 (! (not (! (not @p_34) :named @p_181)) :named @p_184)) :named @p_208) (! (or @p_64 @p_61 @p_34) :named @p_207)) :named @p_235)) (not @p_208) @p_207) :rule equiv_pos2)
(step t127 (cl (= @p_184 @p_34)) :rule rare_rewrite :args ("bool-double-not-elim" @p_34))
(step t128 (cl @p_235) :rule cong :premises (t98 t127))
(step t129 (cl (! (=> (! (and @p_63 @p_87 @p_181) :named @p_209) (! (and @p_87 @p_63 @p_181) :named @p_211)) :named @p_234) @p_209) :rule implies_neg1)
(anchor :step t130)
(assume t130.a0 @p_63)
(assume t130.a1 @p_87)
(assume t130.a2 @p_181)
(step t130.t0 (cl @p_211) :rule and_intro :premises (t130.a1 t130.a0 t130.a2))
(step t130 (cl @p_64 @p_88 @p_184 @p_211) :rule subproof :discharge (t130.a0 t130.a1 t130.a2))
(step t131 (cl (! (not @p_209) :named @p_210) @p_63) :rule and_pos :args (0))
(step t132 (cl @p_210 @p_87) :rule and_pos :args (1))
(step t133 (cl @p_210 @p_181) :rule and_pos :args (2))
(step t134 (cl @p_211 @p_210 @p_210 @p_210) :rule resolution :premises (t130 t131 t132 t133))
(step t135 (cl @p_210 @p_210 @p_210 @p_211) :rule reordering :premises (t134))
(step t136 (cl @p_210 @p_211) :rule contraction :premises (t135))
(step t137 (cl @p_234 @p_211) :rule resolution :premises (t129 t136))
(step t138 (cl @p_234 (! (not @p_211) :named @p_212)) :rule implies_neg2)
(step t139 (cl @p_234 @p_234) :rule resolution :premises (t137 t138))
(step t140 (cl @p_234) :rule contraction :premises (t139))
(step t141 (cl @p_210 @p_211) :rule implies :premises (t140))
(step t142 (cl (! (=> @p_211 false) :named @p_213) @p_211) :rule implies_neg1)
(anchor :step t143)
(assume t143.a0 @p_87)
(assume t143.a1 @p_63)
(assume t143.a2 @p_181)
(step t143.t0 (cl (not (! (= @p_181 (! (not (! (= @p_60 0) :named @p_230)) :named @p_232)) :named @p_233)) @p_184 @p_232) :rule equiv_pos2)
(step t143.t1 (cl (= @p_94 @p_96)) :rule poly_simp)
(step t143.t2 (cl (= @p_230 @p_34)) :rule poly_simp_rel :premises (t143.t1))
(step t143.t3 (cl (= @p_232 @p_181)) :rule cong :premises (t143.t2))
(step t143.t4 (cl @p_233) :rule symm :premises (t143.t3))
(step t143.t5 (cl @p_232) :rule resolution :premises (t143.t0 t143.t4 t143.a2))
(step t143.t6 (cl (or @p_230 (! (not (! (<= @p_60 0) :named @p_216)) :named @p_220) (! (not (! (<= 0 @p_60) :named @p_228)) :named @p_231))) :rule la_disequality)
(step t143.t7 (cl @p_230 @p_220 @p_231) :rule or :premises (t143.t6))
(step t143.t8 (cl (! (= @p_63 @p_228) :named @p_229)) :rule comp_simplify)
(step t143.t9 (cl (not @p_229) @p_64 @p_228) :rule equiv_pos2)
(step t143.t10 (cl @p_228) :rule resolution :premises (t143.t8 t143.t9 t143.a1))
(step t143.t11 (cl (! (= (! (> @p_60 0) :named @p_214) @p_220) :named @p_224)) :rule comp_simplify)
(step t143.t12 (cl (not @p_224) @p_214 (! (not @p_220) :named @p_227)) :rule equiv_pos1)
(step t143.t13 (cl @p_214 @p_227) :rule resolution :premises (t143.t11 t143.t12))
(step t143.t14 (cl @p_214) :rule resolution :premises (t143.t5 t143.t7 t143.t10 t143.t13))
(step t143.t15 (cl (not (! (= @p_216 (! (not @p_214) :named @p_215)) :named @p_219)) @p_220 @p_215) :rule equiv_pos2)
(step t143.t16 (cl (= @p_216 (! (not (! (>= @p_60 (! (+ 0 1) :named @p_221)) :named @p_222)) :named @p_223))) :rule rare_rewrite :args ("arith-leq-norm" @p_60 0))
(step t143.t17 (cl (= @p_221 1)) :rule evaluate)
(step t143.t18 (cl (= @p_222 @p_61)) :rule cong :premises (t143.t17))
(step t143.t19 (cl (= @p_223 @p_87)) :rule cong :premises (t143.t18))
(step t143.t20 (cl (= @p_216 @p_87)) :rule trans :premises (t143.t16 t143.t19))
(step t143.t21 (cl (= @p_214 (! (not (! (>= 0 @p_60) :named @p_225)) :named @p_226))) :rule rare_rewrite :args ("arith-elim-gt" @p_60 0))
(step t143.t22 (cl (= @p_216 @p_225)) :rule rare_rewrite :args ("arith-elim-leq" @p_60 0))
(step t143.t23 (cl (= @p_225 @p_216)) :rule symm :premises (t143.t22))
(step t143.t24 (cl (= @p_226 @p_220)) :rule cong :premises (t143.t23))
(step t143.t25 (cl @p_224) :rule trans :premises (t143.t21 t143.t24))
(step t143.t26 (cl (= @p_220 @p_88)) :rule cong :premises (t143.t20))
(step t143.t27 (cl (= @p_220 @p_61)) :rule trans :premises (t143.t26 t98))
(step t143.t28 (cl (= @p_214 @p_61)) :rule trans :premises (t143.t25 t143.t27))
(step t143.t29 (cl (= @p_215 @p_87)) :rule cong :premises (t143.t28))
(step t143.t30 (cl (= @p_87 @p_215)) :rule symm :premises (t143.t29))
(step t143.t31 (cl @p_219) :rule trans :premises (t143.t20 t143.t30))
(step t143.t32 (cl (not (! (< @p_60 1) :named @p_217)) @p_216) :rule la_generic :args (1/1 1/1))
(step t143.t33 (cl (not (! (= @p_87 @p_217) :named @p_218)) @p_88 @p_217) :rule equiv_pos2)
(step t143.t34 (cl (= @p_217 @p_87)) :rule rare_rewrite :args ("arith-elim-lt" @p_60 1))
(step t143.t35 (cl @p_218) :rule symm :premises (t143.t34))
(step t143.t36 (cl @p_217) :rule resolution :premises (t143.t33 t143.t35 t143.a0))
(step t143.t37 (cl @p_216) :rule resolution :premises (t143.t32 t143.t36))
(step t143.t38 (cl @p_215) :rule resolution :premises (t143.t15 t143.t31 t143.t37))
(step t143.t39 (cl) :rule resolution :premises (t143.t14 t143.t38))
(step t143 (cl @p_88 @p_64 @p_184 false) :rule subproof :discharge (t143.a0 t143.a1 t143.a2))
(step t144 (cl @p_212 @p_87) :rule and_pos :args (0))
(step t145 (cl @p_212 @p_63) :rule and_pos :args (1))
(step t146 (cl @p_212 @p_181) :rule and_pos :args (2))
(step t147 (cl false @p_212 @p_212 @p_212) :rule resolution :premises (t143 t144 t145 t146))
(step t148 (cl @p_212 @p_212 @p_212 false) :rule reordering :premises (t147))
(step t149 (cl @p_212 false) :rule contraction :premises (t148))
(step t150 (cl @p_213 false) :rule resolution :premises (t142 t149))
(step t151 (cl @p_213 (! (not false) :named @p_153)) :rule implies_neg2)
(step t152 (cl @p_213 @p_213) :rule resolution :premises (t150 t151))
(step t153 (cl @p_213) :rule contraction :premises (t152))
(step t154 (cl (= @p_213 @p_212)) :rule implies_simplify)
(step t155 (cl (not @p_213) @p_212) :rule equiv1 :premises (t154))
(step t156 (cl @p_212) :rule resolution :premises (t153 t155))
(step t157 (cl @p_210) :rule resolution :premises (t141 t156))
(step t158 (cl @p_64 @p_88 @p_184) :rule not_and :premises (t157))
(step t159 (cl @p_208 @p_177) :rule or_neg :args (0))
(step t160 (cl @p_208 (not @p_88)) :rule or_neg :args (1))
(step t161 (cl @p_208 (not @p_184)) :rule or_neg :args (2))
(step t162 (cl @p_208 @p_208 @p_208) :rule resolution :premises (t158 t159 t160 t161))
(step t163 (cl @p_208) :rule contraction :premises (t162))
(step t164 (cl @p_207) :rule resolution :premises (t126 t128 t163))
(step t165 (cl @p_64 @p_61 @p_34) :rule or :premises (t164))
(step t166 (cl @p_34 @p_64 @p_61) :rule reordering :premises (t165))
(step t167 (cl (not @p_71)) :rule not_or :premises (t117) :args (8))
(step t168 (cl @p_181 @p_108) :rule not_and :premises (t167))
(step t169 (cl @p_108 @p_181) :rule reordering :premises (t168))
(step t170 (cl (not (! (= (! (or @p_66 (! (not (! (not @p_5) :named @p_171)) :named @p_174) @p_46) :named @p_187) (! (or @p_66 @p_5 @p_46) :named @p_186)) :named @p_202)) (not @p_187) @p_186) :rule equiv_pos2)
(step t171 (cl (= @p_174 @p_5)) :rule rare_rewrite :args ("bool-double-not-elim" @p_5))
(step t172 (cl (= @p_46 @p_46)) :rule refl)
(step t173 (cl @p_202) :rule cong :premises (t171 t172))
(step t174 (cl (! (and @p_47 @p_171) :named @p_189) @p_66 @p_174) :rule and_neg)
(step t175 (cl (! (=> @p_189 @p_46) :named @p_191) @p_189) :rule implies_neg1)
(anchor :step t176)
(assume t176.a0 @p_47)
(assume t176.a1 @p_171)
(step t176.t0 (cl @p_191 @p_189) :rule implies_neg1)
(anchor :step t176.t1)
(assume t176.t1.a0 @p_47)
(assume t176.t1.a1 @p_171)
(step t176.t1.t0 (cl (not (! (> @p_45 0) :named @p_192)) @p_46) :rule la_generic :args (1/1 1/1))
(step t176.t1.t1 (cl (not (! (= @p_171 (! (not (! (= @p_45 0) :named @p_198)) :named @p_200)) :named @p_201)) @p_174 @p_200) :rule equiv_pos2)
(step t176.t1.t2 (cl (= @p_99 @p_100)) :rule poly_simp)
(step t176.t1.t3 (cl (= @p_198 @p_5)) :rule poly_simp_rel :premises (t176.t1.t2))
(step t176.t1.t4 (cl (= @p_200 @p_171)) :rule cong :premises (t176.t1.t3))
(step t176.t1.t5 (cl @p_201) :rule symm :premises (t176.t1.t4))
(step t176.t1.t6 (cl @p_200) :rule resolution :premises (t176.t1.t1 t176.t1.t5 t176.t1.a1))
(step t176.t1.t7 (cl (or @p_198 (! (not (<= @p_45 0)) :named @p_193) (! (not (! (<= 0 @p_45) :named @p_196)) :named @p_199))) :rule la_disequality)
(step t176.t1.t8 (cl @p_198 @p_193 @p_199) :rule or :premises (t176.t1.t7))
(step t176.t1.t9 (cl (! (= @p_47 @p_196) :named @p_197)) :rule comp_simplify)
(step t176.t1.t10 (cl (not @p_197) @p_66 @p_196) :rule equiv_pos2)
(step t176.t1.t11 (cl @p_196) :rule resolution :premises (t176.t1.t9 t176.t1.t10 t176.t1.a0))
(step t176.t1.t12 (cl (! (= @p_192 @p_193) :named @p_195)) :rule comp_simplify)
(step t176.t1.t13 (cl (not @p_195) @p_192 (! (not @p_193) :named @p_194)) :rule equiv_pos1)
(step t176.t1.t14 (cl @p_192 @p_194) :rule resolution :premises (t176.t1.t12 t176.t1.t13))
(step t176.t1.t15 (cl @p_192) :rule resolution :premises (t176.t1.t6 t176.t1.t8 t176.t1.t11 t176.t1.t14))
(step t176.t1.t16 (cl @p_46) :rule resolution :premises (t176.t1.t0 t176.t1.t15))
(step t176.t1 (cl @p_66 @p_174 @p_46) :rule subproof :discharge (t176.t1.a0 t176.t1.a1))
(step t176.t2 (cl (! (not @p_189) :named @p_190) @p_47) :rule and_pos :args (0))
(step t176.t3 (cl @p_190 @p_171) :rule and_pos :args (1))
(step t176.t4 (cl @p_46 @p_190 @p_190) :rule resolution :premises (t176.t1 t176.t2 t176.t3))
(step t176.t5 (cl @p_190 @p_190 @p_46) :rule reordering :premises (t176.t4))
(step t176.t6 (cl @p_190 @p_46) :rule contraction :premises (t176.t5))
(step t176.t7 (cl @p_191 @p_46) :rule resolution :premises (t176.t0 t176.t6))
(step t176.t8 (cl @p_191 @p_50) :rule implies_neg2)
(step t176.t9 (cl @p_191 @p_191) :rule resolution :premises (t176.t7 t176.t8))
(step t176.t10 (cl @p_191) :rule contraction :premises (t176.t9))
(step t176.t11 (cl @p_190 @p_46) :rule implies :premises (t176.t10))
(step t176.t12 (cl @p_189) :rule and_intro :premises (t176.a0 t176.a1))
(step t176.t13 (cl @p_46) :rule resolution :premises (t176.t11 t176.t12))
(step t176 (cl @p_66 @p_174 @p_46) :rule subproof :discharge (t176.a0 t176.a1))
(step t177 (cl @p_190 @p_47) :rule and_pos :args (0))
(step t178 (cl @p_190 @p_171) :rule and_pos :args (1))
(step t179 (cl @p_46 @p_190 @p_190) :rule resolution :premises (t176 t177 t178))
(step t180 (cl @p_190 @p_190 @p_46) :rule reordering :premises (t179))
(step t181 (cl @p_190 @p_46) :rule contraction :premises (t180))
(step t182 (cl @p_191 @p_46) :rule resolution :premises (t175 t181))
(step t183 (cl @p_191 @p_50) :rule implies_neg2)
(step t184 (cl @p_191 @p_191) :rule resolution :premises (t182 t183))
(step t185 (cl @p_191) :rule contraction :premises (t184))
(step t186 (cl @p_190 @p_46) :rule implies :premises (t185))
(step t187 (cl @p_66 @p_174 @p_46) :rule resolution :premises (t174 t186))
(step t188 (cl @p_187 (! (not @p_66) :named @p_188)) :rule or_neg :args (0))
(step t189 (cl @p_187 (not @p_174)) :rule or_neg :args (1))
(step t190 (cl @p_187 @p_50) :rule or_neg :args (2))
(step t191 (cl @p_187 @p_187 @p_187) :rule resolution :premises (t187 t188 t189 t190))
(step t192 (cl @p_187) :rule contraction :premises (t191))
(step t193 (cl @p_186) :rule resolution :premises (t170 t173 t192))
(step t194 (cl @p_66 @p_5 @p_46) :rule or :premises (t193))
(step t195 (cl @p_5 @p_66 @p_46) :rule reordering :premises (t194))
(step t196 (cl (not @p_59)) :rule not_or :premises (t117) :args (15))
(step t197 (cl @p_171 (! (not @p_1) :named @p_144)) :rule not_and :premises (t196))
(step t198 (cl (not (! (= (! (or @p_144 @p_188) :named @p_237) (! (or @p_144 @p_47) :named @p_236)) :named @p_238)) (not @p_237) @p_236) :rule equiv_pos2)
(step t199 (cl (= @p_188 @p_47)) :rule rare_rewrite :args ("bool-double-not-elim" @p_47))
(step t200 (cl @p_238) :rule cong :premises (t199))
(step t201 (cl (not @p_74)) :rule not_or :premises (t117) :args (4))
(step t202 (cl @p_144 @p_188) :rule not_and :premises (t201))
(step t203 (cl @p_237 (! (not @p_144) :named @p_146)) :rule or_neg :args (0))
(step t204 (cl @p_237 (! (not @p_188) :named @p_205)) :rule or_neg :args (1))
(step t205 (cl @p_237 @p_237) :rule resolution :premises (t202 t203 t204))
(step t206 (cl @p_237) :rule contraction :premises (t205))
(step t207 (cl @p_236) :rule resolution :premises (t198 t200 t206))
(step t208 (cl @p_144 @p_47) :rule or :premises (t207))
(step t209 (cl @p_47 @p_144) :rule reordering :premises (t208))
(step t210 (cl (not (! (= (! (or @p_109 @p_53 @p_146) :named @p_147) (! (or @p_49 @p_53 @p_1) :named @p_145)) :named @p_170)) (not @p_147) @p_145) :rule equiv_pos2)
(step t211 (cl (= @p_53 @p_53)) :rule refl)
(step t212 (cl (= @p_146 @p_1)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1))
(step t213 (cl @p_170) :rule cong :premises (t52 t211 t212))
(step t214 (cl (! (=> (! (and @p_108 @p_51 @p_144) :named @p_148) (! (and @p_1 @p_144) :named @p_150)) :named @p_159) @p_148) :rule implies_neg1)
(anchor :step t215)
(assume t215.a0 @p_108)
(assume t215.a1 @p_51)
(assume t215.a2 @p_144)
(step t215.t0 (cl (! (=> (! (and @p_51 @p_108) :named @p_160) @p_1) :named @p_162) @p_160) :rule implies_neg1)
(anchor :step t215.t1)
(assume t215.t1.a0 @p_51)
(assume t215.t1.a1 @p_108)
(step t215.t1.t0 (cl (not (! (= (! (= @p_48 0) :named @p_154) @p_1) :named @p_157)) (! (not @p_154) :named @p_155) @p_1) :rule equiv_pos2)
(step t215.t1.t1 (cl (= @p_103 @p_105)) :rule poly_simp)
(step t215.t1.t2 (cl @p_157) :rule poly_simp_rel :premises (t215.t1.t1))
(step t215.t1.t3 (cl (not (! (< @p_48 1) :named @p_168)) (! (<= @p_48 0) :named @p_165)) :rule la_generic :args (1/1 1/1))
(step t215.t1.t4 (cl (not (! (= @p_108 @p_168) :named @p_169)) @p_109 @p_168) :rule equiv_pos2)
(step t215.t1.t5 (cl (= @p_168 @p_108)) :rule rare_rewrite :args ("arith-elim-lt" @p_48 1))
(step t215.t1.t6 (cl @p_169) :rule symm :premises (t215.t1.t5))
(step t215.t1.t7 (cl @p_168) :rule resolution :premises (t215.t1.t4 t215.t1.t6 t215.t1.a1))
(step t215.t1.t8 (cl @p_165) :rule resolution :premises (t215.t1.t3 t215.t1.t7))
(step t215.t1.t9 (cl (or @p_154 (! (not @p_165) :named @p_166) (! (not (! (<= 0 @p_48) :named @p_163)) :named @p_167))) :rule la_disequality)
(step t215.t1.t10 (cl @p_154 @p_166 @p_167) :rule or :premises (t215.t1.t9))
(step t215.t1.t11 (cl (! (= @p_51 @p_163) :named @p_164)) :rule comp_simplify)
(step t215.t1.t12 (cl (not @p_164) @p_53 @p_163) :rule equiv_pos2)
(step t215.t1.t13 (cl @p_163) :rule resolution :premises (t215.t1.t11 t215.t1.t12 t215.t1.a0))
(step t215.t1.t14 (cl @p_154) :rule resolution :premises (t215.t1.t8 t215.t1.t10 t215.t1.t13))
(step t215.t1.t15 (cl @p_1) :rule resolution :premises (t215.t1.t0 t215.t1.t2 t215.t1.t14))
(step t215.t1 (cl @p_53 @p_109 @p_1) :rule subproof :discharge (t215.t1.a0 t215.t1.a1))
(step t215.t2 (cl (! (not @p_160) :named @p_161) @p_51) :rule and_pos :args (0))
(step t215.t3 (cl @p_161 @p_108) :rule and_pos :args (1))
(step t215.t4 (cl @p_1 @p_161 @p_161) :rule resolution :premises (t215.t1 t215.t2 t215.t3))
(step t215.t5 (cl @p_161 @p_161 @p_1) :rule reordering :premises (t215.t4))
(step t215.t6 (cl @p_161 @p_1) :rule contraction :premises (t215.t5))
(step t215.t7 (cl @p_162 @p_1) :rule resolution :premises (t215.t0 t215.t6))
(step t215.t8 (cl @p_162 @p_144) :rule implies_neg2)
(step t215.t9 (cl @p_162 @p_162) :rule resolution :premises (t215.t7 t215.t8))
(step t215.t10 (cl @p_162) :rule contraction :premises (t215.t9))
(step t215.t11 (cl @p_161 @p_1) :rule implies :premises (t215.t10))
(step t215.t12 (cl @p_160) :rule and_intro :premises (t215.a1 t215.a0))
(step t215.t13 (cl @p_1) :rule resolution :premises (t215.t11 t215.t12))
(step t215.t14 (cl @p_150) :rule and_intro :premises (t215.t13 t215.a2))
(step t215 (cl @p_109 @p_53 @p_146 @p_150) :rule subproof :discharge (t215.a0 t215.a1 t215.a2))
(step t216 (cl (! (not @p_148) :named @p_149) @p_108) :rule and_pos :args (0))
(step t217 (cl @p_149 @p_51) :rule and_pos :args (1))
(step t218 (cl @p_149 @p_144) :rule and_pos :args (2))
(step t219 (cl @p_150 @p_149 @p_149 @p_149) :rule resolution :premises (t215 t216 t217 t218))
(step t220 (cl @p_149 @p_149 @p_149 @p_150) :rule reordering :premises (t219))
(step t221 (cl @p_149 @p_150) :rule contraction :premises (t220))
(step t222 (cl @p_159 @p_150) :rule resolution :premises (t214 t221))
(step t223 (cl @p_159 (! (not @p_150) :named @p_151)) :rule implies_neg2)
(step t224 (cl @p_159 @p_159) :rule resolution :premises (t222 t223))
(step t225 (cl @p_159) :rule contraction :premises (t224))
(step t226 (cl @p_149 @p_150) :rule implies :premises (t225))
(step t227 (cl (! (=> @p_150 false) :named @p_152) @p_150) :rule implies_neg1)
(anchor :step t228)
(assume t228.a0 @p_1)
(assume t228.a1 @p_144)
(step t228.t0 (cl (not (! (= @p_1 @p_154) :named @p_158)) @p_144 @p_154) :rule equiv_pos2)
(step t228.t1 (cl (= @p_103 @p_105)) :rule poly_simp)
(step t228.t2 (cl @p_157) :rule poly_simp_rel :premises (t228.t1))
(step t228.t3 (cl @p_158) :rule symm :premises (t228.t2))
(step t228.t4 (cl @p_154) :rule resolution :premises (t228.t0 t228.t3 t228.a0))
(step t228.t5 (cl (not (! (= @p_144 @p_155) :named @p_156)) @p_146 @p_155) :rule equiv_pos2)
(step t228.t6 (cl (= @p_155 @p_144)) :rule cong :premises (t228.t2))
(step t228.t7 (cl @p_156) :rule symm :premises (t228.t6))
(step t228.t8 (cl @p_155) :rule resolution :premises (t228.t5 t228.t7 t228.a1))
(step t228.t9 (cl) :rule resolution :premises (t228.t4 t228.t8))
(step t228 (cl @p_144 @p_146 false) :rule subproof :discharge (t228.a0 t228.a1))
(step t229 (cl @p_151 @p_1) :rule and_pos :args (0))
(step t230 (cl @p_151 @p_144) :rule and_pos :args (1))
(step t231 (cl false @p_151 @p_151) :rule resolution :premises (t228 t229 t230))
(step t232 (cl @p_151 @p_151 false) :rule reordering :premises (t231))
(step t233 (cl @p_151 false) :rule contraction :premises (t232))
(step t234 (cl @p_152 false) :rule resolution :premises (t227 t233))
(step t235 (cl @p_152 @p_153) :rule implies_neg2)
(step t236 (cl @p_152 @p_152) :rule resolution :premises (t234 t235))
(step t237 (cl @p_152) :rule contraction :premises (t236))
(step t238 (cl (= @p_152 @p_151)) :rule implies_simplify)
(step t239 (cl (not @p_152) @p_151) :rule equiv1 :premises (t238))
(step t240 (cl @p_151) :rule resolution :premises (t237 t239))
(step t241 (cl @p_149) :rule resolution :premises (t226 t240))
(step t242 (cl @p_109 @p_53 @p_146) :rule not_and :premises (t241))
(step t243 (cl @p_147 (not @p_109)) :rule or_neg :args (0))
(step t244 (cl @p_147 (! (not @p_53) :named @p_54)) :rule or_neg :args (1))
(step t245 (cl @p_147 (not @p_146)) :rule or_neg :args (2))
(step t246 (cl @p_147 @p_147 @p_147) :rule resolution :premises (t242 t243 t244 t245))
(step t247 (cl @p_147) :rule contraction :premises (t246))
(step t248 (cl @p_145) :rule resolution :premises (t210 t213 t247))
(step t249 (cl @p_49 @p_53 @p_1) :rule or :premises (t248))
(step t250 (cl @p_1 @p_49 @p_53) :rule reordering :premises (t249))
(step t251 (cl (not (! (= (! (or @p_188 @p_87) :named @p_204) (! (or @p_47 @p_87) :named @p_203)) :named @p_206)) (not @p_204) @p_203) :rule equiv_pos2)
(step t252 (cl (= @p_87 @p_87)) :rule refl)
(step t253 (cl @p_206) :rule cong :premises (t199 t252))
(step t254 (cl (not @p_67)) :rule not_or :premises (t117) :args (12))
(step t255 (cl @p_188 @p_87) :rule not_and :premises (t254))
(step t256 (cl @p_204 @p_205) :rule or_neg :args (0))
(step t257 (cl @p_204 @p_88) :rule or_neg :args (1))
(step t258 (cl @p_204 @p_204) :rule resolution :premises (t255 t256 t257))
(step t259 (cl @p_204) :rule contraction :premises (t258))
(step t260 (cl @p_203) :rule resolution :premises (t251 t253 t259))
(step t261 (cl @p_47 @p_87) :rule or :premises (t260))
(step t262 (cl (not (! (= (! (or @p_54 @p_181) :named @p_183) (! (or @p_51 @p_181) :named @p_182)) :named @p_185)) (not @p_183) @p_182) :rule equiv_pos2)
(step t263 (cl (= @p_54 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t264 (cl (= @p_181 @p_181)) :rule refl)
(step t265 (cl @p_185) :rule cong :premises (t263 t264))
(step t266 (cl (not @p_68)) :rule not_or :premises (t117) :args (11))
(step t267 (cl @p_54 @p_181) :rule not_and :premises (t266))
(step t268 (cl @p_183 (! (not @p_54) :named @p_56)) :rule or_neg :args (0))
(step t269 (cl @p_183 @p_184) :rule or_neg :args (1))
(step t270 (cl @p_183 @p_183) :rule resolution :premises (t267 t268 t269))
(step t271 (cl @p_183) :rule contraction :premises (t270))
(step t272 (cl @p_182) :rule resolution :premises (t262 t265 t271))
(step t273 (cl @p_51 @p_181) :rule or :premises (t272))
(step t274 (cl (not (! (= (! (or @p_54 @p_177) :named @p_178) (! (or @p_51 @p_63) :named @p_176)) :named @p_180)) (not @p_178) @p_176) :rule equiv_pos2)
(step t275 (cl @p_180) :rule cong :premises (t263 t1))
(step t276 (cl (not @p_69)) :rule not_or :premises (t117) :args (10))
(step t277 (cl @p_54 @p_177) :rule not_and :premises (t276))
(step t278 (cl @p_178 @p_56) :rule or_neg :args (0))
(step t279 (cl @p_178 @p_179) :rule or_neg :args (1))
(step t280 (cl @p_178 @p_178) :rule resolution :premises (t277 t278 t279))
(step t281 (cl @p_178) :rule contraction :premises (t280))
(step t282 (cl @p_176) :rule resolution :premises (t274 t275 t281))
(step t283 (cl @p_51 @p_63) :rule or :premises (t282))
(step t284 (cl @p_63 @p_51) :rule reordering :premises (t283))
(step t285 (cl (not (! (= (! (or @p_171 @p_54) :named @p_173) (! (or @p_171 @p_51) :named @p_172)) :named @p_175)) (not @p_173) @p_172) :rule equiv_pos2)
(step t286 (cl @p_175) :rule cong :premises (t263))
(step t287 (cl (not @p_70)) :rule not_or :premises (t117) :args (9))
(step t288 (cl @p_171 @p_54) :rule not_and :premises (t287))
(step t289 (cl @p_173 @p_174) :rule or_neg :args (0))
(step t290 (cl @p_173 @p_56) :rule or_neg :args (1))
(step t291 (cl @p_173 @p_173) :rule resolution :premises (t288 t289 t290))
(step t292 (cl @p_173) :rule contraction :premises (t291))
(step t293 (cl @p_172) :rule resolution :premises (t285 t286 t292))
(step t294 (cl @p_171 @p_51) :rule or :premises (t293))
(step t295 (cl @p_51 @p_171) :rule reordering :premises (t294))
(step t296 (cl @p_46 @p_51) :rule resolution :premises (t166 t261 t195 t273 t284 t295))
(step t297 (cl (not @p_73)) :rule not_or :premises (t117) :args (6))
(step t298 (cl @p_50 @p_144) :rule not_and :premises (t297))
(step t299 (cl (not (! (= (! (or @p_50 @p_54) :named @p_55) (! (or @p_50 @p_51) :named @p_52)) :named @p_143)) (not @p_55) @p_52) :rule equiv_pos2)
(step t300 (cl @p_143) :rule cong :premises (t263))
(step t301 (cl (not @p_58)) :rule not_or :premises (t117) :args (5))
(step t302 (cl @p_50 @p_54) :rule not_and :premises (t301))
(step t303 (cl @p_55 @p_57) :rule or_neg :args (0))
(step t304 (cl @p_55 @p_56) :rule or_neg :args (1))
(step t305 (cl @p_55 @p_55) :rule resolution :premises (t302 t303 t304))
(step t306 (cl @p_55) :rule contraction :premises (t305))
(step t307 (cl @p_52) :rule resolution :premises (t299 t300 t306))
(step t308 (cl @p_50 @p_51) :rule or :premises (t307))
(step t309 (cl @p_49 @p_50) :rule resolution :premises (t250 t298 t308))
(step t310 (cl @p_49) :rule resolution :premises (t195 t197 t209 t250 t296 t309))
(step t311 (cl @p_181) :rule resolution :premises (t169 t310))
(step t312 (cl (not @p_72)) :rule not_or :premises (t117) :args (7))
(step t313 (cl @p_87 @p_108) :rule not_and :premises (t312))
(step t314 (cl @p_108 @p_87) :rule reordering :premises (t313))
(step t315 (cl @p_87) :rule resolution :premises (t314 t310))
(step t316 (cl @p_64) :rule resolution :premises (t166 t311 t315))
(step t317 (cl (not @p_77)) :rule not_or :premises (t117) :args (1))
(step t318 (cl @p_108 @p_171) :rule not_and :premises (t317))
(step t319 (cl @p_171) :rule resolution :premises (t318 t310))
(step t320 (cl (not (! (= (! (or @p_108 @p_188) :named @p_240) (! (or @p_108 @p_47) :named @p_239)) :named @p_241)) (not @p_240) @p_239) :rule equiv_pos2)
(step t321 (cl @p_241) :rule cong :premises (t199))
(step t322 (cl (not @p_78)) :rule not_or :premises (t117) :args (0))
(step t323 (cl @p_108 @p_188) :rule not_and :premises (t322))
(step t324 (cl @p_240 @p_109) :rule or_neg :args (0))
(step t325 (cl @p_240 @p_205) :rule or_neg :args (1))
(step t326 (cl @p_240 @p_240) :rule resolution :premises (t323 t324 t325))
(step t327 (cl @p_240) :rule contraction :premises (t326))
(step t328 (cl @p_239) :rule resolution :premises (t320 t321 t327))
(step t329 (cl @p_108 @p_47) :rule or :premises (t328))
(step t330 (cl @p_47) :rule resolution :premises (t329 t310))
(step t331 (cl @p_46) :rule resolution :premises (t195 t319 t330))
(step t332 (cl) :rule resolution :premises (t125 t316 t331))
)
b7edaf1ab035f6066f56cfd46be1017d0ccb56ed 29 0
unsat
(
(assume a0 (! (not (! (or (! (< (! (+ x$ x$) :named @p_3) (! (+ (! (* 2/1 x$) :named @p_1) 1/1) :named @p_2)) :named @p_4) (or false @p_4)) :named @p_5)) :named @p_6))
(step t0 (cl (not (! (= @p_6 false) :named @p_8)) (not @p_6) false) :rule equiv_pos2)
(step t1 (cl (= @p_5 @p_4)) :rule aci_simp)
(step t2 (cl (= @p_4 (! (not (! (>= @p_3 @p_2) :named @p_10)) :named @p_11))) :rule rare_rewrite :args ("arith-elim-lt" @p_3 @p_2))
(step t3 (cl (= @p_3 @p_1)) :rule poly_simp)
(step t4 (cl (= @p_2 (! (+ 1/1 @p_1) :named @p_12))) :rule poly_simp)
(step t5 (cl (= @p_10 (! (>= @p_1 @p_12) :named @p_13))) :rule cong :premises (t3 t4))
(step t6 (cl (= @p_13 (! (>= (! (- @p_1 @p_12) :named @p_14) 0/1) :named @p_15))) :rule rare_rewrite :args ("arith-geq-norm1-real" @p_1 @p_12))
(step t7 (cl (= @p_14 -1/1)) :rule poly_simp)
(step t8 (cl (= 0/1 0/1)) :rule refl)
(step t9 (cl (= @p_15 (! (>= -1/1 0/1) :named @p_16))) :rule cong :premises (t7 t8))
(step t10 (cl (= @p_16 false)) :rule evaluate)
(step t11 (cl (= @p_15 false)) :rule trans :premises (t9 t10))
(step t12 (cl (= @p_13 false)) :rule trans :premises (t6 t11))
(step t13 (cl (= @p_10 false)) :rule trans :premises (t5 t12))
(step t14 (cl (= @p_11 (! (not false) :named @p_7))) :rule cong :premises (t13))
(step t15 (cl (= @p_7 true)) :rule evaluate)
(step t16 (cl (= @p_11 true)) :rule trans :premises (t14 t15))
(step t17 (cl (= @p_4 true)) :rule trans :premises (t2 t16))
(step t18 (cl (= @p_5 true)) :rule trans :premises (t1 t17))
(step t19 (cl (= @p_6 (! (not true) :named @p_9))) :rule cong :premises (t18))
(step t20 (cl (= @p_9 false)) :rule evaluate)
(step t21 (cl @p_8) :rule trans :premises (t19 t20))
(step t22 (cl false) :rule resolution :premises (t0 t21 a0))
(step t23 (cl @p_7) :rule false)
(step t24 (cl) :rule resolution :premises (t22 t23))
)
7e1be4d0d991352dfee98010daece13ff9b0c83f 20 0
unsat
(
(assume a0 (! (not (not (exists ((?v0 Int)) false))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_3)) (not @p_1) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 (exists ((?v0 Int)) false))) :rule rare_rewrite :args ("bool-double-not-elim" (exists ((?v0 Int)) false)))
(step t2 (cl (= (exists ((?v0 Int)) false) (! (not (forall ((?v0 Int)) (not false))) :named @p_4))) :rule connective_def)
(anchor :step t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t3.t0 (cl (= (! (not false) :named @p_2) true)) :rule evaluate)
(step t3 (cl (= (forall ((?v0 Int)) (not false)) (forall ((?v0 Int)) true))) :rule bind)
(step t4 (cl (= (forall ((?v0 Int)) true) true)) :rule qnt_rm_unused)
(step t5 (cl (= (forall ((?v0 Int)) (not false)) true)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_4 (! (not true) :named @p_5))) :rule cong :premises (t5))
(step t7 (cl (= @p_5 false)) :rule evaluate)
(step t8 (cl (= @p_4 false)) :rule trans :premises (t6 t7))
(step t9 (cl (= (exists ((?v0 Int)) false) false)) :rule trans :premises (t2 t8))
(step t10 (cl @p_3) :rule trans :premises (t1 t9))
(step t11 (cl false) :rule resolution :premises (t0 t10 a0))
(step t12 (cl @p_2) :rule false)
(step t13 (cl) :rule resolution :premises (t11 t12))
)
827e00f7c9f7b4172f339044d57373e7d144282f 20 0
unsat
(
(assume a0 (! (not (not (exists ((?v0 Real)) false))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_3)) (not @p_1) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 (exists ((?v0 Real)) false))) :rule rare_rewrite :args ("bool-double-not-elim" (exists ((?v0 Real)) false)))
(step t2 (cl (= (exists ((?v0 Real)) false) (! (not (forall ((?v0 Real)) (not false))) :named @p_4))) :rule connective_def)
(anchor :step t3 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t3.t0 (cl (= (! (not false) :named @p_2) true)) :rule evaluate)
(step t3 (cl (= (forall ((?v0 Real)) (not false)) (forall ((?v0 Real)) true))) :rule bind)
(step t4 (cl (= (forall ((?v0 Real)) true) true)) :rule qnt_rm_unused)
(step t5 (cl (= (forall ((?v0 Real)) (not false)) true)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_4 (! (not true) :named @p_5))) :rule cong :premises (t5))
(step t7 (cl (= @p_5 false)) :rule evaluate)
(step t8 (cl (= @p_4 false)) :rule trans :premises (t6 t7))
(step t9 (cl (= (exists ((?v0 Real)) false) false)) :rule trans :premises (t2 t8))
(step t10 (cl @p_3) :rule trans :premises (t1 t9))
(step t11 (cl false) :rule resolution :premises (t0 t10 a0))
(step t12 (cl @p_2) :rule false)
(step t13 (cl) :rule resolution :premises (t11 t12))
)
085072b0197af56c283180c8959fa75b51e41fcc 74 0
unsat
(
(assume a0 (! (not (forall ((?v0 Int) (?v1 Int)) (=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1))))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_3)) (not @p_1) false) :rule equiv_pos2)
(anchor :step t1 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t1.t0 (cl (= (! (=> (! (and (! (= ?v0 0) :named @p_25) (! (= ?v1 1) :named @p_11)) :named @p_32) (! (not (= ?v0 ?v1)) :named @p_26)) :named @p_33) (! (or (! (not @p_32) :named @p_34) (! (not (= ?v0 ?v1)) :named @p_26)) :named @p_35))) :rule rare_rewrite :args ("bool-impl-elim" @p_32 @p_26))
(step t1.t1 (cl (= @p_34 (! (or (! (not @p_25) :named @p_27) (! (not @p_11) :named @p_14)) :named @p_36))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_25 @p_11 rare-list))
(step t1.t2 (cl (= @p_26 @p_26)) :rule refl)
(step t1.t3 (cl (= @p_35 (! (or @p_36 @p_26) :named @p_37))) :rule cong :premises (t1.t1 t1.t2))
(step t1.t4 (cl (= @p_37 (! (or @p_27 @p_14 @p_26) :named @p_31))) :rule aci_simp)
(step t1.t5 (cl (= @p_35 @p_31)) :rule trans :premises (t1.t3 t1.t4))
(step t1.t6 (cl (= @p_33 @p_31)) :rule trans :premises (t1.t0 t1.t5))
(step t1 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule bind)
(step t2 (cl (= (forall ((?v0 Int) (?v1 Int) (?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule qnt_rm_unused)
(step t3 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int) (?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule symm :premises (t2))
(step t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule qnt_rm_unused)
(step t5 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule trans :premises (t3 t4))
(step t6 (cl (= (forall ((?v1 Int)) (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1))))) (forall ((?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule qnt_join)
(step t7 (cl (= (forall ((?v1 Int) (?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v1 Int)) (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1))))))) :rule symm :premises (t6))
(anchor :step t8 :args ((?v1 Int) (:= (?v1 Int) ?v1)))
(anchor :step t8.t0 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t8.t0.t0 (cl (= @p_31 (! (or @p_27 @p_27 @p_14 @p_26) :named @p_28))) :rule aci_simp)
(step t8.t0 (cl (= (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))))) :rule bind)
(anchor :step t8.t1 :args ((:= (?v0 Int) 0)))
(step t8.t1.t0 (cl (= @p_28 (! (or (! (not (! (= 0 0) :named @p_21)) :named @p_22) @p_22 @p_14 (! (not (! (= 0 ?v1) :named @p_19)) :named @p_20)) :named @p_29))) :rule refl)
(step t8.t1.t1 (cl (= @p_29 (! (or @p_22 @p_14 @p_20) :named @p_23))) :rule rare_rewrite :args ("or-not-refl" 0 (rare-list @p_22 @p_14 @p_20)))
(step t8.t1.t2 (cl (= @p_28 @p_23)) :rule trans :premises (t8.t1.t0 t8.t1.t1))
(step t8.t1 (cl (= (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) @p_23)) :rule onepoint)
(step t8.t2 (cl (= (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) @p_23)) :rule trans :premises (t8.t0 t8.t1))
(step t8 (cl (= (forall ((?v1 Int)) (forall ((?v0 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1))))) (forall ((?v1 Int)) (or (not (= 0 0)) (not (= ?v1 1)) (not (= 0 ?v1)))))) :rule bind)
(step t9 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) (forall ((?v1 Int)) (or (not (= 0 0)) (not (= ?v1 1)) (not (= 0 ?v1)))))) :rule trans :premises (t5 t7 t8))
(anchor :step t10 :args ((?v1 Int) (:= (?v1 Int) ?v1)))
(step t10.t0 (cl (= @p_21 true)) :rule evaluate)
(step t10.t1 (cl (= @p_22 (! (not true) :named @p_4))) :rule cong :premises (t10.t0))
(step t10.t2 (cl (= @p_4 false)) :rule evaluate)
(step t10.t3 (cl (= @p_22 false)) :rule trans :premises (t10.t1 t10.t2))
(step t10.t4 (cl (= @p_14 @p_14)) :rule refl)
(step t10.t5 (cl (= (* 1 (- 0 ?v1)) (* -1 (- ?v1 0)))) :rule poly_simp)
(step t10.t6 (cl (= @p_19 (! (= ?v1 0) :named @p_12))) :rule poly_simp_rel :premises (t10.t5))
(step t10.t7 (cl (= @p_20 (! (not @p_12) :named @p_13))) :rule cong :premises (t10.t6))
(step t10.t8 (cl (= @p_23 (! (or false @p_14 @p_13) :named @p_24))) :rule cong :premises (t10.t3 t10.t4 t10.t7))
(step t10.t9 (cl (= @p_24 (! (or @p_14 @p_13) :named @p_18))) :rule aci_simp)
(step t10.t10 (cl (= @p_23 @p_18)) :rule trans :premises (t10.t8 t10.t9))
(step t10 (cl (= (forall ((?v1 Int)) (or (not (= 0 0)) (not (= ?v1 1)) (not (= 0 ?v1)))) (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 0)))))) :rule bind)
(anchor :step t11 :args ((?v1 Int) (:= (?v1 Int) ?v1)))
(step t11.t0 (cl (= @p_18 (! (or @p_14 @p_14 @p_13) :named @p_15))) :rule aci_simp)
(step t11 (cl (= (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 0)))) (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 1)) (not (= ?v1 0)))))) :rule bind)
(anchor :step t12 :args ((:= (?v1 Int) 1)))
(step t12.t0 (cl (= @p_15 (! (or (! (not (! (= 1 1) :named @p_7)) :named @p_8) @p_8 (! (not (! (= 1 0) :named @p_5)) :named @p_6)) :named @p_16))) :rule refl)
(step t12.t1 (cl (= @p_16 (! (or @p_8 @p_6) :named @p_9))) :rule rare_rewrite :args ("or-not-refl" 1 (rare-list @p_8 @p_6)))
(step t12.t2 (cl (= @p_15 @p_9)) :rule trans :premises (t12.t0 t12.t1))
(step t12 (cl (= (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 1)) (not (= ?v1 0)))) @p_9)) :rule onepoint)
(step t13 (cl (= (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 0)))) @p_9)) :rule trans :premises (t11 t12))
(step t14 (cl (= @p_7 true)) :rule evaluate)
(step t15 (cl (= @p_8 @p_4)) :rule cong :premises (t14))
(step t16 (cl (= @p_4 false)) :rule evaluate)
(step t17 (cl (= @p_8 false)) :rule trans :premises (t15 t16))
(step t18 (cl (= @p_5 false)) :rule evaluate)
(step t19 (cl (= @p_6 (! (not false) :named @p_2))) :rule cong :premises (t18))
(step t20 (cl (= @p_2 true)) :rule evaluate)
(step t21 (cl (= @p_6 true)) :rule trans :premises (t19 t20))
(step t22 (cl (= @p_9 (! (or false true) :named @p_10))) :rule cong :premises (t17 t21))
(step t23 (cl (= @p_10 true)) :rule evaluate)
(step t24 (cl (= @p_9 true)) :rule trans :premises (t22 t23))
(step t25 (cl (= (forall ((?v1 Int)) (or (not (= ?v1 1)) (not (= ?v1 0)))) true)) :rule trans :premises (t13 t24))
(step t26 (cl (= (forall ((?v1 Int)) (or (not (= 0 0)) (not (= ?v1 1)) (not (= 0 ?v1)))) true)) :rule trans :premises (t10 t25))
(step t27 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (not (= ?v0 0)) (not (= ?v1 1)) (not (= ?v0 ?v1)))) true)) :rule trans :premises (t9 t26))
(step t28 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (= ?v0 0) (= ?v1 1)) (not (= ?v0 ?v1)))) true)) :rule trans :premises (t1 t27))
(step t29 (cl (= @p_1 @p_4)) :rule cong :premises (t28))
(step t30 (cl @p_3) :rule trans :premises (t29 t16))
(step t31 (cl false) :rule resolution :premises (t0 t30 a0))
(step t32 (cl @p_2) :rule false)
(step t33 (cl) :rule resolution :premises (t31 t32))
)
5553d39ba54241a30455e028ee1ebdac0efd4fe3 45 0
unsat
(
(assume a0 (! (not (forall ((?v0 Int) (?v1 Int)) (=> (< ?v0 ?v1) (< (+ (* 2 ?v0) 1) (* 2 ?v1))))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_2)) (not @p_1) false) :rule equiv_pos2)
(anchor :step t1 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t1.t0 (cl (= (! (< ?v0 ?v1) :named @p_17) (! (not (! (>= ?v0 ?v1) :named @p_26)) :named @p_27))) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v1))
(step t1.t1 (cl (= (* 1 (- ?v0 ?v1)) (* 1 (- (! (+ ?v0 (* -1 ?v1)) :named @p_6) 0)))) :rule poly_simp)
(step t1.t2 (cl (= @p_26 (! (>= @p_6 0) :named @p_7))) :rule poly_simp_rel :premises (t1.t1))
(step t1.t3 (cl (= @p_27 (! (not @p_7) :named @p_8))) :rule cong :premises (t1.t2))
(step t1.t4 (cl (= @p_17 @p_8)) :rule trans :premises (t1.t0 t1.t3))
(step t1.t5 (cl (= (! (< (! (+ (! (* 2 ?v0) :named @p_14) 1) :named @p_15) (! (* 2 ?v1) :named @p_13)) :named @p_16) (! (not (! (>= @p_15 @p_13) :named @p_18)) :named @p_19))) :rule rare_rewrite :args ("arith-elim-lt" @p_15 @p_13))
(step t1.t6 (cl (= @p_15 (! (+ 1 @p_14) :named @p_20))) :rule poly_simp)
(step t1.t7 (cl (= @p_13 @p_13)) :rule refl)
(step t1.t8 (cl (= @p_18 (! (>= @p_20 @p_13) :named @p_21))) :rule cong :premises (t1.t6 t1.t7))
(step t1.t9 (cl (= (* 1/2 (to_real (- @p_20 @p_13))) (* 1/1 (- (! (to_real @p_6) :named @p_22) -1/2)))) :rule poly_simp)
(step t1.t10 (cl (= @p_21 (! (>= @p_22 -1/2) :named @p_23))) :rule poly_simp_rel :premises (t1.t9))
(step t1.t11 (cl (= (= (to_real (! (to_int -1/2) :named @p_24)) -1/2) false)) :rule evaluate)
(step t1.t12 (cl (= (! (+ @p_24 1) :named @p_25) 0)) :rule evaluate)
(step t1.t13 (cl (= 0 @p_25)) :rule symm :premises (t1.t12))
(step t1.t14 (cl (= @p_23 @p_7)) :rule rare_rewrite :premises (t1.t11 t1.t13) :args ("arith-int-geq-tighten" @p_6 -1/2 0))
(step t1.t15 (cl (= @p_21 @p_7)) :rule trans :premises (t1.t10 t1.t14))
(step t1.t16 (cl (= @p_18 @p_7)) :rule trans :premises (t1.t8 t1.t15))
(step t1.t17 (cl (= @p_19 @p_8)) :rule cong :premises (t1.t16))
(step t1.t18 (cl (= @p_16 @p_8)) :rule trans :premises (t1.t5 t1.t17))
(step t1.t19 (cl (= (=> @p_17 @p_16) (! (=> @p_8 @p_8) :named @p_9))) :rule cong :premises (t1.t4 t1.t18))
(step t1 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (< ?v0 ?v1) (< (+ (* 2 ?v0) 1) (* 2 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (=> (not (>= (+ ?v0 (* -1 ?v1)) 0)) (not (>= (+ ?v0 (* -1 ?v1)) 0)))))) :rule bind)
(anchor :step t2 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t2.t0 (cl (= @p_9 (! (or (! (not @p_8) :named @p_11) @p_8) :named @p_12))) :rule rare_rewrite :args ("bool-impl-elim" @p_8 @p_8))
(step t2.t1 (cl (= @p_11 @p_7)) :rule rare_rewrite :args ("bool-double-not-elim" @p_7))
(step t2.t2 (cl (= @p_8 @p_8)) :rule refl)
(step t2.t3 (cl (= @p_12 (! (or @p_7 @p_8) :named @p_10))) :rule cong :premises (t2.t1 t2.t2))
(step t2.t4 (cl (= @p_9 @p_10)) :rule trans :premises (t2.t0 t2.t3))
(step t2.t5 (cl (= @p_10 true)) :rule rare_rewrite :args ("bool-or-taut" rare-list @p_7 rare-list rare-list))
(step t2.t6 (cl (= @p_9 true)) :rule trans :premises (t2.t4 t2.t5))
(step t2 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (>= (+ ?v0 (* -1 ?v1)) 0)) (not (>= (+ ?v0 (* -1 ?v1)) 0)))) (forall ((?v0 Int) (?v1 Int)) true))) :rule bind)
(step t3 (cl (= (forall ((?v0 Int) (?v1 Int)) true) true)) :rule qnt_rm_unused)
(step t4 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (>= (+ ?v0 (* -1 ?v1)) 0)) (not (>= (+ ?v0 (* -1 ?v1)) 0)))) true)) :rule trans :premises (t2 t3))
(step t5 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (< ?v0 ?v1) (< (+ (* 2 ?v0) 1) (* 2 ?v1)))) true)) :rule trans :premises (t1 t4))
(step t6 (cl (= @p_1 (! (not true) :named @p_3))) :rule cong :premises (t5))
(step t7 (cl (= @p_3 false)) :rule evaluate)
(step t8 (cl @p_2) :rule trans :premises (t6 t7))
(step t9 (cl false) :rule resolution :premises (t0 t8 a0))
(step t10 (cl (not false)) :rule false)
(step t11 (cl) :rule resolution :premises (t9 t10))
)
f05d5fb28015c674508ec9a67736e8c43fb7248a 70 0
unsat
(
(define-fun @quantifiers_skolemize_2 () Int (choice ((?v0 Int)) (not (forall ((?v1 Int)) (or (>= (+ ?v0 ?v1) 3) (= ?v0 (+ 2 (* -1 ?v1))) (not (>= (+ ?v0 ?v1) 2)))))))
(define-fun @quantifiers_skolemize_3 () Int (choice ((?v1 Int)) (not (or (>= (+ @quantifiers_skolemize_2 ?v1) 3) (= @quantifiers_skolemize_2 (+ 2 (* -1 ?v1))) (not (>= (+ @quantifiers_skolemize_2 ?v1) 2))))))
(assume a0 (! (not (forall ((?v0 Int) (?v1 Int)) (or (< 2 (+ ?v0 ?v1)) (or (= (+ ?v0 ?v1) 2) (< (+ ?v0 ?v1) 2))))) :named @p_1))
(step t0 (cl (not (! (= (! (or (! (or (! (>= (! (+ @quantifiers_skolemize_2 @quantifiers_skolemize_3) :named @p_2) 3) :named @p_10) (! (= @quantifiers_skolemize_2 (! (+ 2 (* -1 @quantifiers_skolemize_3)) :named @p_12)) :named @p_13) (! (not (! (>= @p_2 2) :named @p_3)) :named @p_4)) :named @p_14) (! (not @p_4) :named @p_44)) :named @p_45) (! (or @p_14 @p_3) :named @p_43)) :named @p_46)) (not @p_45) @p_43) :rule equiv_pos2)
(step t1 (cl (= @p_44 @p_3)) :rule rare_rewrite :args ("bool-double-not-elim" @p_3))
(step t2 (cl @p_46) :rule cong :premises (t1))
(step t3 (cl @p_14 @p_44) :rule or_neg :args (2))
(step t4 (cl @p_45 (! (not @p_14) :named @p_15)) :rule or_neg :args (0))
(step t5 (cl @p_45 (not @p_44)) :rule or_neg :args (1))
(step t6 (cl @p_45 @p_45) :rule resolution :premises (t3 t4 t5))
(step t7 (cl @p_45) :rule contraction :premises (t6))
(step t8 (cl @p_43) :rule resolution :premises (t0 t2 t7))
(step t9 (cl @p_14 @p_3) :rule or :premises (t8))
(step t10 (cl @p_3 @p_14) :rule reordering :premises (t9))
(step t11 (cl (not (! (= (! (not (forall ((?v0 Int) (?v1 Int)) (or (>= (+ ?v0 ?v1) 3) (= ?v0 (+ 2 (* -1 ?v1))) (not (>= (+ ?v0 ?v1) 2))))) :named @p_16) @p_15) :named @p_35)) (not @p_16) @p_15) :rule equiv_pos2)
(anchor :step t12 :args ((:= (?v0 Int) @quantifiers_skolemize_2) (:= (?v1 Int) @quantifiers_skolemize_3)))
(step t12.t0 (cl (= (! (or (! (>= (! (+ ?v0 ?v1) :named @p_18) 3) :named @p_22) (! (= ?v0 (! (+ 2 (* -1 ?v1)) :named @p_20)) :named @p_21) (! (not (>= @p_18 2)) :named @p_19)) :named @p_23) @p_14)) :rule refl)
(step t12 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (>= (+ ?v0 ?v1) 3) (= ?v0 (+ 2 (* -1 ?v1))) (not (>= (+ ?v0 ?v1) 2)))) @p_14)) :rule sko_forall)
(step t13 (cl @p_35) :rule cong :premises (t12))
(step t14 (cl (not (! (= @p_1 @p_16) :named @p_17)) (not @p_1) @p_16) :rule equiv_pos2)
(anchor :step t15 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t15.t0 (cl (= (! (or (! (< 2 @p_18) :named @p_26) (or (! (= @p_18 2) :named @p_25) (! (< @p_18 2) :named @p_24))) :named @p_27) (! (or @p_26 @p_25 @p_24) :named @p_28))) :rule aci_simp)
(step t15.t1 (cl (= @p_26 (! (not (! (>= 2 @p_18) :named @p_29)) :named @p_30))) :rule rare_rewrite :args ("arith-elim-lt" 2 @p_18))
(step t15.t2 (cl (= (! (not @p_22) :named @p_31) (! (>= 3 (! (+ @p_18 1) :named @p_33)) :named @p_34))) :rule rare_rewrite :args ("arith-geq-tighten" @p_18 3))
(step t15.t3 (cl (= (* 2 (- 3 @p_33)) (* 2 (- 2 @p_18)))) :rule poly_simp)
(step t15.t4 (cl (= @p_34 @p_29)) :rule poly_simp_rel :premises (t15.t3))
(step t15.t5 (cl (= @p_31 @p_29)) :rule trans :premises (t15.t2 t15.t4))
(step t15.t6 (cl (= @p_29 @p_31)) :rule symm :premises (t15.t5))
(step t15.t7 (cl (= @p_30 (! (not @p_31) :named @p_32))) :rule cong :premises (t15.t6))
(step t15.t8 (cl (= @p_32 @p_22)) :rule rare_rewrite :args ("bool-double-not-elim" @p_22))
(step t15.t9 (cl (= @p_30 @p_22)) :rule trans :premises (t15.t7 t15.t8))
(step t15.t10 (cl (= @p_26 @p_22)) :rule trans :premises (t15.t1 t15.t9))
(step t15.t11 (cl (= (* -2 (- @p_18 2)) (* -2 (- ?v0 @p_20)))) :rule poly_simp)
(step t15.t12 (cl (= @p_25 @p_21)) :rule poly_simp_rel :premises (t15.t11))
(step t15.t13 (cl (= @p_24 @p_19)) :rule rare_rewrite :args ("arith-elim-lt" @p_18 2))
(step t15.t14 (cl (= @p_28 @p_23)) :rule cong :premises (t15.t10 t15.t12 t15.t13))
(step t15.t15 (cl (= @p_27 @p_23)) :rule trans :premises (t15.t0 t15.t14))
(step t15 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (< 2 (+ ?v0 ?v1)) (or (= (+ ?v0 ?v1) 2) (< (+ ?v0 ?v1) 2)))) (forall ((?v0 Int) (?v1 Int)) (or (>= (+ ?v0 ?v1) 3) (= ?v0 (+ 2 (* -1 ?v1))) (not (>= (+ ?v0 ?v1) 2)))))) :rule bind)
(step t16 (cl @p_17) :rule cong :premises (t15))
(step t17 (cl @p_16) :rule resolution :premises (t14 t16 a0))
(step t18 (cl @p_15) :rule resolution :premises (t11 t13 t17))
(step t19 (cl @p_3) :rule resolution :premises (t10 t18))
(step t20 (cl (not (! (= (! (< @p_2 2) :named @p_5) @p_4) :named @p_42)) (not @p_5) @p_4) :rule equiv_pos2)
(step t21 (cl @p_42) :rule rare_rewrite :args ("arith-elim-lt" @p_2 2))
(step t22 (cl (or (! (= @p_2 2) :named @p_37) (! (not (! (<= @p_2 2) :named @p_8)) :named @p_41) (! (not (<= 2 @p_2)) :named @p_6))) :rule la_disequality)
(step t23 (cl @p_37 @p_41 @p_6) :rule or :premises (t22))
(step t24 (cl (not (! (= (! (not @p_13) :named @p_39) (! (not @p_37) :named @p_38)) :named @p_40)) (not @p_39) @p_38) :rule equiv_pos2)
(step t25 (cl (= (* -2 (- @p_2 2)) (* -2 (- @quantifiers_skolemize_2 @p_12)))) :rule poly_simp)
(step t26 (cl (= @p_37 @p_13)) :rule poly_simp_rel :premises (t25))
(step t27 (cl (= @p_38 @p_39)) :rule cong :premises (t26))
(step t28 (cl @p_40) :rule symm :premises (t27))
(step t29 (cl @p_14 @p_39) :rule or_neg :args (1))
(step t30 (cl @p_39) :rule resolution :premises (t29 t18))
(step t31 (cl @p_38) :rule resolution :premises (t24 t28 t30))
(step t32 (cl (not (! (< @p_2 3) :named @p_9)) @p_8) :rule la_generic :args (1/1 1/1))
(step t33 (cl (not (! (= (! (not @p_10) :named @p_11) @p_9) :named @p_36)) (not @p_11) @p_9) :rule equiv_pos2)
(step t34 (cl (= @p_9 @p_11)) :rule rare_rewrite :args ("arith-elim-lt" @p_2 3))
(step t35 (cl @p_36) :rule symm :premises (t34))
(step t36 (cl @p_14 @p_11) :rule or_neg :args (0))
(step t37 (cl @p_11) :rule resolution :premises (t36 t18))
(step t38 (cl @p_9) :rule resolution :premises (t33 t35 t37))
(step t39 (cl @p_8) :rule resolution :premises (t32 t38))
(step t40 (cl (not (! (= @p_5 @p_6) :named @p_7)) @p_5 (not @p_6)) :rule equiv_pos1)
(step t41 (cl @p_7) :rule comp_simplify)
(step t42 (cl @p_5) :rule resolution :premises (t23 t31 t39 t40 t41))
(step t43 (cl @p_4) :rule resolution :premises (t20 t21 t42))
(step t44 (cl) :rule resolution :premises (t19 t43))
)
c0b0a5f5683a5ffdb226e84feffb1a9ea5607c83 86 0
unsat
(
(define-fun @quantifiers_skolemize_2 () Int (choice ((?v0 Int)) (not (or (not (>= ?v0 1)) (>= ?v0 0)))))
(assume a0 (! (not (forall ((?v0 Int)) (ite (< 0 ?v0) (< 0 (+ ?v0 1)) (< ?v0 1)))) :named @p_1))
(step t0 (cl (not (! (= (! (<= (! (+ @quantifiers_skolemize_2 (! (* -1 @quantifiers_skolemize_2) :named @p_4)) :named @p_5) (! (+ -1 (! (* -1 1) :named @p_2)) :named @p_3)) :named @p_6) false) :named @p_49)) (not @p_6) false) :rule equiv_pos2)
(step t1 (cl (= @p_5 0)) :rule poly_simp)
(step t2 (cl (= @p_2 -1)) :rule evaluate)
(step t3 (cl (= @p_3 (! (+ -1 -1) :named @p_51))) :rule cong :premises (t2))
(step t4 (cl (= @p_51 -2)) :rule evaluate)
(step t5 (cl (= @p_3 -2)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_6 (! (<= 0 -2) :named @p_50))) :rule cong :premises (t1 t5))
(step t7 (cl (= @p_50 false)) :rule evaluate)
(step t8 (cl @p_49) :rule trans :premises (t6 t7))
(step t9 (cl (not (! (<= @quantifiers_skolemize_2 -1) :named @p_45)) (not (! (<= @p_4 @p_2) :named @p_7)) @p_6) :rule la_generic :args (1/1 1/1 1/1))
(step t10 (cl (not (! (< @quantifiers_skolemize_2 0) :named @p_46)) @p_45) :rule la_generic :args (1/1 1/1))
(step t11 (cl (not (! (= (! (not (! (>= @quantifiers_skolemize_2 0) :named @p_11)) :named @p_47) @p_46) :named @p_48)) (not @p_47) @p_46) :rule equiv_pos2)
(step t12 (cl (= @p_46 @p_47)) :rule rare_rewrite :args ("arith-elim-lt" @quantifiers_skolemize_2 0))
(step t13 (cl @p_48) :rule symm :premises (t12))
(step t14 (cl (! (or (! (not (! (>= @quantifiers_skolemize_2 1) :named @p_8)) :named @p_12) @p_11) :named @p_13) @p_47) :rule or_neg :args (1))
(step t15 (cl (not (! (= (! (not (forall ((?v0 Int)) (or (not (>= ?v0 1)) (>= ?v0 0)))) :named @p_15) (! (not @p_13) :named @p_14)) :named @p_39)) (not @p_15) @p_14) :rule equiv_pos2)
(anchor :step t16 :args ((:= (?v0 Int) @quantifiers_skolemize_2)))
(step t16.t0 (cl (= (! (or (! (not (! (>= ?v0 1) :named @p_18)) :named @p_19) (! (>= ?v0 0) :named @p_17)) :named @p_20) @p_13)) :rule refl)
(step t16 (cl (= (forall ((?v0 Int)) (or (not (>= ?v0 1)) (>= ?v0 0))) @p_13)) :rule sko_forall)
(step t17 (cl @p_39) :rule cong :premises (t16))
(step t18 (cl (not (! (= @p_1 @p_15) :named @p_16)) (not @p_1) @p_15) :rule equiv_pos2)
(anchor :step t19 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t19.t0 (cl (= (! (< 0 ?v0) :named @p_24) (! (not (! (>= 0 ?v0) :named @p_35)) :named @p_36))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v0))
(step t19.t1 (cl (= @p_19 (! (>= 1 (! (+ ?v0 1) :named @p_22)) :named @p_38))) :rule rare_rewrite :args ("arith-geq-tighten" ?v0 1))
(step t19.t2 (cl (= (* -1 (- 1 @p_22)) (* -1 (- 0 ?v0)))) :rule poly_simp)
(step t19.t3 (cl (= @p_38 @p_35)) :rule poly_simp_rel :premises (t19.t2))
(step t19.t4 (cl (= @p_19 @p_35)) :rule trans :premises (t19.t1 t19.t3))
(step t19.t5 (cl (= @p_35 @p_19)) :rule symm :premises (t19.t4))
(step t19.t6 (cl (= @p_36 (! (not @p_19) :named @p_37))) :rule cong :premises (t19.t5))
(step t19.t7 (cl (= @p_37 @p_18)) :rule rare_rewrite :args ("bool-double-not-elim" @p_18))
(step t19.t8 (cl (= @p_36 @p_18)) :rule trans :premises (t19.t6 t19.t7))
(step t19.t9 (cl (= @p_24 @p_18)) :rule trans :premises (t19.t0 t19.t8))
(step t19.t10 (cl (= (! (< 0 @p_22) :named @p_23) (! (not (! (>= 0 @p_22) :named @p_28)) :named @p_29))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_22))
(step t19.t11 (cl (= @p_22 (! (+ 1 ?v0) :named @p_32))) :rule poly_simp)
(step t19.t12 (cl (! (= @p_28 (! (>= 0 @p_32) :named @p_33)) :named @p_34)) :rule cong :premises (t19.t11))
(step t19.t13 (cl (= (! (not @p_17) :named @p_30) @p_28)) :rule rare_rewrite :args ("arith-geq-tighten" ?v0 0))
(step t19.t14 (cl @p_34) :rule cong :premises (t19.t11))
(step t19.t15 (cl (= @p_30 @p_33)) :rule trans :premises (t19.t13 t19.t14))
(step t19.t16 (cl (= @p_33 @p_30)) :rule symm :premises (t19.t15))
(step t19.t17 (cl (= @p_28 @p_30)) :rule trans :premises (t19.t12 t19.t16))
(step t19.t18 (cl (= @p_29 (! (not @p_30) :named @p_31))) :rule cong :premises (t19.t17))
(step t19.t19 (cl (= @p_31 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t19.t20 (cl (= @p_29 @p_17)) :rule trans :premises (t19.t18 t19.t19))
(step t19.t21 (cl (= @p_23 @p_17)) :rule trans :premises (t19.t10 t19.t20))
(step t19.t22 (cl (= (! (< ?v0 1) :named @p_21) @p_19)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 1))
(step t19.t23 (cl (= (! (ite @p_24 @p_23 @p_21) :named @p_25) (! (ite @p_18 @p_17 @p_19) :named @p_26))) :rule cong :premises (t19.t9 t19.t21 t19.t22))
(step t19.t24 (cl (= @p_26 (! (ite @p_18 @p_17 true) :named @p_27))) :rule rare_rewrite :args ("ite-else-lookahead-not-self" @p_18 @p_17))
(step t19.t25 (cl (= @p_27 @p_20)) :rule rare_rewrite :args ("ite-else-true" @p_18 @p_17))
(step t19.t26 (cl (= @p_26 @p_20)) :rule trans :premises (t19.t24 t19.t25))
(step t19.t27 (cl (= @p_25 @p_20)) :rule trans :premises (t19.t23 t19.t26))
(step t19 (cl (= (forall ((?v0 Int)) (ite (< 0 ?v0) (< 0 (+ ?v0 1)) (< ?v0 1))) (forall ((?v0 Int)) (or (not (>= ?v0 1)) (>= ?v0 0))))) :rule bind)
(step t20 (cl @p_16) :rule cong :premises (t19))
(step t21 (cl @p_15) :rule resolution :premises (t18 t20 a0))
(step t22 (cl @p_14) :rule resolution :premises (t15 t17 t21))
(step t23 (cl @p_47) :rule resolution :premises (t14 t22))
(step t24 (cl @p_46) :rule resolution :premises (t11 t13 t23))
(step t25 (cl @p_45) :rule resolution :premises (t10 t24))
(step t26 (cl (=> (! (and (! (< -1 0) :named @p_9) @p_8) :named @p_10) @p_7)) :rule la_mult_neg)
(step t27 (cl (not @p_10) @p_7) :rule implies :premises (t26))
(step t28 (cl (= (! (= @p_9 true) :named @p_44) @p_9)) :rule equiv_simplify)
(step t29 (cl (not @p_44) @p_9) :rule equiv1 :premises (t28))
(step t30 (cl @p_44) :rule evaluate)
(step t31 (cl @p_9) :rule resolution :premises (t29 t30))
(step t32 (cl (not (! (= (! (or @p_13 (! (not @p_12) :named @p_41)) :named @p_42) (! (or @p_13 @p_8) :named @p_40)) :named @p_43)) (not @p_42) @p_40) :rule equiv_pos2)
(step t33 (cl (= @p_41 @p_8)) :rule rare_rewrite :args ("bool-double-not-elim" @p_8))
(step t34 (cl @p_43) :rule cong :premises (t33))
(step t35 (cl @p_13 @p_41) :rule or_neg :args (0))
(step t36 (cl @p_42 @p_14) :rule or_neg :args (0))
(step t37 (cl @p_42 (not @p_41)) :rule or_neg :args (1))
(step t38 (cl @p_42 @p_42) :rule resolution :premises (t35 t36 t37))
(step t39 (cl @p_42) :rule contraction :premises (t38))
(step t40 (cl @p_40) :rule resolution :premises (t32 t34 t39))
(step t41 (cl @p_13 @p_8) :rule or :premises (t40))
(step t42 (cl @p_8 @p_13) :rule reordering :premises (t41))
(step t43 (cl @p_8) :rule resolution :premises (t42 t22))
(step t44 (cl @p_10) :rule and_intro :premises (t31 t43))
(step t45 (cl @p_7) :rule resolution :premises (t27 t44))
(step t46 (cl @p_6) :rule resolution :premises (t9 t25 t45))
(step t47 (cl false) :rule resolution :premises (t0 t8 t46))
(step t48 (cl (not false)) :rule false)
(step t49 (cl) :rule resolution :premises (t47 t48))
)
12facc545f505db323cbdaf15d6437ff9f64af5a 270 0
unsat
(
(define-fun @quantifiers_skolemize_2 () Int (choice ((?v1 Int)) (not (forall ((?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))))
(define-fun @quantifiers_skolemize_3 () Int (choice ((?v2 Int)) (not (or (not (>= @quantifiers_skolemize_2 1)) (not (>= ?v2 1)) (>= (+ @quantifiers_skolemize_2 ?v2) 1)))))
(assume a0 (! (not (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2)))))) :named @p_1))
(step t0 (cl (not (! (= (! (or (! (not (! (>= @quantifiers_skolemize_2 1) :named @p_2)) :named @p_7) (! (not (! (>= @quantifiers_skolemize_3 1) :named @p_5)) :named @p_6) (! (not (! (not (! (>= (! (+ @quantifiers_skolemize_2 @quantifiers_skolemize_3) :named @p_3) 1) :named @p_4)) :named @p_58)) :named @p_59)) :named @p_60) (! (or @p_7 @p_6 @p_4) :named @p_8)) :named @p_91)) (not @p_60) @p_8) :rule equiv_pos2)
(step t1 (cl (= @p_59 @p_4)) :rule rare_rewrite :args ("bool-double-not-elim" @p_4))
(step t2 (cl @p_91) :rule cong :premises (t1))
(step t3 (cl (! (=> (! (and @p_2 @p_5 @p_58) :named @p_61) false) :named @p_63) @p_61) :rule implies_neg1)
(anchor :step t4)
(assume t4.a0 @p_2)
(assume t4.a1 @p_5)
(assume t4.a2 @p_58)
(step t4.t0 (cl (! (not (! (= @p_58 (! (< @p_3 1) :named @p_65)) :named @p_80)) :named @p_81) @p_59 @p_65) :rule equiv_pos2)
(step t4.t1 (cl (= @p_65 @p_58)) :rule rare_rewrite :args ("arith-elim-lt" @p_3 1))
(step t4.t2 (cl @p_80) :rule symm :premises (t4.t1))
(step t4.t3 (cl @p_8 @p_58) :rule or_neg :args (2))
(step t4.t4 (cl (not (! (= (! (not (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))) :named @p_10) (! (not @p_8) :named @p_9)) :named @p_49)) (! (not @p_10) :named @p_13) @p_9) :rule equiv_pos2)
(anchor :step t4.t5 :args ((:= (?v1 Int) @quantifiers_skolemize_2) (:= (?v2 Int) @quantifiers_skolemize_3)))
(step t4.t5.t0 (cl (= (! (or (! (not (! (>= ?v1 1) :named @p_20)) :named @p_21) (! (not (! (>= ?v2 1) :named @p_18)) :named @p_19) (! (>= (! (+ ?v1 ?v2) :named @p_16) 1) :named @p_17)) :named @p_22) @p_8)) :rule refl)
(step t4.t5 (cl (= (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))) @p_8)) :rule sko_forall)
(step t4.t6 (cl @p_49) :rule cong :premises (t4.t5))
(step t4.t7 (cl (not (! (= @p_1 @p_10) :named @p_11)) (not @p_1) @p_10) :rule equiv_pos2)
(anchor :step t4.t8 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(anchor :step t4.t8.t0 :args ((?v1 Int) (?v2 Int) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t4.t8.t0.t0 (cl (= (! (< 0 ?v1) :named @p_31) (! (not (! (>= 0 ?v1) :named @p_44)) :named @p_45))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v1))
(step t4.t8.t0.t1 (cl (= @p_21 (! (>= 1 (! (+ ?v1 1) :named @p_47)) :named @p_48))) :rule rare_rewrite :args ("arith-geq-tighten" ?v1 1))
(step t4.t8.t0.t2 (cl (= (* -1 (- 1 @p_47)) (* -1 (- 0 ?v1)))) :rule poly_simp)
(step t4.t8.t0.t3 (cl (= @p_48 @p_44)) :rule poly_simp_rel :premises (t4.t8.t0.t2))
(step t4.t8.t0.t4 (cl (= @p_21 @p_44)) :rule trans :premises (t4.t8.t0.t1 t4.t8.t0.t3))
(step t4.t8.t0.t5 (cl (= @p_44 @p_21)) :rule symm :premises (t4.t8.t0.t4))
(step t4.t8.t0.t6 (cl (= @p_45 (! (not @p_21) :named @p_46))) :rule cong :premises (t4.t8.t0.t5))
(step t4.t8.t0.t7 (cl (= @p_46 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t4.t8.t0.t8 (cl (= @p_45 @p_20)) :rule trans :premises (t4.t8.t0.t6 t4.t8.t0.t7))
(step t4.t8.t0.t9 (cl (= @p_31 @p_20)) :rule trans :premises (t4.t8.t0.t0 t4.t8.t0.t8))
(step t4.t8.t0.t10 (cl (= (! (< 0 ?v2) :named @p_30) (! (not (! (>= 0 ?v2) :named @p_39)) :named @p_40))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v2))
(step t4.t8.t0.t11 (cl (= @p_19 (! (>= 1 (! (+ ?v2 1) :named @p_42)) :named @p_43))) :rule rare_rewrite :args ("arith-geq-tighten" ?v2 1))
(step t4.t8.t0.t12 (cl (= (* -1 (- 1 @p_42)) (* -1 (- 0 ?v2)))) :rule poly_simp)
(step t4.t8.t0.t13 (cl (= @p_43 @p_39)) :rule poly_simp_rel :premises (t4.t8.t0.t12))
(step t4.t8.t0.t14 (cl (= @p_19 @p_39)) :rule trans :premises (t4.t8.t0.t11 t4.t8.t0.t13))
(step t4.t8.t0.t15 (cl (= @p_39 @p_19)) :rule symm :premises (t4.t8.t0.t14))
(step t4.t8.t0.t16 (cl (= @p_40 (! (not @p_19) :named @p_41))) :rule cong :premises (t4.t8.t0.t15))
(step t4.t8.t0.t17 (cl (= @p_41 @p_18)) :rule rare_rewrite :args ("bool-double-not-elim" @p_18))
(step t4.t8.t0.t18 (cl (= @p_40 @p_18)) :rule trans :premises (t4.t8.t0.t16 t4.t8.t0.t17))
(step t4.t8.t0.t19 (cl (= @p_30 @p_18)) :rule trans :premises (t4.t8.t0.t10 t4.t8.t0.t18))
(step t4.t8.t0.t20 (cl (= (! (and @p_31 @p_30) :named @p_32) (! (and @p_20 @p_18) :named @p_23))) :rule cong :premises (t4.t8.t0.t9 t4.t8.t0.t19))
(step t4.t8.t0.t21 (cl (= (! (< 0 @p_16) :named @p_29) (! (not (! (>= 0 @p_16) :named @p_33)) :named @p_34))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_16))
(step t4.t8.t0.t22 (cl (= (! (not @p_17) :named @p_35) (! (>= 1 (! (+ @p_16 1) :named @p_37)) :named @p_38))) :rule rare_rewrite :args ("arith-geq-tighten" @p_16 1))
(step t4.t8.t0.t23 (cl (= (* -1 (- 1 @p_37)) (* -1 (- 0 @p_16)))) :rule poly_simp)
(step t4.t8.t0.t24 (cl (= @p_38 @p_33)) :rule poly_simp_rel :premises (t4.t8.t0.t23))
(step t4.t8.t0.t25 (cl (= @p_35 @p_33)) :rule trans :premises (t4.t8.t0.t22 t4.t8.t0.t24))
(step t4.t8.t0.t26 (cl (= @p_33 @p_35)) :rule symm :premises (t4.t8.t0.t25))
(step t4.t8.t0.t27 (cl (= @p_34 (! (not @p_35) :named @p_36))) :rule cong :premises (t4.t8.t0.t26))
(step t4.t8.t0.t28 (cl (= @p_36 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t4.t8.t0.t29 (cl (= @p_34 @p_17)) :rule trans :premises (t4.t8.t0.t27 t4.t8.t0.t28))
(step t4.t8.t0.t30 (cl (= @p_29 @p_17)) :rule trans :premises (t4.t8.t0.t21 t4.t8.t0.t29))
(step t4.t8.t0.t31 (cl (= (=> @p_32 @p_29) (! (=> @p_23 @p_17) :named @p_24))) :rule cong :premises (t4.t8.t0.t20 t4.t8.t0.t30))
(step t4.t8.t0 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2)))) (forall ((?v1 Int) (?v2 Int)) (=> (and (>= ?v1 1) (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule bind)
(anchor :step t4.t8.t1 :args ((?v1 Int) (?v2 Int) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t4.t8.t1.t0 (cl (= @p_24 (! (or (! (not @p_23) :named @p_25) @p_17) :named @p_26))) :rule rare_rewrite :args ("bool-impl-elim" @p_23 @p_17))
(step t4.t8.t1.t1 (cl (= @p_25 (! (or @p_21 @p_19) :named @p_27))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_20 @p_18 rare-list))
(step t4.t8.t1.t2 (cl (= @p_17 @p_17)) :rule refl)
(step t4.t8.t1.t3 (cl (= @p_26 (! (or @p_27 @p_17) :named @p_28))) :rule cong :premises (t4.t8.t1.t1 t4.t8.t1.t2))
(step t4.t8.t1.t4 (cl (= @p_28 @p_22)) :rule aci_simp)
(step t4.t8.t1.t5 (cl (= @p_26 @p_22)) :rule trans :premises (t4.t8.t1.t3 t4.t8.t1.t4))
(step t4.t8.t1.t6 (cl (= @p_24 @p_22)) :rule trans :premises (t4.t8.t1.t0 t4.t8.t1.t5))
(step t4.t8.t1 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (>= ?v1 1) (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule bind)
(step t4.t8.t2 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2)))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t4.t8.t0 t4.t8.t1))
(step t4.t8 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))) (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))))) :rule bind)
(step t4.t9 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))) (! (not (forall ((?v0 Int)) (not (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))))) :named @p_12))) :rule connective_def)
(step t4.t10 (cl (= (forall ((?v0 Int)) (not (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) @p_10)) :rule qnt_rm_unused)
(step t4.t11 (cl (= @p_12 @p_13)) :rule cong :premises (t4.t10))
(step t4.t12 (cl (= @p_13 (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))))
(step t4.t13 (cl (= @p_12 (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t4.t11 t4.t12))
(step t4.t14 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t4.t9 t4.t13))
(step t4.t15 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t4.t8 t4.t14))
(step t4.t16 (cl @p_11) :rule cong :premises (t4.t15))
(step t4.t17 (cl @p_10) :rule resolution :premises (t4.t7 t4.t16 a0))
(step t4.t18 (cl @p_9) :rule resolution :premises (t4.t4 t4.t6 t4.t17))
(step t4.t19 (cl @p_58) :rule resolution :premises (t4.t3 t4.t18))
(step t4.t20 (cl @p_65) :rule resolution :premises (t4.t0 t4.t2 t4.t19))
(step t4.t21 (cl (not (! (= @p_4 (! (not @p_65) :named @p_66)) :named @p_90)) @p_58 @p_66) :rule equiv_pos2)
(step t4.t22 (cl (= @p_66 @p_59)) :rule cong :premises (t4.t1))
(step t4.t23 (cl (! (= @p_66 @p_4) :named @p_89)) :rule trans :premises (t4.t22 t1))
(step t4.t24 (cl @p_90) :rule symm :premises (t4.t23))
(step t4.t25 (cl (not @p_89) (not @p_66) @p_4) :rule equiv_pos2)
(step t4.t26 (cl (! (=> @p_65 false) :named @p_67) @p_65) :rule implies_neg1)
(anchor :step t4.t27)
(assume t4.t27.a0 @p_65)
(step t4.t27.t0 (cl (not (! (= (! (< (! (+ @p_3 (! (* -1 @quantifiers_skolemize_3) :named @p_71) (! (* -1 @quantifiers_skolemize_2) :named @p_70)) :named @p_72) (! (+ 1 (! (* -1 1) :named @p_68) @p_68) :named @p_69)) :named @p_73) false) :named @p_82)) (not @p_73) false) :rule equiv_pos2)
(step t4.t27.t1 (cl (= @p_73 (! (not (! (>= @p_72 @p_69) :named @p_83)) :named @p_84))) :rule rare_rewrite :args ("arith-elim-lt" @p_72 @p_69))
(step t4.t27.t2 (cl (= @p_72 (! (+ @p_70 @p_71 @quantifiers_skolemize_3 @quantifiers_skolemize_2) :named @p_88))) :rule poly_simp)
(step t4.t27.t3 (cl (= @p_88 0)) :rule poly_simp)
(step t4.t27.t4 (cl (= @p_72 0)) :rule trans :premises (t4.t27.t2 t4.t27.t3))
(step t4.t27.t5 (cl (= @p_68 -1)) :rule evaluate)
(step t4.t27.t6 (cl (= @p_69 (! (+ 1 -1 -1) :named @p_87))) :rule cong :premises (t4.t27.t5 t4.t27.t5))
(step t4.t27.t7 (cl (= @p_87 -1)) :rule evaluate)
(step t4.t27.t8 (cl (= @p_69 -1)) :rule trans :premises (t4.t27.t6 t4.t27.t7))
(step t4.t27.t9 (cl (= @p_83 (! (>= 0 -1) :named @p_86))) :rule cong :premises (t4.t27.t4 t4.t27.t8))
(step t4.t27.t10 (cl (= @p_86 true)) :rule evaluate)
(step t4.t27.t11 (cl (= @p_83 true)) :rule trans :premises (t4.t27.t9 t4.t27.t10))
(step t4.t27.t12 (cl (= @p_84 (! (not true) :named @p_85))) :rule cong :premises (t4.t27.t11))
(step t4.t27.t13 (cl (= @p_85 false)) :rule evaluate)
(step t4.t27.t14 (cl (= @p_84 false)) :rule trans :premises (t4.t27.t12 t4.t27.t13))
(step t4.t27.t15 (cl @p_82) :rule trans :premises (t4.t27.t1 t4.t27.t14))
(step t4.t27.t16 (cl @p_66 (not (! (<= @p_71 @p_68) :named @p_78)) (not (! (<= @p_70 @p_68) :named @p_74)) @p_73) :rule la_generic :args (1/1 1/1 1/1 1/1))
(step t4.t27.t17 (cl @p_81 @p_59 @p_65) :rule equiv_pos2)
(step t4.t27.t18 (cl @p_58) :rule resolution :premises (t4.t3 t4.t18))
(step t4.t27.t19 (cl @p_65) :rule resolution :premises (t4.t27.t17 t4.t2 t4.t27.t18))
(step t4.t27.t20 (cl (=> (! (and (! (< -1 0) :named @p_75) @p_5) :named @p_79) @p_78)) :rule la_mult_neg)
(step t4.t27.t21 (cl (not @p_79) @p_78) :rule implies :premises (t4.t27.t20))
(step t4.t27.t22 (cl (= (! (= @p_75 true) :named @p_77) @p_75)) :rule equiv_simplify)
(step t4.t27.t23 (cl (not @p_77) @p_75) :rule equiv1 :premises (t4.t27.t22))
(step t4.t27.t24 (cl @p_77) :rule evaluate)
(step t4.t27.t25 (cl @p_75) :rule resolution :premises (t4.t27.t23 t4.t27.t24))
(step t4.t27.t26 (cl (not (! (= (! (or @p_8 (! (not @p_6) :named @p_55)) :named @p_56) (! (or @p_8 @p_5) :named @p_54)) :named @p_57)) (not @p_56) @p_54) :rule equiv_pos2)
(step t4.t27.t27 (cl (= @p_55 @p_5)) :rule rare_rewrite :args ("bool-double-not-elim" @p_5))
(step t4.t27.t28 (cl @p_57) :rule cong :premises (t4.t27.t27))
(step t4.t27.t29 (cl @p_8 @p_55) :rule or_neg :args (1))
(step t4.t27.t30 (cl @p_56 @p_9) :rule or_neg :args (0))
(step t4.t27.t31 (cl @p_56 (not @p_55)) :rule or_neg :args (1))
(step t4.t27.t32 (cl @p_56 @p_56) :rule resolution :premises (t4.t27.t29 t4.t27.t30 t4.t27.t31))
(step t4.t27.t33 (cl @p_56) :rule contraction :premises (t4.t27.t32))
(step t4.t27.t34 (cl @p_54) :rule resolution :premises (t4.t27.t26 t4.t27.t28 t4.t27.t33))
(step t4.t27.t35 (cl @p_8 @p_5) :rule or :premises (t4.t27.t34))
(step t4.t27.t36 (cl @p_5 @p_8) :rule reordering :premises (t4.t27.t35))
(step t4.t27.t37 (cl @p_5) :rule resolution :premises (t4.t27.t36 t4.t18))
(step t4.t27.t38 (cl @p_79) :rule and_intro :premises (t4.t27.t25 t4.t27.t37))
(step t4.t27.t39 (cl @p_78) :rule resolution :premises (t4.t27.t21 t4.t27.t38))
(step t4.t27.t40 (cl (=> (! (and @p_75 @p_2) :named @p_76) @p_74)) :rule la_mult_neg)
(step t4.t27.t41 (cl (not @p_76) @p_74) :rule implies :premises (t4.t27.t40))
(step t4.t27.t42 (cl (not (! (= (! (or @p_8 (! (not @p_7) :named @p_51)) :named @p_52) (! (or @p_8 @p_2) :named @p_50)) :named @p_53)) (not @p_52) @p_50) :rule equiv_pos2)
(step t4.t27.t43 (cl (= @p_51 @p_2)) :rule rare_rewrite :args ("bool-double-not-elim" @p_2))
(step t4.t27.t44 (cl @p_53) :rule cong :premises (t4.t27.t43))
(step t4.t27.t45 (cl @p_8 @p_51) :rule or_neg :args (0))
(step t4.t27.t46 (cl @p_52 @p_9) :rule or_neg :args (0))
(step t4.t27.t47 (cl @p_52 (not @p_51)) :rule or_neg :args (1))
(step t4.t27.t48 (cl @p_52 @p_52) :rule resolution :premises (t4.t27.t45 t4.t27.t46 t4.t27.t47))
(step t4.t27.t49 (cl @p_52) :rule contraction :premises (t4.t27.t48))
(step t4.t27.t50 (cl @p_50) :rule resolution :premises (t4.t27.t42 t4.t27.t44 t4.t27.t49))
(step t4.t27.t51 (cl @p_8 @p_2) :rule or :premises (t4.t27.t50))
(step t4.t27.t52 (cl @p_2 @p_8) :rule reordering :premises (t4.t27.t51))
(step t4.t27.t53 (cl @p_2) :rule resolution :premises (t4.t27.t52 t4.t18))
(step t4.t27.t54 (cl @p_76) :rule and_intro :premises (t4.t27.t25 t4.t27.t53))
(step t4.t27.t55 (cl @p_74) :rule resolution :premises (t4.t27.t41 t4.t27.t54))
(step t4.t27.t56 (cl @p_73) :rule resolution :premises (t4.t27.t16 t4.t27.t19 t4.t27.t39 t4.t27.t55))
(step t4.t27.t57 (cl false) :rule resolution :premises (t4.t27.t0 t4.t27.t15 t4.t27.t56))
(step t4.t27 (cl @p_66 false) :rule subproof :discharge (t4.t27.a0))
(step t4.t28 (cl @p_67 false) :rule resolution :premises (t4.t26 t4.t27))
(step t4.t29 (cl @p_67 (! (not false) :named @p_64)) :rule implies_neg2)
(step t4.t30 (cl @p_67 @p_67) :rule resolution :premises (t4.t28 t4.t29))
(step t4.t31 (cl @p_67) :rule contraction :premises (t4.t30))
(step t4.t32 (cl (= @p_67 @p_66)) :rule implies_simplify)
(step t4.t33 (cl (not @p_67) @p_66) :rule equiv1 :premises (t4.t32))
(step t4.t34 (cl @p_66) :rule resolution :premises (t4.t31 t4.t33))
(step t4.t35 (cl @p_4) :rule resolution :premises (t4.t25 t4.t23 t4.t34))
(step t4.t36 (cl @p_66) :rule resolution :premises (t4.t21 t4.t24 t4.t35))
(step t4.t37 (cl) :rule resolution :premises (t4.t20 t4.t36))
(step t4 (cl @p_7 @p_6 @p_59 false) :rule subproof :discharge (t4.a0 t4.a1 t4.a2))
(step t5 (cl (! (not @p_61) :named @p_62) @p_2) :rule and_pos :args (0))
(step t6 (cl @p_62 @p_5) :rule and_pos :args (1))
(step t7 (cl @p_62 @p_58) :rule and_pos :args (2))
(step t8 (cl false @p_62 @p_62 @p_62) :rule resolution :premises (t4 t5 t6 t7))
(step t9 (cl @p_62 @p_62 @p_62 false) :rule reordering :premises (t8))
(step t10 (cl @p_62 false) :rule contraction :premises (t9))
(step t11 (cl @p_63 false) :rule resolution :premises (t3 t10))
(step t12 (cl @p_63 @p_64) :rule implies_neg2)
(step t13 (cl @p_63 @p_63) :rule resolution :premises (t11 t12))
(step t14 (cl @p_63) :rule contraction :premises (t13))
(step t15 (cl (= @p_63 @p_62)) :rule implies_simplify)
(step t16 (cl (not @p_63) @p_62) :rule equiv1 :premises (t15))
(step t17 (cl @p_62) :rule resolution :premises (t14 t16))
(step t18 (cl @p_7 @p_6 @p_59) :rule not_and :premises (t17))
(step t19 (cl @p_60 @p_51) :rule or_neg :args (0))
(step t20 (cl @p_60 @p_55) :rule or_neg :args (1))
(step t21 (cl @p_60 (not @p_59)) :rule or_neg :args (2))
(step t22 (cl @p_60 @p_60 @p_60) :rule resolution :premises (t18 t19 t20 t21))
(step t23 (cl @p_60) :rule contraction :premises (t22))
(step t24 (cl @p_8) :rule resolution :premises (t0 t2 t23))
(step t25 (cl @p_7 @p_6 @p_4) :rule or :premises (t24))
(step t26 (cl @p_8 @p_58) :rule or_neg :args (2))
(step t27 (cl (not @p_49) @p_13 @p_9) :rule equiv_pos2)
(anchor :step t28 :args ((:= (?v1 Int) @quantifiers_skolemize_2) (:= (?v2 Int) @quantifiers_skolemize_3)))
(step t28.t0 (cl (= @p_22 @p_8)) :rule refl)
(step t28 (cl (= (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))) @p_8)) :rule sko_forall)
(step t29 (cl @p_49) :rule cong :premises (t28))
(step t30 (cl (not @p_11) (not @p_1) @p_10) :rule equiv_pos2)
(anchor :step t31 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(anchor :step t31.t0 :args ((?v1 Int) (?v2 Int) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t31.t0.t0 (cl (= @p_31 @p_45)) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v1))
(step t31.t0.t1 (cl (= @p_21 @p_48)) :rule rare_rewrite :args ("arith-geq-tighten" ?v1 1))
(step t31.t0.t2 (cl (= (* -1 (- 1 @p_47)) (* -1 (- 0 ?v1)))) :rule poly_simp)
(step t31.t0.t3 (cl (= @p_48 @p_44)) :rule poly_simp_rel :premises (t31.t0.t2))
(step t31.t0.t4 (cl (= @p_21 @p_44)) :rule trans :premises (t31.t0.t1 t31.t0.t3))
(step t31.t0.t5 (cl (= @p_44 @p_21)) :rule symm :premises (t31.t0.t4))
(step t31.t0.t6 (cl (= @p_45 @p_46)) :rule cong :premises (t31.t0.t5))
(step t31.t0.t7 (cl (= @p_46 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t31.t0.t8 (cl (= @p_45 @p_20)) :rule trans :premises (t31.t0.t6 t31.t0.t7))
(step t31.t0.t9 (cl (= @p_31 @p_20)) :rule trans :premises (t31.t0.t0 t31.t0.t8))
(step t31.t0.t10 (cl (= @p_30 @p_40)) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v2))
(step t31.t0.t11 (cl (= @p_19 @p_43)) :rule rare_rewrite :args ("arith-geq-tighten" ?v2 1))
(step t31.t0.t12 (cl (= (* -1 (- 1 @p_42)) (* -1 (- 0 ?v2)))) :rule poly_simp)
(step t31.t0.t13 (cl (= @p_43 @p_39)) :rule poly_simp_rel :premises (t31.t0.t12))
(step t31.t0.t14 (cl (= @p_19 @p_39)) :rule trans :premises (t31.t0.t11 t31.t0.t13))
(step t31.t0.t15 (cl (= @p_39 @p_19)) :rule symm :premises (t31.t0.t14))
(step t31.t0.t16 (cl (= @p_40 @p_41)) :rule cong :premises (t31.t0.t15))
(step t31.t0.t17 (cl (= @p_41 @p_18)) :rule rare_rewrite :args ("bool-double-not-elim" @p_18))
(step t31.t0.t18 (cl (= @p_40 @p_18)) :rule trans :premises (t31.t0.t16 t31.t0.t17))
(step t31.t0.t19 (cl (= @p_30 @p_18)) :rule trans :premises (t31.t0.t10 t31.t0.t18))
(step t31.t0.t20 (cl (= @p_32 @p_23)) :rule cong :premises (t31.t0.t9 t31.t0.t19))
(step t31.t0.t21 (cl (= @p_29 @p_34)) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_16))
(step t31.t0.t22 (cl (= @p_35 @p_38)) :rule rare_rewrite :args ("arith-geq-tighten" @p_16 1))
(step t31.t0.t23 (cl (= (* -1 (- 1 @p_37)) (* -1 (- 0 @p_16)))) :rule poly_simp)
(step t31.t0.t24 (cl (= @p_38 @p_33)) :rule poly_simp_rel :premises (t31.t0.t23))
(step t31.t0.t25 (cl (= @p_35 @p_33)) :rule trans :premises (t31.t0.t22 t31.t0.t24))
(step t31.t0.t26 (cl (= @p_33 @p_35)) :rule symm :premises (t31.t0.t25))
(step t31.t0.t27 (cl (= @p_34 @p_36)) :rule cong :premises (t31.t0.t26))
(step t31.t0.t28 (cl (= @p_36 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t31.t0.t29 (cl (= @p_34 @p_17)) :rule trans :premises (t31.t0.t27 t31.t0.t28))
(step t31.t0.t30 (cl (= @p_29 @p_17)) :rule trans :premises (t31.t0.t21 t31.t0.t29))
(step t31.t0.t31 (cl (= (=> @p_32 @p_29) @p_24)) :rule cong :premises (t31.t0.t20 t31.t0.t30))
(step t31.t0 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2)))) (forall ((?v1 Int) (?v2 Int)) (=> (and (>= ?v1 1) (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule bind)
(anchor :step t31.t1 :args ((?v1 Int) (?v2 Int) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t31.t1.t0 (cl (= @p_24 @p_26)) :rule rare_rewrite :args ("bool-impl-elim" @p_23 @p_17))
(step t31.t1.t1 (cl (= @p_25 @p_27)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_20 @p_18 rare-list))
(step t31.t1.t2 (cl (= @p_17 @p_17)) :rule refl)
(step t31.t1.t3 (cl (= @p_26 @p_28)) :rule cong :premises (t31.t1.t1 t31.t1.t2))
(step t31.t1.t4 (cl (= @p_28 @p_22)) :rule aci_simp)
(step t31.t1.t5 (cl (= @p_26 @p_22)) :rule trans :premises (t31.t1.t3 t31.t1.t4))
(step t31.t1.t6 (cl (= @p_24 @p_22)) :rule trans :premises (t31.t1.t0 t31.t1.t5))
(step t31.t1 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (>= ?v1 1) (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule bind)
(step t31.t2 (cl (= (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2)))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t31.t0 t31.t1))
(step t31 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))) (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))))) :rule bind)
(step t32 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))) @p_12)) :rule connective_def)
(step t33 (cl (= (forall ((?v0 Int)) (not (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) @p_10)) :rule qnt_rm_unused)
(step t34 (cl (= @p_12 @p_13)) :rule cong :premises (t33))
(step t35 (cl (= @p_13 (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))))
(step t36 (cl (= @p_12 (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t34 t35))
(step t37 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1)))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t32 t36))
(step t38 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Int)) (=> (and (< 0 ?v1) (< 0 ?v2)) (< 0 (+ ?v1 ?v2))))) (forall ((?v1 Int) (?v2 Int)) (or (not (>= ?v1 1)) (not (>= ?v2 1)) (>= (+ ?v1 ?v2) 1))))) :rule trans :premises (t31 t37))
(step t39 (cl @p_11) :rule cong :premises (t38))
(step t40 (cl @p_10) :rule resolution :premises (t30 t39 a0))
(step t41 (cl @p_9) :rule resolution :premises (t27 t29 t40))
(step t42 (cl @p_58) :rule resolution :premises (t26 t41))
(step t43 (cl (not @p_57) (not @p_56) @p_54) :rule equiv_pos2)
(step t44 (cl (= @p_55 @p_5)) :rule rare_rewrite :args ("bool-double-not-elim" @p_5))
(step t45 (cl @p_57) :rule cong :premises (t44))
(step t46 (cl @p_8 @p_55) :rule or_neg :args (1))
(step t47 (cl @p_56 @p_9) :rule or_neg :args (0))
(step t48 (cl @p_56 (not @p_55)) :rule or_neg :args (1))
(step t49 (cl @p_56 @p_56) :rule resolution :premises (t46 t47 t48))
(step t50 (cl @p_56) :rule contraction :premises (t49))
(step t51 (cl @p_54) :rule resolution :premises (t43 t45 t50))
(step t52 (cl @p_8 @p_5) :rule or :premises (t51))
(step t53 (cl @p_5 @p_8) :rule reordering :premises (t52))
(step t54 (cl @p_5) :rule resolution :premises (t53 t41))
(step t55 (cl (not @p_53) (not @p_52) @p_50) :rule equiv_pos2)
(step t56 (cl (= @p_51 @p_2)) :rule rare_rewrite :args ("bool-double-not-elim" @p_2))
(step t57 (cl @p_53) :rule cong :premises (t56))
(step t58 (cl @p_8 @p_51) :rule or_neg :args (0))
(step t59 (cl @p_52 @p_9) :rule or_neg :args (0))
(step t60 (cl @p_52 (not @p_51)) :rule or_neg :args (1))
(step t61 (cl @p_52 @p_52) :rule resolution :premises (t58 t59 t60))
(step t62 (cl @p_52) :rule contraction :premises (t61))
(step t63 (cl @p_50) :rule resolution :premises (t55 t57 t62))
(step t64 (cl @p_8 @p_2) :rule or :premises (t63))
(step t65 (cl @p_2 @p_8) :rule reordering :premises (t64))
(step t66 (cl @p_2) :rule resolution :premises (t65 t41))
(step t67 (cl) :rule resolution :premises (t25 t42 t54 t66))
)
cf50d85b2da62042de0d190564d7957d8b01003d 281 0
unsat
(
(assume a0 (! (not (! (< 0 (! (ite (forall ((?v0 Int)) (or (< ?v0 0) (< 0 ?v0))) (! (- 1) :named @p_1) 3) :named @p_2)) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= (! (or (! (not (! (= (! (ite (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) -1 3) :named @p_5) 3) :named @p_30)) :named @p_47) (! (not (! (not (! (>= @p_5 1) :named @p_6)) :named @p_7)) :named @p_15)) :named @p_49) (! (or @p_47 @p_6) :named @p_48)) :named @p_77)) (not @p_49) @p_48) :rule equiv_pos2)
(step t1 (cl (! (= @p_15 @p_6) :named @p_16)) :rule rare_rewrite :args ("bool-double-not-elim" @p_6))
(step t2 (cl @p_77) :rule cong :premises (t1))
(step t3 (cl (! (=> (! (and @p_30 @p_7) :named @p_50) (! (and (! (= 3 @p_5) :named @p_52) @p_7) :named @p_53)) :named @p_75) @p_50) :rule implies_neg1)
(anchor :step t4)
(assume t4.a0 @p_30)
(assume t4.a1 @p_7)
(step t4.t0 (cl (! (=> @p_30 @p_52) :named @p_76) @p_30) :rule implies_neg1)
(anchor :step t4.t1)
(assume t4.t1.a0 @p_30)
(step t4.t1.t0 (cl @p_52) :rule symm :premises (t4.t1.a0))
(step t4.t1 (cl @p_47 @p_52) :rule subproof :discharge (t4.t1.a0))
(step t4.t2 (cl @p_76 @p_52) :rule resolution :premises (t4.t0 t4.t1))
(step t4.t3 (cl @p_76 (! (not @p_52) :named @p_57)) :rule implies_neg2)
(step t4.t4 (cl @p_76 @p_76) :rule resolution :premises (t4.t2 t4.t3))
(step t4.t5 (cl @p_76) :rule contraction :premises (t4.t4))
(step t4.t6 (cl @p_47 @p_52) :rule implies :premises (t4.t5))
(step t4.t7 (cl @p_52) :rule resolution :premises (t4.t6 t4.a0))
(step t4.t8 (cl (not (! (= @p_4 @p_7) :named @p_8)) (not @p_4) @p_7) :rule equiv_pos2)
(step t4.t9 (cl (= @p_3 (! (not (! (>= 0 @p_2) :named @p_13)) :named @p_14))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_2))
(anchor :step t4.t10 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t4.t10.t0 (cl (= (! (< ?v0 0) :named @p_23) (! (not (>= ?v0 0)) :named @p_21))) :rule rare_rewrite :args ("arith-elim-lt" ?v0 0))
(step t4.t10.t1 (cl (= (! (< 0 ?v0) :named @p_22) (! (not (! (>= 0 ?v0) :named @p_24)) :named @p_25))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v0))
(step t4.t10.t2 (cl (= (! (not (! (>= ?v0 1) :named @p_20)) :named @p_26) (! (>= 1 (! (+ ?v0 1) :named @p_28)) :named @p_29))) :rule rare_rewrite :args ("arith-geq-tighten" ?v0 1))
(step t4.t10.t3 (cl (= (* -1 (- 1 @p_28)) (* -1 (- 0 ?v0)))) :rule poly_simp)
(step t4.t10.t4 (cl (= @p_29 @p_24)) :rule poly_simp_rel :premises (t4.t10.t3))
(step t4.t10.t5 (cl (= @p_26 @p_24)) :rule trans :premises (t4.t10.t2 t4.t10.t4))
(step t4.t10.t6 (cl (= @p_24 @p_26)) :rule symm :premises (t4.t10.t5))
(step t4.t10.t7 (cl (= @p_25 (! (not @p_26) :named @p_27))) :rule cong :premises (t4.t10.t6))
(step t4.t10.t8 (cl (= @p_27 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t4.t10.t9 (cl (= @p_25 @p_20)) :rule trans :premises (t4.t10.t7 t4.t10.t8))
(step t4.t10.t10 (cl (= @p_22 @p_20)) :rule trans :premises (t4.t10.t1 t4.t10.t9))
(step t4.t10.t11 (cl (= (or @p_23 @p_22) (or @p_21 @p_20))) :rule cong :premises (t4.t10.t0 t4.t10.t10))
(step t4.t10 (cl (= (forall ((?v0 Int)) (or (< ?v0 0) (< 0 ?v0))) (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))))) :rule bind)
(step t4.t11 (cl (= @p_1 -1)) :rule evaluate)
(step t4.t12 (cl (= 3 3)) :rule refl)
(step t4.t13 (cl (= @p_2 @p_5)) :rule cong :premises (t4.t10 t4.t11 t4.t12))
(step t4.t14 (cl (= @p_13 (! (>= 0 @p_5) :named @p_17))) :rule cong :premises (t4.t13))
(step t4.t15 (cl (= @p_7 (! (>= 1 (! (+ @p_5 1) :named @p_18)) :named @p_19))) :rule rare_rewrite :args ("arith-geq-tighten" @p_5 1))
(step t4.t16 (cl (= (* -1 (- 1 @p_18)) (* -1 (- 0 @p_5)))) :rule poly_simp)
(step t4.t17 (cl (= @p_19 @p_17)) :rule poly_simp_rel :premises (t4.t16))
(step t4.t18 (cl (= @p_7 @p_17)) :rule trans :premises (t4.t15 t4.t17))
(step t4.t19 (cl (= @p_17 @p_7)) :rule symm :premises (t4.t18))
(step t4.t20 (cl (= @p_13 @p_7)) :rule trans :premises (t4.t14 t4.t19))
(step t4.t21 (cl (= @p_14 @p_15)) :rule cong :premises (t4.t20))
(step t4.t22 (cl @p_16) :rule rare_rewrite :args ("bool-double-not-elim" @p_6))
(step t4.t23 (cl (= @p_14 @p_6)) :rule trans :premises (t4.t21 t4.t22))
(step t4.t24 (cl (= @p_3 @p_6)) :rule trans :premises (t4.t9 t4.t23))
(step t4.t25 (cl @p_8) :rule cong :premises (t4.t24))
(step t4.t26 (cl (= (! (= (! (= @p_5 @p_5) :named @p_9) true) :named @p_10) @p_9)) :rule equiv_simplify)
(step t4.t27 (cl (not @p_10) @p_9) :rule equiv1 :premises (t4.t26))
(step t4.t28 (cl (= (* -1 (! (- @p_5 @p_5) :named @p_12)) (* 1 @p_12))) :rule poly_simp)
(step t4.t29 (cl (! (= @p_9 @p_9) :named @p_11)) :rule poly_simp_rel :premises (t4.t28))
(step t4.t30 (cl @p_9) :rule refl)
(step t4.t31 (cl @p_9) :rule refl)
(step t4.t32 (cl @p_11) :rule cong :premises (t4.t30 t4.t31))
(step t4.t33 (cl @p_10) :rule rare_rewrite :args ("eq-refl" @p_5))
(step t4.t34 (cl @p_10) :rule trans :premises (t4.t29 t4.t32 t4.t33))
(step t4.t35 (cl @p_9) :rule resolution :premises (t4.t27 t4.t34))
(step t4.t36 (cl (= 1 1)) :rule refl)
(step t4.t37 (cl (= @p_6 @p_6)) :rule cong :premises (t4.t35 t4.t36))
(step t4.t38 (cl (= @p_7 @p_7)) :rule cong :premises (t4.t37))
(step t4.t39 (cl @p_8) :rule trans :premises (t4.t25 t4.t38))
(step t4.t40 (cl @p_7) :rule resolution :premises (t4.t8 t4.t39 a0))
(step t4.t41 (cl @p_53) :rule and_intro :premises (t4.t7 t4.t40))
(step t4 (cl @p_47 @p_15 @p_53) :rule subproof :discharge (t4.a0 t4.a1))
(step t5 (cl (! (not @p_50) :named @p_51) @p_30) :rule and_pos :args (0))
(step t6 (cl @p_51 @p_7) :rule and_pos :args (1))
(step t7 (cl @p_53 @p_51 @p_51) :rule resolution :premises (t4 t5 t6))
(step t8 (cl @p_51 @p_51 @p_53) :rule reordering :premises (t7))
(step t9 (cl @p_51 @p_53) :rule contraction :premises (t8))
(step t10 (cl @p_75 @p_53) :rule resolution :premises (t3 t9))
(step t11 (cl @p_75 (! (not @p_53) :named @p_54)) :rule implies_neg2)
(step t12 (cl @p_75 @p_75) :rule resolution :premises (t10 t11))
(step t13 (cl @p_75) :rule contraction :premises (t12))
(step t14 (cl @p_51 @p_53) :rule implies :premises (t13))
(step t15 (cl (! (=> @p_53 false) :named @p_55) @p_53) :rule implies_neg1)
(anchor :step t16)
(assume t16.a0 @p_52)
(assume t16.a1 @p_7)
(step t16.t0 (cl @p_30) :rule symm :premises (t16.a0))
(step t16.t1 (cl (! (=> @p_30 false) :named @p_58) @p_30) :rule implies_neg1)
(anchor :step t16.t2)
(assume t16.t2.a0 @p_30)
(step t16.t2.t0 (cl (not (! (= (! (<= (! (+ (! (* -1 @p_5) :named @p_61) @p_5) :named @p_62) (! (+ (! (* -1 3) :named @p_59) 0) :named @p_60)) :named @p_63) false) :named @p_72)) (not @p_63) false) :rule equiv_pos2)
(step t16.t2.t1 (cl (= @p_62 0)) :rule poly_simp)
(step t16.t2.t2 (cl (= @p_59 -3)) :rule evaluate)
(step t16.t2.t3 (cl (= 0 0)) :rule refl)
(step t16.t2.t4 (cl (= @p_60 (! (+ -3 0) :named @p_74))) :rule cong :premises (t16.t2.t2 t16.t2.t3))
(step t16.t2.t5 (cl (= @p_74 -3)) :rule evaluate)
(step t16.t2.t6 (cl (= @p_60 -3)) :rule trans :premises (t16.t2.t4 t16.t2.t5))
(step t16.t2.t7 (cl (= @p_63 (! (<= 0 -3) :named @p_73))) :rule cong :premises (t16.t2.t1 t16.t2.t6))
(step t16.t2.t8 (cl (= @p_73 false)) :rule evaluate)
(step t16.t2.t9 (cl @p_72) :rule trans :premises (t16.t2.t7 t16.t2.t8))
(step t16.t2.t10 (cl (not (! (= @p_61 @p_59) :named @p_67)) (not (! (<= @p_5 0) :named @p_64)) @p_63) :rule la_generic :args (-1/1 1/1 1/1))
(step t16.t2.t11 (cl (=> (! (and (! (< -1 0) :named @p_68) @p_30) :named @p_69) @p_67)) :rule la_mult_neg)
(step t16.t2.t12 (cl (not @p_69) @p_67) :rule implies :premises (t16.t2.t11))
(step t16.t2.t13 (cl (= (! (= @p_68 true) :named @p_71) @p_68)) :rule equiv_simplify)
(step t16.t2.t14 (cl (not @p_71) @p_68) :rule equiv1 :premises (t16.t2.t13))
(step t16.t2.t15 (cl @p_71) :rule evaluate)
(step t16.t2.t16 (cl @p_68) :rule resolution :premises (t16.t2.t14 t16.t2.t15))
(step t16.t2.t17 (cl @p_69) :rule and_intro :premises (t16.t2.t16 t16.t2.a0))
(step t16.t2.t18 (cl @p_67) :rule resolution :premises (t16.t2.t12 t16.t2.t17))
(step t16.t2.t19 (cl (not (! (< @p_5 1) :named @p_65)) @p_64) :rule la_generic :args (1/1 1/1))
(step t16.t2.t20 (cl (not (! (= @p_7 @p_65) :named @p_66)) @p_15 @p_65) :rule equiv_pos2)
(step t16.t2.t21 (cl (= @p_65 @p_7)) :rule rare_rewrite :args ("arith-elim-lt" @p_5 1))
(step t16.t2.t22 (cl @p_66) :rule symm :premises (t16.t2.t21))
(step t16.t2.t23 (cl (not @p_8) (not @p_4) @p_7) :rule equiv_pos2)
(step t16.t2.t24 (cl (= @p_3 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_2))
(anchor :step t16.t2.t25 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t16.t2.t25.t0 (cl (= @p_23 @p_21)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 0))
(step t16.t2.t25.t1 (cl (= @p_22 @p_25)) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v0))
(step t16.t2.t25.t2 (cl (= @p_26 @p_29)) :rule rare_rewrite :args ("arith-geq-tighten" ?v0 1))
(step t16.t2.t25.t3 (cl (= (* -1 (- 1 @p_28)) (* -1 (- 0 ?v0)))) :rule poly_simp)
(step t16.t2.t25.t4 (cl (= @p_29 @p_24)) :rule poly_simp_rel :premises (t16.t2.t25.t3))
(step t16.t2.t25.t5 (cl (= @p_26 @p_24)) :rule trans :premises (t16.t2.t25.t2 t16.t2.t25.t4))
(step t16.t2.t25.t6 (cl (= @p_24 @p_26)) :rule symm :premises (t16.t2.t25.t5))
(step t16.t2.t25.t7 (cl (= @p_25 @p_27)) :rule cong :premises (t16.t2.t25.t6))
(step t16.t2.t25.t8 (cl (= @p_27 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t16.t2.t25.t9 (cl (= @p_25 @p_20)) :rule trans :premises (t16.t2.t25.t7 t16.t2.t25.t8))
(step t16.t2.t25.t10 (cl (= @p_22 @p_20)) :rule trans :premises (t16.t2.t25.t1 t16.t2.t25.t9))
(step t16.t2.t25.t11 (cl (= (or @p_23 @p_22) (or @p_21 @p_20))) :rule cong :premises (t16.t2.t25.t0 t16.t2.t25.t10))
(step t16.t2.t25 (cl (= (forall ((?v0 Int)) (or (< ?v0 0) (< 0 ?v0))) (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))))) :rule bind)
(step t16.t2.t26 (cl (= @p_1 -1)) :rule evaluate)
(step t16.t2.t27 (cl (= 3 3)) :rule refl)
(step t16.t2.t28 (cl (= @p_2 @p_5)) :rule cong :premises (t16.t2.t25 t16.t2.t26 t16.t2.t27))
(step t16.t2.t29 (cl (= @p_13 @p_17)) :rule cong :premises (t16.t2.t28))
(step t16.t2.t30 (cl (= @p_7 @p_19)) :rule rare_rewrite :args ("arith-geq-tighten" @p_5 1))
(step t16.t2.t31 (cl (= (* -1 (- 1 @p_18)) (* -1 (- 0 @p_5)))) :rule poly_simp)
(step t16.t2.t32 (cl (= @p_19 @p_17)) :rule poly_simp_rel :premises (t16.t2.t31))
(step t16.t2.t33 (cl (= @p_7 @p_17)) :rule trans :premises (t16.t2.t30 t16.t2.t32))
(step t16.t2.t34 (cl (= @p_17 @p_7)) :rule symm :premises (t16.t2.t33))
(step t16.t2.t35 (cl (= @p_13 @p_7)) :rule trans :premises (t16.t2.t29 t16.t2.t34))
(step t16.t2.t36 (cl (= @p_14 @p_15)) :rule cong :premises (t16.t2.t35))
(step t16.t2.t37 (cl @p_16) :rule rare_rewrite :args ("bool-double-not-elim" @p_6))
(step t16.t2.t38 (cl (= @p_14 @p_6)) :rule trans :premises (t16.t2.t36 t16.t2.t37))
(step t16.t2.t39 (cl (= @p_3 @p_6)) :rule trans :premises (t16.t2.t24 t16.t2.t38))
(step t16.t2.t40 (cl @p_8) :rule cong :premises (t16.t2.t39))
(step t16.t2.t41 (cl (= @p_10 @p_9)) :rule equiv_simplify)
(step t16.t2.t42 (cl (not @p_10) @p_9) :rule equiv1 :premises (t16.t2.t41))
(step t16.t2.t43 (cl (= (* -1 @p_12) (* 1 @p_12))) :rule poly_simp)
(step t16.t2.t44 (cl @p_11) :rule poly_simp_rel :premises (t16.t2.t43))
(step t16.t2.t45 (cl @p_9) :rule refl)
(step t16.t2.t46 (cl @p_9) :rule refl)
(step t16.t2.t47 (cl @p_11) :rule cong :premises (t16.t2.t45 t16.t2.t46))
(step t16.t2.t48 (cl @p_10) :rule rare_rewrite :args ("eq-refl" @p_5))
(step t16.t2.t49 (cl @p_10) :rule trans :premises (t16.t2.t44 t16.t2.t47 t16.t2.t48))
(step t16.t2.t50 (cl @p_9) :rule resolution :premises (t16.t2.t42 t16.t2.t49))
(step t16.t2.t51 (cl (= 1 1)) :rule refl)
(step t16.t2.t52 (cl (= @p_6 @p_6)) :rule cong :premises (t16.t2.t50 t16.t2.t51))
(step t16.t2.t53 (cl (= @p_7 @p_7)) :rule cong :premises (t16.t2.t52))
(step t16.t2.t54 (cl @p_8) :rule trans :premises (t16.t2.t40 t16.t2.t53))
(step t16.t2.t55 (cl @p_7) :rule resolution :premises (t16.t2.t23 t16.t2.t54 a0))
(step t16.t2.t56 (cl @p_65) :rule resolution :premises (t16.t2.t20 t16.t2.t22 t16.t2.t55))
(step t16.t2.t57 (cl @p_64) :rule resolution :premises (t16.t2.t19 t16.t2.t56))
(step t16.t2.t58 (cl @p_63) :rule resolution :premises (t16.t2.t10 t16.t2.t18 t16.t2.t57))
(step t16.t2.t59 (cl false) :rule resolution :premises (t16.t2.t0 t16.t2.t9 t16.t2.t58))
(step t16.t2 (cl @p_47 false) :rule subproof :discharge (t16.t2.a0))
(step t16.t3 (cl @p_58 false) :rule resolution :premises (t16.t1 t16.t2))
(step t16.t4 (cl @p_58 (! (not false) :named @p_56)) :rule implies_neg2)
(step t16.t5 (cl @p_58 @p_58) :rule resolution :premises (t16.t3 t16.t4))
(step t16.t6 (cl @p_58) :rule contraction :premises (t16.t5))
(step t16.t7 (cl (= @p_58 @p_47)) :rule implies_simplify)
(step t16.t8 (cl (not @p_58) @p_47) :rule equiv1 :premises (t16.t7))
(step t16.t9 (cl @p_47) :rule resolution :premises (t16.t6 t16.t8))
(step t16.t10 (cl) :rule resolution :premises (t16.t0 t16.t9))
(step t16 (cl @p_57 @p_15 false) :rule subproof :discharge (t16.a0 t16.a1))
(step t17 (cl @p_54 @p_52) :rule and_pos :args (0))
(step t18 (cl @p_54 @p_7) :rule and_pos :args (1))
(step t19 (cl false @p_54 @p_54) :rule resolution :premises (t16 t17 t18))
(step t20 (cl @p_54 @p_54 false) :rule reordering :premises (t19))
(step t21 (cl @p_54 false) :rule contraction :premises (t20))
(step t22 (cl @p_55 false) :rule resolution :premises (t15 t21))
(step t23 (cl @p_55 @p_56) :rule implies_neg2)
(step t24 (cl @p_55 @p_55) :rule resolution :premises (t22 t23))
(step t25 (cl @p_55) :rule contraction :premises (t24))
(step t26 (cl (= @p_55 @p_54)) :rule implies_simplify)
(step t27 (cl (not @p_55) @p_54) :rule equiv1 :premises (t26))
(step t28 (cl @p_54) :rule resolution :premises (t25 t27))
(step t29 (cl @p_51) :rule resolution :premises (t14 t28))
(step t30 (cl @p_47 @p_15) :rule not_and :premises (t29))
(step t31 (cl @p_49 (not @p_47)) :rule or_neg :args (0))
(step t32 (cl @p_49 (not @p_15)) :rule or_neg :args (1))
(step t33 (cl @p_49 @p_49) :rule resolution :premises (t30 t31 t32))
(step t34 (cl @p_49) :rule contraction :premises (t33))
(step t35 (cl @p_48) :rule resolution :premises (t0 t2 t34))
(step t36 (cl @p_47 @p_6) :rule or :premises (t35))
(step t37 (cl @p_6 @p_47) :rule reordering :premises (t36))
(step t38 (cl (not (! (= (! (ite (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) (! (= @p_5 -1) :named @p_44) @p_30) :named @p_45) @p_45) :named @p_46)) (not @p_45) @p_45) :rule equiv_pos2)
(step t39 (cl (= @p_10 @p_9)) :rule equiv_simplify)
(step t40 (cl (not @p_10) @p_9) :rule equiv1 :premises (t39))
(step t41 (cl (= (* -1 @p_12) (* 1 @p_12))) :rule poly_simp)
(step t42 (cl @p_11) :rule poly_simp_rel :premises (t41))
(step t43 (cl @p_9) :rule refl)
(step t44 (cl @p_9) :rule refl)
(step t45 (cl @p_11) :rule cong :premises (t43 t44))
(step t46 (cl @p_10) :rule rare_rewrite :args ("eq-refl" @p_5))
(step t47 (cl @p_10) :rule trans :premises (t42 t45 t46))
(step t48 (cl @p_9) :rule resolution :premises (t40 t47))
(step t49 (cl (= -1 -1)) :rule refl)
(step t50 (cl (= @p_44 @p_44)) :rule cong :premises (t48 t49))
(step t51 (cl (= 3 3)) :rule refl)
(step t52 (cl (= @p_30 @p_30)) :rule cong :premises (t48 t51))
(step t53 (cl @p_46) :rule cong :premises (t50 t52))
(step t54 (cl (= @p_45 true)) :rule rare_rewrite :args ("ite-eq" (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) -1 3))
(step t55 (cl @p_45 (! (not true) :named @p_42)) :rule equiv2 :premises (t54))
(step t56 (cl true) :rule true)
(step t57 (cl @p_45) :rule resolution :premises (t55 t56))
(step t58 (cl @p_45) :rule resolution :premises (t38 t53 t57))
(step t59 (cl (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) @p_30) :rule ite1 :premises (t58))
(step t60 (cl (not (! (= (! (=> (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) (! (or (! (not (! (>= (! (* -1 0) :named @p_32) 0) :named @p_34)) :named @p_35) (! (>= @p_32 1) :named @p_33)) :named @p_36)) :named @p_37) (! (not (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1)))) :named @p_31)) :named @p_38)) (not @p_37) @p_31) :rule equiv_pos2)
(step t61 (cl (= @p_32 0)) :rule evaluate)
(step t62 (cl (= 0 0)) :rule refl)
(step t63 (cl (= @p_34 (! (>= 0 0) :named @p_43))) :rule cong :premises (t61 t62))
(step t64 (cl (= @p_43 true)) :rule evaluate)
(step t65 (cl (= @p_34 true)) :rule trans :premises (t63 t64))
(step t66 (cl (= @p_35 @p_42)) :rule cong :premises (t65))
(step t67 (cl (= @p_42 false)) :rule evaluate)
(step t68 (cl (= @p_35 false)) :rule trans :premises (t66 t67))
(step t69 (cl (= 1 1)) :rule refl)
(step t70 (cl (= @p_33 (! (>= 0 1) :named @p_41))) :rule cong :premises (t61 t69))
(step t71 (cl (= @p_41 false)) :rule evaluate)
(step t72 (cl (= @p_33 false)) :rule trans :premises (t70 t71))
(step t73 (cl (= @p_36 (! (or false false) :named @p_40))) :rule cong :premises (t68 t72))
(step t74 (cl (= @p_40 false)) :rule evaluate)
(step t75 (cl (= @p_36 false)) :rule trans :premises (t73 t74))
(step t76 (cl (= @p_37 (! (=> (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))) false) :named @p_39))) :rule cong :premises (t75))
(step t77 (cl (= @p_39 @p_31)) :rule rare_rewrite :args ("bool-impl-false1" (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1)))))
(step t78 (cl @p_38) :rule trans :premises (t76 t77))
(step t79 (cl @p_37 (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1)))) :rule implies_neg1)
(anchor :step t80)
(assume t80.a0 (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))))
(step t80.t0 (cl (or @p_31 @p_36)) :rule forall_inst :args (@p_32))
(step t80.t1 (cl @p_31 @p_36) :rule or :premises (t80.t0))
(step t80.t2 (cl @p_36) :rule resolution :premises (t80.t1 t80.a0))
(step t80 (cl @p_31 @p_36) :rule subproof :discharge (t80.a0))
(step t81 (cl @p_37 @p_36) :rule resolution :premises (t79 t80))
(step t82 (cl @p_37 (not @p_36)) :rule implies_neg2)
(step t83 (cl @p_37 @p_37) :rule resolution :premises (t81 t82))
(step t84 (cl @p_37) :rule contraction :premises (t83))
(step t85 (cl @p_31) :rule resolution :premises (t60 t78 t84))
(step t86 (cl @p_30) :rule resolution :premises (t59 t85))
(step t87 (cl (not @p_8) (not @p_4) @p_7) :rule equiv_pos2)
(step t88 (cl (= @p_3 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_2))
(anchor :step t89 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t89.t0 (cl (= @p_23 @p_21)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 0))
(step t89.t1 (cl (= @p_22 @p_25)) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v0))
(step t89.t2 (cl (= @p_26 @p_29)) :rule rare_rewrite :args ("arith-geq-tighten" ?v0 1))
(step t89.t3 (cl (= (* -1 (- 1 @p_28)) (* -1 (- 0 ?v0)))) :rule poly_simp)
(step t89.t4 (cl (= @p_29 @p_24)) :rule poly_simp_rel :premises (t89.t3))
(step t89.t5 (cl (= @p_26 @p_24)) :rule trans :premises (t89.t2 t89.t4))
(step t89.t6 (cl (= @p_24 @p_26)) :rule symm :premises (t89.t5))
(step t89.t7 (cl (= @p_25 @p_27)) :rule cong :premises (t89.t6))
(step t89.t8 (cl (= @p_27 @p_20)) :rule rare_rewrite :args ("bool-double-not-elim" @p_20))
(step t89.t9 (cl (= @p_25 @p_20)) :rule trans :premises (t89.t7 t89.t8))
(step t89.t10 (cl (= @p_22 @p_20)) :rule trans :premises (t89.t1 t89.t9))
(step t89.t11 (cl (= (or @p_23 @p_22) (or @p_21 @p_20))) :rule cong :premises (t89.t0 t89.t10))
(step t89 (cl (= (forall ((?v0 Int)) (or (< ?v0 0) (< 0 ?v0))) (forall ((?v0 Int)) (or (not (>= ?v0 0)) (>= ?v0 1))))) :rule bind)
(step t90 (cl (= @p_1 -1)) :rule evaluate)
(step t91 (cl (= @p_2 @p_5)) :rule cong :premises (t89 t90 t51))
(step t92 (cl (= @p_13 @p_17)) :rule cong :premises (t91))
(step t93 (cl (= @p_7 @p_19)) :rule rare_rewrite :args ("arith-geq-tighten" @p_5 1))
(step t94 (cl (= (* -1 (- 1 @p_18)) (* -1 (- 0 @p_5)))) :rule poly_simp)
(step t95 (cl (= @p_19 @p_17)) :rule poly_simp_rel :premises (t94))
(step t96 (cl (= @p_7 @p_17)) :rule trans :premises (t93 t95))
(step t97 (cl (= @p_17 @p_7)) :rule symm :premises (t96))
(step t98 (cl (= @p_13 @p_7)) :rule trans :premises (t92 t97))
(step t99 (cl (= @p_14 @p_15)) :rule cong :premises (t98))
(step t100 (cl @p_16) :rule rare_rewrite :args ("bool-double-not-elim" @p_6))
(step t101 (cl (= @p_14 @p_6)) :rule trans :premises (t99 t100))
(step t102 (cl (= @p_3 @p_6)) :rule trans :premises (t88 t101))
(step t103 (cl @p_8) :rule cong :premises (t102))
(step t104 (cl (= @p_6 @p_6)) :rule cong :premises (t48 t69))
(step t105 (cl (= @p_7 @p_7)) :rule cong :premises (t104))
(step t106 (cl @p_8) :rule trans :premises (t103 t105))
(step t107 (cl @p_7) :rule resolution :premises (t87 t106 a0))
(step t108 (cl) :rule resolution :premises (t37 t86 t107))
)
5a8fe6d576851386f17726a66e41043f40a9faba 31 0
unsat
(
(assume a0 (! (not (forall ((?v0 Int) (?v1 Int)) (or (< 0 ?v1) (< ?v1 1)))) :named @p_1))
(step t0 (cl (not (! (= @p_1 false) :named @p_2)) (not @p_1) false) :rule equiv_pos2)
(anchor :step t1 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t1.t0 (cl (= (! (< 0 ?v1) :named @p_10) (! (not (! (>= 0 ?v1) :named @p_11)) :named @p_12))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v1))
(step t1.t1 (cl (= (! (not (! (>= ?v1 1) :named @p_6)) :named @p_7) (! (>= 1 (! (+ ?v1 1) :named @p_14)) :named @p_15))) :rule rare_rewrite :args ("arith-geq-tighten" ?v1 1))
(step t1.t2 (cl (= (* -1 (- 1 @p_14)) (* -1 (- 0 ?v1)))) :rule poly_simp)
(step t1.t3 (cl (= @p_15 @p_11)) :rule poly_simp_rel :premises (t1.t2))
(step t1.t4 (cl (= @p_7 @p_11)) :rule trans :premises (t1.t1 t1.t3))
(step t1.t5 (cl (= @p_11 @p_7)) :rule symm :premises (t1.t4))
(step t1.t6 (cl (= @p_12 (! (not @p_7) :named @p_13))) :rule cong :premises (t1.t5))
(step t1.t7 (cl (= @p_13 @p_6)) :rule rare_rewrite :args ("bool-double-not-elim" @p_6))
(step t1.t8 (cl (= @p_12 @p_6)) :rule trans :premises (t1.t6 t1.t7))
(step t1.t9 (cl (= @p_10 @p_6)) :rule trans :premises (t1.t0 t1.t8))
(step t1.t10 (cl (= (! (< ?v1 1) :named @p_9) @p_7)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 1))
(step t1.t11 (cl (= (or @p_10 @p_9) (! (or @p_6 @p_7) :named @p_8))) :rule cong :premises (t1.t9 t1.t10))
(step t1 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (< 0 ?v1) (< ?v1 1))) (forall ((?v0 Int) (?v1 Int)) (or (>= ?v1 1) (not (>= ?v1 1)))))) :rule bind)
(anchor :step t2 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t2.t0 (cl (= @p_8 true)) :rule rare_rewrite :args ("bool-or-taut" rare-list @p_6 rare-list rare-list))
(step t2 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (>= ?v1 1) (not (>= ?v1 1)))) (forall ((?v0 Int) (?v1 Int)) true))) :rule bind)
(step t3 (cl (= (forall ((?v0 Int) (?v1 Int)) true) true)) :rule qnt_rm_unused)
(step t4 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (>= ?v1 1) (not (>= ?v1 1)))) true)) :rule trans :premises (t2 t3))
(step t5 (cl (= (forall ((?v0 Int) (?v1 Int)) (or (< 0 ?v1) (< ?v1 1))) true)) :rule trans :premises (t1 t4))
(step t6 (cl (= @p_1 (! (not true) :named @p_3))) :rule cong :premises (t5))
(step t7 (cl (= @p_3 false)) :rule evaluate)
(step t8 (cl @p_2) :rule trans :premises (t6 t7))
(step t9 (cl false) :rule resolution :premises (t0 t8 a0))
(step t10 (cl (not false)) :rule false)
(step t11 (cl) :rule resolution :premises (t9 t10))
)
28658d9872dd3c3e5b43013f781e4fa2f0d9932b 143 0
unsat
(
(define-fun @quantifiers_skolemize_2 () Int (choice ((?v1 Int)) (not (or (not (>= ?v1 1)) (>= ?v1 0)))))
(assume a0 (! (not (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Real)) (=> (and (< 0 ?v1) (< 0/1 ?v2)) (< (- 1) ?v1))))) :named @p_1))
(step t0 (cl (not (! (= (! (<= (! (+ @quantifiers_skolemize_2 (! (* -1 @quantifiers_skolemize_2) :named @p_5)) :named @p_6) (! (+ -1 (! (* -1 1) :named @p_3)) :named @p_4)) :named @p_7) false) :named @p_75)) (not @p_7) false) :rule equiv_pos2)
(step t1 (cl (= @p_6 0)) :rule poly_simp)
(step t2 (cl (= @p_3 -1)) :rule evaluate)
(step t3 (cl (= @p_4 (! (+ -1 -1) :named @p_77))) :rule cong :premises (t2))
(step t4 (cl (= @p_77 -2)) :rule evaluate)
(step t5 (cl (= @p_4 -2)) :rule trans :premises (t3 t4))
(step t6 (cl (= @p_7 (! (<= 0 -2) :named @p_76))) :rule cong :premises (t1 t5))
(step t7 (cl (= @p_76 false)) :rule evaluate)
(step t8 (cl @p_75) :rule trans :premises (t6 t7))
(step t9 (cl (not (! (<= @quantifiers_skolemize_2 -1) :named @p_71)) (not (! (<= @p_5 @p_3) :named @p_8)) @p_7) :rule la_generic :args (1/1 1/1 1/1))
(step t10 (cl (not (! (< @quantifiers_skolemize_2 0) :named @p_72)) @p_71) :rule la_generic :args (1/1 1/1))
(step t11 (cl (not (! (= (! (not (! (>= @quantifiers_skolemize_2 0) :named @p_12)) :named @p_73) @p_72) :named @p_74)) (not @p_73) @p_72) :rule equiv_pos2)
(step t12 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("arith-elim-lt" @quantifiers_skolemize_2 0))
(step t13 (cl @p_74) :rule symm :premises (t12))
(step t14 (cl (! (or (! (not (! (>= @quantifiers_skolemize_2 1) :named @p_9)) :named @p_13) @p_12) :named @p_14) @p_73) :rule or_neg :args (1))
(step t15 (cl (not (! (= (! (not (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))) :named @p_16) (! (not @p_14) :named @p_15)) :named @p_65)) (! (not @p_16) :named @p_19) @p_15) :rule equiv_pos2)
(anchor :step t16 :args ((:= (?v1 Int) @quantifiers_skolemize_2)))
(step t16.t0 (cl (= (! (or (! (not (! (>= ?v1 1) :named @p_34)) :named @p_35) (! (>= ?v1 0) :named @p_33)) :named @p_36) @p_14)) :rule refl)
(step t16 (cl (= (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))) @p_14)) :rule sko_forall)
(step t17 (cl @p_65) :rule cong :premises (t16))
(step t18 (cl (not (! (= @p_1 @p_16) :named @p_17)) (not @p_1) @p_16) :rule equiv_pos2)
(anchor :step t19 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(anchor :step t19.t0 :args ((?v1 Int) (?v2 Real) (:= (?v1 Int) ?v1) (:= (?v2 Real) ?v2)))
(step t19.t0.t0 (cl (= (! (< 0 ?v1) :named @p_50) (! (not (! (>= 0 ?v1) :named @p_61)) :named @p_62))) :rule rare_rewrite :args ("arith-elim-lt" 0 ?v1))
(step t19.t0.t1 (cl (= @p_35 (! (>= 1 (! (+ ?v1 1) :named @p_57)) :named @p_64))) :rule rare_rewrite :args ("arith-geq-tighten" ?v1 1))
(step t19.t0.t2 (cl (= (* -1 (- 1 @p_57)) (* -1 (- 0 ?v1)))) :rule poly_simp)
(step t19.t0.t3 (cl (= @p_64 @p_61)) :rule poly_simp_rel :premises (t19.t0.t2))
(step t19.t0.t4 (cl (= @p_35 @p_61)) :rule trans :premises (t19.t0.t1 t19.t0.t3))
(step t19.t0.t5 (cl (= @p_61 @p_35)) :rule symm :premises (t19.t0.t4))
(step t19.t0.t6 (cl (= @p_62 (! (not @p_35) :named @p_63))) :rule cong :premises (t19.t0.t5))
(step t19.t0.t7 (cl (= @p_63 @p_34)) :rule rare_rewrite :args ("bool-double-not-elim" @p_34))
(step t19.t0.t8 (cl (= @p_62 @p_34)) :rule trans :premises (t19.t0.t6 t19.t0.t7))
(step t19.t0.t9 (cl (= @p_50 @p_34)) :rule trans :premises (t19.t0.t0 t19.t0.t8))
(step t19.t0.t10 (cl (= (! (< 0/1 ?v2) :named @p_49) (! (not (! (>= 0/1 ?v2) :named @p_59)) :named @p_60))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v2))
(step t19.t0.t11 (cl (= (* -1/1 (- 0/1 ?v2)) (* -1/1 (- (! (* -1/1 ?v2) :named @p_31) 0/1)))) :rule poly_simp)
(step t19.t0.t12 (cl (= @p_59 (! (>= @p_31 0/1) :named @p_32))) :rule poly_simp_rel :premises (t19.t0.t11))
(step t19.t0.t13 (cl (= @p_60 (! (not @p_32) :named @p_38))) :rule cong :premises (t19.t0.t12))
(step t19.t0.t14 (cl (= @p_49 @p_38)) :rule trans :premises (t19.t0.t10 t19.t0.t13))
(step t19.t0.t15 (cl (= (! (and @p_50 @p_49) :named @p_51) (! (and @p_34 @p_38) :named @p_39))) :rule cong :premises (t19.t0.t9 t19.t0.t14))
(step t19.t0.t16 (cl (= (! (< (! (- 1) :named @p_47) ?v1) :named @p_48) (! (not (! (>= @p_47 ?v1) :named @p_52)) :named @p_53))) :rule rare_rewrite :args ("arith-elim-lt" @p_47 ?v1))
(step t19.t0.t17 (cl (= @p_47 -1)) :rule evaluate)
(step t19.t0.t18 (cl (! (= ?v1 ?v1) :named @p_29)) :rule refl)
(step t19.t0.t19 (cl (= @p_52 (! (>= -1 ?v1) :named @p_56))) :rule cong :premises (t19.t0.t17 t19.t0.t18))
(step t19.t0.t20 (cl (= (! (not @p_33) :named @p_54) (! (>= 0 @p_57) :named @p_58))) :rule rare_rewrite :args ("arith-geq-tighten" ?v1 0))
(step t19.t0.t21 (cl (= (* -1 (- 0 @p_57)) (* -1 (- -1 ?v1)))) :rule poly_simp)
(step t19.t0.t22 (cl (= @p_58 @p_56)) :rule poly_simp_rel :premises (t19.t0.t21))
(step t19.t0.t23 (cl (= @p_54 @p_56)) :rule trans :premises (t19.t0.t20 t19.t0.t22))
(step t19.t0.t24 (cl (= @p_56 @p_54)) :rule symm :premises (t19.t0.t23))
(step t19.t0.t25 (cl (= @p_52 @p_54)) :rule trans :premises (t19.t0.t19 t19.t0.t24))
(step t19.t0.t26 (cl (= @p_53 (! (not @p_54) :named @p_55))) :rule cong :premises (t19.t0.t25))
(step t19.t0.t27 (cl (= @p_55 @p_33)) :rule rare_rewrite :args ("bool-double-not-elim" @p_33))
(step t19.t0.t28 (cl (= @p_53 @p_33)) :rule trans :premises (t19.t0.t26 t19.t0.t27))
(step t19.t0.t29 (cl (= @p_48 @p_33)) :rule trans :premises (t19.t0.t16 t19.t0.t28))
(step t19.t0.t30 (cl (= (=> @p_51 @p_48) (! (=> @p_39 @p_33) :named @p_40))) :rule cong :premises (t19.t0.t15 t19.t0.t29))
(step t19.t0 (cl (= (forall ((?v1 Int) (?v2 Real)) (=> (and (< 0 ?v1) (< 0/1 ?v2)) (< (- 1) ?v1))) (forall ((?v1 Int) (?v2 Real)) (=> (and (>= ?v1 1) (not (>= (* -1/1 ?v2) 0/1))) (>= ?v1 0))))) :rule bind)
(anchor :step t19.t1 :args ((?v1 Int) (?v2 Real) (:= (?v1 Int) ?v1) (:= (?v2 Real) ?v2)))
(step t19.t1.t0 (cl (= @p_40 (! (or (! (not @p_39) :named @p_41) @p_33) :named @p_42))) :rule rare_rewrite :args ("bool-impl-elim" @p_39 @p_33))
(step t19.t1.t1 (cl (= @p_41 (! (or @p_35 (! (not @p_38) :named @p_45)) :named @p_46))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_34 @p_38 rare-list))
(step t19.t1.t2 (cl (= @p_45 @p_32)) :rule rare_rewrite :args ("bool-double-not-elim" @p_32))
(step t19.t1.t3 (cl (= @p_46 (! (or @p_35 @p_32) :named @p_43))) :rule cong :premises (t19.t1.t2))
(step t19.t1.t4 (cl (= @p_41 @p_43)) :rule trans :premises (t19.t1.t1 t19.t1.t3))
(step t19.t1.t5 (cl (= @p_33 @p_33)) :rule refl)
(step t19.t1.t6 (cl (= @p_42 (! (or @p_43 @p_33) :named @p_44))) :rule cong :premises (t19.t1.t4 t19.t1.t5))
(step t19.t1.t7 (cl (= @p_44 (! (or @p_35 @p_32 @p_33) :named @p_37))) :rule aci_simp)
(step t19.t1.t8 (cl (= @p_42 @p_37)) :rule trans :premises (t19.t1.t6 t19.t1.t7))
(step t19.t1.t9 (cl (= @p_40 @p_37)) :rule trans :premises (t19.t1.t0 t19.t1.t8))
(step t19.t1 (cl (= (forall ((?v1 Int) (?v2 Real)) (=> (and (>= ?v1 1) (not (>= (* -1/1 ?v2) 0/1))) (>= ?v1 0))) (forall ((?v1 Int) (?v2 Real)) (or (not (>= ?v1 1)) (>= (* -1/1 ?v2) 0/1) (>= ?v1 0))))) :rule bind)
(anchor :step t19.t2 :args ((?v1 Int) (?v2 Real) (:= (?v1 Int) ?v1) (:= (?v2 Real) ?v2)))
(step t19.t2.t0 (cl (= @p_37 (or @p_36 @p_32))) :rule aci_simp)
(step t19.t2 (cl (= (forall ((?v1 Int) (?v2 Real)) (or (not (>= ?v1 1)) (>= (* -1/1 ?v2) 0/1) (>= ?v1 0))) (forall ((?v1 Int) (?v2 Real)) (or (or (not (>= ?v1 1)) (>= ?v1 0)) (>= (* -1/1 ?v2) 0/1))))) :rule bind)
(step t19.t3 (cl (= (forall ((?v1 Int) (?v2 Real)) (or (or (not (>= ?v1 1)) (>= ?v1 0)) (>= (* -1/1 ?v2) 0/1))) (! (or (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))) (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1))) :named @p_20))) :rule miniscope_split)
(step t19.t4 (cl (= (forall ((?v1 Int) (?v2 Real)) (or (not (>= ?v1 1)) (>= (* -1/1 ?v2) 0/1) (>= ?v1 0))) @p_20)) :rule trans :premises (t19.t2 t19.t3))
(step t19.t5 (cl (= (! (= (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1)) false) :named @p_22) (! (not (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1))) :named @p_23))) :rule equiv_simplify)
(step t19.t6 (cl @p_22 (! (not @p_23) :named @p_28)) :rule equiv2 :premises (t19.t5))
(step t19.t7 (cl (not @p_28) (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1))) :rule not_not)
(step t19.t8 (cl @p_22 (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1))) :rule resolution :premises (t19.t6 t19.t7))
(step t19.t9 (cl (! (=> (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1)) false) :named @p_24) (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1))) :rule implies_neg1)
(anchor :step t19.t10)
(assume t19.t10.a0 (forall ((?v2 Real)) (>= (* -1/1 ?v2) 0/1)))
(step t19.t10.t0 (cl (not (! (= (! (>= (* -1/1 (! (+ 0/1 1/1) :named @p_25)) 0/1) :named @p_26) false) :named @p_27)) (not @p_26) false) :rule equiv_pos2)
(step t19.t10.t1 (cl @p_27) :rule evaluate)
(step t19.t10.t2 (cl (or @p_23 @p_26)) :rule forall_inst :args (@p_25))
(step t19.t10.t3 (cl @p_23 @p_26) :rule or :premises (t19.t10.t2))
(step t19.t10.t4 (cl @p_26) :rule resolution :premises (t19.t10.t3 t19.t10.a0))
(step t19.t10.t5 (cl false) :rule resolution :premises (t19.t10.t0 t19.t10.t1 t19.t10.t4))
(step t19.t10 (cl @p_23 false) :rule subproof :discharge (t19.t10.a0))
(step t19.t11 (cl @p_24 false) :rule resolution :premises (t19.t9 t19.t10))
(step t19.t12 (cl @p_24 (! (not false) :named @p_2)) :rule implies_neg2)
(step t19.t13 (cl @p_24 @p_24) :rule resolution :premises (t19.t11 t19.t12))
(step t19.t14 (cl @p_24) :rule contraction :premises (t19.t13))
(step t19.t15 (cl (= @p_24 @p_23)) :rule implies_simplify)
(step t19.t16 (cl (not @p_24) @p_23) :rule equiv1 :premises (t19.t15))
(step t19.t17 (cl @p_23) :rule resolution :premises (t19.t14 t19.t16))
(step t19.t18 (cl @p_22) :rule resolution :premises (t19.t8 t19.t17))
(step t19.t19 (cl (= @p_20 (! (or (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))) false) :named @p_21))) :rule cong :premises (t19.t18))
(step t19.t20 (cl (= @p_21 (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule aci_simp)
(step t19.t21 (cl (= @p_20 (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t19.t19 t19.t20))
(step t19.t22 (cl (= (forall ((?v1 Int) (?v2 Real)) (or (not (>= ?v1 1)) (>= (* -1/1 ?v2) 0/1) (>= ?v1 0))) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t19.t4 t19.t21))
(step t19.t23 (cl (= (forall ((?v1 Int) (?v2 Real)) (=> (and (>= ?v1 1) (not (>= (* -1/1 ?v2) 0/1))) (>= ?v1 0))) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t19.t1 t19.t22))
(step t19.t24 (cl (= (forall ((?v1 Int) (?v2 Real)) (=> (and (< 0 ?v1) (< 0/1 ?v2)) (< (- 1) ?v1))) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t19.t0 t19.t23))
(step t19 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Real)) (=> (and (< 0 ?v1) (< 0/1 ?v2)) (< (- 1) ?v1)))) (exists ((?v0 Int)) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))))) :rule bind)
(step t20 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))) (! (not (forall ((?v0 Int)) (not (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))))) :named @p_18))) :rule connective_def)
(step t21 (cl (= (forall ((?v0 Int)) (not (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) @p_16)) :rule qnt_rm_unused)
(step t22 (cl (= @p_18 @p_19)) :rule cong :premises (t21))
(step t23 (cl (= @p_19 (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))))
(step t24 (cl (= @p_18 (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t22 t23))
(step t25 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0)))) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t20 t24))
(step t26 (cl (= (exists ((?v0 Int)) (forall ((?v1 Int) (?v2 Real)) (=> (and (< 0 ?v1) (< 0/1 ?v2)) (< (- 1) ?v1)))) (forall ((?v1 Int)) (or (not (>= ?v1 1)) (>= ?v1 0))))) :rule trans :premises (t19 t25))
(step t27 (cl @p_17) :rule cong :premises (t26))
(step t28 (cl @p_16) :rule resolution :premises (t18 t27 a0))
(step t29 (cl @p_15) :rule resolution :premises (t15 t17 t28))
(step t30 (cl @p_73) :rule resolution :premises (t14 t29))
(step t31 (cl @p_72) :rule resolution :premises (t11 t13 t30))
(step t32 (cl @p_71) :rule resolution :premises (t10 t31))
(step t33 (cl (=> (! (and (! (< -1 0) :named @p_10) @p_9) :named @p_11) @p_8)) :rule la_mult_neg)
(step t34 (cl (not @p_11) @p_8) :rule implies :premises (t33))
(step t35 (cl (= (! (= @p_10 true) :named @p_70) @p_10)) :rule equiv_simplify)
(step t36 (cl (not @p_70) @p_10) :rule equiv1 :premises (t35))
(step t37 (cl @p_70) :rule evaluate)
(step t38 (cl @p_10) :rule resolution :premises (t36 t37))
(step t39 (cl (not (! (= (! (or @p_14 (! (not @p_13) :named @p_67)) :named @p_68) (! (or @p_14 @p_9) :named @p_66)) :named @p_69)) (not @p_68) @p_66) :rule equiv_pos2)
(step t40 (cl (= @p_67 @p_9)) :rule rare_rewrite :args ("bool-double-not-elim" @p_9))
(step t41 (cl @p_69) :rule cong :premises (t40))
(step t42 (cl @p_14 @p_67) :rule or_neg :args (0))
(step t43 (cl @p_68 @p_15) :rule or_neg :args (0))
(step t44 (cl @p_68 (not @p_67)) :rule or_neg :args (1))
(step t45 (cl @p_68 @p_68) :rule resolution :premises (t42 t43 t44))
(step t46 (cl @p_68) :rule contraction :premises (t45))
(step t47 (cl @p_66) :rule resolution :premises (t39 t41 t46))
(step t48 (cl @p_14 @p_9) :rule or :premises (t47))
(step t49 (cl @p_9 @p_14) :rule reordering :premises (t48))
(step t50 (cl @p_9) :rule resolution :premises (t49 t29))
(step t51 (cl @p_11) :rule and_intro :premises (t38 t50))
(step t52 (cl @p_8) :rule resolution :premises (t34 t51))
(step t53 (cl @p_7) :rule resolution :premises (t9 t32 t52))
(step t54 (cl false) :rule resolution :premises (t0 t8 t53))
(step t55 (cl @p_2) :rule false)
(step t56 (cl) :rule resolution :premises (t54 t55))
)
a8894a1afe8f47e3aaed09019959026d6fa2069d 19 0
unsat
(
(assume a0 (! (not (! (= (! (* 2 (! (+ 5 1) :named @p_1)) :named @p_2) 12) :named @p_3)) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_1 6)) :rule evaluate)
(step t2 (cl (= @p_2 (! (* 2 6) :named @p_8))) :rule cong :premises (t1))
(step t3 (cl (= @p_8 12)) :rule evaluate)
(step t4 (cl @p_3) :rule trans :premises (t2 t3))
(step t5 (cl (! (= 12 12) :named @p_7)) :rule refl)
(step t6 (cl (= @p_3 @p_7)) :rule cong :premises (t4 t5))
(step t7 (cl (= @p_7 true)) :rule evaluate)
(step t8 (cl (= @p_3 true)) :rule trans :premises (t6 t7))
(step t9 (cl (= @p_4 (! (not true) :named @p_6))) :rule cong :premises (t8))
(step t10 (cl (= @p_6 false)) :rule evaluate)
(step t11 (cl @p_5) :rule trans :premises (t9 t10))
(step t12 (cl false) :rule resolution :premises (t0 t11 a0))
(step t13 (cl (not false)) :rule false)
(step t14 (cl) :rule resolution :premises (t12 t13))
)
52d6069a2507c5f71d68d6d08c4f368641115c13 17 0
unsat
(
(assume a0 (! (not (not (! (= (! (* 2 (! (of_nat$ x$) :named @p_1)) :named @p_2) 1) :named @p_3))) :named @p_4))
(step t0 (cl (not (! (= @p_4 false) :named @p_5)) (not @p_4) false) :rule equiv_pos2)
(step t1 (cl (= @p_4 @p_3)) :rule rare_rewrite :args ("bool-double-not-elim" @p_3))
(step t2 (cl (= (* -1/1 (to_real (- @p_2 1))) (* -1/1 (! (- (! (to_real @p_2) :named @p_9) (! (to_real 1) :named @p_8)) :named @p_11)))) :rule poly_simp)
(step t3 (cl (= @p_3 (! (= @p_9 @p_8) :named @p_10))) :rule poly_simp_rel :premises (t2))
(step t4 (cl (= (* -1/2 @p_11) (* -1/1 (- (! (to_real @p_1) :named @p_6) 1/2)))) :rule poly_simp)
(step t5 (cl (= @p_10 (! (= @p_6 1/2) :named @p_7))) :rule poly_simp_rel :premises (t4))
(step t6 (cl (= (= (to_real (to_int 1/2)) 1/2) false)) :rule evaluate)
(step t7 (cl (= @p_7 false)) :rule rare_rewrite :premises (t6) :args ("arith-int-eq-conflict" @p_1 1/2))
(step t8 (cl (= @p_3 false)) :rule trans :premises (t3 t5 t7))
(step t9 (cl @p_5) :rule trans :premises (t1 t8))
(step t10 (cl false) :rule resolution :premises (t0 t9 a0))
(step t11 (cl (not false)) :rule false)
(step t12 (cl) :rule resolution :premises (t10 t11))
)
02d55697217b311482e44da66d3aedf739428639 53 0
unsat
(
(assume a0 (! (not (! (=> (! (< (! (of_nat$ a$) :named @p_1) 3) :named @p_4) (! (< (! (* 2 @p_1) :named @p_2) 7) :named @p_3)) :named @p_5)) :named @p_6))
(step t0 (cl (not (! (= (! (< (! (+ @p_1 (! (* -1 @p_1) :named @p_9)) :named @p_10) (! (+ 3 (! (* -1 4) :named @p_7)) :named @p_8)) :named @p_11) false) :named @p_30)) (not @p_11) false) :rule equiv_pos2)
(step t1 (cl (= @p_11 (! (not (! (>= @p_10 @p_8) :named @p_31)) :named @p_32))) :rule rare_rewrite :args ("arith-elim-lt" @p_10 @p_8))
(step t2 (cl (= @p_10 0)) :rule poly_simp)
(step t3 (cl (= @p_7 -4)) :rule evaluate)
(step t4 (cl (= @p_8 (! (+ 3 -4) :named @p_35))) :rule cong :premises (t3))
(step t5 (cl (= @p_35 -1)) :rule evaluate)
(step t6 (cl (= @p_8 -1)) :rule trans :premises (t4 t5))
(step t7 (cl (= @p_31 (! (>= 0 -1) :named @p_34))) :rule cong :premises (t2 t6))
(step t8 (cl (= @p_34 true)) :rule evaluate)
(step t9 (cl (= @p_31 true)) :rule trans :premises (t7 t8))
(step t10 (cl (= @p_32 (! (not true) :named @p_33))) :rule cong :premises (t9))
(step t11 (cl (= @p_33 false)) :rule evaluate)
(step t12 (cl (= @p_32 false)) :rule trans :premises (t10 t11))
(step t13 (cl @p_30) :rule trans :premises (t1 t12))
(step t14 (cl (not @p_4) (not (! (<= @p_9 @p_7) :named @p_12)) @p_11) :rule la_generic :args (1/1 1/1 1/1))
(step t15 (cl (not (! (= (! (not (>= @p_1 3)) :named @p_18) @p_4) :named @p_29)) (not @p_18) @p_4) :rule equiv_pos2)
(step t16 (cl (= @p_4 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" @p_1 3))
(step t17 (cl @p_29) :rule symm :premises (t16))
(step t18 (cl (not (! (= @p_6 (! (not (! (=> @p_18 (! (not (! (>= @p_1 4) :named @p_13)) :named @p_16)) :named @p_19)) :named @p_20)) :named @p_21)) (not @p_6) @p_20) :rule equiv_pos2)
(step t19 (cl (= @p_3 (! (not (! (>= @p_2 7) :named @p_22)) :named @p_23))) :rule rare_rewrite :args ("arith-elim-lt" @p_2 7))
(step t20 (cl (= (* -7/2 (to_real (- @p_2 7))) (* -7/1 (- (! (to_real @p_1) :named @p_24) 7/2)))) :rule poly_simp)
(step t21 (cl (= @p_22 (! (>= @p_24 7/2) :named @p_25))) :rule poly_simp_rel :premises (t20))
(step t22 (cl (= (= (to_real (! (to_int 7/2) :named @p_26)) 7/2) false)) :rule evaluate)
(step t23 (cl (= (! (+ @p_26 1) :named @p_27) 4)) :rule evaluate)
(step t24 (cl (= 4 @p_27)) :rule symm :premises (t23))
(step t25 (cl (= @p_25 @p_13)) :rule rare_rewrite :premises (t22 t24) :args ("arith-int-geq-tighten" @p_1 7/2 4))
(step t26 (cl (= @p_22 @p_13)) :rule trans :premises (t21 t25))
(step t27 (cl (= @p_23 @p_16)) :rule cong :premises (t26))
(step t28 (cl (= @p_3 @p_16)) :rule trans :premises (t19 t27))
(step t29 (cl (= @p_5 @p_19)) :rule cong :premises (t16 t28))
(step t30 (cl @p_21) :rule cong :premises (t29))
(step t31 (cl @p_20) :rule resolution :premises (t18 t30 a0))
(step t32 (cl @p_18) :rule not_implies1 :premises (t31))
(step t33 (cl @p_4) :rule resolution :premises (t15 t17 t32))
(step t34 (cl (=> (! (and (! (< -1 0) :named @p_14) @p_13) :named @p_15) @p_12)) :rule la_mult_neg)
(step t35 (cl (not @p_15) @p_12) :rule implies :premises (t34))
(step t36 (cl (= (! (= @p_14 true) :named @p_28) @p_14)) :rule equiv_simplify)
(step t37 (cl (not @p_28) @p_14) :rule equiv1 :premises (t36))
(step t38 (cl @p_28) :rule evaluate)
(step t39 (cl @p_14) :rule resolution :premises (t37 t38))
(step t40 (cl (not (! (not @p_16) :named @p_17)) @p_13) :rule not_not)
(step t41 (cl @p_17) :rule not_implies2 :premises (t31))
(step t42 (cl @p_13) :rule resolution :premises (t40 t41))
(step t43 (cl @p_15) :rule and_intro :premises (t39 t42))
(step t44 (cl @p_12) :rule resolution :premises (t35 t43))
(step t45 (cl @p_11) :rule resolution :premises (t14 t33 t44))
(step t46 (cl false) :rule resolution :premises (t0 t13 t45))
(step t47 (cl (not false)) :rule false)
(step t48 (cl) :rule resolution :premises (t46 t47))
)
7a239375a2fd07fadb46231ace1251f58938c76a 40 0
unsat
(
(assume a0 (! (not (! (< (! (* 0 (! (+ 1 (! (of_nat$ y$) :named @p_1)) :named @p_2)) :named @p_6) (! (ite (! (< @p_2 @p_1) :named @p_4) 0 (! (- @p_2 @p_1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_8))
(step t0 (cl (not (! (= @p_8 false) :named @p_10)) (not @p_8) false) :rule equiv_pos2)
(step t1 (cl (= @p_7 (! (not (! (>= @p_6 @p_5) :named @p_12)) :named @p_13))) :rule rare_rewrite :args ("arith-elim-lt" @p_6 @p_5))
(step t2 (cl (= @p_6 0)) :rule poly_simp)
(step t3 (cl (= @p_4 (! (not (! (>= @p_2 @p_1) :named @p_21)) :named @p_22))) :rule rare_rewrite :args ("arith-elim-lt" @p_2 @p_1))
(step t4 (cl (= @p_21 (! (>= @p_3 0) :named @p_23))) :rule rare_rewrite :args ("arith-geq-norm1-int" @p_2 @p_1))
(step t5 (cl (! (= @p_3 1) :named @p_16)) :rule poly_simp)
(step t6 (cl (! (= 0 0) :named @p_20)) :rule refl)
(step t7 (cl (= @p_23 (! (>= 1 0) :named @p_24))) :rule cong :premises (t5 t6))
(step t8 (cl (= @p_24 true)) :rule evaluate)
(step t9 (cl (= @p_23 true)) :rule trans :premises (t7 t8))
(step t10 (cl (= @p_21 true)) :rule trans :premises (t4 t9))
(step t11 (cl (= @p_22 (! (not true) :named @p_11))) :rule cong :premises (t10))
(step t12 (cl (= @p_11 false)) :rule evaluate)
(step t13 (cl (= @p_22 false)) :rule trans :premises (t11 t12))
(step t14 (cl (= @p_4 false)) :rule trans :premises (t3 t13))
(step t15 (cl @p_20) :rule refl)
(step t16 (cl (= @p_3 (! (+ @p_2 (! (* -1 @p_1) :named @p_17)) :named @p_18))) :rule poly_simp)
(step t17 (cl (= @p_18 (! (+ @p_17 @p_1 1) :named @p_19))) :rule poly_simp)
(step t18 (cl (= @p_19 1)) :rule poly_simp)
(step t19 (cl (= @p_18 1)) :rule trans :premises (t17 t18))
(step t20 (cl @p_16) :rule trans :premises (t16 t19))
(step t21 (cl (= @p_5 (! (ite false 0 1) :named @p_15))) :rule cong :premises (t14 t15 t20))
(step t22 (cl (= @p_15 1)) :rule evaluate)
(step t23 (cl (= @p_5 1)) :rule trans :premises (t21 t22))
(step t24 (cl (= @p_12 (! (>= 0 1) :named @p_14))) :rule cong :premises (t2 t23))
(step t25 (cl (= @p_14 false)) :rule evaluate)
(step t26 (cl (= @p_12 false)) :rule trans :premises (t24 t25))
(step t27 (cl (= @p_13 (! (not false) :named @p_9))) :rule cong :premises (t26))
(step t28 (cl (= @p_9 true)) :rule evaluate)
(step t29 (cl (= @p_13 true)) :rule trans :premises (t27 t28))
(step t30 (cl (= @p_7 true)) :rule trans :premises (t1 t29))
(step t31 (cl (= @p_8 @p_11)) :rule cong :premises (t30))
(step t32 (cl @p_10) :rule trans :premises (t31 t12))
(step t33 (cl false) :rule resolution :premises (t0 t32 a0))
(step t34 (cl @p_9) :rule false)
(step t35 (cl) :rule resolution :premises (t33 t34))
)
9c2e4b047388a21b49195e2315b51253610241ae 53 0
unsat
(
(assume a0 (! (not (! (or false (! (or (! (= (! (ite (! (< 0 (! (+ 1 (! (of_nat$ y$) :named @p_1)) :named @p_2)) :named @p_3) true false) :named @p_4) (! (= (! (ite (! (< @p_2 1) :named @p_8) 0 (! (- @p_2 1) :named @p_7)) :named @p_9) (! (of_nat$ y$) :named @p_1)) :named @p_10)) :named @p_11) (! (=> (! (not @p_4) :named @p_5) false) :named @p_6)) :named @p_12)) :named @p_13)) :named @p_14))
(assume a1 (! (<= 0 @p_1) :named @p_15))
(step t0 (cl (! (or (! (= (! (>= @p_1 0) :named @p_16) (! (= @p_1 (! (ite @p_16 @p_1 0) :named @p_17)) :named @p_18)) :named @p_19) @p_16) :named @p_20) (! (not @p_16) :named @p_25)) :rule or_neg :args (1))
(step t1 (cl (not (! (= @p_15 @p_16) :named @p_36)) (not @p_15) @p_16) :rule equiv_pos2)
(step t2 (cl @p_36) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_1))
(step t3 (cl @p_16) :rule resolution :premises (t1 t2 a1))
(step t4 (cl @p_20) :rule resolution :premises (t0 t3))
(step t5 (cl (not (! (= @p_14 (! (not @p_20) :named @p_21)) :named @p_22)) (not @p_14) @p_21) :rule equiv_pos2)
(step t6 (cl (= @p_13 @p_12)) :rule aci_simp)
(step t7 (cl (= @p_4 (! (or @p_3 false) :named @p_29))) :rule rare_rewrite :args ("ite-then-true" @p_3 false))
(step t8 (cl (= @p_29 @p_3)) :rule aci_simp)
(step t9 (cl (= @p_4 @p_3)) :rule trans :premises (t7 t8))
(step t10 (cl (= @p_3 (! (not (! (>= 0 @p_2) :named @p_23)) :named @p_24))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_2))
(step t11 (cl (= @p_25 (! (>= 0 (! (+ @p_1 1) :named @p_27)) :named @p_28))) :rule rare_rewrite :args ("arith-geq-tighten" @p_1 0))
(step t12 (cl (= @p_27 @p_2)) :rule poly_simp)
(step t13 (cl (= @p_28 @p_23)) :rule cong :premises (t12))
(step t14 (cl (= @p_25 @p_23)) :rule trans :premises (t11 t13))
(step t15 (cl (= @p_23 @p_25)) :rule symm :premises (t14))
(step t16 (cl (= @p_24 (! (not @p_25) :named @p_26))) :rule cong :premises (t15))
(step t17 (cl (= @p_26 @p_16)) :rule rare_rewrite :args ("bool-double-not-elim" @p_16))
(step t18 (cl (= @p_24 @p_16)) :rule trans :premises (t16 t17))
(step t19 (cl (= @p_3 @p_16)) :rule trans :premises (t10 t18))
(step t20 (cl (= @p_4 @p_16)) :rule trans :premises (t9 t19))
(step t21 (cl (= @p_8 (! (not (! (>= @p_2 1) :named @p_34)) :named @p_35))) :rule rare_rewrite :args ("arith-elim-lt" @p_2 1))
(step t22 (cl (= (* 1 @p_7) (* 1 (- @p_1 0)))) :rule poly_simp)
(step t23 (cl (= @p_34 @p_16)) :rule poly_simp_rel :premises (t22))
(step t24 (cl (= @p_35 @p_25)) :rule cong :premises (t23))
(step t25 (cl (= @p_8 @p_25)) :rule trans :premises (t21 t24))
(step t26 (cl (= 0 0)) :rule refl)
(step t27 (cl (= @p_7 (! (+ @p_2 (* -1 1)) :named @p_33))) :rule poly_simp)
(step t28 (cl (= @p_33 @p_1)) :rule poly_simp)
(step t29 (cl (= @p_7 @p_1)) :rule trans :premises (t27 t28))
(step t30 (cl (= @p_9 (! (ite @p_25 0 @p_1) :named @p_32))) :rule cong :premises (t25 t26 t29))
(step t31 (cl (= @p_32 @p_17)) :rule rare_rewrite :args ("ite-not-cond" @p_16 0 @p_1))
(step t32 (cl (= @p_9 @p_17)) :rule trans :premises (t30 t31))
(step t33 (cl (= @p_1 @p_1)) :rule refl)
(step t34 (cl (= @p_10 (! (= @p_17 @p_1) :named @p_31))) :rule cong :premises (t32 t33))
(step t35 (cl (= (* 1 (- @p_17 @p_1)) (* -1 (- @p_1 @p_17)))) :rule poly_simp)
(step t36 (cl (= @p_31 @p_18)) :rule poly_simp_rel :premises (t35))
(step t37 (cl (= @p_10 @p_18)) :rule trans :premises (t34 t36))
(step t38 (cl (= @p_11 @p_19)) :rule cong :premises (t20 t37))
(step t39 (cl (= @p_6 (! (not @p_5) :named @p_30))) :rule rare_rewrite :args ("bool-impl-false1" @p_5))
(step t40 (cl (= @p_30 @p_4)) :rule rare_rewrite :args ("bool-double-not-elim" @p_4))
(step t41 (cl (= @p_6 @p_4)) :rule trans :premises (t39 t40))
(step t42 (cl (= @p_6 @p_16)) :rule trans :premises (t41 t20))
(step t43 (cl (= @p_12 @p_20)) :rule cong :premises (t38 t42))
(step t44 (cl (= @p_13 @p_20)) :rule trans :premises (t6 t43))
(step t45 (cl @p_22) :rule cong :premises (t44))
(step t46 (cl @p_21) :rule resolution :premises (t5 t45 a0))
(step t47 (cl) :rule resolution :premises (t4 t46))
)
2f4eef59b39b612905b6a741cc50223a17ab3ffd 744 0
unsat
(
(assume a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0))))
(assume a1 (! (not (! (= (! (of_nat$ (! (nat$ (! (ite (! (< x$ 0) :named @p_2) (! (- x$) :named @p_1) x$) :named @p_3)) :named @p_4)) :named @p_5) @p_3) :named @p_6)) :named @p_7))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= x$ 0) :named @p_9)) :named @p_28)) :named @p_75) (! (not (! (= x$ (! (* -1 (! (ite (! (>= x$ 0) :named @p_9) x$ (! (* -1 x$) :named @p_8)) :named @p_10)) :named @p_59)) :named @p_60)) :named @p_108) (! (not (! (not (! (>= @p_10 0) :named @p_11)) :named @p_12)) :named @p_72)) :named @p_110) (! (or @p_9 @p_108 @p_11) :named @p_109)) :named @p_135)) (not @p_110) @p_109) :rule equiv_pos2)
(step t1 (cl (= @p_75 @p_9)) :rule rare_rewrite :args ("bool-double-not-elim" @p_9))
(step t2 (cl (= @p_108 @p_108)) :rule refl)
(step t3 (cl (= @p_72 @p_11)) :rule rare_rewrite :args ("bool-double-not-elim" @p_11))
(step t4 (cl @p_135) :rule cong :premises (t1 t2 t3))
(step t5 (cl (! (=> (! (and @p_28 @p_60 @p_12) :named @p_111) (! (and @p_28 @p_12 @p_60) :named @p_113)) :named @p_134) @p_111) :rule implies_neg1)
(anchor :step t6)
(assume t6.a0 @p_28)
(assume t6.a1 @p_60)
(assume t6.a2 @p_12)
(step t6.t0 (cl (not (! (= (! (ite @p_11 (! (= (! (ite @p_11 @p_10 0) :named @p_13) @p_10) :named @p_51) (! (= @p_13 0) :named @p_49)) :named @p_52) (! (ite @p_11 (! (= @p_10 @p_13) :named @p_14) (! (= @p_13 0) :named @p_49)) :named @p_50)) :named @p_57)) (! (not @p_52) :named @p_56) @p_50) :rule equiv_pos2)
(step t6.t1 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t6.t2 (cl (= @p_51 @p_14)) :rule poly_simp_rel :premises (t6.t1))
(step t6.t3 (cl (! (= @p_49 @p_49) :named @p_55)) :rule refl)
(step t6.t4 (cl @p_57) :rule cong :premises (t6.t2 t6.t3))
(step t6.t5 (cl (not (! (= @p_52 @p_52) :named @p_54)) @p_56 @p_52) :rule equiv_pos2)
(step t6.t6 (cl (= (! (= (! (= @p_13 @p_13) :named @p_45) true) :named @p_46) @p_45)) :rule equiv_simplify)
(step t6.t7 (cl (not @p_46) @p_45) :rule equiv1 :premises (t6.t6))
(step t6.t8 (cl (= (* -1 (! (- @p_13 @p_13) :named @p_48)) (* 1 @p_48))) :rule poly_simp)
(step t6.t9 (cl (! (= @p_45 @p_45) :named @p_47)) :rule poly_simp_rel :premises (t6.t8))
(step t6.t10 (cl @p_45) :rule refl)
(step t6.t11 (cl (! (= @p_10 @p_10) :named @p_23)) :rule refl)
(step t6.t12 (cl (= 0 0)) :rule refl)
(step t6.t13 (cl (= @p_11 @p_11)) :rule cong :premises (t6.t11 t6.t12))
(step t6.t14 (cl @p_45) :rule cong :premises (t6.t13 t6.t11 t6.t12))
(step t6.t15 (cl @p_45) :rule trans :premises (t6.t10 t6.t14))
(step t6.t16 (cl @p_47) :rule cong :premises (t6.t15 t6.t14))
(step t6.t17 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_13))
(step t6.t18 (cl @p_46) :rule trans :premises (t6.t9 t6.t16 t6.t17))
(step t6.t19 (cl @p_45) :rule resolution :premises (t6.t7 t6.t18))
(step t6.t20 (cl @p_23) :rule refl)
(step t6.t21 (cl (= @p_51 @p_51)) :rule cong :premises (t6.t19 t6.t20))
(step t6.t22 (cl @p_55) :rule cong :premises (t6.t19 t6.t12))
(step t6.t23 (cl @p_54) :rule cong :premises (t6.t21 t6.t22))
(step t6.t24 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_11 @p_10 0))
(step t6.t25 (cl @p_52 (! (not true) :named @p_53)) :rule equiv2 :premises (t6.t24))
(step t6.t26 (cl true) :rule true)
(step t6.t27 (cl @p_52) :rule resolution :premises (t6.t25 t6.t26))
(step t6.t28 (cl @p_52) :rule resolution :premises (t6.t5 t6.t23 t6.t27))
(step t6.t29 (cl @p_50) :rule resolution :premises (t6.t0 t6.t4 t6.t28))
(step t6.t30 (cl @p_12 @p_14) :rule ite2 :premises (t6.t29))
(step t6.t31 (cl @p_14 @p_12) :rule reordering :premises (t6.t30))
(step t6.t32 (cl (= (! (= @p_14 false) :named @p_16) (! (not @p_14) :named @p_15))) :rule equiv_simplify)
(step t6.t33 (cl (not @p_16) @p_15) :rule equiv1 :premises (t6.t32))
(step t6.t34 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))) (! (= (! (of_nat$ (! (nat$ @p_10) :named @p_17)) :named @p_18) @p_13) :named @p_41)) :named @p_42) (! (=> (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))) (! (= @p_13 @p_18) :named @p_31)) :named @p_40)) :named @p_43)) (not @p_42) @p_40) :rule equiv_pos2)
(step t6.t35 (cl (= @p_41 @p_41)) :rule cong :premises (t6.t19))
(step t6.t36 (cl (= (* -1 (- @p_18 @p_13)) (* 1 (- @p_13 @p_18)))) :rule poly_simp)
(step t6.t37 (cl (! (= @p_41 @p_31) :named @p_44)) :rule poly_simp_rel :premises (t6.t36))
(step t6.t38 (cl @p_44) :rule trans :premises (t6.t35 t6.t37))
(step t6.t39 (cl @p_43) :rule cong :premises (t6.t38))
(step t6.t40 (cl @p_42 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t6.t41)
(assume t6.t41.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t6.t41.t0 (cl (or (! (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :named @p_39) @p_41)) :rule forall_inst :args (@p_10))
(step t6.t41.t1 (cl @p_39 @p_41) :rule or :premises (t6.t41.t0))
(step t6.t41.t2 (cl (not (! (= (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :named @p_32)) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t6.t41.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t6.t41.t3.t0 (cl (= (! (<= 0 ?v0) :named @p_37) (! (>= ?v0 0) :named @p_34))) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t6.t41.t3.t1 (cl (! (= ?v0 ?v0) :named @p_33)) :rule refl)
(step t6.t41.t3.t2 (cl (= (! (ite @p_37 ?v0 0) :named @p_38) (! (ite @p_34 ?v0 0) :named @p_35))) :rule cong :premises (t6.t41.t3.t0 t6.t41.t3.t1 t6.t12))
(step t6.t41.t3.t3 (cl (= (= (! (of_nat$ (nat$ ?v0)) :named @p_36) @p_38) (= @p_36 @p_35))) :rule cong :premises (t6.t41.t3.t2))
(step t6.t41.t3 (cl @p_32) :rule bind)
(step t6.t41.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t6.t41.t2 t6.t41.t3 a0))
(step t6.t41.t5 (cl @p_41) :rule resolution :premises (t6.t41.t1 t6.t41.t4))
(step t6.t41 (cl @p_39 @p_41) :rule subproof :discharge (t6.t41.a0))
(step t6.t42 (cl @p_42 @p_41) :rule resolution :premises (t6.t40 t6.t41))
(step t6.t43 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t6.t44 (cl @p_42 @p_42) :rule resolution :premises (t6.t42 t6.t43))
(step t6.t45 (cl @p_42) :rule contraction :premises (t6.t44))
(step t6.t46 (cl @p_40) :rule resolution :premises (t6.t34 t6.t39 t6.t45))
(step t6.t47 (cl @p_39 @p_31) :rule implies :premises (t6.t46))
(step t6.t48 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t6.t49 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t6.t49.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t6.t49.t1 (cl @p_33) :rule refl)
(step t6.t49.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t6.t49.t0 t6.t49.t1 t6.t12))
(step t6.t49.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t6.t49.t2))
(step t6.t49 (cl @p_32) :rule bind)
(step t6.t50 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t6.t48 t6.t49 a0))
(step t6.t51 (cl @p_31) :rule resolution :premises (t6.t47 t6.t50))
(step t6.t52 (cl (= @p_14 (! (= @p_10 @p_18) :named @p_19))) :rule cong :premises (t6.t51))
(step t6.t53 (cl (= (! (= @p_19 false) :named @p_20) (! (not @p_19) :named @p_21))) :rule equiv_simplify)
(step t6.t54 (cl @p_20 (! (not @p_21) :named @p_30)) :rule equiv2 :premises (t6.t53))
(step t6.t55 (cl (not @p_30) @p_19) :rule not_not)
(step t6.t56 (cl @p_20 @p_19) :rule resolution :premises (t6.t54 t6.t55))
(step t6.t57 (cl (not (! (= @p_7 @p_21) :named @p_22)) (not @p_7) @p_21) :rule equiv_pos2)
(step t6.t58 (cl (= @p_2 @p_28)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0))
(step t6.t59 (cl (= @p_1 @p_8)) :rule poly_simp)
(step t6.t60 (cl (= x$ x$)) :rule refl)
(step t6.t61 (cl (= @p_3 (! (ite @p_28 @p_8 x$) :named @p_29))) :rule cong :premises (t6.t58 t6.t59 t6.t60))
(step t6.t62 (cl (= @p_29 @p_10)) :rule rare_rewrite :args ("ite-not-cond" @p_9 @p_8 x$))
(step t6.t63 (cl (= @p_3 @p_10)) :rule trans :premises (t6.t61 t6.t62))
(step t6.t64 (cl (= @p_4 @p_17)) :rule cong :premises (t6.t63))
(step t6.t65 (cl (= @p_5 @p_18)) :rule cong :premises (t6.t64))
(step t6.t66 (cl (= @p_6 (! (= @p_18 @p_10) :named @p_27))) :rule cong :premises (t6.t65 t6.t63))
(step t6.t67 (cl (= (* 1 (- @p_18 @p_10)) (* -1 (- @p_10 @p_18)))) :rule poly_simp)
(step t6.t68 (cl (= @p_27 @p_19)) :rule poly_simp_rel :premises (t6.t67))
(step t6.t69 (cl (= @p_6 @p_19)) :rule trans :premises (t6.t66 t6.t68))
(step t6.t70 (cl @p_22) :rule cong :premises (t6.t69))
(step t6.t71 (cl (= (! (= @p_23 true) :named @p_24) @p_23)) :rule equiv_simplify)
(step t6.t72 (cl (not @p_24) @p_23) :rule equiv1 :premises (t6.t71))
(step t6.t73 (cl (= (* -1 (! (- @p_10 @p_10) :named @p_26)) (* 1 @p_26))) :rule poly_simp)
(step t6.t74 (cl (! (= @p_23 @p_23) :named @p_25)) :rule poly_simp_rel :premises (t6.t73))
(step t6.t75 (cl @p_23) :rule refl)
(step t6.t76 (cl @p_25) :rule cong :premises (t6.t11 t6.t75))
(step t6.t77 (cl @p_24) :rule rare_rewrite :args ("eq-refl" @p_10))
(step t6.t78 (cl @p_24) :rule trans :premises (t6.t74 t6.t76 t6.t77))
(step t6.t79 (cl @p_23) :rule resolution :premises (t6.t72 t6.t78))
(step t6.t80 (cl (= @p_17 @p_17)) :rule cong :premises (t6.t79))
(step t6.t81 (cl (= @p_18 @p_18)) :rule cong :premises (t6.t80))
(step t6.t82 (cl (= @p_19 @p_19)) :rule cong :premises (t6.t79 t6.t81))
(step t6.t83 (cl (= @p_21 @p_21)) :rule cong :premises (t6.t82))
(step t6.t84 (cl @p_22) :rule trans :premises (t6.t70 t6.t83))
(step t6.t85 (cl @p_21) :rule resolution :premises (t6.t57 t6.t84 a1))
(step t6.t86 (cl @p_20) :rule resolution :premises (t6.t56 t6.t85))
(step t6.t87 (cl @p_16) :rule trans :premises (t6.t52 t6.t86))
(step t6.t88 (cl @p_15) :rule resolution :premises (t6.t33 t6.t87))
(step t6.t89 (cl @p_12) :rule resolution :premises (t6.t31 t6.t88))
(step t6.t90 (cl @p_113) :rule and_intro :premises (t6.a0 t6.t89 t6.a1))
(step t6 (cl @p_75 @p_108 @p_72 @p_113) :rule subproof :discharge (t6.a0 t6.a1 t6.a2))
(step t7 (cl (! (not @p_111) :named @p_112) @p_28) :rule and_pos :args (0))
(step t8 (cl @p_112 @p_60) :rule and_pos :args (1))
(step t9 (cl @p_112 @p_12) :rule and_pos :args (2))
(step t10 (cl @p_113 @p_112 @p_112 @p_112) :rule resolution :premises (t6 t7 t8 t9))
(step t11 (cl @p_112 @p_112 @p_112 @p_113) :rule reordering :premises (t10))
(step t12 (cl @p_112 @p_113) :rule contraction :premises (t11))
(step t13 (cl @p_134 @p_113) :rule resolution :premises (t5 t12))
(step t14 (cl @p_134 (! (not @p_113) :named @p_114)) :rule implies_neg2)
(step t15 (cl @p_134 @p_134) :rule resolution :premises (t13 t14))
(step t16 (cl @p_134) :rule contraction :premises (t15))
(step t17 (cl @p_112 @p_113) :rule implies :premises (t16))
(step t18 (cl (! (=> @p_113 false) :named @p_115) @p_113) :rule implies_neg1)
(anchor :step t19)
(assume t19.a0 @p_28)
(assume t19.a1 @p_12)
(assume t19.a2 @p_60)
(step t19.t0 (cl (not (! (= @p_60 (! (= (! (+ x$ @p_10) :named @p_116) 0) :named @p_117)) :named @p_133)) @p_108 @p_117) :rule equiv_pos2)
(step t19.t1 (cl (= (* 1 (- @p_116 0)) (! (* 1 (- x$ @p_59)) :named @p_68))) :rule poly_simp)
(step t19.t2 (cl (= @p_117 @p_60)) :rule poly_simp_rel :premises (t19.t1))
(step t19.t3 (cl @p_133) :rule symm :premises (t19.t2))
(step t19.t4 (cl @p_117) :rule resolution :premises (t19.t0 t19.t3 t19.a2))
(step t19.t5 (cl (! (=> @p_117 false) :named @p_119) @p_117) :rule implies_neg1)
(anchor :step t19.t6)
(assume t19.t6.a0 @p_117)
(step t19.t6.t0 (cl (not (! (= (! (< (! (+ (! (* -1 @p_116) :named @p_121) @p_10 x$) :named @p_122) (! (+ (! (* -1 0) :named @p_86) 0 0) :named @p_120)) :named @p_123) false) :named @p_127)) (not @p_123) false) :rule equiv_pos2)
(step t19.t6.t1 (cl (= @p_123 (! (not (! (>= @p_122 @p_120) :named @p_128)) :named @p_129))) :rule rare_rewrite :args ("arith-elim-lt" @p_122 @p_120))
(step t19.t6.t2 (cl (= @p_121 (! (+ @p_8 @p_59) :named @p_130))) :rule poly_simp)
(step t19.t6.t3 (cl @p_23) :rule refl)
(step t19.t6.t4 (cl (= x$ x$)) :rule refl)
(step t19.t6.t5 (cl (= @p_122 (! (+ @p_130 @p_10 x$) :named @p_131))) :rule cong :premises (t19.t6.t2 t19.t6.t3 t19.t6.t4))
(step t19.t6.t6 (cl (= @p_131 0)) :rule poly_simp)
(step t19.t6.t7 (cl (= @p_122 0)) :rule trans :premises (t19.t6.t5 t19.t6.t6))
(step t19.t6.t8 (cl (= @p_86 0)) :rule evaluate)
(step t19.t6.t9 (cl (= 0 0)) :rule refl)
(step t19.t6.t10 (cl (= @p_120 (! (+ 0 0 0) :named @p_102))) :rule cong :premises (t19.t6.t8 t19.t6.t9 t19.t6.t9))
(step t19.t6.t11 (cl (= @p_102 0)) :rule evaluate)
(step t19.t6.t12 (cl (= @p_120 0)) :rule trans :premises (t19.t6.t10 t19.t6.t11))
(step t19.t6.t13 (cl (= @p_128 (! (>= 0 0) :named @p_101))) :rule cong :premises (t19.t6.t7 t19.t6.t12))
(step t19.t6.t14 (cl (= @p_101 true)) :rule evaluate)
(step t19.t6.t15 (cl (= @p_128 true)) :rule trans :premises (t19.t6.t13 t19.t6.t14))
(step t19.t6.t16 (cl (= @p_129 @p_53)) :rule cong :premises (t19.t6.t15))
(step t19.t6.t17 (cl (= @p_53 false)) :rule evaluate)
(step t19.t6.t18 (cl (= @p_129 false)) :rule trans :premises (t19.t6.t16 t19.t6.t17))
(step t19.t6.t19 (cl @p_127) :rule trans :premises (t19.t6.t1 t19.t6.t18))
(step t19.t6.t20 (cl (not (! (= @p_121 @p_86) :named @p_125)) (! (not (! (< @p_10 0) :named @p_94)) :named @p_97) (not @p_2) @p_123) :rule la_generic :args (-1/1 1/1 1/1 1/1))
(step t19.t6.t21 (cl (=> (! (and (! (< -1 0) :named @p_91) @p_117) :named @p_126) @p_125)) :rule la_mult_neg)
(step t19.t6.t22 (cl (not @p_126) @p_125) :rule implies :premises (t19.t6.t21))
(step t19.t6.t23 (cl (= (! (= @p_91 true) :named @p_93) @p_91)) :rule equiv_simplify)
(step t19.t6.t24 (cl (not @p_93) @p_91) :rule equiv1 :premises (t19.t6.t23))
(step t19.t6.t25 (cl @p_93) :rule evaluate)
(step t19.t6.t26 (cl @p_91) :rule resolution :premises (t19.t6.t24 t19.t6.t25))
(step t19.t6.t27 (cl @p_126) :rule and_intro :premises (t19.t6.t26 t19.t6.a0))
(step t19.t6.t28 (cl @p_125) :rule resolution :premises (t19.t6.t22 t19.t6.t27))
(step t19.t6.t29 (cl (not (! (= @p_12 @p_94) :named @p_95)) @p_72 @p_94) :rule equiv_pos2)
(step t19.t6.t30 (cl (= @p_94 @p_12)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 0))
(step t19.t6.t31 (cl @p_95) :rule symm :premises (t19.t6.t30))
(step t19.t6.t32 (cl (not @p_57) @p_56 @p_50) :rule equiv_pos2)
(step t19.t6.t33 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t19.t6.t34 (cl (= @p_51 @p_14)) :rule poly_simp_rel :premises (t19.t6.t33))
(step t19.t6.t35 (cl @p_55) :rule refl)
(step t19.t6.t36 (cl @p_57) :rule cong :premises (t19.t6.t34 t19.t6.t35))
(step t19.t6.t37 (cl (not @p_54) @p_56 @p_52) :rule equiv_pos2)
(step t19.t6.t38 (cl (= @p_46 @p_45)) :rule equiv_simplify)
(step t19.t6.t39 (cl (not @p_46) @p_45) :rule equiv1 :premises (t19.t6.t38))
(step t19.t6.t40 (cl (= (* -1 @p_48) (* 1 @p_48))) :rule poly_simp)
(step t19.t6.t41 (cl @p_47) :rule poly_simp_rel :premises (t19.t6.t40))
(step t19.t6.t42 (cl @p_45) :rule refl)
(step t19.t6.t43 (cl @p_23) :rule refl)
(step t19.t6.t44 (cl (= @p_11 @p_11)) :rule cong :premises (t19.t6.t43 t19.t6.t9))
(step t19.t6.t45 (cl @p_45) :rule cong :premises (t19.t6.t44 t19.t6.t43 t19.t6.t9))
(step t19.t6.t46 (cl @p_45) :rule trans :premises (t19.t6.t42 t19.t6.t45))
(step t19.t6.t47 (cl @p_47) :rule cong :premises (t19.t6.t46 t19.t6.t45))
(step t19.t6.t48 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_13))
(step t19.t6.t49 (cl @p_46) :rule trans :premises (t19.t6.t41 t19.t6.t47 t19.t6.t48))
(step t19.t6.t50 (cl @p_45) :rule resolution :premises (t19.t6.t39 t19.t6.t49))
(step t19.t6.t51 (cl (= @p_51 @p_51)) :rule cong :premises (t19.t6.t50 t19.t6.t3))
(step t19.t6.t52 (cl @p_55) :rule cong :premises (t19.t6.t50 t19.t6.t9))
(step t19.t6.t53 (cl @p_54) :rule cong :premises (t19.t6.t51 t19.t6.t52))
(step t19.t6.t54 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_11 @p_10 0))
(step t19.t6.t55 (cl @p_52 @p_53) :rule equiv2 :premises (t19.t6.t54))
(step t19.t6.t56 (cl true) :rule true)
(step t19.t6.t57 (cl @p_52) :rule resolution :premises (t19.t6.t55 t19.t6.t56))
(step t19.t6.t58 (cl @p_52) :rule resolution :premises (t19.t6.t37 t19.t6.t53 t19.t6.t57))
(step t19.t6.t59 (cl @p_50) :rule resolution :premises (t19.t6.t32 t19.t6.t36 t19.t6.t58))
(step t19.t6.t60 (cl @p_12 @p_14) :rule ite2 :premises (t19.t6.t59))
(step t19.t6.t61 (cl @p_14 @p_12) :rule reordering :premises (t19.t6.t60))
(step t19.t6.t62 (cl (= @p_16 @p_15)) :rule equiv_simplify)
(step t19.t6.t63 (cl (not @p_16) @p_15) :rule equiv1 :premises (t19.t6.t62))
(step t19.t6.t64 (cl (not @p_43) (not @p_42) @p_40) :rule equiv_pos2)
(step t19.t6.t65 (cl (= @p_41 @p_41)) :rule cong :premises (t19.t6.t50))
(step t19.t6.t66 (cl (= (* -1 (- @p_18 @p_13)) (* 1 (- @p_13 @p_18)))) :rule poly_simp)
(step t19.t6.t67 (cl @p_44) :rule poly_simp_rel :premises (t19.t6.t66))
(step t19.t6.t68 (cl @p_44) :rule trans :premises (t19.t6.t65 t19.t6.t67))
(step t19.t6.t69 (cl @p_43) :rule cong :premises (t19.t6.t68))
(step t19.t6.t70 (cl @p_42 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t19.t6.t71)
(assume t19.t6.t71.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t19.t6.t71.t0 (cl (or @p_39 @p_41)) :rule forall_inst :args (@p_10))
(step t19.t6.t71.t1 (cl @p_39 @p_41) :rule or :premises (t19.t6.t71.t0))
(step t19.t6.t71.t2 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t19.t6.t71.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t19.t6.t71.t3.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t19.t6.t71.t3.t1 (cl @p_33) :rule refl)
(step t19.t6.t71.t3.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t19.t6.t71.t3.t0 t19.t6.t71.t3.t1 t19.t6.t9))
(step t19.t6.t71.t3.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t19.t6.t71.t3.t2))
(step t19.t6.t71.t3 (cl @p_32) :rule bind)
(step t19.t6.t71.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t19.t6.t71.t2 t19.t6.t71.t3 a0))
(step t19.t6.t71.t5 (cl @p_41) :rule resolution :premises (t19.t6.t71.t1 t19.t6.t71.t4))
(step t19.t6.t71 (cl @p_39 @p_41) :rule subproof :discharge (t19.t6.t71.a0))
(step t19.t6.t72 (cl @p_42 @p_41) :rule resolution :premises (t19.t6.t70 t19.t6.t71))
(step t19.t6.t73 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t19.t6.t74 (cl @p_42 @p_42) :rule resolution :premises (t19.t6.t72 t19.t6.t73))
(step t19.t6.t75 (cl @p_42) :rule contraction :premises (t19.t6.t74))
(step t19.t6.t76 (cl @p_40) :rule resolution :premises (t19.t6.t64 t19.t6.t69 t19.t6.t75))
(step t19.t6.t77 (cl @p_39 @p_31) :rule implies :premises (t19.t6.t76))
(step t19.t6.t78 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t19.t6.t79 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t19.t6.t79.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t19.t6.t79.t1 (cl @p_33) :rule refl)
(step t19.t6.t79.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t19.t6.t79.t0 t19.t6.t79.t1 t19.t6.t9))
(step t19.t6.t79.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t19.t6.t79.t2))
(step t19.t6.t79 (cl @p_32) :rule bind)
(step t19.t6.t80 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t19.t6.t78 t19.t6.t79 a0))
(step t19.t6.t81 (cl @p_31) :rule resolution :premises (t19.t6.t77 t19.t6.t80))
(step t19.t6.t82 (cl (= @p_14 @p_19)) :rule cong :premises (t19.t6.t81))
(step t19.t6.t83 (cl (= @p_20 @p_21)) :rule equiv_simplify)
(step t19.t6.t84 (cl @p_20 @p_30) :rule equiv2 :premises (t19.t6.t83))
(step t19.t6.t85 (cl (not @p_30) @p_19) :rule not_not)
(step t19.t6.t86 (cl @p_20 @p_19) :rule resolution :premises (t19.t6.t84 t19.t6.t85))
(step t19.t6.t87 (cl (not @p_22) (not @p_7) @p_21) :rule equiv_pos2)
(step t19.t6.t88 (cl (= @p_2 @p_28)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0))
(step t19.t6.t89 (cl (= @p_1 @p_8)) :rule poly_simp)
(step t19.t6.t90 (cl (= @p_3 @p_29)) :rule cong :premises (t19.t6.t88 t19.t6.t89 t19.t6.t4))
(step t19.t6.t91 (cl (= @p_29 @p_10)) :rule rare_rewrite :args ("ite-not-cond" @p_9 @p_8 x$))
(step t19.t6.t92 (cl (= @p_3 @p_10)) :rule trans :premises (t19.t6.t90 t19.t6.t91))
(step t19.t6.t93 (cl (= @p_4 @p_17)) :rule cong :premises (t19.t6.t92))
(step t19.t6.t94 (cl (= @p_5 @p_18)) :rule cong :premises (t19.t6.t93))
(step t19.t6.t95 (cl (= @p_6 @p_27)) :rule cong :premises (t19.t6.t94 t19.t6.t92))
(step t19.t6.t96 (cl (= (* 1 (- @p_18 @p_10)) (* -1 (- @p_10 @p_18)))) :rule poly_simp)
(step t19.t6.t97 (cl (= @p_27 @p_19)) :rule poly_simp_rel :premises (t19.t6.t96))
(step t19.t6.t98 (cl (= @p_6 @p_19)) :rule trans :premises (t19.t6.t95 t19.t6.t97))
(step t19.t6.t99 (cl @p_22) :rule cong :premises (t19.t6.t98))
(step t19.t6.t100 (cl (= @p_24 @p_23)) :rule equiv_simplify)
(step t19.t6.t101 (cl (not @p_24) @p_23) :rule equiv1 :premises (t19.t6.t100))
(step t19.t6.t102 (cl (= (* -1 @p_26) (* 1 @p_26))) :rule poly_simp)
(step t19.t6.t103 (cl @p_25) :rule poly_simp_rel :premises (t19.t6.t102))
(step t19.t6.t104 (cl @p_23) :rule refl)
(step t19.t6.t105 (cl @p_25) :rule cong :premises (t19.t6.t43 t19.t6.t104))
(step t19.t6.t106 (cl @p_24) :rule rare_rewrite :args ("eq-refl" @p_10))
(step t19.t6.t107 (cl @p_24) :rule trans :premises (t19.t6.t103 t19.t6.t105 t19.t6.t106))
(step t19.t6.t108 (cl @p_23) :rule resolution :premises (t19.t6.t101 t19.t6.t107))
(step t19.t6.t109 (cl (= @p_17 @p_17)) :rule cong :premises (t19.t6.t108))
(step t19.t6.t110 (cl (= @p_18 @p_18)) :rule cong :premises (t19.t6.t109))
(step t19.t6.t111 (cl (= @p_19 @p_19)) :rule cong :premises (t19.t6.t108 t19.t6.t110))
(step t19.t6.t112 (cl (= @p_21 @p_21)) :rule cong :premises (t19.t6.t111))
(step t19.t6.t113 (cl @p_22) :rule trans :premises (t19.t6.t99 t19.t6.t112))
(step t19.t6.t114 (cl @p_21) :rule resolution :premises (t19.t6.t87 t19.t6.t113 a1))
(step t19.t6.t115 (cl @p_20) :rule resolution :premises (t19.t6.t86 t19.t6.t114))
(step t19.t6.t116 (cl @p_16) :rule trans :premises (t19.t6.t82 t19.t6.t115))
(step t19.t6.t117 (cl @p_15) :rule resolution :premises (t19.t6.t63 t19.t6.t116))
(step t19.t6.t118 (cl @p_12) :rule resolution :premises (t19.t6.t61 t19.t6.t117))
(step t19.t6.t119 (cl @p_94) :rule resolution :premises (t19.t6.t29 t19.t6.t31 t19.t6.t118))
(step t19.t6.t120 (cl (not (! (= @p_28 @p_2) :named @p_124)) @p_75 @p_2) :rule equiv_pos2)
(step t19.t6.t121 (cl @p_124) :rule symm :premises (t19.t6.t88))
(step t19.t6.t122 (cl @p_2) :rule resolution :premises (t19.t6.t120 t19.t6.t121 t19.a0))
(step t19.t6.t123 (cl @p_123) :rule resolution :premises (t19.t6.t20 t19.t6.t28 t19.t6.t119 t19.t6.t122))
(step t19.t6.t124 (cl false) :rule resolution :premises (t19.t6.t0 t19.t6.t19 t19.t6.t123))
(step t19.t6 (cl (! (not @p_117) :named @p_118) false) :rule subproof :discharge (t19.t6.a0))
(step t19.t7 (cl @p_119 false) :rule resolution :premises (t19.t5 t19.t6))
(step t19.t8 (cl @p_119 (! (not false) :named @p_81)) :rule implies_neg2)
(step t19.t9 (cl @p_119 @p_119) :rule resolution :premises (t19.t7 t19.t8))
(step t19.t10 (cl @p_119) :rule contraction :premises (t19.t9))
(step t19.t11 (cl (= @p_119 @p_118)) :rule implies_simplify)
(step t19.t12 (cl (not @p_119) @p_118) :rule equiv1 :premises (t19.t11))
(step t19.t13 (cl @p_118) :rule resolution :premises (t19.t10 t19.t12))
(step t19.t14 (cl) :rule resolution :premises (t19.t4 t19.t13))
(step t19 (cl @p_75 @p_72 @p_108 false) :rule subproof :discharge (t19.a0 t19.a1 t19.a2))
(step t20 (cl @p_114 @p_28) :rule and_pos :args (0))
(step t21 (cl @p_114 @p_12) :rule and_pos :args (1))
(step t22 (cl @p_114 @p_60) :rule and_pos :args (2))
(step t23 (cl false @p_114 @p_114 @p_114) :rule resolution :premises (t19 t20 t21 t22))
(step t24 (cl @p_114 @p_114 @p_114 false) :rule reordering :premises (t23))
(step t25 (cl @p_114 false) :rule contraction :premises (t24))
(step t26 (cl @p_115 false) :rule resolution :premises (t18 t25))
(step t27 (cl @p_115 @p_81) :rule implies_neg2)
(step t28 (cl @p_115 @p_115) :rule resolution :premises (t26 t27))
(step t29 (cl @p_115) :rule contraction :premises (t28))
(step t30 (cl (= @p_115 @p_114)) :rule implies_simplify)
(step t31 (cl (not @p_115) @p_114) :rule equiv1 :premises (t30))
(step t32 (cl @p_114) :rule resolution :premises (t29 t31))
(step t33 (cl @p_112) :rule resolution :premises (t17 t32))
(step t34 (cl @p_75 @p_108 @p_72) :rule not_and :premises (t33))
(step t35 (cl @p_110 (not @p_75)) :rule or_neg :args (0))
(step t36 (cl @p_110 (not @p_108)) :rule or_neg :args (1))
(step t37 (cl @p_110 (! (not @p_72) :named @p_74)) :rule or_neg :args (2))
(step t38 (cl @p_110 @p_110 @p_110) :rule resolution :premises (t34 t35 t36 t37))
(step t39 (cl @p_110) :rule contraction :premises (t38))
(step t40 (cl @p_109) :rule resolution :premises (t0 t4 t39))
(step t41 (cl @p_9 @p_108 @p_11) :rule or :premises (t40))
(step t42 (cl (not (! (= (! (ite @p_9 (! (= @p_10 x$) :named @p_63) (! (= @p_10 @p_8) :named @p_62)) :named @p_64) (! (ite @p_9 (! (= x$ @p_10) :named @p_58) @p_60) :named @p_61)) :named @p_67)) (! (not @p_64) :named @p_66) @p_61) :rule equiv_pos2)
(step t43 (cl (= (* 1 (- @p_10 x$)) (* -1 (! (- x$ @p_10) :named @p_69)))) :rule poly_simp)
(step t44 (cl (= @p_63 @p_58)) :rule poly_simp_rel :premises (t43))
(step t45 (cl (= (* 1 (- @p_10 @p_8)) @p_68)) :rule poly_simp)
(step t46 (cl (= @p_62 @p_60)) :rule poly_simp_rel :premises (t45))
(step t47 (cl @p_67) :rule cong :premises (t44 t46))
(step t48 (cl (not (! (= @p_64 @p_64) :named @p_65)) @p_66 @p_64) :rule equiv_pos2)
(step t49 (cl (= @p_24 @p_23)) :rule equiv_simplify)
(step t50 (cl (not @p_24) @p_23) :rule equiv1 :premises (t49))
(step t51 (cl (= (* -1 @p_26) (* 1 @p_26))) :rule poly_simp)
(step t52 (cl @p_25) :rule poly_simp_rel :premises (t51))
(step t53 (cl @p_23) :rule refl)
(step t54 (cl @p_23) :rule refl)
(step t55 (cl @p_25) :rule cong :premises (t53 t54))
(step t56 (cl @p_24) :rule rare_rewrite :args ("eq-refl" @p_10))
(step t57 (cl @p_24) :rule trans :premises (t52 t55 t56))
(step t58 (cl @p_23) :rule resolution :premises (t50 t57))
(step t59 (cl (= x$ x$)) :rule refl)
(step t60 (cl (= @p_63 @p_63)) :rule cong :premises (t58 t59))
(step t61 (cl (= @p_8 @p_8)) :rule refl)
(step t62 (cl (= @p_62 @p_62)) :rule cong :premises (t58 t61))
(step t63 (cl @p_65) :rule cong :premises (t60 t62))
(step t64 (cl (= @p_64 true)) :rule rare_rewrite :args ("ite-eq" @p_9 x$ @p_8))
(step t65 (cl @p_64 @p_53) :rule equiv2 :premises (t64))
(step t66 (cl true) :rule true)
(step t67 (cl @p_64) :rule resolution :premises (t65 t66))
(step t68 (cl @p_64) :rule resolution :premises (t48 t63 t67))
(step t69 (cl @p_61) :rule resolution :premises (t42 t47 t68))
(step t70 (cl @p_9 @p_60) :rule ite1 :premises (t69))
(step t71 (cl (not (! (= (! (or @p_28 (! (not @p_58) :named @p_70) @p_72) :named @p_73) (! (or @p_28 @p_70 @p_11) :named @p_71)) :named @p_107)) (not @p_73) @p_71) :rule equiv_pos2)
(step t72 (cl @p_107) :rule cong :premises (t3))
(step t73 (cl (! (=> (! (and @p_9 @p_58 @p_12) :named @p_76) (! (and @p_9 @p_12 @p_58) :named @p_78)) :named @p_106) @p_76) :rule implies_neg1)
(anchor :step t74)
(assume t74.a0 @p_9)
(assume t74.a1 @p_58)
(assume t74.a2 @p_12)
(step t74.t0 (cl (not @p_57) @p_56 @p_50) :rule equiv_pos2)
(step t74.t1 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t74.t2 (cl (= @p_51 @p_14)) :rule poly_simp_rel :premises (t74.t1))
(step t74.t3 (cl @p_55) :rule refl)
(step t74.t4 (cl @p_57) :rule cong :premises (t74.t2 t74.t3))
(step t74.t5 (cl (not @p_54) @p_56 @p_52) :rule equiv_pos2)
(step t74.t6 (cl (= @p_46 @p_45)) :rule equiv_simplify)
(step t74.t7 (cl (not @p_46) @p_45) :rule equiv1 :premises (t74.t6))
(step t74.t8 (cl (= (* -1 @p_48) (* 1 @p_48))) :rule poly_simp)
(step t74.t9 (cl @p_47) :rule poly_simp_rel :premises (t74.t8))
(step t74.t10 (cl @p_45) :rule refl)
(step t74.t11 (cl (= 0 0)) :rule refl)
(step t74.t12 (cl (= @p_11 @p_11)) :rule cong :premises (t53 t74.t11))
(step t74.t13 (cl @p_45) :rule cong :premises (t74.t12 t53 t74.t11))
(step t74.t14 (cl @p_45) :rule trans :premises (t74.t10 t74.t13))
(step t74.t15 (cl @p_47) :rule cong :premises (t74.t14 t74.t13))
(step t74.t16 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_13))
(step t74.t17 (cl @p_46) :rule trans :premises (t74.t9 t74.t15 t74.t16))
(step t74.t18 (cl @p_45) :rule resolution :premises (t74.t7 t74.t17))
(step t74.t19 (cl @p_23) :rule refl)
(step t74.t20 (cl (= @p_51 @p_51)) :rule cong :premises (t74.t18 t74.t19))
(step t74.t21 (cl @p_55) :rule cong :premises (t74.t18 t74.t11))
(step t74.t22 (cl @p_54) :rule cong :premises (t74.t20 t74.t21))
(step t74.t23 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_11 @p_10 0))
(step t74.t24 (cl @p_52 @p_53) :rule equiv2 :premises (t74.t23))
(step t74.t25 (cl true) :rule true)
(step t74.t26 (cl @p_52) :rule resolution :premises (t74.t24 t74.t25))
(step t74.t27 (cl @p_52) :rule resolution :premises (t74.t5 t74.t22 t74.t26))
(step t74.t28 (cl @p_50) :rule resolution :premises (t74.t0 t74.t4 t74.t27))
(step t74.t29 (cl @p_12 @p_14) :rule ite2 :premises (t74.t28))
(step t74.t30 (cl @p_14 @p_12) :rule reordering :premises (t74.t29))
(step t74.t31 (cl (= @p_16 @p_15)) :rule equiv_simplify)
(step t74.t32 (cl (not @p_16) @p_15) :rule equiv1 :premises (t74.t31))
(step t74.t33 (cl (not @p_43) (not @p_42) @p_40) :rule equiv_pos2)
(step t74.t34 (cl (= @p_41 @p_41)) :rule cong :premises (t74.t18))
(step t74.t35 (cl (= (* -1 (- @p_18 @p_13)) (* 1 (- @p_13 @p_18)))) :rule poly_simp)
(step t74.t36 (cl @p_44) :rule poly_simp_rel :premises (t74.t35))
(step t74.t37 (cl @p_44) :rule trans :premises (t74.t34 t74.t36))
(step t74.t38 (cl @p_43) :rule cong :premises (t74.t37))
(step t74.t39 (cl @p_42 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t74.t40)
(assume t74.t40.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t74.t40.t0 (cl (or @p_39 @p_41)) :rule forall_inst :args (@p_10))
(step t74.t40.t1 (cl @p_39 @p_41) :rule or :premises (t74.t40.t0))
(step t74.t40.t2 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t74.t40.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t74.t40.t3.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t74.t40.t3.t1 (cl @p_33) :rule refl)
(step t74.t40.t3.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t74.t40.t3.t0 t74.t40.t3.t1 t74.t11))
(step t74.t40.t3.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t74.t40.t3.t2))
(step t74.t40.t3 (cl @p_32) :rule bind)
(step t74.t40.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t74.t40.t2 t74.t40.t3 a0))
(step t74.t40.t5 (cl @p_41) :rule resolution :premises (t74.t40.t1 t74.t40.t4))
(step t74.t40 (cl @p_39 @p_41) :rule subproof :discharge (t74.t40.a0))
(step t74.t41 (cl @p_42 @p_41) :rule resolution :premises (t74.t39 t74.t40))
(step t74.t42 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t74.t43 (cl @p_42 @p_42) :rule resolution :premises (t74.t41 t74.t42))
(step t74.t44 (cl @p_42) :rule contraction :premises (t74.t43))
(step t74.t45 (cl @p_40) :rule resolution :premises (t74.t33 t74.t38 t74.t44))
(step t74.t46 (cl @p_39 @p_31) :rule implies :premises (t74.t45))
(step t74.t47 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t74.t48 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t74.t48.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t74.t48.t1 (cl @p_33) :rule refl)
(step t74.t48.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t74.t48.t0 t74.t48.t1 t74.t11))
(step t74.t48.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t74.t48.t2))
(step t74.t48 (cl @p_32) :rule bind)
(step t74.t49 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t74.t47 t74.t48 a0))
(step t74.t50 (cl @p_31) :rule resolution :premises (t74.t46 t74.t49))
(step t74.t51 (cl (= @p_14 @p_19)) :rule cong :premises (t74.t50))
(step t74.t52 (cl (= @p_20 @p_21)) :rule equiv_simplify)
(step t74.t53 (cl @p_20 @p_30) :rule equiv2 :premises (t74.t52))
(step t74.t54 (cl (not @p_30) @p_19) :rule not_not)
(step t74.t55 (cl @p_20 @p_19) :rule resolution :premises (t74.t53 t74.t54))
(step t74.t56 (cl (not @p_22) (not @p_7) @p_21) :rule equiv_pos2)
(step t74.t57 (cl (= @p_2 @p_28)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0))
(step t74.t58 (cl (= @p_1 @p_8)) :rule poly_simp)
(step t74.t59 (cl (= @p_3 @p_29)) :rule cong :premises (t74.t57 t74.t58 t59))
(step t74.t60 (cl (= @p_29 @p_10)) :rule rare_rewrite :args ("ite-not-cond" @p_9 @p_8 x$))
(step t74.t61 (cl (= @p_3 @p_10)) :rule trans :premises (t74.t59 t74.t60))
(step t74.t62 (cl (= @p_4 @p_17)) :rule cong :premises (t74.t61))
(step t74.t63 (cl (= @p_5 @p_18)) :rule cong :premises (t74.t62))
(step t74.t64 (cl (= @p_6 @p_27)) :rule cong :premises (t74.t63 t74.t61))
(step t74.t65 (cl (= (* 1 (- @p_18 @p_10)) (* -1 (- @p_10 @p_18)))) :rule poly_simp)
(step t74.t66 (cl (= @p_27 @p_19)) :rule poly_simp_rel :premises (t74.t65))
(step t74.t67 (cl (= @p_6 @p_19)) :rule trans :premises (t74.t64 t74.t66))
(step t74.t68 (cl @p_22) :rule cong :premises (t74.t67))
(step t74.t69 (cl (= @p_17 @p_17)) :rule cong :premises (t58))
(step t74.t70 (cl (= @p_18 @p_18)) :rule cong :premises (t74.t69))
(step t74.t71 (cl (= @p_19 @p_19)) :rule cong :premises (t58 t74.t70))
(step t74.t72 (cl (= @p_21 @p_21)) :rule cong :premises (t74.t71))
(step t74.t73 (cl @p_22) :rule trans :premises (t74.t68 t74.t72))
(step t74.t74 (cl @p_21) :rule resolution :premises (t74.t56 t74.t73 a1))
(step t74.t75 (cl @p_20) :rule resolution :premises (t74.t55 t74.t74))
(step t74.t76 (cl @p_16) :rule trans :premises (t74.t51 t74.t75))
(step t74.t77 (cl @p_15) :rule resolution :premises (t74.t32 t74.t76))
(step t74.t78 (cl @p_12) :rule resolution :premises (t74.t30 t74.t77))
(step t74.t79 (cl @p_78) :rule and_intro :premises (t74.a0 t74.t78 t74.a1))
(step t74 (cl @p_28 @p_70 @p_72 @p_78) :rule subproof :discharge (t74.a0 t74.a1 t74.a2))
(step t75 (cl (! (not @p_76) :named @p_77) @p_9) :rule and_pos :args (0))
(step t76 (cl @p_77 @p_58) :rule and_pos :args (1))
(step t77 (cl @p_77 @p_12) :rule and_pos :args (2))
(step t78 (cl @p_78 @p_77 @p_77 @p_77) :rule resolution :premises (t74 t75 t76 t77))
(step t79 (cl @p_77 @p_77 @p_77 @p_78) :rule reordering :premises (t78))
(step t80 (cl @p_77 @p_78) :rule contraction :premises (t79))
(step t81 (cl @p_106 @p_78) :rule resolution :premises (t73 t80))
(step t82 (cl @p_106 (! (not @p_78) :named @p_79)) :rule implies_neg2)
(step t83 (cl @p_106 @p_106) :rule resolution :premises (t81 t82))
(step t84 (cl @p_106) :rule contraction :premises (t83))
(step t85 (cl @p_77 @p_78) :rule implies :premises (t84))
(step t86 (cl (! (=> @p_78 false) :named @p_80) @p_78) :rule implies_neg1)
(anchor :step t87)
(assume t87.a0 @p_9)
(assume t87.a1 @p_12)
(assume t87.a2 @p_58)
(step t87.t0 (cl (not (! (= @p_58 (! (= (! (+ x$ @p_59) :named @p_82) 0) :named @p_83)) :named @p_105)) @p_70 @p_83) :rule equiv_pos2)
(step t87.t1 (cl (= (* 1 (- @p_82 0)) (* 1 @p_69))) :rule poly_simp)
(step t87.t2 (cl (= @p_83 @p_58)) :rule poly_simp_rel :premises (t87.t1))
(step t87.t3 (cl @p_105) :rule symm :premises (t87.t2))
(step t87.t4 (cl @p_83) :rule resolution :premises (t87.t0 t87.t3 t87.a2))
(step t87.t5 (cl (! (=> @p_83 false) :named @p_85) @p_83) :rule implies_neg1)
(anchor :step t87.t6)
(assume t87.t6.a0 @p_83)
(step t87.t6.t0 (cl (not (! (= (! (< (! (+ @p_82 @p_10 @p_8) :named @p_88) (! (+ 0 0 @p_86) :named @p_87)) :named @p_89) false) :named @p_98)) (not @p_89) false) :rule equiv_pos2)
(step t87.t6.t1 (cl (= @p_89 (! (not (! (>= @p_88 @p_87) :named @p_99)) :named @p_100))) :rule rare_rewrite :args ("arith-elim-lt" @p_88 @p_87))
(step t87.t6.t2 (cl (= @p_88 (! (+ @p_59 @p_10 @p_8 x$) :named @p_103))) :rule poly_simp)
(step t87.t6.t3 (cl (= @p_103 0)) :rule poly_simp)
(step t87.t6.t4 (cl (= @p_88 0)) :rule trans :premises (t87.t6.t2 t87.t6.t3))
(step t87.t6.t5 (cl (= @p_86 0)) :rule evaluate)
(step t87.t6.t6 (cl (= @p_87 @p_102)) :rule cong :premises (t87.t6.t5))
(step t87.t6.t7 (cl (= @p_102 0)) :rule evaluate)
(step t87.t6.t8 (cl (= @p_87 0)) :rule trans :premises (t87.t6.t6 t87.t6.t7))
(step t87.t6.t9 (cl (= @p_99 @p_101)) :rule cong :premises (t87.t6.t4 t87.t6.t8))
(step t87.t6.t10 (cl (= @p_101 true)) :rule evaluate)
(step t87.t6.t11 (cl (= @p_99 true)) :rule trans :premises (t87.t6.t9 t87.t6.t10))
(step t87.t6.t12 (cl (= @p_100 @p_53)) :rule cong :premises (t87.t6.t11))
(step t87.t6.t13 (cl (= @p_53 false)) :rule evaluate)
(step t87.t6.t14 (cl (= @p_100 false)) :rule trans :premises (t87.t6.t12 t87.t6.t13))
(step t87.t6.t15 (cl @p_98) :rule trans :premises (t87.t6.t1 t87.t6.t14))
(step t87.t6.t16 (cl (! (not @p_83) :named @p_84) @p_97 (not (! (<= @p_8 @p_86) :named @p_90)) @p_89) :rule la_generic :args (-1/1 1/1 1/1 1/1))
(step t87.t6.t17 (cl (not @p_95) @p_72 @p_94) :rule equiv_pos2)
(step t87.t6.t18 (cl (= @p_94 @p_12)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 0))
(step t87.t6.t19 (cl @p_95) :rule symm :premises (t87.t6.t18))
(step t87.t6.t20 (cl (not @p_57) @p_56 @p_50) :rule equiv_pos2)
(step t87.t6.t21 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t87.t6.t22 (cl (= @p_51 @p_14)) :rule poly_simp_rel :premises (t87.t6.t21))
(step t87.t6.t23 (cl @p_55) :rule refl)
(step t87.t6.t24 (cl @p_57) :rule cong :premises (t87.t6.t22 t87.t6.t23))
(step t87.t6.t25 (cl (not @p_54) @p_56 @p_52) :rule equiv_pos2)
(step t87.t6.t26 (cl (= @p_46 @p_45)) :rule equiv_simplify)
(step t87.t6.t27 (cl (not @p_46) @p_45) :rule equiv1 :premises (t87.t6.t26))
(step t87.t6.t28 (cl (= (* -1 @p_48) (* 1 @p_48))) :rule poly_simp)
(step t87.t6.t29 (cl @p_47) :rule poly_simp_rel :premises (t87.t6.t28))
(step t87.t6.t30 (cl @p_45) :rule refl)
(step t87.t6.t31 (cl (= 0 0)) :rule refl)
(step t87.t6.t32 (cl (= @p_11 @p_11)) :rule cong :premises (t53 t87.t6.t31))
(step t87.t6.t33 (cl @p_45) :rule cong :premises (t87.t6.t32 t53 t87.t6.t31))
(step t87.t6.t34 (cl @p_45) :rule trans :premises (t87.t6.t30 t87.t6.t33))
(step t87.t6.t35 (cl @p_47) :rule cong :premises (t87.t6.t34 t87.t6.t33))
(step t87.t6.t36 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_13))
(step t87.t6.t37 (cl @p_46) :rule trans :premises (t87.t6.t29 t87.t6.t35 t87.t6.t36))
(step t87.t6.t38 (cl @p_45) :rule resolution :premises (t87.t6.t27 t87.t6.t37))
(step t87.t6.t39 (cl @p_23) :rule refl)
(step t87.t6.t40 (cl (= @p_51 @p_51)) :rule cong :premises (t87.t6.t38 t87.t6.t39))
(step t87.t6.t41 (cl @p_55) :rule cong :premises (t87.t6.t38 t87.t6.t31))
(step t87.t6.t42 (cl @p_54) :rule cong :premises (t87.t6.t40 t87.t6.t41))
(step t87.t6.t43 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_11 @p_10 0))
(step t87.t6.t44 (cl @p_52 @p_53) :rule equiv2 :premises (t87.t6.t43))
(step t87.t6.t45 (cl true) :rule true)
(step t87.t6.t46 (cl @p_52) :rule resolution :premises (t87.t6.t44 t87.t6.t45))
(step t87.t6.t47 (cl @p_52) :rule resolution :premises (t87.t6.t25 t87.t6.t42 t87.t6.t46))
(step t87.t6.t48 (cl @p_50) :rule resolution :premises (t87.t6.t20 t87.t6.t24 t87.t6.t47))
(step t87.t6.t49 (cl @p_12 @p_14) :rule ite2 :premises (t87.t6.t48))
(step t87.t6.t50 (cl @p_14 @p_12) :rule reordering :premises (t87.t6.t49))
(step t87.t6.t51 (cl (= @p_16 @p_15)) :rule equiv_simplify)
(step t87.t6.t52 (cl (not @p_16) @p_15) :rule equiv1 :premises (t87.t6.t51))
(step t87.t6.t53 (cl (not @p_43) (not @p_42) @p_40) :rule equiv_pos2)
(step t87.t6.t54 (cl (= @p_41 @p_41)) :rule cong :premises (t87.t6.t38))
(step t87.t6.t55 (cl (= (* -1 (- @p_18 @p_13)) (* 1 (- @p_13 @p_18)))) :rule poly_simp)
(step t87.t6.t56 (cl @p_44) :rule poly_simp_rel :premises (t87.t6.t55))
(step t87.t6.t57 (cl @p_44) :rule trans :premises (t87.t6.t54 t87.t6.t56))
(step t87.t6.t58 (cl @p_43) :rule cong :premises (t87.t6.t57))
(step t87.t6.t59 (cl @p_42 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t87.t6.t60)
(assume t87.t6.t60.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t87.t6.t60.t0 (cl (or @p_39 @p_41)) :rule forall_inst :args (@p_10))
(step t87.t6.t60.t1 (cl @p_39 @p_41) :rule or :premises (t87.t6.t60.t0))
(step t87.t6.t60.t2 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t87.t6.t60.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t87.t6.t60.t3.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t87.t6.t60.t3.t1 (cl @p_33) :rule refl)
(step t87.t6.t60.t3.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t87.t6.t60.t3.t0 t87.t6.t60.t3.t1 t87.t6.t31))
(step t87.t6.t60.t3.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t87.t6.t60.t3.t2))
(step t87.t6.t60.t3 (cl @p_32) :rule bind)
(step t87.t6.t60.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t87.t6.t60.t2 t87.t6.t60.t3 a0))
(step t87.t6.t60.t5 (cl @p_41) :rule resolution :premises (t87.t6.t60.t1 t87.t6.t60.t4))
(step t87.t6.t60 (cl @p_39 @p_41) :rule subproof :discharge (t87.t6.t60.a0))
(step t87.t6.t61 (cl @p_42 @p_41) :rule resolution :premises (t87.t6.t59 t87.t6.t60))
(step t87.t6.t62 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t87.t6.t63 (cl @p_42 @p_42) :rule resolution :premises (t87.t6.t61 t87.t6.t62))
(step t87.t6.t64 (cl @p_42) :rule contraction :premises (t87.t6.t63))
(step t87.t6.t65 (cl @p_40) :rule resolution :premises (t87.t6.t53 t87.t6.t58 t87.t6.t64))
(step t87.t6.t66 (cl @p_39 @p_31) :rule implies :premises (t87.t6.t65))
(step t87.t6.t67 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t87.t6.t68 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t87.t6.t68.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t87.t6.t68.t1 (cl @p_33) :rule refl)
(step t87.t6.t68.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t87.t6.t68.t0 t87.t6.t68.t1 t87.t6.t31))
(step t87.t6.t68.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t87.t6.t68.t2))
(step t87.t6.t68 (cl @p_32) :rule bind)
(step t87.t6.t69 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t87.t6.t67 t87.t6.t68 a0))
(step t87.t6.t70 (cl @p_31) :rule resolution :premises (t87.t6.t66 t87.t6.t69))
(step t87.t6.t71 (cl (= @p_14 @p_19)) :rule cong :premises (t87.t6.t70))
(step t87.t6.t72 (cl (= @p_20 @p_21)) :rule equiv_simplify)
(step t87.t6.t73 (cl @p_20 @p_30) :rule equiv2 :premises (t87.t6.t72))
(step t87.t6.t74 (cl (not @p_30) @p_19) :rule not_not)
(step t87.t6.t75 (cl @p_20 @p_19) :rule resolution :premises (t87.t6.t73 t87.t6.t74))
(step t87.t6.t76 (cl (not @p_22) (not @p_7) @p_21) :rule equiv_pos2)
(step t87.t6.t77 (cl (= @p_2 @p_28)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0))
(step t87.t6.t78 (cl (= @p_1 @p_8)) :rule poly_simp)
(step t87.t6.t79 (cl (= @p_3 @p_29)) :rule cong :premises (t87.t6.t77 t87.t6.t78 t59))
(step t87.t6.t80 (cl (= @p_29 @p_10)) :rule rare_rewrite :args ("ite-not-cond" @p_9 @p_8 x$))
(step t87.t6.t81 (cl (= @p_3 @p_10)) :rule trans :premises (t87.t6.t79 t87.t6.t80))
(step t87.t6.t82 (cl (= @p_4 @p_17)) :rule cong :premises (t87.t6.t81))
(step t87.t6.t83 (cl (= @p_5 @p_18)) :rule cong :premises (t87.t6.t82))
(step t87.t6.t84 (cl (= @p_6 @p_27)) :rule cong :premises (t87.t6.t83 t87.t6.t81))
(step t87.t6.t85 (cl (= (* 1 (- @p_18 @p_10)) (* -1 (- @p_10 @p_18)))) :rule poly_simp)
(step t87.t6.t86 (cl (= @p_27 @p_19)) :rule poly_simp_rel :premises (t87.t6.t85))
(step t87.t6.t87 (cl (= @p_6 @p_19)) :rule trans :premises (t87.t6.t84 t87.t6.t86))
(step t87.t6.t88 (cl @p_22) :rule cong :premises (t87.t6.t87))
(step t87.t6.t89 (cl (= @p_17 @p_17)) :rule cong :premises (t58))
(step t87.t6.t90 (cl (= @p_18 @p_18)) :rule cong :premises (t87.t6.t89))
(step t87.t6.t91 (cl (= @p_19 @p_19)) :rule cong :premises (t58 t87.t6.t90))
(step t87.t6.t92 (cl (= @p_21 @p_21)) :rule cong :premises (t87.t6.t91))
(step t87.t6.t93 (cl @p_22) :rule trans :premises (t87.t6.t88 t87.t6.t92))
(step t87.t6.t94 (cl @p_21) :rule resolution :premises (t87.t6.t76 t87.t6.t93 a1))
(step t87.t6.t95 (cl @p_20) :rule resolution :premises (t87.t6.t75 t87.t6.t94))
(step t87.t6.t96 (cl @p_16) :rule trans :premises (t87.t6.t71 t87.t6.t95))
(step t87.t6.t97 (cl @p_15) :rule resolution :premises (t87.t6.t52 t87.t6.t96))
(step t87.t6.t98 (cl @p_12) :rule resolution :premises (t87.t6.t50 t87.t6.t97))
(step t87.t6.t99 (cl @p_94) :rule resolution :premises (t87.t6.t17 t87.t6.t19 t87.t6.t98))
(step t87.t6.t100 (cl (=> (! (and @p_91 @p_9) :named @p_92) @p_90)) :rule la_mult_neg)
(step t87.t6.t101 (cl (not @p_92) @p_90) :rule implies :premises (t87.t6.t100))
(step t87.t6.t102 (cl (= @p_93 @p_91)) :rule equiv_simplify)
(step t87.t6.t103 (cl (not @p_93) @p_91) :rule equiv1 :premises (t87.t6.t102))
(step t87.t6.t104 (cl @p_93) :rule evaluate)
(step t87.t6.t105 (cl @p_91) :rule resolution :premises (t87.t6.t103 t87.t6.t104))
(step t87.t6.t106 (cl @p_92) :rule and_intro :premises (t87.t6.t105 t87.a0))
(step t87.t6.t107 (cl @p_90) :rule resolution :premises (t87.t6.t101 t87.t6.t106))
(step t87.t6.t108 (cl @p_89) :rule resolution :premises (t87.t6.t16 t87.t6.a0 t87.t6.t99 t87.t6.t107))
(step t87.t6.t109 (cl false) :rule resolution :premises (t87.t6.t0 t87.t6.t15 t87.t6.t108))
(step t87.t6 (cl @p_84 false) :rule subproof :discharge (t87.t6.a0))
(step t87.t7 (cl @p_85 false) :rule resolution :premises (t87.t5 t87.t6))
(step t87.t8 (cl @p_85 @p_81) :rule implies_neg2)
(step t87.t9 (cl @p_85 @p_85) :rule resolution :premises (t87.t7 t87.t8))
(step t87.t10 (cl @p_85) :rule contraction :premises (t87.t9))
(step t87.t11 (cl (= @p_85 @p_84)) :rule implies_simplify)
(step t87.t12 (cl (not @p_85) @p_84) :rule equiv1 :premises (t87.t11))
(step t87.t13 (cl @p_84) :rule resolution :premises (t87.t10 t87.t12))
(step t87.t14 (cl) :rule resolution :premises (t87.t4 t87.t13))
(step t87 (cl @p_28 @p_72 @p_70 false) :rule subproof :discharge (t87.a0 t87.a1 t87.a2))
(step t88 (cl @p_79 @p_9) :rule and_pos :args (0))
(step t89 (cl @p_79 @p_12) :rule and_pos :args (1))
(step t90 (cl @p_79 @p_58) :rule and_pos :args (2))
(step t91 (cl false @p_79 @p_79 @p_79) :rule resolution :premises (t87 t88 t89 t90))
(step t92 (cl @p_79 @p_79 @p_79 false) :rule reordering :premises (t91))
(step t93 (cl @p_79 false) :rule contraction :premises (t92))
(step t94 (cl @p_80 false) :rule resolution :premises (t86 t93))
(step t95 (cl @p_80 @p_81) :rule implies_neg2)
(step t96 (cl @p_80 @p_80) :rule resolution :premises (t94 t95))
(step t97 (cl @p_80) :rule contraction :premises (t96))
(step t98 (cl (= @p_80 @p_79)) :rule implies_simplify)
(step t99 (cl (not @p_80) @p_79) :rule equiv1 :premises (t98))
(step t100 (cl @p_79) :rule resolution :premises (t97 t99))
(step t101 (cl @p_77) :rule resolution :premises (t85 t100))
(step t102 (cl @p_28 @p_70 @p_72) :rule not_and :premises (t101))
(step t103 (cl @p_73 @p_75) :rule or_neg :args (0))
(step t104 (cl @p_73 (not @p_70)) :rule or_neg :args (1))
(step t105 (cl @p_73 @p_74) :rule or_neg :args (2))
(step t106 (cl @p_73 @p_73 @p_73) :rule resolution :premises (t102 t103 t104 t105))
(step t107 (cl @p_73) :rule contraction :premises (t106))
(step t108 (cl @p_71) :rule resolution :premises (t71 t72 t107))
(step t109 (cl @p_28 @p_70 @p_11) :rule or :premises (t108))
(step t110 (cl (not @p_57) @p_56 @p_50) :rule equiv_pos2)
(step t111 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t112 (cl (= @p_51 @p_14)) :rule poly_simp_rel :premises (t111))
(step t113 (cl @p_55) :rule refl)
(step t114 (cl @p_57) :rule cong :premises (t112 t113))
(step t115 (cl (not @p_54) @p_56 @p_52) :rule equiv_pos2)
(step t116 (cl (= @p_46 @p_45)) :rule equiv_simplify)
(step t117 (cl (not @p_46) @p_45) :rule equiv1 :premises (t116))
(step t118 (cl (= (* -1 @p_48) (* 1 @p_48))) :rule poly_simp)
(step t119 (cl @p_47) :rule poly_simp_rel :premises (t118))
(step t120 (cl @p_45) :rule refl)
(step t121 (cl (= 0 0)) :rule refl)
(step t122 (cl (= @p_11 @p_11)) :rule cong :premises (t53 t121))
(step t123 (cl @p_45) :rule cong :premises (t122 t53 t121))
(step t124 (cl @p_45) :rule trans :premises (t120 t123))
(step t125 (cl @p_47) :rule cong :premises (t124 t123))
(step t126 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_13))
(step t127 (cl @p_46) :rule trans :premises (t119 t125 t126))
(step t128 (cl @p_45) :rule resolution :premises (t117 t127))
(step t129 (cl @p_23) :rule refl)
(step t130 (cl (= @p_51 @p_51)) :rule cong :premises (t128 t129))
(step t131 (cl @p_55) :rule cong :premises (t128 t121))
(step t132 (cl @p_54) :rule cong :premises (t130 t131))
(step t133 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_11 @p_10 0))
(step t134 (cl @p_52 @p_53) :rule equiv2 :premises (t133))
(step t135 (cl true) :rule true)
(step t136 (cl @p_52) :rule resolution :premises (t134 t135))
(step t137 (cl @p_52) :rule resolution :premises (t115 t132 t136))
(step t138 (cl @p_50) :rule resolution :premises (t110 t114 t137))
(step t139 (cl @p_12 @p_14) :rule ite2 :premises (t138))
(step t140 (cl @p_14 @p_12) :rule reordering :premises (t139))
(step t141 (cl (= @p_16 @p_15)) :rule equiv_simplify)
(step t142 (cl (not @p_16) @p_15) :rule equiv1 :premises (t141))
(step t143 (cl (not @p_43) (not @p_42) @p_40) :rule equiv_pos2)
(step t144 (cl (= @p_41 @p_41)) :rule cong :premises (t128))
(step t145 (cl (= (* -1 (- @p_18 @p_13)) (* 1 (- @p_13 @p_18)))) :rule poly_simp)
(step t146 (cl @p_44) :rule poly_simp_rel :premises (t145))
(step t147 (cl @p_44) :rule trans :premises (t144 t146))
(step t148 (cl @p_43) :rule cong :premises (t147))
(step t149 (cl @p_42 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t150)
(assume t150.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t150.t0 (cl (or @p_39 @p_41)) :rule forall_inst :args (@p_10))
(step t150.t1 (cl @p_39 @p_41) :rule or :premises (t150.t0))
(step t150.t2 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t150.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t150.t3.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t150.t3.t1 (cl @p_33) :rule refl)
(step t150.t3.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t150.t3.t0 t150.t3.t1 t121))
(step t150.t3.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t150.t3.t2))
(step t150.t3 (cl @p_32) :rule bind)
(step t150.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t150.t2 t150.t3 a0))
(step t150.t5 (cl @p_41) :rule resolution :premises (t150.t1 t150.t4))
(step t150 (cl @p_39 @p_41) :rule subproof :discharge (t150.a0))
(step t151 (cl @p_42 @p_41) :rule resolution :premises (t149 t150))
(step t152 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t153 (cl @p_42 @p_42) :rule resolution :premises (t151 t152))
(step t154 (cl @p_42) :rule contraction :premises (t153))
(step t155 (cl @p_40) :rule resolution :premises (t143 t148 t154))
(step t156 (cl @p_39 @p_31) :rule implies :premises (t155))
(step t157 (cl (not @p_32) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t158 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t158.t0 (cl (= @p_37 @p_34)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t158.t1 (cl @p_33) :rule refl)
(step t158.t2 (cl (= @p_38 @p_35)) :rule cong :premises (t158.t0 t158.t1 t121))
(step t158.t3 (cl (= (= @p_36 @p_38) (= @p_36 @p_35))) :rule cong :premises (t158.t2))
(step t158 (cl @p_32) :rule bind)
(step t159 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t157 t158 a0))
(step t160 (cl @p_31) :rule resolution :premises (t156 t159))
(step t161 (cl (= @p_14 @p_19)) :rule cong :premises (t160))
(step t162 (cl (= @p_20 @p_21)) :rule equiv_simplify)
(step t163 (cl @p_20 @p_30) :rule equiv2 :premises (t162))
(step t164 (cl (not @p_30) @p_19) :rule not_not)
(step t165 (cl @p_20 @p_19) :rule resolution :premises (t163 t164))
(step t166 (cl (not @p_22) (not @p_7) @p_21) :rule equiv_pos2)
(step t167 (cl (= @p_2 @p_28)) :rule rare_rewrite :args ("arith-elim-lt" x$ 0))
(step t168 (cl (= @p_1 @p_8)) :rule poly_simp)
(step t169 (cl (= @p_3 @p_29)) :rule cong :premises (t167 t168 t59))
(step t170 (cl (= @p_29 @p_10)) :rule rare_rewrite :args ("ite-not-cond" @p_9 @p_8 x$))
(step t171 (cl (= @p_3 @p_10)) :rule trans :premises (t169 t170))
(step t172 (cl (= @p_4 @p_17)) :rule cong :premises (t171))
(step t173 (cl (= @p_5 @p_18)) :rule cong :premises (t172))
(step t174 (cl (= @p_6 @p_27)) :rule cong :premises (t173 t171))
(step t175 (cl (= (* 1 (- @p_18 @p_10)) (* -1 (- @p_10 @p_18)))) :rule poly_simp)
(step t176 (cl (= @p_27 @p_19)) :rule poly_simp_rel :premises (t175))
(step t177 (cl (= @p_6 @p_19)) :rule trans :premises (t174 t176))
(step t178 (cl @p_22) :rule cong :premises (t177))
(step t179 (cl (= @p_17 @p_17)) :rule cong :premises (t58))
(step t180 (cl (= @p_18 @p_18)) :rule cong :premises (t179))
(step t181 (cl (= @p_19 @p_19)) :rule cong :premises (t58 t180))
(step t182 (cl (= @p_21 @p_21)) :rule cong :premises (t181))
(step t183 (cl @p_22) :rule trans :premises (t178 t182))
(step t184 (cl @p_21) :rule resolution :premises (t166 t183 a1))
(step t185 (cl @p_20) :rule resolution :premises (t165 t184))
(step t186 (cl @p_16) :rule trans :premises (t161 t185))
(step t187 (cl @p_15) :rule resolution :premises (t142 t186))
(step t188 (cl @p_12) :rule resolution :premises (t140 t187))
(step t189 (cl @p_28 @p_58) :rule ite2 :premises (t69))
(step t190 (cl @p_28) :rule resolution :premises (t109 t188 t189))
(step t191 (cl @p_60) :rule resolution :premises (t70 t190))
(step t192 (cl) :rule resolution :premises (t41 t191 t190 t188))
)
05e5dc7cfed714741f98c3a39c88b31a9648b00e 655 0
unsat
(
(assume a0 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0)))))))))
(assume a1 (! (not (! (=> (! (prime_nat$ (! (nat$ (! (+ (! (* 4 (! (of_nat$ m$) :named @p_1)) :named @p_3) 1) :named @p_4)) :named @p_5)) :named @p_6) (! (<= 1 @p_1) :named @p_2)) :named @p_7)) :named @p_8))
(assume a2 (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0))))
(assume a4 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0))))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= @p_1 1) :named @p_9)) :named @p_10)) :named @p_98) (! (not (! (>= (! (of_nat$ (! (nat$ (! (+ 1 @p_3) :named @p_11)) :named @p_12)) :named @p_17) 2) :named @p_55)) :named @p_94) (! (not (! (= (! (ite (! (>= @p_1 0) :named @p_18) @p_11 0) :named @p_19) @p_11) :named @p_47)) :named @p_96) (! (not (! (= @p_19 @p_17) :named @p_20)) :named @p_95)) :named @p_99) (! (or @p_9 @p_94 @p_96 @p_95) :named @p_97)) :named @p_142)) (not @p_99) @p_97) :rule equiv_pos2)
(step t1 (cl (= @p_98 @p_9)) :rule rare_rewrite :args ("bool-double-not-elim" @p_9))
(step t2 (cl (= @p_94 @p_94)) :rule refl)
(step t3 (cl (= @p_96 @p_96)) :rule refl)
(step t4 (cl (= @p_95 @p_95)) :rule refl)
(step t5 (cl @p_142) :rule cong :premises (t1 t2 t3 t4))
(step t6 (cl (! (=> (! (and @p_10 @p_55 @p_47 @p_20) :named @p_100) (! (and @p_10 @p_55 (! (= @p_11 @p_17) :named @p_102)) :named @p_103)) :named @p_141) @p_100) :rule implies_neg1)
(anchor :step t7)
(assume t7.a0 @p_10)
(assume t7.a1 @p_55)
(assume t7.a2 @p_47)
(assume t7.a3 @p_20)
(step t7.t0 (cl (not (! (= @p_8 (! (not (! (=> (! (prime_nat$ @p_12) :named @p_13) @p_9) :named @p_14)) :named @p_15)) :named @p_16)) (not @p_8) @p_15) :rule equiv_pos2)
(step t7.t1 (cl (= @p_4 @p_11)) :rule poly_simp)
(step t7.t2 (cl (= @p_5 @p_12)) :rule cong :premises (t7.t1))
(step t7.t3 (cl (= @p_6 @p_13)) :rule cong :premises (t7.t2))
(step t7.t4 (cl (= @p_2 @p_9)) :rule rare_rewrite :args ("arith-elim-leq" 1 @p_1))
(step t7.t5 (cl (= @p_7 @p_14)) :rule cong :premises (t7.t3 t7.t4))
(step t7.t6 (cl @p_16) :rule cong :premises (t7.t5))
(step t7.t7 (cl @p_15) :rule resolution :premises (t7.t0 t7.t6 a1))
(step t7.t8 (cl @p_10) :rule not_implies2 :premises (t7.t7))
(step t7.t9 (cl (! (not (! (and @p_55 (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$))))))))) :named @p_56)) :named @p_93) @p_55) :rule and_pos :args (0))
(step t7.t10 (cl @p_55 @p_93) :rule reordering :premises (t7.t9))
(step t7.t11 (cl (! (not (! (= @p_13 @p_56) :named @p_57)) :named @p_92) (! (not @p_13) :named @p_91) @p_56) :rule equiv_pos2)
(step t7.t12 (cl @p_91 @p_56 @p_92) :rule reordering :premises (t7.t11))
(step t7.t13 (cl @p_13) :rule not_implies1 :premises (t7.t7))
(step t7.t14 (cl (not (! (= (! (=> (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) (! (= @p_13 (! (and @p_55 (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$))))) (of_nat$ ?v1))))) :named @p_84)) :named @p_85)) :named @p_86) (! (=> (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) @p_57) :named @p_83)) :named @p_87)) (not @p_86) @p_83) :rule equiv_pos2)
(anchor :step t7.t15 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t7.t15.t0 (cl (= (* 1 (- @p_17 (! (of_nat$ ?v1) :named @p_65))) (* -1 (- @p_65 @p_17)))) :rule poly_simp)
(step t7.t15.t1 (cl (= (! (= @p_17 @p_65) :named @p_90) (! (= @p_65 @p_17) :named @p_88))) :rule poly_simp_rel :premises (t7.t15.t0))
(step t7.t15.t2 (cl (= (or (! (not (dvd$ ?v1 @p_12)) :named @p_89) (! (= @p_65 1) :named @p_67) @p_90) (or @p_89 @p_67 @p_88))) :rule cong :premises (t7.t15.t1))
(step t7.t15 (cl (= (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$))))) (of_nat$ ?v1)))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$)))))))))) :rule bind)
(step t7.t16 (cl (= @p_84 @p_56)) :rule cong :premises (t7.t15))
(step t7.t17 (cl (= @p_85 @p_57)) :rule cong :premises (t7.t16))
(step t7.t18 (cl @p_87) :rule cong :premises (t7.t17))
(step t7.t19 (cl @p_86 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule implies_neg1)
(anchor :step t7.t20)
(assume t7.t20.a0 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))))
(step t7.t20.t0 (cl (or (! (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :named @p_82) @p_85)) :rule forall_inst :args (@p_12))
(step t7.t20.t1 (cl @p_82 @p_85) :rule or :premises (t7.t20.t0))
(step t7.t20.t2 (cl (not (! (= (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0)))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :named @p_58)) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t7.t20.t3 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t7.t20.t3.t0 (cl (= (! (< 1 (! (of_nat$ ?v0) :named @p_50)) :named @p_62) (! (not (! (>= 1 @p_50) :named @p_76)) :named @p_77))) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t7.t20.t3.t1 (cl (= (! (not (! (>= @p_50 2) :named @p_59)) :named @p_78) (! (>= 2 (! (+ @p_50 1) :named @p_80)) :named @p_81))) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t7.t20.t3.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t7.t20.t3.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t7.t20.t3.t2))
(step t7.t20.t3.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t7.t20.t3.t1 t7.t20.t3.t3))
(step t7.t20.t3.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t7.t20.t3.t4))
(step t7.t20.t3.t6 (cl (= @p_77 (! (not @p_78) :named @p_79))) :rule cong :premises (t7.t20.t3.t5))
(step t7.t20.t3.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t7.t20.t3.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t7.t20.t3.t6 t7.t20.t3.t7))
(step t7.t20.t3.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t7.t20.t3.t0 t7.t20.t3.t8))
(anchor :step t7.t20.t3.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t7.t20.t3.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t7.t20.t3.t10.t1 (cl (= (! (= @p_65 @p_50) :named @p_74) (! (= @p_50 @p_65) :named @p_66))) :rule poly_simp_rel :premises (t7.t20.t3.t10.t0))
(step t7.t20.t3.t10.t2 (cl (= (! (or @p_67 @p_74) :named @p_75) (! (or @p_67 @p_66) :named @p_71))) :rule cong :premises (t7.t20.t3.t10.t1))
(step t7.t20.t3.t10.t3 (cl (= (=> (! (dvd$ ?v1 ?v0) :named @p_68) @p_75) (! (=> @p_68 @p_71) :named @p_72))) :rule cong :premises (t7.t20.t3.t10.t2))
(step t7.t20.t3.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t7.t20.t3.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t7.t20.t3.t11.t0 (cl (= @p_72 (! (or (! (not @p_68) :named @p_69) @p_71) :named @p_73))) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t7.t20.t3.t11.t1 (cl (= @p_73 (! (or @p_69 @p_67 @p_66) :named @p_70))) :rule aci_simp)
(step t7.t20.t3.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t7.t20.t3.t11.t0 t7.t20.t3.t11.t1))
(step t7.t20.t3.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t7.t20.t3.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t7.t20.t3.t10 t7.t20.t3.t11))
(step t7.t20.t3.t13 (cl (= (! (and @p_62 (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0)))))) :named @p_63) (! (and @p_59 (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) :named @p_60))) :rule cong :premises (t7.t20.t3.t9 t7.t20.t3.t12))
(step t7.t20.t3.t14 (cl (= (= (! (prime_nat$ ?v0) :named @p_61) @p_63) (= @p_61 @p_60))) :rule cong :premises (t7.t20.t3.t13))
(step t7.t20.t3 (cl @p_58) :rule bind)
(step t7.t20.t4 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t7.t20.t2 t7.t20.t3 a0))
(step t7.t20.t5 (cl @p_85) :rule resolution :premises (t7.t20.t1 t7.t20.t4))
(step t7.t20 (cl @p_82 @p_85) :rule subproof :discharge (t7.t20.a0))
(step t7.t21 (cl @p_86 @p_85) :rule resolution :premises (t7.t19 t7.t20))
(step t7.t22 (cl @p_86 (not @p_85)) :rule implies_neg2)
(step t7.t23 (cl @p_86 @p_86) :rule resolution :premises (t7.t21 t7.t22))
(step t7.t24 (cl @p_86) :rule contraction :premises (t7.t23))
(step t7.t25 (cl @p_83) :rule resolution :premises (t7.t14 t7.t18 t7.t24))
(step t7.t26 (cl @p_82 @p_57) :rule implies :premises (t7.t25))
(step t7.t27 (cl (not @p_58) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t7.t28 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t7.t28.t0 (cl (= @p_62 @p_77)) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t7.t28.t1 (cl (= @p_78 @p_81)) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t7.t28.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t7.t28.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t7.t28.t2))
(step t7.t28.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t7.t28.t1 t7.t28.t3))
(step t7.t28.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t7.t28.t4))
(step t7.t28.t6 (cl (= @p_77 @p_79)) :rule cong :premises (t7.t28.t5))
(step t7.t28.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t7.t28.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t7.t28.t6 t7.t28.t7))
(step t7.t28.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t7.t28.t0 t7.t28.t8))
(anchor :step t7.t28.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t7.t28.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t7.t28.t10.t1 (cl (= @p_74 @p_66)) :rule poly_simp_rel :premises (t7.t28.t10.t0))
(step t7.t28.t10.t2 (cl (= @p_75 @p_71)) :rule cong :premises (t7.t28.t10.t1))
(step t7.t28.t10.t3 (cl (= (=> @p_68 @p_75) @p_72)) :rule cong :premises (t7.t28.t10.t2))
(step t7.t28.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t7.t28.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t7.t28.t11.t0 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t7.t28.t11.t1 (cl (= @p_73 @p_70)) :rule aci_simp)
(step t7.t28.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t7.t28.t11.t0 t7.t28.t11.t1))
(step t7.t28.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t7.t28.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t7.t28.t10 t7.t28.t11))
(step t7.t28.t13 (cl (= @p_63 @p_60)) :rule cong :premises (t7.t28.t9 t7.t28.t12))
(step t7.t28.t14 (cl (= (= @p_61 @p_63) (= @p_61 @p_60))) :rule cong :premises (t7.t28.t13))
(step t7.t28 (cl @p_58) :rule bind)
(step t7.t29 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t7.t27 t7.t28 a0))
(step t7.t30 (cl @p_57) :rule resolution :premises (t7.t26 t7.t29))
(step t7.t31 (cl @p_56) :rule resolution :premises (t7.t12 t7.t13 t7.t30))
(step t7.t32 (cl @p_55) :rule resolution :premises (t7.t10 t7.t31))
(step t7.t33 (cl (not (! (= (! (ite @p_18 @p_47 (! (= @p_19 0) :named @p_52)) :named @p_53) @p_53) :named @p_54)) (not @p_53) @p_53) :rule equiv_pos2)
(step t7.t34 (cl (= (! (= (! (= @p_19 @p_19) :named @p_43) true) :named @p_44) @p_43)) :rule equiv_simplify)
(step t7.t35 (cl (not @p_44) @p_43) :rule equiv1 :premises (t7.t34))
(step t7.t36 (cl (= (* -1 (! (- @p_19 @p_19) :named @p_46)) (* 1 @p_46))) :rule poly_simp)
(step t7.t37 (cl (! (= @p_43 @p_43) :named @p_45)) :rule poly_simp_rel :premises (t7.t36))
(step t7.t38 (cl @p_43) :rule refl)
(step t7.t39 (cl @p_43) :rule refl)
(step t7.t40 (cl @p_45) :rule cong :premises (t7.t38 t7.t39))
(step t7.t41 (cl @p_44) :rule rare_rewrite :args ("eq-refl" @p_19))
(step t7.t42 (cl @p_44) :rule trans :premises (t7.t37 t7.t40 t7.t41))
(step t7.t43 (cl @p_43) :rule resolution :premises (t7.t35 t7.t42))
(step t7.t44 (cl (= @p_11 @p_11)) :rule refl)
(step t7.t45 (cl (= @p_47 @p_47)) :rule cong :premises (t7.t43 t7.t44))
(step t7.t46 (cl (= 0 0)) :rule refl)
(step t7.t47 (cl (= @p_52 @p_52)) :rule cong :premises (t7.t43 t7.t46))
(step t7.t48 (cl @p_54) :rule cong :premises (t7.t45 t7.t47))
(step t7.t49 (cl (= @p_53 true)) :rule rare_rewrite :args ("ite-eq" @p_18 @p_11 0))
(step t7.t50 (cl @p_53 (not true)) :rule equiv2 :premises (t7.t49))
(step t7.t51 (cl true) :rule true)
(step t7.t52 (cl @p_53) :rule resolution :premises (t7.t50 t7.t51))
(step t7.t53 (cl @p_53) :rule resolution :premises (t7.t33 t7.t48 t7.t52))
(step t7.t54 (cl (not @p_18) @p_47) :rule ite2 :premises (t7.t53))
(step t7.t55 (cl (or (! (not (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :named @p_51) @p_18)) :rule forall_inst :args (m$))
(step t7.t56 (cl @p_51 @p_18) :rule or :premises (t7.t55))
(step t7.t57 (cl (not (! (= (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :named @p_48)) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t7.t58 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t7.t58.t0 (cl (= (<= 0 @p_50) (>= @p_50 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_50))
(step t7.t58 (cl @p_48) :rule bind)
(step t7.t59 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t7.t57 t7.t58 a2))
(step t7.t60 (cl @p_18) :rule resolution :premises (t7.t56 t7.t59))
(step t7.t61 (cl @p_47) :rule resolution :premises (t7.t54 t7.t60))
(step t7.t62 (cl (= @p_11 @p_19)) :rule symm :premises (t7.t61))
(step t7.t63 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))) (! (= @p_17 @p_19) :named @p_30)) :named @p_31) (! (=> (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))) @p_20) :named @p_29)) :named @p_41)) (not @p_31) @p_29) :rule equiv_pos2)
(step t7.t64 (cl (= @p_30 @p_30)) :rule cong :premises (t7.t43))
(step t7.t65 (cl (= (* -1 (- @p_17 @p_19)) (* 1 (- @p_19 @p_17)))) :rule poly_simp)
(step t7.t66 (cl (! (= @p_30 @p_20) :named @p_42)) :rule poly_simp_rel :premises (t7.t65))
(step t7.t67 (cl @p_42) :rule trans :premises (t7.t64 t7.t66))
(step t7.t68 (cl @p_41) :rule cong :premises (t7.t67))
(step t7.t69 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))) (! (= @p_17 (! (ite (! (>= @p_11 0) :named @p_32) @p_11 0) :named @p_33)) :named @p_34)) :named @p_35) @p_31) :named @p_36)) (not @p_35) @p_31) :rule equiv_pos2)
(step t7.t70 (cl (= (* 1/4 (to_real (- @p_11 0))) (* 1/1 (- (! (to_real @p_1) :named @p_37) -1/4)))) :rule poly_simp)
(step t7.t71 (cl (= @p_32 (! (>= @p_37 -1/4) :named @p_38))) :rule poly_simp_rel :premises (t7.t70))
(step t7.t72 (cl (= (= (to_real (! (to_int -1/4) :named @p_39)) -1/4) false)) :rule evaluate)
(step t7.t73 (cl (= (! (+ @p_39 1) :named @p_40) 0)) :rule evaluate)
(step t7.t74 (cl (= 0 @p_40)) :rule symm :premises (t7.t73))
(step t7.t75 (cl (= @p_38 @p_18)) :rule rare_rewrite :premises (t7.t72 t7.t74) :args ("arith-int-geq-tighten" @p_1 -1/4 0))
(step t7.t76 (cl (= @p_32 @p_18)) :rule trans :premises (t7.t71 t7.t75))
(step t7.t77 (cl (= @p_33 @p_19)) :rule cong :premises (t7.t76 t7.t44 t7.t46))
(step t7.t78 (cl (= @p_34 @p_30)) :rule cong :premises (t7.t77))
(step t7.t79 (cl @p_36) :rule cong :premises (t7.t78))
(step t7.t80 (cl @p_35 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t7.t81)
(assume t7.t81.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t7.t81.t0 (cl (or (! (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :named @p_28) @p_34)) :rule forall_inst :args (@p_11))
(step t7.t81.t1 (cl @p_28 @p_34) :rule or :premises (t7.t81.t0))
(step t7.t81.t2 (cl (not (! (= (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :named @p_21)) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t7.t81.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t7.t81.t3.t0 (cl (= (! (<= 0 ?v0) :named @p_26) (! (>= ?v0 0) :named @p_23))) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t7.t81.t3.t1 (cl (! (= ?v0 ?v0) :named @p_22)) :rule refl)
(step t7.t81.t3.t2 (cl (= (! (ite @p_26 ?v0 0) :named @p_27) (! (ite @p_23 ?v0 0) :named @p_24))) :rule cong :premises (t7.t81.t3.t0 t7.t81.t3.t1 t7.t46))
(step t7.t81.t3.t3 (cl (= (= (! (of_nat$ (nat$ ?v0)) :named @p_25) @p_27) (= @p_25 @p_24))) :rule cong :premises (t7.t81.t3.t2))
(step t7.t81.t3 (cl @p_21) :rule bind)
(step t7.t81.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t7.t81.t2 t7.t81.t3 a4))
(step t7.t81.t5 (cl @p_34) :rule resolution :premises (t7.t81.t1 t7.t81.t4))
(step t7.t81 (cl @p_28 @p_34) :rule subproof :discharge (t7.t81.a0))
(step t7.t82 (cl @p_35 @p_34) :rule resolution :premises (t7.t80 t7.t81))
(step t7.t83 (cl @p_35 (not @p_34)) :rule implies_neg2)
(step t7.t84 (cl @p_35 @p_35) :rule resolution :premises (t7.t82 t7.t83))
(step t7.t85 (cl @p_35) :rule contraction :premises (t7.t84))
(step t7.t86 (cl @p_31) :rule resolution :premises (t7.t69 t7.t79 t7.t85))
(step t7.t87 (cl @p_29) :rule resolution :premises (t7.t63 t7.t68 t7.t86))
(step t7.t88 (cl @p_28 @p_20) :rule implies :premises (t7.t87))
(step t7.t89 (cl (not @p_21) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t7.t90 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t7.t90.t0 (cl (= @p_26 @p_23)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t7.t90.t1 (cl @p_22) :rule refl)
(step t7.t90.t2 (cl (= @p_27 @p_24)) :rule cong :premises (t7.t90.t0 t7.t90.t1 t7.t46))
(step t7.t90.t3 (cl (= (= @p_25 @p_27) (= @p_25 @p_24))) :rule cong :premises (t7.t90.t2))
(step t7.t90 (cl @p_21) :rule bind)
(step t7.t91 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t7.t89 t7.t90 a4))
(step t7.t92 (cl @p_20) :rule resolution :premises (t7.t88 t7.t91))
(step t7.t93 (cl @p_102) :rule trans :premises (t7.t62 t7.t92))
(step t7.t94 (cl @p_103) :rule and_intro :premises (t7.t8 t7.t32 t7.t93))
(step t7 (cl @p_98 @p_94 @p_96 @p_95 @p_103) :rule subproof :discharge (t7.a0 t7.a1 t7.a2 t7.a3))
(step t8 (cl (! (not @p_100) :named @p_101) @p_10) :rule and_pos :args (0))
(step t9 (cl @p_101 @p_55) :rule and_pos :args (1))
(step t10 (cl @p_101 @p_47) :rule and_pos :args (2))
(step t11 (cl @p_101 @p_20) :rule and_pos :args (3))
(step t12 (cl @p_103 @p_101 @p_101 @p_101 @p_101) :rule resolution :premises (t7 t8 t9 t10 t11))
(step t13 (cl @p_101 @p_101 @p_101 @p_101 @p_103) :rule reordering :premises (t12))
(step t14 (cl @p_101 @p_103) :rule contraction :premises (t13))
(step t15 (cl @p_141 @p_103) :rule resolution :premises (t6 t14))
(step t16 (cl @p_141 (! (not @p_103) :named @p_104)) :rule implies_neg2)
(step t17 (cl @p_141 @p_141) :rule resolution :premises (t15 t16))
(step t18 (cl @p_141) :rule contraction :premises (t17))
(step t19 (cl @p_101 @p_103) :rule implies :premises (t18))
(step t20 (cl (! (=> @p_103 false) :named @p_105) @p_103) :rule implies_neg1)
(anchor :step t21)
(assume t21.a0 @p_10)
(assume t21.a1 @p_55)
(assume t21.a2 @p_102)
(step t21.t0 (cl (not (! (= @p_102 (! (= (! (+ @p_3 (! (* -1 @p_17) :named @p_108)) :named @p_109) -1) :named @p_110)) :named @p_138)) (! (not @p_102) :named @p_107) @p_110) :rule equiv_pos2)
(step t21.t1 (cl (= (* -1 (- @p_11 @p_17)) (! (* 1 (- @p_17 @p_11)) :named @p_140))) :rule poly_simp)
(step t21.t2 (cl (= @p_102 (! (= @p_17 @p_11) :named @p_139))) :rule poly_simp_rel :premises (t21.t1))
(step t21.t3 (cl (= (* -1 (- @p_109 -1)) @p_140)) :rule poly_simp)
(step t21.t4 (cl (= @p_110 @p_139)) :rule poly_simp_rel :premises (t21.t3))
(step t21.t5 (cl (= @p_139 @p_110)) :rule symm :premises (t21.t4))
(step t21.t6 (cl @p_138) :rule trans :premises (t21.t2 t21.t5))
(step t21.t7 (cl (not @p_54) (not @p_53) @p_53) :rule equiv_pos2)
(step t21.t8 (cl (= @p_44 @p_43)) :rule equiv_simplify)
(step t21.t9 (cl (not @p_44) @p_43) :rule equiv1 :premises (t21.t8))
(step t21.t10 (cl (= (* -1 @p_46) (* 1 @p_46))) :rule poly_simp)
(step t21.t11 (cl @p_45) :rule poly_simp_rel :premises (t21.t10))
(step t21.t12 (cl @p_43) :rule refl)
(step t21.t13 (cl @p_43) :rule refl)
(step t21.t14 (cl @p_45) :rule cong :premises (t21.t12 t21.t13))
(step t21.t15 (cl @p_44) :rule rare_rewrite :args ("eq-refl" @p_19))
(step t21.t16 (cl @p_44) :rule trans :premises (t21.t11 t21.t14 t21.t15))
(step t21.t17 (cl @p_43) :rule resolution :premises (t21.t9 t21.t16))
(step t21.t18 (cl (= @p_11 @p_11)) :rule refl)
(step t21.t19 (cl (= @p_47 @p_47)) :rule cong :premises (t21.t17 t21.t18))
(step t21.t20 (cl (= 0 0)) :rule refl)
(step t21.t21 (cl (= @p_52 @p_52)) :rule cong :premises (t21.t17 t21.t20))
(step t21.t22 (cl @p_54) :rule cong :premises (t21.t19 t21.t21))
(step t21.t23 (cl (= @p_53 true)) :rule rare_rewrite :args ("ite-eq" @p_18 @p_11 0))
(step t21.t24 (cl @p_53 (not true)) :rule equiv2 :premises (t21.t23))
(step t21.t25 (cl true) :rule true)
(step t21.t26 (cl @p_53) :rule resolution :premises (t21.t24 t21.t25))
(step t21.t27 (cl @p_53) :rule resolution :premises (t21.t7 t21.t22 t21.t26))
(step t21.t28 (cl (not @p_18) @p_47) :rule ite2 :premises (t21.t27))
(step t21.t29 (cl (or @p_51 @p_18)) :rule forall_inst :args (m$))
(step t21.t30 (cl @p_51 @p_18) :rule or :premises (t21.t29))
(step t21.t31 (cl (not @p_48) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t21.t32 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t21.t32.t0 (cl (= (<= 0 @p_50) (>= @p_50 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_50))
(step t21.t32 (cl @p_48) :rule bind)
(step t21.t33 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t21.t31 t21.t32 a2))
(step t21.t34 (cl @p_18) :rule resolution :premises (t21.t30 t21.t33))
(step t21.t35 (cl @p_47) :rule resolution :premises (t21.t28 t21.t34))
(step t21.t36 (cl (= @p_11 @p_19)) :rule symm :premises (t21.t35))
(step t21.t37 (cl (not @p_41) (not @p_31) @p_29) :rule equiv_pos2)
(step t21.t38 (cl (= @p_30 @p_30)) :rule cong :premises (t21.t17))
(step t21.t39 (cl (= (* -1 (- @p_17 @p_19)) (* 1 (- @p_19 @p_17)))) :rule poly_simp)
(step t21.t40 (cl @p_42) :rule poly_simp_rel :premises (t21.t39))
(step t21.t41 (cl @p_42) :rule trans :premises (t21.t38 t21.t40))
(step t21.t42 (cl @p_41) :rule cong :premises (t21.t41))
(step t21.t43 (cl (not @p_36) (not @p_35) @p_31) :rule equiv_pos2)
(step t21.t44 (cl (= (* 1/4 (to_real (- @p_11 0))) (* 1/1 (- @p_37 -1/4)))) :rule poly_simp)
(step t21.t45 (cl (= @p_32 @p_38)) :rule poly_simp_rel :premises (t21.t44))
(step t21.t46 (cl (= (= (to_real @p_39) -1/4) false)) :rule evaluate)
(step t21.t47 (cl (= @p_40 0)) :rule evaluate)
(step t21.t48 (cl (= 0 @p_40)) :rule symm :premises (t21.t47))
(step t21.t49 (cl (= @p_38 @p_18)) :rule rare_rewrite :premises (t21.t46 t21.t48) :args ("arith-int-geq-tighten" @p_1 -1/4 0))
(step t21.t50 (cl (= @p_32 @p_18)) :rule trans :premises (t21.t45 t21.t49))
(step t21.t51 (cl (= @p_33 @p_19)) :rule cong :premises (t21.t50 t21.t18 t21.t20))
(step t21.t52 (cl (= @p_34 @p_30)) :rule cong :premises (t21.t51))
(step t21.t53 (cl @p_36) :rule cong :premises (t21.t52))
(step t21.t54 (cl @p_35 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t21.t55)
(assume t21.t55.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t21.t55.t0 (cl (or @p_28 @p_34)) :rule forall_inst :args (@p_11))
(step t21.t55.t1 (cl @p_28 @p_34) :rule or :premises (t21.t55.t0))
(step t21.t55.t2 (cl (not @p_21) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t21.t55.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t21.t55.t3.t0 (cl (= @p_26 @p_23)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t21.t55.t3.t1 (cl @p_22) :rule refl)
(step t21.t55.t3.t2 (cl (= @p_27 @p_24)) :rule cong :premises (t21.t55.t3.t0 t21.t55.t3.t1 t21.t20))
(step t21.t55.t3.t3 (cl (= (= @p_25 @p_27) (= @p_25 @p_24))) :rule cong :premises (t21.t55.t3.t2))
(step t21.t55.t3 (cl @p_21) :rule bind)
(step t21.t55.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t21.t55.t2 t21.t55.t3 a4))
(step t21.t55.t5 (cl @p_34) :rule resolution :premises (t21.t55.t1 t21.t55.t4))
(step t21.t55 (cl @p_28 @p_34) :rule subproof :discharge (t21.t55.a0))
(step t21.t56 (cl @p_35 @p_34) :rule resolution :premises (t21.t54 t21.t55))
(step t21.t57 (cl @p_35 (not @p_34)) :rule implies_neg2)
(step t21.t58 (cl @p_35 @p_35) :rule resolution :premises (t21.t56 t21.t57))
(step t21.t59 (cl @p_35) :rule contraction :premises (t21.t58))
(step t21.t60 (cl @p_31) :rule resolution :premises (t21.t43 t21.t53 t21.t59))
(step t21.t61 (cl @p_29) :rule resolution :premises (t21.t37 t21.t42 t21.t60))
(step t21.t62 (cl @p_28 @p_20) :rule implies :premises (t21.t61))
(step t21.t63 (cl (not @p_21) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t21.t64 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t21.t64.t0 (cl (= @p_26 @p_23)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t21.t64.t1 (cl @p_22) :rule refl)
(step t21.t64.t2 (cl (= @p_27 @p_24)) :rule cong :premises (t21.t64.t0 t21.t64.t1 t21.t20))
(step t21.t64.t3 (cl (= (= @p_25 @p_27) (= @p_25 @p_24))) :rule cong :premises (t21.t64.t2))
(step t21.t64 (cl @p_21) :rule bind)
(step t21.t65 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t21.t63 t21.t64 a4))
(step t21.t66 (cl @p_20) :rule resolution :premises (t21.t62 t21.t65))
(step t21.t67 (cl @p_102) :rule trans :premises (t21.t36 t21.t66))
(step t21.t68 (cl @p_110) :rule resolution :premises (t21.t0 t21.t6 t21.t67))
(step t21.t69 (cl (! (=> @p_110 false) :named @p_112) @p_110) :rule implies_neg1)
(anchor :step t21.t70)
(assume t21.t70.a0 @p_110)
(step t21.t70.t0 (cl (not (! (= (! (<= (! (+ (! (* -1 @p_109) :named @p_117) @p_108 @p_3) :named @p_118) (! (+ (! (* -1 -1) :named @p_115) (! (* -1 2) :named @p_114) (! (* 4 0) :named @p_113)) :named @p_116)) :named @p_119) false) :named @p_133)) (not @p_119) false) :rule equiv_pos2)
(step t21.t70.t1 (cl (= @p_117 (! (+ (* -4 @p_1) @p_17) :named @p_136))) :rule poly_simp)
(step t21.t70.t2 (cl (= @p_108 @p_108)) :rule refl)
(step t21.t70.t3 (cl (= @p_3 @p_3)) :rule refl)
(step t21.t70.t4 (cl (= @p_118 (! (+ @p_136 @p_108 @p_3) :named @p_137))) :rule cong :premises (t21.t70.t1 t21.t70.t2 t21.t70.t3))
(step t21.t70.t5 (cl (= @p_137 0)) :rule poly_simp)
(step t21.t70.t6 (cl (= @p_118 0)) :rule trans :premises (t21.t70.t4 t21.t70.t5))
(step t21.t70.t7 (cl (= @p_115 1)) :rule evaluate)
(step t21.t70.t8 (cl (= @p_114 -2)) :rule evaluate)
(step t21.t70.t9 (cl (= @p_113 0)) :rule evaluate)
(step t21.t70.t10 (cl (= @p_116 (! (+ 1 -2 0) :named @p_135))) :rule cong :premises (t21.t70.t7 t21.t70.t8 t21.t70.t9))
(step t21.t70.t11 (cl (= @p_135 -1)) :rule evaluate)
(step t21.t70.t12 (cl (= @p_116 -1)) :rule trans :premises (t21.t70.t10 t21.t70.t11))
(step t21.t70.t13 (cl (= @p_119 (! (<= 0 -1) :named @p_134))) :rule cong :premises (t21.t70.t6 t21.t70.t12))
(step t21.t70.t14 (cl (= @p_134 false)) :rule evaluate)
(step t21.t70.t15 (cl @p_133) :rule trans :premises (t21.t70.t13 t21.t70.t14))
(step t21.t70.t16 (cl (not (! (= @p_117 @p_115) :named @p_131)) (not (! (<= @p_108 @p_114) :named @p_127)) (not (! (<= @p_3 @p_113) :named @p_120)) @p_119) :rule la_generic :args (-1/1 1/1 1/1 1/1))
(step t21.t70.t17 (cl (=> (! (and (! (< -1 0) :named @p_128) @p_110) :named @p_132) @p_131)) :rule la_mult_neg)
(step t21.t70.t18 (cl (not @p_132) @p_131) :rule implies :premises (t21.t70.t17))
(step t21.t70.t19 (cl (= (! (= @p_128 true) :named @p_130) @p_128)) :rule equiv_simplify)
(step t21.t70.t20 (cl (not @p_130) @p_128) :rule equiv1 :premises (t21.t70.t19))
(step t21.t70.t21 (cl @p_130) :rule evaluate)
(step t21.t70.t22 (cl @p_128) :rule resolution :premises (t21.t70.t20 t21.t70.t21))
(step t21.t70.t23 (cl @p_132) :rule and_intro :premises (t21.t70.t22 t21.t70.a0))
(step t21.t70.t24 (cl @p_131) :rule resolution :premises (t21.t70.t18 t21.t70.t23))
(step t21.t70.t25 (cl (=> (! (and @p_128 @p_55) :named @p_129) @p_127)) :rule la_mult_neg)
(step t21.t70.t26 (cl (not @p_129) @p_127) :rule implies :premises (t21.t70.t25))
(step t21.t70.t27 (cl @p_93 @p_55) :rule and_pos :args (0))
(step t21.t70.t28 (cl @p_55 @p_93) :rule reordering :premises (t21.t70.t27))
(step t21.t70.t29 (cl @p_92 @p_91 @p_56) :rule equiv_pos2)
(step t21.t70.t30 (cl @p_91 @p_56 @p_92) :rule reordering :premises (t21.t70.t29))
(step t21.t70.t31 (cl (not @p_16) (not @p_8) @p_15) :rule equiv_pos2)
(step t21.t70.t32 (cl (= @p_4 @p_11)) :rule poly_simp)
(step t21.t70.t33 (cl (= @p_5 @p_12)) :rule cong :premises (t21.t70.t32))
(step t21.t70.t34 (cl (= @p_6 @p_13)) :rule cong :premises (t21.t70.t33))
(step t21.t70.t35 (cl (= @p_2 @p_9)) :rule rare_rewrite :args ("arith-elim-leq" 1 @p_1))
(step t21.t70.t36 (cl (= @p_7 @p_14)) :rule cong :premises (t21.t70.t34 t21.t70.t35))
(step t21.t70.t37 (cl @p_16) :rule cong :premises (t21.t70.t36))
(step t21.t70.t38 (cl @p_15) :rule resolution :premises (t21.t70.t31 t21.t70.t37 a1))
(step t21.t70.t39 (cl @p_13) :rule not_implies1 :premises (t21.t70.t38))
(step t21.t70.t40 (cl (not @p_87) (not @p_86) @p_83) :rule equiv_pos2)
(anchor :step t21.t70.t41 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t21.t70.t41.t0 (cl (= (* 1 (- @p_17 @p_65)) (* -1 (- @p_65 @p_17)))) :rule poly_simp)
(step t21.t70.t41.t1 (cl (= @p_90 @p_88)) :rule poly_simp_rel :premises (t21.t70.t41.t0))
(step t21.t70.t41.t2 (cl (= (or @p_89 @p_67 @p_90) (or @p_89 @p_67 @p_88))) :rule cong :premises (t21.t70.t41.t1))
(step t21.t70.t41 (cl (= (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$))))) (of_nat$ ?v1)))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$)))))))))) :rule bind)
(step t21.t70.t42 (cl (= @p_84 @p_56)) :rule cong :premises (t21.t70.t41))
(step t21.t70.t43 (cl (= @p_85 @p_57)) :rule cong :premises (t21.t70.t42))
(step t21.t70.t44 (cl @p_87) :rule cong :premises (t21.t70.t43))
(step t21.t70.t45 (cl @p_86 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule implies_neg1)
(anchor :step t21.t70.t46)
(assume t21.t70.t46.a0 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))))
(step t21.t70.t46.t0 (cl (or @p_82 @p_85)) :rule forall_inst :args (@p_12))
(step t21.t70.t46.t1 (cl @p_82 @p_85) :rule or :premises (t21.t70.t46.t0))
(step t21.t70.t46.t2 (cl (not @p_58) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t21.t70.t46.t3 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t21.t70.t46.t3.t0 (cl (= @p_62 @p_77)) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t21.t70.t46.t3.t1 (cl (= @p_78 @p_81)) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t21.t70.t46.t3.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t21.t70.t46.t3.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t21.t70.t46.t3.t2))
(step t21.t70.t46.t3.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t21.t70.t46.t3.t1 t21.t70.t46.t3.t3))
(step t21.t70.t46.t3.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t21.t70.t46.t3.t4))
(step t21.t70.t46.t3.t6 (cl (= @p_77 @p_79)) :rule cong :premises (t21.t70.t46.t3.t5))
(step t21.t70.t46.t3.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t21.t70.t46.t3.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t21.t70.t46.t3.t6 t21.t70.t46.t3.t7))
(step t21.t70.t46.t3.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t21.t70.t46.t3.t0 t21.t70.t46.t3.t8))
(anchor :step t21.t70.t46.t3.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t21.t70.t46.t3.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t21.t70.t46.t3.t10.t1 (cl (= @p_74 @p_66)) :rule poly_simp_rel :premises (t21.t70.t46.t3.t10.t0))
(step t21.t70.t46.t3.t10.t2 (cl (= @p_75 @p_71)) :rule cong :premises (t21.t70.t46.t3.t10.t1))
(step t21.t70.t46.t3.t10.t3 (cl (= (=> @p_68 @p_75) @p_72)) :rule cong :premises (t21.t70.t46.t3.t10.t2))
(step t21.t70.t46.t3.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t21.t70.t46.t3.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t21.t70.t46.t3.t11.t0 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t21.t70.t46.t3.t11.t1 (cl (= @p_73 @p_70)) :rule aci_simp)
(step t21.t70.t46.t3.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t21.t70.t46.t3.t11.t0 t21.t70.t46.t3.t11.t1))
(step t21.t70.t46.t3.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t21.t70.t46.t3.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t21.t70.t46.t3.t10 t21.t70.t46.t3.t11))
(step t21.t70.t46.t3.t13 (cl (= @p_63 @p_60)) :rule cong :premises (t21.t70.t46.t3.t9 t21.t70.t46.t3.t12))
(step t21.t70.t46.t3.t14 (cl (= (= @p_61 @p_63) (= @p_61 @p_60))) :rule cong :premises (t21.t70.t46.t3.t13))
(step t21.t70.t46.t3 (cl @p_58) :rule bind)
(step t21.t70.t46.t4 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t21.t70.t46.t2 t21.t70.t46.t3 a0))
(step t21.t70.t46.t5 (cl @p_85) :rule resolution :premises (t21.t70.t46.t1 t21.t70.t46.t4))
(step t21.t70.t46 (cl @p_82 @p_85) :rule subproof :discharge (t21.t70.t46.a0))
(step t21.t70.t47 (cl @p_86 @p_85) :rule resolution :premises (t21.t70.t45 t21.t70.t46))
(step t21.t70.t48 (cl @p_86 (not @p_85)) :rule implies_neg2)
(step t21.t70.t49 (cl @p_86 @p_86) :rule resolution :premises (t21.t70.t47 t21.t70.t48))
(step t21.t70.t50 (cl @p_86) :rule contraction :premises (t21.t70.t49))
(step t21.t70.t51 (cl @p_83) :rule resolution :premises (t21.t70.t40 t21.t70.t44 t21.t70.t50))
(step t21.t70.t52 (cl @p_82 @p_57) :rule implies :premises (t21.t70.t51))
(step t21.t70.t53 (cl (not @p_58) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t21.t70.t54 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t21.t70.t54.t0 (cl (= @p_62 @p_77)) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t21.t70.t54.t1 (cl (= @p_78 @p_81)) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t21.t70.t54.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t21.t70.t54.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t21.t70.t54.t2))
(step t21.t70.t54.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t21.t70.t54.t1 t21.t70.t54.t3))
(step t21.t70.t54.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t21.t70.t54.t4))
(step t21.t70.t54.t6 (cl (= @p_77 @p_79)) :rule cong :premises (t21.t70.t54.t5))
(step t21.t70.t54.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t21.t70.t54.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t21.t70.t54.t6 t21.t70.t54.t7))
(step t21.t70.t54.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t21.t70.t54.t0 t21.t70.t54.t8))
(anchor :step t21.t70.t54.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t21.t70.t54.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t21.t70.t54.t10.t1 (cl (= @p_74 @p_66)) :rule poly_simp_rel :premises (t21.t70.t54.t10.t0))
(step t21.t70.t54.t10.t2 (cl (= @p_75 @p_71)) :rule cong :premises (t21.t70.t54.t10.t1))
(step t21.t70.t54.t10.t3 (cl (= (=> @p_68 @p_75) @p_72)) :rule cong :premises (t21.t70.t54.t10.t2))
(step t21.t70.t54.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t21.t70.t54.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t21.t70.t54.t11.t0 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t21.t70.t54.t11.t1 (cl (= @p_73 @p_70)) :rule aci_simp)
(step t21.t70.t54.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t21.t70.t54.t11.t0 t21.t70.t54.t11.t1))
(step t21.t70.t54.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t21.t70.t54.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t21.t70.t54.t10 t21.t70.t54.t11))
(step t21.t70.t54.t13 (cl (= @p_63 @p_60)) :rule cong :premises (t21.t70.t54.t9 t21.t70.t54.t12))
(step t21.t70.t54.t14 (cl (= (= @p_61 @p_63) (= @p_61 @p_60))) :rule cong :premises (t21.t70.t54.t13))
(step t21.t70.t54 (cl @p_58) :rule bind)
(step t21.t70.t55 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t21.t70.t53 t21.t70.t54 a0))
(step t21.t70.t56 (cl @p_57) :rule resolution :premises (t21.t70.t52 t21.t70.t55))
(step t21.t70.t57 (cl @p_56) :rule resolution :premises (t21.t70.t30 t21.t70.t39 t21.t70.t56))
(step t21.t70.t58 (cl @p_55) :rule resolution :premises (t21.t70.t28 t21.t70.t57))
(step t21.t70.t59 (cl @p_129) :rule and_intro :premises (t21.t70.t22 t21.t70.t58))
(step t21.t70.t60 (cl @p_127) :rule resolution :premises (t21.t70.t26 t21.t70.t59))
(step t21.t70.t61 (cl (=> (! (and (! (> 4 0) :named @p_122) (! (<= @p_1 0) :named @p_121)) :named @p_123) @p_120)) :rule la_mult_pos)
(step t21.t70.t62 (cl (not @p_123) @p_120) :rule implies :premises (t21.t70.t61))
(step t21.t70.t63 (cl (= (! (= @p_122 true) :named @p_126) @p_122)) :rule equiv_simplify)
(step t21.t70.t64 (cl (not @p_126) @p_122) :rule equiv1 :premises (t21.t70.t63))
(step t21.t70.t65 (cl @p_126) :rule evaluate)
(step t21.t70.t66 (cl @p_122) :rule resolution :premises (t21.t70.t64 t21.t70.t65))
(step t21.t70.t67 (cl (not (! (< @p_1 1) :named @p_124)) @p_121) :rule la_generic :args (1/1 1/1))
(step t21.t70.t68 (cl (not (! (= @p_10 @p_124) :named @p_125)) @p_98 @p_124) :rule equiv_pos2)
(step t21.t70.t69 (cl (= @p_124 @p_10)) :rule rare_rewrite :args ("arith-elim-lt" @p_1 1))
(step t21.t70.t70 (cl @p_125) :rule symm :premises (t21.t70.t69))
(step t21.t70.t71 (cl @p_10) :rule not_implies2 :premises (t21.t70.t38))
(step t21.t70.t72 (cl @p_124) :rule resolution :premises (t21.t70.t68 t21.t70.t70 t21.t70.t71))
(step t21.t70.t73 (cl @p_121) :rule resolution :premises (t21.t70.t67 t21.t70.t72))
(step t21.t70.t74 (cl @p_123) :rule and_intro :premises (t21.t70.t66 t21.t70.t73))
(step t21.t70.t75 (cl @p_120) :rule resolution :premises (t21.t70.t62 t21.t70.t74))
(step t21.t70.t76 (cl @p_119) :rule resolution :premises (t21.t70.t16 t21.t70.t24 t21.t70.t60 t21.t70.t75))
(step t21.t70.t77 (cl false) :rule resolution :premises (t21.t70.t0 t21.t70.t15 t21.t70.t76))
(step t21.t70 (cl (! (not @p_110) :named @p_111) false) :rule subproof :discharge (t21.t70.a0))
(step t21.t71 (cl @p_112 false) :rule resolution :premises (t21.t69 t21.t70))
(step t21.t72 (cl @p_112 (! (not false) :named @p_106)) :rule implies_neg2)
(step t21.t73 (cl @p_112 @p_112) :rule resolution :premises (t21.t71 t21.t72))
(step t21.t74 (cl @p_112) :rule contraction :premises (t21.t73))
(step t21.t75 (cl (= @p_112 @p_111)) :rule implies_simplify)
(step t21.t76 (cl (not @p_112) @p_111) :rule equiv1 :premises (t21.t75))
(step t21.t77 (cl @p_111) :rule resolution :premises (t21.t74 t21.t76))
(step t21.t78 (cl) :rule resolution :premises (t21.t68 t21.t77))
(step t21 (cl @p_98 @p_94 @p_107 false) :rule subproof :discharge (t21.a0 t21.a1 t21.a2))
(step t22 (cl @p_104 @p_10) :rule and_pos :args (0))
(step t23 (cl @p_104 @p_55) :rule and_pos :args (1))
(step t24 (cl @p_104 @p_102) :rule and_pos :args (2))
(step t25 (cl false @p_104 @p_104 @p_104) :rule resolution :premises (t21 t22 t23 t24))
(step t26 (cl @p_104 @p_104 @p_104 false) :rule reordering :premises (t25))
(step t27 (cl @p_104 false) :rule contraction :premises (t26))
(step t28 (cl @p_105 false) :rule resolution :premises (t20 t27))
(step t29 (cl @p_105 @p_106) :rule implies_neg2)
(step t30 (cl @p_105 @p_105) :rule resolution :premises (t28 t29))
(step t31 (cl @p_105) :rule contraction :premises (t30))
(step t32 (cl (= @p_105 @p_104)) :rule implies_simplify)
(step t33 (cl (not @p_105) @p_104) :rule equiv1 :premises (t32))
(step t34 (cl @p_104) :rule resolution :premises (t31 t33))
(step t35 (cl @p_101) :rule resolution :premises (t19 t34))
(step t36 (cl @p_98 @p_94 @p_96 @p_95) :rule not_and :premises (t35))
(step t37 (cl @p_99 (not @p_98)) :rule or_neg :args (0))
(step t38 (cl @p_99 (not @p_94)) :rule or_neg :args (1))
(step t39 (cl @p_99 (not @p_96)) :rule or_neg :args (2))
(step t40 (cl @p_99 (not @p_95)) :rule or_neg :args (3))
(step t41 (cl @p_99 @p_99 @p_99 @p_99) :rule resolution :premises (t36 t37 t38 t39 t40))
(step t42 (cl @p_99) :rule contraction :premises (t41))
(step t43 (cl @p_97) :rule resolution :premises (t0 t5 t42))
(step t44 (cl @p_9 @p_94 @p_96 @p_95) :rule or :premises (t43))
(step t45 (cl @p_9 @p_94 @p_95 @p_96) :rule reordering :premises (t44))
(step t46 (cl @p_93 @p_55) :rule and_pos :args (0))
(step t47 (cl @p_55 @p_93) :rule reordering :premises (t46))
(step t48 (cl @p_92 @p_91 @p_56) :rule equiv_pos2)
(step t49 (cl @p_91 @p_56 @p_92) :rule reordering :premises (t48))
(step t50 (cl (not @p_16) (not @p_8) @p_15) :rule equiv_pos2)
(step t51 (cl (= @p_4 @p_11)) :rule poly_simp)
(step t52 (cl (= @p_5 @p_12)) :rule cong :premises (t51))
(step t53 (cl (= @p_6 @p_13)) :rule cong :premises (t52))
(step t54 (cl (= @p_2 @p_9)) :rule rare_rewrite :args ("arith-elim-leq" 1 @p_1))
(step t55 (cl (= @p_7 @p_14)) :rule cong :premises (t53 t54))
(step t56 (cl @p_16) :rule cong :premises (t55))
(step t57 (cl @p_15) :rule resolution :premises (t50 t56 a1))
(step t58 (cl @p_13) :rule not_implies1 :premises (t57))
(step t59 (cl (not @p_87) (not @p_86) @p_83) :rule equiv_pos2)
(anchor :step t60 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t60.t0 (cl (= (* 1 (- @p_17 @p_65)) (* -1 (- @p_65 @p_17)))) :rule poly_simp)
(step t60.t1 (cl (= @p_90 @p_88)) :rule poly_simp_rel :premises (t60.t0))
(step t60.t2 (cl (= (or @p_89 @p_67 @p_90) (or @p_89 @p_67 @p_88))) :rule cong :premises (t60.t1))
(step t60 (cl (= (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$))))) (of_nat$ ?v1)))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 (nat$ (+ 1 (* 4 (of_nat$ m$)))))) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ (nat$ (+ 1 (* 4 (of_nat$ m$)))))))))) :rule bind)
(step t61 (cl (= @p_84 @p_56)) :rule cong :premises (t60))
(step t62 (cl (= @p_85 @p_57)) :rule cong :premises (t61))
(step t63 (cl @p_87) :rule cong :premises (t62))
(step t64 (cl @p_86 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule implies_neg1)
(anchor :step t65)
(assume t65.a0 (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))))
(step t65.t0 (cl (or @p_82 @p_85)) :rule forall_inst :args (@p_12))
(step t65.t1 (cl @p_82 @p_85) :rule or :premises (t65.t0))
(step t65.t2 (cl (not @p_58) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t65.t3 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t65.t3.t0 (cl (= @p_62 @p_77)) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t65.t3.t1 (cl (= @p_78 @p_81)) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t65.t3.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t65.t3.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t65.t3.t2))
(step t65.t3.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t65.t3.t1 t65.t3.t3))
(step t65.t3.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t65.t3.t4))
(step t65.t3.t6 (cl (= @p_77 @p_79)) :rule cong :premises (t65.t3.t5))
(step t65.t3.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t65.t3.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t65.t3.t6 t65.t3.t7))
(step t65.t3.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t65.t3.t0 t65.t3.t8))
(anchor :step t65.t3.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t65.t3.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t65.t3.t10.t1 (cl (= @p_74 @p_66)) :rule poly_simp_rel :premises (t65.t3.t10.t0))
(step t65.t3.t10.t2 (cl (= @p_75 @p_71)) :rule cong :premises (t65.t3.t10.t1))
(step t65.t3.t10.t3 (cl (= (=> @p_68 @p_75) @p_72)) :rule cong :premises (t65.t3.t10.t2))
(step t65.t3.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t65.t3.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t65.t3.t11.t0 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t65.t3.t11.t1 (cl (= @p_73 @p_70)) :rule aci_simp)
(step t65.t3.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t65.t3.t11.t0 t65.t3.t11.t1))
(step t65.t3.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t65.t3.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t65.t3.t10 t65.t3.t11))
(step t65.t3.t13 (cl (= @p_63 @p_60)) :rule cong :premises (t65.t3.t9 t65.t3.t12))
(step t65.t3.t14 (cl (= (= @p_61 @p_63) (= @p_61 @p_60))) :rule cong :premises (t65.t3.t13))
(step t65.t3 (cl @p_58) :rule bind)
(step t65.t4 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t65.t2 t65.t3 a0))
(step t65.t5 (cl @p_85) :rule resolution :premises (t65.t1 t65.t4))
(step t65 (cl @p_82 @p_85) :rule subproof :discharge (t65.a0))
(step t66 (cl @p_86 @p_85) :rule resolution :premises (t64 t65))
(step t67 (cl @p_86 (not @p_85)) :rule implies_neg2)
(step t68 (cl @p_86 @p_86) :rule resolution :premises (t66 t67))
(step t69 (cl @p_86) :rule contraction :premises (t68))
(step t70 (cl @p_83) :rule resolution :premises (t59 t63 t69))
(step t71 (cl @p_82 @p_57) :rule implies :premises (t70))
(step t72 (cl (not @p_58) (not (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (< 1 (of_nat$ ?v0)) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))))))) (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule equiv_pos2)
(anchor :step t73 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t73.t0 (cl (= @p_62 @p_77)) :rule rare_rewrite :args ("arith-elim-lt" 1 @p_50))
(step t73.t1 (cl (= @p_78 @p_81)) :rule rare_rewrite :args ("arith-geq-tighten" @p_50 2))
(step t73.t2 (cl (= (* 1 (- 2 @p_80)) (* 1 (- 1 @p_50)))) :rule poly_simp)
(step t73.t3 (cl (= @p_81 @p_76)) :rule poly_simp_rel :premises (t73.t2))
(step t73.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t73.t1 t73.t3))
(step t73.t5 (cl (= @p_76 @p_78)) :rule symm :premises (t73.t4))
(step t73.t6 (cl (= @p_77 @p_79)) :rule cong :premises (t73.t5))
(step t73.t7 (cl (= @p_79 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t73.t8 (cl (= @p_77 @p_59)) :rule trans :premises (t73.t6 t73.t7))
(step t73.t9 (cl (= @p_62 @p_59)) :rule trans :premises (t73.t0 t73.t8))
(anchor :step t73.t10 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t73.t10.t0 (cl (= (* 1 (- @p_65 @p_50)) (* -1 (- @p_50 @p_65)))) :rule poly_simp)
(step t73.t10.t1 (cl (= @p_74 @p_66)) :rule poly_simp_rel :premises (t73.t10.t0))
(step t73.t10.t2 (cl (= @p_75 @p_71)) :rule cong :premises (t73.t10.t1))
(step t73.t10.t3 (cl (= (=> @p_68 @p_75) @p_72)) :rule cong :premises (t73.t10.t2))
(step t73.t10 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))))) :rule bind)
(anchor :step t73.t11 :args ((?v1 Nat$) (:= (?v1 Nat$) ?v1)))
(step t73.t11.t0 (cl (= @p_72 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_68 @p_71))
(step t73.t11.t1 (cl (= @p_73 @p_70)) :rule aci_simp)
(step t73.t11.t2 (cl (= @p_72 @p_70)) :rule trans :premises (t73.t11.t0 t73.t11.t1))
(step t73.t11 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule bind)
(step t73.t12 (cl (= (forall ((?v1 Nat$)) (=> (dvd$ ?v1 ?v0) (or (= (of_nat$ ?v1) 1) (= (of_nat$ ?v1) (of_nat$ ?v0))))) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))) :rule trans :premises (t73.t10 t73.t11))
(step t73.t13 (cl (= @p_63 @p_60)) :rule cong :premises (t73.t9 t73.t12))
(step t73.t14 (cl (= (= @p_61 @p_63) (= @p_61 @p_60))) :rule cong :premises (t73.t13))
(step t73 (cl @p_58) :rule bind)
(step t74 (cl (forall ((?v0 Nat$)) (= (prime_nat$ ?v0) (and (>= (of_nat$ ?v0) 2) (forall ((?v1 Nat$)) (or (not (dvd$ ?v1 ?v0)) (= (of_nat$ ?v1) 1) (= (of_nat$ ?v0) (of_nat$ ?v1)))))))) :rule resolution :premises (t72 t73 a0))
(step t75 (cl @p_57) :rule resolution :premises (t71 t74))
(step t76 (cl @p_56) :rule resolution :premises (t49 t58 t75))
(step t77 (cl @p_55) :rule resolution :premises (t47 t76))
(step t78 (cl (not @p_54) (not @p_53) @p_53) :rule equiv_pos2)
(step t79 (cl (= @p_44 @p_43)) :rule equiv_simplify)
(step t80 (cl (not @p_44) @p_43) :rule equiv1 :premises (t79))
(step t81 (cl (= (* -1 @p_46) (* 1 @p_46))) :rule poly_simp)
(step t82 (cl @p_45) :rule poly_simp_rel :premises (t81))
(step t83 (cl @p_43) :rule refl)
(step t84 (cl @p_43) :rule refl)
(step t85 (cl @p_45) :rule cong :premises (t83 t84))
(step t86 (cl @p_44) :rule rare_rewrite :args ("eq-refl" @p_19))
(step t87 (cl @p_44) :rule trans :premises (t82 t85 t86))
(step t88 (cl @p_43) :rule resolution :premises (t80 t87))
(step t89 (cl (= @p_11 @p_11)) :rule refl)
(step t90 (cl (= @p_47 @p_47)) :rule cong :premises (t88 t89))
(step t91 (cl (= 0 0)) :rule refl)
(step t92 (cl (= @p_52 @p_52)) :rule cong :premises (t88 t91))
(step t93 (cl @p_54) :rule cong :premises (t90 t92))
(step t94 (cl (= @p_53 true)) :rule rare_rewrite :args ("ite-eq" @p_18 @p_11 0))
(step t95 (cl @p_53 (not true)) :rule equiv2 :premises (t94))
(step t96 (cl true) :rule true)
(step t97 (cl @p_53) :rule resolution :premises (t95 t96))
(step t98 (cl @p_53) :rule resolution :premises (t78 t93 t97))
(step t99 (cl (not @p_18) @p_47) :rule ite2 :premises (t98))
(step t100 (cl (or @p_51 @p_18)) :rule forall_inst :args (m$))
(step t101 (cl @p_51 @p_18) :rule or :premises (t100))
(step t102 (cl (not @p_48) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t103 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t103.t0 (cl (= (<= 0 @p_50) (>= @p_50 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_50))
(step t103 (cl @p_48) :rule bind)
(step t104 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t102 t103 a2))
(step t105 (cl @p_18) :rule resolution :premises (t101 t104))
(step t106 (cl @p_47) :rule resolution :premises (t99 t105))
(step t107 (cl (not @p_41) (not @p_31) @p_29) :rule equiv_pos2)
(step t108 (cl (= @p_30 @p_30)) :rule cong :premises (t88))
(step t109 (cl (= (* -1 (- @p_17 @p_19)) (* 1 (- @p_19 @p_17)))) :rule poly_simp)
(step t110 (cl @p_42) :rule poly_simp_rel :premises (t109))
(step t111 (cl @p_42) :rule trans :premises (t108 t110))
(step t112 (cl @p_41) :rule cong :premises (t111))
(step t113 (cl (not @p_36) (not @p_35) @p_31) :rule equiv_pos2)
(step t114 (cl (= (* 1/4 (to_real (- @p_11 0))) (* 1/1 (- @p_37 -1/4)))) :rule poly_simp)
(step t115 (cl (= @p_32 @p_38)) :rule poly_simp_rel :premises (t114))
(step t116 (cl (= (= (to_real @p_39) -1/4) false)) :rule evaluate)
(step t117 (cl (= @p_40 0)) :rule evaluate)
(step t118 (cl (= 0 @p_40)) :rule symm :premises (t117))
(step t119 (cl (= @p_38 @p_18)) :rule rare_rewrite :premises (t116 t118) :args ("arith-int-geq-tighten" @p_1 -1/4 0))
(step t120 (cl (= @p_32 @p_18)) :rule trans :premises (t115 t119))
(step t121 (cl (= @p_33 @p_19)) :rule cong :premises (t120 t89 t91))
(step t122 (cl (= @p_34 @p_30)) :rule cong :premises (t121))
(step t123 (cl @p_36) :rule cong :premises (t122))
(step t124 (cl @p_35 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule implies_neg1)
(anchor :step t125)
(assume t125.a0 (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0))))
(step t125.t0 (cl (or @p_28 @p_34)) :rule forall_inst :args (@p_11))
(step t125.t1 (cl @p_28 @p_34) :rule or :premises (t125.t0))
(step t125.t2 (cl (not @p_21) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t125.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t125.t3.t0 (cl (= @p_26 @p_23)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t125.t3.t1 (cl @p_22) :rule refl)
(step t125.t3.t2 (cl (= @p_27 @p_24)) :rule cong :premises (t125.t3.t0 t125.t3.t1 t91))
(step t125.t3.t3 (cl (= (= @p_25 @p_27) (= @p_25 @p_24))) :rule cong :premises (t125.t3.t2))
(step t125.t3 (cl @p_21) :rule bind)
(step t125.t4 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t125.t2 t125.t3 a4))
(step t125.t5 (cl @p_34) :rule resolution :premises (t125.t1 t125.t4))
(step t125 (cl @p_28 @p_34) :rule subproof :discharge (t125.a0))
(step t126 (cl @p_35 @p_34) :rule resolution :premises (t124 t125))
(step t127 (cl @p_35 (not @p_34)) :rule implies_neg2)
(step t128 (cl @p_35 @p_35) :rule resolution :premises (t126 t127))
(step t129 (cl @p_35) :rule contraction :premises (t128))
(step t130 (cl @p_31) :rule resolution :premises (t113 t123 t129))
(step t131 (cl @p_29) :rule resolution :premises (t107 t112 t130))
(step t132 (cl @p_28 @p_20) :rule implies :premises (t131))
(step t133 (cl (not @p_21) (not (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (<= 0 ?v0) ?v0 0)))) (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule equiv_pos2)
(anchor :step t134 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t134.t0 (cl (= @p_26 @p_23)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t134.t1 (cl @p_22) :rule refl)
(step t134.t2 (cl (= @p_27 @p_24)) :rule cong :premises (t134.t0 t134.t1 t91))
(step t134.t3 (cl (= (= @p_25 @p_27) (= @p_25 @p_24))) :rule cong :premises (t134.t2))
(step t134 (cl @p_21) :rule bind)
(step t135 (cl (forall ((?v0 Int)) (= (of_nat$ (nat$ ?v0)) (ite (>= ?v0 0) ?v0 0)))) :rule resolution :premises (t133 t134 a4))
(step t136 (cl @p_20) :rule resolution :premises (t132 t135))
(step t137 (cl @p_10) :rule not_implies2 :premises (t57))
(step t138 (cl) :rule resolution :premises (t45 t77 t106 t136 t137))
)
1685da81022d656484d0d27b6daf504d8afa2561 17 0
unsat
(
(assume a0 (! (not (not (! (= (! (* 2 x$) :named @p_1) 1) :named @p_2))) :named @p_3))
(step t0 (cl (not (! (= @p_3 false) :named @p_4)) (not @p_3) false) :rule equiv_pos2)
(step t1 (cl (= @p_3 @p_2)) :rule rare_rewrite :args ("bool-double-not-elim" @p_2))
(step t2 (cl (= (* -1/1 (to_real (- @p_1 1))) (* -1/1 (! (- (! (to_real @p_1) :named @p_8) (! (to_real 1) :named @p_7)) :named @p_10)))) :rule poly_simp)
(step t3 (cl (= @p_2 (! (= @p_8 @p_7) :named @p_9))) :rule poly_simp_rel :premises (t2))
(step t4 (cl (= (* -1/2 @p_10) (* -1/1 (- (! (to_real x$) :named @p_5) 1/2)))) :rule poly_simp)
(step t5 (cl (= @p_9 (! (= @p_5 1/2) :named @p_6))) :rule poly_simp_rel :premises (t4))
(step t6 (cl (= (= (to_real (to_int 1/2)) 1/2) false)) :rule evaluate)
(step t7 (cl (= @p_6 false)) :rule rare_rewrite :premises (t6) :args ("arith-int-eq-conflict" x$ 1/2))
(step t8 (cl (= @p_2 false)) :rule trans :premises (t3 t5 t7))
(step t9 (cl @p_4) :rule trans :premises (t1 t8))
(step t10 (cl false) :rule resolution :premises (t0 t9 a0))
(step t11 (cl (not false)) :rule false)
(step t12 (cl) :rule resolution :premises (t10 t11))
)
c4e2724f31fd49f83367ce789a6ff850174cba52 52 0
unsat
(
(assume a0 (forall ((?v0 A$) (?v1 B$)) (= (fst$ (pair$ ?v0 ?v1)) ?v0)))
(assume a1 (! (not (! (=> (! (= (! (fst$ (pair$ x$ y$)) :named @p_2) a$) :named @p_3) (! (= x$ a$) :named @p_1)) :named @p_4)) :named @p_5))
(step t0 (cl (! (=> (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1)))) (! (= x$ @p_2) :named @p_8)) :named @p_23) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1)))))
(step t1.t0 (cl (or (! (not (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :named @p_22) @p_8)) :rule forall_inst :args (x$ y$))
(step t1.t1 (cl @p_22 @p_8) :rule or :premises (t1.t0))
(step t1.t2 (cl (not (! (= (forall ((?v0 A$) (?v1 B$)) (= (fst$ (pair$ ?v0 ?v1)) ?v0)) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :named @p_6)) (not (forall ((?v0 A$) (?v1 B$)) (= (fst$ (pair$ ?v0 ?v1)) ?v0))) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t1.t3 :args ((?v0 A$) (?v1 B$) (:= (?v0 A$) ?v0) (:= (?v1 B$) ?v1)))
(step t1.t3.t0 (cl (= (= (! (fst$ (pair$ ?v0 ?v1)) :named @p_7) ?v0) (= ?v0 @p_7))) :rule rare_rewrite :args ("eq-symm" @p_7 ?v0))
(step t1.t3 (cl @p_6) :rule bind)
(step t1.t4 (cl (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :rule resolution :premises (t1.t2 t1.t3 a0))
(step t1.t5 (cl @p_8) :rule resolution :premises (t1.t1 t1.t4))
(step t1 (cl @p_22 @p_8) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_23 @p_8) :rule resolution :premises (t0 t1))
(step t3 (cl @p_23 (! (not @p_8) :named @p_9)) :rule implies_neg2)
(step t4 (cl @p_23 @p_23) :rule resolution :premises (t2 t3))
(step t5 (cl @p_23) :rule contraction :premises (t4))
(step t6 (cl @p_22 @p_8) :rule implies :premises (t5))
(step t7 (cl @p_8 @p_22) :rule reordering :premises (t6))
(step t8 (cl (not (! (= @p_5 @p_9) :named @p_10)) (! (not @p_5) :named @p_21) @p_9) :rule equiv_pos2)
(step t9 (cl (= @p_3 (! (= a$ @p_2) :named @p_12))) :rule rare_rewrite :args ("eq-symm" @p_2 a$))
(step t10 (cl (= @p_1 (! (= a$ x$) :named @p_11))) :rule rare_rewrite :args ("eq-symm" x$ a$))
(step t11 (cl (= @p_4 (! (=> @p_12 @p_11) :named @p_13))) :rule cong :premises (t9 t10))
(step t12 (cl (! (= @p_5 (! (not @p_13) :named @p_14)) :named @p_20)) :rule cong :premises (t11))
(step t13 (cl (not @p_20) @p_21 @p_14) :rule equiv_pos2)
(step t14 (cl @p_14) :rule resolution :premises (t13 t12 a1))
(step t15 (cl @p_12) :rule not_implies1 :premises (t14))
(step t16 (cl (! (= @p_2 @p_2) :named @p_16)) :rule refl)
(step t17 (cl (= @p_12 @p_16)) :rule cong :premises (t15 t16))
(step t18 (cl (= x$ x$)) :rule refl)
(step t19 (cl (= @p_11 (! (= @p_2 x$) :named @p_15))) :rule cong :premises (t15 t18))
(step t20 (cl (= @p_13 (! (=> @p_16 @p_15) :named @p_17))) :rule cong :premises (t17 t19))
(step t21 (cl (= @p_14 (! (not @p_17) :named @p_18))) :rule cong :premises (t20))
(step t22 (cl (= @p_16 true)) :rule rare_rewrite :args ("eq-refl" @p_2))
(step t23 (cl (= @p_15 @p_8)) :rule rare_rewrite :args ("eq-symm" @p_2 x$))
(step t24 (cl (= @p_17 (! (=> true @p_8) :named @p_19))) :rule cong :premises (t22 t23))
(step t25 (cl (= @p_19 @p_8)) :rule rare_rewrite :args ("bool-impl-true2" @p_8))
(step t26 (cl (= @p_17 @p_8)) :rule trans :premises (t24 t25))
(step t27 (cl (= @p_18 @p_9)) :rule cong :premises (t26))
(step t28 (cl (= @p_14 @p_9)) :rule trans :premises (t21 t27))
(step t29 (cl @p_10) :rule trans :premises (t12 t28))
(step t30 (cl @p_9) :rule resolution :premises (t8 t29 a1))
(step t31 (cl (not @p_6) (not (forall ((?v0 A$) (?v1 B$)) (= (fst$ (pair$ ?v0 ?v1)) ?v0))) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t32 :args ((?v0 A$) (?v1 B$) (:= (?v0 A$) ?v0) (:= (?v1 B$) ?v1)))
(step t32.t0 (cl (= (= @p_7 ?v0) (= ?v0 @p_7))) :rule rare_rewrite :args ("eq-symm" @p_7 ?v0))
(step t32 (cl @p_6) :rule bind)
(step t33 (cl (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$ (pair$ ?v0 ?v1))))) :rule resolution :premises (t31 t32 a0))
(step t34 (cl) :rule resolution :premises (t7 t30 t33))
)
0267962f13bf4f8fdda541de9bb05f7afa73303b 65 0
unsat
(
(assume a1 (forall ((?v0 A$) (?v1 B$)) (= (fst$a (pair$a ?v0 ?v1)) ?v0)))
(assume a3 (forall ((?v0 B$) (?v1 A$)) (= (snd$a (pair$ ?v0 ?v1)) ?v1)))
(assume a4 (! (not (! (=> (! (and (! (= p1$ (! (pair$a x$ y$) :named @p_6)) :named @p_7) (! (= p2$ (! (pair$ y$ x$) :named @p_4)) :named @p_5)) :named @p_8) (! (= (! (fst$a p1$) :named @p_2) (! (snd$a p2$) :named @p_1)) :named @p_3)) :named @p_9)) :named @p_10))
(step t0 (cl (not (! (= (! (= false true) :named @p_11) false) :named @p_36)) (not @p_11) false) :rule equiv_pos2)
(step t1 (cl @p_36) :rule evaluate)
(step t2 (cl (= (! (= (! (= (! (snd$a @p_4) :named @p_13) (! (fst$a @p_6) :named @p_12)) :named @p_14) false) :named @p_25) (! (not @p_14) :named @p_24))) :rule equiv_simplify)
(step t3 (cl @p_25 (! (not @p_24) :named @p_35)) :rule equiv2 :premises (t2))
(step t4 (cl (not @p_35) @p_14) :rule not_not)
(step t5 (cl @p_25 @p_14) :rule resolution :premises (t3 t4))
(step t6 (cl (not (! (= @p_10 @p_24) :named @p_26)) (not @p_10) @p_24) :rule equiv_pos2)
(step t7 (cl @p_8) :rule not_implies1 :premises (a4))
(step t8 (cl @p_7) :rule and :premises (t7) :args (0))
(step t9 (cl (! (= @p_6 @p_6) :named @p_29)) :rule refl)
(step t10 (cl (= @p_7 @p_29)) :rule cong :premises (t8 t9))
(step t11 (cl @p_5) :rule and :premises (t7) :args (1))
(step t12 (cl (! (= @p_4 @p_4) :named @p_28)) :rule refl)
(step t13 (cl (= @p_5 @p_28)) :rule cong :premises (t11 t12))
(step t14 (cl (= @p_8 (! (and @p_29 @p_28) :named @p_30))) :rule cong :premises (t10 t13))
(step t15 (cl (= @p_2 @p_12)) :rule cong :premises (t8))
(step t16 (cl (= @p_1 @p_13)) :rule cong :premises (t11))
(step t17 (cl (= @p_3 (! (= @p_12 @p_13) :named @p_27))) :rule cong :premises (t15 t16))
(step t18 (cl (= @p_9 (! (=> @p_30 @p_27) :named @p_31))) :rule cong :premises (t14 t17))
(step t19 (cl (= @p_10 (! (not @p_31) :named @p_32))) :rule cong :premises (t18))
(step t20 (cl (= @p_29 true)) :rule rare_rewrite :args ("eq-refl" @p_6))
(step t21 (cl (= @p_28 true)) :rule rare_rewrite :args ("eq-refl" @p_4))
(step t22 (cl (= @p_30 (! (and true true) :named @p_34))) :rule cong :premises (t20 t21))
(step t23 (cl (= @p_34 true)) :rule evaluate)
(step t24 (cl (= @p_30 true)) :rule trans :premises (t22 t23))
(step t25 (cl (= @p_27 @p_14)) :rule rare_rewrite :args ("eq-symm" @p_12 @p_13))
(step t26 (cl (= @p_31 (! (=> true @p_14) :named @p_33))) :rule cong :premises (t24 t25))
(step t27 (cl (= @p_33 @p_14)) :rule rare_rewrite :args ("bool-impl-true2" @p_14))
(step t28 (cl (= @p_31 @p_14)) :rule trans :premises (t26 t27))
(step t29 (cl (= @p_32 @p_24)) :rule cong :premises (t28))
(step t30 (cl @p_26) :rule trans :premises (t19 t29))
(step t31 (cl @p_24) :rule resolution :premises (t6 t30 a4))
(step t32 (cl @p_25) :rule resolution :premises (t5 t31))
(step t33 (cl (= false @p_14)) :rule symm :premises (t32))
(step t34 (cl (= (! (= @p_14 true) :named @p_15) @p_14)) :rule equiv_simplify)
(step t35 (cl @p_15 @p_24) :rule equiv2 :premises (t34))
(step t36 (cl (or (! (not (forall ((?v0 B$) (?v1 A$)) (= ?v1 (snd$a (pair$ ?v0 ?v1))))) :named @p_23) (! (= x$ @p_13) :named @p_20))) :rule forall_inst :args (y$ x$))
(step t37 (cl @p_23 @p_20) :rule or :premises (t36))
(step t38 (cl (not (! (= (forall ((?v0 B$) (?v1 A$)) (= (snd$a (pair$ ?v0 ?v1)) ?v1)) (forall ((?v0 B$) (?v1 A$)) (= ?v1 (snd$a (pair$ ?v0 ?v1))))) :named @p_21)) (not (forall ((?v0 B$) (?v1 A$)) (= (snd$a (pair$ ?v0 ?v1)) ?v1))) (forall ((?v0 B$) (?v1 A$)) (= ?v1 (snd$a (pair$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t39 :args ((?v0 B$) (?v1 A$) (:= (?v0 B$) ?v0) (:= (?v1 A$) ?v1)))
(step t39.t0 (cl (= (= (! (snd$a (pair$ ?v0 ?v1)) :named @p_22) ?v1) (= ?v1 @p_22))) :rule rare_rewrite :args ("eq-symm" @p_22 ?v1))
(step t39 (cl @p_21) :rule bind)
(step t40 (cl (forall ((?v0 B$) (?v1 A$)) (= ?v1 (snd$a (pair$ ?v0 ?v1))))) :rule resolution :premises (t38 t39 a3))
(step t41 (cl @p_20) :rule resolution :premises (t37 t40))
(step t42 (cl (= @p_13 x$)) :rule symm :premises (t41))
(step t43 (cl (or (! (not (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$a (pair$a ?v0 ?v1))))) :named @p_19) (! (= x$ @p_12) :named @p_16))) :rule forall_inst :args (x$ y$))
(step t44 (cl @p_19 @p_16) :rule or :premises (t43))
(step t45 (cl (not (! (= (forall ((?v0 A$) (?v1 B$)) (= (fst$a (pair$a ?v0 ?v1)) ?v0)) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$a (pair$a ?v0 ?v1))))) :named @p_17)) (not (forall ((?v0 A$) (?v1 B$)) (= (fst$a (pair$a ?v0 ?v1)) ?v0))) (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$a (pair$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t46 :args ((?v0 A$) (?v1 B$) (:= (?v0 A$) ?v0) (:= (?v1 B$) ?v1)))
(step t46.t0 (cl (= (= (! (fst$a (pair$a ?v0 ?v1)) :named @p_18) ?v0) (= ?v0 @p_18))) :rule rare_rewrite :args ("eq-symm" @p_18 ?v0))
(step t46 (cl @p_17) :rule bind)
(step t47 (cl (forall ((?v0 A$) (?v1 B$)) (= ?v0 (fst$a (pair$a ?v0 ?v1))))) :rule resolution :premises (t45 t46 a1))
(step t48 (cl @p_16) :rule resolution :premises (t44 t47))
(step t49 (cl @p_14) :rule trans :premises (t42 t48))
(step t50 (cl @p_15) :rule resolution :premises (t35 t49))
(step t51 (cl @p_11) :rule trans :premises (t33 t50))
(step t52 (cl false) :rule resolution :premises (t0 t1 t51))
(step t53 (cl (not false)) :rule false)
(step t54 (cl) :rule resolution :premises (t52 t53))
)
bf5183aca2d5a74809a43b256c2f26f90a263ce3 142 0
unsat
(
(assume a1 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))))
(assume a2 (! (not (=> (! (and (! (not (! (= i$ i1$) :named @p_7)) :named @p_8) (! (not (! (= i$ i2$) :named @p_5)) :named @p_6)) :named @p_9) (! (= (! (fun_app$ (fun_upd$ (! (fun_upd$ f$ i1$ v1$) :named @p_2) i2$ v2$) i$) :named @p_3) (! (fun_app$ f$ i$) :named @p_1)) :named @p_4))) :named @p_10))
(step t0 (cl (not (! (= (! (= false true) :named @p_11) false) :named @p_67)) (not @p_11) false) :rule equiv_pos2)
(step t1 (cl @p_67) :rule evaluate)
(step t2 (cl (= (! (= @p_4 false) :named @p_65) (! (not @p_4) :named @p_64))) :rule equiv_simplify)
(step t3 (cl @p_65 (! (not @p_64) :named @p_66)) :rule equiv2 :premises (t2))
(step t4 (cl (not @p_66) @p_4) :rule not_not)
(step t5 (cl @p_65 @p_4) :rule resolution :premises (t3 t4))
(step t6 (cl @p_64) :rule not_implies2 :premises (a2))
(step t7 (cl @p_65) :rule resolution :premises (t5 t6))
(step t8 (cl (= false @p_4)) :rule symm :premises (t7))
(step t9 (cl (= (! (= @p_4 true) :named @p_12) @p_4)) :rule equiv_simplify)
(step t10 (cl @p_12 @p_64) :rule equiv2 :premises (t9))
(step t11 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))) (! (= @p_3 (! (ite @p_5 v2$ (! (fun_app$ @p_2 i$) :named @p_13)) :named @p_14)) :named @p_56)) :named @p_57) @p_57) :named @p_63)) (not @p_57) @p_57) :rule equiv_pos2)
(step t12 (cl (= (! (= (! (= @p_14 @p_14) :named @p_23) true) :named @p_24) @p_23)) :rule equiv_simplify)
(step t13 (cl (not @p_24) @p_23) :rule equiv1 :premises (t12))
(step t14 (cl @p_23) :rule refl)
(step t15 (cl (= @p_23 @p_23)) :rule cong :premises (t14))
(step t16 (cl @p_24) :rule rare_rewrite :args ("eq-refl" @p_14))
(step t17 (cl @p_24) :rule trans :premises (t15 t16))
(step t18 (cl @p_23) :rule resolution :premises (t13 t17))
(step t19 (cl (= @p_56 @p_56)) :rule cong :premises (t18))
(step t20 (cl @p_63) :rule cong :premises (t19))
(step t21 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))) (! (= @p_3 (! (ite (! (= i2$ i$) :named @p_58) v2$ @p_13) :named @p_59)) :named @p_60)) :named @p_61) @p_57) :named @p_62)) (not @p_61) @p_57) :rule equiv_pos2)
(step t22 (cl (= @p_58 @p_5)) :rule rare_rewrite :args ("eq-symm" i2$ i$))
(step t23 (cl (= v2$ v2$)) :rule refl)
(step t24 (cl (= @p_13 @p_13)) :rule refl)
(step t25 (cl (= @p_59 @p_14)) :rule cong :premises (t22 t23 t24))
(step t26 (cl (= @p_60 @p_56)) :rule cong :premises (t25))
(step t27 (cl @p_62) :rule cong :premises (t26))
(step t28 (cl @p_61 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule implies_neg1)
(anchor :step t29)
(assume t29.a0 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))))
(step t29.t0 (cl (or (! (not (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :named @p_37) @p_60)) :rule forall_inst :args (@p_2 i2$ v2$ i$))
(step t29.t1 (cl @p_37 @p_60) :rule or :premises (t29.t0))
(step t29.t2 (cl (not (! (= (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3)))) (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :named @p_29)) (not (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3))))) (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule equiv_pos2)
(anchor :step t29.t3 :args ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) (:= (?v0 A_b_fun$) ?v0) (:= (?v1 A$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 A$) ?v3)))
(step t29.t3.t0 (cl (= (! (= ?v3 ?v1) :named @p_35) (! (= ?v1 ?v3) :named @p_32))) :rule rare_rewrite :args ("eq-symm" ?v3 ?v1))
(step t29.t3.t1 (cl (! (= ?v2 ?v2) :named @p_30)) :rule refl)
(step t29.t3.t2 (cl (= (! (fun_app$ ?v0 ?v3) :named @p_31) @p_31)) :rule refl)
(step t29.t3.t3 (cl (= (! (ite @p_35 ?v2 @p_31) :named @p_36) (! (ite @p_32 ?v2 @p_31) :named @p_33))) :rule cong :premises (t29.t3.t0 t29.t3.t1 t29.t3.t2))
(step t29.t3.t4 (cl (= (= (! (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) :named @p_34) @p_36) (= @p_34 @p_33))) :rule cong :premises (t29.t3.t3))
(step t29.t3 (cl @p_29) :rule bind)
(step t29.t4 (cl (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule resolution :premises (t29.t2 t29.t3 a1))
(step t29.t5 (cl @p_60) :rule resolution :premises (t29.t1 t29.t4))
(step t29 (cl @p_37 @p_60) :rule subproof :discharge (t29.a0))
(step t30 (cl @p_61 @p_60) :rule resolution :premises (t28 t29))
(step t31 (cl @p_61 (not @p_60)) :rule implies_neg2)
(step t32 (cl @p_61 @p_61) :rule resolution :premises (t30 t31))
(step t33 (cl @p_61) :rule contraction :premises (t32))
(step t34 (cl @p_57) :rule resolution :premises (t21 t27 t33))
(step t35 (cl @p_57) :rule resolution :premises (t11 t20 t34))
(step t36 (cl @p_37 @p_56) :rule implies :premises (t35))
(step t37 (cl (not @p_29) (not (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v3 ?v1) ?v2 (fun_app$ ?v0 ?v3))))) (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule equiv_pos2)
(anchor :step t38 :args ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$) (:= (?v0 A_b_fun$) ?v0) (:= (?v1 A$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 A$) ?v3)))
(step t38.t0 (cl (= @p_35 @p_32)) :rule rare_rewrite :args ("eq-symm" ?v3 ?v1))
(step t38.t1 (cl @p_30) :rule refl)
(step t38.t2 (cl (= @p_31 @p_31)) :rule refl)
(step t38.t3 (cl (= @p_36 @p_33)) :rule cong :premises (t38.t0 t38.t1 t38.t2))
(step t38.t4 (cl (= (= @p_34 @p_36) (= @p_34 @p_33))) :rule cong :premises (t38.t3))
(step t38 (cl @p_29) :rule bind)
(step t39 (cl (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule resolution :premises (t37 t38 a1))
(step t40 (cl @p_56) :rule resolution :premises (t36 t39))
(step t41 (cl (not (! (= (! (ite @p_7 (! (= (! (ite @p_7 v1$ @p_1) :named @p_27) v1$) :named @p_51) (! (= @p_27 @p_1) :named @p_50)) :named @p_52) (! (ite @p_7 (! (= v1$ @p_27) :named @p_48) (! (= @p_1 @p_27) :named @p_47)) :named @p_49)) :named @p_55)) (! (not @p_52) :named @p_54) @p_49) :rule equiv_pos2)
(step t42 (cl (= @p_51 @p_48)) :rule rare_rewrite :args ("eq-symm" @p_27 v1$))
(step t43 (cl (= @p_50 @p_47)) :rule rare_rewrite :args ("eq-symm" @p_27 @p_1))
(step t44 (cl @p_55) :rule cong :premises (t42 t43))
(step t45 (cl (not (! (= @p_52 @p_52) :named @p_53)) @p_54 @p_52) :rule equiv_pos2)
(step t46 (cl (= (! (= (! (= @p_27 @p_27) :named @p_45) true) :named @p_46) @p_45)) :rule equiv_simplify)
(step t47 (cl (not @p_46) @p_45) :rule equiv1 :premises (t46))
(step t48 (cl @p_45) :rule refl)
(step t49 (cl (= @p_45 @p_45)) :rule cong :premises (t48))
(step t50 (cl @p_46) :rule rare_rewrite :args ("eq-refl" @p_27))
(step t51 (cl @p_46) :rule trans :premises (t49 t50))
(step t52 (cl @p_45) :rule resolution :premises (t47 t51))
(step t53 (cl (= v1$ v1$)) :rule refl)
(step t54 (cl (= @p_51 @p_51)) :rule cong :premises (t52 t53))
(step t55 (cl (= @p_1 @p_1)) :rule refl)
(step t56 (cl (= @p_50 @p_50)) :rule cong :premises (t52 t55))
(step t57 (cl @p_53) :rule cong :premises (t54 t56))
(step t58 (cl (= @p_52 true)) :rule rare_rewrite :args ("ite-eq" @p_7 v1$ @p_1))
(step t59 (cl @p_52 (! (not true) :named @p_21)) :rule equiv2 :premises (t58))
(step t60 (cl true) :rule true)
(step t61 (cl @p_52) :rule resolution :premises (t59 t60))
(step t62 (cl @p_52) :rule resolution :premises (t45 t57 t61))
(step t63 (cl @p_49) :rule resolution :premises (t41 t44 t62))
(step t64 (cl @p_7 @p_47) :rule ite1 :premises (t63))
(step t65 (cl @p_9) :rule not_implies1 :premises (a2))
(step t66 (cl @p_8) :rule and :premises (t65) :args (0))
(step t67 (cl @p_47) :rule resolution :premises (t64 t66))
(step t68 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))) (! (= @p_13 @p_27) :named @p_28)) :named @p_38) @p_38) :named @p_44)) (not @p_38) @p_38) :rule equiv_pos2)
(step t69 (cl (= @p_28 @p_28)) :rule cong :premises (t52))
(step t70 (cl @p_44) :rule cong :premises (t69))
(step t71 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))) (! (= @p_13 (! (ite (! (= i1$ i$) :named @p_39) v1$ @p_1) :named @p_40)) :named @p_41)) :named @p_42) @p_38) :named @p_43)) (not @p_42) @p_38) :rule equiv_pos2)
(step t72 (cl (= @p_39 @p_7)) :rule rare_rewrite :args ("eq-symm" i1$ i$))
(step t73 (cl (= @p_40 @p_27)) :rule cong :premises (t72 t53 t55))
(step t74 (cl (= @p_41 @p_28)) :rule cong :premises (t73))
(step t75 (cl @p_43) :rule cong :premises (t74))
(step t76 (cl @p_42 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3))))) :rule implies_neg1)
(anchor :step t77)
(assume t77.a0 (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (= (fun_app$ (fun_upd$ ?v0 ?v1 ?v2) ?v3) (ite (= ?v1 ?v3) ?v2 (fun_app$ ?v0 ?v3)))))
(step t77.t0 (cl (or @p_37 @p_41)) :rule forall_inst :args (f$ i1$ v1$ i$))
(step t77.t1 (cl @p_37 @p_41) :rule or :premises (t77.t0))
(step t77.t2 (cl @p_41) :rule resolution :premises (t77.t1 t39))
(step t77 (cl @p_37 @p_41) :rule subproof :discharge (t77.a0))
(step t78 (cl @p_42 @p_41) :rule resolution :premises (t76 t77))
(step t79 (cl @p_42 (not @p_41)) :rule implies_neg2)
(step t80 (cl @p_42 @p_42) :rule resolution :premises (t78 t79))
(step t81 (cl @p_42) :rule contraction :premises (t80))
(step t82 (cl @p_38) :rule resolution :premises (t71 t75 t81))
(step t83 (cl @p_38) :rule resolution :premises (t68 t70 t82))
(step t84 (cl @p_37 @p_28) :rule implies :premises (t83))
(step t85 (cl @p_28) :rule resolution :premises (t84 t39))
(step t86 (cl (= @p_27 @p_13)) :rule symm :premises (t85))
(step t87 (cl (not (! (= (! (ite @p_5 (! (= @p_14 v2$) :named @p_19) (! (= @p_14 @p_13) :named @p_18)) :named @p_20) (! (ite @p_5 (! (= v2$ @p_14) :named @p_16) (! (= @p_13 @p_14) :named @p_15)) :named @p_17)) :named @p_26)) (! (not @p_20) :named @p_25) @p_17) :rule equiv_pos2)
(step t88 (cl (= @p_19 @p_16)) :rule rare_rewrite :args ("eq-symm" @p_14 v2$))
(step t89 (cl (= @p_18 @p_15)) :rule rare_rewrite :args ("eq-symm" @p_14 @p_13))
(step t90 (cl @p_26) :rule cong :premises (t88 t89))
(step t91 (cl (not (! (= @p_20 @p_20) :named @p_22)) @p_25 @p_20) :rule equiv_pos2)
(step t92 (cl (= @p_19 @p_19)) :rule cong :premises (t18 t23))
(step t93 (cl (= @p_18 @p_18)) :rule cong :premises (t18 t24))
(step t94 (cl @p_22) :rule cong :premises (t92 t93))
(step t95 (cl (= @p_20 true)) :rule rare_rewrite :args ("ite-eq" @p_5 v2$ @p_13))
(step t96 (cl @p_20 @p_21) :rule equiv2 :premises (t95))
(step t97 (cl true) :rule true)
(step t98 (cl @p_20) :rule resolution :premises (t96 t97))
(step t99 (cl @p_20) :rule resolution :premises (t91 t94 t98))
(step t100 (cl @p_17) :rule resolution :premises (t87 t90 t99))
(step t101 (cl @p_5 @p_15) :rule ite1 :premises (t100))
(step t102 (cl @p_6) :rule and :premises (t65) :args (1))
(step t103 (cl @p_15) :rule resolution :premises (t101 t102))
(step t104 (cl (= @p_1 @p_14)) :rule trans :premises (t67 t86 t103))
(step t105 (cl (= @p_14 @p_1)) :rule symm :premises (t104))
(step t106 (cl @p_4) :rule trans :premises (t40 t105))
(step t107 (cl @p_12) :rule resolution :premises (t10 t106))
(step t108 (cl @p_11) :rule trans :premises (t8 t107))
(step t109 (cl false) :rule resolution :premises (t0 t1 t108))
(step t110 (cl (not false)) :rule false)
(step t111 (cl) :rule resolution :premises (t109 t110))
)
8723937c32b983c1856a7fdd03bc94c377eb4742 20 0
unsat
(
(assume a0 (! (not (! (or (! (= (! (f$ g$ x$) :named @p_3) (! (and (! (fun_app$ g$ x$) :named @p_1) true) :named @p_5)) :named @p_6) (or (! (= @p_3 true) :named @p_4) (! (= @p_1 true) :named @p_2))) :named @p_7)) :named @p_8))
(step t0 (cl (not (! (= @p_8 (! (not (! (or (! (= @p_3 @p_1) :named @p_9) @p_3 @p_1) :named @p_10)) :named @p_11)) :named @p_12)) (not @p_8) @p_11) :rule equiv_pos2)
(step t1 (cl (= @p_7 (! (or @p_6 @p_4 @p_2) :named @p_13))) :rule aci_simp)
(step t2 (cl (= @p_5 @p_1)) :rule aci_simp)
(step t3 (cl (= @p_6 @p_9)) :rule cong :premises (t2))
(step t4 (cl (= @p_4 @p_3)) :rule rare_rewrite :args ("bool-eq-true" @p_3))
(step t5 (cl (= @p_2 @p_1)) :rule rare_rewrite :args ("bool-eq-true" @p_1))
(step t6 (cl (= @p_13 @p_10)) :rule cong :premises (t3 t4 t5))
(step t7 (cl (= @p_7 @p_10)) :rule trans :premises (t1 t6))
(step t8 (cl @p_12) :rule cong :premises (t7))
(step t9 (cl @p_11) :rule resolution :premises (t0 t8 a0))
(step t10 (cl (not @p_9)) :rule not_or :premises (t9) :args (0))
(step t11 (cl @p_3 @p_1) :rule not_equiv1 :premises (t10))
(step t12 (cl (not @p_3)) :rule not_or :premises (t9) :args (1))
(step t13 (cl @p_1) :rule resolution :premises (t11 t12))
(step t14 (cl (not @p_1)) :rule not_or :premises (t9) :args (2))
(step t15 (cl) :rule resolution :premises (t13 t14))
)
0025eb12061eb9eaded956ac2d525a1a2b7c81e8 61 0
unsat
(
(assume a0 (forall ((?v0 A$)) (= (id$ ?v0) ?v0)))
(assume a1 (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)))
(assume a2 (! (not (! (and (! (= (! (id$ x$) :named @p_3) x$) :named @p_4) (! (= (! (id$a true) :named @p_1) true) :named @p_2)) :named @p_5)) :named @p_6))
(step t0 (cl (not (! (= (! (=> (forall ((?v0 Bool)) (= ?v0 (id$a ?v0))) @p_1) :named @p_20) @p_20) :named @p_24)) (not @p_20) @p_20) :rule equiv_pos2)
(step t1 (cl (! (= true true) :named @p_17)) :rule refl)
(step t2 (cl @p_17) :rule symm :premises (t1))
(step t3 (cl (= @p_1 @p_1)) :rule cong :premises (t2))
(step t4 (cl @p_24) :rule cong :premises (t3))
(step t5 (cl (not (! (= (! (=> (forall ((?v0 Bool)) (= ?v0 (id$a ?v0))) (! (= true @p_1) :named @p_21)) :named @p_22) @p_20) :named @p_23)) (not @p_22) @p_20) :rule equiv_pos2)
(step t6 (cl (= @p_21 @p_2)) :rule rare_rewrite :args ("eq-symm" true @p_1))
(step t7 (cl (! (= @p_2 @p_1) :named @p_18)) :rule rare_rewrite :args ("bool-eq-true" @p_1))
(step t8 (cl (= @p_21 @p_1)) :rule trans :premises (t6 t7))
(step t9 (cl @p_23) :rule cong :premises (t8))
(step t10 (cl @p_22 (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :rule implies_neg1)
(anchor :step t11)
(assume t11.a0 (forall ((?v0 Bool)) (= ?v0 (id$a ?v0))))
(step t11.t0 (cl (or (! (not (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :named @p_19) @p_21)) :rule forall_inst :args (true))
(step t11.t1 (cl @p_19 @p_21) :rule or :premises (t11.t0))
(step t11.t2 (cl (not (! (= (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)) (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :named @p_7)) (not (forall ((?v0 Bool)) (= (id$a ?v0) ?v0))) (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :rule equiv_pos2)
(anchor :step t11.t3 :args ((?v0 Bool) (:= (?v0 Bool) ?v0)))
(step t11.t3.t0 (cl (= (= (! (id$a ?v0) :named @p_8) ?v0) (= ?v0 @p_8))) :rule rare_rewrite :args ("eq-symm" @p_8 ?v0))
(step t11.t3 (cl @p_7) :rule bind)
(step t11.t4 (cl (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :rule resolution :premises (t11.t2 t11.t3 a1))
(step t11.t5 (cl @p_21) :rule resolution :premises (t11.t1 t11.t4))
(step t11 (cl @p_19 @p_21) :rule subproof :discharge (t11.a0))
(step t12 (cl @p_22 @p_21) :rule resolution :premises (t10 t11))
(step t13 (cl @p_22 (not @p_21)) :rule implies_neg2)
(step t14 (cl @p_22 @p_22) :rule resolution :premises (t12 t13))
(step t15 (cl @p_22) :rule contraction :premises (t14))
(step t16 (cl @p_20) :rule resolution :premises (t5 t9 t15))
(step t17 (cl @p_20) :rule resolution :premises (t0 t4 t16))
(step t18 (cl @p_19 @p_1) :rule implies :premises (t17))
(step t19 (cl @p_1 @p_19) :rule reordering :premises (t18))
(step t20 (cl (not (! (= @p_6 (! (not (! (and (! (= x$ @p_3) :named @p_10) @p_1) :named @p_14)) :named @p_15)) :named @p_16)) (not @p_6) @p_15) :rule equiv_pos2)
(step t21 (cl (= @p_4 @p_10)) :rule rare_rewrite :args ("eq-symm" @p_3 x$))
(step t22 (cl @p_18) :rule rare_rewrite :args ("bool-eq-true" @p_1))
(step t23 (cl (= @p_5 @p_14)) :rule cong :premises (t21 t22))
(step t24 (cl @p_16) :rule cong :premises (t23))
(step t25 (cl (= @p_14 @p_14)) :rule cong :premises (t3))
(step t26 (cl (= @p_15 @p_15)) :rule cong :premises (t25))
(step t27 (cl @p_16) :rule trans :premises (t24 t26))
(step t28 (cl @p_15) :rule resolution :premises (t20 t27 a2))
(step t29 (cl (not @p_10) (! (not @p_1) :named @p_9)) :rule not_and :premises (t28))
(step t30 (cl (or (! (not (forall ((?v0 A$)) (= ?v0 (id$ ?v0)))) :named @p_13) @p_10)) :rule forall_inst :args (x$))
(step t31 (cl @p_13 @p_10) :rule or :premises (t30))
(step t32 (cl (not (! (= (forall ((?v0 A$)) (= (id$ ?v0) ?v0)) (forall ((?v0 A$)) (= ?v0 (id$ ?v0)))) :named @p_11)) (not (forall ((?v0 A$)) (= (id$ ?v0) ?v0))) (forall ((?v0 A$)) (= ?v0 (id$ ?v0)))) :rule equiv_pos2)
(anchor :step t33 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t33.t0 (cl (= (= (! (id$ ?v0) :named @p_12) ?v0) (= ?v0 @p_12))) :rule rare_rewrite :args ("eq-symm" @p_12 ?v0))
(step t33 (cl @p_11) :rule bind)
(step t34 (cl (forall ((?v0 A$)) (= ?v0 (id$ ?v0)))) :rule resolution :premises (t32 t33 a0))
(step t35 (cl @p_10) :rule resolution :premises (t31 t34))
(step t36 (cl @p_9) :rule resolution :premises (t29 t35))
(step t37 (cl (not @p_7) (not (forall ((?v0 Bool)) (= (id$a ?v0) ?v0))) (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :rule equiv_pos2)
(anchor :step t38 :args ((?v0 Bool) (:= (?v0 Bool) ?v0)))
(step t38.t0 (cl (= (= @p_8 ?v0) (= ?v0 @p_8))) :rule rare_rewrite :args ("eq-symm" @p_8 ?v0))
(step t38 (cl @p_7) :rule bind)
(step t39 (cl (forall ((?v0 Bool)) (= ?v0 (id$a ?v0)))) :rule resolution :premises (t37 t38 a1))
(step t40 (cl) :rule resolution :premises (t19 t36 t39))
)
de79b9011ad740b673bdea5276b0f980afd7fa3a 12 0
unsat
(
(assume a0 (! (not (! (=> (! (f$ (exists ((?v0 A$)) (g$ ?v0))) :named @p_1) true) :named @p_2)) :named @p_3))
(step t0 (cl (not (! (= @p_3 false) :named @p_4)) (not @p_3) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 true)) :rule rare_rewrite :args ("bool-impl-true1" @p_1))
(step t2 (cl (= @p_3 (! (not true) :named @p_5))) :rule cong :premises (t1))
(step t3 (cl (= @p_5 false)) :rule evaluate)
(step t4 (cl @p_4) :rule trans :premises (t2 t3))
(step t5 (cl false) :rule resolution :premises (t0 t4 a0))
(step t6 (cl (not false)) :rule false)
(step t7 (cl) :rule resolution :premises (t5 t6))
)
d45dd56f7437bb5529752ff01c191fb9bfcd6caa 74 0
unsat
(
(assume a0 (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (<= ?v0 ?v1))))
(assume a1 (! (not (! (=> (! (= le$ uu$) :named @p_3) (! (fun_app$ (! (fun_app$a le$ 3) :named @p_1) 42) :named @p_2)) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1)))) (! (= (! (fun_app$ (! (fun_app$a uu$ 3) :named @p_15) 42) :named @p_16) (! (not (! (>= (! (+ 3 (! (* -1 42) :named @p_25)) :named @p_26) 1) :named @p_27)) :named @p_28)) :named @p_29)) :named @p_30) (! (=> (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1)))) @p_16) :named @p_24)) :named @p_31)) (not @p_30) @p_24) :rule equiv_pos2)
(step t1 (cl (= @p_25 -42)) :rule evaluate)
(step t2 (cl (= @p_26 (! (+ 3 -42) :named @p_35))) :rule cong :premises (t1))
(step t3 (cl (= @p_35 -39)) :rule evaluate)
(step t4 (cl (= @p_26 -39)) :rule trans :premises (t2 t3))
(step t5 (cl (= 1 1)) :rule refl)
(step t6 (cl (= @p_27 (! (>= -39 1) :named @p_34))) :rule cong :premises (t4 t5))
(step t7 (cl (= @p_34 false)) :rule evaluate)
(step t8 (cl (= @p_27 false)) :rule trans :premises (t6 t7))
(step t9 (cl (= @p_28 (! (not false) :named @p_33))) :rule cong :premises (t8))
(step t10 (cl (= @p_33 true)) :rule evaluate)
(step t11 (cl (= @p_28 true)) :rule trans :premises (t9 t10))
(step t12 (cl (= @p_29 (! (= @p_16 true) :named @p_32))) :rule cong :premises (t11))
(step t13 (cl (= @p_32 @p_16)) :rule rare_rewrite :args ("bool-eq-true" @p_16))
(step t14 (cl (= @p_29 @p_16)) :rule trans :premises (t12 t13))
(step t15 (cl @p_31) :rule cong :premises (t14))
(step t16 (cl @p_30 (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :rule implies_neg1)
(anchor :step t17)
(assume t17.a0 (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1)))))
(step t17.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :named @p_23) @p_29)) :rule forall_inst :args (3 42))
(step t17.t1 (cl @p_23 @p_29) :rule or :premises (t17.t0))
(step t17.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (<= ?v0 ?v1))) (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :named @p_6)) (not (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (<= ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :rule equiv_pos2)
(anchor :step t17.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t17.t3.t0 (cl (= (! (<= ?v0 ?v1) :named @p_11) (! (not (! (>= ?v0 (! (+ ?v1 1) :named @p_12)) :named @p_13)) :named @p_14))) :rule rare_rewrite :args ("arith-leq-norm" ?v0 ?v1))
(step t17.t3.t1 (cl (= (* -1 (- ?v0 @p_12)) (* -1 (- (! (+ ?v0 (* -1 ?v1)) :named @p_7) 1)))) :rule poly_simp)
(step t17.t3.t2 (cl (= @p_13 (! (>= @p_7 1) :named @p_8))) :rule poly_simp_rel :premises (t17.t3.t1))
(step t17.t3.t3 (cl (= @p_14 (! (not @p_8) :named @p_9))) :rule cong :premises (t17.t3.t2))
(step t17.t3.t4 (cl (= @p_11 @p_9)) :rule trans :premises (t17.t3.t0 t17.t3.t3))
(step t17.t3.t5 (cl (= (= (! (fun_app$ (fun_app$a uu$ ?v0) ?v1) :named @p_10) @p_11) (= @p_10 @p_9))) :rule cong :premises (t17.t3.t4))
(step t17.t3 (cl @p_6) :rule bind)
(step t17.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :rule resolution :premises (t17.t2 t17.t3 a0))
(step t17.t5 (cl @p_29) :rule resolution :premises (t17.t1 t17.t4))
(step t17 (cl @p_23 @p_29) :rule subproof :discharge (t17.a0))
(step t18 (cl @p_30 @p_29) :rule resolution :premises (t16 t17))
(step t19 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t20 (cl @p_30 @p_30) :rule resolution :premises (t18 t19))
(step t21 (cl @p_30) :rule contraction :premises (t20))
(step t22 (cl @p_24) :rule resolution :premises (t0 t15 t21))
(step t23 (cl @p_23 @p_16) :rule implies :premises (t22))
(step t24 (cl @p_16 @p_23) :rule reordering :premises (t23))
(step t25 (cl (not (! (= @p_5 (! (not @p_16) :named @p_17)) :named @p_18)) (not @p_5) @p_17) :rule equiv_pos2)
(step t26 (cl @p_3) :rule not_implies1 :premises (a1))
(step t27 (cl (! (= uu$ uu$) :named @p_19)) :rule refl)
(step t28 (cl (= @p_3 @p_19)) :rule cong :premises (t26 t27))
(step t29 (cl (= 3 3)) :rule refl)
(step t30 (cl (= @p_1 @p_15)) :rule cong :premises (t26 t29))
(step t31 (cl (= 42 42)) :rule refl)
(step t32 (cl (= @p_2 @p_16)) :rule cong :premises (t30 t31))
(step t33 (cl (= @p_4 (! (=> @p_19 @p_16) :named @p_20))) :rule cong :premises (t28 t32))
(step t34 (cl (= @p_5 (! (not @p_20) :named @p_21))) :rule cong :premises (t33))
(step t35 (cl (= @p_19 true)) :rule rare_rewrite :args ("eq-refl" uu$))
(step t36 (cl (= @p_16 @p_16)) :rule refl)
(step t37 (cl (= @p_20 (! (=> true @p_16) :named @p_22))) :rule cong :premises (t35 t36))
(step t38 (cl (= @p_22 @p_16)) :rule rare_rewrite :args ("bool-impl-true2" @p_16))
(step t39 (cl (= @p_20 @p_16)) :rule trans :premises (t37 t38))
(step t40 (cl (= @p_21 @p_17)) :rule cong :premises (t39))
(step t41 (cl @p_18) :rule trans :premises (t34 t40))
(step t42 (cl @p_17) :rule resolution :premises (t25 t41 a1))
(step t43 (cl (not @p_6) (not (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (<= ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :rule equiv_pos2)
(anchor :step t44 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t44.t0 (cl (= @p_11 @p_14)) :rule rare_rewrite :args ("arith-leq-norm" ?v0 ?v1))
(step t44.t1 (cl (= (* -1 (- ?v0 @p_12)) (* -1 (- @p_7 1)))) :rule poly_simp)
(step t44.t2 (cl (= @p_13 @p_8)) :rule poly_simp_rel :premises (t44.t1))
(step t44.t3 (cl (= @p_14 @p_9)) :rule cong :premises (t44.t2))
(step t44.t4 (cl (= @p_11 @p_9)) :rule trans :premises (t44.t0 t44.t3))
(step t44.t5 (cl (= (= @p_10 @p_11) (= @p_10 @p_9))) :rule cong :premises (t44.t4))
(step t44 (cl @p_6) :rule bind)
(step t45 (cl (forall ((?v0 Int) (?v1 Int)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (not (>= (+ ?v0 (* -1 ?v1)) 1))))) :rule resolution :premises (t43 t44 a0))
(step t46 (cl) :rule resolution :premises (t24 t42 t45))
)
5f4b8323db2585eb56925efce6530272240482f4 9 0
unsat
(
(assume a0 (! (not (or (forall ((?v0 A$)) (p$ ?v0)) (! (not (forall ((?v0 A$)) (p$ ?v0))) :named @p_1))) :named @p_2))
(step t0 (cl (not (! (not @p_1) :named @p_3)) (forall ((?v0 A$)) (p$ ?v0))) :rule not_not)
(step t1 (cl @p_3) :rule not_or :premises (a0) :args (1))
(step t2 (cl (forall ((?v0 A$)) (p$ ?v0))) :rule resolution :premises (t0 t1))
(step t3 (cl @p_1) :rule not_or :premises (a0) :args (0))
(step t4 (cl) :rule resolution :premises (t2 t3))
)
97631e970dccb650a0dc6d371d0edef0bf6118c8 12 0
unsat
(
(assume a0 (! (not (! (=> (! (f$ (forall ((?v0 A$)) (g$ ?v0))) :named @p_1) true) :named @p_2)) :named @p_3))
(step t0 (cl (not (! (= @p_3 false) :named @p_4)) (not @p_3) false) :rule equiv_pos2)
(step t1 (cl (= @p_2 true)) :rule rare_rewrite :args ("bool-impl-true1" @p_1))
(step t2 (cl (= @p_3 (! (not true) :named @p_5))) :rule cong :premises (t1))
(step t3 (cl (= @p_5 false)) :rule evaluate)
(step t4 (cl @p_4) :rule trans :premises (t2 t3))
(step t5 (cl false) :rule resolution :premises (t0 t4 a0))
(step t6 (cl (not false)) :rule false)
(step t7 (cl) :rule resolution :premises (t5 t6))
)
6fcd80d71fd6a4be05ee7f1be295793ff5ba85e3 173 0
unsat
(
(assume a0 (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1))))
(assume a1 (forall ((?v0 Int_int_fun$)) (= (map$ ?v0 nil$) nil$)))
(assume a2 (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$)) (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2)))))
(assume a3 (! (not (! (= (! (map$ uu$ (cons$ 0 (! (cons$ 1 nil$) :named @p_3))) :named @p_4) (! (cons$ 1 (! (cons$ 2 nil$) :named @p_1)) :named @p_2)) :named @p_5)) :named @p_6))
(step t0 (cl (! (and (! (= @p_4 (! (cons$ (! (fun_app$ uu$ 0) :named @p_8) (! (map$ uu$ @p_3) :named @p_7)) :named @p_9)) :named @p_10) (! (= @p_8 1) :named @p_12) (! (= @p_7 (! (cons$ (! (fun_app$ uu$ 1) :named @p_28) (! (map$ uu$ nil$) :named @p_27)) :named @p_29)) :named @p_30) (! (= nil$ @p_27) :named @p_31) (! (= @p_28 2) :named @p_35)) :named @p_46) (! (not @p_10) :named @p_41) (! (not @p_12) :named @p_42) (! (not @p_30) :named @p_43) (! (not @p_31) :named @p_44) (! (not @p_35) :named @p_45)) :rule and_neg)
(step t1 (cl (! (=> @p_46 @p_5) :named @p_48) @p_46) :rule implies_neg1)
(anchor :step t2)
(assume t2.a0 @p_10)
(assume t2.a1 @p_12)
(assume t2.a2 @p_30)
(assume t2.a3 @p_31)
(assume t2.a4 @p_35)
(step t2.t0 (cl (or (! (not (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$)) (= (map$ ?v0 (cons$ ?v1 ?v2)) (cons$ (fun_app$ ?v0 ?v1) (map$ ?v0 ?v2))))) :named @p_11) @p_10)) :rule forall_inst :args (uu$ 0 @p_3))
(step t2.t1 (cl @p_11 @p_10) :rule or :premises (t2.t0))
(step t2.t2 (cl @p_10) :rule resolution :premises (t2.t1 a2))
(step t2.t3 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))) (! (= 0 (! (+ -1 @p_8) :named @p_23)) :named @p_24)) :named @p_25) (! (=> (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))) @p_12) :named @p_22)) :named @p_26)) (not @p_25) @p_22) :rule equiv_pos2)
(step t2.t4 (cl (= (* -1 (- 0 @p_23)) (* 1 (- @p_8 1)))) :rule poly_simp)
(step t2.t5 (cl (= @p_24 @p_12)) :rule poly_simp_rel :premises (t2.t4))
(step t2.t6 (cl @p_26) :rule cong :premises (t2.t5))
(step t2.t7 (cl @p_25 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule implies_neg1)
(anchor :step t2.t8)
(assume t2.t8.a0 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))))
(step t2.t8.t0 (cl (or (! (not (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :named @p_21) @p_24)) :rule forall_inst :args (0))
(step t2.t8.t1 (cl @p_21 @p_24) :rule or :premises (t2.t8.t0))
(step t2.t8.t2 (cl (not (! (= (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1))) (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :named @p_13)) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1)))) (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule equiv_pos2)
(anchor :step t2.t8.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t2.t8.t3.t0 (cl (= (! (+ ?v0 1) :named @p_17) (! (+ 1 ?v0) :named @p_19))) :rule poly_simp)
(step t2.t8.t3.t1 (cl (= (! (= (! (fun_app$ uu$ ?v0) :named @p_14) @p_17) :named @p_18) (! (= @p_14 @p_19) :named @p_20))) :rule cong :premises (t2.t8.t3.t0))
(step t2.t8.t3.t2 (cl (= (* 1 (- @p_14 @p_19)) (* -1 (- ?v0 (! (+ -1 @p_14) :named @p_15))))) :rule poly_simp)
(step t2.t8.t3.t3 (cl (= @p_20 (! (= ?v0 @p_15) :named @p_16))) :rule poly_simp_rel :premises (t2.t8.t3.t2))
(step t2.t8.t3.t4 (cl (= @p_18 @p_16)) :rule trans :premises (t2.t8.t3.t1 t2.t8.t3.t3))
(step t2.t8.t3 (cl @p_13) :rule bind)
(step t2.t8.t4 (cl (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule resolution :premises (t2.t8.t2 t2.t8.t3 a0))
(step t2.t8.t5 (cl @p_24) :rule resolution :premises (t2.t8.t1 t2.t8.t4))
(step t2.t8 (cl @p_21 @p_24) :rule subproof :discharge (t2.t8.a0))
(step t2.t9 (cl @p_25 @p_24) :rule resolution :premises (t2.t7 t2.t8))
(step t2.t10 (cl @p_25 (not @p_24)) :rule implies_neg2)
(step t2.t11 (cl @p_25 @p_25) :rule resolution :premises (t2.t9 t2.t10))
(step t2.t12 (cl @p_25) :rule contraction :premises (t2.t11))
(step t2.t13 (cl @p_22) :rule resolution :premises (t2.t3 t2.t6 t2.t12))
(step t2.t14 (cl @p_21 @p_12) :rule implies :premises (t2.t13))
(step t2.t15 (cl (not @p_13) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1)))) (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule equiv_pos2)
(anchor :step t2.t16 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t2.t16.t0 (cl (= @p_17 @p_19)) :rule poly_simp)
(step t2.t16.t1 (cl (= @p_18 @p_20)) :rule cong :premises (t2.t16.t0))
(step t2.t16.t2 (cl (= (* 1 (- @p_14 @p_19)) (* -1 (- ?v0 @p_15)))) :rule poly_simp)
(step t2.t16.t3 (cl (= @p_20 @p_16)) :rule poly_simp_rel :premises (t2.t16.t2))
(step t2.t16.t4 (cl (= @p_18 @p_16)) :rule trans :premises (t2.t16.t1 t2.t16.t3))
(step t2.t16 (cl @p_13) :rule bind)
(step t2.t17 (cl (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule resolution :premises (t2.t15 t2.t16 a0))
(step t2.t18 (cl @p_12) :rule resolution :premises (t2.t14 t2.t17))
(step t2.t19 (cl (or @p_11 @p_30)) :rule forall_inst :args (uu$ 1 nil$))
(step t2.t20 (cl @p_11 @p_30) :rule or :premises (t2.t19))
(step t2.t21 (cl @p_30) :rule resolution :premises (t2.t20 a2))
(step t2.t22 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))) (! (= 1 (! (+ -1 @p_28) :named @p_37)) :named @p_38)) :named @p_39) (! (=> (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))) @p_35) :named @p_36)) :named @p_40)) (not @p_39) @p_36) :rule equiv_pos2)
(step t2.t23 (cl (= (* -2 (- 1 @p_37)) (* 2 (- @p_28 2)))) :rule poly_simp)
(step t2.t24 (cl (= @p_38 @p_35)) :rule poly_simp_rel :premises (t2.t23))
(step t2.t25 (cl @p_40) :rule cong :premises (t2.t24))
(step t2.t26 (cl @p_39 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule implies_neg1)
(anchor :step t2.t27)
(assume t2.t27.a0 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))))
(step t2.t27.t0 (cl (or @p_21 @p_38)) :rule forall_inst :args (1))
(step t2.t27.t1 (cl @p_21 @p_38) :rule or :premises (t2.t27.t0))
(step t2.t27.t2 (cl @p_38) :rule resolution :premises (t2.t27.t1 t2.t17))
(step t2.t27 (cl @p_21 @p_38) :rule subproof :discharge (t2.t27.a0))
(step t2.t28 (cl @p_39 @p_38) :rule resolution :premises (t2.t26 t2.t27))
(step t2.t29 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t2.t30 (cl @p_39 @p_39) :rule resolution :premises (t2.t28 t2.t29))
(step t2.t31 (cl @p_39) :rule contraction :premises (t2.t30))
(step t2.t32 (cl @p_36) :rule resolution :premises (t2.t22 t2.t25 t2.t31))
(step t2.t33 (cl @p_21 @p_35) :rule implies :premises (t2.t32))
(step t2.t34 (cl @p_35) :rule resolution :premises (t2.t33 t2.t17))
(step t2.t35 (cl (or (! (not (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :named @p_34) @p_31)) :rule forall_inst :args (uu$))
(step t2.t36 (cl @p_34 @p_31) :rule or :premises (t2.t35))
(step t2.t37 (cl (not (! (= (forall ((?v0 Int_int_fun$)) (= (map$ ?v0 nil$) nil$)) (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :named @p_32)) (not (forall ((?v0 Int_int_fun$)) (= (map$ ?v0 nil$) nil$))) (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :rule equiv_pos2)
(anchor :step t2.t38 :args ((?v0 Int_int_fun$) (:= (?v0 Int_int_fun$) ?v0)))
(step t2.t38.t0 (cl (= (= (! (map$ ?v0 nil$) :named @p_33) nil$) (= nil$ @p_33))) :rule rare_rewrite :args ("eq-symm" @p_33 nil$))
(step t2.t38 (cl @p_32) :rule bind)
(step t2.t39 (cl (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :rule resolution :premises (t2.t37 t2.t38 a1))
(step t2.t40 (cl @p_31) :rule resolution :premises (t2.t36 t2.t39))
(step t2.t41 (cl (= @p_27 nil$)) :rule symm :premises (t2.t40))
(step t2.t42 (cl (= @p_29 @p_1)) :rule cong :premises (t2.t34 t2.t41))
(step t2.t43 (cl (= @p_7 @p_1)) :rule trans :premises (t2.t21 t2.t42))
(step t2.t44 (cl (= @p_9 @p_2)) :rule cong :premises (t2.t18 t2.t43))
(step t2.t45 (cl @p_5) :rule trans :premises (t2.t2 t2.t44))
(step t2 (cl @p_41 @p_42 @p_43 @p_44 @p_45 @p_5) :rule subproof :discharge (t2.a0 t2.a1 t2.a2 t2.a3 t2.a4))
(step t3 (cl (! (not @p_46) :named @p_47) @p_10) :rule and_pos :args (0))
(step t4 (cl @p_47 @p_12) :rule and_pos :args (1))
(step t5 (cl @p_47 @p_30) :rule and_pos :args (2))
(step t6 (cl @p_47 @p_31) :rule and_pos :args (3))
(step t7 (cl @p_47 @p_35) :rule and_pos :args (4))
(step t8 (cl @p_5 @p_47 @p_47 @p_47 @p_47 @p_47) :rule resolution :premises (t2 t3 t4 t5 t6 t7))
(step t9 (cl @p_47 @p_47 @p_47 @p_47 @p_47 @p_5) :rule reordering :premises (t8))
(step t10 (cl @p_47 @p_5) :rule contraction :premises (t9))
(step t11 (cl @p_48 @p_5) :rule resolution :premises (t1 t10))
(step t12 (cl @p_48 @p_6) :rule implies_neg2)
(step t13 (cl @p_48 @p_48) :rule resolution :premises (t11 t12))
(step t14 (cl @p_48) :rule contraction :premises (t13))
(step t15 (cl @p_47 @p_5) :rule implies :premises (t14))
(step t16 (cl @p_41 @p_42 @p_43 @p_44 @p_45 @p_5) :rule resolution :premises (t0 t15))
(step t17 (cl @p_5 @p_41 @p_42 @p_43 @p_44 @p_45) :rule reordering :premises (t16))
(step t18 (cl (not @p_40) (not @p_39) @p_36) :rule equiv_pos2)
(step t19 (cl (= (* -2 (- 1 @p_37)) (* 2 (- @p_28 2)))) :rule poly_simp)
(step t20 (cl (= @p_38 @p_35)) :rule poly_simp_rel :premises (t19))
(step t21 (cl @p_40) :rule cong :premises (t20))
(step t22 (cl @p_39 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule implies_neg1)
(anchor :step t23)
(assume t23.a0 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))))
(step t23.t0 (cl (or @p_21 @p_38)) :rule forall_inst :args (1))
(step t23.t1 (cl @p_21 @p_38) :rule or :premises (t23.t0))
(step t23.t2 (cl (not @p_13) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1)))) (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule equiv_pos2)
(anchor :step t23.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t23.t3.t0 (cl (= @p_17 @p_19)) :rule poly_simp)
(step t23.t3.t1 (cl (= @p_18 @p_20)) :rule cong :premises (t23.t3.t0))
(step t23.t3.t2 (cl (= (* 1 (- @p_14 @p_19)) (* -1 (- ?v0 @p_15)))) :rule poly_simp)
(step t23.t3.t3 (cl (= @p_20 @p_16)) :rule poly_simp_rel :premises (t23.t3.t2))
(step t23.t3.t4 (cl (= @p_18 @p_16)) :rule trans :premises (t23.t3.t1 t23.t3.t3))
(step t23.t3 (cl @p_13) :rule bind)
(step t23.t4 (cl (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule resolution :premises (t23.t2 t23.t3 a0))
(step t23.t5 (cl @p_38) :rule resolution :premises (t23.t1 t23.t4))
(step t23 (cl @p_21 @p_38) :rule subproof :discharge (t23.a0))
(step t24 (cl @p_39 @p_38) :rule resolution :premises (t22 t23))
(step t25 (cl @p_39 (not @p_38)) :rule implies_neg2)
(step t26 (cl @p_39 @p_39) :rule resolution :premises (t24 t25))
(step t27 (cl @p_39) :rule contraction :premises (t26))
(step t28 (cl @p_36) :rule resolution :premises (t18 t21 t27))
(step t29 (cl @p_21 @p_35) :rule implies :premises (t28))
(step t30 (cl (not @p_13) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (+ ?v0 1)))) (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule equiv_pos2)
(anchor :step t31 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t31.t0 (cl (= @p_17 @p_19)) :rule poly_simp)
(step t31.t1 (cl (= @p_18 @p_20)) :rule cong :premises (t31.t0))
(step t31.t2 (cl (= (* 1 (- @p_14 @p_19)) (* -1 (- ?v0 @p_15)))) :rule poly_simp)
(step t31.t3 (cl (= @p_20 @p_16)) :rule poly_simp_rel :premises (t31.t2))
(step t31.t4 (cl (= @p_18 @p_16)) :rule trans :premises (t31.t1 t31.t3))
(step t31 (cl @p_13) :rule bind)
(step t32 (cl (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule resolution :premises (t30 t31 a0))
(step t33 (cl @p_35) :rule resolution :premises (t29 t32))
(step t34 (cl (or @p_34 @p_31)) :rule forall_inst :args (uu$))
(step t35 (cl @p_34 @p_31) :rule or :premises (t34))
(step t36 (cl (not @p_32) (not (forall ((?v0 Int_int_fun$)) (= (map$ ?v0 nil$) nil$))) (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :rule equiv_pos2)
(anchor :step t37 :args ((?v0 Int_int_fun$) (:= (?v0 Int_int_fun$) ?v0)))
(step t37.t0 (cl (= (= @p_33 nil$) (= nil$ @p_33))) :rule rare_rewrite :args ("eq-symm" @p_33 nil$))
(step t37 (cl @p_32) :rule bind)
(step t38 (cl (forall ((?v0 Int_int_fun$)) (= nil$ (map$ ?v0 nil$)))) :rule resolution :premises (t36 t37 a1))
(step t39 (cl @p_31) :rule resolution :premises (t35 t38))
(step t40 (cl (or @p_11 @p_30)) :rule forall_inst :args (uu$ 1 nil$))
(step t41 (cl @p_11 @p_30) :rule or :premises (t40))
(step t42 (cl @p_30) :rule resolution :premises (t41 a2))
(step t43 (cl (not @p_26) (not @p_25) @p_22) :rule equiv_pos2)
(step t44 (cl (= (* -1 (- 0 @p_23)) (* 1 (- @p_8 1)))) :rule poly_simp)
(step t45 (cl (= @p_24 @p_12)) :rule poly_simp_rel :premises (t44))
(step t46 (cl @p_26) :rule cong :premises (t45))
(step t47 (cl @p_25 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0))))) :rule implies_neg1)
(anchor :step t48)
(assume t48.a0 (forall ((?v0 Int)) (= ?v0 (+ -1 (fun_app$ uu$ ?v0)))))
(step t48.t0 (cl (or @p_21 @p_24)) :rule forall_inst :args (0))
(step t48.t1 (cl @p_21 @p_24) :rule or :premises (t48.t0))
(step t48.t2 (cl @p_24) :rule resolution :premises (t48.t1 t32))
(step t48 (cl @p_21 @p_24) :rule subproof :discharge (t48.a0))
(step t49 (cl @p_25 @p_24) :rule resolution :premises (t47 t48))
(step t50 (cl @p_25 (not @p_24)) :rule implies_neg2)
(step t51 (cl @p_25 @p_25) :rule resolution :premises (t49 t50))
(step t52 (cl @p_25) :rule contraction :premises (t51))
(step t53 (cl @p_22) :rule resolution :premises (t43 t46 t52))
(step t54 (cl @p_21 @p_12) :rule implies :premises (t53))
(step t55 (cl @p_12) :rule resolution :premises (t54 t32))
(step t56 (cl (or @p_11 @p_10)) :rule forall_inst :args (uu$ 0 @p_3))
(step t57 (cl @p_11 @p_10) :rule or :premises (t56))
(step t58 (cl @p_10) :rule resolution :premises (t57 a2))
(step t59 (cl) :rule resolution :premises (t17 t33 t39 t42 t55 t58 a3))
)
9efe98d5bda537590a0692db009be0ac74e20ac2 45 0
unsat
(
(assume a2 (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))))
(assume a3 (! (less_eq$ (! (sup$ (collect$ uu$)) :named @p_2) (! (sup$ (collect$ uua$)) :named @p_1)) :named @p_3))
(assume a4 (! (less_eq$ @p_1 @p_2) :named @p_4))
(assume a5 (! (not (! (less_eq$ @p_2 @p_2) :named @p_5)) :named @p_6))
(step t0 (cl (! (=> (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) (! (or (! (not @p_3) :named @p_21) (! (not @p_4) :named @p_20) @p_5) :named @p_22)) :named @p_25) (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))))
(step t1.t0 (cl (or (! (not (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :named @p_24) @p_22)) :rule forall_inst :args (@p_2 @p_1 @p_2))
(step t1.t1 (cl @p_24 @p_22) :rule or :premises (t1.t0))
(step t1.t2 (cl (not (! (= (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2))) (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :named @p_7)) (not (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :rule equiv_pos2)
(anchor :step t1.t3 :args ((?v0 A$) (?v1 A$) (?v2 A$) (:= (?v0 A$) ?v0) (:= (?v1 A$) ?v1) (:= (?v2 A$) ?v2)))
(step t1.t3.t0 (cl (= (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_11) (! (less_eq$ ?v1 ?v2) :named @p_9)) :named @p_14) (! (less_eq$ ?v0 ?v2) :named @p_8)) :named @p_15) (! (or (! (not @p_14) :named @p_16) (! (less_eq$ ?v0 ?v2) :named @p_8)) :named @p_17))) :rule rare_rewrite :args ("bool-impl-elim" @p_14 @p_8))
(step t1.t3.t1 (cl (= @p_16 (! (or (! (not @p_11) :named @p_12) (! (not @p_9) :named @p_10)) :named @p_18))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_11 @p_9 rare-list))
(step t1.t3.t2 (cl (= @p_8 @p_8)) :rule refl)
(step t1.t3.t3 (cl (= @p_17 (! (or @p_18 @p_8) :named @p_19))) :rule cong :premises (t1.t3.t1 t1.t3.t2))
(step t1.t3.t4 (cl (= @p_19 (! (or @p_12 @p_10 @p_8) :named @p_13))) :rule aci_simp)
(step t1.t3.t5 (cl (= @p_17 @p_13)) :rule trans :premises (t1.t3.t3 t1.t3.t4))
(step t1.t3.t6 (cl (= @p_15 @p_13)) :rule trans :premises (t1.t3.t0 t1.t3.t5))
(step t1.t3 (cl @p_7) :rule bind)
(step t1.t4 (cl (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :rule resolution :premises (t1.t2 t1.t3 a2))
(step t1.t5 (cl @p_22) :rule resolution :premises (t1.t1 t1.t4))
(step t1 (cl @p_24 @p_22) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_25 @p_22) :rule resolution :premises (t0 t1))
(step t3 (cl @p_25 (! (not @p_22) :named @p_23)) :rule implies_neg2)
(step t4 (cl @p_25 @p_25) :rule resolution :premises (t2 t3))
(step t5 (cl @p_25) :rule contraction :premises (t4))
(step t6 (cl @p_24 @p_22) :rule implies :premises (t5))
(step t7 (cl @p_23 @p_21 @p_20 @p_5) :rule or_pos)
(step t8 (cl @p_5 @p_21 @p_20 @p_23) :rule reordering :premises (t7))
(step t9 (cl @p_23) :rule resolution :premises (t8 a5 a3 a4))
(step t10 (cl (not @p_7) (not (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (=> (and (less_eq$ ?v0 ?v1) (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :rule equiv_pos2)
(anchor :step t11 :args ((?v0 A$) (?v1 A$) (?v2 A$) (:= (?v0 A$) ?v0) (:= (?v1 A$) ?v1) (:= (?v2 A$) ?v2)))
(step t11.t0 (cl (= @p_15 @p_17)) :rule rare_rewrite :args ("bool-impl-elim" @p_14 @p_8))
(step t11.t1 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_11 @p_9 rare-list))
(step t11.t2 (cl (= @p_8 @p_8)) :rule refl)
(step t11.t3 (cl (= @p_17 @p_19)) :rule cong :premises (t11.t1 t11.t2))
(step t11.t4 (cl (= @p_19 @p_13)) :rule aci_simp)
(step t11.t5 (cl (= @p_17 @p_13)) :rule trans :premises (t11.t3 t11.t4))
(step t11.t6 (cl (= @p_15 @p_13)) :rule trans :premises (t11.t0 t11.t5))
(step t11 (cl @p_7) :rule bind)
(step t12 (cl (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (or (not (less_eq$ ?v0 ?v1)) (not (less_eq$ ?v1 ?v2)) (less_eq$ ?v0 ?v2)))) :rule resolution :premises (t10 t11 a2))
(step t13 (cl) :rule resolution :premises (t6 t9 t12))
)
5431755f4ffc36c9ff8b78645011361476c6d1b3 842 0
unsat
(
(assume a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10))))))
(assume a1 (! (not (! (= (! (dec_10$ (! (* 4 (! (dec_10$ 4) :named @p_1)) :named @p_2)) :named @p_3) 6) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (= (! (or (! (not @p_5) :named @p_141) (! (not (! (= @p_1 4) :named @p_6)) :named @p_58) (! (not (! (= (! (ite (! (>= @p_1 3) :named @p_36) (! (dec_10$ (! (+ -10 @p_2) :named @p_34)) :named @p_35) @p_2) :named @p_37) (! (dec_10$ (! (+ -10 @p_2) :named @p_34)) :named @p_35)) :named @p_57)) :named @p_137) (! (not (! (= @p_37 @p_3) :named @p_38)) :named @p_136) (! (not (! (= (! (ite (! (>= @p_1 5) :named @p_90) (! (dec_10$ (! (+ -20 @p_2) :named @p_88)) :named @p_89) @p_34) :named @p_91) @p_34) :named @p_110)) :named @p_139) (! (not (! (= @p_91 @p_35) :named @p_92)) :named @p_138)) :named @p_142) (! (or @p_4 @p_58 @p_137 @p_136 @p_139 @p_138) :named @p_140)) :named @p_167)) (not @p_142) @p_140) :rule equiv_pos2)
(step t1 (cl (= @p_141 @p_4)) :rule rare_rewrite :args ("bool-double-not-elim" @p_4))
(step t2 (cl (= @p_58 @p_58)) :rule refl)
(step t3 (cl (= @p_137 @p_137)) :rule refl)
(step t4 (cl (= @p_136 @p_136)) :rule refl)
(step t5 (cl (= @p_139 @p_139)) :rule refl)
(step t6 (cl (= @p_138 @p_138)) :rule refl)
(step t7 (cl @p_167) :rule cong :premises (t1 t2 t3 t4 t5 t6))
(step t8 (cl (! (=> (! (and @p_5 @p_6 @p_57 @p_38 @p_110 @p_92) :named @p_144) (! (and (! (= 4 @p_1) :named @p_61) (! (not (! (= 6 @p_34) :named @p_146)) :named @p_147)) :named @p_148)) :named @p_154) @p_144) :rule implies_neg1)
(anchor :step t9)
(assume t9.a0 @p_5)
(assume t9.a1 @p_6)
(assume t9.a2 @p_57)
(assume t9.a3 @p_38)
(assume t9.a4 @p_110)
(assume t9.a5 @p_92)
(step t9.t0 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) (! (= @p_1 (! (ite (! (>= 4 10) :named @p_27) (! (dec_10$ (! (+ -10 4) :named @p_25)) :named @p_26) 4) :named @p_28)) :named @p_29)) :named @p_30) (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) @p_6) :named @p_24)) :named @p_31)) (not @p_30) @p_24) :rule equiv_pos2)
(step t9.t1 (cl (= @p_27 false)) :rule evaluate)
(step t9.t2 (cl (= @p_25 -6)) :rule evaluate)
(step t9.t3 (cl (= @p_26 (! (dec_10$ -6) :named @p_32))) :rule cong :premises (t9.t2))
(step t9.t4 (cl (= 4 4)) :rule refl)
(step t9.t5 (cl (= @p_28 (! (ite false @p_32 4) :named @p_33))) :rule cong :premises (t9.t1 t9.t3 t9.t4))
(step t9.t6 (cl (= @p_33 4)) :rule rare_rewrite :args ("ite-false-cond" @p_32 4))
(step t9.t7 (cl (= @p_28 4)) :rule trans :premises (t9.t5 t9.t6))
(step t9.t8 (cl (= @p_29 @p_6)) :rule cong :premises (t9.t7))
(step t9.t9 (cl @p_31) :rule cong :premises (t9.t8))
(step t9.t10 (cl @p_30 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t9.t11)
(assume t9.t11.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t9.t11.t0 (cl (or (! (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :named @p_23) @p_29)) :rule forall_inst :args (4))
(step t9.t11.t1 (cl @p_23 @p_29) :rule or :premises (t9.t11.t0))
(step t9.t11.t2 (cl (not (! (= (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :named @p_7)) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t9.t11.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t9.t11.t3.t0 (cl (= (! (< ?v0 10) :named @p_16) (! (not (! (>= ?v0 10) :named @p_11)) :named @p_18))) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t9.t11.t3.t1 (cl (! (= ?v0 ?v0) :named @p_8)) :rule refl)
(step t9.t11.t3.t2 (cl (= (! (- ?v0 10) :named @p_14) (! (+ ?v0 (! (* -1 10) :named @p_20)) :named @p_21))) :rule poly_simp)
(step t9.t11.t3.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t9.t11.t3.t4 (cl (= @p_21 (! (+ ?v0 -10) :named @p_22))) :rule cong :premises (t9.t11.t3.t3))
(step t9.t11.t3.t5 (cl (= @p_22 (! (+ -10 ?v0) :named @p_9))) :rule poly_simp)
(step t9.t11.t3.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t9.t11.t3.t4 t9.t11.t3.t5))
(step t9.t11.t3.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t9.t11.t3.t2 t9.t11.t3.t6))
(step t9.t11.t3.t8 (cl (= (! (dec_10$ @p_14) :named @p_15) (! (dec_10$ @p_9) :named @p_10))) :rule cong :premises (t9.t11.t3.t7))
(step t9.t11.t3.t9 (cl (= (! (ite @p_16 ?v0 @p_15) :named @p_17) (! (ite @p_18 ?v0 @p_10) :named @p_19))) :rule cong :premises (t9.t11.t3.t0 t9.t11.t3.t1 t9.t11.t3.t8))
(step t9.t11.t3.t10 (cl (= @p_19 (! (ite @p_11 @p_10 ?v0) :named @p_12))) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t9.t11.t3.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t9.t11.t3.t9 t9.t11.t3.t10))
(step t9.t11.t3.t12 (cl (= (= (! (dec_10$ ?v0) :named @p_13) @p_17) (= @p_13 @p_12))) :rule cong :premises (t9.t11.t3.t11))
(step t9.t11.t3 (cl @p_7) :rule bind)
(step t9.t11.t4 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t9.t11.t2 t9.t11.t3 a0))
(step t9.t11.t5 (cl @p_29) :rule resolution :premises (t9.t11.t1 t9.t11.t4))
(step t9.t11 (cl @p_23 @p_29) :rule subproof :discharge (t9.t11.a0))
(step t9.t12 (cl @p_30 @p_29) :rule resolution :premises (t9.t10 t9.t11))
(step t9.t13 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t9.t14 (cl @p_30 @p_30) :rule resolution :premises (t9.t12 t9.t13))
(step t9.t15 (cl @p_30) :rule contraction :premises (t9.t14))
(step t9.t16 (cl @p_24) :rule resolution :premises (t9.t0 t9.t9 t9.t15))
(step t9.t17 (cl @p_23 @p_6) :rule implies :premises (t9.t16))
(step t9.t18 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t9.t19 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t9.t19.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t9.t19.t1 (cl @p_8) :rule refl)
(step t9.t19.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t9.t19.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t9.t19.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t9.t19.t3))
(step t9.t19.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t9.t19.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t9.t19.t4 t9.t19.t5))
(step t9.t19.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t9.t19.t2 t9.t19.t6))
(step t9.t19.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t9.t19.t7))
(step t9.t19.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t9.t19.t0 t9.t19.t1 t9.t19.t8))
(step t9.t19.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t9.t19.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t9.t19.t9 t9.t19.t10))
(step t9.t19.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t9.t19.t11))
(step t9.t19 (cl @p_7) :rule bind)
(step t9.t20 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t9.t18 t9.t19 a0))
(step t9.t21 (cl @p_6) :rule resolution :premises (t9.t17 t9.t20))
(step t9.t22 (cl @p_61) :rule symm :premises (t9.t21))
(step t9.t23 (cl (! (=> (! (and @p_110 @p_92 @p_57 @p_38 @p_5) :named @p_155) @p_147) :named @p_159) @p_155) :rule implies_neg1)
(anchor :step t9.t24)
(assume t9.t24.a0 @p_110)
(assume t9.t24.a1 @p_92)
(assume t9.t24.a2 @p_57)
(assume t9.t24.a3 @p_38)
(assume t9.t24.a4 @p_5)
(step t9.t24.t0 (cl (! (= (! (= @p_146 false) :named @p_160) @p_147) :named @p_165)) :rule equiv_simplify)
(step t9.t24.t1 (cl (not @p_160) @p_147) :rule equiv1 :premises (t9.t24.t0))
(step t9.t24.t2 (cl (not (! (= (! (= (! (= @p_34 6) :named @p_161) false) :named @p_162) @p_160) :named @p_164)) (not @p_162) @p_160) :rule equiv_pos2)
(step t9.t24.t3 (cl (= @p_162 (! (not @p_161) :named @p_166))) :rule rare_rewrite :args ("bool-eq-false" @p_161))
(step t9.t24.t4 (cl (= (* -4 (- @p_34 6)) (* -16 (! (- @p_1 4) :named @p_153)))) :rule poly_simp)
(step t9.t24.t5 (cl (= @p_161 @p_6)) :rule poly_simp_rel :premises (t9.t24.t4))
(step t9.t24.t6 (cl (= @p_166 @p_58)) :rule cong :premises (t9.t24.t5))
(step t9.t24.t7 (cl (= @p_162 @p_58)) :rule trans :premises (t9.t24.t3 t9.t24.t6))
(step t9.t24.t8 (cl @p_165) :rule rare_rewrite :args ("bool-eq-false" @p_146))
(step t9.t24.t9 (cl (= (* -4 (- 6 @p_34)) (* 16 @p_153))) :rule poly_simp)
(step t9.t24.t10 (cl (= @p_146 @p_6)) :rule poly_simp_rel :premises (t9.t24.t9))
(step t9.t24.t11 (cl (! (= @p_147 @p_58) :named @p_152)) :rule cong :premises (t9.t24.t10))
(step t9.t24.t12 (cl (= @p_160 @p_58)) :rule trans :premises (t9.t24.t8 t9.t24.t11))
(step t9.t24.t13 (cl (= @p_58 @p_160)) :rule symm :premises (t9.t24.t12))
(step t9.t24.t14 (cl @p_164) :rule trans :premises (t9.t24.t7 t9.t24.t13))
(step t9.t24.t15 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) (! (= @p_3 @p_37) :named @p_40)) :named @p_41) (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) @p_38) :named @p_39)) :named @p_51)) (not @p_41) @p_39) :rule equiv_pos2)
(step t9.t24.t16 (cl (= (! (= (! (= @p_37 @p_37) :named @p_53) true) :named @p_54) @p_53)) :rule equiv_simplify)
(step t9.t24.t17 (cl (not @p_54) @p_53) :rule equiv1 :premises (t9.t24.t16))
(step t9.t24.t18 (cl (= (* -1 (! (- @p_37 @p_37) :named @p_56)) (* 1 @p_56))) :rule poly_simp)
(step t9.t24.t19 (cl (! (= @p_53 @p_53) :named @p_55)) :rule poly_simp_rel :premises (t9.t24.t18))
(step t9.t24.t20 (cl @p_53) :rule refl)
(step t9.t24.t21 (cl @p_53) :rule refl)
(step t9.t24.t22 (cl @p_55) :rule cong :premises (t9.t24.t20 t9.t24.t21))
(step t9.t24.t23 (cl @p_54) :rule rare_rewrite :args ("eq-refl" @p_37))
(step t9.t24.t24 (cl @p_54) :rule trans :premises (t9.t24.t19 t9.t24.t22 t9.t24.t23))
(step t9.t24.t25 (cl @p_53) :rule resolution :premises (t9.t24.t17 t9.t24.t24))
(step t9.t24.t26 (cl (= @p_40 @p_40)) :rule cong :premises (t9.t24.t25))
(step t9.t24.t27 (cl (= (* -1 (- @p_3 @p_37)) (* 1 (- @p_37 @p_3)))) :rule poly_simp)
(step t9.t24.t28 (cl (! (= @p_40 @p_38) :named @p_52)) :rule poly_simp_rel :premises (t9.t24.t27))
(step t9.t24.t29 (cl @p_52) :rule trans :premises (t9.t24.t26 t9.t24.t28))
(step t9.t24.t30 (cl @p_51) :rule cong :premises (t9.t24.t29))
(step t9.t24.t31 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) (! (= @p_3 (! (ite (! (>= @p_2 10) :named @p_42) @p_35 @p_2) :named @p_43)) :named @p_44)) :named @p_45) @p_41) :named @p_46)) (not @p_45) @p_41) :rule equiv_pos2)
(step t9.t24.t32 (cl (= (* -5/2 (to_real (- @p_2 10))) (* -10/1 (- (! (to_real @p_1) :named @p_47) 5/2)))) :rule poly_simp)
(step t9.t24.t33 (cl (= @p_42 (! (>= @p_47 5/2) :named @p_48))) :rule poly_simp_rel :premises (t9.t24.t32))
(step t9.t24.t34 (cl (= (= (to_real (! (to_int 5/2) :named @p_49)) 5/2) false)) :rule evaluate)
(step t9.t24.t35 (cl (= (! (+ @p_49 1) :named @p_50) 3)) :rule evaluate)
(step t9.t24.t36 (cl (= 3 @p_50)) :rule symm :premises (t9.t24.t35))
(step t9.t24.t37 (cl (= @p_48 @p_36)) :rule rare_rewrite :premises (t9.t24.t34 t9.t24.t36) :args ("arith-int-geq-tighten" @p_1 5/2 3))
(step t9.t24.t38 (cl (= @p_42 @p_36)) :rule trans :premises (t9.t24.t33 t9.t24.t37))
(step t9.t24.t39 (cl (= @p_35 @p_35)) :rule refl)
(step t9.t24.t40 (cl (= @p_2 @p_2)) :rule refl)
(step t9.t24.t41 (cl (= @p_43 @p_37)) :rule cong :premises (t9.t24.t38 t9.t24.t39 t9.t24.t40))
(step t9.t24.t42 (cl (= @p_44 @p_40)) :rule cong :premises (t9.t24.t41))
(step t9.t24.t43 (cl @p_46) :rule cong :premises (t9.t24.t42))
(step t9.t24.t44 (cl @p_45 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t9.t24.t45)
(assume t9.t24.t45.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t9.t24.t45.t0 (cl (or @p_23 @p_44)) :rule forall_inst :args (@p_2))
(step t9.t24.t45.t1 (cl @p_23 @p_44) :rule or :premises (t9.t24.t45.t0))
(step t9.t24.t45.t2 (cl @p_44) :rule resolution :premises (t9.t24.t45.t1 t9.t20))
(step t9.t24.t45 (cl @p_23 @p_44) :rule subproof :discharge (t9.t24.t45.a0))
(step t9.t24.t46 (cl @p_45 @p_44) :rule resolution :premises (t9.t24.t44 t9.t24.t45))
(step t9.t24.t47 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t9.t24.t48 (cl @p_45 @p_45) :rule resolution :premises (t9.t24.t46 t9.t24.t47))
(step t9.t24.t49 (cl @p_45) :rule contraction :premises (t9.t24.t48))
(step t9.t24.t50 (cl @p_41) :rule resolution :premises (t9.t24.t31 t9.t24.t43 t9.t24.t49))
(step t9.t24.t51 (cl @p_39) :rule resolution :premises (t9.t24.t15 t9.t24.t30 t9.t24.t50))
(step t9.t24.t52 (cl @p_23 @p_38) :rule implies :premises (t9.t24.t51))
(step t9.t24.t53 (cl @p_38) :rule resolution :premises (t9.t24.t52 t9.t20))
(step t9.t24.t54 (cl @p_40) :rule symm :premises (t9.t24.t53))
(step t9.t24.t55 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) (! (= @p_35 @p_91) :named @p_94)) :named @p_95) (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) @p_92) :named @p_93)) :named @p_104)) (not @p_95) @p_93) :rule equiv_pos2)
(step t9.t24.t56 (cl (= (! (= (! (= @p_91 @p_91) :named @p_106) true) :named @p_107) @p_106)) :rule equiv_simplify)
(step t9.t24.t57 (cl (not @p_107) @p_106) :rule equiv1 :premises (t9.t24.t56))
(step t9.t24.t58 (cl (= (* -1 (! (- @p_91 @p_91) :named @p_109)) (* 1 @p_109))) :rule poly_simp)
(step t9.t24.t59 (cl (! (= @p_106 @p_106) :named @p_108)) :rule poly_simp_rel :premises (t9.t24.t58))
(step t9.t24.t60 (cl @p_106) :rule refl)
(step t9.t24.t61 (cl @p_106) :rule refl)
(step t9.t24.t62 (cl @p_108) :rule cong :premises (t9.t24.t60 t9.t24.t61))
(step t9.t24.t63 (cl @p_107) :rule rare_rewrite :args ("eq-refl" @p_91))
(step t9.t24.t64 (cl @p_107) :rule trans :premises (t9.t24.t59 t9.t24.t62 t9.t24.t63))
(step t9.t24.t65 (cl @p_106) :rule resolution :premises (t9.t24.t57 t9.t24.t64))
(step t9.t24.t66 (cl (= @p_94 @p_94)) :rule cong :premises (t9.t24.t65))
(step t9.t24.t67 (cl (= (* -1 (- @p_35 @p_91)) (* 1 (- @p_91 @p_35)))) :rule poly_simp)
(step t9.t24.t68 (cl (! (= @p_94 @p_92) :named @p_105)) :rule poly_simp_rel :premises (t9.t24.t67))
(step t9.t24.t69 (cl @p_105) :rule trans :premises (t9.t24.t66 t9.t24.t68))
(step t9.t24.t70 (cl @p_104) :rule cong :premises (t9.t24.t69))
(step t9.t24.t71 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))) (! (= @p_35 (! (ite (! (>= @p_34 10) :named @p_98) (! (dec_10$ (! (+ -10 @p_34) :named @p_96)) :named @p_97) @p_34) :named @p_99)) :named @p_100)) :named @p_101) @p_95) :named @p_102)) (not @p_101) @p_95) :rule equiv_pos2)
(step t9.t24.t72 (cl (= (* -5 (- @p_34 10)) (* -20 (- @p_1 5)))) :rule poly_simp)
(step t9.t24.t73 (cl (= @p_98 @p_90)) :rule poly_simp_rel :premises (t9.t24.t72))
(step t9.t24.t74 (cl (= @p_96 (! (+ @p_2 -20) :named @p_103))) :rule poly_simp)
(step t9.t24.t75 (cl (= @p_103 @p_88)) :rule poly_simp)
(step t9.t24.t76 (cl (= @p_96 @p_88)) :rule trans :premises (t9.t24.t74 t9.t24.t75))
(step t9.t24.t77 (cl (= @p_97 @p_89)) :rule cong :premises (t9.t24.t76))
(step t9.t24.t78 (cl (= @p_34 @p_34)) :rule refl)
(step t9.t24.t79 (cl (= @p_99 @p_91)) :rule cong :premises (t9.t24.t73 t9.t24.t77 t9.t24.t78))
(step t9.t24.t80 (cl (= @p_100 @p_94)) :rule cong :premises (t9.t24.t79))
(step t9.t24.t81 (cl @p_102) :rule cong :premises (t9.t24.t80))
(step t9.t24.t82 (cl @p_101 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t9.t24.t83)
(assume t9.t24.t83.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t9.t24.t83.t0 (cl (or @p_23 @p_100)) :rule forall_inst :args (@p_34))
(step t9.t24.t83.t1 (cl @p_23 @p_100) :rule or :premises (t9.t24.t83.t0))
(step t9.t24.t83.t2 (cl @p_100) :rule resolution :premises (t9.t24.t83.t1 t9.t20))
(step t9.t24.t83 (cl @p_23 @p_100) :rule subproof :discharge (t9.t24.t83.a0))
(step t9.t24.t84 (cl @p_101 @p_100) :rule resolution :premises (t9.t24.t82 t9.t24.t83))
(step t9.t24.t85 (cl @p_101 (not @p_100)) :rule implies_neg2)
(step t9.t24.t86 (cl @p_101 @p_101) :rule resolution :premises (t9.t24.t84 t9.t24.t85))
(step t9.t24.t87 (cl @p_101) :rule contraction :premises (t9.t24.t86))
(step t9.t24.t88 (cl @p_95) :rule resolution :premises (t9.t24.t71 t9.t24.t81 t9.t24.t87))
(step t9.t24.t89 (cl @p_93) :rule resolution :premises (t9.t24.t55 t9.t24.t70 t9.t24.t88))
(step t9.t24.t90 (cl @p_23 @p_92) :rule implies :premises (t9.t24.t89))
(step t9.t24.t91 (cl @p_92) :rule resolution :premises (t9.t24.t90 t9.t20))
(step t9.t24.t92 (cl @p_94) :rule symm :premises (t9.t24.t91))
(step t9.t24.t93 (cl (= @p_3 @p_34)) :rule trans :premises (t9.t24.t54 t9.t24.a2 t9.t24.t92 t9.t24.a0))
(step t9.t24.t94 (cl (= @p_34 @p_3)) :rule symm :premises (t9.t24.t93))
(step t9.t24.t95 (cl (= 6 6)) :rule refl)
(step t9.t24.t96 (cl (= @p_161 @p_4)) :rule cong :premises (t9.t24.t94 t9.t24.t95))
(step t9.t24.t97 (cl (= (! (= @p_4 false) :named @p_163) @p_5)) :rule equiv_simplify)
(step t9.t24.t98 (cl @p_163 @p_141) :rule equiv2 :premises (t9.t24.t97))
(step t9.t24.t99 (cl (! (not @p_141) :named @p_143) @p_4) :rule not_not)
(step t9.t24.t100 (cl @p_163 @p_4) :rule resolution :premises (t9.t24.t98 t9.t24.t99))
(step t9.t24.t101 (cl @p_163) :rule resolution :premises (t9.t24.t100 t9.t24.a4))
(step t9.t24.t102 (cl @p_162) :rule trans :premises (t9.t24.t96 t9.t24.t101))
(step t9.t24.t103 (cl @p_160) :rule resolution :premises (t9.t24.t2 t9.t24.t14 t9.t24.t102))
(step t9.t24.t104 (cl @p_147) :rule resolution :premises (t9.t24.t1 t9.t24.t103))
(step t9.t24 (cl @p_139 @p_138 @p_137 @p_136 @p_141 @p_147) :rule subproof :discharge (t9.t24.a0 t9.t24.a1 t9.t24.a2 t9.t24.a3 t9.t24.a4))
(step t9.t25 (cl (! (not @p_155) :named @p_158) @p_110) :rule and_pos :args (0))
(step t9.t26 (cl @p_158 @p_92) :rule and_pos :args (1))
(step t9.t27 (cl @p_158 @p_57) :rule and_pos :args (2))
(step t9.t28 (cl @p_158 @p_38) :rule and_pos :args (3))
(step t9.t29 (cl @p_158 @p_5) :rule and_pos :args (4))
(step t9.t30 (cl @p_147 @p_158 @p_158 @p_158 @p_158 @p_158) :rule resolution :premises (t9.t24 t9.t25 t9.t26 t9.t27 t9.t28 t9.t29))
(step t9.t31 (cl @p_158 @p_158 @p_158 @p_158 @p_158 @p_147) :rule reordering :premises (t9.t30))
(step t9.t32 (cl @p_158 @p_147) :rule contraction :premises (t9.t31))
(step t9.t33 (cl @p_159 @p_147) :rule resolution :premises (t9.t23 t9.t32))
(step t9.t34 (cl @p_159 (! (not @p_147) :named @p_151)) :rule implies_neg2)
(step t9.t35 (cl @p_159 @p_159) :rule resolution :premises (t9.t33 t9.t34))
(step t9.t36 (cl @p_159) :rule contraction :premises (t9.t35))
(step t9.t37 (cl @p_158 @p_147) :rule implies :premises (t9.t36))
(step t9.t38 (cl (not @p_104) (not @p_95) @p_93) :rule equiv_pos2)
(step t9.t39 (cl (= @p_107 @p_106)) :rule equiv_simplify)
(step t9.t40 (cl (not @p_107) @p_106) :rule equiv1 :premises (t9.t39))
(step t9.t41 (cl (= (* -1 @p_109) (* 1 @p_109))) :rule poly_simp)
(step t9.t42 (cl @p_108) :rule poly_simp_rel :premises (t9.t41))
(step t9.t43 (cl @p_106) :rule refl)
(step t9.t44 (cl @p_106) :rule refl)
(step t9.t45 (cl @p_108) :rule cong :premises (t9.t43 t9.t44))
(step t9.t46 (cl @p_107) :rule rare_rewrite :args ("eq-refl" @p_91))
(step t9.t47 (cl @p_107) :rule trans :premises (t9.t42 t9.t45 t9.t46))
(step t9.t48 (cl @p_106) :rule resolution :premises (t9.t40 t9.t47))
(step t9.t49 (cl (= @p_94 @p_94)) :rule cong :premises (t9.t48))
(step t9.t50 (cl (= (* -1 (- @p_35 @p_91)) (* 1 (- @p_91 @p_35)))) :rule poly_simp)
(step t9.t51 (cl @p_105) :rule poly_simp_rel :premises (t9.t50))
(step t9.t52 (cl @p_105) :rule trans :premises (t9.t49 t9.t51))
(step t9.t53 (cl @p_104) :rule cong :premises (t9.t52))
(step t9.t54 (cl (not @p_102) (not @p_101) @p_95) :rule equiv_pos2)
(step t9.t55 (cl (= (* -5 (- @p_34 10)) (* -20 (- @p_1 5)))) :rule poly_simp)
(step t9.t56 (cl (= @p_98 @p_90)) :rule poly_simp_rel :premises (t9.t55))
(step t9.t57 (cl (= @p_96 @p_103)) :rule poly_simp)
(step t9.t58 (cl (= @p_103 @p_88)) :rule poly_simp)
(step t9.t59 (cl (= @p_96 @p_88)) :rule trans :premises (t9.t57 t9.t58))
(step t9.t60 (cl (= @p_97 @p_89)) :rule cong :premises (t9.t59))
(step t9.t61 (cl (= @p_34 @p_34)) :rule refl)
(step t9.t62 (cl (= @p_99 @p_91)) :rule cong :premises (t9.t56 t9.t60 t9.t61))
(step t9.t63 (cl (= @p_100 @p_94)) :rule cong :premises (t9.t62))
(step t9.t64 (cl @p_102) :rule cong :premises (t9.t63))
(step t9.t65 (cl @p_101 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t9.t66)
(assume t9.t66.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t9.t66.t0 (cl (or @p_23 @p_100)) :rule forall_inst :args (@p_34))
(step t9.t66.t1 (cl @p_23 @p_100) :rule or :premises (t9.t66.t0))
(step t9.t66.t2 (cl @p_100) :rule resolution :premises (t9.t66.t1 t9.t20))
(step t9.t66 (cl @p_23 @p_100) :rule subproof :discharge (t9.t66.a0))
(step t9.t67 (cl @p_101 @p_100) :rule resolution :premises (t9.t65 t9.t66))
(step t9.t68 (cl @p_101 (not @p_100)) :rule implies_neg2)
(step t9.t69 (cl @p_101 @p_101) :rule resolution :premises (t9.t67 t9.t68))
(step t9.t70 (cl @p_101) :rule contraction :premises (t9.t69))
(step t9.t71 (cl @p_95) :rule resolution :premises (t9.t54 t9.t64 t9.t70))
(step t9.t72 (cl @p_93) :rule resolution :premises (t9.t38 t9.t53 t9.t71))
(step t9.t73 (cl @p_23 @p_92) :rule implies :premises (t9.t72))
(step t9.t74 (cl @p_92) :rule resolution :premises (t9.t73 t9.t20))
(step t9.t75 (cl (not @p_51) (not @p_41) @p_39) :rule equiv_pos2)
(step t9.t76 (cl (= @p_54 @p_53)) :rule equiv_simplify)
(step t9.t77 (cl (not @p_54) @p_53) :rule equiv1 :premises (t9.t76))
(step t9.t78 (cl (= (* -1 @p_56) (* 1 @p_56))) :rule poly_simp)
(step t9.t79 (cl @p_55) :rule poly_simp_rel :premises (t9.t78))
(step t9.t80 (cl @p_53) :rule refl)
(step t9.t81 (cl @p_53) :rule refl)
(step t9.t82 (cl @p_55) :rule cong :premises (t9.t80 t9.t81))
(step t9.t83 (cl @p_54) :rule rare_rewrite :args ("eq-refl" @p_37))
(step t9.t84 (cl @p_54) :rule trans :premises (t9.t79 t9.t82 t9.t83))
(step t9.t85 (cl @p_53) :rule resolution :premises (t9.t77 t9.t84))
(step t9.t86 (cl (= @p_40 @p_40)) :rule cong :premises (t9.t85))
(step t9.t87 (cl (= (* -1 (- @p_3 @p_37)) (* 1 (- @p_37 @p_3)))) :rule poly_simp)
(step t9.t88 (cl @p_52) :rule poly_simp_rel :premises (t9.t87))
(step t9.t89 (cl @p_52) :rule trans :premises (t9.t86 t9.t88))
(step t9.t90 (cl @p_51) :rule cong :premises (t9.t89))
(step t9.t91 (cl (not @p_46) (not @p_45) @p_41) :rule equiv_pos2)
(step t9.t92 (cl (= (* -5/2 (to_real (- @p_2 10))) (* -10/1 (- @p_47 5/2)))) :rule poly_simp)
(step t9.t93 (cl (= @p_42 @p_48)) :rule poly_simp_rel :premises (t9.t92))
(step t9.t94 (cl (= (= (to_real @p_49) 5/2) false)) :rule evaluate)
(step t9.t95 (cl (= @p_50 3)) :rule evaluate)
(step t9.t96 (cl (= 3 @p_50)) :rule symm :premises (t9.t95))
(step t9.t97 (cl (= @p_48 @p_36)) :rule rare_rewrite :premises (t9.t94 t9.t96) :args ("arith-int-geq-tighten" @p_1 5/2 3))
(step t9.t98 (cl (= @p_42 @p_36)) :rule trans :premises (t9.t93 t9.t97))
(step t9.t99 (cl (= @p_35 @p_35)) :rule refl)
(step t9.t100 (cl (= @p_2 @p_2)) :rule refl)
(step t9.t101 (cl (= @p_43 @p_37)) :rule cong :premises (t9.t98 t9.t99 t9.t100))
(step t9.t102 (cl (= @p_44 @p_40)) :rule cong :premises (t9.t101))
(step t9.t103 (cl @p_46) :rule cong :premises (t9.t102))
(step t9.t104 (cl @p_45 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t9.t105)
(assume t9.t105.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t9.t105.t0 (cl (or @p_23 @p_44)) :rule forall_inst :args (@p_2))
(step t9.t105.t1 (cl @p_23 @p_44) :rule or :premises (t9.t105.t0))
(step t9.t105.t2 (cl @p_44) :rule resolution :premises (t9.t105.t1 t9.t20))
(step t9.t105 (cl @p_23 @p_44) :rule subproof :discharge (t9.t105.a0))
(step t9.t106 (cl @p_45 @p_44) :rule resolution :premises (t9.t104 t9.t105))
(step t9.t107 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t9.t108 (cl @p_45 @p_45) :rule resolution :premises (t9.t106 t9.t107))
(step t9.t109 (cl @p_45) :rule contraction :premises (t9.t108))
(step t9.t110 (cl @p_41) :rule resolution :premises (t9.t91 t9.t103 t9.t109))
(step t9.t111 (cl @p_39) :rule resolution :premises (t9.t75 t9.t90 t9.t110))
(step t9.t112 (cl @p_23 @p_38) :rule implies :premises (t9.t111))
(step t9.t113 (cl @p_38) :rule resolution :premises (t9.t112 t9.t20))
(step t9.t114 (cl @p_155) :rule and_intro :premises (t9.a4 t9.t74 t9.a2 t9.t113 t9.a0))
(step t9.t115 (cl @p_147) :rule resolution :premises (t9.t37 t9.t114))
(step t9.t116 (cl @p_148) :rule and_intro :premises (t9.t22 t9.t115))
(step t9 (cl @p_141 @p_58 @p_137 @p_136 @p_139 @p_138 @p_148) :rule subproof :discharge (t9.a0 t9.a1 t9.a2 t9.a3 t9.a4 t9.a5))
(step t10 (cl (! (not @p_144) :named @p_145) @p_5) :rule and_pos :args (0))
(step t11 (cl @p_145 @p_6) :rule and_pos :args (1))
(step t12 (cl @p_145 @p_57) :rule and_pos :args (2))
(step t13 (cl @p_145 @p_38) :rule and_pos :args (3))
(step t14 (cl @p_145 @p_110) :rule and_pos :args (4))
(step t15 (cl @p_145 @p_92) :rule and_pos :args (5))
(step t16 (cl @p_148 @p_145 @p_145 @p_145 @p_145 @p_145 @p_145) :rule resolution :premises (t9 t10 t11 t12 t13 t14 t15))
(step t17 (cl @p_145 @p_145 @p_145 @p_145 @p_145 @p_145 @p_148) :rule reordering :premises (t16))
(step t18 (cl @p_145 @p_148) :rule contraction :premises (t17))
(step t19 (cl @p_154 @p_148) :rule resolution :premises (t8 t18))
(step t20 (cl @p_154 (! (not @p_148) :named @p_149)) :rule implies_neg2)
(step t21 (cl @p_154 @p_154) :rule resolution :premises (t19 t20))
(step t22 (cl @p_154) :rule contraction :premises (t21))
(step t23 (cl @p_145 @p_148) :rule implies :premises (t22))
(step t24 (cl (! (=> @p_148 false) :named @p_150) @p_148) :rule implies_neg1)
(anchor :step t25)
(assume t25.a0 @p_61)
(assume t25.a1 @p_147)
(step t25.t0 (cl (not @p_31) (not @p_30) @p_24) :rule equiv_pos2)
(step t25.t1 (cl (= @p_27 false)) :rule evaluate)
(step t25.t2 (cl (= @p_25 -6)) :rule evaluate)
(step t25.t3 (cl (= @p_26 @p_32)) :rule cong :premises (t25.t2))
(step t25.t4 (cl (= 4 4)) :rule refl)
(step t25.t5 (cl (= @p_28 @p_33)) :rule cong :premises (t25.t1 t25.t3 t25.t4))
(step t25.t6 (cl (= @p_33 4)) :rule rare_rewrite :args ("ite-false-cond" @p_32 4))
(step t25.t7 (cl (= @p_28 4)) :rule trans :premises (t25.t5 t25.t6))
(step t25.t8 (cl (= @p_29 @p_6)) :rule cong :premises (t25.t7))
(step t25.t9 (cl @p_31) :rule cong :premises (t25.t8))
(step t25.t10 (cl @p_30 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t25.t11)
(assume t25.t11.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t25.t11.t0 (cl (or @p_23 @p_29)) :rule forall_inst :args (4))
(step t25.t11.t1 (cl @p_23 @p_29) :rule or :premises (t25.t11.t0))
(step t25.t11.t2 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t25.t11.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t25.t11.t3.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t25.t11.t3.t1 (cl @p_8) :rule refl)
(step t25.t11.t3.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t25.t11.t3.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t25.t11.t3.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t25.t11.t3.t3))
(step t25.t11.t3.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t25.t11.t3.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t25.t11.t3.t4 t25.t11.t3.t5))
(step t25.t11.t3.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t25.t11.t3.t2 t25.t11.t3.t6))
(step t25.t11.t3.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t25.t11.t3.t7))
(step t25.t11.t3.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t25.t11.t3.t0 t25.t11.t3.t1 t25.t11.t3.t8))
(step t25.t11.t3.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t25.t11.t3.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t25.t11.t3.t9 t25.t11.t3.t10))
(step t25.t11.t3.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t25.t11.t3.t11))
(step t25.t11.t3 (cl @p_7) :rule bind)
(step t25.t11.t4 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t25.t11.t2 t25.t11.t3 a0))
(step t25.t11.t5 (cl @p_29) :rule resolution :premises (t25.t11.t1 t25.t11.t4))
(step t25.t11 (cl @p_23 @p_29) :rule subproof :discharge (t25.t11.a0))
(step t25.t12 (cl @p_30 @p_29) :rule resolution :premises (t25.t10 t25.t11))
(step t25.t13 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t25.t14 (cl @p_30 @p_30) :rule resolution :premises (t25.t12 t25.t13))
(step t25.t15 (cl @p_30) :rule contraction :premises (t25.t14))
(step t25.t16 (cl @p_24) :rule resolution :premises (t25.t0 t25.t9 t25.t15))
(step t25.t17 (cl @p_23 @p_6) :rule implies :premises (t25.t16))
(step t25.t18 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t25.t19 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t25.t19.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t25.t19.t1 (cl @p_8) :rule refl)
(step t25.t19.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t25.t19.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t25.t19.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t25.t19.t3))
(step t25.t19.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t25.t19.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t25.t19.t4 t25.t19.t5))
(step t25.t19.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t25.t19.t2 t25.t19.t6))
(step t25.t19.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t25.t19.t7))
(step t25.t19.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t25.t19.t0 t25.t19.t1 t25.t19.t8))
(step t25.t19.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t25.t19.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t25.t19.t9 t25.t19.t10))
(step t25.t19.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t25.t19.t11))
(step t25.t19 (cl @p_7) :rule bind)
(step t25.t20 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t25.t18 t25.t19 a0))
(step t25.t21 (cl @p_6) :rule resolution :premises (t25.t17 t25.t20))
(step t25.t22 (cl (not @p_152) @p_151 @p_58) :rule equiv_pos2)
(step t25.t23 (cl (= (* -4 (- 6 @p_34)) (* 16 @p_153))) :rule poly_simp)
(step t25.t24 (cl (= @p_146 @p_6)) :rule poly_simp_rel :premises (t25.t23))
(step t25.t25 (cl @p_152) :rule cong :premises (t25.t24))
(step t25.t26 (cl @p_58) :rule resolution :premises (t25.t22 t25.t25 t25.a1))
(step t25.t27 (cl) :rule resolution :premises (t25.t21 t25.t26))
(step t25 (cl (! (not @p_61) :named @p_62) @p_151 false) :rule subproof :discharge (t25.a0 t25.a1))
(step t26 (cl @p_149 @p_61) :rule and_pos :args (0))
(step t27 (cl @p_149 @p_147) :rule and_pos :args (1))
(step t28 (cl false @p_149 @p_149) :rule resolution :premises (t25 t26 t27))
(step t29 (cl @p_149 @p_149 false) :rule reordering :premises (t28))
(step t30 (cl @p_149 false) :rule contraction :premises (t29))
(step t31 (cl @p_150 false) :rule resolution :premises (t24 t30))
(step t32 (cl @p_150 (! (not false) :named @p_67)) :rule implies_neg2)
(step t33 (cl @p_150 @p_150) :rule resolution :premises (t31 t32))
(step t34 (cl @p_150) :rule contraction :premises (t33))
(step t35 (cl (= @p_150 @p_149)) :rule implies_simplify)
(step t36 (cl (not @p_150) @p_149) :rule equiv1 :premises (t35))
(step t37 (cl @p_149) :rule resolution :premises (t34 t36))
(step t38 (cl @p_145) :rule resolution :premises (t23 t37))
(step t39 (cl @p_141 @p_58 @p_137 @p_136 @p_139 @p_138) :rule not_and :premises (t38))
(step t40 (cl @p_142 @p_143) :rule or_neg :args (0))
(step t41 (cl @p_142 (not @p_58)) :rule or_neg :args (1))
(step t42 (cl @p_142 (not @p_137)) :rule or_neg :args (2))
(step t43 (cl @p_142 (not @p_136)) :rule or_neg :args (3))
(step t44 (cl @p_142 (not @p_139)) :rule or_neg :args (4))
(step t45 (cl @p_142 (not @p_138)) :rule or_neg :args (5))
(step t46 (cl @p_142 @p_142 @p_142 @p_142 @p_142 @p_142) :rule resolution :premises (t39 t40 t41 t42 t43 t44 t45))
(step t47 (cl @p_142) :rule contraction :premises (t46))
(step t48 (cl @p_140) :rule resolution :premises (t0 t7 t47))
(step t49 (cl @p_4 @p_58 @p_137 @p_136 @p_139 @p_138) :rule or :premises (t48))
(step t50 (cl @p_4 @p_58 @p_136 @p_137 @p_138 @p_139) :rule reordering :premises (t49))
(step t51 (cl (not (! (= (! (ite @p_90 (! (= @p_91 @p_89) :named @p_133) @p_110) :named @p_134) @p_134) :named @p_135)) (not @p_134) @p_134) :rule equiv_pos2)
(step t52 (cl (= @p_107 @p_106)) :rule equiv_simplify)
(step t53 (cl (not @p_107) @p_106) :rule equiv1 :premises (t52))
(step t54 (cl (= (* -1 @p_109) (* 1 @p_109))) :rule poly_simp)
(step t55 (cl @p_108) :rule poly_simp_rel :premises (t54))
(step t56 (cl @p_106) :rule refl)
(step t57 (cl @p_106) :rule refl)
(step t58 (cl @p_108) :rule cong :premises (t56 t57))
(step t59 (cl @p_107) :rule rare_rewrite :args ("eq-refl" @p_91))
(step t60 (cl @p_107) :rule trans :premises (t55 t58 t59))
(step t61 (cl @p_106) :rule resolution :premises (t53 t60))
(step t62 (cl (= @p_89 @p_89)) :rule refl)
(step t63 (cl (= @p_133 @p_133)) :rule cong :premises (t61 t62))
(step t64 (cl (= @p_34 @p_34)) :rule refl)
(step t65 (cl (= @p_110 @p_110)) :rule cong :premises (t61 t64))
(step t66 (cl @p_135) :rule cong :premises (t63 t65))
(step t67 (cl (= @p_134 true)) :rule rare_rewrite :args ("ite-eq" @p_90 @p_89 @p_34))
(step t68 (cl @p_134 (! (not true) :named @p_80)) :rule equiv2 :premises (t67))
(step t69 (cl true) :rule true)
(step t70 (cl @p_134) :rule resolution :premises (t68 t69))
(step t71 (cl @p_134) :rule resolution :premises (t51 t66 t70))
(step t72 (cl @p_90 @p_110) :rule ite1 :premises (t71))
(step t73 (cl (! (=> (! (and @p_6 @p_90) :named @p_112) (! (and @p_90 @p_61) :named @p_114)) :named @p_132) @p_112) :rule implies_neg1)
(anchor :step t74)
(assume t74.a0 @p_6)
(assume t74.a1 @p_90)
(step t74.t0 (cl (not @p_31) (not @p_30) @p_24) :rule equiv_pos2)
(step t74.t1 (cl (= @p_27 false)) :rule evaluate)
(step t74.t2 (cl (= @p_25 -6)) :rule evaluate)
(step t74.t3 (cl (= @p_26 @p_32)) :rule cong :premises (t74.t2))
(step t74.t4 (cl (= 4 4)) :rule refl)
(step t74.t5 (cl (= @p_28 @p_33)) :rule cong :premises (t74.t1 t74.t3 t74.t4))
(step t74.t6 (cl (= @p_33 4)) :rule rare_rewrite :args ("ite-false-cond" @p_32 4))
(step t74.t7 (cl (= @p_28 4)) :rule trans :premises (t74.t5 t74.t6))
(step t74.t8 (cl (= @p_29 @p_6)) :rule cong :premises (t74.t7))
(step t74.t9 (cl @p_31) :rule cong :premises (t74.t8))
(step t74.t10 (cl @p_30 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t74.t11)
(assume t74.t11.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t74.t11.t0 (cl (or @p_23 @p_29)) :rule forall_inst :args (4))
(step t74.t11.t1 (cl @p_23 @p_29) :rule or :premises (t74.t11.t0))
(step t74.t11.t2 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t74.t11.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t74.t11.t3.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t74.t11.t3.t1 (cl @p_8) :rule refl)
(step t74.t11.t3.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t74.t11.t3.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t74.t11.t3.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t74.t11.t3.t3))
(step t74.t11.t3.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t74.t11.t3.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t74.t11.t3.t4 t74.t11.t3.t5))
(step t74.t11.t3.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t74.t11.t3.t2 t74.t11.t3.t6))
(step t74.t11.t3.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t74.t11.t3.t7))
(step t74.t11.t3.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t74.t11.t3.t0 t74.t11.t3.t1 t74.t11.t3.t8))
(step t74.t11.t3.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t74.t11.t3.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t74.t11.t3.t9 t74.t11.t3.t10))
(step t74.t11.t3.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t74.t11.t3.t11))
(step t74.t11.t3 (cl @p_7) :rule bind)
(step t74.t11.t4 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t74.t11.t2 t74.t11.t3 a0))
(step t74.t11.t5 (cl @p_29) :rule resolution :premises (t74.t11.t1 t74.t11.t4))
(step t74.t11 (cl @p_23 @p_29) :rule subproof :discharge (t74.t11.a0))
(step t74.t12 (cl @p_30 @p_29) :rule resolution :premises (t74.t10 t74.t11))
(step t74.t13 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t74.t14 (cl @p_30 @p_30) :rule resolution :premises (t74.t12 t74.t13))
(step t74.t15 (cl @p_30) :rule contraction :premises (t74.t14))
(step t74.t16 (cl @p_24) :rule resolution :premises (t74.t0 t74.t9 t74.t15))
(step t74.t17 (cl @p_23 @p_6) :rule implies :premises (t74.t16))
(step t74.t18 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t74.t19 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t74.t19.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t74.t19.t1 (cl @p_8) :rule refl)
(step t74.t19.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t74.t19.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t74.t19.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t74.t19.t3))
(step t74.t19.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t74.t19.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t74.t19.t4 t74.t19.t5))
(step t74.t19.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t74.t19.t2 t74.t19.t6))
(step t74.t19.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t74.t19.t7))
(step t74.t19.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t74.t19.t0 t74.t19.t1 t74.t19.t8))
(step t74.t19.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t74.t19.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t74.t19.t9 t74.t19.t10))
(step t74.t19.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t74.t19.t11))
(step t74.t19 (cl @p_7) :rule bind)
(step t74.t20 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t74.t18 t74.t19 a0))
(step t74.t21 (cl @p_6) :rule resolution :premises (t74.t17 t74.t20))
(step t74.t22 (cl @p_61) :rule symm :premises (t74.t21))
(step t74.t23 (cl @p_114) :rule and_intro :premises (t74.a1 t74.t22))
(step t74 (cl @p_58 (! (not @p_90) :named @p_111) @p_114) :rule subproof :discharge (t74.a0 t74.a1))
(step t75 (cl (! (not @p_112) :named @p_113) @p_6) :rule and_pos :args (0))
(step t76 (cl @p_113 @p_90) :rule and_pos :args (1))
(step t77 (cl @p_114 @p_113 @p_113) :rule resolution :premises (t74 t75 t76))
(step t78 (cl @p_113 @p_113 @p_114) :rule reordering :premises (t77))
(step t79 (cl @p_113 @p_114) :rule contraction :premises (t78))
(step t80 (cl @p_132 @p_114) :rule resolution :premises (t73 t79))
(step t81 (cl @p_132 (! (not @p_114) :named @p_115)) :rule implies_neg2)
(step t82 (cl @p_132 @p_132) :rule resolution :premises (t80 t81))
(step t83 (cl @p_132) :rule contraction :premises (t82))
(step t84 (cl @p_113 @p_114) :rule implies :premises (t83))
(step t85 (cl (! (=> @p_114 false) :named @p_116) @p_114) :rule implies_neg1)
(anchor :step t86)
(assume t86.a0 @p_90)
(assume t86.a1 @p_61)
(step t86.t0 (cl (not (! (= @p_111 (! (< @p_1 5) :named @p_117)) :named @p_131)) (! (not @p_111) :named @p_120) @p_117) :rule equiv_pos2)
(step t86.t1 (cl (= @p_117 @p_111)) :rule rare_rewrite :args ("arith-elim-lt" @p_1 5))
(step t86.t2 (cl @p_131) :rule symm :premises (t86.t1))
(step t86.t3 (cl (! (=> @p_90 false) :named @p_121) @p_90) :rule implies_neg1)
(anchor :step t86.t4)
(assume t86.t4.a0 @p_90)
(step t86.t4.t0 (cl (not (! (= (! (<= (! (+ (! (* -1 @p_1) :named @p_70) @p_1) :named @p_124) (! (+ (! (* -1 5) :named @p_122) 4) :named @p_123)) :named @p_125) false) :named @p_128)) (not @p_125) false) :rule equiv_pos2)
(step t86.t4.t1 (cl (= @p_124 0)) :rule poly_simp)
(step t86.t4.t2 (cl (= @p_122 -5)) :rule evaluate)
(step t86.t4.t3 (cl (= 4 4)) :rule refl)
(step t86.t4.t4 (cl (= @p_123 (! (+ -5 4) :named @p_130))) :rule cong :premises (t86.t4.t2 t86.t4.t3))
(step t86.t4.t5 (cl (= @p_130 -1)) :rule evaluate)
(step t86.t4.t6 (cl (= @p_123 -1)) :rule trans :premises (t86.t4.t4 t86.t4.t5))
(step t86.t4.t7 (cl (= @p_125 (! (<= 0 -1) :named @p_129))) :rule cong :premises (t86.t4.t1 t86.t4.t6))
(step t86.t4.t8 (cl (= @p_129 false)) :rule evaluate)
(step t86.t4.t9 (cl @p_128) :rule trans :premises (t86.t4.t7 t86.t4.t8))
(step t86.t4.t10 (cl (not (! (<= @p_70 @p_122) :named @p_126)) @p_58 @p_125) :rule la_generic :args (1/1 -1/1 1/1))
(step t86.t4.t11 (cl (=> (! (and (! (< -1 0) :named @p_74) @p_90) :named @p_127) @p_126)) :rule la_mult_neg)
(step t86.t4.t12 (cl (not @p_127) @p_126) :rule implies :premises (t86.t4.t11))
(step t86.t4.t13 (cl (= (! (= @p_74 true) :named @p_76) @p_74)) :rule equiv_simplify)
(step t86.t4.t14 (cl (not @p_76) @p_74) :rule equiv1 :premises (t86.t4.t13))
(step t86.t4.t15 (cl @p_76) :rule evaluate)
(step t86.t4.t16 (cl @p_74) :rule resolution :premises (t86.t4.t14 t86.t4.t15))
(step t86.t4.t17 (cl @p_127) :rule and_intro :premises (t86.t4.t16 t86.t4.a0))
(step t86.t4.t18 (cl @p_126) :rule resolution :premises (t86.t4.t12 t86.t4.t17))
(step t86.t4.t19 (cl (not @p_31) (not @p_30) @p_24) :rule equiv_pos2)
(step t86.t4.t20 (cl (= @p_27 false)) :rule evaluate)
(step t86.t4.t21 (cl (= @p_25 -6)) :rule evaluate)
(step t86.t4.t22 (cl (= @p_26 @p_32)) :rule cong :premises (t86.t4.t21))
(step t86.t4.t23 (cl (= @p_28 @p_33)) :rule cong :premises (t86.t4.t20 t86.t4.t22 t86.t4.t3))
(step t86.t4.t24 (cl (= @p_33 4)) :rule rare_rewrite :args ("ite-false-cond" @p_32 4))
(step t86.t4.t25 (cl (= @p_28 4)) :rule trans :premises (t86.t4.t23 t86.t4.t24))
(step t86.t4.t26 (cl (= @p_29 @p_6)) :rule cong :premises (t86.t4.t25))
(step t86.t4.t27 (cl @p_31) :rule cong :premises (t86.t4.t26))
(step t86.t4.t28 (cl @p_30 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t86.t4.t29)
(assume t86.t4.t29.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t86.t4.t29.t0 (cl (or @p_23 @p_29)) :rule forall_inst :args (4))
(step t86.t4.t29.t1 (cl @p_23 @p_29) :rule or :premises (t86.t4.t29.t0))
(step t86.t4.t29.t2 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t86.t4.t29.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t86.t4.t29.t3.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t86.t4.t29.t3.t1 (cl @p_8) :rule refl)
(step t86.t4.t29.t3.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t86.t4.t29.t3.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t86.t4.t29.t3.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t86.t4.t29.t3.t3))
(step t86.t4.t29.t3.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t86.t4.t29.t3.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t86.t4.t29.t3.t4 t86.t4.t29.t3.t5))
(step t86.t4.t29.t3.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t86.t4.t29.t3.t2 t86.t4.t29.t3.t6))
(step t86.t4.t29.t3.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t86.t4.t29.t3.t7))
(step t86.t4.t29.t3.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t86.t4.t29.t3.t0 t86.t4.t29.t3.t1 t86.t4.t29.t3.t8))
(step t86.t4.t29.t3.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t86.t4.t29.t3.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t86.t4.t29.t3.t9 t86.t4.t29.t3.t10))
(step t86.t4.t29.t3.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t86.t4.t29.t3.t11))
(step t86.t4.t29.t3 (cl @p_7) :rule bind)
(step t86.t4.t29.t4 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t86.t4.t29.t2 t86.t4.t29.t3 a0))
(step t86.t4.t29.t5 (cl @p_29) :rule resolution :premises (t86.t4.t29.t1 t86.t4.t29.t4))
(step t86.t4.t29 (cl @p_23 @p_29) :rule subproof :discharge (t86.t4.t29.a0))
(step t86.t4.t30 (cl @p_30 @p_29) :rule resolution :premises (t86.t4.t28 t86.t4.t29))
(step t86.t4.t31 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t86.t4.t32 (cl @p_30 @p_30) :rule resolution :premises (t86.t4.t30 t86.t4.t31))
(step t86.t4.t33 (cl @p_30) :rule contraction :premises (t86.t4.t32))
(step t86.t4.t34 (cl @p_24) :rule resolution :premises (t86.t4.t19 t86.t4.t27 t86.t4.t33))
(step t86.t4.t35 (cl @p_23 @p_6) :rule implies :premises (t86.t4.t34))
(step t86.t4.t36 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t86.t4.t37 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t86.t4.t37.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t86.t4.t37.t1 (cl @p_8) :rule refl)
(step t86.t4.t37.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t86.t4.t37.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t86.t4.t37.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t86.t4.t37.t3))
(step t86.t4.t37.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t86.t4.t37.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t86.t4.t37.t4 t86.t4.t37.t5))
(step t86.t4.t37.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t86.t4.t37.t2 t86.t4.t37.t6))
(step t86.t4.t37.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t86.t4.t37.t7))
(step t86.t4.t37.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t86.t4.t37.t0 t86.t4.t37.t1 t86.t4.t37.t8))
(step t86.t4.t37.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t86.t4.t37.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t86.t4.t37.t9 t86.t4.t37.t10))
(step t86.t4.t37.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t86.t4.t37.t11))
(step t86.t4.t37 (cl @p_7) :rule bind)
(step t86.t4.t38 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t86.t4.t36 t86.t4.t37 a0))
(step t86.t4.t39 (cl @p_6) :rule resolution :premises (t86.t4.t35 t86.t4.t38))
(step t86.t4.t40 (cl @p_125) :rule resolution :premises (t86.t4.t10 t86.t4.t18 t86.t4.t39))
(step t86.t4.t41 (cl false) :rule resolution :premises (t86.t4.t0 t86.t4.t9 t86.t4.t40))
(step t86.t4 (cl @p_111 false) :rule subproof :discharge (t86.t4.a0))
(step t86.t5 (cl @p_121 false) :rule resolution :premises (t86.t3 t86.t4))
(step t86.t6 (cl @p_121 @p_67) :rule implies_neg2)
(step t86.t7 (cl @p_121 @p_121) :rule resolution :premises (t86.t5 t86.t6))
(step t86.t8 (cl @p_121) :rule contraction :premises (t86.t7))
(step t86.t9 (cl (= @p_121 @p_111)) :rule implies_simplify)
(step t86.t10 (cl (not @p_121) @p_111) :rule equiv1 :premises (t86.t9))
(step t86.t11 (cl @p_111) :rule resolution :premises (t86.t8 t86.t10))
(step t86.t12 (cl @p_117) :rule resolution :premises (t86.t0 t86.t2 t86.t11))
(step t86.t13 (cl (not (! (= @p_90 (! (not @p_117) :named @p_118)) :named @p_119)) @p_111 @p_118) :rule equiv_pos2)
(step t86.t14 (cl (= @p_118 @p_120)) :rule cong :premises (t86.t1))
(step t86.t15 (cl (= @p_120 @p_90)) :rule rare_rewrite :args ("bool-double-not-elim" @p_90))
(step t86.t16 (cl (= @p_118 @p_90)) :rule trans :premises (t86.t14 t86.t15))
(step t86.t17 (cl @p_119) :rule symm :premises (t86.t16))
(step t86.t18 (cl @p_118) :rule resolution :premises (t86.t13 t86.t17 t86.a0))
(step t86.t19 (cl) :rule resolution :premises (t86.t12 t86.t18))
(step t86 (cl @p_111 @p_62 false) :rule subproof :discharge (t86.a0 t86.a1))
(step t87 (cl @p_115 @p_90) :rule and_pos :args (0))
(step t88 (cl @p_115 @p_61) :rule and_pos :args (1))
(step t89 (cl false @p_115 @p_115) :rule resolution :premises (t86 t87 t88))
(step t90 (cl @p_115 @p_115 false) :rule reordering :premises (t89))
(step t91 (cl @p_115 false) :rule contraction :premises (t90))
(step t92 (cl @p_116 false) :rule resolution :premises (t85 t91))
(step t93 (cl @p_116 @p_67) :rule implies_neg2)
(step t94 (cl @p_116 @p_116) :rule resolution :premises (t92 t93))
(step t95 (cl @p_116) :rule contraction :premises (t94))
(step t96 (cl (= @p_116 @p_115)) :rule implies_simplify)
(step t97 (cl (not @p_116) @p_115) :rule equiv1 :premises (t96))
(step t98 (cl @p_115) :rule resolution :premises (t95 t97))
(step t99 (cl @p_113) :rule resolution :premises (t84 t98))
(step t100 (cl @p_58 @p_111) :rule not_and :premises (t99))
(step t101 (cl (not @p_31) (not @p_30) @p_24) :rule equiv_pos2)
(step t102 (cl (= @p_27 false)) :rule evaluate)
(step t103 (cl (= @p_25 -6)) :rule evaluate)
(step t104 (cl (= @p_26 @p_32)) :rule cong :premises (t103))
(step t105 (cl (= 4 4)) :rule refl)
(step t106 (cl (= @p_28 @p_33)) :rule cong :premises (t102 t104 t105))
(step t107 (cl (= @p_33 4)) :rule rare_rewrite :args ("ite-false-cond" @p_32 4))
(step t108 (cl (= @p_28 4)) :rule trans :premises (t106 t107))
(step t109 (cl (= @p_29 @p_6)) :rule cong :premises (t108))
(step t110 (cl @p_31) :rule cong :premises (t109))
(step t111 (cl @p_30 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t112)
(assume t112.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t112.t0 (cl (or @p_23 @p_29)) :rule forall_inst :args (4))
(step t112.t1 (cl @p_23 @p_29) :rule or :premises (t112.t0))
(step t112.t2 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t112.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t112.t3.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t112.t3.t1 (cl @p_8) :rule refl)
(step t112.t3.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t112.t3.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t112.t3.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t112.t3.t3))
(step t112.t3.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t112.t3.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t112.t3.t4 t112.t3.t5))
(step t112.t3.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t112.t3.t2 t112.t3.t6))
(step t112.t3.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t112.t3.t7))
(step t112.t3.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t112.t3.t0 t112.t3.t1 t112.t3.t8))
(step t112.t3.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t112.t3.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t112.t3.t9 t112.t3.t10))
(step t112.t3.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t112.t3.t11))
(step t112.t3 (cl @p_7) :rule bind)
(step t112.t4 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t112.t2 t112.t3 a0))
(step t112.t5 (cl @p_29) :rule resolution :premises (t112.t1 t112.t4))
(step t112 (cl @p_23 @p_29) :rule subproof :discharge (t112.a0))
(step t113 (cl @p_30 @p_29) :rule resolution :premises (t111 t112))
(step t114 (cl @p_30 (not @p_29)) :rule implies_neg2)
(step t115 (cl @p_30 @p_30) :rule resolution :premises (t113 t114))
(step t116 (cl @p_30) :rule contraction :premises (t115))
(step t117 (cl @p_24) :rule resolution :premises (t101 t110 t116))
(step t118 (cl @p_23 @p_6) :rule implies :premises (t117))
(step t119 (cl (not @p_7) (not (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (< ?v0 10) ?v0 (dec_10$ (- ?v0 10)))))) (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule equiv_pos2)
(anchor :step t120 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t120.t0 (cl (= @p_16 @p_18)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 10))
(step t120.t1 (cl @p_8) :rule refl)
(step t120.t2 (cl (= @p_14 @p_21)) :rule poly_simp)
(step t120.t3 (cl (= @p_20 -10)) :rule evaluate)
(step t120.t4 (cl (= @p_21 @p_22)) :rule cong :premises (t120.t3))
(step t120.t5 (cl (= @p_22 @p_9)) :rule poly_simp)
(step t120.t6 (cl (= @p_21 @p_9)) :rule trans :premises (t120.t4 t120.t5))
(step t120.t7 (cl (= @p_14 @p_9)) :rule trans :premises (t120.t2 t120.t6))
(step t120.t8 (cl (= @p_15 @p_10)) :rule cong :premises (t120.t7))
(step t120.t9 (cl (= @p_17 @p_19)) :rule cong :premises (t120.t0 t120.t1 t120.t8))
(step t120.t10 (cl (= @p_19 @p_12)) :rule rare_rewrite :args ("ite-not-cond" @p_11 ?v0 @p_10))
(step t120.t11 (cl (= @p_17 @p_12)) :rule trans :premises (t120.t9 t120.t10))
(step t120.t12 (cl (= (= @p_13 @p_17) (= @p_13 @p_12))) :rule cong :premises (t120.t11))
(step t120 (cl @p_7) :rule bind)
(step t121 (cl (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule resolution :premises (t119 t120 a0))
(step t122 (cl @p_6) :rule resolution :premises (t118 t121))
(step t123 (cl @p_111) :rule resolution :premises (t100 t122))
(step t124 (cl @p_110) :rule resolution :premises (t72 t123))
(step t125 (cl (not @p_104) (not @p_95) @p_93) :rule equiv_pos2)
(step t126 (cl (= @p_94 @p_94)) :rule cong :premises (t61))
(step t127 (cl (= (* -1 (- @p_35 @p_91)) (* 1 (- @p_91 @p_35)))) :rule poly_simp)
(step t128 (cl @p_105) :rule poly_simp_rel :premises (t127))
(step t129 (cl @p_105) :rule trans :premises (t126 t128))
(step t130 (cl @p_104) :rule cong :premises (t129))
(step t131 (cl (not @p_102) (not @p_101) @p_95) :rule equiv_pos2)
(step t132 (cl (= (* -5 (- @p_34 10)) (* -20 (- @p_1 5)))) :rule poly_simp)
(step t133 (cl (= @p_98 @p_90)) :rule poly_simp_rel :premises (t132))
(step t134 (cl (= @p_96 @p_103)) :rule poly_simp)
(step t135 (cl (= @p_103 @p_88)) :rule poly_simp)
(step t136 (cl (= @p_96 @p_88)) :rule trans :premises (t134 t135))
(step t137 (cl (= @p_97 @p_89)) :rule cong :premises (t136))
(step t138 (cl (= @p_99 @p_91)) :rule cong :premises (t133 t137 t64))
(step t139 (cl (= @p_100 @p_94)) :rule cong :premises (t138))
(step t140 (cl @p_102) :rule cong :premises (t139))
(step t141 (cl @p_101 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t142)
(assume t142.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t142.t0 (cl (or @p_23 @p_100)) :rule forall_inst :args (@p_34))
(step t142.t1 (cl @p_23 @p_100) :rule or :premises (t142.t0))
(step t142.t2 (cl @p_100) :rule resolution :premises (t142.t1 t121))
(step t142 (cl @p_23 @p_100) :rule subproof :discharge (t142.a0))
(step t143 (cl @p_101 @p_100) :rule resolution :premises (t141 t142))
(step t144 (cl @p_101 (not @p_100)) :rule implies_neg2)
(step t145 (cl @p_101 @p_101) :rule resolution :premises (t143 t144))
(step t146 (cl @p_101) :rule contraction :premises (t145))
(step t147 (cl @p_95) :rule resolution :premises (t131 t140 t146))
(step t148 (cl @p_93) :rule resolution :premises (t125 t130 t147))
(step t149 (cl @p_23 @p_92) :rule implies :premises (t148))
(step t150 (cl @p_92) :rule resolution :premises (t149 t121))
(step t151 (cl (not (! (= (! (ite @p_36 @p_57 (! (= @p_37 @p_2) :named @p_85)) :named @p_86) @p_86) :named @p_87)) (not @p_86) @p_86) :rule equiv_pos2)
(step t152 (cl (= @p_54 @p_53)) :rule equiv_simplify)
(step t153 (cl (not @p_54) @p_53) :rule equiv1 :premises (t152))
(step t154 (cl (= (* -1 @p_56) (* 1 @p_56))) :rule poly_simp)
(step t155 (cl @p_55) :rule poly_simp_rel :premises (t154))
(step t156 (cl @p_53) :rule refl)
(step t157 (cl @p_53) :rule refl)
(step t158 (cl @p_55) :rule cong :premises (t156 t157))
(step t159 (cl @p_54) :rule rare_rewrite :args ("eq-refl" @p_37))
(step t160 (cl @p_54) :rule trans :premises (t155 t158 t159))
(step t161 (cl @p_53) :rule resolution :premises (t153 t160))
(step t162 (cl (= @p_35 @p_35)) :rule refl)
(step t163 (cl (= @p_57 @p_57)) :rule cong :premises (t161 t162))
(step t164 (cl (= @p_2 @p_2)) :rule refl)
(step t165 (cl (= @p_85 @p_85)) :rule cong :premises (t161 t164))
(step t166 (cl @p_87) :rule cong :premises (t163 t165))
(step t167 (cl (= @p_86 true)) :rule rare_rewrite :args ("ite-eq" @p_36 @p_35 @p_2))
(step t168 (cl @p_86 @p_80) :rule equiv2 :premises (t167))
(step t169 (cl true) :rule true)
(step t170 (cl @p_86) :rule resolution :premises (t168 t169))
(step t171 (cl @p_86) :rule resolution :premises (t151 t166 t170))
(step t172 (cl (! (not @p_36) :named @p_60) @p_57) :rule ite2 :premises (t171))
(step t173 (cl @p_57 @p_60) :rule reordering :premises (t172))
(step t174 (cl (! (=> @p_6 @p_36) :named @p_59) @p_6) :rule implies_neg1)
(anchor :step t175)
(assume t175.a0 @p_6)
(step t175.t0 (cl (! (=> @p_61 @p_36) :named @p_63) @p_61) :rule implies_neg1)
(anchor :step t175.t1)
(assume t175.t1.a0 @p_61)
(step t175.t1.t0 (cl (not (! (= (! (not (! (< @p_1 3) :named @p_64)) :named @p_65) @p_36) :named @p_83)) (not @p_65) @p_36) :rule equiv_pos2)
(step t175.t1.t1 (cl (= @p_64 @p_60)) :rule rare_rewrite :args ("arith-elim-lt" @p_1 3))
(step t175.t1.t2 (cl (= @p_65 (! (not @p_60) :named @p_84))) :rule cong :premises (t175.t1.t1))
(step t175.t1.t3 (cl (= @p_84 @p_36)) :rule rare_rewrite :args ("bool-double-not-elim" @p_36))
(step t175.t1.t4 (cl @p_83) :rule trans :premises (t175.t1.t2 t175.t1.t3))
(step t175.t1.t5 (cl (! (=> @p_64 false) :named @p_66) @p_64) :rule implies_neg1)
(anchor :step t175.t1.t6)
(assume t175.t1.t6.a0 @p_64)
(step t175.t1.t6.t0 (cl (not (! (= (! (< (! (+ @p_1 @p_70) :named @p_71) (! (+ 3 (! (* -1 4) :named @p_68)) :named @p_69)) :named @p_72) false) :named @p_77)) (not @p_72) false) :rule equiv_pos2)
(step t175.t1.t6.t1 (cl (= @p_72 (! (not (! (>= @p_71 @p_69) :named @p_78)) :named @p_79))) :rule rare_rewrite :args ("arith-elim-lt" @p_71 @p_69))
(step t175.t1.t6.t2 (cl (= @p_71 0)) :rule poly_simp)
(step t175.t1.t6.t3 (cl (= @p_68 -4)) :rule evaluate)
(step t175.t1.t6.t4 (cl (= @p_69 (! (+ 3 -4) :named @p_82))) :rule cong :premises (t175.t1.t6.t3))
(step t175.t1.t6.t5 (cl (= @p_82 -1)) :rule evaluate)
(step t175.t1.t6.t6 (cl (= @p_69 -1)) :rule trans :premises (t175.t1.t6.t4 t175.t1.t6.t5))
(step t175.t1.t6.t7 (cl (= @p_78 (! (>= 0 -1) :named @p_81))) :rule cong :premises (t175.t1.t6.t2 t175.t1.t6.t6))
(step t175.t1.t6.t8 (cl (= @p_81 true)) :rule evaluate)
(step t175.t1.t6.t9 (cl (= @p_78 true)) :rule trans :premises (t175.t1.t6.t7 t175.t1.t6.t8))
(step t175.t1.t6.t10 (cl (= @p_79 @p_80)) :rule cong :premises (t175.t1.t6.t9))
(step t175.t1.t6.t11 (cl (= @p_80 false)) :rule evaluate)
(step t175.t1.t6.t12 (cl (= @p_79 false)) :rule trans :premises (t175.t1.t6.t10 t175.t1.t6.t11))
(step t175.t1.t6.t13 (cl @p_77) :rule trans :premises (t175.t1.t6.t1 t175.t1.t6.t12))
(step t175.t1.t6.t14 (cl @p_65 (not (! (= @p_70 @p_68) :named @p_73)) @p_72) :rule la_generic :args (1/1 -1/1 1/1))
(step t175.t1.t6.t15 (cl (=> (! (and @p_74 @p_6) :named @p_75) @p_73)) :rule la_mult_neg)
(step t175.t1.t6.t16 (cl (not @p_75) @p_73) :rule implies :premises (t175.t1.t6.t15))
(step t175.t1.t6.t17 (cl (= @p_76 @p_74)) :rule equiv_simplify)
(step t175.t1.t6.t18 (cl (not @p_76) @p_74) :rule equiv1 :premises (t175.t1.t6.t17))
(step t175.t1.t6.t19 (cl @p_76) :rule evaluate)
(step t175.t1.t6.t20 (cl @p_74) :rule resolution :premises (t175.t1.t6.t18 t175.t1.t6.t19))
(step t175.t1.t6.t21 (cl @p_75) :rule and_intro :premises (t175.t1.t6.t20 t122))
(step t175.t1.t6.t22 (cl @p_73) :rule resolution :premises (t175.t1.t6.t16 t175.t1.t6.t21))
(step t175.t1.t6.t23 (cl @p_72) :rule resolution :premises (t175.t1.t6.t14 t175.t1.t6.a0 t175.t1.t6.t22))
(step t175.t1.t6.t24 (cl false) :rule resolution :premises (t175.t1.t6.t0 t175.t1.t6.t13 t175.t1.t6.t23))
(step t175.t1.t6 (cl @p_65 false) :rule subproof :discharge (t175.t1.t6.a0))
(step t175.t1.t7 (cl @p_66 false) :rule resolution :premises (t175.t1.t5 t175.t1.t6))
(step t175.t1.t8 (cl @p_66 @p_67) :rule implies_neg2)
(step t175.t1.t9 (cl @p_66 @p_66) :rule resolution :premises (t175.t1.t7 t175.t1.t8))
(step t175.t1.t10 (cl @p_66) :rule contraction :premises (t175.t1.t9))
(step t175.t1.t11 (cl (= @p_66 @p_65)) :rule implies_simplify)
(step t175.t1.t12 (cl (not @p_66) @p_65) :rule equiv1 :premises (t175.t1.t11))
(step t175.t1.t13 (cl @p_65) :rule resolution :premises (t175.t1.t10 t175.t1.t12))
(step t175.t1.t14 (cl @p_36) :rule resolution :premises (t175.t1.t0 t175.t1.t4 t175.t1.t13))
(step t175.t1 (cl @p_62 @p_36) :rule subproof :discharge (t175.t1.a0))
(step t175.t2 (cl @p_63 @p_36) :rule resolution :premises (t175.t0 t175.t1))
(step t175.t3 (cl @p_63 @p_60) :rule implies_neg2)
(step t175.t4 (cl @p_63 @p_63) :rule resolution :premises (t175.t2 t175.t3))
(step t175.t5 (cl @p_63) :rule contraction :premises (t175.t4))
(step t175.t6 (cl @p_62 @p_36) :rule implies :premises (t175.t5))
(step t175.t7 (cl @p_61) :rule symm :premises (t122))
(step t175.t8 (cl @p_36) :rule resolution :premises (t175.t6 t175.t7))
(step t175 (cl @p_58 @p_36) :rule subproof :discharge (t175.a0))
(step t176 (cl @p_59 @p_36) :rule resolution :premises (t174 t175))
(step t177 (cl @p_59 @p_60) :rule implies_neg2)
(step t178 (cl @p_59 @p_59) :rule resolution :premises (t176 t177))
(step t179 (cl @p_59) :rule contraction :premises (t178))
(step t180 (cl @p_58 @p_36) :rule implies :premises (t179))
(step t181 (cl @p_36 @p_58) :rule reordering :premises (t180))
(step t182 (cl @p_36) :rule resolution :premises (t181 t122))
(step t183 (cl @p_57) :rule resolution :premises (t173 t182))
(step t184 (cl (not @p_51) (not @p_41) @p_39) :rule equiv_pos2)
(step t185 (cl (= @p_40 @p_40)) :rule cong :premises (t161))
(step t186 (cl (= (* -1 (- @p_3 @p_37)) (* 1 (- @p_37 @p_3)))) :rule poly_simp)
(step t187 (cl @p_52) :rule poly_simp_rel :premises (t186))
(step t188 (cl @p_52) :rule trans :premises (t185 t187))
(step t189 (cl @p_51) :rule cong :premises (t188))
(step t190 (cl (not @p_46) (not @p_45) @p_41) :rule equiv_pos2)
(step t191 (cl (= (* -5/2 (to_real (- @p_2 10))) (* -10/1 (- @p_47 5/2)))) :rule poly_simp)
(step t192 (cl (= @p_42 @p_48)) :rule poly_simp_rel :premises (t191))
(step t193 (cl (= (= (to_real @p_49) 5/2) false)) :rule evaluate)
(step t194 (cl (= @p_50 3)) :rule evaluate)
(step t195 (cl (= 3 @p_50)) :rule symm :premises (t194))
(step t196 (cl (= @p_48 @p_36)) :rule rare_rewrite :premises (t193 t195) :args ("arith-int-geq-tighten" @p_1 5/2 3))
(step t197 (cl (= @p_42 @p_36)) :rule trans :premises (t192 t196))
(step t198 (cl (= @p_43 @p_37)) :rule cong :premises (t197 t162 t164))
(step t199 (cl (= @p_44 @p_40)) :rule cong :premises (t198))
(step t200 (cl @p_46) :rule cong :premises (t199))
(step t201 (cl @p_45 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0)))) :rule implies_neg1)
(anchor :step t202)
(assume t202.a0 (forall ((?v0 Int)) (= (dec_10$ ?v0) (ite (>= ?v0 10) (dec_10$ (+ -10 ?v0)) ?v0))))
(step t202.t0 (cl (or @p_23 @p_44)) :rule forall_inst :args (@p_2))
(step t202.t1 (cl @p_23 @p_44) :rule or :premises (t202.t0))
(step t202.t2 (cl @p_44) :rule resolution :premises (t202.t1 t121))
(step t202 (cl @p_23 @p_44) :rule subproof :discharge (t202.a0))
(step t203 (cl @p_45 @p_44) :rule resolution :premises (t201 t202))
(step t204 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t205 (cl @p_45 @p_45) :rule resolution :premises (t203 t204))
(step t206 (cl @p_45) :rule contraction :premises (t205))
(step t207 (cl @p_41) :rule resolution :premises (t190 t200 t206))
(step t208 (cl @p_39) :rule resolution :premises (t184 t189 t207))
(step t209 (cl @p_23 @p_38) :rule implies :premises (t208))
(step t210 (cl @p_38) :rule resolution :premises (t209 t121))
(step t211 (cl) :rule resolution :premises (t50 t124 t150 t183 t210 t122 a1))
)
95635a25decbf98f76c25eed1f4778a8affead72 217 0
unsat
(
(assume a0 (! (< 0/1 (! (+ x$ (! (* 2/1 y$) :named @p_1)) :named @p_2)) :named @p_3))
(assume a1 (! (< 0/1 (! (- x$ @p_1) :named @p_4)) :named @p_5))
(assume a2 (! (< x$ 0/1) :named @p_6))
(step t0 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ (! (* -1/1 x$) :named @p_8) (! (* -2/1 y$) :named @p_7)) :named @p_9) 0/1) :named @p_10)) :named @p_11)) :named @p_35) (! (not (! (not (! (>= (! (+ @p_8 @p_1) :named @p_16) 0/1) :named @p_17)) :named @p_18)) :named @p_34) (! (not (! (not (! (>= x$ 0/1) :named @p_29)) :named @p_30)) :named @p_33)) :named @p_36) (! (or @p_10 @p_17 @p_29) :named @p_32)) :named @p_83)) (not @p_36) @p_32) :rule equiv_pos2)
(step t1 (cl (= @p_35 @p_10)) :rule rare_rewrite :args ("bool-double-not-elim" @p_10))
(step t2 (cl (= @p_34 @p_17)) :rule rare_rewrite :args ("bool-double-not-elim" @p_17))
(step t3 (cl (= @p_33 @p_29)) :rule rare_rewrite :args ("bool-double-not-elim" @p_29))
(step t4 (cl @p_83) :rule cong :premises (t1 t2 t3))
(step t5 (cl (! (=> (! (and @p_11 @p_18 @p_30) :named @p_37) (! (and @p_30 @p_11 @p_18) :named @p_39)) :named @p_82) @p_37) :rule implies_neg1)
(anchor :step t6)
(assume t6.a0 @p_11)
(assume t6.a1 @p_18)
(assume t6.a2 @p_30)
(step t6.t0 (cl (not (! (= @p_6 @p_30) :named @p_31)) (not @p_6) @p_30) :rule equiv_pos2)
(step t6.t1 (cl @p_31) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t6.t2 (cl @p_30) :rule resolution :premises (t6.t0 t6.t1 a2))
(step t6.t3 (cl (not (! (= @p_3 @p_11) :named @p_12)) (not @p_3) @p_11) :rule equiv_pos2)
(step t6.t4 (cl (= @p_3 (! (not (! (>= 0/1 @p_2) :named @p_13)) :named @p_14))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_2))
(step t6.t5 (cl (= (* -1/1 (- 0/1 @p_2)) (* -1/1 (- @p_9 0/1)))) :rule poly_simp)
(step t6.t6 (cl (! (= @p_13 @p_10) :named @p_15)) :rule poly_simp_rel :premises (t6.t5))
(step t6.t7 (cl (= @p_14 @p_11)) :rule cong :premises (t6.t6))
(step t6.t8 (cl @p_12) :rule trans :premises (t6.t4 t6.t7))
(step t6.t9 (cl @p_11) :rule resolution :premises (t6.t3 t6.t8 a0))
(step t6.t10 (cl (! (not (! (= @p_5 @p_18) :named @p_19)) :named @p_27) (! (not @p_5) :named @p_28) @p_18) :rule equiv_pos2)
(step t6.t11 (cl (= @p_5 (! (not (! (>= 0/1 @p_4) :named @p_20)) :named @p_21))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_4))
(step t6.t12 (cl (= @p_4 (! (+ x$ (! (* -1/1 @p_1) :named @p_25)) :named @p_26))) :rule poly_simp)
(step t6.t13 (cl (= @p_25 @p_7)) :rule poly_simp)
(step t6.t14 (cl (= @p_26 (! (+ x$ @p_7) :named @p_22))) :rule cong :premises (t6.t13))
(step t6.t15 (cl (= @p_4 @p_22)) :rule trans :premises (t6.t12 t6.t14))
(step t6.t16 (cl (= @p_20 (! (>= 0/1 @p_22) :named @p_23))) :rule cong :premises (t6.t15))
(step t6.t17 (cl (= (* -1/1 (- 0/1 @p_22)) (* -1/1 (- @p_16 0/1)))) :rule poly_simp)
(step t6.t18 (cl (! (= @p_23 @p_17) :named @p_24)) :rule poly_simp_rel :premises (t6.t17))
(step t6.t19 (cl (= @p_20 @p_17)) :rule trans :premises (t6.t16 t6.t18))
(step t6.t20 (cl (= @p_21 @p_18)) :rule cong :premises (t6.t19))
(step t6.t21 (cl @p_19) :rule trans :premises (t6.t11 t6.t20))
(step t6.t22 (cl @p_18) :rule resolution :premises (t6.t10 t6.t21 a1))
(step t6.t23 (cl @p_39) :rule and_intro :premises (t6.t2 t6.t9 t6.t22))
(step t6 (cl @p_35 @p_34 @p_33 @p_39) :rule subproof :discharge (t6.a0 t6.a1 t6.a2))
(step t7 (cl (! (not @p_37) :named @p_38) @p_11) :rule and_pos :args (0))
(step t8 (cl @p_38 @p_18) :rule and_pos :args (1))
(step t9 (cl @p_38 @p_30) :rule and_pos :args (2))
(step t10 (cl @p_39 @p_38 @p_38 @p_38) :rule resolution :premises (t6 t7 t8 t9))
(step t11 (cl @p_38 @p_38 @p_38 @p_39) :rule reordering :premises (t10))
(step t12 (cl @p_38 @p_39) :rule contraction :premises (t11))
(step t13 (cl @p_82 @p_39) :rule resolution :premises (t5 t12))
(step t14 (cl @p_82 (! (not @p_39) :named @p_40)) :rule implies_neg2)
(step t15 (cl @p_82 @p_82) :rule resolution :premises (t13 t14))
(step t16 (cl @p_82) :rule contraction :premises (t15))
(step t17 (cl @p_38 @p_39) :rule implies :premises (t16))
(step t18 (cl (! (=> @p_39 false) :named @p_41) @p_39) :rule implies_neg1)
(anchor :step t19)
(assume t19.a0 @p_30)
(assume t19.a1 @p_11)
(assume t19.a2 @p_18)
(step t19.t0 (cl (! (not (! (= @p_18 (! (> @p_22 0/1) :named @p_43)) :named @p_69)) :named @p_72) @p_34 @p_43) :rule equiv_pos2)
(step t19.t1 (cl (= @p_43 (! (not @p_23) :named @p_71))) :rule rare_rewrite :args ("arith-elim-gt" @p_22 0/1))
(step t19.t2 (cl (= (! (<= @p_22 0/1) :named @p_45) @p_23)) :rule rare_rewrite :args ("arith-elim-leq" @p_22 0/1))
(step t19.t3 (cl (= @p_23 @p_45)) :rule symm :premises (t19.t2))
(step t19.t4 (cl (= @p_71 (! (not @p_45) :named @p_70))) :rule cong :premises (t19.t3))
(step t19.t5 (cl (= @p_43 @p_70)) :rule trans :premises (t19.t1 t19.t4))
(step t19.t6 (cl (= (* -1/1 (- 0/1 @p_22)) (* -1/1 (- @p_16 0/1)))) :rule poly_simp)
(step t19.t7 (cl @p_24) :rule poly_simp_rel :premises (t19.t6))
(step t19.t8 (cl (= @p_45 @p_17)) :rule trans :premises (t19.t2 t19.t7))
(step t19.t9 (cl (= @p_70 @p_18)) :rule cong :premises (t19.t8))
(step t19.t10 (cl (= @p_43 @p_18)) :rule trans :premises (t19.t5 t19.t9))
(step t19.t11 (cl @p_69) :rule symm :premises (t19.t10))
(step t19.t12 (cl @p_27 @p_28 @p_18) :rule equiv_pos2)
(step t19.t13 (cl (= @p_5 @p_21)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_4))
(step t19.t14 (cl (= @p_4 @p_26)) :rule poly_simp)
(step t19.t15 (cl (= @p_25 @p_7)) :rule poly_simp)
(step t19.t16 (cl (= @p_26 @p_22)) :rule cong :premises (t19.t15))
(step t19.t17 (cl (= @p_4 @p_22)) :rule trans :premises (t19.t14 t19.t16))
(step t19.t18 (cl (= @p_20 @p_23)) :rule cong :premises (t19.t17))
(step t19.t19 (cl @p_24) :rule poly_simp_rel :premises (t19.t6))
(step t19.t20 (cl (= @p_20 @p_17)) :rule trans :premises (t19.t18 t19.t19))
(step t19.t21 (cl (= @p_21 @p_18)) :rule cong :premises (t19.t20))
(step t19.t22 (cl @p_19) :rule trans :premises (t19.t13 t19.t21))
(step t19.t23 (cl @p_18) :rule resolution :premises (t19.t12 t19.t22 a1))
(step t19.t24 (cl @p_43) :rule resolution :premises (t19.t0 t19.t11 t19.t23))
(step t19.t25 (cl (not (! (= @p_45 (! (not @p_43) :named @p_44)) :named @p_81)) @p_70 @p_44) :rule equiv_pos2)
(step t19.t26 (cl (= @p_44 @p_34)) :rule cong :premises (t19.t10))
(step t19.t27 (cl (= @p_44 @p_17)) :rule trans :premises (t19.t26 t2))
(step t19.t28 (cl (= @p_17 @p_44)) :rule symm :premises (t19.t27))
(step t19.t29 (cl @p_81) :rule trans :premises (t19.t8 t19.t28))
(step t19.t30 (cl (not (! (= @p_44 @p_45) :named @p_80)) (not @p_44) @p_45) :rule equiv_pos2)
(step t19.t31 (cl (= @p_17 @p_45)) :rule symm :premises (t19.t8))
(step t19.t32 (cl @p_80) :rule trans :premises (t19.t27 t19.t31))
(step t19.t33 (cl (! (=> @p_43 false) :named @p_46) @p_43) :rule implies_neg1)
(anchor :step t19.t34)
(assume t19.t34.a0 @p_43)
(step t19.t34.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_22) :named @p_52) (! (* -1/1 @p_2) :named @p_51) (! (* 2/1 x$) :named @p_50)) :named @p_53) (! (+ (! (* -1/1 0/1) :named @p_48) @p_48 (! (* 2/1 0/1) :named @p_47)) :named @p_49)) :named @p_54) false) :named @p_73)) (not @p_54) false) :rule equiv_pos2)
(step t19.t34.t1 (cl (= @p_54 (! (not (! (>= @p_53 @p_49) :named @p_74)) :named @p_75))) :rule rare_rewrite :args ("arith-elim-lt" @p_53 @p_49))
(step t19.t34.t2 (cl (= @p_52 @p_16)) :rule poly_simp)
(step t19.t34.t3 (cl (= @p_51 @p_9)) :rule poly_simp)
(step t19.t34.t4 (cl (= @p_50 @p_50)) :rule refl)
(step t19.t34.t5 (cl (= @p_53 (! (+ @p_16 @p_9 @p_50) :named @p_79))) :rule cong :premises (t19.t34.t2 t19.t34.t3 t19.t34.t4))
(step t19.t34.t6 (cl (= @p_79 0/1)) :rule poly_simp)
(step t19.t34.t7 (cl (= @p_53 0/1)) :rule trans :premises (t19.t34.t5 t19.t34.t6))
(step t19.t34.t8 (cl (= @p_48 0/1)) :rule evaluate)
(step t19.t34.t9 (cl (= @p_47 0/1)) :rule evaluate)
(step t19.t34.t10 (cl (= @p_49 (! (+ 0/1 0/1 0/1) :named @p_78))) :rule cong :premises (t19.t34.t8 t19.t34.t8 t19.t34.t9))
(step t19.t34.t11 (cl (= @p_78 0/1)) :rule evaluate)
(step t19.t34.t12 (cl (= @p_49 0/1)) :rule trans :premises (t19.t34.t10 t19.t34.t11))
(step t19.t34.t13 (cl (= @p_74 (! (>= 0/1 0/1) :named @p_77))) :rule cong :premises (t19.t34.t7 t19.t34.t12))
(step t19.t34.t14 (cl (= @p_77 true)) :rule evaluate)
(step t19.t34.t15 (cl (= @p_74 true)) :rule trans :premises (t19.t34.t13 t19.t34.t14))
(step t19.t34.t16 (cl (= @p_75 (! (not true) :named @p_76))) :rule cong :premises (t19.t34.t15))
(step t19.t34.t17 (cl (= @p_76 false)) :rule evaluate)
(step t19.t34.t18 (cl (= @p_75 false)) :rule trans :premises (t19.t34.t16 t19.t34.t17))
(step t19.t34.t19 (cl @p_73) :rule trans :premises (t19.t34.t1 t19.t34.t18))
(step t19.t34.t20 (cl (not (! (< @p_52 @p_48) :named @p_67)) (not (! (< @p_51 @p_48) :named @p_59)) (not (! (< @p_50 @p_47) :named @p_55)) @p_54) :rule la_generic :args (1/1 1/1 1/1 1/1))
(step t19.t34.t21 (cl (=> (! (and (! (< -1/1 0/1) :named @p_61) @p_43) :named @p_68) @p_67)) :rule la_mult_neg)
(step t19.t34.t22 (cl (not @p_68) @p_67) :rule implies :premises (t19.t34.t21))
(step t19.t34.t23 (cl (= (! (= @p_61 true) :named @p_66) @p_61)) :rule equiv_simplify)
(step t19.t34.t24 (cl (not @p_66) @p_61) :rule equiv1 :premises (t19.t34.t23))
(step t19.t34.t25 (cl @p_66) :rule evaluate)
(step t19.t34.t26 (cl @p_61) :rule resolution :premises (t19.t34.t24 t19.t34.t25))
(step t19.t34.t27 (cl @p_72 @p_34 @p_43) :rule equiv_pos2)
(step t19.t34.t28 (cl @p_27 @p_28 @p_18) :rule equiv_pos2)
(step t19.t34.t29 (cl @p_18) :rule resolution :premises (t19.t34.t28 t19.t22 a1))
(step t19.t34.t30 (cl @p_43) :rule resolution :premises (t19.t34.t27 t19.t11 t19.t34.t29))
(step t19.t34.t31 (cl @p_68) :rule and_intro :premises (t19.t34.t26 t19.t34.t30))
(step t19.t34.t32 (cl @p_67) :rule resolution :premises (t19.t34.t22 t19.t34.t31))
(step t19.t34.t33 (cl (=> (! (and @p_61 (! (> @p_2 0/1) :named @p_60)) :named @p_62) @p_59)) :rule la_mult_neg)
(step t19.t34.t34 (cl (not @p_62) @p_59) :rule implies :premises (t19.t34.t33))
(step t19.t34.t35 (cl (not (! (= @p_11 @p_60) :named @p_63)) @p_35 @p_60) :rule equiv_pos2)
(step t19.t34.t36 (cl (= @p_60 @p_14)) :rule rare_rewrite :args ("arith-elim-gt" @p_2 0/1))
(step t19.t34.t37 (cl (= (! (<= @p_2 0/1) :named @p_64) @p_13)) :rule rare_rewrite :args ("arith-elim-leq" @p_2 0/1))
(step t19.t34.t38 (cl (= @p_13 @p_64)) :rule symm :premises (t19.t34.t37))
(step t19.t34.t39 (cl (= @p_14 (! (not @p_64) :named @p_65))) :rule cong :premises (t19.t34.t38))
(step t19.t34.t40 (cl (= @p_60 @p_65)) :rule trans :premises (t19.t34.t36 t19.t34.t39))
(step t19.t34.t41 (cl (= (* -1/1 (- 0/1 @p_2)) (* -1/1 (- @p_9 0/1)))) :rule poly_simp)
(step t19.t34.t42 (cl @p_15) :rule poly_simp_rel :premises (t19.t34.t41))
(step t19.t34.t43 (cl (= @p_64 @p_10)) :rule trans :premises (t19.t34.t37 t19.t34.t42))
(step t19.t34.t44 (cl (= @p_65 @p_11)) :rule cong :premises (t19.t34.t43))
(step t19.t34.t45 (cl (= @p_60 @p_11)) :rule trans :premises (t19.t34.t40 t19.t34.t44))
(step t19.t34.t46 (cl @p_63) :rule symm :premises (t19.t34.t45))
(step t19.t34.t47 (cl (not @p_12) (not @p_3) @p_11) :rule equiv_pos2)
(step t19.t34.t48 (cl (= @p_3 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_2))
(step t19.t34.t49 (cl @p_15) :rule poly_simp_rel :premises (t19.t34.t41))
(step t19.t34.t50 (cl (= @p_14 @p_11)) :rule cong :premises (t19.t34.t49))
(step t19.t34.t51 (cl @p_12) :rule trans :premises (t19.t34.t48 t19.t34.t50))
(step t19.t34.t52 (cl @p_11) :rule resolution :premises (t19.t34.t47 t19.t34.t51 a0))
(step t19.t34.t53 (cl @p_60) :rule resolution :premises (t19.t34.t35 t19.t34.t46 t19.t34.t52))
(step t19.t34.t54 (cl @p_62) :rule and_intro :premises (t19.t34.t26 t19.t34.t53))
(step t19.t34.t55 (cl @p_59) :rule resolution :premises (t19.t34.t34 t19.t34.t54))
(step t19.t34.t56 (cl (=> (! (and (! (> 2/1 0/1) :named @p_56) @p_6) :named @p_57) @p_55)) :rule la_mult_pos)
(step t19.t34.t57 (cl (not @p_57) @p_55) :rule implies :premises (t19.t34.t56))
(step t19.t34.t58 (cl (= (! (= @p_56 true) :named @p_58) @p_56)) :rule equiv_simplify)
(step t19.t34.t59 (cl (not @p_58) @p_56) :rule equiv1 :premises (t19.t34.t58))
(step t19.t34.t60 (cl @p_58) :rule evaluate)
(step t19.t34.t61 (cl @p_56) :rule resolution :premises (t19.t34.t59 t19.t34.t60))
(step t19.t34.t62 (cl @p_57) :rule and_intro :premises (t19.t34.t61 a2))
(step t19.t34.t63 (cl @p_55) :rule resolution :premises (t19.t34.t57 t19.t34.t62))
(step t19.t34.t64 (cl @p_54) :rule resolution :premises (t19.t34.t20 t19.t34.t32 t19.t34.t55 t19.t34.t63))
(step t19.t34.t65 (cl false) :rule resolution :premises (t19.t34.t0 t19.t34.t19 t19.t34.t64))
(step t19.t34 (cl @p_44 false) :rule subproof :discharge (t19.t34.a0))
(step t19.t35 (cl @p_46 false) :rule resolution :premises (t19.t33 t19.t34))
(step t19.t36 (cl @p_46 (! (not false) :named @p_42)) :rule implies_neg2)
(step t19.t37 (cl @p_46 @p_46) :rule resolution :premises (t19.t35 t19.t36))
(step t19.t38 (cl @p_46) :rule contraction :premises (t19.t37))
(step t19.t39 (cl (= @p_46 @p_44)) :rule implies_simplify)
(step t19.t40 (cl (not @p_46) @p_44) :rule equiv1 :premises (t19.t39))
(step t19.t41 (cl @p_44) :rule resolution :premises (t19.t38 t19.t40))
(step t19.t42 (cl @p_45) :rule resolution :premises (t19.t30 t19.t32 t19.t41))
(step t19.t43 (cl @p_44) :rule resolution :premises (t19.t25 t19.t29 t19.t42))
(step t19.t44 (cl) :rule resolution :premises (t19.t24 t19.t43))
(step t19 (cl @p_33 @p_35 @p_34 false) :rule subproof :discharge (t19.a0 t19.a1 t19.a2))
(step t20 (cl @p_40 @p_30) :rule and_pos :args (0))
(step t21 (cl @p_40 @p_11) :rule and_pos :args (1))
(step t22 (cl @p_40 @p_18) :rule and_pos :args (2))
(step t23 (cl false @p_40 @p_40 @p_40) :rule resolution :premises (t19 t20 t21 t22))
(step t24 (cl @p_40 @p_40 @p_40 false) :rule reordering :premises (t23))
(step t25 (cl @p_40 false) :rule contraction :premises (t24))
(step t26 (cl @p_41 false) :rule resolution :premises (t18 t25))
(step t27 (cl @p_41 @p_42) :rule implies_neg2)
(step t28 (cl @p_41 @p_41) :rule resolution :premises (t26 t27))
(step t29 (cl @p_41) :rule contraction :premises (t28))
(step t30 (cl (= @p_41 @p_40)) :rule implies_simplify)
(step t31 (cl (not @p_41) @p_40) :rule equiv1 :premises (t30))
(step t32 (cl @p_40) :rule resolution :premises (t29 t31))
(step t33 (cl @p_38) :rule resolution :premises (t17 t32))
(step t34 (cl @p_35 @p_34 @p_33) :rule not_and :premises (t33))
(step t35 (cl @p_36 (not @p_35)) :rule or_neg :args (0))
(step t36 (cl @p_36 (not @p_34)) :rule or_neg :args (1))
(step t37 (cl @p_36 (not @p_33)) :rule or_neg :args (2))
(step t38 (cl @p_36 @p_36 @p_36) :rule resolution :premises (t34 t35 t36 t37))
(step t39 (cl @p_36) :rule contraction :premises (t38))
(step t40 (cl @p_32) :rule resolution :premises (t0 t4 t39))
(step t41 (cl @p_10 @p_17 @p_29) :rule or :premises (t40))
(step t42 (cl (not @p_31) (not @p_6) @p_30) :rule equiv_pos2)
(step t43 (cl @p_31) :rule rare_rewrite :args ("arith-elim-lt" x$ 0/1))
(step t44 (cl @p_30) :rule resolution :premises (t42 t43 a2))
(step t45 (cl @p_27 @p_28 @p_18) :rule equiv_pos2)
(step t46 (cl (= @p_5 @p_21)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_4))
(step t47 (cl (= @p_4 @p_26)) :rule poly_simp)
(step t48 (cl (= @p_25 @p_7)) :rule poly_simp)
(step t49 (cl (= @p_26 @p_22)) :rule cong :premises (t48))
(step t50 (cl (= @p_4 @p_22)) :rule trans :premises (t47 t49))
(step t51 (cl (= @p_20 @p_23)) :rule cong :premises (t50))
(step t52 (cl (= (* -1/1 (- 0/1 @p_22)) (* -1/1 (- @p_16 0/1)))) :rule poly_simp)
(step t53 (cl @p_24) :rule poly_simp_rel :premises (t52))
(step t54 (cl (= @p_20 @p_17)) :rule trans :premises (t51 t53))
(step t55 (cl (= @p_21 @p_18)) :rule cong :premises (t54))
(step t56 (cl @p_19) :rule trans :premises (t46 t55))
(step t57 (cl @p_18) :rule resolution :premises (t45 t56 a1))
(step t58 (cl (not @p_12) (not @p_3) @p_11) :rule equiv_pos2)
(step t59 (cl (= @p_3 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_2))
(step t60 (cl (= (* -1/1 (- 0/1 @p_2)) (* -1/1 (- @p_9 0/1)))) :rule poly_simp)
(step t61 (cl @p_15) :rule poly_simp_rel :premises (t60))
(step t62 (cl (= @p_14 @p_11)) :rule cong :premises (t61))
(step t63 (cl @p_12) :rule trans :premises (t59 t62))
(step t64 (cl @p_11) :rule resolution :premises (t58 t63 a0))
(step t65 (cl) :rule resolution :premises (t41 t44 t57 t64))
)
1539bb417c629eb3e6c54696bbf76d9187d9d2bc 916 0
unsat
(
(assume a0 (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ j$ bot$)))))
(assume a1 (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ i$ bot$)))))
(assume a2 (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (= (case_prod$ ?v0 ?v1) (fun_app$a (fun_app$ ?v0 (fst$ ?v1)) (snd$ ?v1)))))
(assume a3 (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (=> (= (insert$ ?v0 bot$) (insert$ ?v1 bot$)) (= ?v0 ?v1))))
(assume a4 (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= (snd$ (pair$ ?v0 ?v1)) ?v1)))
(assume a5 (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1)))
(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_1) one_chain_typeI$) :named @p_2))
(assume a7 (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (= (= bot$ (inf$ ?v0 (insert$ ?v1 ?v2))) (and (not (member$a ?v1 ?v0)) (= bot$ (inf$ ?v0 ?v2))))))
(assume a8 (! (finite$ bot$) :named @p_3))
(assume a9 (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (=> (finite$ ?v0) (finite$ (insert$ ?v1 ?v0)))))
(assume a10 (! (= i$ (! (fun_app$b (pair$a 1/1) 0/1) :named @p_4)) :named @p_5))
(assume a11 (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1))))
(assume a12 (! (= j$ (! (fun_app$b (pair$a 0/1) 1/1) :named @p_6)) :named @p_7))
(assume a13 (forall ((?v0 Real_real_prod_set$)) (= (inf$ ?v0 bot$) bot$)))
(assume a14 (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (= (insert$ ?v0 (insert$ ?v1 ?v2)) (insert$ ?v1 (insert$ ?v0 ?v2)))))
(assume a15 (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (= (insert$ ?v0 ?v1) (sup$ (insert$ ?v0 bot$) ?v1))))
(assume a16 (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (and (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (and (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (and (= (sup$ ?v2 ?v4) ?v0) (= (inf$ ?v2 ?v4) bot$))))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))
(assume a17 (! (and (= (one_chain_line_integral$ f$ (! (insert$ i$ bot$) :named @p_9) one_chain_typeI$) (one_chain_line_integral$ f$ @p_9 one_chain_typeII$)) (! (and (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uu$ ?v0))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeII$) (case_prod$ uu$ ?v0)))) :named @p_8)) :named @p_10))
(assume a18 (! (and (= (one_chain_line_integral$ f$ (! (insert$ j$ bot$) :named @p_12) one_chain_typeII$) (one_chain_line_integral$ f$ @p_12 one_chain_typeI$)) (! (and (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeII$) (case_prod$ uua$ ?v0))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uua$ ?v0)))) :named @p_11)) :named @p_13))
(assume a19 (! (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_12) :named @p_17) g$) :named @p_18) (! (+ (! (line_integral$ f$ @p_9 g$) :named @p_15) (! (line_integral$ f$ @p_12 g$) :named @p_14)) :named @p_16)) :named @p_19)) :named @p_20))
(step t0 (cl (! (=> (! (and (! (= @p_4 @p_6) :named @p_36) (! (= (! (snd$a @p_4) :named @p_21) 0/1) :named @p_22) (! (= (! (snd$a @p_6) :named @p_30) 1/1) :named @p_31)) :named @p_369) (! (and @p_22 @p_36 @p_31) :named @p_371)) :named @p_376) @p_369) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 @p_36)
(assume t1.a1 @p_22)
(assume t1.a2 @p_31)
(step t1.t0 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))) (! (= 0/1 @p_21) :named @p_27)) :named @p_28) (! (=> (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))) @p_22) :named @p_26)) :named @p_29)) (not @p_28) @p_26) :rule equiv_pos2)
(step t1.t1 (cl (= (* 1/1 (- 0/1 @p_21)) (* -1/1 (- @p_21 0/1)))) :rule poly_simp)
(step t1.t2 (cl (= @p_27 @p_22)) :rule poly_simp_rel :premises (t1.t1))
(step t1.t3 (cl @p_29) :rule cong :premises (t1.t2))
(step t1.t4 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t1.t5)
(assume t1.t5.a0 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))))
(step t1.t5.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :named @p_25) @p_27)) :rule forall_inst :args (1/1 0/1))
(step t1.t5.t1 (cl @p_25 @p_27) :rule or :premises (t1.t5.t0))
(step t1.t5.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1)) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :named @p_23)) (not (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1))) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t1.t5.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t1.t5.t3.t0 (cl (= (* 1/1 (- (! (snd$a (fun_app$b (pair$a ?v0) ?v1)) :named @p_24) ?v1)) (* -1/1 (- ?v1 @p_24)))) :rule poly_simp)
(step t1.t5.t3.t1 (cl (= (= @p_24 ?v1) (= ?v1 @p_24))) :rule poly_simp_rel :premises (t1.t5.t3.t0))
(step t1.t5.t3 (cl @p_23) :rule bind)
(step t1.t5.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule resolution :premises (t1.t5.t2 t1.t5.t3 a5))
(step t1.t5.t5 (cl @p_27) :rule resolution :premises (t1.t5.t1 t1.t5.t4))
(step t1.t5 (cl @p_25 @p_27) :rule subproof :discharge (t1.t5.a0))
(step t1.t6 (cl @p_28 @p_27) :rule resolution :premises (t1.t4 t1.t5))
(step t1.t7 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t1.t8 (cl @p_28 @p_28) :rule resolution :premises (t1.t6 t1.t7))
(step t1.t9 (cl @p_28) :rule contraction :premises (t1.t8))
(step t1.t10 (cl @p_26) :rule resolution :premises (t1.t0 t1.t3 t1.t9))
(step t1.t11 (cl @p_25 @p_22) :rule implies :premises (t1.t10))
(step t1.t12 (cl (not @p_23) (not (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1))) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t1.t13 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t1.t13.t0 (cl (= (* 1/1 (- @p_24 ?v1)) (* -1/1 (- ?v1 @p_24)))) :rule poly_simp)
(step t1.t13.t1 (cl (= (= @p_24 ?v1) (= ?v1 @p_24))) :rule poly_simp_rel :premises (t1.t13.t0))
(step t1.t13 (cl @p_23) :rule bind)
(step t1.t14 (cl (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule resolution :premises (t1.t12 t1.t13 a5))
(step t1.t15 (cl @p_22) :rule resolution :premises (t1.t11 t1.t14))
(step t1.t16 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))) (! (= 1/1 @p_30) :named @p_33)) :named @p_34) (! (=> (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))) @p_31) :named @p_32)) :named @p_35)) (not @p_34) @p_32) :rule equiv_pos2)
(step t1.t17 (cl (= (* -1/1 (- 1/1 @p_30)) (* 1/1 (- @p_30 1/1)))) :rule poly_simp)
(step t1.t18 (cl (= @p_33 @p_31)) :rule poly_simp_rel :premises (t1.t17))
(step t1.t19 (cl @p_35) :rule cong :premises (t1.t18))
(step t1.t20 (cl @p_34 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t1.t21)
(assume t1.t21.a0 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))))
(step t1.t21.t0 (cl (or @p_25 @p_33)) :rule forall_inst :args (0/1 1/1))
(step t1.t21.t1 (cl @p_25 @p_33) :rule or :premises (t1.t21.t0))
(step t1.t21.t2 (cl @p_33) :rule resolution :premises (t1.t21.t1 t1.t14))
(step t1.t21 (cl @p_25 @p_33) :rule subproof :discharge (t1.t21.a0))
(step t1.t22 (cl @p_34 @p_33) :rule resolution :premises (t1.t20 t1.t21))
(step t1.t23 (cl @p_34 (not @p_33)) :rule implies_neg2)
(step t1.t24 (cl @p_34 @p_34) :rule resolution :premises (t1.t22 t1.t23))
(step t1.t25 (cl @p_34) :rule contraction :premises (t1.t24))
(step t1.t26 (cl @p_32) :rule resolution :premises (t1.t16 t1.t19 t1.t25))
(step t1.t27 (cl @p_25 @p_31) :rule implies :premises (t1.t26))
(step t1.t28 (cl @p_31) :rule resolution :premises (t1.t27 t1.t14))
(step t1.t29 (cl @p_371) :rule and_intro :premises (t1.t15 t1.a0 t1.t28))
(step t1 (cl (! (not @p_36) :named @p_366) (! (not @p_22) :named @p_367) (! (not @p_31) :named @p_368) @p_371) :rule subproof :discharge (t1.a0 t1.a1 t1.a2))
(step t2 (cl (! (not @p_369) :named @p_370) @p_36) :rule and_pos :args (0))
(step t3 (cl @p_370 @p_22) :rule and_pos :args (1))
(step t4 (cl @p_370 @p_31) :rule and_pos :args (2))
(step t5 (cl @p_371 @p_370 @p_370 @p_370) :rule resolution :premises (t1 t2 t3 t4))
(step t6 (cl @p_370 @p_370 @p_370 @p_371) :rule reordering :premises (t5))
(step t7 (cl @p_370 @p_371) :rule contraction :premises (t6))
(step t8 (cl @p_376 @p_371) :rule resolution :premises (t0 t7))
(step t9 (cl @p_376 (! (not @p_371) :named @p_372)) :rule implies_neg2)
(step t10 (cl @p_376 @p_376) :rule resolution :premises (t8 t9))
(step t11 (cl @p_376) :rule contraction :premises (t10))
(step t12 (cl @p_370 @p_371) :rule implies :premises (t11))
(step t13 (cl (! (=> @p_371 false) :named @p_373) @p_371) :rule implies_neg1)
(anchor :step t14)
(assume t14.a0 @p_22)
(assume t14.a1 @p_36)
(assume t14.a2 @p_31)
(step t14.t0 (cl (not (! (= (! (= 1/1 0/1) :named @p_374) false) :named @p_375)) (not @p_374) false) :rule equiv_pos2)
(step t14.t1 (cl @p_375) :rule evaluate)
(step t14.t2 (cl (or @p_25 @p_33)) :rule forall_inst :args (0/1 1/1))
(step t14.t3 (cl @p_25 @p_33) :rule or :premises (t14.t2))
(step t14.t4 (cl (not @p_23) (not (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1))) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t14.t5 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t14.t5.t0 (cl (= (* 1/1 (- @p_24 ?v1)) (* -1/1 (- ?v1 @p_24)))) :rule poly_simp)
(step t14.t5.t1 (cl (= (= @p_24 ?v1) (= ?v1 @p_24))) :rule poly_simp_rel :premises (t14.t5.t0))
(step t14.t5 (cl @p_23) :rule bind)
(step t14.t6 (cl (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule resolution :premises (t14.t4 t14.t5 a5))
(step t14.t7 (cl @p_33) :rule resolution :premises (t14.t3 t14.t6))
(step t14.t8 (cl (= @p_6 @p_4)) :rule symm :premises (t14.a1))
(step t14.t9 (cl (= @p_30 @p_21)) :rule cong :premises (t14.t8))
(step t14.t10 (cl (not @p_29) (not @p_28) @p_26) :rule equiv_pos2)
(step t14.t11 (cl (= (* 1/1 (- 0/1 @p_21)) (* -1/1 (- @p_21 0/1)))) :rule poly_simp)
(step t14.t12 (cl (= @p_27 @p_22)) :rule poly_simp_rel :premises (t14.t11))
(step t14.t13 (cl @p_29) :rule cong :premises (t14.t12))
(step t14.t14 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t14.t15)
(assume t14.t15.a0 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))))
(step t14.t15.t0 (cl (or @p_25 @p_27)) :rule forall_inst :args (1/1 0/1))
(step t14.t15.t1 (cl @p_25 @p_27) :rule or :premises (t14.t15.t0))
(step t14.t15.t2 (cl @p_27) :rule resolution :premises (t14.t15.t1 t14.t6))
(step t14.t15 (cl @p_25 @p_27) :rule subproof :discharge (t14.t15.a0))
(step t14.t16 (cl @p_28 @p_27) :rule resolution :premises (t14.t14 t14.t15))
(step t14.t17 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t14.t18 (cl @p_28 @p_28) :rule resolution :premises (t14.t16 t14.t17))
(step t14.t19 (cl @p_28) :rule contraction :premises (t14.t18))
(step t14.t20 (cl @p_26) :rule resolution :premises (t14.t10 t14.t13 t14.t19))
(step t14.t21 (cl @p_25 @p_22) :rule implies :premises (t14.t20))
(step t14.t22 (cl @p_22) :rule resolution :premises (t14.t21 t14.t6))
(step t14.t23 (cl @p_374) :rule trans :premises (t14.t7 t14.t9 t14.t22))
(step t14.t24 (cl false) :rule resolution :premises (t14.t0 t14.t1 t14.t23))
(step t14 (cl @p_367 @p_366 @p_368 false) :rule subproof :discharge (t14.a0 t14.a1 t14.a2))
(step t15 (cl @p_372 @p_22) :rule and_pos :args (0))
(step t16 (cl @p_372 @p_36) :rule and_pos :args (1))
(step t17 (cl @p_372 @p_31) :rule and_pos :args (2))
(step t18 (cl false @p_372 @p_372 @p_372) :rule resolution :premises (t14 t15 t16 t17))
(step t19 (cl @p_372 @p_372 @p_372 false) :rule reordering :premises (t18))
(step t20 (cl @p_372 false) :rule contraction :premises (t19))
(step t21 (cl @p_373 false) :rule resolution :premises (t13 t20))
(step t22 (cl @p_373 (! (not false) :named @p_185)) :rule implies_neg2)
(step t23 (cl @p_373 @p_373) :rule resolution :premises (t21 t22))
(step t24 (cl @p_373) :rule contraction :premises (t23))
(step t25 (cl (= @p_373 @p_372)) :rule implies_simplify)
(step t26 (cl (not @p_373) @p_372) :rule equiv1 :premises (t25))
(step t27 (cl @p_372) :rule resolution :premises (t24 t26))
(step t28 (cl @p_370) :rule resolution :premises (t12 t27))
(step t29 (cl @p_366 @p_367 @p_368) :rule not_and :premises (t28))
(step t30 (cl (! (not (! (or (! (not (! (= (! (insert$ @p_4 bot$) :named @p_38) (! (insert$ @p_6 bot$) :named @p_37)) :named @p_39)) :named @p_40) @p_36) :named @p_41)) :named @p_365) @p_40 @p_36) :rule or_pos)
(step t31 (cl @p_40 @p_36 @p_365) :rule reordering :premises (t30))
(step t32 (cl (! (and (! (= @p_37 (! (insert$ @p_4 @p_37) :named @p_155)) :named @p_289) (! (= @p_155 (! (insert$ @p_6 @p_38) :named @p_48)) :named @p_287) (! (= @p_38 @p_48) :named @p_49)) :named @p_362) (! (not @p_289) :named @p_360) (! (not @p_287) :named @p_308) (! (not @p_49) :named @p_361)) :rule and_neg)
(step t33 (cl (! (=> @p_362 @p_39) :named @p_364) @p_362) :rule implies_neg1)
(anchor :step t34)
(assume t34.a0 @p_289)
(assume t34.a1 @p_287)
(assume t34.a2 @p_49)
(step t34.t0 (cl @p_364 @p_362) :rule implies_neg1)
(anchor :step t34.t1)
(assume t34.t1.a0 @p_289)
(assume t34.t1.a1 @p_287)
(assume t34.t1.a2 @p_49)
(step t34.t1.t0 (cl (or (! (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (= (insert$ ?v0 (insert$ ?v1 ?v2)) (insert$ ?v1 (insert$ ?v0 ?v2))))) :named @p_288) @p_287)) :rule forall_inst :args (@p_4 @p_6 bot$))
(step t34.t1.t1 (cl @p_288 @p_287) :rule or :premises (t34.t1.t0))
(step t34.t1.t2 (cl @p_287) :rule resolution :premises (t34.t1.t1 a14))
(step t34.t1.t3 (cl (= @p_48 @p_155)) :rule symm :premises (t34.t1.t2))
(step t34.t1.t4 (cl (= @p_155 @p_37)) :rule symm :premises (t34.t1.a0))
(step t34.t1.t5 (cl @p_39) :rule trans :premises (t34.t1.a2 t34.t1.t3 t34.t1.t4))
(step t34.t1 (cl @p_360 @p_308 @p_361 @p_39) :rule subproof :discharge (t34.t1.a0 t34.t1.a1 t34.t1.a2))
(step t34.t2 (cl (! (not @p_362) :named @p_363) @p_289) :rule and_pos :args (0))
(step t34.t3 (cl @p_363 @p_287) :rule and_pos :args (1))
(step t34.t4 (cl @p_363 @p_49) :rule and_pos :args (2))
(step t34.t5 (cl @p_39 @p_363 @p_363 @p_363) :rule resolution :premises (t34.t1 t34.t2 t34.t3 t34.t4))
(step t34.t6 (cl @p_363 @p_363 @p_363 @p_39) :rule reordering :premises (t34.t5))
(step t34.t7 (cl @p_363 @p_39) :rule contraction :premises (t34.t6))
(step t34.t8 (cl @p_364 @p_39) :rule resolution :premises (t34.t0 t34.t7))
(step t34.t9 (cl @p_364 @p_40) :rule implies_neg2)
(step t34.t10 (cl @p_364 @p_364) :rule resolution :premises (t34.t8 t34.t9))
(step t34.t11 (cl @p_364) :rule contraction :premises (t34.t10))
(step t34.t12 (cl @p_363 @p_39) :rule implies :premises (t34.t11))
(step t34.t13 (cl (or @p_288 @p_287)) :rule forall_inst :args (@p_4 @p_6 bot$))
(step t34.t14 (cl @p_288 @p_287) :rule or :premises (t34.t13))
(step t34.t15 (cl @p_287) :rule resolution :premises (t34.t14 a14))
(step t34.t16 (cl @p_362) :rule and_intro :premises (t34.a0 t34.t15 t34.a2))
(step t34.t17 (cl @p_39) :rule resolution :premises (t34.t12 t34.t16))
(step t34 (cl @p_360 @p_308 @p_361 @p_39) :rule subproof :discharge (t34.a0 t34.a1 t34.a2))
(step t35 (cl @p_363 @p_289) :rule and_pos :args (0))
(step t36 (cl @p_363 @p_287) :rule and_pos :args (1))
(step t37 (cl @p_363 @p_49) :rule and_pos :args (2))
(step t38 (cl @p_39 @p_363 @p_363 @p_363) :rule resolution :premises (t34 t35 t36 t37))
(step t39 (cl @p_363 @p_363 @p_363 @p_39) :rule reordering :premises (t38))
(step t40 (cl @p_363 @p_39) :rule contraction :premises (t39))
(step t41 (cl @p_364 @p_39) :rule resolution :premises (t33 t40))
(step t42 (cl @p_364 @p_40) :rule implies_neg2)
(step t43 (cl @p_364 @p_364) :rule resolution :premises (t41 t42))
(step t44 (cl @p_364) :rule contraction :premises (t43))
(step t45 (cl @p_363 @p_39) :rule implies :premises (t44))
(step t46 (cl @p_360 @p_308 @p_361 @p_39) :rule resolution :premises (t32 t45))
(step t47 (cl @p_39 @p_360 @p_308 @p_361) :rule reordering :premises (t46))
(step t48 (cl (! (not (! (or (! (not (! (member$a @p_4 @p_37) :named @p_290)) :named @p_291) @p_289) :named @p_292)) :named @p_359) @p_291 @p_289) :rule or_pos)
(step t49 (cl @p_291 @p_289 @p_359) :rule reordering :premises (t48))
(step t50 (cl (not (! (= (! (or (! (and @p_291 (! (= bot$ (inf$ @p_37 bot$)) :named @p_293)) :named @p_294) (! (not @p_291) :named @p_356) (! (not @p_293) :named @p_354)) :named @p_357) (! (or @p_294 @p_290 @p_354) :named @p_355)) :named @p_358)) (not @p_357) @p_355) :rule equiv_pos2)
(step t51 (cl (= @p_356 @p_290)) :rule rare_rewrite :args ("bool-double-not-elim" @p_290))
(step t52 (cl (= @p_354 @p_354)) :rule refl)
(step t53 (cl @p_358) :rule cong :premises (t51 t52))
(step t54 (cl @p_294 @p_356 @p_354) :rule and_neg)
(step t55 (cl @p_357 (! (not @p_294) :named @p_295)) :rule or_neg :args (0))
(step t56 (cl @p_357 (not @p_356)) :rule or_neg :args (1))
(step t57 (cl @p_357 (not @p_354)) :rule or_neg :args (2))
(step t58 (cl @p_357 @p_357 @p_357) :rule resolution :premises (t54 t55 t56 t57))
(step t59 (cl @p_357) :rule contraction :premises (t58))
(step t60 (cl @p_355) :rule resolution :premises (t50 t53 t59))
(step t61 (cl @p_294 @p_290 @p_354) :rule or :premises (t60))
(step t62 (cl @p_290 @p_354 @p_294) :rule reordering :premises (t61))
(step t63 (cl (or (! (not (forall ((?v0 Real_real_prod_set$)) (= bot$ (inf$ ?v0 bot$)))) :named @p_280) @p_293)) :rule forall_inst :args (@p_37))
(step t64 (cl @p_280 @p_293) :rule or :premises (t63))
(step t65 (cl (not (! (= (forall ((?v0 Real_real_prod_set$)) (= (inf$ ?v0 bot$) bot$)) (forall ((?v0 Real_real_prod_set$)) (= bot$ (inf$ ?v0 bot$)))) :named @p_278)) (not (forall ((?v0 Real_real_prod_set$)) (= (inf$ ?v0 bot$) bot$))) (forall ((?v0 Real_real_prod_set$)) (= bot$ (inf$ ?v0 bot$)))) :rule equiv_pos2)
(anchor :step t66 :args ((?v0 Real_real_prod_set$) (:= (?v0 Real_real_prod_set$) ?v0)))
(step t66.t0 (cl (= (= (! (inf$ ?v0 bot$) :named @p_279) bot$) (= bot$ @p_279))) :rule rare_rewrite :args ("eq-symm" @p_279 bot$))
(step t66 (cl @p_278) :rule bind)
(step t67 (cl (forall ((?v0 Real_real_prod_set$)) (= bot$ (inf$ ?v0 bot$)))) :rule resolution :premises (t65 t66 a13))
(step t68 (cl @p_293) :rule resolution :premises (t64 t67))
(step t69 (cl (! (not (! (= (! (= bot$ (inf$ @p_37 @p_38)) :named @p_296) @p_294) :named @p_297)) :named @p_353) @p_296 @p_295) :rule equiv_pos1)
(step t70 (cl @p_296 @p_295 @p_353) :rule reordering :premises (t69))
(step t71 (cl (! (not (! (or (! (not (! (finite$ (! (sup$ @p_37 @p_38) :named @p_299)) :named @p_303)) :named @p_304) (! (not (! (fun_app$a (! (line_integral_exists$ f$ @p_37) :named @p_75) g$) :named @p_76)) :named @p_77) (! (not (! (fun_app$a (! (line_integral_exists$ f$ @p_38) :named @p_78) g$) :named @p_79)) :named @p_80) (! (not @p_296) :named @p_298) (! (= (! (line_integral$ f$ @p_37 g$) :named @p_73) (! (+ (! (* -1/1 (! (line_integral$ f$ @p_38 g$) :named @p_70)) :named @p_71) (! (line_integral$ f$ @p_299 g$) :named @p_300)) :named @p_301)) :named @p_302)) :named @p_305)) :named @p_352) @p_304 @p_77 @p_80 @p_298 @p_302) :rule or_pos)
(step t72 (cl @p_80 @p_77 @p_304 @p_298 @p_302 @p_352) :rule reordering :premises (t71))
(step t73 (cl (= (! (= @p_79 true) :named @p_241) @p_79)) :rule equiv_simplify)
(step t74 (cl (not @p_241) @p_79) :rule equiv1 :premises (t73))
(step t75 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$)))) (! (= (! (fun_app$ uu$ (! (fst$ @p_1) :named @p_209)) :named @p_242) @p_78) :named @p_260)) :named @p_261) (! (=> (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$)))) (! (= @p_78 @p_242) :named @p_254)) :named @p_259)) :named @p_262)) (not @p_261) @p_259) :rule equiv_pos2)
(step t76 (cl (= @p_260 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_242 @p_78))
(step t77 (cl @p_262) :rule cong :premises (t76))
(step t78 (cl @p_261 (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :rule implies_neg1)
(anchor :step t79)
(assume t79.a0 (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$)))))
(step t79.t0 (cl (or (! (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :named @p_258) @p_260)) :rule forall_inst :args (@p_209))
(step t79.t1 (cl @p_258 @p_260) :rule or :premises (t79.t0))
(step t79.t2 (cl (not (! (= (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ i$ bot$)))) (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :named @p_255)) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ i$ bot$))))) (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :rule equiv_pos2)
(anchor :step t79.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t79.t3.t0 (cl (= bot$ bot$)) :rule refl)
(step t79.t3.t1 (cl (= @p_9 @p_38)) :rule cong :premises (a10 t79.t3.t0))
(step t79.t3.t2 (cl (= (! (line_integral_exists$ f$ @p_9) :named @p_257) @p_78)) :rule cong :premises (t79.t3.t1))
(step t79.t3.t3 (cl (= (= (! (fun_app$ uu$ ?v0) :named @p_256) @p_257) (= @p_256 @p_78))) :rule cong :premises (t79.t3.t2))
(step t79.t3 (cl @p_255) :rule bind)
(step t79.t4 (cl (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :rule resolution :premises (t79.t2 t79.t3 a1))
(step t79.t5 (cl @p_260) :rule resolution :premises (t79.t1 t79.t4))
(step t79 (cl @p_258 @p_260) :rule subproof :discharge (t79.a0))
(step t80 (cl @p_261 @p_260) :rule resolution :premises (t78 t79))
(step t81 (cl @p_261 (not @p_260)) :rule implies_neg2)
(step t82 (cl @p_261 @p_261) :rule resolution :premises (t80 t81))
(step t83 (cl @p_261) :rule contraction :premises (t82))
(step t84 (cl @p_259) :rule resolution :premises (t75 t77 t83))
(step t85 (cl @p_258 @p_254) :rule implies :premises (t84))
(step t86 (cl (not @p_255) (not (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ i$ bot$))))) (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :rule equiv_pos2)
(anchor :step t87 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t87.t0 (cl (= bot$ bot$)) :rule refl)
(step t87.t1 (cl (= @p_9 @p_38)) :rule cong :premises (a10 t87.t0))
(step t87.t2 (cl (= @p_257 @p_78)) :rule cong :premises (t87.t1))
(step t87.t3 (cl (= (= @p_256 @p_257) (= @p_256 @p_78))) :rule cong :premises (t87.t2))
(step t87 (cl @p_255) :rule bind)
(step t88 (cl (forall ((?v0 Int)) (= (fun_app$ uu$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 1/1) 0/1) bot$))))) :rule resolution :premises (t86 t87 a1))
(step t89 (cl @p_254) :rule resolution :premises (t85 t88))
(step t90 (cl (or (! (not (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= ?v1 (snd$ (pair$ ?v0 ?v1))))) :named @p_231) (! (= g$ (! (snd$ @p_1) :named @p_208)) :named @p_227))) :rule forall_inst :args (k$ g$))
(step t91 (cl @p_231 @p_227) :rule or :premises (t90))
(step t92 (cl (not (! (= (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= (snd$ (pair$ ?v0 ?v1)) ?v1)) (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= ?v1 (snd$ (pair$ ?v0 ?v1))))) :named @p_228)) (not (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= (snd$ (pair$ ?v0 ?v1)) ?v1))) (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= ?v1 (snd$ (pair$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t93 :args ((?v0 Int) (?v1 Real_real_real_prod_fun$) (:= (?v0 Int) ?v0) (:= (?v1 Real_real_real_prod_fun$) ?v1)))
(step t93.t0 (cl (= (= (! (snd$ (pair$ ?v0 ?v1)) :named @p_230) ?v1) (= ?v1 @p_230))) :rule rare_rewrite :args ("eq-symm" @p_230 ?v1))
(step t93 (cl @p_228) :rule bind)
(step t94 (cl (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (= ?v1 (snd$ (pair$ ?v0 ?v1))))) :rule resolution :premises (t92 t93 a4))
(step t95 (cl @p_227) :rule resolution :premises (t91 t94))
(step t96 (cl (= @p_79 (! (fun_app$a @p_242 @p_208) :named @p_243))) :rule cong :premises (t89 t95))
(step t97 (cl (= (! (= @p_243 true) :named @p_244) @p_243)) :rule equiv_simplify)
(step t98 (cl @p_244 (not @p_243)) :rule equiv2 :premises (t97))
(step t99 (cl (! (not (! (= (! (case_prod$ uu$ @p_1) :named @p_245) @p_243) :named @p_246)) :named @p_253) (! (not @p_245) :named @p_252) @p_243) :rule equiv_pos2)
(step t100 (cl @p_252 @p_243 @p_253) :rule reordering :premises (t99))
(step t101 (cl (! (not (! (or (! (not @p_2) :named @p_216) @p_245) :named @p_247)) :named @p_251) @p_216 @p_245) :rule or_pos)
(step t102 (cl @p_216 @p_245 @p_251) :rule reordering :premises (t101))
(step t103 (cl (or (! (not (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uu$ ?v0)))) :named @p_250) @p_247)) :rule forall_inst :args (@p_1))
(step t104 (cl @p_250 @p_247) :rule or :premises (t103))
(step t105 (cl (not (! (= (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uu$ ?v0))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uu$ ?v0)))) :named @p_248)) (not (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uu$ ?v0)))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uu$ ?v0)))) :rule equiv_pos2)
(anchor :step t106 :args ((?v0 Int_real_real_real_prod_fun_prod$) (:= (?v0 Int_real_real_real_prod_fun_prod$) ?v0)))
(step t106.t0 (cl (= (=> (! (member$ ?v0 one_chain_typeI$) :named @p_221) (! (case_prod$ uu$ ?v0) :named @p_249)) (or (! (not @p_221) :named @p_222) (! (case_prod$ uu$ ?v0) :named @p_249)))) :rule rare_rewrite :args ("bool-impl-elim" @p_221 @p_249))
(step t106 (cl @p_248) :rule bind)
(step t107 (cl @p_8) :rule and :premises (a17) :args (1))
(step t108 (cl (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uu$ ?v0)))) :rule and :premises (t107) :args (0))
(step t109 (cl (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uu$ ?v0)))) :rule resolution :premises (t105 t106 t108))
(step t110 (cl @p_247) :rule resolution :premises (t104 t109))
(step t111 (cl @p_245) :rule resolution :premises (t102 a6 t110))
(step t112 (cl (or (! (not (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (= (case_prod$ ?v0 ?v1) (fun_app$a (fun_app$ ?v0 (fst$ ?v1)) (snd$ ?v1))))) :named @p_215) @p_246)) :rule forall_inst :args (uu$ @p_1))
(step t113 (cl @p_215 @p_246) :rule or :premises (t112))
(step t114 (cl @p_246) :rule resolution :premises (t113 a2))
(step t115 (cl @p_243) :rule resolution :premises (t100 t111 t114))
(step t116 (cl @p_244) :rule resolution :premises (t98 t115))
(step t117 (cl @p_241) :rule trans :premises (t96 t116))
(step t118 (cl @p_79) :rule resolution :premises (t74 t117))
(step t119 (cl (= (! (= @p_76 true) :named @p_207) @p_76)) :rule equiv_simplify)
(step t120 (cl (not @p_207) @p_76) :rule equiv1 :premises (t119))
(step t121 (cl (not (! (= (! (=> (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$)))) (! (= (! (fun_app$ uua$ @p_209) :named @p_210) @p_75) :named @p_238)) :named @p_239) (! (=> (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$)))) (! (= @p_75 @p_210) :named @p_232)) :named @p_237)) :named @p_240)) (not @p_239) @p_237) :rule equiv_pos2)
(step t122 (cl (= @p_238 @p_232)) :rule rare_rewrite :args ("eq-symm" @p_210 @p_75))
(step t123 (cl @p_240) :rule cong :premises (t122))
(step t124 (cl @p_239 (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :rule implies_neg1)
(anchor :step t125)
(assume t125.a0 (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$)))))
(step t125.t0 (cl (or (! (not (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :named @p_236) @p_238)) :rule forall_inst :args (@p_209))
(step t125.t1 (cl @p_236 @p_238) :rule or :premises (t125.t0))
(step t125.t2 (cl (not (! (= (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ j$ bot$)))) (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :named @p_233)) (not (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ j$ bot$))))) (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :rule equiv_pos2)
(anchor :step t125.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t125.t3.t0 (cl (= bot$ bot$)) :rule refl)
(step t125.t3.t1 (cl (= @p_12 @p_37)) :rule cong :premises (a12 t125.t3.t0))
(step t125.t3.t2 (cl (= (! (line_integral_exists$ f$ @p_12) :named @p_235) @p_75)) :rule cong :premises (t125.t3.t1))
(step t125.t3.t3 (cl (= (= (! (fun_app$ uua$ ?v0) :named @p_234) @p_235) (= @p_234 @p_75))) :rule cong :premises (t125.t3.t2))
(step t125.t3 (cl @p_233) :rule bind)
(step t125.t4 (cl (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :rule resolution :premises (t125.t2 t125.t3 a0))
(step t125.t5 (cl @p_238) :rule resolution :premises (t125.t1 t125.t4))
(step t125 (cl @p_236 @p_238) :rule subproof :discharge (t125.a0))
(step t126 (cl @p_239 @p_238) :rule resolution :premises (t124 t125))
(step t127 (cl @p_239 (not @p_238)) :rule implies_neg2)
(step t128 (cl @p_239 @p_239) :rule resolution :premises (t126 t127))
(step t129 (cl @p_239) :rule contraction :premises (t128))
(step t130 (cl @p_237) :rule resolution :premises (t121 t123 t129))
(step t131 (cl @p_236 @p_232) :rule implies :premises (t130))
(step t132 (cl (not @p_233) (not (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ j$ bot$))))) (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :rule equiv_pos2)
(anchor :step t133 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t133.t0 (cl (= bot$ bot$)) :rule refl)
(step t133.t1 (cl (= @p_12 @p_37)) :rule cong :premises (a12 t133.t0))
(step t133.t2 (cl (= @p_235 @p_75)) :rule cong :premises (t133.t1))
(step t133.t3 (cl (= (= @p_234 @p_235) (= @p_234 @p_75))) :rule cong :premises (t133.t2))
(step t133 (cl @p_233) :rule bind)
(step t134 (cl (forall ((?v0 Int)) (= (fun_app$ uua$ ?v0) (line_integral_exists$ f$ (insert$ (fun_app$b (pair$a 0/1) 1/1) bot$))))) :rule resolution :premises (t132 t133 a0))
(step t135 (cl @p_232) :rule resolution :premises (t131 t134))
(step t136 (cl (= @p_76 (! (fun_app$a @p_210 @p_208) :named @p_211))) :rule cong :premises (t135 t95))
(step t137 (cl (= (! (= @p_211 true) :named @p_212) @p_211)) :rule equiv_simplify)
(step t138 (cl @p_212 (not @p_211)) :rule equiv2 :premises (t137))
(step t139 (cl (! (not (! (= (! (case_prod$ uua$ @p_1) :named @p_213) @p_211) :named @p_214)) :named @p_226) (! (not @p_213) :named @p_225) @p_211) :rule equiv_pos2)
(step t140 (cl @p_225 @p_211 @p_226) :rule reordering :premises (t139))
(step t141 (cl (! (not (! (or @p_216 @p_213) :named @p_217)) :named @p_224) @p_216 @p_213) :rule or_pos)
(step t142 (cl @p_216 @p_213 @p_224) :rule reordering :premises (t141))
(step t143 (cl (or (! (not (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uua$ ?v0)))) :named @p_223) @p_217)) :rule forall_inst :args (@p_1))
(step t144 (cl @p_223 @p_217) :rule or :premises (t143))
(step t145 (cl (not (! (= (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uua$ ?v0))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uua$ ?v0)))) :named @p_218)) (not (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uua$ ?v0)))) (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uua$ ?v0)))) :rule equiv_pos2)
(anchor :step t146 :args ((?v0 Int_real_real_real_prod_fun_prod$) (:= (?v0 Int_real_real_real_prod_fun_prod$) ?v0)))
(step t146.t0 (cl (= (=> @p_221 (! (case_prod$ uua$ ?v0) :named @p_220)) (or @p_222 @p_220))) :rule rare_rewrite :args ("bool-impl-elim" @p_221 @p_220))
(step t146 (cl @p_218) :rule bind)
(step t147 (cl @p_11) :rule and :premises (a18) :args (1))
(step t148 (cl (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (=> (member$ ?v0 one_chain_typeI$) (case_prod$ uua$ ?v0)))) :rule and :premises (t147) :args (1))
(step t149 (cl (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (or (not (member$ ?v0 one_chain_typeI$)) (case_prod$ uua$ ?v0)))) :rule resolution :premises (t145 t146 t148))
(step t150 (cl @p_217) :rule resolution :premises (t144 t149))
(step t151 (cl @p_213) :rule resolution :premises (t142 a6 t150))
(step t152 (cl (or @p_215 @p_214)) :rule forall_inst :args (uua$ @p_1))
(step t153 (cl @p_215 @p_214) :rule or :premises (t152))
(step t154 (cl @p_214) :rule resolution :premises (t153 a2))
(step t155 (cl @p_211) :rule resolution :premises (t140 t151 t154))
(step t156 (cl @p_212) :rule resolution :premises (t138 t155))
(step t157 (cl @p_207) :rule trans :premises (t136 t156))
(step t158 (cl @p_76) :rule resolution :premises (t120 t157))
(step t159 (cl (= (! (= @p_303 true) :named @p_351) @p_303)) :rule equiv_simplify)
(step t160 (cl (not @p_351) @p_303) :rule equiv1 :premises (t159))
(step t161 (cl (or (! (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (= (insert$ ?v0 ?v1) (sup$ (insert$ ?v0 bot$) ?v1)))) :named @p_157) (! (= @p_48 @p_299) :named @p_307))) :rule forall_inst :args (@p_6 @p_38))
(step t162 (cl @p_157 @p_307) :rule or :premises (t161))
(step t163 (cl @p_307) :rule resolution :premises (t162 a15))
(step t164 (cl (= @p_299 @p_48)) :rule symm :premises (t163))
(step t165 (cl (or @p_288 @p_287)) :rule forall_inst :args (@p_4 @p_6 bot$))
(step t166 (cl @p_288 @p_287) :rule or :premises (t165))
(step t167 (cl @p_287) :rule resolution :premises (t166 a14))
(step t168 (cl (= @p_48 @p_155)) :rule symm :premises (t167))
(step t169 (cl (= @p_299 @p_155)) :rule trans :premises (t164 t168))
(step t170 (cl (= @p_303 (! (finite$ @p_155) :named @p_264))) :rule cong :premises (t169))
(step t171 (cl (= (! (= @p_264 true) :named @p_265) @p_264)) :rule equiv_simplify)
(step t172 (cl @p_265 (not @p_264)) :rule equiv2 :premises (t171))
(step t173 (cl (! (not (! (or (! (not (! (finite$ @p_37) :named @p_266)) :named @p_267) @p_264) :named @p_268)) :named @p_275) @p_267 @p_264) :rule or_pos)
(step t174 (cl @p_267 @p_264 @p_275) :rule reordering :premises (t173))
(step t175 (cl (! (not (! (or (! (not @p_3) :named @p_272) @p_266) :named @p_273)) :named @p_274) @p_272 @p_266) :rule or_pos)
(step t176 (cl @p_272 @p_266 @p_274) :rule reordering :premises (t175))
(step t177 (cl (or (! (not (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (or (not (finite$ ?v0)) (finite$ (insert$ ?v1 ?v0))))) :named @p_271) @p_273)) :rule forall_inst :args (bot$ @p_6))
(step t178 (cl @p_271 @p_273) :rule or :premises (t177))
(step t179 (cl (not (! (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (=> (finite$ ?v0) (finite$ (insert$ ?v1 ?v0)))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (or (not (finite$ ?v0)) (finite$ (insert$ ?v1 ?v0))))) :named @p_269)) (not (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (=> (finite$ ?v0) (finite$ (insert$ ?v1 ?v0))))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (or (not (finite$ ?v0)) (finite$ (insert$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t180 :args ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (:= (?v0 Real_real_prod_set$) ?v0) (:= (?v1 Real_real_prod$) ?v1)))
(step t180.t0 (cl (= (=> (! (finite$ ?v0) :named @p_114) (! (finite$ (insert$ ?v1 ?v0)) :named @p_270)) (or (! (not @p_114) :named @p_115) (! (finite$ (insert$ ?v1 ?v0)) :named @p_270)))) :rule rare_rewrite :args ("bool-impl-elim" @p_114 @p_270))
(step t180 (cl @p_269) :rule bind)
(step t181 (cl (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (or (not (finite$ ?v0)) (finite$ (insert$ ?v1 ?v0))))) :rule resolution :premises (t179 t180 a9))
(step t182 (cl @p_273) :rule resolution :premises (t178 t181))
(step t183 (cl @p_266) :rule resolution :premises (t176 a8 t182))
(step t184 (cl (or @p_271 @p_268)) :rule forall_inst :args (@p_37 @p_4))
(step t185 (cl @p_271 @p_268) :rule or :premises (t184))
(step t186 (cl @p_268) :rule resolution :premises (t185 t181))
(step t187 (cl @p_264) :rule resolution :premises (t174 t183 t186))
(step t188 (cl @p_265) :rule resolution :premises (t172 t187))
(step t189 (cl @p_351) :rule trans :premises (t170 t188))
(step t190 (cl @p_303) :rule resolution :premises (t160 t189))
(step t191 (cl (not (! (= (! (or @p_308 (! (not (! (= @p_155 (! (sup$ @p_38 @p_37) :named @p_68)) :named @p_156)) :named @p_170) (! (not @p_307) :named @p_309) (! (not (! (not (! (= @p_73 (! (+ @p_71 (! (line_integral$ f$ @p_68 g$) :named @p_69)) :named @p_72)) :named @p_74)) :named @p_154)) :named @p_174) (! (not @p_302) :named @p_306)) :named @p_311) (! (or @p_308 @p_170 @p_309 @p_74 @p_306) :named @p_310)) :named @p_350)) (not @p_311) @p_310) :rule equiv_pos2)
(step t192 (cl (= @p_174 @p_74)) :rule rare_rewrite :args ("bool-double-not-elim" @p_74))
(step t193 (cl (= @p_306 @p_306)) :rule refl)
(step t194 (cl @p_350) :rule cong :premises (t192 t193))
(step t195 (cl (! (=> (! (and @p_287 @p_156 @p_307 @p_154 @p_302) :named @p_313) (! (and (! (not (! (= @p_72 @p_301) :named @p_316)) :named @p_317) (! (= (! (line_integral$ f$ @p_155 g$) :named @p_159) @p_300) :named @p_315) (! (= @p_159 @p_69) :named @p_181)) :named @p_318)) :named @p_339) @p_313) :rule implies_neg1)
(anchor :step t196)
(assume t196.a0 @p_287)
(assume t196.a1 @p_156)
(assume t196.a2 @p_307)
(assume t196.a3 @p_154)
(assume t196.a4 @p_302)
(step t196.t0 (cl (! (=> (! (and @p_302 @p_154) :named @p_340) @p_317) :named @p_342) @p_340) :rule implies_neg1)
(anchor :step t196.t1)
(assume t196.t1.a0 @p_302)
(assume t196.t1.a1 @p_154)
(step t196.t1.t0 (cl (! (= (! (= @p_316 false) :named @p_343) @p_317) :named @p_348)) :rule equiv_simplify)
(step t196.t1.t1 (cl (not @p_343) @p_317) :rule equiv1 :premises (t196.t1.t0))
(step t196.t1.t2 (cl (not (! (= (! (= (! (= @p_301 @p_72) :named @p_344) false) :named @p_345) @p_343) :named @p_347)) (not @p_345) @p_343) :rule equiv_pos2)
(step t196.t1.t3 (cl (= @p_345 (! (not @p_344) :named @p_349))) :rule rare_rewrite :args ("bool-eq-false" @p_344))
(step t196.t1.t4 (cl (= (* 1/1 (- @p_301 @p_72)) (* -1/1 (! (- @p_69 @p_300) :named @p_331)))) :rule poly_simp)
(step t196.t1.t5 (cl (= @p_344 (! (= @p_69 @p_300) :named @p_323))) :rule poly_simp_rel :premises (t196.t1.t4))
(step t196.t1.t6 (cl (= @p_349 (! (not @p_323) :named @p_325))) :rule cong :premises (t196.t1.t5))
(step t196.t1.t7 (cl (= @p_345 @p_325)) :rule trans :premises (t196.t1.t3 t196.t1.t6))
(step t196.t1.t8 (cl @p_348) :rule rare_rewrite :args ("bool-eq-false" @p_316))
(step t196.t1.t9 (cl (= (* 1/1 (- @p_72 @p_301)) (! (* 1/1 @p_331) :named @p_332))) :rule poly_simp)
(step t196.t1.t10 (cl (= @p_316 @p_323)) :rule poly_simp_rel :premises (t196.t1.t9))
(step t196.t1.t11 (cl (= @p_317 @p_325)) :rule cong :premises (t196.t1.t10))
(step t196.t1.t12 (cl (= @p_343 @p_325)) :rule trans :premises (t196.t1.t8 t196.t1.t11))
(step t196.t1.t13 (cl (= @p_325 @p_343)) :rule symm :premises (t196.t1.t12))
(step t196.t1.t14 (cl @p_347) :rule trans :premises (t196.t1.t7 t196.t1.t13))
(step t196.t1.t15 (cl (= @p_301 @p_73)) :rule symm :premises (t196.t1.a0))
(step t196.t1.t16 (cl (= @p_72 @p_72)) :rule refl)
(step t196.t1.t17 (cl (= @p_344 @p_74)) :rule cong :premises (t196.t1.t15 t196.t1.t16))
(step t196.t1.t18 (cl (= (! (= @p_74 false) :named @p_346) @p_154)) :rule equiv_simplify)
(step t196.t1.t19 (cl @p_346 @p_174) :rule equiv2 :premises (t196.t1.t18))
(step t196.t1.t20 (cl (! (not @p_174) :named @p_312) @p_74) :rule not_not)
(step t196.t1.t21 (cl @p_346 @p_74) :rule resolution :premises (t196.t1.t19 t196.t1.t20))
(step t196.t1.t22 (cl @p_346) :rule resolution :premises (t196.t1.t21 t196.t1.a1))
(step t196.t1.t23 (cl @p_345) :rule trans :premises (t196.t1.t17 t196.t1.t22))
(step t196.t1.t24 (cl @p_343) :rule resolution :premises (t196.t1.t2 t196.t1.t14 t196.t1.t23))
(step t196.t1.t25 (cl @p_317) :rule resolution :premises (t196.t1.t1 t196.t1.t24))
(step t196.t1 (cl @p_306 @p_174 @p_317) :rule subproof :discharge (t196.t1.a0 t196.t1.a1))
(step t196.t2 (cl (! (not @p_340) :named @p_341) @p_302) :rule and_pos :args (0))
(step t196.t3 (cl @p_341 @p_154) :rule and_pos :args (1))
(step t196.t4 (cl @p_317 @p_341 @p_341) :rule resolution :premises (t196.t1 t196.t2 t196.t3))
(step t196.t5 (cl @p_341 @p_341 @p_317) :rule reordering :premises (t196.t4))
(step t196.t6 (cl @p_341 @p_317) :rule contraction :premises (t196.t5))
(step t196.t7 (cl @p_342 @p_317) :rule resolution :premises (t196.t0 t196.t6))
(step t196.t8 (cl @p_342 (! (not @p_317) :named @p_322)) :rule implies_neg2)
(step t196.t9 (cl @p_342 @p_342) :rule resolution :premises (t196.t7 t196.t8))
(step t196.t10 (cl @p_342) :rule contraction :premises (t196.t9))
(step t196.t11 (cl @p_341 @p_317) :rule implies :premises (t196.t10))
(step t196.t12 (cl @p_340) :rule and_intro :premises (t196.a4 t196.a3))
(step t196.t13 (cl @p_317) :rule resolution :premises (t196.t11 t196.t12))
(step t196.t14 (cl (! (or @p_157 @p_156) :named @p_158)) :rule forall_inst :args (@p_4 @p_37))
(step t196.t15 (cl @p_157 @p_156) :rule or :premises (t196.t14))
(step t196.t16 (cl @p_156) :rule resolution :premises (t196.t15 a15))
(step t196.t17 (cl (! (= g$ g$) :named @p_169)) :rule refl)
(step t196.t18 (cl @p_181) :rule cong :premises (t196.t16 t196.t17))
(step t196.t19 (cl (= @p_68 @p_155)) :rule symm :premises (t196.t16))
(step t196.t20 (cl (= @p_155 @p_299)) :rule trans :premises (t167 t163))
(step t196.t21 (cl (= @p_68 @p_299)) :rule trans :premises (t196.t19 t196.t20))
(step t196.t22 (cl @p_323) :rule cong :premises (t196.t21 t196.t17))
(step t196.t23 (cl @p_315) :rule trans :premises (t196.t18 t196.t22))
(step t196.t24 (cl @p_318) :rule and_intro :premises (t196.t13 t196.t23 t196.t18))
(step t196 (cl @p_308 @p_170 @p_309 @p_174 @p_306 @p_318) :rule subproof :discharge (t196.a0 t196.a1 t196.a2 t196.a3 t196.a4))
(step t197 (cl (! (not @p_313) :named @p_314) @p_287) :rule and_pos :args (0))
(step t198 (cl @p_314 @p_156) :rule and_pos :args (1))
(step t199 (cl @p_314 @p_307) :rule and_pos :args (2))
(step t200 (cl @p_314 @p_154) :rule and_pos :args (3))
(step t201 (cl @p_314 @p_302) :rule and_pos :args (4))
(step t202 (cl @p_318 @p_314 @p_314 @p_314 @p_314 @p_314) :rule resolution :premises (t196 t197 t198 t199 t200 t201))
(step t203 (cl @p_314 @p_314 @p_314 @p_314 @p_314 @p_318) :rule reordering :premises (t202))
(step t204 (cl @p_314 @p_318) :rule contraction :premises (t203))
(step t205 (cl @p_339 @p_318) :rule resolution :premises (t195 t204))
(step t206 (cl @p_339 (! (not @p_318) :named @p_319)) :rule implies_neg2)
(step t207 (cl @p_339 @p_339) :rule resolution :premises (t205 t206))
(step t208 (cl @p_339) :rule contraction :premises (t207))
(step t209 (cl @p_314 @p_318) :rule implies :premises (t208))
(step t210 (cl (not (! (= (! (=> @p_318 (! (= true false) :named @p_320)) :named @p_321) @p_319) :named @p_335)) (not @p_321) @p_319) :rule equiv_pos2)
(step t211 (cl (= (* 1/1 (- @p_72 @p_301)) @p_332)) :rule poly_simp)
(step t212 (cl (= @p_316 @p_323)) :rule poly_simp_rel :premises (t211))
(step t213 (cl (= @p_317 @p_325)) :rule cong :premises (t212))
(step t214 (cl (= @p_315 @p_315)) :rule refl)
(step t215 (cl (= @p_181 @p_181)) :rule refl)
(step t216 (cl (= @p_318 (! (and @p_325 @p_315 @p_181) :named @p_336))) :rule cong :premises (t213 t214 t215))
(step t217 (cl (= @p_320 false)) :rule evaluate)
(step t218 (cl (= @p_321 (! (=> @p_336 false) :named @p_338))) :rule cong :premises (t216 t217))
(step t219 (cl (= @p_338 (! (not @p_336) :named @p_337))) :rule rare_rewrite :args ("bool-impl-false1" @p_336))
(step t220 (cl (= @p_321 @p_337)) :rule trans :premises (t218 t219))
(step t221 (cl (= @p_319 @p_337)) :rule cong :premises (t216))
(step t222 (cl (= @p_337 @p_319)) :rule symm :premises (t221))
(step t223 (cl @p_335) :rule trans :premises (t220 t222))
(step t224 (cl @p_321 @p_318) :rule implies_neg1)
(anchor :step t225)
(assume t225.a0 @p_317)
(assume t225.a1 @p_315)
(assume t225.a2 @p_181)
(step t225.t0 (cl (= (! (= @p_323 true) :named @p_334) @p_323)) :rule equiv_simplify)
(step t225.t1 (cl @p_334 @p_325) :rule equiv2 :premises (t225.t0))
(step t225.t2 (cl @p_158) :rule forall_inst :args (@p_4 @p_37))
(step t225.t3 (cl @p_157 @p_156) :rule or :premises (t225.t2))
(step t225.t4 (cl @p_156) :rule resolution :premises (t225.t3 a15))
(step t225.t5 (cl (= @p_68 @p_155)) :rule symm :premises (t225.t4))
(step t225.t6 (cl (= @p_155 @p_299)) :rule trans :premises (t167 t163))
(step t225.t7 (cl (= @p_68 @p_299)) :rule trans :premises (t225.t5 t225.t6))
(step t225.t8 (cl @p_169) :rule refl)
(step t225.t9 (cl @p_323) :rule cong :premises (t225.t7 t225.t8))
(step t225.t10 (cl @p_334) :rule resolution :premises (t225.t1 t225.t9))
(step t225.t11 (cl (= true @p_323)) :rule symm :premises (t225.t10))
(step t225.t12 (cl (= (! (= @p_323 false) :named @p_324) @p_325)) :rule equiv_simplify)
(step t225.t13 (cl @p_324 (! (not @p_325) :named @p_333)) :rule equiv2 :premises (t225.t12))
(step t225.t14 (cl (not @p_333) @p_323) :rule not_not)
(step t225.t15 (cl @p_324 @p_323) :rule resolution :premises (t225.t13 t225.t14))
(step t225.t16 (cl (not (! (= (! (not (! (= (! (+ @p_69 (* -1/1 @p_300)) :named @p_326) 0/1) :named @p_327)) :named @p_328) @p_325) :named @p_330)) (not @p_328) @p_325) :rule equiv_pos2)
(step t225.t17 (cl (= (* 1/1 (- @p_326 0/1)) @p_332)) :rule poly_simp)
(step t225.t18 (cl (= @p_327 @p_323)) :rule poly_simp_rel :premises (t225.t17))
(step t225.t19 (cl @p_330) :rule cong :premises (t225.t18))
(step t225.t20 (cl (not (! (= @p_317 @p_328) :named @p_329)) @p_322 @p_328) :rule equiv_pos2)
(step t225.t21 (cl (= @p_325 @p_328)) :rule symm :premises (t225.t19))
(step t225.t22 (cl @p_329) :rule trans :premises (t213 t225.t21))
(step t225.t23 (cl @p_328) :rule resolution :premises (t225.t20 t225.t22 t225.a0))
(step t225.t24 (cl @p_325) :rule resolution :premises (t225.t16 t225.t19 t225.t23))
(step t225.t25 (cl @p_324) :rule resolution :premises (t225.t15 t225.t24))
(step t225.t26 (cl @p_320) :rule trans :premises (t225.t11 t225.t25))
(step t225 (cl @p_322 (not @p_315) (! (not @p_181) :named @p_186) @p_320) :rule subproof :discharge (t225.a0 t225.a1 t225.a2))
(step t226 (cl @p_319 @p_317) :rule and_pos :args (0))
(step t227 (cl @p_319 @p_315) :rule and_pos :args (1))
(step t228 (cl @p_319 @p_181) :rule and_pos :args (2))
(step t229 (cl @p_320 @p_319 @p_319 @p_319) :rule resolution :premises (t225 t226 t227 t228))
(step t230 (cl @p_319 @p_319 @p_319 @p_320) :rule reordering :premises (t229))
(step t231 (cl @p_319 @p_320) :rule contraction :premises (t230))
(step t232 (cl @p_321 @p_320) :rule resolution :premises (t224 t231))
(step t233 (cl @p_321 (not @p_320)) :rule implies_neg2)
(step t234 (cl @p_321 @p_321) :rule resolution :premises (t232 t233))
(step t235 (cl @p_321) :rule contraction :premises (t234))
(step t236 (cl @p_319) :rule resolution :premises (t210 t223 t235))
(step t237 (cl @p_314) :rule resolution :premises (t209 t236))
(step t238 (cl @p_308 @p_170 @p_309 @p_174 @p_306) :rule not_and :premises (t237))
(step t239 (cl @p_311 (not @p_308)) :rule or_neg :args (0))
(step t240 (cl @p_311 (! (not @p_170) :named @p_175)) :rule or_neg :args (1))
(step t241 (cl @p_311 (not @p_309)) :rule or_neg :args (2))
(step t242 (cl @p_311 @p_312) :rule or_neg :args (3))
(step t243 (cl @p_311 (not @p_306)) :rule or_neg :args (4))
(step t244 (cl @p_311 @p_311 @p_311 @p_311 @p_311) :rule resolution :premises (t238 t239 t240 t241 t242 t243))
(step t245 (cl @p_311) :rule contraction :premises (t244))
(step t246 (cl @p_310) :rule resolution :premises (t191 t194 t245))
(step t247 (cl @p_308 @p_170 @p_309 @p_74 @p_306) :rule or :premises (t246))
(step t248 (cl @p_308 @p_170 @p_74 @p_309 @p_306) :rule reordering :premises (t247))
(step t249 (cl @p_158) :rule forall_inst :args (@p_4 @p_37))
(step t250 (cl @p_157 @p_156) :rule or :premises (t249))
(step t251 (cl @p_156) :rule resolution :premises (t250 a15))
(step t252 (cl (not (! (= (! (or (! (not (! (not (! (= @p_73 (! (+ @p_71 @p_159) :named @p_160)) :named @p_161)) :named @p_162)) :named @p_172) @p_170 @p_154) :named @p_173) (! (or @p_161 @p_170 @p_154) :named @p_171)) :named @p_206)) (not @p_173) @p_171) :rule equiv_pos2)
(step t253 (cl (= @p_172 @p_161)) :rule rare_rewrite :args ("bool-double-not-elim" @p_161))
(step t254 (cl (= @p_170 @p_170)) :rule refl)
(step t255 (cl (= @p_154 @p_154)) :rule refl)
(step t256 (cl @p_206) :rule cong :premises (t253 t254 t255))
(step t257 (cl (! (=> (! (and @p_162 @p_156 @p_74) :named @p_177) (! (and @p_181 (! (not (! (= @p_160 @p_72) :named @p_179)) :named @p_180)) :named @p_182)) :named @p_195) @p_177) :rule implies_neg1)
(anchor :step t258)
(assume t258.a0 @p_162)
(assume t258.a1 @p_156)
(assume t258.a2 @p_74)
(step t258.t0 (cl @p_169) :rule refl)
(step t258.t1 (cl @p_181) :rule cong :premises (t251 t258.t0))
(step t258.t2 (cl (! (=> (! (and @p_74 @p_162) :named @p_196) @p_180) :named @p_198) @p_196) :rule implies_neg1)
(anchor :step t258.t3)
(assume t258.t3.a0 @p_74)
(assume t258.t3.a1 @p_162)
(step t258.t3.t0 (cl (! (= (! (= @p_179 false) :named @p_199) @p_180) :named @p_204)) :rule equiv_simplify)
(step t258.t3.t1 (cl (not @p_199) @p_180) :rule equiv1 :premises (t258.t3.t0))
(step t258.t3.t2 (cl (not (! (= (! (= (! (= @p_72 @p_160) :named @p_200) false) :named @p_201) @p_199) :named @p_203)) (not @p_201) @p_199) :rule equiv_pos2)
(step t258.t3.t3 (cl (= @p_201 (! (not @p_200) :named @p_205))) :rule rare_rewrite :args ("bool-eq-false" @p_200))
(step t258.t3.t4 (cl (= (* 1/1 (- @p_72 @p_160)) (* -1/1 (! (- @p_159 @p_69) :named @p_192)))) :rule poly_simp)
(step t258.t3.t5 (cl (= @p_200 @p_181)) :rule poly_simp_rel :premises (t258.t3.t4))
(step t258.t3.t6 (cl (= @p_205 @p_186)) :rule cong :premises (t258.t3.t5))
(step t258.t3.t7 (cl (= @p_201 @p_186)) :rule trans :premises (t258.t3.t3 t258.t3.t6))
(step t258.t3.t8 (cl @p_204) :rule rare_rewrite :args ("bool-eq-false" @p_179))
(step t258.t3.t9 (cl (= (* 1/1 (- @p_160 @p_72)) (! (* 1/1 @p_192) :named @p_193))) :rule poly_simp)
(step t258.t3.t10 (cl (= @p_179 @p_181)) :rule poly_simp_rel :premises (t258.t3.t9))
(step t258.t3.t11 (cl (= @p_180 @p_186)) :rule cong :premises (t258.t3.t10))
(step t258.t3.t12 (cl (= @p_199 @p_186)) :rule trans :premises (t258.t3.t8 t258.t3.t11))
(step t258.t3.t13 (cl (= @p_186 @p_199)) :rule symm :premises (t258.t3.t12))
(step t258.t3.t14 (cl @p_203) :rule trans :premises (t258.t3.t7 t258.t3.t13))
(step t258.t3.t15 (cl (= @p_72 @p_73)) :rule symm :premises (t258.t3.a0))
(step t258.t3.t16 (cl (= @p_160 @p_160)) :rule refl)
(step t258.t3.t17 (cl (= @p_200 @p_161)) :rule cong :premises (t258.t3.t15 t258.t3.t16))
(step t258.t3.t18 (cl (= (! (= @p_161 false) :named @p_202) @p_162)) :rule equiv_simplify)
(step t258.t3.t19 (cl @p_202 @p_172) :rule equiv2 :premises (t258.t3.t18))
(step t258.t3.t20 (cl (! (not @p_172) :named @p_176) @p_161) :rule not_not)
(step t258.t3.t21 (cl @p_202 @p_161) :rule resolution :premises (t258.t3.t19 t258.t3.t20))
(step t258.t3.t22 (cl (not (! (= @p_20 @p_162) :named @p_163)) (not @p_20) @p_162) :rule equiv_pos2)
(step t258.t3.t23 (cl (= bot$ bot$)) :rule refl)
(step t258.t3.t24 (cl (= @p_12 @p_37)) :rule cong :premises (a12 t258.t3.t23))
(step t258.t3.t25 (cl (= @p_17 @p_155)) :rule cong :premises (a10 t258.t3.t24))
(step t258.t3.t26 (cl (= @p_18 @p_159)) :rule cong :premises (t258.t3.t25 t258.t0))
(step t258.t3.t27 (cl (= @p_9 @p_38)) :rule cong :premises (a10 t258.t3.t23))
(step t258.t3.t28 (cl (= @p_15 @p_70)) :rule cong :premises (t258.t3.t27 t258.t0))
(step t258.t3.t29 (cl (= @p_14 @p_73)) :rule cong :premises (t258.t3.t24 t258.t0))
(step t258.t3.t30 (cl (= @p_16 (! (+ @p_70 @p_73) :named @p_164))) :rule cong :premises (t258.t3.t28 t258.t3.t29))
(step t258.t3.t31 (cl (= @p_19 (! (= @p_159 @p_164) :named @p_165))) :rule cong :premises (t258.t3.t26 t258.t3.t30))
(step t258.t3.t32 (cl (= @p_20 (! (not @p_165) :named @p_166))) :rule cong :premises (t258.t3.t31))
(step t258.t3.t33 (cl (= @p_164 (! (+ @p_73 @p_70) :named @p_167))) :rule poly_simp)
(step t258.t3.t34 (cl (= @p_165 (! (= @p_159 @p_167) :named @p_168))) :rule cong :premises (t258.t3.t33))
(step t258.t3.t35 (cl (= (* 1/1 (- @p_159 @p_167)) (* -1/1 (- @p_73 @p_160)))) :rule poly_simp)
(step t258.t3.t36 (cl (= @p_168 @p_161)) :rule poly_simp_rel :premises (t258.t3.t35))
(step t258.t3.t37 (cl (= @p_165 @p_161)) :rule trans :premises (t258.t3.t34 t258.t3.t36))
(step t258.t3.t38 (cl (= @p_166 @p_162)) :rule cong :premises (t258.t3.t37))
(step t258.t3.t39 (cl @p_163) :rule trans :premises (t258.t3.t32 t258.t3.t38))
(step t258.t3.t40 (cl @p_162) :rule resolution :premises (t258.t3.t22 t258.t3.t39 a19))
(step t258.t3.t41 (cl @p_202) :rule resolution :premises (t258.t3.t21 t258.t3.t40))
(step t258.t3.t42 (cl @p_201) :rule trans :premises (t258.t3.t17 t258.t3.t41))
(step t258.t3.t43 (cl @p_199) :rule resolution :premises (t258.t3.t2 t258.t3.t14 t258.t3.t42))
(step t258.t3.t44 (cl @p_180) :rule resolution :premises (t258.t3.t1 t258.t3.t43))
(step t258.t3 (cl @p_154 @p_172 @p_180) :rule subproof :discharge (t258.t3.a0 t258.t3.a1))
(step t258.t4 (cl (! (not @p_196) :named @p_197) @p_74) :rule and_pos :args (0))
(step t258.t5 (cl @p_197 @p_162) :rule and_pos :args (1))
(step t258.t6 (cl @p_180 @p_197 @p_197) :rule resolution :premises (t258.t3 t258.t4 t258.t5))
(step t258.t7 (cl @p_197 @p_197 @p_180) :rule reordering :premises (t258.t6))
(step t258.t8 (cl @p_197 @p_180) :rule contraction :premises (t258.t7))
(step t258.t9 (cl @p_198 @p_180) :rule resolution :premises (t258.t2 t258.t8))
(step t258.t10 (cl @p_198 (! (not @p_180) :named @p_187)) :rule implies_neg2)
(step t258.t11 (cl @p_198 @p_198) :rule resolution :premises (t258.t9 t258.t10))
(step t258.t12 (cl @p_198) :rule contraction :premises (t258.t11))
(step t258.t13 (cl @p_197 @p_180) :rule implies :premises (t258.t12))
(step t258.t14 (cl (not @p_163) (not @p_20) @p_162) :rule equiv_pos2)
(step t258.t15 (cl (= bot$ bot$)) :rule refl)
(step t258.t16 (cl (= @p_12 @p_37)) :rule cong :premises (a12 t258.t15))
(step t258.t17 (cl (= @p_17 @p_155)) :rule cong :premises (a10 t258.t16))
(step t258.t18 (cl (= @p_18 @p_159)) :rule cong :premises (t258.t17 t258.t0))
(step t258.t19 (cl (= @p_9 @p_38)) :rule cong :premises (a10 t258.t15))
(step t258.t20 (cl (= @p_15 @p_70)) :rule cong :premises (t258.t19 t258.t0))
(step t258.t21 (cl (= @p_14 @p_73)) :rule cong :premises (t258.t16 t258.t0))
(step t258.t22 (cl (= @p_16 @p_164)) :rule cong :premises (t258.t20 t258.t21))
(step t258.t23 (cl (= @p_19 @p_165)) :rule cong :premises (t258.t18 t258.t22))
(step t258.t24 (cl (= @p_20 @p_166)) :rule cong :premises (t258.t23))
(step t258.t25 (cl (= @p_164 @p_167)) :rule poly_simp)
(step t258.t26 (cl (= @p_165 @p_168)) :rule cong :premises (t258.t25))
(step t258.t27 (cl (= (* 1/1 (- @p_159 @p_167)) (* -1/1 (- @p_73 @p_160)))) :rule poly_simp)
(step t258.t28 (cl (= @p_168 @p_161)) :rule poly_simp_rel :premises (t258.t27))
(step t258.t29 (cl (= @p_165 @p_161)) :rule trans :premises (t258.t26 t258.t28))
(step t258.t30 (cl (= @p_166 @p_162)) :rule cong :premises (t258.t29))
(step t258.t31 (cl @p_163) :rule trans :premises (t258.t24 t258.t30))
(step t258.t32 (cl @p_162) :rule resolution :premises (t258.t14 t258.t31 a19))
(step t258.t33 (cl @p_196) :rule and_intro :premises (t258.a2 t258.t32))
(step t258.t34 (cl @p_180) :rule resolution :premises (t258.t13 t258.t33))
(step t258.t35 (cl @p_182) :rule and_intro :premises (t258.t1 t258.t34))
(step t258 (cl @p_172 @p_170 @p_154 @p_182) :rule subproof :discharge (t258.a0 t258.a1 t258.a2))
(step t259 (cl (! (not @p_177) :named @p_178) @p_162) :rule and_pos :args (0))
(step t260 (cl @p_178 @p_156) :rule and_pos :args (1))
(step t261 (cl @p_178 @p_74) :rule and_pos :args (2))
(step t262 (cl @p_182 @p_178 @p_178 @p_178) :rule resolution :premises (t258 t259 t260 t261))
(step t263 (cl @p_178 @p_178 @p_178 @p_182) :rule reordering :premises (t262))
(step t264 (cl @p_178 @p_182) :rule contraction :premises (t263))
(step t265 (cl @p_195 @p_182) :rule resolution :premises (t257 t264))
(step t266 (cl @p_195 (! (not @p_182) :named @p_183)) :rule implies_neg2)
(step t267 (cl @p_195 @p_195) :rule resolution :premises (t265 t266))
(step t268 (cl @p_195) :rule contraction :premises (t267))
(step t269 (cl @p_178 @p_182) :rule implies :premises (t268))
(step t270 (cl (! (=> @p_182 false) :named @p_184) @p_182) :rule implies_neg1)
(anchor :step t271)
(assume t271.a0 @p_181)
(assume t271.a1 @p_180)
(step t271.t0 (cl (not (! (= @p_181 (! (= (! (+ @p_159 (* -1/1 @p_69)) :named @p_188) 0/1) :named @p_189)) :named @p_194)) @p_186 @p_189) :rule equiv_pos2)
(step t271.t1 (cl (= (* 1/1 (- @p_188 0/1)) @p_193)) :rule poly_simp)
(step t271.t2 (cl (= @p_189 @p_181)) :rule poly_simp_rel :premises (t271.t1))
(step t271.t3 (cl @p_194) :rule symm :premises (t271.t2))
(step t271.t4 (cl @p_158) :rule forall_inst :args (@p_4 @p_37))
(step t271.t5 (cl @p_157 @p_156) :rule or :premises (t271.t4))
(step t271.t6 (cl @p_156) :rule resolution :premises (t271.t5 a15))
(step t271.t7 (cl @p_169) :rule refl)
(step t271.t8 (cl @p_181) :rule cong :premises (t271.t6 t271.t7))
(step t271.t9 (cl @p_189) :rule resolution :premises (t271.t0 t271.t3 t271.t8))
(step t271.t10 (cl (not (! (= @p_180 (! (not @p_189) :named @p_190)) :named @p_191)) @p_187 @p_190) :rule equiv_pos2)
(step t271.t11 (cl (= (* 1/1 (- @p_160 @p_72)) @p_193)) :rule poly_simp)
(step t271.t12 (cl (= @p_179 @p_181)) :rule poly_simp_rel :premises (t271.t11))
(step t271.t13 (cl (= @p_180 @p_186)) :rule cong :premises (t271.t12))
(step t271.t14 (cl (= @p_190 @p_186)) :rule cong :premises (t271.t2))
(step t271.t15 (cl (= @p_186 @p_190)) :rule symm :premises (t271.t14))
(step t271.t16 (cl @p_191) :rule trans :premises (t271.t13 t271.t15))
(step t271.t17 (cl @p_190) :rule resolution :premises (t271.t10 t271.t16 t271.a1))
(step t271.t18 (cl) :rule resolution :premises (t271.t9 t271.t17))
(step t271 (cl @p_186 @p_187 false) :rule subproof :discharge (t271.a0 t271.a1))
(step t272 (cl @p_183 @p_181) :rule and_pos :args (0))
(step t273 (cl @p_183 @p_180) :rule and_pos :args (1))
(step t274 (cl false @p_183 @p_183) :rule resolution :premises (t271 t272 t273))
(step t275 (cl @p_183 @p_183 false) :rule reordering :premises (t274))
(step t276 (cl @p_183 false) :rule contraction :premises (t275))
(step t277 (cl @p_184 false) :rule resolution :premises (t270 t276))
(step t278 (cl @p_184 @p_185) :rule implies_neg2)
(step t279 (cl @p_184 @p_184) :rule resolution :premises (t277 t278))
(step t280 (cl @p_184) :rule contraction :premises (t279))
(step t281 (cl (= @p_184 @p_183)) :rule implies_simplify)
(step t282 (cl (not @p_184) @p_183) :rule equiv1 :premises (t281))
(step t283 (cl @p_183) :rule resolution :premises (t280 t282))
(step t284 (cl @p_178) :rule resolution :premises (t269 t283))
(step t285 (cl @p_172 @p_170 @p_154) :rule not_and :premises (t284))
(step t286 (cl @p_173 @p_176) :rule or_neg :args (0))
(step t287 (cl @p_173 @p_175) :rule or_neg :args (1))
(step t288 (cl @p_173 @p_174) :rule or_neg :args (2))
(step t289 (cl @p_173 @p_173 @p_173) :rule resolution :premises (t285 t286 t287 t288))
(step t290 (cl @p_173) :rule contraction :premises (t289))
(step t291 (cl @p_171) :rule resolution :premises (t252 t256 t290))
(step t292 (cl @p_161 @p_170 @p_154) :rule or :premises (t291))
(step t293 (cl (not @p_163) (not @p_20) @p_162) :rule equiv_pos2)
(step t294 (cl (= bot$ bot$)) :rule refl)
(step t295 (cl (= @p_12 @p_37)) :rule cong :premises (a12 t294))
(step t296 (cl (= @p_17 @p_155)) :rule cong :premises (a10 t295))
(step t297 (cl @p_169) :rule refl)
(step t298 (cl (= @p_18 @p_159)) :rule cong :premises (t296 t297))
(step t299 (cl (= @p_9 @p_38)) :rule cong :premises (a10 t294))
(step t300 (cl (= @p_15 @p_70)) :rule cong :premises (t299 t297))
(step t301 (cl (= @p_14 @p_73)) :rule cong :premises (t295 t297))
(step t302 (cl (= @p_16 @p_164)) :rule cong :premises (t300 t301))
(step t303 (cl (= @p_19 @p_165)) :rule cong :premises (t298 t302))
(step t304 (cl (= @p_20 @p_166)) :rule cong :premises (t303))
(step t305 (cl (= @p_164 @p_167)) :rule poly_simp)
(step t306 (cl (= @p_165 @p_168)) :rule cong :premises (t305))
(step t307 (cl (= (* 1/1 (- @p_159 @p_167)) (* -1/1 (- @p_73 @p_160)))) :rule poly_simp)
(step t308 (cl (= @p_168 @p_161)) :rule poly_simp_rel :premises (t307))
(step t309 (cl (= @p_165 @p_161)) :rule trans :premises (t306 t308))
(step t310 (cl (= @p_166 @p_162)) :rule cong :premises (t309))
(step t311 (cl @p_163) :rule trans :premises (t304 t310))
(step t312 (cl @p_162) :rule resolution :premises (t293 t311 a19))
(step t313 (cl @p_154) :rule resolution :premises (t292 t312 t251))
(step t314 (cl @p_306) :rule resolution :premises (t248 t167 t251 t313 t163))
(step t315 (cl (or (! (not (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3)))))) :named @p_147) @p_305)) :rule forall_inst :args (f$ @p_37 g$ @p_38))
(step t316 (cl @p_147 @p_305) :rule or :premises (t315))
(step t317 (cl (not (! (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (and (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (and (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (and (= (sup$ ?v2 ?v4) ?v0) (= (inf$ ?v2 ?v4) bot$))))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3)))))) :named @p_84)) (not (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (and (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (and (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (and (= (sup$ ?v2 ?v4) ?v0) (= (inf$ ?v2 ?v4) bot$))))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3)))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3)))))) :rule equiv_pos2)
(anchor :step t318 :args ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (:= (?v0 Real_real_prod_set$) ?v0) (:= (?v1 Real_real_prod_real_real_prod_fun$) ?v1) (:= (?v2 Real_real_prod_set$) ?v2) (:= (?v3 Real_real_real_prod_fun$) ?v3) (:= (?v4 Real_real_prod_set$) ?v4)))
(step t318.t0 (cl (= (! (and (! (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) :named @p_98) (and (! (= (! (sup$ ?v2 ?v4) :named @p_89) ?v0) :named @p_138) (! (= (! (inf$ ?v2 ?v4) :named @p_95) bot$) :named @p_137))) :named @p_139) (! (and @p_98 @p_138 @p_137) :named @p_145))) :rule aci_simp)
(step t318.t1 (cl (= (! (and (! (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) :named @p_100) @p_139) :named @p_140) (! (and @p_100 @p_145) :named @p_146))) :rule cong :premises (t318.t0))
(step t318.t2 (cl (= @p_146 (! (and @p_100 @p_98 @p_138 @p_137) :named @p_143))) :rule aci_simp)
(step t318.t3 (cl (= @p_140 @p_143)) :rule trans :premises (t318.t1 t318.t2))
(step t318.t4 (cl (= (! (and @p_114 @p_140) :named @p_141) (! (and @p_114 @p_143) :named @p_144))) :rule cong :premises (t318.t3))
(step t318.t5 (cl (= @p_144 (! (and @p_114 @p_100 @p_98 @p_138 @p_137) :named @p_142))) :rule aci_simp)
(step t318.t6 (cl (= @p_141 @p_142)) :rule trans :premises (t318.t4 t318.t5))
(step t318.t7 (cl (= @p_138 (! (= ?v0 @p_89) :named @p_111))) :rule rare_rewrite :args ("eq-symm" @p_89 ?v0))
(step t318.t8 (cl (= @p_137 (! (= bot$ @p_95) :named @p_96))) :rule rare_rewrite :args ("eq-symm" @p_95 bot$))
(step t318.t9 (cl (= @p_142 (! (and @p_114 @p_100 @p_98 @p_111 @p_96) :named @p_120))) :rule cong :premises (t318.t7 t318.t8))
(step t318.t10 (cl (= @p_141 @p_120)) :rule trans :premises (t318.t6 t318.t9))
(step t318.t11 (cl (! (= (! (= (line_integral$ ?v1 ?v0 ?v3) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_93) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_91)) :named @p_104)) :named @p_112) @p_112) :named @p_126)) :rule refl)
(step t318.t12 (cl (= (=> @p_141 @p_112) (! (=> @p_120 @p_112) :named @p_121))) :rule cong :premises (t318.t10 t318.t11))
(step t318 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (and (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (and (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (and (= (sup$ ?v2 ?v4) ?v0) (= (inf$ ?v2 ?v4) bot$))))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (= ?v0 (sup$ ?v2 ?v4)) (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule bind)
(anchor :step t319 :args ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (:= (?v0 Real_real_prod_set$) ?v0) (:= (?v1 Real_real_prod_real_real_prod_fun$) ?v1) (:= (?v2 Real_real_prod_set$) ?v2) (:= (?v3 Real_real_real_prod_fun$) ?v3) (:= (?v4 Real_real_prod_set$) ?v4)))
(step t319.t0 (cl (= @p_121 (! (or (! (not @p_120) :named @p_122) @p_112) :named @p_123))) :rule rare_rewrite :args ("bool-impl-elim" @p_120 @p_112))
(step t319.t1 (cl (= @p_122 (! (or @p_115 (! (not (and @p_100 @p_98 @p_111 @p_96)) :named @p_131)) :named @p_132))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_114 @p_100 (rare-list @p_98 @p_111 @p_96)))
(step t319.t2 (cl (= @p_131 (! (or (! (not @p_100) :named @p_101) (! (not (and @p_98 @p_111 @p_96)) :named @p_133)) :named @p_134))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_100 @p_98 (rare-list @p_111 @p_96)))
(step t319.t3 (cl (= @p_133 (! (or (! (not @p_98) :named @p_99) (! (not (and @p_111 @p_96)) :named @p_135)) :named @p_136))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_98 @p_111 (rare-list @p_96)))
(step t319.t4 (cl (= @p_135 (! (or (! (not @p_111) :named @p_113) (! (not @p_96) :named @p_97)) :named @p_127))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_111 @p_96 rare-list))
(step t319.t5 (cl (= @p_136 (! (or @p_99 @p_127) :named @p_128))) :rule cong :premises (t319.t4))
(step t319.t6 (cl (= @p_133 @p_128)) :rule trans :premises (t319.t3 t319.t5))
(step t319.t7 (cl (= @p_134 (! (or @p_101 @p_128) :named @p_129))) :rule cong :premises (t319.t6))
(step t319.t8 (cl (= @p_131 @p_129)) :rule trans :premises (t319.t2 t319.t7))
(step t319.t9 (cl (= @p_132 (! (or @p_115 @p_129) :named @p_130))) :rule cong :premises (t319.t8))
(step t319.t10 (cl (= @p_122 @p_130)) :rule trans :premises (t319.t1 t319.t9))
(step t319.t11 (cl (= @p_130 (! (or @p_115 @p_101 @p_99 @p_113 @p_97) :named @p_124))) :rule aci_simp)
(step t319.t12 (cl (= @p_122 @p_124)) :rule trans :premises (t319.t10 t319.t11))
(step t319.t13 (cl @p_126) :rule refl)
(step t319.t14 (cl (= @p_123 (! (or @p_124 @p_112) :named @p_125))) :rule cong :premises (t319.t12 t319.t13))
(step t319.t15 (cl (= @p_125 (! (or @p_115 @p_101 @p_99 @p_113 @p_97 @p_112) :named @p_119))) :rule aci_simp)
(step t319.t16 (cl (= @p_123 @p_119)) :rule trans :premises (t319.t14 t319.t15))
(step t319.t17 (cl (= @p_121 @p_119)) :rule trans :premises (t319.t0 t319.t16))
(step t319 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (= ?v0 (sup$ ?v2 ?v4)) (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule bind)
(step t320 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule qnt_rm_unused)
(step t321 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule symm :premises (t320))
(step t322 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule qnt_rm_unused)
(step t323 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule trans :premises (t321 t322))
(step t324 (cl (= (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (forall ((?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3)))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule qnt_join)
(step t325 (cl (= (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (forall ((?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3)))))))) :rule symm :premises (t324))
(anchor :step t326 :args ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (:= (?v1 Real_real_prod_real_real_prod_fun$) ?v1) (:= (?v2 Real_real_prod_set$) ?v2) (:= (?v3 Real_real_real_prod_fun$) ?v3) (:= (?v4 Real_real_prod_set$) ?v4)))
(anchor :step t326.t0 :args ((?v0 Real_real_prod_set$) (:= (?v0 Real_real_prod_set$) ?v0)))
(step t326.t0.t0 (cl (= @p_119 (! (or @p_113 @p_115 @p_101 @p_99 @p_113 @p_97 @p_112) :named @p_116))) :rule aci_simp)
(step t326.t0 (cl (= (forall ((?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v0 Real_real_prod_set$)) (or (not (= ?v0 (sup$ ?v2 ?v4))) (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule bind)
(anchor :step t326.t1 :args ((:= (?v0 Real_real_prod_set$) @p_89)))
(step t326.t1.t0 (cl (= @p_116 (! (or (! (not (! (= @p_89 @p_89) :named @p_106)) :named @p_107) (! (not (finite$ @p_89)) :named @p_102) @p_101 @p_99 @p_107 @p_97 (! (= (! (line_integral$ ?v1 @p_89 ?v3) :named @p_90) @p_104) :named @p_105)) :named @p_117))) :rule refl)
(step t326.t1.t1 (cl (= @p_117 (! (or @p_102 @p_101 @p_99 @p_107 @p_97 @p_105) :named @p_108))) :rule rare_rewrite :args ("or-not-refl" @p_89 (rare-list @p_102 @p_101 @p_99 @p_107 @p_97 @p_105)))
(step t326.t1.t2 (cl (= @p_116 @p_108)) :rule trans :premises (t326.t1.t0 t326.t1.t1))
(step t326.t1 (cl (= (forall ((?v0 Real_real_prod_set$)) (or (not (= ?v0 (sup$ ?v2 ?v4))) (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) @p_108)) :rule onepoint)
(step t326.t2 (cl (= (forall ((?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) @p_108)) :rule trans :premises (t326.t0 t326.t1))
(step t326 (cl (= (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (forall ((?v0 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3)))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= (sup$ ?v2 ?v4) (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule bind)
(step t327 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= (sup$ ?v2 ?v4) (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))))) :rule trans :premises (t323 t325 t326))
(anchor :step t328 :args ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$) (:= (?v1 Real_real_prod_real_real_prod_fun$) ?v1) (:= (?v2 Real_real_prod_set$) ?v2) (:= (?v3 Real_real_real_prod_fun$) ?v3) (:= (?v4 Real_real_prod_set$) ?v4)))
(step t328.t0 (cl (= @p_106 true)) :rule rare_rewrite :args ("eq-refl" @p_89))
(step t328.t1 (cl (= @p_107 (! (not true) :named @p_110))) :rule cong :premises (t328.t0))
(step t328.t2 (cl (= @p_110 false)) :rule evaluate)
(step t328.t3 (cl (= @p_107 false)) :rule trans :premises (t328.t1 t328.t2))
(step t328.t4 (cl (= @p_97 @p_97)) :rule refl)
(step t328.t5 (cl (= (* 1/1 (- @p_90 @p_104)) (* -1/1 (- @p_93 (! (+ (* -1/1 @p_91) @p_90) :named @p_92))))) :rule poly_simp)
(step t328.t6 (cl (= @p_105 (! (= @p_93 @p_92) :named @p_94))) :rule poly_simp_rel :premises (t328.t5))
(step t328.t7 (cl (= @p_108 (! (or @p_102 @p_101 @p_99 false @p_97 @p_94) :named @p_109))) :rule cong :premises (t328.t3 t328.t4 t328.t6))
(step t328.t8 (cl (= @p_109 (! (or @p_102 @p_101 @p_99 @p_97 @p_94) :named @p_103))) :rule aci_simp)
(step t328.t9 (cl (= @p_108 @p_103)) :rule trans :premises (t328.t7 t328.t8))
(step t328 (cl (= (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= (sup$ ?v2 ?v4) (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))))) :rule bind)
(step t329 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ ?v0)) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= ?v0 (sup$ ?v2 ?v4))) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))))) :rule trans :premises (t327 t328))
(step t330 (cl (= (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (=> (and (finite$ ?v0) (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3) (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3) (= ?v0 (sup$ ?v2 ?v4)) (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v0 ?v3) (+ (line_integral$ ?v1 ?v2 ?v3) (line_integral$ ?v1 ?v4 ?v3))))) (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))))) :rule trans :premises (t319 t329))
(step t331 (cl @p_84) :rule trans :premises (t318 t330))
(step t332 (cl (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3)))))) :rule resolution :premises (t317 t331 a16))
(step t333 (cl @p_305) :rule resolution :premises (t316 t332))
(step t334 (cl @p_298) :rule resolution :premises (t72 t118 t158 t190 t314 t333))
(step t335 (cl (or (! (not (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (= (= bot$ (inf$ ?v0 (insert$ ?v1 ?v2))) (and (not (member$a ?v1 ?v0)) (= bot$ (inf$ ?v0 ?v2)))))) :named @p_66) @p_297)) :rule forall_inst :args (@p_37 @p_4 bot$))
(step t336 (cl @p_66 @p_297) :rule or :premises (t335))
(step t337 (cl @p_297) :rule resolution :premises (t336 a7))
(step t338 (cl @p_295) :rule resolution :premises (t70 t334 t337))
(step t339 (cl @p_290) :rule resolution :premises (t62 t68 t338))
(step t340 (cl (or (! (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (or (not (member$a ?v0 ?v1)) (= ?v1 (insert$ ?v0 ?v1))))) :named @p_60) @p_292)) :rule forall_inst :args (@p_4 @p_37))
(step t341 (cl @p_60 @p_292) :rule or :premises (t340))
(step t342 (cl (not (! (= (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (or (not (member$a ?v0 ?v1)) (= ?v1 (insert$ ?v0 ?v1))))) :named @p_53)) (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1)))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (or (not (member$a ?v0 ?v1)) (= ?v1 (insert$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t343 :args ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$) (:= (?v0 Real_real_prod$) ?v0) (:= (?v1 Real_real_prod_set$) ?v1)))
(step t343.t0 (cl (= (! (= (! (insert$ ?v0 ?v1) :named @p_55) ?v1) :named @p_59) (! (= ?v1 @p_55) :named @p_56))) :rule rare_rewrite :args ("eq-symm" @p_55 ?v1))
(step t343.t1 (cl (= (=> (! (member$a ?v0 ?v1) :named @p_57) @p_59) (! (=> @p_57 @p_56) :named @p_58))) :rule cong :premises (t343.t0))
(step t343 (cl (= (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= (insert$ ?v0 ?v1) ?v1))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= ?v1 (insert$ ?v0 ?v1)))))) :rule bind)
(anchor :step t344 :args ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$) (:= (?v0 Real_real_prod$) ?v0) (:= (?v1 Real_real_prod_set$) ?v1)))
(step t344.t0 (cl (= @p_58 (or (not @p_57) @p_56))) :rule rare_rewrite :args ("bool-impl-elim" @p_57 @p_56))
(step t344 (cl (= (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (=> (member$a ?v0 ?v1) (= ?v1 (insert$ ?v0 ?v1)))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (or (not (member$a ?v0 ?v1)) (= ?v1 (insert$ ?v0 ?v1)))))) :rule bind)
(step t345 (cl @p_53) :rule trans :premises (t343 t344))
(step t346 (cl (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (or (not (member$a ?v0 ?v1)) (= ?v1 (insert$ ?v0 ?v1))))) :rule resolution :premises (t342 t345 a11))
(step t347 (cl @p_292) :rule resolution :premises (t341 t346))
(step t348 (cl @p_289) :rule resolution :premises (t49 t339 t347))
(step t349 (cl (! (not (! (or (! (not (! (member$a @p_6 @p_38) :named @p_50)) :named @p_51) @p_49) :named @p_52)) :named @p_286) @p_51 @p_49) :rule or_pos)
(step t350 (cl @p_51 @p_49 @p_286) :rule reordering :premises (t349))
(step t351 (cl (not (! (= (! (or (! (and @p_51 (! (= bot$ (inf$ @p_38 bot$)) :named @p_61)) :named @p_62) (! (not @p_51) :named @p_283) (! (not @p_61) :named @p_281)) :named @p_284) (! (or @p_62 @p_50 @p_281) :named @p_282)) :named @p_285)) (not @p_284) @p_282) :rule equiv_pos2)
(step t352 (cl (= @p_283 @p_50)) :rule rare_rewrite :args ("bool-double-not-elim" @p_50))
(step t353 (cl (= @p_281 @p_281)) :rule refl)
(step t354 (cl @p_285) :rule cong :premises (t352 t353))
(step t355 (cl @p_62 @p_283 @p_281) :rule and_neg)
(step t356 (cl @p_284 (! (not @p_62) :named @p_63)) :rule or_neg :args (0))
(step t357 (cl @p_284 (not @p_283)) :rule or_neg :args (1))
(step t358 (cl @p_284 (not @p_281)) :rule or_neg :args (2))
(step t359 (cl @p_284 @p_284 @p_284) :rule resolution :premises (t355 t356 t357 t358))
(step t360 (cl @p_284) :rule contraction :premises (t359))
(step t361 (cl @p_282) :rule resolution :premises (t351 t354 t360))
(step t362 (cl @p_62 @p_50 @p_281) :rule or :premises (t361))
(step t363 (cl @p_50 @p_281 @p_62) :rule reordering :premises (t362))
(step t364 (cl (or @p_280 @p_61)) :rule forall_inst :args (@p_38))
(step t365 (cl @p_280 @p_61) :rule or :premises (t364))
(step t366 (cl @p_61) :rule resolution :premises (t365 t67))
(step t367 (cl (! (not (! (= (! (= bot$ (inf$ @p_38 @p_37)) :named @p_64) @p_62) :named @p_65)) :named @p_277) @p_64 @p_63) :rule equiv_pos1)
(step t368 (cl @p_64 @p_63 @p_277) :rule reordering :premises (t367))
(step t369 (cl (! (not (! (or (! (not (! (finite$ @p_68) :named @p_81)) :named @p_82) @p_80 @p_77 (! (not @p_64) :named @p_67) @p_74) :named @p_83)) :named @p_276) @p_82 @p_80 @p_77 @p_67 @p_74) :rule or_pos)
(step t370 (cl @p_82 @p_80 @p_77 @p_67 @p_74 @p_276) :rule reordering :premises (t369))
(step t371 (cl (= (! (= @p_81 true) :named @p_263) @p_81)) :rule equiv_simplify)
(step t372 (cl (not @p_263) @p_81) :rule equiv1 :premises (t371))
(step t373 (cl (= @p_68 @p_155)) :rule symm :premises (t251))
(step t374 (cl (= @p_81 @p_264)) :rule cong :premises (t373))
(step t375 (cl @p_263) :rule trans :premises (t374 t188))
(step t376 (cl @p_81) :rule resolution :premises (t372 t375))
(step t377 (cl (not (! (= (! (=> (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))) (! (or @p_82 @p_80 @p_77 @p_67 (! (= @p_70 (! (+ (* -1/1 @p_73) @p_69) :named @p_149)) :named @p_150)) :named @p_151)) :named @p_152) (! (=> (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))) @p_83) :named @p_148)) :named @p_153)) (not @p_152) @p_148) :rule equiv_pos2)
(step t378 (cl (= (* 1/1 (- @p_70 @p_149)) (* 1/1 (- @p_73 @p_72)))) :rule poly_simp)
(step t379 (cl (= @p_150 @p_74)) :rule poly_simp_rel :premises (t378))
(step t380 (cl (= @p_151 @p_83)) :rule cong :premises (t379))
(step t381 (cl @p_153) :rule cong :premises (t380))
(step t382 (cl @p_152 (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3)))))) :rule implies_neg1)
(anchor :step t383)
(assume t383.a0 (forall ((?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (or (not (finite$ (sup$ ?v2 ?v4))) (not (fun_app$a (line_integral_exists$ ?v1 ?v2) ?v3)) (not (fun_app$a (line_integral_exists$ ?v1 ?v4) ?v3)) (not (= bot$ (inf$ ?v2 ?v4))) (= (line_integral$ ?v1 ?v2 ?v3) (+ (* -1/1 (line_integral$ ?v1 ?v4 ?v3)) (line_integral$ ?v1 (sup$ ?v2 ?v4) ?v3))))))
(step t383.t0 (cl (or @p_147 @p_151)) :rule forall_inst :args (f$ @p_38 g$ @p_37))
(step t383.t1 (cl @p_147 @p_151) :rule or :premises (t383.t0))
(step t383.t2 (cl @p_151) :rule resolution :premises (t383.t1 t332))
(step t383 (cl @p_147 @p_151) :rule subproof :discharge (t383.a0))
(step t384 (cl @p_152 @p_151) :rule resolution :premises (t382 t383))
(step t385 (cl @p_152 (not @p_151)) :rule implies_neg2)
(step t386 (cl @p_152 @p_152) :rule resolution :premises (t384 t385))
(step t387 (cl @p_152) :rule contraction :premises (t386))
(step t388 (cl @p_148) :rule resolution :premises (t377 t381 t387))
(step t389 (cl @p_147 @p_83) :rule implies :premises (t388))
(step t390 (cl @p_83) :rule resolution :premises (t389 t332))
(step t391 (cl @p_67) :rule resolution :premises (t370 t376 t118 t158 t313 t390))
(step t392 (cl (or @p_66 @p_65)) :rule forall_inst :args (@p_38 @p_6 bot$))
(step t393 (cl @p_66 @p_65) :rule or :premises (t392))
(step t394 (cl @p_65) :rule resolution :premises (t393 a7))
(step t395 (cl @p_63) :rule resolution :premises (t368 t391 t394))
(step t396 (cl @p_50) :rule resolution :premises (t363 t366 t395))
(step t397 (cl (or @p_60 @p_52)) :rule forall_inst :args (@p_6 @p_38))
(step t398 (cl @p_60 @p_52) :rule or :premises (t397))
(step t399 (cl @p_52) :rule resolution :premises (t398 t346))
(step t400 (cl @p_49) :rule resolution :premises (t350 t396 t399))
(step t401 (cl @p_39) :rule resolution :premises (t47 t348 t167 t400))
(step t402 (cl (or (! (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (or (not (= (insert$ ?v0 bot$) (insert$ ?v1 bot$))) (= ?v0 ?v1)))) :named @p_47) @p_41)) :rule forall_inst :args (@p_4 @p_6))
(step t403 (cl @p_47 @p_41) :rule or :premises (t402))
(step t404 (cl (not (! (= (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (=> (= (insert$ ?v0 bot$) (insert$ ?v1 bot$)) (= ?v0 ?v1))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (or (not (= (insert$ ?v0 bot$) (insert$ ?v1 bot$))) (= ?v0 ?v1)))) :named @p_42)) (not (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (=> (= (insert$ ?v0 bot$) (insert$ ?v1 bot$)) (= ?v0 ?v1)))) (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (or (not (= (insert$ ?v0 bot$) (insert$ ?v1 bot$))) (= ?v0 ?v1)))) :rule equiv_pos2)
(anchor :step t405 :args ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (:= (?v0 Real_real_prod$) ?v0) (:= (?v1 Real_real_prod$) ?v1)))
(step t405.t0 (cl (= (=> (! (= (insert$ ?v0 bot$) (insert$ ?v1 bot$)) :named @p_46) (! (= ?v0 ?v1) :named @p_45)) (or (not @p_46) @p_45))) :rule rare_rewrite :args ("bool-impl-elim" @p_46 @p_45))
(step t405 (cl @p_42) :rule bind)
(step t406 (cl (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (or (not (= (insert$ ?v0 bot$) (insert$ ?v1 bot$))) (= ?v0 ?v1)))) :rule resolution :premises (t404 t405 a3))
(step t407 (cl @p_41) :rule resolution :premises (t403 t406))
(step t408 (cl @p_36) :rule resolution :premises (t31 t401 t407))
(step t409 (cl (not @p_35) (not @p_34) @p_32) :rule equiv_pos2)
(step t410 (cl (= (* -1/1 (- 1/1 @p_30)) (* 1/1 (- @p_30 1/1)))) :rule poly_simp)
(step t411 (cl (= @p_33 @p_31)) :rule poly_simp_rel :premises (t410))
(step t412 (cl @p_35) :rule cong :premises (t411))
(step t413 (cl @p_34 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t414)
(assume t414.a0 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))))
(step t414.t0 (cl (or @p_25 @p_33)) :rule forall_inst :args (0/1 1/1))
(step t414.t1 (cl @p_25 @p_33) :rule or :premises (t414.t0))
(step t414.t2 (cl (not @p_23) (not (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1))) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t414.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t414.t3.t0 (cl (= (* 1/1 (- @p_24 ?v1)) (* -1/1 (- ?v1 @p_24)))) :rule poly_simp)
(step t414.t3.t1 (cl (= (= @p_24 ?v1) (= ?v1 @p_24))) :rule poly_simp_rel :premises (t414.t3.t0))
(step t414.t3 (cl @p_23) :rule bind)
(step t414.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule resolution :premises (t414.t2 t414.t3 a5))
(step t414.t5 (cl @p_33) :rule resolution :premises (t414.t1 t414.t4))
(step t414 (cl @p_25 @p_33) :rule subproof :discharge (t414.a0))
(step t415 (cl @p_34 @p_33) :rule resolution :premises (t413 t414))
(step t416 (cl @p_34 (not @p_33)) :rule implies_neg2)
(step t417 (cl @p_34 @p_34) :rule resolution :premises (t415 t416))
(step t418 (cl @p_34) :rule contraction :premises (t417))
(step t419 (cl @p_32) :rule resolution :premises (t409 t412 t418))
(step t420 (cl @p_25 @p_31) :rule implies :premises (t419))
(step t421 (cl (not @p_23) (not (forall ((?v0 Real) (?v1 Real)) (= (snd$a (fun_app$b (pair$a ?v0) ?v1)) ?v1))) (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t422 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t422.t0 (cl (= (* 1/1 (- @p_24 ?v1)) (* -1/1 (- ?v1 @p_24)))) :rule poly_simp)
(step t422.t1 (cl (= (= @p_24 ?v1) (= ?v1 @p_24))) :rule poly_simp_rel :premises (t422.t0))
(step t422 (cl @p_23) :rule bind)
(step t423 (cl (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule resolution :premises (t421 t422 a5))
(step t424 (cl @p_31) :rule resolution :premises (t420 t423))
(step t425 (cl (not @p_29) (not @p_28) @p_26) :rule equiv_pos2)
(step t426 (cl (= (* 1/1 (- 0/1 @p_21)) (* -1/1 (- @p_21 0/1)))) :rule poly_simp)
(step t427 (cl (= @p_27 @p_22)) :rule poly_simp_rel :premises (t426))
(step t428 (cl @p_29) :rule cong :premises (t427))
(step t429 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t430)
(assume t430.a0 (forall ((?v0 Real) (?v1 Real)) (= ?v1 (snd$a (fun_app$b (pair$a ?v0) ?v1)))))
(step t430.t0 (cl (or @p_25 @p_27)) :rule forall_inst :args (1/1 0/1))
(step t430.t1 (cl @p_25 @p_27) :rule or :premises (t430.t0))
(step t430.t2 (cl @p_27) :rule resolution :premises (t430.t1 t423))
(step t430 (cl @p_25 @p_27) :rule subproof :discharge (t430.a0))
(step t431 (cl @p_28 @p_27) :rule resolution :premises (t429 t430))
(step t432 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t433 (cl @p_28 @p_28) :rule resolution :premises (t431 t432))
(step t434 (cl @p_28) :rule contraction :premises (t433))
(step t435 (cl @p_26) :rule resolution :premises (t425 t428 t434))
(step t436 (cl @p_25 @p_22) :rule implies :premises (t435))
(step t437 (cl @p_22) :rule resolution :premises (t436 t423))
(step t438 (cl) :rule resolution :premises (t29 t408 t424 t437))
)
ed6453d028cbfe649db725b93db7d2f134d9a7dd 1277 0
unsat
(
(assume a0 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$))))))
(assume a3 (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1))))))))
(assume a4 (! (< 0/1 d$) :named @p_1))
(assume a6 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))))
(assume a8 (forall ((?v0 Real) (?v1 Real)) (= (divide$ (- ?v0) ?v1) (- (divide$ ?v0 ?v1)))))
(assume a9 (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1)))))
(assume a10 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))))
(assume a11 (! (not (! (=> (! (and (not (= uu$ uua$)) (! (= uub$ uuc$) :named @p_2)) :named @p_3) false) :named @p_4)) :named @p_5))
(step t0 (cl (not (! (= (! (or (! (not (! (= (! (times$ 0/1 d$) :named @p_6) 0/1) :named @p_7)) :named @p_269) (! (not (! (not (! (>= (! (* -1/1 (! (divide$ d$ 2/1) :named @p_33)) :named @p_34) 0/1) :named @p_35)) :named @p_36)) :named @p_155) (! (not (! (= @p_33 (! (* -1/1 @p_6) :named @p_30)) :named @p_205)) :named @p_270)) :named @p_272) (! (or @p_269 @p_35 @p_270) :named @p_271)) :named @p_299)) (not @p_272) @p_271) :rule equiv_pos2)
(step t1 (cl (= @p_155 @p_35)) :rule rare_rewrite :args ("bool-double-not-elim" @p_35))
(step t2 (cl (= @p_270 @p_270)) :rule refl)
(step t3 (cl @p_299) :rule cong :premises (t1 t2))
(step t4 (cl (! (=> (! (and @p_7 @p_36 @p_205) :named @p_273) (! (and @p_36 (! (= 0/1 @p_6) :named @p_275) @p_205) :named @p_276)) :named @p_298) @p_273) :rule implies_neg1)
(anchor :step t5)
(assume t5.a0 @p_7)
(assume t5.a1 @p_36)
(assume t5.a2 @p_205)
(step t5.t0 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1)))) (! (= @p_6 (! (* -1/1 (! (times$ (! (* -1/1 0/1) :named @p_24) d$) :named @p_25)) :named @p_26)) :named @p_27)) :named @p_28) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1)))) @p_7) :named @p_23)) :named @p_29)) (not @p_28) @p_23) :rule equiv_pos2)
(step t5.t1 (cl (! (= @p_24 0/1) :named @p_32)) :rule evaluate)
(step t5.t2 (cl (= d$ d$)) :rule refl)
(step t5.t3 (cl (= @p_25 @p_6)) :rule cong :premises (t5.t1 t5.t2))
(step t5.t4 (cl (= @p_26 @p_30)) :rule cong :premises (t5.t3))
(step t5.t5 (cl (= @p_27 (! (= @p_6 @p_30) :named @p_31))) :rule cong :premises (t5.t4))
(step t5.t6 (cl (= (* 1/1 (- @p_6 @p_30)) (* 2/1 (- @p_6 0/1)))) :rule poly_simp)
(step t5.t7 (cl (= @p_31 @p_7)) :rule poly_simp_rel :premises (t5.t6))
(step t5.t8 (cl (= @p_27 @p_7)) :rule trans :premises (t5.t5 t5.t7))
(step t5.t9 (cl @p_29) :rule cong :premises (t5.t8))
(step t5.t10 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t5.t11)
(assume t5.t11.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1)))))
(step t5.t11.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :named @p_22) @p_27)) :rule forall_inst :args (0/1 d$))
(step t5.t11.t1 (cl @p_22 @p_27) :rule or :premises (t5.t11.t0))
(step t5.t11.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1)))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :named @p_8)) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t5.t11.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t5.t11.t3.t0 (cl (= (! (- ?v0) :named @p_17) (! (* -1/1 ?v0) :named @p_11))) :rule poly_simp)
(step t5.t11.t3.t1 (cl (! (= ?v1 ?v1) :named @p_10)) :rule refl)
(step t5.t11.t3.t2 (cl (= (! (times$ @p_17 ?v1) :named @p_18) (! (times$ @p_11 ?v1) :named @p_12))) :rule cong :premises (t5.t11.t3.t0 t5.t11.t3.t1))
(step t5.t11.t3.t3 (cl (= (! (- (! (times$ ?v0 ?v1) :named @p_14)) :named @p_16) (! (* -1/1 @p_14) :named @p_20))) :rule poly_simp)
(step t5.t11.t3.t4 (cl (= (! (= @p_18 @p_16) :named @p_19) (! (= @p_12 @p_20) :named @p_21))) :rule cong :premises (t5.t11.t3.t2 t5.t11.t3.t3))
(step t5.t11.t3.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 (! (* -1/1 @p_12) :named @p_13))))) :rule poly_simp)
(step t5.t11.t3.t6 (cl (= @p_21 (! (= @p_14 @p_13) :named @p_15))) :rule poly_simp_rel :premises (t5.t11.t3.t5))
(step t5.t11.t3.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t5.t11.t3.t4 t5.t11.t3.t6))
(step t5.t11.t3 (cl @p_8) :rule bind)
(step t5.t11.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t5.t11.t2 t5.t11.t3 a9))
(step t5.t11.t5 (cl @p_27) :rule resolution :premises (t5.t11.t1 t5.t11.t4))
(step t5.t11 (cl @p_22 @p_27) :rule subproof :discharge (t5.t11.a0))
(step t5.t12 (cl @p_28 @p_27) :rule resolution :premises (t5.t10 t5.t11))
(step t5.t13 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t5.t14 (cl @p_28 @p_28) :rule resolution :premises (t5.t12 t5.t13))
(step t5.t15 (cl @p_28) :rule contraction :premises (t5.t14))
(step t5.t16 (cl @p_23) :rule resolution :premises (t5.t0 t5.t9 t5.t15))
(step t5.t17 (cl @p_22 @p_7) :rule implies :premises (t5.t16))
(step t5.t18 (cl (not @p_8) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t5.t19 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t5.t19.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t5.t19.t1 (cl @p_10) :rule refl)
(step t5.t19.t2 (cl (= @p_18 @p_12)) :rule cong :premises (t5.t19.t0 t5.t19.t1))
(step t5.t19.t3 (cl (= @p_16 @p_20)) :rule poly_simp)
(step t5.t19.t4 (cl (= @p_19 @p_21)) :rule cong :premises (t5.t19.t2 t5.t19.t3))
(step t5.t19.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 @p_13)))) :rule poly_simp)
(step t5.t19.t6 (cl (= @p_21 @p_15)) :rule poly_simp_rel :premises (t5.t19.t5))
(step t5.t19.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t5.t19.t4 t5.t19.t6))
(step t5.t19 (cl @p_8) :rule bind)
(step t5.t20 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t5.t18 t5.t19 a9))
(step t5.t21 (cl @p_7) :rule resolution :premises (t5.t17 t5.t20))
(step t5.t22 (cl @p_275) :rule symm :premises (t5.t21))
(step t5.t23 (cl (! (not (! (and @p_205 (! (= (! (diamond_y$ @p_6) :named @p_209) (! (times$ (+ -1/1 (* 2/1 (! (divide$ 1/1 2/1) :named @p_207))) (! (diamond_y$ @p_34) :named @p_206)) :named @p_208)) :named @p_210)) :named @p_211)) :named @p_268) @p_205) :rule and_pos :args (0))
(step t5.t24 (cl @p_205 @p_268) :rule reordering :premises (t5.t23))
(step t5.t25 (cl (! (not (! (= (! (= (! (pair$ @p_6 @p_209) :named @p_213) (! (pair$ @p_34 @p_208) :named @p_212)) :named @p_214) @p_211) :named @p_215)) :named @p_267) (! (not @p_214) :named @p_266) @p_211) :rule equiv_pos2)
(step t5.t26 (cl @p_211 @p_266 @p_267) :rule reordering :premises (t5.t25))
(step t5.t27 (cl (not (! (= (! (=> (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$))))) (! (= (! (fun_app$ uuc$ @p_207) :named @p_224) (! (pair$ (! (times$ (! (+ @p_207 (! (* -1/1 @p_207) :named @p_248)) :named @p_259) d$) :named @p_260) (! (diamond_y$ @p_260) :named @p_261)) :named @p_262)) :named @p_263)) :named @p_264) (! (=> (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$))))) (! (= @p_224 @p_213) :named @p_246)) :named @p_258)) :named @p_265)) (not @p_264) @p_258) :rule equiv_pos2)
(step t5.t28 (cl (= @p_259 0/1)) :rule poly_simp)
(step t5.t29 (cl (= @p_260 @p_6)) :rule cong :premises (t5.t28 t5.t2))
(step t5.t30 (cl (= @p_261 @p_209)) :rule cong :premises (t5.t29))
(step t5.t31 (cl (= @p_262 @p_213)) :rule cong :premises (t5.t29 t5.t30))
(step t5.t32 (cl (= @p_263 @p_246)) :rule cong :premises (t5.t31))
(step t5.t33 (cl @p_265) :rule cong :premises (t5.t32))
(step t5.t34 (cl @p_264 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule implies_neg1)
(anchor :step t5.t35)
(assume t5.t35.a0 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$))))))
(step t5.t35.t0 (cl (or (! (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :named @p_257) @p_263)) :rule forall_inst :args (@p_207))
(step t5.t35.t1 (cl @p_257 @p_263) :rule or :premises (t5.t35.t0))
(step t5.t35.t2 (cl (not (! (= (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :named @p_247)) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t5.t35.t3 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t5.t35.t3.t0 (cl (= (! (- ?v0 @p_207) :named @p_253) (! (+ ?v0 @p_248) :named @p_249))) :rule poly_simp)
(step t5.t35.t3.t1 (cl (= (! (times$ @p_253 d$) :named @p_254) (! (times$ @p_249 d$) :named @p_250))) :rule cong :premises (t5.t35.t3.t0 t5.t2))
(step t5.t35.t3.t2 (cl (= (! (diamond_y$ @p_254) :named @p_255) (! (diamond_y$ @p_250) :named @p_251))) :rule cong :premises (t5.t35.t3.t1))
(step t5.t35.t3.t3 (cl (= (! (pair$ @p_254 @p_255) :named @p_256) (! (pair$ @p_250 @p_251) :named @p_252))) :rule cong :premises (t5.t35.t3.t1 t5.t35.t3.t2))
(step t5.t35.t3.t4 (cl (= (= (! (fun_app$ uuc$ ?v0) :named @p_231) @p_256) (= @p_231 @p_252))) :rule cong :premises (t5.t35.t3.t3))
(step t5.t35.t3 (cl @p_247) :rule bind)
(step t5.t35.t4 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t5.t35.t2 t5.t35.t3 a0))
(step t5.t35.t5 (cl @p_263) :rule resolution :premises (t5.t35.t1 t5.t35.t4))
(step t5.t35 (cl @p_257 @p_263) :rule subproof :discharge (t5.t35.a0))
(step t5.t36 (cl @p_264 @p_263) :rule resolution :premises (t5.t34 t5.t35))
(step t5.t37 (cl @p_264 (not @p_263)) :rule implies_neg2)
(step t5.t38 (cl @p_264 @p_264) :rule resolution :premises (t5.t36 t5.t37))
(step t5.t39 (cl @p_264) :rule contraction :premises (t5.t38))
(step t5.t40 (cl @p_258) :rule resolution :premises (t5.t27 t5.t33 t5.t39))
(step t5.t41 (cl @p_257 @p_246) :rule implies :premises (t5.t40))
(step t5.t42 (cl (not @p_247) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t5.t43 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t5.t43.t0 (cl (= @p_253 @p_249)) :rule poly_simp)
(step t5.t43.t1 (cl (= @p_254 @p_250)) :rule cong :premises (t5.t43.t0 t5.t2))
(step t5.t43.t2 (cl (= @p_255 @p_251)) :rule cong :premises (t5.t43.t1))
(step t5.t43.t3 (cl (= @p_256 @p_252)) :rule cong :premises (t5.t43.t1 t5.t43.t2))
(step t5.t43.t4 (cl (= (= @p_231 @p_256) (= @p_231 @p_252))) :rule cong :premises (t5.t43.t3))
(step t5.t43 (cl @p_247) :rule bind)
(step t5.t44 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t5.t42 t5.t43 a0))
(step t5.t45 (cl @p_246) :rule resolution :premises (t5.t41 t5.t44))
(step t5.t46 (cl (= @p_213 @p_224)) :rule symm :premises (t5.t45))
(step t5.t47 (cl (or (! (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :named @p_245) (! (= @p_224 @p_212) :named @p_225))) :rule forall_inst :args (@p_207))
(step t5.t48 (cl @p_245 @p_225) :rule or :premises (t5.t47))
(step t5.t49 (cl (not (! (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :named @p_226)) (not (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1)))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule equiv_pos2)
(anchor :step t5.t50 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t5.t50.t0 (cl (= (! (- @p_33) :named @p_237) @p_34)) :rule poly_simp)
(step t5.t50.t1 (cl (= (! (- (! (* 2/1 ?v0) :named @p_227) 1/1) :named @p_239) (! (+ (! (* 2/1 ?v0) :named @p_227) (! (* -1/1 1/1) :named @p_242)) :named @p_243))) :rule poly_simp)
(step t5.t50.t2 (cl (= @p_242 -1/1)) :rule evaluate)
(step t5.t50.t3 (cl (= @p_243 (! (+ @p_227 -1/1) :named @p_244))) :rule cong :premises (t5.t50.t2))
(step t5.t50.t4 (cl (= @p_244 (! (+ -1/1 @p_227) :named @p_228))) :rule poly_simp)
(step t5.t50.t5 (cl (= @p_243 @p_228)) :rule trans :premises (t5.t50.t3 t5.t50.t4))
(step t5.t50.t6 (cl (= @p_239 @p_228)) :rule trans :premises (t5.t50.t1 t5.t50.t5))
(step t5.t50.t7 (cl (= (! (diamond_y$ @p_237) :named @p_238) @p_206)) :rule cong :premises (t5.t50.t0))
(step t5.t50.t8 (cl (= (! (times$ @p_239 @p_238) :named @p_240) (! (times$ @p_228 @p_206) :named @p_229))) :rule cong :premises (t5.t50.t6 t5.t50.t7))
(step t5.t50.t9 (cl (= (! (pair$ @p_237 @p_240) :named @p_241) (! (pair$ @p_34 @p_229) :named @p_230))) :rule cong :premises (t5.t50.t0 t5.t50.t8))
(step t5.t50.t10 (cl (= (= (! (fun_app$ uub$ ?v0) :named @p_232) @p_241) (! (= @p_232 @p_230) :named @p_233))) :rule cong :premises (t5.t50.t9))
(step t5.t50 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(anchor :step t5.t51 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t5.t51.t0 (cl (not (! (= @p_5 @p_3) :named @p_234)) (not @p_5) @p_3) :rule equiv_pos2)
(step t5.t51.t1 (cl (= @p_4 (! (not @p_3) :named @p_235))) :rule rare_rewrite :args ("bool-impl-false1" @p_3))
(step t5.t51.t2 (cl (= @p_5 (! (not @p_235) :named @p_236))) :rule cong :premises (t5.t51.t1))
(step t5.t51.t3 (cl (= @p_236 @p_3)) :rule rare_rewrite :args ("bool-double-not-elim" @p_3))
(step t5.t51.t4 (cl @p_234) :rule trans :premises (t5.t51.t2 t5.t51.t3))
(step t5.t51.t5 (cl @p_3) :rule resolution :premises (t5.t51.t0 t5.t51.t4 a11))
(step t5.t51.t6 (cl @p_2) :rule and :premises (t5.t51.t5) :args (1))
(step t5.t51.t7 (cl (! (= ?v0 ?v0) :named @p_9)) :rule refl)
(step t5.t51.t8 (cl (= @p_232 @p_231)) :rule cong :premises (t5.t51.t6 t5.t51.t7))
(step t5.t51.t9 (cl (= @p_230 @p_230)) :rule refl)
(step t5.t51.t10 (cl (= @p_233 (= @p_231 @p_230))) :rule cong :premises (t5.t51.t8 t5.t51.t9))
(step t5.t51 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(step t5.t52 (cl @p_226) :rule trans :premises (t5.t50 t5.t51))
(step t5.t53 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule resolution :premises (t5.t49 t5.t52 a3))
(step t5.t54 (cl @p_225) :rule resolution :premises (t5.t48 t5.t53))
(step t5.t55 (cl @p_214) :rule trans :premises (t5.t46 t5.t54))
(step t5.t56 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) (! (= @p_214 (! (and (! (= @p_6 @p_34) :named @p_218) @p_210) :named @p_219)) :named @p_220)) :named @p_221) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) @p_215) :named @p_217)) :named @p_222)) (not @p_221) @p_217) :rule equiv_pos2)
(step t5.t57 (cl (= (* 1/1 (- @p_6 @p_34)) (! (* 1/1 (- @p_33 @p_30)) :named @p_223))) :rule poly_simp)
(step t5.t58 (cl (= @p_218 @p_205)) :rule poly_simp_rel :premises (t5.t57))
(step t5.t59 (cl (= @p_210 @p_210)) :rule refl)
(step t5.t60 (cl (= @p_219 @p_211)) :rule cong :premises (t5.t58 t5.t59))
(step t5.t61 (cl (= @p_220 @p_215)) :rule cong :premises (t5.t60))
(step t5.t62 (cl @p_222) :rule cong :premises (t5.t61))
(step t5.t63 (cl @p_221 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) :rule implies_neg1)
(anchor :step t5.t64)
(assume t5.t64.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))))
(step t5.t64.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) :named @p_216) @p_220)) :rule forall_inst :args (@p_6 @p_209 @p_34 @p_208))
(step t5.t64.t1 (cl @p_216 @p_220) :rule or :premises (t5.t64.t0))
(step t5.t64.t2 (cl @p_220) :rule resolution :premises (t5.t64.t1 t5.t64.a0))
(step t5.t64 (cl @p_216 @p_220) :rule subproof :discharge (t5.t64.a0))
(step t5.t65 (cl @p_221 @p_220) :rule resolution :premises (t5.t63 t5.t64))
(step t5.t66 (cl @p_221 (not @p_220)) :rule implies_neg2)
(step t5.t67 (cl @p_221 @p_221) :rule resolution :premises (t5.t65 t5.t66))
(step t5.t68 (cl @p_221) :rule contraction :premises (t5.t67))
(step t5.t69 (cl @p_217) :rule resolution :premises (t5.t56 t5.t62 t5.t68))
(step t5.t70 (cl @p_216 @p_215) :rule implies :premises (t5.t69))
(step t5.t71 (cl @p_215) :rule resolution :premises (t5.t70 a10))
(step t5.t72 (cl @p_211) :rule resolution :premises (t5.t26 t5.t55 t5.t71))
(step t5.t73 (cl @p_205) :rule resolution :premises (t5.t24 t5.t72))
(step t5.t74 (cl @p_276) :rule and_intro :premises (t5.a1 t5.t22 t5.t73))
(step t5 (cl @p_269 @p_155 @p_270 @p_276) :rule subproof :discharge (t5.a0 t5.a1 t5.a2))
(step t6 (cl (! (not @p_273) :named @p_274) @p_7) :rule and_pos :args (0))
(step t7 (cl @p_274 @p_36) :rule and_pos :args (1))
(step t8 (cl @p_274 @p_205) :rule and_pos :args (2))
(step t9 (cl @p_276 @p_274 @p_274 @p_274) :rule resolution :premises (t5 t6 t7 t8))
(step t10 (cl @p_274 @p_274 @p_274 @p_276) :rule reordering :premises (t9))
(step t11 (cl @p_274 @p_276) :rule contraction :premises (t10))
(step t12 (cl @p_298 @p_276) :rule resolution :premises (t4 t11))
(step t13 (cl @p_298 (! (not @p_276) :named @p_277)) :rule implies_neg2)
(step t14 (cl @p_298 @p_298) :rule resolution :premises (t12 t13))
(step t15 (cl @p_298) :rule contraction :premises (t14))
(step t16 (cl @p_274 @p_276) :rule implies :premises (t15))
(step t17 (cl (! (=> @p_276 false) :named @p_278) @p_276) :rule implies_neg1)
(anchor :step t18)
(assume t18.a0 @p_36)
(assume t18.a1 @p_275)
(assume t18.a2 @p_205)
(step t18.t0 (cl (! (not (! (= @p_205 (! (= (! (+ @p_33 @p_6) :named @p_279) 0/1) :named @p_280)) :named @p_292)) :named @p_293) @p_270 @p_280) :rule equiv_pos2)
(step t18.t1 (cl (= (* 1/1 (- @p_279 0/1)) @p_223)) :rule poly_simp)
(step t18.t2 (cl (= @p_280 @p_205)) :rule poly_simp_rel :premises (t18.t1))
(step t18.t3 (cl @p_292) :rule symm :premises (t18.t2))
(step t18.t4 (cl @p_268 @p_205) :rule and_pos :args (0))
(step t18.t5 (cl @p_205 @p_268) :rule reordering :premises (t18.t4))
(step t18.t6 (cl @p_267 @p_266 @p_211) :rule equiv_pos2)
(step t18.t7 (cl @p_211 @p_266 @p_267) :rule reordering :premises (t18.t6))
(step t18.t8 (cl (not @p_265) (not @p_264) @p_258) :rule equiv_pos2)
(step t18.t9 (cl (= @p_259 0/1)) :rule poly_simp)
(step t18.t10 (cl (= d$ d$)) :rule refl)
(step t18.t11 (cl (= @p_260 @p_6)) :rule cong :premises (t18.t9 t18.t10))
(step t18.t12 (cl (= @p_261 @p_209)) :rule cong :premises (t18.t11))
(step t18.t13 (cl (= @p_262 @p_213)) :rule cong :premises (t18.t11 t18.t12))
(step t18.t14 (cl (= @p_263 @p_246)) :rule cong :premises (t18.t13))
(step t18.t15 (cl @p_265) :rule cong :premises (t18.t14))
(step t18.t16 (cl @p_264 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule implies_neg1)
(anchor :step t18.t17)
(assume t18.t17.a0 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$))))))
(step t18.t17.t0 (cl (or @p_257 @p_263)) :rule forall_inst :args (@p_207))
(step t18.t17.t1 (cl @p_257 @p_263) :rule or :premises (t18.t17.t0))
(step t18.t17.t2 (cl (not @p_247) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t18.t17.t3 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t18.t17.t3.t0 (cl (= @p_253 @p_249)) :rule poly_simp)
(step t18.t17.t3.t1 (cl (= @p_254 @p_250)) :rule cong :premises (t18.t17.t3.t0 t18.t10))
(step t18.t17.t3.t2 (cl (= @p_255 @p_251)) :rule cong :premises (t18.t17.t3.t1))
(step t18.t17.t3.t3 (cl (= @p_256 @p_252)) :rule cong :premises (t18.t17.t3.t1 t18.t17.t3.t2))
(step t18.t17.t3.t4 (cl (= (= @p_231 @p_256) (= @p_231 @p_252))) :rule cong :premises (t18.t17.t3.t3))
(step t18.t17.t3 (cl @p_247) :rule bind)
(step t18.t17.t4 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t18.t17.t2 t18.t17.t3 a0))
(step t18.t17.t5 (cl @p_263) :rule resolution :premises (t18.t17.t1 t18.t17.t4))
(step t18.t17 (cl @p_257 @p_263) :rule subproof :discharge (t18.t17.a0))
(step t18.t18 (cl @p_264 @p_263) :rule resolution :premises (t18.t16 t18.t17))
(step t18.t19 (cl @p_264 (not @p_263)) :rule implies_neg2)
(step t18.t20 (cl @p_264 @p_264) :rule resolution :premises (t18.t18 t18.t19))
(step t18.t21 (cl @p_264) :rule contraction :premises (t18.t20))
(step t18.t22 (cl @p_258) :rule resolution :premises (t18.t8 t18.t15 t18.t21))
(step t18.t23 (cl @p_257 @p_246) :rule implies :premises (t18.t22))
(step t18.t24 (cl (not @p_247) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t18.t25 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t18.t25.t0 (cl (= @p_253 @p_249)) :rule poly_simp)
(step t18.t25.t1 (cl (= @p_254 @p_250)) :rule cong :premises (t18.t25.t0 t18.t10))
(step t18.t25.t2 (cl (= @p_255 @p_251)) :rule cong :premises (t18.t25.t1))
(step t18.t25.t3 (cl (= @p_256 @p_252)) :rule cong :premises (t18.t25.t1 t18.t25.t2))
(step t18.t25.t4 (cl (= (= @p_231 @p_256) (= @p_231 @p_252))) :rule cong :premises (t18.t25.t3))
(step t18.t25 (cl @p_247) :rule bind)
(step t18.t26 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t18.t24 t18.t25 a0))
(step t18.t27 (cl @p_246) :rule resolution :premises (t18.t23 t18.t26))
(step t18.t28 (cl (= @p_213 @p_224)) :rule symm :premises (t18.t27))
(step t18.t29 (cl (or @p_245 @p_225)) :rule forall_inst :args (@p_207))
(step t18.t30 (cl @p_245 @p_225) :rule or :premises (t18.t29))
(step t18.t31 (cl (not @p_226) (not (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1)))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule equiv_pos2)
(anchor :step t18.t32 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t18.t32.t0 (cl (= @p_237 @p_34)) :rule poly_simp)
(step t18.t32.t1 (cl (= @p_239 @p_243)) :rule poly_simp)
(step t18.t32.t2 (cl (= @p_242 -1/1)) :rule evaluate)
(step t18.t32.t3 (cl (= @p_243 @p_244)) :rule cong :premises (t18.t32.t2))
(step t18.t32.t4 (cl (= @p_244 @p_228)) :rule poly_simp)
(step t18.t32.t5 (cl (= @p_243 @p_228)) :rule trans :premises (t18.t32.t3 t18.t32.t4))
(step t18.t32.t6 (cl (= @p_239 @p_228)) :rule trans :premises (t18.t32.t1 t18.t32.t5))
(step t18.t32.t7 (cl (= @p_238 @p_206)) :rule cong :premises (t18.t32.t0))
(step t18.t32.t8 (cl (= @p_240 @p_229)) :rule cong :premises (t18.t32.t6 t18.t32.t7))
(step t18.t32.t9 (cl (= @p_241 @p_230)) :rule cong :premises (t18.t32.t0 t18.t32.t8))
(step t18.t32.t10 (cl (= (= @p_232 @p_241) @p_233)) :rule cong :premises (t18.t32.t9))
(step t18.t32 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(anchor :step t18.t33 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t18.t33.t0 (cl (not @p_234) (not @p_5) @p_3) :rule equiv_pos2)
(step t18.t33.t1 (cl (= @p_4 @p_235)) :rule rare_rewrite :args ("bool-impl-false1" @p_3))
(step t18.t33.t2 (cl (= @p_5 @p_236)) :rule cong :premises (t18.t33.t1))
(step t18.t33.t3 (cl (= @p_236 @p_3)) :rule rare_rewrite :args ("bool-double-not-elim" @p_3))
(step t18.t33.t4 (cl @p_234) :rule trans :premises (t18.t33.t2 t18.t33.t3))
(step t18.t33.t5 (cl @p_3) :rule resolution :premises (t18.t33.t0 t18.t33.t4 a11))
(step t18.t33.t6 (cl @p_2) :rule and :premises (t18.t33.t5) :args (1))
(step t18.t33.t7 (cl @p_9) :rule refl)
(step t18.t33.t8 (cl (= @p_232 @p_231)) :rule cong :premises (t18.t33.t6 t18.t33.t7))
(step t18.t33.t9 (cl (= @p_230 @p_230)) :rule refl)
(step t18.t33.t10 (cl (= @p_233 (= @p_231 @p_230))) :rule cong :premises (t18.t33.t8 t18.t33.t9))
(step t18.t33 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(step t18.t34 (cl @p_226) :rule trans :premises (t18.t32 t18.t33))
(step t18.t35 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule resolution :premises (t18.t31 t18.t34 a3))
(step t18.t36 (cl @p_225) :rule resolution :premises (t18.t30 t18.t35))
(step t18.t37 (cl @p_214) :rule trans :premises (t18.t28 t18.t36))
(step t18.t38 (cl (not @p_222) (not @p_221) @p_217) :rule equiv_pos2)
(step t18.t39 (cl (= (* 1/1 (- @p_6 @p_34)) @p_223)) :rule poly_simp)
(step t18.t40 (cl (= @p_218 @p_205)) :rule poly_simp_rel :premises (t18.t39))
(step t18.t41 (cl (= @p_210 @p_210)) :rule refl)
(step t18.t42 (cl (= @p_219 @p_211)) :rule cong :premises (t18.t40 t18.t41))
(step t18.t43 (cl (= @p_220 @p_215)) :rule cong :premises (t18.t42))
(step t18.t44 (cl @p_222) :rule cong :premises (t18.t43))
(step t18.t45 (cl @p_221 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) :rule implies_neg1)
(anchor :step t18.t46)
(assume t18.t46.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))))
(step t18.t46.t0 (cl (or @p_216 @p_220)) :rule forall_inst :args (@p_6 @p_209 @p_34 @p_208))
(step t18.t46.t1 (cl @p_216 @p_220) :rule or :premises (t18.t46.t0))
(step t18.t46.t2 (cl @p_220) :rule resolution :premises (t18.t46.t1 t18.t46.a0))
(step t18.t46 (cl @p_216 @p_220) :rule subproof :discharge (t18.t46.a0))
(step t18.t47 (cl @p_221 @p_220) :rule resolution :premises (t18.t45 t18.t46))
(step t18.t48 (cl @p_221 (not @p_220)) :rule implies_neg2)
(step t18.t49 (cl @p_221 @p_221) :rule resolution :premises (t18.t47 t18.t48))
(step t18.t50 (cl @p_221) :rule contraction :premises (t18.t49))
(step t18.t51 (cl @p_217) :rule resolution :premises (t18.t38 t18.t44 t18.t50))
(step t18.t52 (cl @p_216 @p_215) :rule implies :premises (t18.t51))
(step t18.t53 (cl @p_215) :rule resolution :premises (t18.t52 a10))
(step t18.t54 (cl @p_211) :rule resolution :premises (t18.t7 t18.t37 t18.t53))
(step t18.t55 (cl @p_205) :rule resolution :premises (t18.t5 t18.t54))
(step t18.t56 (cl @p_280) :rule resolution :premises (t18.t0 t18.t3 t18.t55))
(step t18.t57 (cl (! (=> @p_280 false) :named @p_282) @p_280) :rule implies_neg1)
(anchor :step t18.t58)
(assume t18.t58.a0 @p_280)
(step t18.t58.t0 (cl (not (! (= (! (< (! (+ @p_279 @p_30 @p_34) :named @p_284) (! (+ 0/1 @p_24 @p_24) :named @p_283)) :named @p_285) false) :named @p_294)) (not @p_285) false) :rule equiv_pos2)
(step t18.t58.t1 (cl (= @p_285 (! (not (! (>= @p_284 @p_283) :named @p_295)) :named @p_296))) :rule rare_rewrite :args ("arith-elim-lt" @p_284 @p_283))
(step t18.t58.t2 (cl (= @p_284 (! (+ @p_30 @p_34 @p_6 @p_33) :named @p_297))) :rule poly_simp)
(step t18.t58.t3 (cl (= @p_297 0/1)) :rule poly_simp)
(step t18.t58.t4 (cl (= @p_284 0/1)) :rule trans :premises (t18.t58.t2 t18.t58.t3))
(step t18.t58.t5 (cl @p_32) :rule evaluate)
(step t18.t58.t6 (cl (= @p_283 (! (+ 0/1 0/1 0/1) :named @p_192))) :rule cong :premises (t18.t58.t5 t18.t58.t5))
(step t18.t58.t7 (cl (= @p_192 0/1)) :rule evaluate)
(step t18.t58.t8 (cl (= @p_283 0/1)) :rule trans :premises (t18.t58.t6 t18.t58.t7))
(step t18.t58.t9 (cl (= @p_295 (! (>= 0/1 0/1) :named @p_191))) :rule cong :premises (t18.t58.t4 t18.t58.t8))
(step t18.t58.t10 (cl (= @p_191 true)) :rule evaluate)
(step t18.t58.t11 (cl (= @p_295 true)) :rule trans :premises (t18.t58.t9 t18.t58.t10))
(step t18.t58.t12 (cl (= @p_296 (! (not true) :named @p_190))) :rule cong :premises (t18.t58.t11))
(step t18.t58.t13 (cl (= @p_190 false)) :rule evaluate)
(step t18.t58.t14 (cl (= @p_296 false)) :rule trans :premises (t18.t58.t12 t18.t58.t13))
(step t18.t58.t15 (cl @p_294) :rule trans :premises (t18.t58.t1 t18.t58.t14))
(step t18.t58.t16 (cl (! (not @p_280) :named @p_281) (not (! (= @p_30 @p_24) :named @p_290)) (not (! (< @p_34 @p_24) :named @p_286)) @p_285) :rule la_generic :args (-1/1 -1/1 1/1 1/1))
(step t18.t58.t17 (cl @p_293 @p_270 @p_280) :rule equiv_pos2)
(step t18.t58.t18 (cl @p_205) :rule resolution :premises (t18.t5 t18.t54))
(step t18.t58.t19 (cl @p_280) :rule resolution :premises (t18.t58.t17 t18.t3 t18.t58.t18))
(step t18.t58.t20 (cl (=> (! (and (! (< -1/1 0/1) :named @p_287) @p_7) :named @p_291) @p_290)) :rule la_mult_neg)
(step t18.t58.t21 (cl (not @p_291) @p_290) :rule implies :premises (t18.t58.t20))
(step t18.t58.t22 (cl (= (! (= @p_287 true) :named @p_289) @p_287)) :rule equiv_simplify)
(step t18.t58.t23 (cl (not @p_289) @p_287) :rule equiv1 :premises (t18.t58.t22))
(step t18.t58.t24 (cl @p_289) :rule evaluate)
(step t18.t58.t25 (cl @p_287) :rule resolution :premises (t18.t58.t23 t18.t58.t24))
(step t18.t58.t26 (cl (not @p_29) (not @p_28) @p_23) :rule equiv_pos2)
(step t18.t58.t27 (cl @p_32) :rule evaluate)
(step t18.t58.t28 (cl (= @p_25 @p_6)) :rule cong :premises (t18.t58.t27 t18.t10))
(step t18.t58.t29 (cl (= @p_26 @p_30)) :rule cong :premises (t18.t58.t28))
(step t18.t58.t30 (cl (= @p_27 @p_31)) :rule cong :premises (t18.t58.t29))
(step t18.t58.t31 (cl (= (* 1/1 (- @p_6 @p_30)) (* 2/1 (- @p_6 0/1)))) :rule poly_simp)
(step t18.t58.t32 (cl (= @p_31 @p_7)) :rule poly_simp_rel :premises (t18.t58.t31))
(step t18.t58.t33 (cl (= @p_27 @p_7)) :rule trans :premises (t18.t58.t30 t18.t58.t32))
(step t18.t58.t34 (cl @p_29) :rule cong :premises (t18.t58.t33))
(step t18.t58.t35 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t18.t58.t36)
(assume t18.t58.t36.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1)))))
(step t18.t58.t36.t0 (cl (or @p_22 @p_27)) :rule forall_inst :args (0/1 d$))
(step t18.t58.t36.t1 (cl @p_22 @p_27) :rule or :premises (t18.t58.t36.t0))
(step t18.t58.t36.t2 (cl (not @p_8) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t18.t58.t36.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t18.t58.t36.t3.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t18.t58.t36.t3.t1 (cl @p_10) :rule refl)
(step t18.t58.t36.t3.t2 (cl (= @p_18 @p_12)) :rule cong :premises (t18.t58.t36.t3.t0 t18.t58.t36.t3.t1))
(step t18.t58.t36.t3.t3 (cl (= @p_16 @p_20)) :rule poly_simp)
(step t18.t58.t36.t3.t4 (cl (= @p_19 @p_21)) :rule cong :premises (t18.t58.t36.t3.t2 t18.t58.t36.t3.t3))
(step t18.t58.t36.t3.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 @p_13)))) :rule poly_simp)
(step t18.t58.t36.t3.t6 (cl (= @p_21 @p_15)) :rule poly_simp_rel :premises (t18.t58.t36.t3.t5))
(step t18.t58.t36.t3.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t18.t58.t36.t3.t4 t18.t58.t36.t3.t6))
(step t18.t58.t36.t3 (cl @p_8) :rule bind)
(step t18.t58.t36.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t18.t58.t36.t2 t18.t58.t36.t3 a9))
(step t18.t58.t36.t5 (cl @p_27) :rule resolution :premises (t18.t58.t36.t1 t18.t58.t36.t4))
(step t18.t58.t36 (cl @p_22 @p_27) :rule subproof :discharge (t18.t58.t36.a0))
(step t18.t58.t37 (cl @p_28 @p_27) :rule resolution :premises (t18.t58.t35 t18.t58.t36))
(step t18.t58.t38 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t18.t58.t39 (cl @p_28 @p_28) :rule resolution :premises (t18.t58.t37 t18.t58.t38))
(step t18.t58.t40 (cl @p_28) :rule contraction :premises (t18.t58.t39))
(step t18.t58.t41 (cl @p_23) :rule resolution :premises (t18.t58.t26 t18.t58.t34 t18.t58.t40))
(step t18.t58.t42 (cl @p_22 @p_7) :rule implies :premises (t18.t58.t41))
(step t18.t58.t43 (cl (not @p_8) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t18.t58.t44 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t18.t58.t44.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t18.t58.t44.t1 (cl @p_10) :rule refl)
(step t18.t58.t44.t2 (cl (= @p_18 @p_12)) :rule cong :premises (t18.t58.t44.t0 t18.t58.t44.t1))
(step t18.t58.t44.t3 (cl (= @p_16 @p_20)) :rule poly_simp)
(step t18.t58.t44.t4 (cl (= @p_19 @p_21)) :rule cong :premises (t18.t58.t44.t2 t18.t58.t44.t3))
(step t18.t58.t44.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 @p_13)))) :rule poly_simp)
(step t18.t58.t44.t6 (cl (= @p_21 @p_15)) :rule poly_simp_rel :premises (t18.t58.t44.t5))
(step t18.t58.t44.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t18.t58.t44.t4 t18.t58.t44.t6))
(step t18.t58.t44 (cl @p_8) :rule bind)
(step t18.t58.t45 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t18.t58.t43 t18.t58.t44 a9))
(step t18.t58.t46 (cl @p_7) :rule resolution :premises (t18.t58.t42 t18.t58.t45))
(step t18.t58.t47 (cl @p_291) :rule and_intro :premises (t18.t58.t25 t18.t58.t46))
(step t18.t58.t48 (cl @p_290) :rule resolution :premises (t18.t58.t21 t18.t58.t47))
(step t18.t58.t49 (cl (=> (! (and @p_287 (! (> @p_33 0/1) :named @p_163)) :named @p_288) @p_286)) :rule la_mult_neg)
(step t18.t58.t50 (cl (not @p_288) @p_286) :rule implies :premises (t18.t58.t49))
(step t18.t58.t51 (cl (not (! (= @p_36 @p_163) :named @p_198)) @p_155 @p_163) :rule equiv_pos2)
(step t18.t58.t52 (cl (= @p_163 (! (not (! (>= 0/1 @p_33) :named @p_199)) :named @p_201))) :rule rare_rewrite :args ("arith-elim-gt" @p_33 0/1))
(step t18.t58.t53 (cl (= (! (<= @p_33 0/1) :named @p_161) @p_199)) :rule rare_rewrite :args ("arith-elim-leq" @p_33 0/1))
(step t18.t58.t54 (cl (= @p_199 @p_161)) :rule symm :premises (t18.t58.t53))
(step t18.t58.t55 (cl (= @p_201 (! (not @p_161) :named @p_162))) :rule cong :premises (t18.t58.t54))
(step t18.t58.t56 (cl (! (= @p_163 @p_162) :named @p_200)) :rule trans :premises (t18.t58.t52 t18.t58.t55))
(step t18.t58.t57 (cl (= (* -1/1 (- 0/1 @p_33)) (* -1/1 (- @p_34 0/1)))) :rule poly_simp)
(step t18.t58.t58 (cl (= @p_199 @p_35)) :rule poly_simp_rel :premises (t18.t58.t57))
(step t18.t58.t59 (cl (= @p_161 @p_35)) :rule trans :premises (t18.t58.t53 t18.t58.t58))
(step t18.t58.t60 (cl (= @p_162 @p_36)) :rule cong :premises (t18.t58.t59))
(step t18.t58.t61 (cl (= @p_163 @p_36)) :rule trans :premises (t18.t58.t56 t18.t58.t60))
(step t18.t58.t62 (cl @p_198) :rule symm :premises (t18.t58.t61))
(step t18.t58.t63 (cl @p_163) :rule resolution :premises (t18.t58.t51 t18.t58.t62 t18.a0))
(step t18.t58.t64 (cl @p_288) :rule and_intro :premises (t18.t58.t25 t18.t58.t63))
(step t18.t58.t65 (cl @p_286) :rule resolution :premises (t18.t58.t50 t18.t58.t64))
(step t18.t58.t66 (cl @p_285) :rule resolution :premises (t18.t58.t16 t18.t58.t19 t18.t58.t48 t18.t58.t65))
(step t18.t58.t67 (cl false) :rule resolution :premises (t18.t58.t0 t18.t58.t15 t18.t58.t66))
(step t18.t58 (cl @p_281 false) :rule subproof :discharge (t18.t58.a0))
(step t18.t59 (cl @p_282 false) :rule resolution :premises (t18.t57 t18.t58))
(step t18.t60 (cl @p_282 (! (not false) :named @p_118)) :rule implies_neg2)
(step t18.t61 (cl @p_282 @p_282) :rule resolution :premises (t18.t59 t18.t60))
(step t18.t62 (cl @p_282) :rule contraction :premises (t18.t61))
(step t18.t63 (cl (= @p_282 @p_281)) :rule implies_simplify)
(step t18.t64 (cl (not @p_282) @p_281) :rule equiv1 :premises (t18.t63))
(step t18.t65 (cl @p_281) :rule resolution :premises (t18.t62 t18.t64))
(step t18.t66 (cl) :rule resolution :premises (t18.t56 t18.t65))
(step t18 (cl @p_155 (not @p_275) @p_270 false) :rule subproof :discharge (t18.a0 t18.a1 t18.a2))
(step t19 (cl @p_277 @p_36) :rule and_pos :args (0))
(step t20 (cl @p_277 @p_275) :rule and_pos :args (1))
(step t21 (cl @p_277 @p_205) :rule and_pos :args (2))
(step t22 (cl false @p_277 @p_277 @p_277) :rule resolution :premises (t18 t19 t20 t21))
(step t23 (cl @p_277 @p_277 @p_277 false) :rule reordering :premises (t22))
(step t24 (cl @p_277 false) :rule contraction :premises (t23))
(step t25 (cl @p_278 false) :rule resolution :premises (t17 t24))
(step t26 (cl @p_278 @p_118) :rule implies_neg2)
(step t27 (cl @p_278 @p_278) :rule resolution :premises (t25 t26))
(step t28 (cl @p_278) :rule contraction :premises (t27))
(step t29 (cl (= @p_278 @p_277)) :rule implies_simplify)
(step t30 (cl (not @p_278) @p_277) :rule equiv1 :premises (t29))
(step t31 (cl @p_277) :rule resolution :premises (t28 t30))
(step t32 (cl @p_274) :rule resolution :premises (t16 t31))
(step t33 (cl @p_269 @p_155 @p_270) :rule not_and :premises (t32))
(step t34 (cl @p_272 (not @p_269)) :rule or_neg :args (0))
(step t35 (cl @p_272 (not @p_155)) :rule or_neg :args (1))
(step t36 (cl @p_272 (not @p_270)) :rule or_neg :args (2))
(step t37 (cl @p_272 @p_272 @p_272) :rule resolution :premises (t33 t34 t35 t36))
(step t38 (cl @p_272) :rule contraction :premises (t37))
(step t39 (cl @p_271) :rule resolution :premises (t0 t3 t38))
(step t40 (cl @p_269 @p_35 @p_270) :rule or :premises (t39))
(step t41 (cl @p_268 @p_205) :rule and_pos :args (0))
(step t42 (cl @p_205 @p_268) :rule reordering :premises (t41))
(step t43 (cl @p_267 @p_266 @p_211) :rule equiv_pos2)
(step t44 (cl @p_211 @p_266 @p_267) :rule reordering :premises (t43))
(step t45 (cl (not @p_265) (not @p_264) @p_258) :rule equiv_pos2)
(step t46 (cl (= @p_259 0/1)) :rule poly_simp)
(step t47 (cl (= d$ d$)) :rule refl)
(step t48 (cl (= @p_260 @p_6)) :rule cong :premises (t46 t47))
(step t49 (cl (= @p_261 @p_209)) :rule cong :premises (t48))
(step t50 (cl (= @p_262 @p_213)) :rule cong :premises (t48 t49))
(step t51 (cl (= @p_263 @p_246)) :rule cong :premises (t50))
(step t52 (cl @p_265) :rule cong :premises (t51))
(step t53 (cl @p_264 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule implies_neg1)
(anchor :step t54)
(assume t54.a0 (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$))))))
(step t54.t0 (cl (or @p_257 @p_263)) :rule forall_inst :args (@p_207))
(step t54.t1 (cl @p_257 @p_263) :rule or :premises (t54.t0))
(step t54.t2 (cl (not @p_247) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t54.t3 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t54.t3.t0 (cl (= @p_253 @p_249)) :rule poly_simp)
(step t54.t3.t1 (cl (= @p_254 @p_250)) :rule cong :premises (t54.t3.t0 t47))
(step t54.t3.t2 (cl (= @p_255 @p_251)) :rule cong :premises (t54.t3.t1))
(step t54.t3.t3 (cl (= @p_256 @p_252)) :rule cong :premises (t54.t3.t1 t54.t3.t2))
(step t54.t3.t4 (cl (= (= @p_231 @p_256) (= @p_231 @p_252))) :rule cong :premises (t54.t3.t3))
(step t54.t3 (cl @p_247) :rule bind)
(step t54.t4 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t54.t2 t54.t3 a0))
(step t54.t5 (cl @p_263) :rule resolution :premises (t54.t1 t54.t4))
(step t54 (cl @p_257 @p_263) :rule subproof :discharge (t54.a0))
(step t55 (cl @p_264 @p_263) :rule resolution :premises (t53 t54))
(step t56 (cl @p_264 (not @p_263)) :rule implies_neg2)
(step t57 (cl @p_264 @p_264) :rule resolution :premises (t55 t56))
(step t58 (cl @p_264) :rule contraction :premises (t57))
(step t59 (cl @p_258) :rule resolution :premises (t45 t52 t58))
(step t60 (cl @p_257 @p_246) :rule implies :premises (t59))
(step t61 (cl (not @p_247) (not (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$) (diamond_y$ (times$ (- ?v0 (divide$ 1/1 2/1)) d$)))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule equiv_pos2)
(anchor :step t62 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t62.t0 (cl (= @p_253 @p_249)) :rule poly_simp)
(step t62.t1 (cl (= @p_254 @p_250)) :rule cong :premises (t62.t0 t47))
(step t62.t2 (cl (= @p_255 @p_251)) :rule cong :premises (t62.t1))
(step t62.t3 (cl (= @p_256 @p_252)) :rule cong :premises (t62.t1 t62.t2))
(step t62.t4 (cl (= (= @p_231 @p_256) (= @p_231 @p_252))) :rule cong :premises (t62.t3))
(step t62 (cl @p_247) :rule bind)
(step t63 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$) (diamond_y$ (times$ (+ ?v0 (* -1/1 (divide$ 1/1 2/1))) d$)))))) :rule resolution :premises (t61 t62 a0))
(step t64 (cl @p_246) :rule resolution :premises (t60 t63))
(step t65 (cl (= @p_213 @p_224)) :rule symm :premises (t64))
(step t66 (cl (or @p_245 @p_225)) :rule forall_inst :args (@p_207))
(step t67 (cl @p_245 @p_225) :rule or :premises (t66))
(step t68 (cl (not @p_226) (not (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1)))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule equiv_pos2)
(anchor :step t69 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t69.t0 (cl (= @p_237 @p_34)) :rule poly_simp)
(step t69.t1 (cl (= @p_239 @p_243)) :rule poly_simp)
(step t69.t2 (cl (= @p_242 -1/1)) :rule evaluate)
(step t69.t3 (cl (= @p_243 @p_244)) :rule cong :premises (t69.t2))
(step t69.t4 (cl (= @p_244 @p_228)) :rule poly_simp)
(step t69.t5 (cl (= @p_243 @p_228)) :rule trans :premises (t69.t3 t69.t4))
(step t69.t6 (cl (= @p_239 @p_228)) :rule trans :premises (t69.t1 t69.t5))
(step t69.t7 (cl (= @p_238 @p_206)) :rule cong :premises (t69.t0))
(step t69.t8 (cl (= @p_240 @p_229)) :rule cong :premises (t69.t6 t69.t7))
(step t69.t9 (cl (= @p_241 @p_230)) :rule cong :premises (t69.t0 t69.t8))
(step t69.t10 (cl (= (= @p_232 @p_241) @p_233)) :rule cong :premises (t69.t9))
(step t69 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (- (divide$ d$ 2/1)) (times$ (- (* 2/1 ?v0) 1/1) (diamond_y$ (- (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(anchor :step t70 :args ((?v0 Real) (:= (?v0 Real) ?v0)))
(step t70.t0 (cl (not @p_234) (not @p_5) @p_3) :rule equiv_pos2)
(step t70.t1 (cl (= @p_4 @p_235)) :rule rare_rewrite :args ("bool-impl-false1" @p_3))
(step t70.t2 (cl (= @p_5 @p_236)) :rule cong :premises (t70.t1))
(step t70.t3 (cl (= @p_236 @p_3)) :rule rare_rewrite :args ("bool-double-not-elim" @p_3))
(step t70.t4 (cl @p_234) :rule trans :premises (t70.t2 t70.t3))
(step t70.t5 (cl @p_3) :rule resolution :premises (t70.t0 t70.t4 a11))
(step t70.t6 (cl @p_2) :rule and :premises (t70.t5) :args (1))
(step t70.t7 (cl @p_9) :rule refl)
(step t70.t8 (cl (= @p_232 @p_231)) :rule cong :premises (t70.t6 t70.t7))
(step t70.t9 (cl (= @p_230 @p_230)) :rule refl)
(step t70.t10 (cl (= @p_233 (= @p_231 @p_230))) :rule cong :premises (t70.t8 t70.t9))
(step t70 (cl (= (forall ((?v0 Real)) (= (fun_app$ uub$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))) (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1))))))))) :rule bind)
(step t71 (cl @p_226) :rule trans :premises (t69 t70))
(step t72 (cl (forall ((?v0 Real)) (= (fun_app$ uuc$ ?v0) (pair$ (* -1/1 (divide$ d$ 2/1)) (times$ (+ -1/1 (* 2/1 ?v0)) (diamond_y$ (* -1/1 (divide$ d$ 2/1)))))))) :rule resolution :premises (t68 t71 a3))
(step t73 (cl @p_225) :rule resolution :premises (t67 t72))
(step t74 (cl @p_214) :rule trans :premises (t65 t73))
(step t75 (cl (not @p_222) (not @p_221) @p_217) :rule equiv_pos2)
(step t76 (cl (= (* 1/1 (- @p_6 @p_34)) @p_223)) :rule poly_simp)
(step t77 (cl (= @p_218 @p_205)) :rule poly_simp_rel :premises (t76))
(step t78 (cl (= @p_210 @p_210)) :rule refl)
(step t79 (cl (= @p_219 @p_211)) :rule cong :premises (t77 t78))
(step t80 (cl (= @p_220 @p_215)) :rule cong :premises (t79))
(step t81 (cl @p_222) :rule cong :premises (t80))
(step t82 (cl @p_221 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) :rule implies_neg1)
(anchor :step t83)
(assume t83.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (= (= (pair$ ?v0 ?v1) (pair$ ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))))
(step t83.t0 (cl (or @p_216 @p_220)) :rule forall_inst :args (@p_6 @p_209 @p_34 @p_208))
(step t83.t1 (cl @p_216 @p_220) :rule or :premises (t83.t0))
(step t83.t2 (cl @p_220) :rule resolution :premises (t83.t1 t83.a0))
(step t83 (cl @p_216 @p_220) :rule subproof :discharge (t83.a0))
(step t84 (cl @p_221 @p_220) :rule resolution :premises (t82 t83))
(step t85 (cl @p_221 (not @p_220)) :rule implies_neg2)
(step t86 (cl @p_221 @p_221) :rule resolution :premises (t84 t85))
(step t87 (cl @p_221) :rule contraction :premises (t86))
(step t88 (cl @p_217) :rule resolution :premises (t75 t81 t87))
(step t89 (cl @p_216 @p_215) :rule implies :premises (t88))
(step t90 (cl @p_215) :rule resolution :premises (t89 a10))
(step t91 (cl @p_211) :rule resolution :premises (t44 t74 t90))
(step t92 (cl @p_205) :rule resolution :premises (t42 t91))
(step t93 (cl (not (! (= (! (or (! (not (! (= @p_33 (! (* -1/1 (! (divide$ (! (* -1/1 d$) :named @p_37) 2/1) :named @p_38)) :named @p_140)) :named @p_141)) :named @p_152) @p_36 (! (not (! (not (! (>= (! (+ @p_34 @p_38) :named @p_39) 0/1) :named @p_40)) :named @p_41)) :named @p_138)) :named @p_154) (! (or @p_152 @p_36 @p_40) :named @p_153)) :named @p_204)) (not @p_154) @p_153) :rule equiv_pos2)
(step t94 (cl (= @p_138 @p_40)) :rule rare_rewrite :args ("bool-double-not-elim" @p_40))
(step t95 (cl @p_204) :rule cong :premises (t94))
(step t96 (cl (! (=> (! (and @p_141 @p_35 @p_41) :named @p_156) (! (and @p_41 @p_141 @p_35) :named @p_158)) :named @p_203) @p_156) :rule implies_neg1)
(anchor :step t97)
(assume t97.a0 @p_141)
(assume t97.a1 @p_35)
(assume t97.a2 @p_41)
(step t97.t0 (cl (not (! (= (! (or (! (not (! (= (! (not (! (>= @p_37 0/1) :named @p_42)) :named @p_43) @p_41) :named @p_44)) :named @p_134) (! (not @p_43) :named @p_136) @p_41) :named @p_137) (! (or @p_134 @p_42 @p_41) :named @p_135)) :named @p_139)) (not @p_137) @p_135) :rule equiv_pos2)
(step t97.t1 (cl (= @p_136 @p_42)) :rule rare_rewrite :args ("bool-double-not-elim" @p_42))
(step t97.t2 (cl (= @p_41 @p_41)) :rule refl)
(step t97.t3 (cl @p_139) :rule cong :premises (t97.t1 t97.t2))
(step t97.t4 (cl @p_134 @p_136 @p_41) :rule equiv_pos2)
(step t97.t5 (cl @p_137 (not @p_134)) :rule or_neg :args (0))
(step t97.t6 (cl @p_137 (not @p_136)) :rule or_neg :args (1))
(step t97.t7 (cl @p_137 @p_138) :rule or_neg :args (2))
(step t97.t8 (cl @p_137 @p_137 @p_137) :rule resolution :premises (t97.t4 t97.t5 t97.t6 t97.t7))
(step t97.t9 (cl @p_137) :rule contraction :premises (t97.t8))
(step t97.t10 (cl @p_135) :rule resolution :premises (t97.t0 t97.t3 t97.t9))
(step t97.t11 (cl @p_134 @p_42 @p_41) :rule or :premises (t97.t10))
(step t97.t12 (cl @p_42 @p_41 @p_134) :rule reordering :premises (t97.t11))
(step t97.t13 (cl (not (! (= @p_1 @p_43) :named @p_131)) (not @p_1) @p_43) :rule equiv_pos2)
(step t97.t14 (cl (= @p_1 (! (not (! (>= 0/1 d$) :named @p_132)) :named @p_133))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 d$))
(step t97.t15 (cl (= (* -1/1 (- 0/1 d$)) (* -1/1 (! (- @p_37 0/1) :named @p_129)))) :rule poly_simp)
(step t97.t16 (cl (= @p_132 @p_42)) :rule poly_simp_rel :premises (t97.t15))
(step t97.t17 (cl (= @p_133 @p_43)) :rule cong :premises (t97.t16))
(step t97.t18 (cl @p_131) :rule trans :premises (t97.t14 t97.t17))
(step t97.t19 (cl @p_43) :rule resolution :premises (t97.t13 t97.t18 a4))
(step t97.t20 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (! (= (! (not (! (>= (! (+ @p_38 @p_34) :named @p_110) 0/1) :named @p_111)) :named @p_112) (! (and (! (or (! (>= (! (* -1/1 2/1) :named @p_106) 0/1) :named @p_107) (! (not (! (>= (! (+ @p_37 @p_37) :named @p_103) 0/1) :named @p_104)) :named @p_105)) :named @p_108) (! (or (! (>= 2/1 0/1) :named @p_101) (! (not (! (>= (! (+ (! (* -1/1 @p_37) :named @p_97) d$) :named @p_98) 0/1) :named @p_99)) :named @p_100)) :named @p_102) (! (not (! (= 2/1 0/1) :named @p_95)) :named @p_96)) :named @p_109)) :named @p_113)) :named @p_114) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) @p_44) :named @p_94)) :named @p_115)) (not @p_114) @p_94) :rule equiv_pos2)
(step t97.t21 (cl (= @p_110 @p_39)) :rule poly_simp)
(step t97.t22 (cl (! (= 0/1 0/1) :named @p_124)) :rule refl)
(step t97.t23 (cl (= @p_111 @p_40)) :rule cong :premises (t97.t21 t97.t22))
(step t97.t24 (cl (= @p_112 @p_41)) :rule cong :premises (t97.t23))
(step t97.t25 (cl (= @p_106 -2/1)) :rule evaluate)
(step t97.t26 (cl @p_124) :rule refl)
(step t97.t27 (cl (= @p_107 (! (>= -2/1 0/1) :named @p_130))) :rule cong :premises (t97.t25 t97.t26))
(step t97.t28 (cl (= @p_130 false)) :rule evaluate)
(step t97.t29 (cl (= @p_107 false)) :rule trans :premises (t97.t27 t97.t28))
(step t97.t30 (cl (= @p_103 (! (* -2/1 d$) :named @p_127))) :rule poly_simp)
(step t97.t31 (cl @p_124) :rule refl)
(step t97.t32 (cl (= @p_104 (! (>= @p_127 0/1) :named @p_128))) :rule cong :premises (t97.t30 t97.t31))
(step t97.t33 (cl (= (* -1/1 (- @p_127 0/1)) (* -2/1 @p_129))) :rule poly_simp)
(step t97.t34 (cl (= @p_128 @p_42)) :rule poly_simp_rel :premises (t97.t33))
(step t97.t35 (cl (= @p_104 @p_42)) :rule trans :premises (t97.t32 t97.t34))
(step t97.t36 (cl (= @p_105 @p_43)) :rule cong :premises (t97.t35))
(step t97.t37 (cl (= @p_108 (! (or false @p_43) :named @p_126))) :rule cong :premises (t97.t29 t97.t36))
(step t97.t38 (cl (= @p_126 @p_43)) :rule aci_simp)
(step t97.t39 (cl (= @p_108 @p_43)) :rule trans :premises (t97.t37 t97.t38))
(step t97.t40 (cl (= @p_101 true)) :rule evaluate)
(step t97.t41 (cl (= @p_97 d$)) :rule poly_simp)
(step t97.t42 (cl (= @p_98 (! (+ d$ d$) :named @p_125))) :rule cong :premises (t97.t41 t47))
(step t97.t43 (cl (= @p_125 (! (* 2/1 d$) :named @p_122))) :rule poly_simp)
(step t97.t44 (cl (= @p_98 @p_122)) :rule trans :premises (t97.t42 t97.t43))
(step t97.t45 (cl @p_124) :rule refl)
(step t97.t46 (cl (= @p_99 (! (>= @p_122 0/1) :named @p_123))) :rule cong :premises (t97.t44 t97.t45))
(step t97.t47 (cl (= (* 1/1 (- @p_122 0/1)) (* 2/1 (- d$ 0/1)))) :rule poly_simp)
(step t97.t48 (cl (= @p_123 (! (>= d$ 0/1) :named @p_119))) :rule poly_simp_rel :premises (t97.t47))
(step t97.t49 (cl (= @p_99 @p_119)) :rule trans :premises (t97.t46 t97.t48))
(step t97.t50 (cl (= @p_100 (! (not @p_119) :named @p_120))) :rule cong :premises (t97.t49))
(step t97.t51 (cl (= @p_102 (! (or true @p_120) :named @p_121))) :rule cong :premises (t97.t40 t97.t50))
(step t97.t52 (cl (= @p_121 true)) :rule or_simplify)
(step t97.t53 (cl (= @p_102 true)) :rule trans :premises (t97.t51 t97.t52))
(step t97.t54 (cl (= @p_95 false)) :rule evaluate)
(step t97.t55 (cl (= @p_96 @p_118)) :rule cong :premises (t97.t54))
(step t97.t56 (cl (= @p_118 true)) :rule evaluate)
(step t97.t57 (cl (= @p_96 true)) :rule trans :premises (t97.t55 t97.t56))
(step t97.t58 (cl (= @p_109 (! (and @p_43 true true) :named @p_117))) :rule cong :premises (t97.t39 t97.t53 t97.t57))
(step t97.t59 (cl (= @p_117 @p_43)) :rule aci_simp)
(step t97.t60 (cl (= @p_109 @p_43)) :rule trans :premises (t97.t58 t97.t59))
(step t97.t61 (cl (= @p_113 (! (= @p_41 @p_43) :named @p_116))) :rule cong :premises (t97.t24 t97.t60))
(step t97.t62 (cl (= @p_116 @p_44)) :rule rare_rewrite :args ("eq-symm" @p_41 @p_43))
(step t97.t63 (cl (= @p_113 @p_44)) :rule trans :premises (t97.t61 t97.t62))
(step t97.t64 (cl @p_115) :rule cong :premises (t97.t63))
(step t97.t65 (cl @p_114 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule implies_neg1)
(anchor :step t97.t66)
(assume t97.t66.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))
(step t97.t66.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :named @p_93) @p_113)) :rule forall_inst :args (@p_37 2/1 d$))
(step t97.t66.t1 (cl @p_93 @p_113) :rule or :premises (t97.t66.t0))
(step t97.t66.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :named @p_45)) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t97.t66.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t97.t66.t3.t0 (cl (= (! (< (! (divide$ ?v0 ?v1) :named @p_61) (! (divide$ ?v2 ?v1) :named @p_60)) :named @p_83) (! (not (! (>= @p_61 @p_60) :named @p_91)) :named @p_92))) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t97.t66.t3.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- (! (+ @p_61 (* -1/1 @p_60)) :named @p_62) 0/1)))) :rule poly_simp)
(step t97.t66.t3.t2 (cl (= @p_91 (! (>= @p_62 0/1) :named @p_63))) :rule poly_simp_rel :premises (t97.t66.t3.t1))
(step t97.t66.t3.t3 (cl (= @p_92 (! (not @p_63) :named @p_64))) :rule cong :premises (t97.t66.t3.t2))
(step t97.t66.t3.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t97.t66.t3.t0 t97.t66.t3.t3))
(step t97.t66.t3.t5 (cl (= (! (and (! (=> (! (< 0/1 ?v1) :named @p_80) (! (< ?v0 ?v2) :named @p_79)) :named @p_81) (and (! (=> (! (< ?v1 0/1) :named @p_77) (! (< ?v2 ?v0) :named @p_76)) :named @p_78) (! (not (= ?v1 0/1)) :named @p_47))) :named @p_82) (! (and @p_81 @p_78 @p_47) :named @p_84))) :rule aci_simp)
(step t97.t66.t3.t6 (cl (= @p_80 (! (not (! (>= 0/1 ?v1) :named @p_89)) :named @p_90))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t97.t66.t3.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- (! (* -1/1 ?v1) :named @p_56) 0/1)))) :rule poly_simp)
(step t97.t66.t3.t8 (cl (= @p_89 (! (>= @p_56 0/1) :named @p_57))) :rule poly_simp_rel :premises (t97.t66.t3.t7))
(step t97.t66.t3.t9 (cl (= @p_90 (! (not @p_57) :named @p_67))) :rule cong :premises (t97.t66.t3.t8))
(step t97.t66.t3.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t97.t66.t3.t6 t97.t66.t3.t9))
(step t97.t66.t3.t11 (cl (= @p_79 (! (not (! (>= ?v0 ?v2) :named @p_87)) :named @p_88))) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t97.t66.t3.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- (! (+ ?v0 (* -1/1 ?v2)) :named @p_53) 0/1)))) :rule poly_simp)
(step t97.t66.t3.t13 (cl (= @p_87 (! (>= @p_53 0/1) :named @p_54))) :rule poly_simp_rel :premises (t97.t66.t3.t12))
(step t97.t66.t3.t14 (cl (= @p_88 (! (not @p_54) :named @p_55))) :rule cong :premises (t97.t66.t3.t13))
(step t97.t66.t3.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t97.t66.t3.t11 t97.t66.t3.t14))
(step t97.t66.t3.t16 (cl (= @p_81 (! (=> @p_67 @p_55) :named @p_68))) :rule cong :premises (t97.t66.t3.t10 t97.t66.t3.t15))
(step t97.t66.t3.t17 (cl (= @p_77 (! (not (! (>= ?v1 0/1) :named @p_51)) :named @p_65))) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t97.t66.t3.t18 (cl (= @p_76 (! (not (! (>= ?v2 ?v0) :named @p_85)) :named @p_86))) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t97.t66.t3.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- (! (+ @p_11 ?v2) :named @p_48) 0/1)))) :rule poly_simp)
(step t97.t66.t3.t20 (cl (= @p_85 (! (>= @p_48 0/1) :named @p_49))) :rule poly_simp_rel :premises (t97.t66.t3.t19))
(step t97.t66.t3.t21 (cl (= @p_86 (! (not @p_49) :named @p_50))) :rule cong :premises (t97.t66.t3.t20))
(step t97.t66.t3.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t97.t66.t3.t18 t97.t66.t3.t21))
(step t97.t66.t3.t23 (cl (= @p_78 (! (=> @p_65 @p_50) :named @p_66))) :rule cong :premises (t97.t66.t3.t17 t97.t66.t3.t22))
(step t97.t66.t3.t24 (cl (! (= @p_47 @p_47) :named @p_71)) :rule refl)
(step t97.t66.t3.t25 (cl (= @p_84 (! (and @p_68 @p_66 @p_47) :named @p_69))) :rule cong :premises (t97.t66.t3.t16 t97.t66.t3.t23 t97.t66.t3.t24))
(step t97.t66.t3.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t97.t66.t3.t5 t97.t66.t3.t25))
(step t97.t66.t3.t27 (cl (= (= @p_83 @p_82) (! (= @p_64 @p_69) :named @p_70))) :rule cong :premises (t97.t66.t3.t4 t97.t66.t3.t26))
(step t97.t66.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t97.t66.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t97.t66.t4.t0 (cl (= @p_68 (! (or (! (not @p_67) :named @p_74) @p_55) :named @p_75))) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t97.t66.t4.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t97.t66.t4.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t97.t66.t4.t3 (cl (= @p_75 (! (or @p_57 @p_55) :named @p_58))) :rule cong :premises (t97.t66.t4.t1 t97.t66.t4.t2))
(step t97.t66.t4.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t97.t66.t4.t0 t97.t66.t4.t3))
(step t97.t66.t4.t5 (cl (= @p_66 (! (or (! (not @p_65) :named @p_72) @p_50) :named @p_73))) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t97.t66.t4.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t97.t66.t4.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t97.t66.t4.t8 (cl (= @p_73 (! (or @p_51 @p_50) :named @p_52))) :rule cong :premises (t97.t66.t4.t6 t97.t66.t4.t7))
(step t97.t66.t4.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t97.t66.t4.t5 t97.t66.t4.t8))
(step t97.t66.t4.t10 (cl @p_71) :rule refl)
(step t97.t66.t4.t11 (cl (= @p_69 (! (and @p_58 @p_52 @p_47) :named @p_59))) :rule cong :premises (t97.t66.t4.t4 t97.t66.t4.t9 t97.t66.t4.t10))
(step t97.t66.t4.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t97.t66.t4.t11))
(step t97.t66.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t97.t66.t5 (cl @p_45) :rule trans :premises (t97.t66.t3 t97.t66.t4))
(step t97.t66.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t97.t66.t2 t97.t66.t5 a6))
(step t97.t66.t7 (cl @p_113) :rule resolution :premises (t97.t66.t1 t97.t66.t6))
(step t97.t66 (cl @p_93 @p_113) :rule subproof :discharge (t97.t66.a0))
(step t97.t67 (cl @p_114 @p_113) :rule resolution :premises (t97.t65 t97.t66))
(step t97.t68 (cl @p_114 (not @p_113)) :rule implies_neg2)
(step t97.t69 (cl @p_114 @p_114) :rule resolution :premises (t97.t67 t97.t68))
(step t97.t70 (cl @p_114) :rule contraction :premises (t97.t69))
(step t97.t71 (cl @p_94) :rule resolution :premises (t97.t20 t97.t64 t97.t70))
(step t97.t72 (cl @p_93 @p_44) :rule implies :premises (t97.t71))
(step t97.t73 (cl (not @p_45) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t97.t74 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t97.t74.t0 (cl (= @p_83 @p_92)) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t97.t74.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t97.t74.t2 (cl (= @p_91 @p_63)) :rule poly_simp_rel :premises (t97.t74.t1))
(step t97.t74.t3 (cl (= @p_92 @p_64)) :rule cong :premises (t97.t74.t2))
(step t97.t74.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t97.t74.t0 t97.t74.t3))
(step t97.t74.t5 (cl (= @p_82 @p_84)) :rule aci_simp)
(step t97.t74.t6 (cl (= @p_80 @p_90)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t97.t74.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- @p_56 0/1)))) :rule poly_simp)
(step t97.t74.t8 (cl (= @p_89 @p_57)) :rule poly_simp_rel :premises (t97.t74.t7))
(step t97.t74.t9 (cl (= @p_90 @p_67)) :rule cong :premises (t97.t74.t8))
(step t97.t74.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t97.t74.t6 t97.t74.t9))
(step t97.t74.t11 (cl (= @p_79 @p_88)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t97.t74.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- @p_53 0/1)))) :rule poly_simp)
(step t97.t74.t13 (cl (= @p_87 @p_54)) :rule poly_simp_rel :premises (t97.t74.t12))
(step t97.t74.t14 (cl (= @p_88 @p_55)) :rule cong :premises (t97.t74.t13))
(step t97.t74.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t97.t74.t11 t97.t74.t14))
(step t97.t74.t16 (cl (= @p_81 @p_68)) :rule cong :premises (t97.t74.t10 t97.t74.t15))
(step t97.t74.t17 (cl (= @p_77 @p_65)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t97.t74.t18 (cl (= @p_76 @p_86)) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t97.t74.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- @p_48 0/1)))) :rule poly_simp)
(step t97.t74.t20 (cl (= @p_85 @p_49)) :rule poly_simp_rel :premises (t97.t74.t19))
(step t97.t74.t21 (cl (= @p_86 @p_50)) :rule cong :premises (t97.t74.t20))
(step t97.t74.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t97.t74.t18 t97.t74.t21))
(step t97.t74.t23 (cl (= @p_78 @p_66)) :rule cong :premises (t97.t74.t17 t97.t74.t22))
(step t97.t74.t24 (cl @p_71) :rule refl)
(step t97.t74.t25 (cl (= @p_84 @p_69)) :rule cong :premises (t97.t74.t16 t97.t74.t23 t97.t74.t24))
(step t97.t74.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t97.t74.t5 t97.t74.t25))
(step t97.t74.t27 (cl (= (= @p_83 @p_82) @p_70)) :rule cong :premises (t97.t74.t4 t97.t74.t26))
(step t97.t74 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t97.t75 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t97.t75.t0 (cl (= @p_68 @p_75)) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t97.t75.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t97.t75.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t97.t75.t3 (cl (= @p_75 @p_58)) :rule cong :premises (t97.t75.t1 t97.t75.t2))
(step t97.t75.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t97.t75.t0 t97.t75.t3))
(step t97.t75.t5 (cl (= @p_66 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t97.t75.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t97.t75.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t97.t75.t8 (cl (= @p_73 @p_52)) :rule cong :premises (t97.t75.t6 t97.t75.t7))
(step t97.t75.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t97.t75.t5 t97.t75.t8))
(step t97.t75.t10 (cl @p_71) :rule refl)
(step t97.t75.t11 (cl (= @p_69 @p_59)) :rule cong :premises (t97.t75.t4 t97.t75.t9 t97.t75.t10))
(step t97.t75.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t97.t75.t11))
(step t97.t75 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t97.t76 (cl @p_45) :rule trans :premises (t97.t74 t97.t75))
(step t97.t77 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t97.t73 t97.t76 a6))
(step t97.t78 (cl @p_44) :rule resolution :premises (t97.t72 t97.t77))
(step t97.t79 (cl @p_41) :rule resolution :premises (t97.t12 t97.t19 t97.t78))
(step t97.t80 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :named @p_151) @p_141)) :rule forall_inst :args (d$ 2/1))
(step t97.t81 (cl @p_151 @p_141) :rule or :premises (t97.t80))
(step t97.t82 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (divide$ (- ?v0) ?v1) (- (divide$ ?v0 ?v1)))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :named @p_142)) (not (forall ((?v0 Real) (?v1 Real)) (= (divide$ (- ?v0) ?v1) (- (divide$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t97.t83 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t97.t83.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t97.t83.t1 (cl @p_10) :rule refl)
(step t97.t83.t2 (cl (= (! (divide$ @p_17 ?v1) :named @p_147) (! (divide$ @p_11 ?v1) :named @p_143))) :rule cong :premises (t97.t83.t0 t97.t83.t1))
(step t97.t83.t3 (cl (= (! (- @p_61) :named @p_146) (! (* -1/1 @p_61) :named @p_149))) :rule poly_simp)
(step t97.t83.t4 (cl (= (! (= @p_147 @p_146) :named @p_148) (! (= @p_143 @p_149) :named @p_150))) :rule cong :premises (t97.t83.t2 t97.t83.t3))
(step t97.t83.t5 (cl (= (* 1/1 (- @p_143 @p_149)) (* 1/1 (- @p_61 (! (* -1/1 @p_143) :named @p_144))))) :rule poly_simp)
(step t97.t83.t6 (cl (= @p_150 (! (= @p_61 @p_144) :named @p_145))) :rule poly_simp_rel :premises (t97.t83.t5))
(step t97.t83.t7 (cl (= @p_148 @p_145)) :rule trans :premises (t97.t83.t4 t97.t83.t6))
(step t97.t83 (cl @p_142) :rule bind)
(step t97.t84 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t97.t82 t97.t83 a8))
(step t97.t85 (cl @p_141) :rule resolution :premises (t97.t81 t97.t84))
(step t97.t86 (cl @p_158) :rule and_intro :premises (t97.t79 t97.t85 t97.a1))
(step t97 (cl @p_152 @p_36 @p_138 @p_158) :rule subproof :discharge (t97.a0 t97.a1 t97.a2))
(step t98 (cl (! (not @p_156) :named @p_157) @p_141) :rule and_pos :args (0))
(step t99 (cl @p_157 @p_35) :rule and_pos :args (1))
(step t100 (cl @p_157 @p_41) :rule and_pos :args (2))
(step t101 (cl @p_158 @p_157 @p_157 @p_157) :rule resolution :premises (t97 t98 t99 t100))
(step t102 (cl @p_157 @p_157 @p_157 @p_158) :rule reordering :premises (t101))
(step t103 (cl @p_157 @p_158) :rule contraction :premises (t102))
(step t104 (cl @p_203 @p_158) :rule resolution :premises (t96 t103))
(step t105 (cl @p_203 (! (not @p_158) :named @p_159)) :rule implies_neg2)
(step t106 (cl @p_203 @p_203) :rule resolution :premises (t104 t105))
(step t107 (cl @p_203) :rule contraction :premises (t106))
(step t108 (cl @p_157 @p_158) :rule implies :premises (t107))
(step t109 (cl (! (=> @p_158 false) :named @p_160) @p_158) :rule implies_neg1)
(anchor :step t110)
(assume t110.a0 @p_41)
(assume t110.a1 @p_141)
(assume t110.a2 @p_35)
(step t110.t0 (cl (not (! (= @p_35 @p_161) :named @p_202)) @p_36 @p_161) :rule equiv_pos2)
(step t110.t1 (cl (= @p_161 @p_199)) :rule rare_rewrite :args ("arith-elim-leq" @p_33 0/1))
(step t110.t2 (cl (= (* -1/1 (- 0/1 @p_33)) (* -1/1 (- @p_34 0/1)))) :rule poly_simp)
(step t110.t3 (cl (= @p_199 @p_35)) :rule poly_simp_rel :premises (t110.t2))
(step t110.t4 (cl (= @p_161 @p_35)) :rule trans :premises (t110.t1 t110.t3))
(step t110.t5 (cl @p_202) :rule symm :premises (t110.t4))
(step t110.t6 (cl @p_161) :rule resolution :premises (t110.t0 t110.t5 t110.a2))
(step t110.t7 (cl (not @p_200) (not @p_163) @p_162) :rule equiv_pos2)
(step t110.t8 (cl (= @p_163 @p_201)) :rule rare_rewrite :args ("arith-elim-gt" @p_33 0/1))
(step t110.t9 (cl (= @p_199 @p_161)) :rule symm :premises (t110.t1))
(step t110.t10 (cl (= @p_201 @p_162)) :rule cong :premises (t110.t9))
(step t110.t11 (cl @p_200) :rule trans :premises (t110.t8 t110.t10))
(step t110.t12 (cl (not (! (= @p_162 @p_163) :named @p_197)) (not @p_162) @p_163) :rule equiv_pos2)
(step t110.t13 (cl (= @p_162 @p_36)) :rule cong :premises (t110.t4))
(step t110.t14 (cl (= @p_163 @p_36)) :rule trans :premises (t110.t11 t110.t13))
(step t110.t15 (cl @p_198) :rule symm :premises (t110.t14))
(step t110.t16 (cl @p_197) :rule trans :premises (t110.t13 t110.t15))
(step t110.t17 (cl (! (=> @p_161 false) :named @p_164) @p_161) :rule implies_neg1)
(anchor :step t110.t18)
(assume t110.t18.a0 @p_161)
(step t110.t18.t0 (cl (not (! (= (! (< (! (+ @p_33 (! (* -1/2 (! (+ @p_33 @p_38) :named @p_169)) :named @p_170) (! (* -1/2 (! (+ @p_33 @p_140) :named @p_167)) :named @p_168)) :named @p_171) (! (+ 0/1 (! (* -1/2 0/1) :named @p_165) @p_165) :named @p_166)) :named @p_172) false) :named @p_187)) (not @p_172) false) :rule equiv_pos2)
(step t110.t18.t1 (cl (= @p_172 (! (not (! (>= @p_171 @p_166) :named @p_188)) :named @p_189))) :rule rare_rewrite :args ("arith-elim-lt" @p_171 @p_166))
(step t110.t18.t2 (cl (= @p_170 (! (+ (! (* -1/2 @p_33) :named @p_193) (* -1/2 @p_38)) :named @p_195))) :rule poly_simp)
(step t110.t18.t3 (cl (= @p_168 (! (+ @p_193 (* 1/2 @p_38)) :named @p_194))) :rule poly_simp)
(step t110.t18.t4 (cl (= @p_171 (! (+ @p_33 @p_195 @p_194) :named @p_196))) :rule cong :premises (t110.t18.t2 t110.t18.t3))
(step t110.t18.t5 (cl (= @p_196 0/1)) :rule poly_simp)
(step t110.t18.t6 (cl (= @p_171 0/1)) :rule trans :premises (t110.t18.t4 t110.t18.t5))
(step t110.t18.t7 (cl (= @p_165 0/1)) :rule evaluate)
(step t110.t18.t8 (cl (= @p_166 @p_192)) :rule cong :premises (t110.t18.t7 t110.t18.t7))
(step t110.t18.t9 (cl (= @p_192 0/1)) :rule evaluate)
(step t110.t18.t10 (cl (= @p_166 0/1)) :rule trans :premises (t110.t18.t8 t110.t18.t9))
(step t110.t18.t11 (cl (= @p_188 @p_191)) :rule cong :premises (t110.t18.t6 t110.t18.t10))
(step t110.t18.t12 (cl (= @p_191 true)) :rule evaluate)
(step t110.t18.t13 (cl (= @p_188 true)) :rule trans :premises (t110.t18.t11 t110.t18.t12))
(step t110.t18.t14 (cl (= @p_189 @p_190)) :rule cong :premises (t110.t18.t13))
(step t110.t18.t15 (cl (= @p_190 false)) :rule evaluate)
(step t110.t18.t16 (cl (= @p_189 false)) :rule trans :premises (t110.t18.t14 t110.t18.t15))
(step t110.t18.t17 (cl @p_187) :rule trans :premises (t110.t18.t1 t110.t18.t16))
(step t110.t18.t18 (cl @p_162 (not (! (= @p_170 @p_165) :named @p_183)) (not (! (< @p_168 @p_165) :named @p_173)) @p_172) :rule la_generic :args (1/1 -1/1 1/1 1/1))
(step t110.t18.t19 (cl (=> (! (and (! (< -1/2 0/1) :named @p_175) (! (= @p_169 0/1) :named @p_184)) :named @p_185) @p_183)) :rule la_mult_neg)
(step t110.t18.t20 (cl (not @p_185) @p_183) :rule implies :premises (t110.t18.t19))
(step t110.t18.t21 (cl (= (! (= @p_175 true) :named @p_182) @p_175)) :rule equiv_simplify)
(step t110.t18.t22 (cl (not @p_182) @p_175) :rule equiv1 :premises (t110.t18.t21))
(step t110.t18.t23 (cl @p_182) :rule evaluate)
(step t110.t18.t24 (cl @p_175) :rule resolution :premises (t110.t18.t22 t110.t18.t23))
(step t110.t18.t25 (cl (not (! (= @p_141 @p_184) :named @p_186)) @p_152 @p_184) :rule equiv_pos2)
(step t110.t18.t26 (cl (= (* 1/1 (- @p_169 0/1)) (* 1/1 (- @p_33 @p_140)))) :rule poly_simp)
(step t110.t18.t27 (cl (= @p_184 @p_141)) :rule poly_simp_rel :premises (t110.t18.t26))
(step t110.t18.t28 (cl @p_186) :rule symm :premises (t110.t18.t27))
(step t110.t18.t29 (cl (or @p_151 @p_141)) :rule forall_inst :args (d$ 2/1))
(step t110.t18.t30 (cl @p_151 @p_141) :rule or :premises (t110.t18.t29))
(step t110.t18.t31 (cl (not @p_142) (not (forall ((?v0 Real) (?v1 Real)) (= (divide$ (- ?v0) ?v1) (- (divide$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t110.t18.t32 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t110.t18.t32.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t110.t18.t32.t1 (cl @p_10) :rule refl)
(step t110.t18.t32.t2 (cl (= @p_147 @p_143)) :rule cong :premises (t110.t18.t32.t0 t110.t18.t32.t1))
(step t110.t18.t32.t3 (cl (= @p_146 @p_149)) :rule poly_simp)
(step t110.t18.t32.t4 (cl (= @p_148 @p_150)) :rule cong :premises (t110.t18.t32.t2 t110.t18.t32.t3))
(step t110.t18.t32.t5 (cl (= (* 1/1 (- @p_143 @p_149)) (* 1/1 (- @p_61 @p_144)))) :rule poly_simp)
(step t110.t18.t32.t6 (cl (= @p_150 @p_145)) :rule poly_simp_rel :premises (t110.t18.t32.t5))
(step t110.t18.t32.t7 (cl (= @p_148 @p_145)) :rule trans :premises (t110.t18.t32.t4 t110.t18.t32.t6))
(step t110.t18.t32 (cl @p_142) :rule bind)
(step t110.t18.t33 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t110.t18.t31 t110.t18.t32 a8))
(step t110.t18.t34 (cl @p_141) :rule resolution :premises (t110.t18.t30 t110.t18.t33))
(step t110.t18.t35 (cl @p_184) :rule resolution :premises (t110.t18.t25 t110.t18.t28 t110.t18.t34))
(step t110.t18.t36 (cl @p_185) :rule and_intro :premises (t110.t18.t24 t110.t18.t35))
(step t110.t18.t37 (cl @p_183) :rule resolution :premises (t110.t18.t20 t110.t18.t36))
(step t110.t18.t38 (cl (=> (! (and @p_175 (! (> @p_167 0/1) :named @p_174)) :named @p_176) @p_173)) :rule la_mult_neg)
(step t110.t18.t39 (cl (not @p_176) @p_173) :rule implies :premises (t110.t18.t38))
(step t110.t18.t40 (cl (not (! (= @p_41 @p_174) :named @p_177)) @p_138 @p_174) :rule equiv_pos2)
(step t110.t18.t41 (cl (= @p_174 (! (not (! (>= 0/1 @p_167) :named @p_180)) :named @p_181))) :rule rare_rewrite :args ("arith-elim-gt" @p_167 0/1))
(step t110.t18.t42 (cl (= (! (<= @p_167 0/1) :named @p_178) @p_180)) :rule rare_rewrite :args ("arith-elim-leq" @p_167 0/1))
(step t110.t18.t43 (cl (= @p_180 @p_178)) :rule symm :premises (t110.t18.t42))
(step t110.t18.t44 (cl (= @p_181 (! (not @p_178) :named @p_179))) :rule cong :premises (t110.t18.t43))
(step t110.t18.t45 (cl (= @p_174 @p_179)) :rule trans :premises (t110.t18.t41 t110.t18.t44))
(step t110.t18.t46 (cl (= (* -1/1 (- 0/1 @p_167)) (* -1/1 (- @p_39 0/1)))) :rule poly_simp)
(step t110.t18.t47 (cl (= @p_180 @p_40)) :rule poly_simp_rel :premises (t110.t18.t46))
(step t110.t18.t48 (cl (= @p_178 @p_40)) :rule trans :premises (t110.t18.t42 t110.t18.t47))
(step t110.t18.t49 (cl (= @p_179 @p_41)) :rule cong :premises (t110.t18.t48))
(step t110.t18.t50 (cl (= @p_174 @p_41)) :rule trans :premises (t110.t18.t45 t110.t18.t49))
(step t110.t18.t51 (cl @p_177) :rule symm :premises (t110.t18.t50))
(step t110.t18.t52 (cl (not @p_139) (not @p_137) @p_135) :rule equiv_pos2)
(step t110.t18.t53 (cl (= @p_136 @p_42)) :rule rare_rewrite :args ("bool-double-not-elim" @p_42))
(step t110.t18.t54 (cl (= @p_41 @p_41)) :rule refl)
(step t110.t18.t55 (cl @p_139) :rule cong :premises (t110.t18.t53 t110.t18.t54))
(step t110.t18.t56 (cl @p_134 @p_136 @p_41) :rule equiv_pos2)
(step t110.t18.t57 (cl @p_137 (not @p_134)) :rule or_neg :args (0))
(step t110.t18.t58 (cl @p_137 (not @p_136)) :rule or_neg :args (1))
(step t110.t18.t59 (cl @p_137 @p_138) :rule or_neg :args (2))
(step t110.t18.t60 (cl @p_137 @p_137 @p_137) :rule resolution :premises (t110.t18.t56 t110.t18.t57 t110.t18.t58 t110.t18.t59))
(step t110.t18.t61 (cl @p_137) :rule contraction :premises (t110.t18.t60))
(step t110.t18.t62 (cl @p_135) :rule resolution :premises (t110.t18.t52 t110.t18.t55 t110.t18.t61))
(step t110.t18.t63 (cl @p_134 @p_42 @p_41) :rule or :premises (t110.t18.t62))
(step t110.t18.t64 (cl @p_42 @p_41 @p_134) :rule reordering :premises (t110.t18.t63))
(step t110.t18.t65 (cl (not @p_131) (not @p_1) @p_43) :rule equiv_pos2)
(step t110.t18.t66 (cl (= @p_1 @p_133)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 d$))
(step t110.t18.t67 (cl (= (* -1/1 (- 0/1 d$)) (* -1/1 @p_129))) :rule poly_simp)
(step t110.t18.t68 (cl (= @p_132 @p_42)) :rule poly_simp_rel :premises (t110.t18.t67))
(step t110.t18.t69 (cl (= @p_133 @p_43)) :rule cong :premises (t110.t18.t68))
(step t110.t18.t70 (cl @p_131) :rule trans :premises (t110.t18.t66 t110.t18.t69))
(step t110.t18.t71 (cl @p_43) :rule resolution :premises (t110.t18.t65 t110.t18.t70 a4))
(step t110.t18.t72 (cl (not @p_115) (not @p_114) @p_94) :rule equiv_pos2)
(step t110.t18.t73 (cl (= @p_110 @p_39)) :rule poly_simp)
(step t110.t18.t74 (cl @p_124) :rule refl)
(step t110.t18.t75 (cl (= @p_111 @p_40)) :rule cong :premises (t110.t18.t73 t110.t18.t74))
(step t110.t18.t76 (cl (= @p_112 @p_41)) :rule cong :premises (t110.t18.t75))
(step t110.t18.t77 (cl (= @p_106 -2/1)) :rule evaluate)
(step t110.t18.t78 (cl @p_124) :rule refl)
(step t110.t18.t79 (cl (= @p_107 @p_130)) :rule cong :premises (t110.t18.t77 t110.t18.t78))
(step t110.t18.t80 (cl (= @p_130 false)) :rule evaluate)
(step t110.t18.t81 (cl (= @p_107 false)) :rule trans :premises (t110.t18.t79 t110.t18.t80))
(step t110.t18.t82 (cl (= @p_103 @p_127)) :rule poly_simp)
(step t110.t18.t83 (cl @p_124) :rule refl)
(step t110.t18.t84 (cl (= @p_104 @p_128)) :rule cong :premises (t110.t18.t82 t110.t18.t83))
(step t110.t18.t85 (cl (= (* -1/1 (- @p_127 0/1)) (* -2/1 @p_129))) :rule poly_simp)
(step t110.t18.t86 (cl (= @p_128 @p_42)) :rule poly_simp_rel :premises (t110.t18.t85))
(step t110.t18.t87 (cl (= @p_104 @p_42)) :rule trans :premises (t110.t18.t84 t110.t18.t86))
(step t110.t18.t88 (cl (= @p_105 @p_43)) :rule cong :premises (t110.t18.t87))
(step t110.t18.t89 (cl (= @p_108 @p_126)) :rule cong :premises (t110.t18.t81 t110.t18.t88))
(step t110.t18.t90 (cl (= @p_126 @p_43)) :rule aci_simp)
(step t110.t18.t91 (cl (= @p_108 @p_43)) :rule trans :premises (t110.t18.t89 t110.t18.t90))
(step t110.t18.t92 (cl (= @p_101 true)) :rule evaluate)
(step t110.t18.t93 (cl (= @p_97 d$)) :rule poly_simp)
(step t110.t18.t94 (cl (= @p_98 @p_125)) :rule cong :premises (t110.t18.t93 t47))
(step t110.t18.t95 (cl (= @p_125 @p_122)) :rule poly_simp)
(step t110.t18.t96 (cl (= @p_98 @p_122)) :rule trans :premises (t110.t18.t94 t110.t18.t95))
(step t110.t18.t97 (cl @p_124) :rule refl)
(step t110.t18.t98 (cl (= @p_99 @p_123)) :rule cong :premises (t110.t18.t96 t110.t18.t97))
(step t110.t18.t99 (cl (= (* 1/1 (- @p_122 0/1)) (* 2/1 (- d$ 0/1)))) :rule poly_simp)
(step t110.t18.t100 (cl (= @p_123 @p_119)) :rule poly_simp_rel :premises (t110.t18.t99))
(step t110.t18.t101 (cl (= @p_99 @p_119)) :rule trans :premises (t110.t18.t98 t110.t18.t100))
(step t110.t18.t102 (cl (= @p_100 @p_120)) :rule cong :premises (t110.t18.t101))
(step t110.t18.t103 (cl (= @p_102 @p_121)) :rule cong :premises (t110.t18.t92 t110.t18.t102))
(step t110.t18.t104 (cl (= @p_121 true)) :rule or_simplify)
(step t110.t18.t105 (cl (= @p_102 true)) :rule trans :premises (t110.t18.t103 t110.t18.t104))
(step t110.t18.t106 (cl (= @p_95 false)) :rule evaluate)
(step t110.t18.t107 (cl (= @p_96 @p_118)) :rule cong :premises (t110.t18.t106))
(step t110.t18.t108 (cl (= @p_118 true)) :rule evaluate)
(step t110.t18.t109 (cl (= @p_96 true)) :rule trans :premises (t110.t18.t107 t110.t18.t108))
(step t110.t18.t110 (cl (= @p_109 @p_117)) :rule cong :premises (t110.t18.t91 t110.t18.t105 t110.t18.t109))
(step t110.t18.t111 (cl (= @p_117 @p_43)) :rule aci_simp)
(step t110.t18.t112 (cl (= @p_109 @p_43)) :rule trans :premises (t110.t18.t110 t110.t18.t111))
(step t110.t18.t113 (cl (= @p_113 @p_116)) :rule cong :premises (t110.t18.t76 t110.t18.t112))
(step t110.t18.t114 (cl (= @p_116 @p_44)) :rule rare_rewrite :args ("eq-symm" @p_41 @p_43))
(step t110.t18.t115 (cl (= @p_113 @p_44)) :rule trans :premises (t110.t18.t113 t110.t18.t114))
(step t110.t18.t116 (cl @p_115) :rule cong :premises (t110.t18.t115))
(step t110.t18.t117 (cl @p_114 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule implies_neg1)
(anchor :step t110.t18.t118)
(assume t110.t18.t118.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))
(step t110.t18.t118.t0 (cl (or @p_93 @p_113)) :rule forall_inst :args (@p_37 2/1 d$))
(step t110.t18.t118.t1 (cl @p_93 @p_113) :rule or :premises (t110.t18.t118.t0))
(step t110.t18.t118.t2 (cl (not @p_45) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t110.t18.t118.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t110.t18.t118.t3.t0 (cl (= @p_83 @p_92)) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t110.t18.t118.t3.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t110.t18.t118.t3.t2 (cl (= @p_91 @p_63)) :rule poly_simp_rel :premises (t110.t18.t118.t3.t1))
(step t110.t18.t118.t3.t3 (cl (= @p_92 @p_64)) :rule cong :premises (t110.t18.t118.t3.t2))
(step t110.t18.t118.t3.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t110.t18.t118.t3.t0 t110.t18.t118.t3.t3))
(step t110.t18.t118.t3.t5 (cl (= @p_82 @p_84)) :rule aci_simp)
(step t110.t18.t118.t3.t6 (cl (= @p_80 @p_90)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t110.t18.t118.t3.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- @p_56 0/1)))) :rule poly_simp)
(step t110.t18.t118.t3.t8 (cl (= @p_89 @p_57)) :rule poly_simp_rel :premises (t110.t18.t118.t3.t7))
(step t110.t18.t118.t3.t9 (cl (= @p_90 @p_67)) :rule cong :premises (t110.t18.t118.t3.t8))
(step t110.t18.t118.t3.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t110.t18.t118.t3.t6 t110.t18.t118.t3.t9))
(step t110.t18.t118.t3.t11 (cl (= @p_79 @p_88)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t110.t18.t118.t3.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- @p_53 0/1)))) :rule poly_simp)
(step t110.t18.t118.t3.t13 (cl (= @p_87 @p_54)) :rule poly_simp_rel :premises (t110.t18.t118.t3.t12))
(step t110.t18.t118.t3.t14 (cl (= @p_88 @p_55)) :rule cong :premises (t110.t18.t118.t3.t13))
(step t110.t18.t118.t3.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t110.t18.t118.t3.t11 t110.t18.t118.t3.t14))
(step t110.t18.t118.t3.t16 (cl (= @p_81 @p_68)) :rule cong :premises (t110.t18.t118.t3.t10 t110.t18.t118.t3.t15))
(step t110.t18.t118.t3.t17 (cl (= @p_77 @p_65)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t110.t18.t118.t3.t18 (cl (= @p_76 @p_86)) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t110.t18.t118.t3.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- @p_48 0/1)))) :rule poly_simp)
(step t110.t18.t118.t3.t20 (cl (= @p_85 @p_49)) :rule poly_simp_rel :premises (t110.t18.t118.t3.t19))
(step t110.t18.t118.t3.t21 (cl (= @p_86 @p_50)) :rule cong :premises (t110.t18.t118.t3.t20))
(step t110.t18.t118.t3.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t110.t18.t118.t3.t18 t110.t18.t118.t3.t21))
(step t110.t18.t118.t3.t23 (cl (= @p_78 @p_66)) :rule cong :premises (t110.t18.t118.t3.t17 t110.t18.t118.t3.t22))
(step t110.t18.t118.t3.t24 (cl @p_71) :rule refl)
(step t110.t18.t118.t3.t25 (cl (= @p_84 @p_69)) :rule cong :premises (t110.t18.t118.t3.t16 t110.t18.t118.t3.t23 t110.t18.t118.t3.t24))
(step t110.t18.t118.t3.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t110.t18.t118.t3.t5 t110.t18.t118.t3.t25))
(step t110.t18.t118.t3.t27 (cl (= (= @p_83 @p_82) @p_70)) :rule cong :premises (t110.t18.t118.t3.t4 t110.t18.t118.t3.t26))
(step t110.t18.t118.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t110.t18.t118.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t110.t18.t118.t4.t0 (cl (= @p_68 @p_75)) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t110.t18.t118.t4.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t110.t18.t118.t4.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t110.t18.t118.t4.t3 (cl (= @p_75 @p_58)) :rule cong :premises (t110.t18.t118.t4.t1 t110.t18.t118.t4.t2))
(step t110.t18.t118.t4.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t110.t18.t118.t4.t0 t110.t18.t118.t4.t3))
(step t110.t18.t118.t4.t5 (cl (= @p_66 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t110.t18.t118.t4.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t110.t18.t118.t4.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t110.t18.t118.t4.t8 (cl (= @p_73 @p_52)) :rule cong :premises (t110.t18.t118.t4.t6 t110.t18.t118.t4.t7))
(step t110.t18.t118.t4.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t110.t18.t118.t4.t5 t110.t18.t118.t4.t8))
(step t110.t18.t118.t4.t10 (cl @p_71) :rule refl)
(step t110.t18.t118.t4.t11 (cl (= @p_69 @p_59)) :rule cong :premises (t110.t18.t118.t4.t4 t110.t18.t118.t4.t9 t110.t18.t118.t4.t10))
(step t110.t18.t118.t4.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t110.t18.t118.t4.t11))
(step t110.t18.t118.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t110.t18.t118.t5 (cl @p_45) :rule trans :premises (t110.t18.t118.t3 t110.t18.t118.t4))
(step t110.t18.t118.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t110.t18.t118.t2 t110.t18.t118.t5 a6))
(step t110.t18.t118.t7 (cl @p_113) :rule resolution :premises (t110.t18.t118.t1 t110.t18.t118.t6))
(step t110.t18.t118 (cl @p_93 @p_113) :rule subproof :discharge (t110.t18.t118.a0))
(step t110.t18.t119 (cl @p_114 @p_113) :rule resolution :premises (t110.t18.t117 t110.t18.t118))
(step t110.t18.t120 (cl @p_114 (not @p_113)) :rule implies_neg2)
(step t110.t18.t121 (cl @p_114 @p_114) :rule resolution :premises (t110.t18.t119 t110.t18.t120))
(step t110.t18.t122 (cl @p_114) :rule contraction :premises (t110.t18.t121))
(step t110.t18.t123 (cl @p_94) :rule resolution :premises (t110.t18.t72 t110.t18.t116 t110.t18.t122))
(step t110.t18.t124 (cl @p_93 @p_44) :rule implies :premises (t110.t18.t123))
(step t110.t18.t125 (cl (not @p_45) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t110.t18.t126 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t110.t18.t126.t0 (cl (= @p_83 @p_92)) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t110.t18.t126.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t110.t18.t126.t2 (cl (= @p_91 @p_63)) :rule poly_simp_rel :premises (t110.t18.t126.t1))
(step t110.t18.t126.t3 (cl (= @p_92 @p_64)) :rule cong :premises (t110.t18.t126.t2))
(step t110.t18.t126.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t110.t18.t126.t0 t110.t18.t126.t3))
(step t110.t18.t126.t5 (cl (= @p_82 @p_84)) :rule aci_simp)
(step t110.t18.t126.t6 (cl (= @p_80 @p_90)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t110.t18.t126.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- @p_56 0/1)))) :rule poly_simp)
(step t110.t18.t126.t8 (cl (= @p_89 @p_57)) :rule poly_simp_rel :premises (t110.t18.t126.t7))
(step t110.t18.t126.t9 (cl (= @p_90 @p_67)) :rule cong :premises (t110.t18.t126.t8))
(step t110.t18.t126.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t110.t18.t126.t6 t110.t18.t126.t9))
(step t110.t18.t126.t11 (cl (= @p_79 @p_88)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t110.t18.t126.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- @p_53 0/1)))) :rule poly_simp)
(step t110.t18.t126.t13 (cl (= @p_87 @p_54)) :rule poly_simp_rel :premises (t110.t18.t126.t12))
(step t110.t18.t126.t14 (cl (= @p_88 @p_55)) :rule cong :premises (t110.t18.t126.t13))
(step t110.t18.t126.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t110.t18.t126.t11 t110.t18.t126.t14))
(step t110.t18.t126.t16 (cl (= @p_81 @p_68)) :rule cong :premises (t110.t18.t126.t10 t110.t18.t126.t15))
(step t110.t18.t126.t17 (cl (= @p_77 @p_65)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t110.t18.t126.t18 (cl (= @p_76 @p_86)) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t110.t18.t126.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- @p_48 0/1)))) :rule poly_simp)
(step t110.t18.t126.t20 (cl (= @p_85 @p_49)) :rule poly_simp_rel :premises (t110.t18.t126.t19))
(step t110.t18.t126.t21 (cl (= @p_86 @p_50)) :rule cong :premises (t110.t18.t126.t20))
(step t110.t18.t126.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t110.t18.t126.t18 t110.t18.t126.t21))
(step t110.t18.t126.t23 (cl (= @p_78 @p_66)) :rule cong :premises (t110.t18.t126.t17 t110.t18.t126.t22))
(step t110.t18.t126.t24 (cl @p_71) :rule refl)
(step t110.t18.t126.t25 (cl (= @p_84 @p_69)) :rule cong :premises (t110.t18.t126.t16 t110.t18.t126.t23 t110.t18.t126.t24))
(step t110.t18.t126.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t110.t18.t126.t5 t110.t18.t126.t25))
(step t110.t18.t126.t27 (cl (= (= @p_83 @p_82) @p_70)) :rule cong :premises (t110.t18.t126.t4 t110.t18.t126.t26))
(step t110.t18.t126 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t110.t18.t127 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t110.t18.t127.t0 (cl (= @p_68 @p_75)) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t110.t18.t127.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t110.t18.t127.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t110.t18.t127.t3 (cl (= @p_75 @p_58)) :rule cong :premises (t110.t18.t127.t1 t110.t18.t127.t2))
(step t110.t18.t127.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t110.t18.t127.t0 t110.t18.t127.t3))
(step t110.t18.t127.t5 (cl (= @p_66 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t110.t18.t127.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t110.t18.t127.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t110.t18.t127.t8 (cl (= @p_73 @p_52)) :rule cong :premises (t110.t18.t127.t6 t110.t18.t127.t7))
(step t110.t18.t127.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t110.t18.t127.t5 t110.t18.t127.t8))
(step t110.t18.t127.t10 (cl @p_71) :rule refl)
(step t110.t18.t127.t11 (cl (= @p_69 @p_59)) :rule cong :premises (t110.t18.t127.t4 t110.t18.t127.t9 t110.t18.t127.t10))
(step t110.t18.t127.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t110.t18.t127.t11))
(step t110.t18.t127 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t110.t18.t128 (cl @p_45) :rule trans :premises (t110.t18.t126 t110.t18.t127))
(step t110.t18.t129 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t110.t18.t125 t110.t18.t128 a6))
(step t110.t18.t130 (cl @p_44) :rule resolution :premises (t110.t18.t124 t110.t18.t129))
(step t110.t18.t131 (cl @p_41) :rule resolution :premises (t110.t18.t64 t110.t18.t71 t110.t18.t130))
(step t110.t18.t132 (cl @p_174) :rule resolution :premises (t110.t18.t40 t110.t18.t51 t110.t18.t131))
(step t110.t18.t133 (cl @p_176) :rule and_intro :premises (t110.t18.t24 t110.t18.t132))
(step t110.t18.t134 (cl @p_173) :rule resolution :premises (t110.t18.t39 t110.t18.t133))
(step t110.t18.t135 (cl @p_172) :rule resolution :premises (t110.t18.t18 t110.t18.a0 t110.t18.t37 t110.t18.t134))
(step t110.t18.t136 (cl false) :rule resolution :premises (t110.t18.t0 t110.t18.t17 t110.t18.t135))
(step t110.t18 (cl @p_162 false) :rule subproof :discharge (t110.t18.a0))
(step t110.t19 (cl @p_164 false) :rule resolution :premises (t110.t17 t110.t18))
(step t110.t20 (cl @p_164 @p_118) :rule implies_neg2)
(step t110.t21 (cl @p_164 @p_164) :rule resolution :premises (t110.t19 t110.t20))
(step t110.t22 (cl @p_164) :rule contraction :premises (t110.t21))
(step t110.t23 (cl (= @p_164 @p_162)) :rule implies_simplify)
(step t110.t24 (cl (not @p_164) @p_162) :rule equiv1 :premises (t110.t23))
(step t110.t25 (cl @p_162) :rule resolution :premises (t110.t22 t110.t24))
(step t110.t26 (cl @p_163) :rule resolution :premises (t110.t12 t110.t16 t110.t25))
(step t110.t27 (cl @p_162) :rule resolution :premises (t110.t7 t110.t11 t110.t26))
(step t110.t28 (cl) :rule resolution :premises (t110.t6 t110.t27))
(step t110 (cl @p_138 @p_152 @p_36 false) :rule subproof :discharge (t110.a0 t110.a1 t110.a2))
(step t111 (cl @p_159 @p_41) :rule and_pos :args (0))
(step t112 (cl @p_159 @p_141) :rule and_pos :args (1))
(step t113 (cl @p_159 @p_35) :rule and_pos :args (2))
(step t114 (cl false @p_159 @p_159 @p_159) :rule resolution :premises (t110 t111 t112 t113))
(step t115 (cl @p_159 @p_159 @p_159 false) :rule reordering :premises (t114))
(step t116 (cl @p_159 false) :rule contraction :premises (t115))
(step t117 (cl @p_160 false) :rule resolution :premises (t109 t116))
(step t118 (cl @p_160 @p_118) :rule implies_neg2)
(step t119 (cl @p_160 @p_160) :rule resolution :premises (t117 t118))
(step t120 (cl @p_160) :rule contraction :premises (t119))
(step t121 (cl (= @p_160 @p_159)) :rule implies_simplify)
(step t122 (cl (not @p_160) @p_159) :rule equiv1 :premises (t121))
(step t123 (cl @p_159) :rule resolution :premises (t120 t122))
(step t124 (cl @p_157) :rule resolution :premises (t108 t123))
(step t125 (cl @p_152 @p_36 @p_138) :rule not_and :premises (t124))
(step t126 (cl @p_154 (not @p_152)) :rule or_neg :args (0))
(step t127 (cl @p_154 @p_155) :rule or_neg :args (1))
(step t128 (cl @p_154 (not @p_138)) :rule or_neg :args (2))
(step t129 (cl @p_154 @p_154 @p_154) :rule resolution :premises (t125 t126 t127 t128))
(step t130 (cl @p_154) :rule contraction :premises (t129))
(step t131 (cl @p_153) :rule resolution :premises (t93 t95 t130))
(step t132 (cl @p_152 @p_36 @p_40) :rule or :premises (t131))
(step t133 (cl @p_152 @p_40 @p_36) :rule reordering :premises (t132))
(step t134 (cl (or @p_151 @p_141)) :rule forall_inst :args (d$ 2/1))
(step t135 (cl @p_151 @p_141) :rule or :premises (t134))
(step t136 (cl (not @p_142) (not (forall ((?v0 Real) (?v1 Real)) (= (divide$ (- ?v0) ?v1) (- (divide$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t137 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t137.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t137.t1 (cl @p_10) :rule refl)
(step t137.t2 (cl (= @p_147 @p_143)) :rule cong :premises (t137.t0 t137.t1))
(step t137.t3 (cl (= @p_146 @p_149)) :rule poly_simp)
(step t137.t4 (cl (= @p_148 @p_150)) :rule cong :premises (t137.t2 t137.t3))
(step t137.t5 (cl (= (* 1/1 (- @p_143 @p_149)) (* 1/1 (- @p_61 @p_144)))) :rule poly_simp)
(step t137.t6 (cl (= @p_150 @p_145)) :rule poly_simp_rel :premises (t137.t5))
(step t137.t7 (cl (= @p_148 @p_145)) :rule trans :premises (t137.t4 t137.t6))
(step t137 (cl @p_142) :rule bind)
(step t138 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ ?v0 ?v1) (* -1/1 (divide$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t136 t137 a8))
(step t139 (cl @p_141) :rule resolution :premises (t135 t138))
(step t140 (cl (not @p_139) (not @p_137) @p_135) :rule equiv_pos2)
(step t141 (cl (= @p_136 @p_42)) :rule rare_rewrite :args ("bool-double-not-elim" @p_42))
(step t142 (cl (= @p_41 @p_41)) :rule refl)
(step t143 (cl @p_139) :rule cong :premises (t141 t142))
(step t144 (cl @p_134 @p_136 @p_41) :rule equiv_pos2)
(step t145 (cl @p_137 (not @p_134)) :rule or_neg :args (0))
(step t146 (cl @p_137 (not @p_136)) :rule or_neg :args (1))
(step t147 (cl @p_137 @p_138) :rule or_neg :args (2))
(step t148 (cl @p_137 @p_137 @p_137) :rule resolution :premises (t144 t145 t146 t147))
(step t149 (cl @p_137) :rule contraction :premises (t148))
(step t150 (cl @p_135) :rule resolution :premises (t140 t143 t149))
(step t151 (cl @p_134 @p_42 @p_41) :rule or :premises (t150))
(step t152 (cl @p_42 @p_41 @p_134) :rule reordering :premises (t151))
(step t153 (cl (not @p_131) (not @p_1) @p_43) :rule equiv_pos2)
(step t154 (cl (= @p_1 @p_133)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 d$))
(step t155 (cl (= (* -1/1 (- 0/1 d$)) (* -1/1 @p_129))) :rule poly_simp)
(step t156 (cl (= @p_132 @p_42)) :rule poly_simp_rel :premises (t155))
(step t157 (cl (= @p_133 @p_43)) :rule cong :premises (t156))
(step t158 (cl @p_131) :rule trans :premises (t154 t157))
(step t159 (cl @p_43) :rule resolution :premises (t153 t158 a4))
(step t160 (cl (not @p_115) (not @p_114) @p_94) :rule equiv_pos2)
(step t161 (cl (= @p_110 @p_39)) :rule poly_simp)
(step t162 (cl @p_124) :rule refl)
(step t163 (cl (= @p_111 @p_40)) :rule cong :premises (t161 t162))
(step t164 (cl (= @p_112 @p_41)) :rule cong :premises (t163))
(step t165 (cl (= @p_106 -2/1)) :rule evaluate)
(step t166 (cl @p_124) :rule refl)
(step t167 (cl (= @p_107 @p_130)) :rule cong :premises (t165 t166))
(step t168 (cl (= @p_130 false)) :rule evaluate)
(step t169 (cl (= @p_107 false)) :rule trans :premises (t167 t168))
(step t170 (cl (= @p_103 @p_127)) :rule poly_simp)
(step t171 (cl @p_124) :rule refl)
(step t172 (cl (= @p_104 @p_128)) :rule cong :premises (t170 t171))
(step t173 (cl (= (* -1/1 (- @p_127 0/1)) (* -2/1 @p_129))) :rule poly_simp)
(step t174 (cl (= @p_128 @p_42)) :rule poly_simp_rel :premises (t173))
(step t175 (cl (= @p_104 @p_42)) :rule trans :premises (t172 t174))
(step t176 (cl (= @p_105 @p_43)) :rule cong :premises (t175))
(step t177 (cl (= @p_108 @p_126)) :rule cong :premises (t169 t176))
(step t178 (cl (= @p_126 @p_43)) :rule aci_simp)
(step t179 (cl (= @p_108 @p_43)) :rule trans :premises (t177 t178))
(step t180 (cl (= @p_101 true)) :rule evaluate)
(step t181 (cl (= @p_97 d$)) :rule poly_simp)
(step t182 (cl (= @p_98 @p_125)) :rule cong :premises (t181 t47))
(step t183 (cl (= @p_125 @p_122)) :rule poly_simp)
(step t184 (cl (= @p_98 @p_122)) :rule trans :premises (t182 t183))
(step t185 (cl @p_124) :rule refl)
(step t186 (cl (= @p_99 @p_123)) :rule cong :premises (t184 t185))
(step t187 (cl (= (* 1/1 (- @p_122 0/1)) (* 2/1 (- d$ 0/1)))) :rule poly_simp)
(step t188 (cl (= @p_123 @p_119)) :rule poly_simp_rel :premises (t187))
(step t189 (cl (= @p_99 @p_119)) :rule trans :premises (t186 t188))
(step t190 (cl (= @p_100 @p_120)) :rule cong :premises (t189))
(step t191 (cl (= @p_102 @p_121)) :rule cong :premises (t180 t190))
(step t192 (cl (= @p_121 true)) :rule or_simplify)
(step t193 (cl (= @p_102 true)) :rule trans :premises (t191 t192))
(step t194 (cl (= @p_95 false)) :rule evaluate)
(step t195 (cl (= @p_96 @p_118)) :rule cong :premises (t194))
(step t196 (cl (= @p_118 true)) :rule evaluate)
(step t197 (cl (= @p_96 true)) :rule trans :premises (t195 t196))
(step t198 (cl (= @p_109 @p_117)) :rule cong :premises (t179 t193 t197))
(step t199 (cl (= @p_117 @p_43)) :rule aci_simp)
(step t200 (cl (= @p_109 @p_43)) :rule trans :premises (t198 t199))
(step t201 (cl (= @p_113 @p_116)) :rule cong :premises (t164 t200))
(step t202 (cl (= @p_116 @p_44)) :rule rare_rewrite :args ("eq-symm" @p_41 @p_43))
(step t203 (cl (= @p_113 @p_44)) :rule trans :premises (t201 t202))
(step t204 (cl @p_115) :rule cong :premises (t203))
(step t205 (cl @p_114 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule implies_neg1)
(anchor :step t206)
(assume t206.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))
(step t206.t0 (cl (or @p_93 @p_113)) :rule forall_inst :args (@p_37 2/1 d$))
(step t206.t1 (cl @p_93 @p_113) :rule or :premises (t206.t0))
(step t206.t2 (cl (not @p_45) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t206.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t206.t3.t0 (cl (= @p_83 @p_92)) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t206.t3.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t206.t3.t2 (cl (= @p_91 @p_63)) :rule poly_simp_rel :premises (t206.t3.t1))
(step t206.t3.t3 (cl (= @p_92 @p_64)) :rule cong :premises (t206.t3.t2))
(step t206.t3.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t206.t3.t0 t206.t3.t3))
(step t206.t3.t5 (cl (= @p_82 @p_84)) :rule aci_simp)
(step t206.t3.t6 (cl (= @p_80 @p_90)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t206.t3.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- @p_56 0/1)))) :rule poly_simp)
(step t206.t3.t8 (cl (= @p_89 @p_57)) :rule poly_simp_rel :premises (t206.t3.t7))
(step t206.t3.t9 (cl (= @p_90 @p_67)) :rule cong :premises (t206.t3.t8))
(step t206.t3.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t206.t3.t6 t206.t3.t9))
(step t206.t3.t11 (cl (= @p_79 @p_88)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t206.t3.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- @p_53 0/1)))) :rule poly_simp)
(step t206.t3.t13 (cl (= @p_87 @p_54)) :rule poly_simp_rel :premises (t206.t3.t12))
(step t206.t3.t14 (cl (= @p_88 @p_55)) :rule cong :premises (t206.t3.t13))
(step t206.t3.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t206.t3.t11 t206.t3.t14))
(step t206.t3.t16 (cl (= @p_81 @p_68)) :rule cong :premises (t206.t3.t10 t206.t3.t15))
(step t206.t3.t17 (cl (= @p_77 @p_65)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t206.t3.t18 (cl (= @p_76 @p_86)) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t206.t3.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- @p_48 0/1)))) :rule poly_simp)
(step t206.t3.t20 (cl (= @p_85 @p_49)) :rule poly_simp_rel :premises (t206.t3.t19))
(step t206.t3.t21 (cl (= @p_86 @p_50)) :rule cong :premises (t206.t3.t20))
(step t206.t3.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t206.t3.t18 t206.t3.t21))
(step t206.t3.t23 (cl (= @p_78 @p_66)) :rule cong :premises (t206.t3.t17 t206.t3.t22))
(step t206.t3.t24 (cl @p_71) :rule refl)
(step t206.t3.t25 (cl (= @p_84 @p_69)) :rule cong :premises (t206.t3.t16 t206.t3.t23 t206.t3.t24))
(step t206.t3.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t206.t3.t5 t206.t3.t25))
(step t206.t3.t27 (cl (= (= @p_83 @p_82) @p_70)) :rule cong :premises (t206.t3.t4 t206.t3.t26))
(step t206.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t206.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t206.t4.t0 (cl (= @p_68 @p_75)) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t206.t4.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t206.t4.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t206.t4.t3 (cl (= @p_75 @p_58)) :rule cong :premises (t206.t4.t1 t206.t4.t2))
(step t206.t4.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t206.t4.t0 t206.t4.t3))
(step t206.t4.t5 (cl (= @p_66 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t206.t4.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t206.t4.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t206.t4.t8 (cl (= @p_73 @p_52)) :rule cong :premises (t206.t4.t6 t206.t4.t7))
(step t206.t4.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t206.t4.t5 t206.t4.t8))
(step t206.t4.t10 (cl @p_71) :rule refl)
(step t206.t4.t11 (cl (= @p_69 @p_59)) :rule cong :premises (t206.t4.t4 t206.t4.t9 t206.t4.t10))
(step t206.t4.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t206.t4.t11))
(step t206.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t206.t5 (cl @p_45) :rule trans :premises (t206.t3 t206.t4))
(step t206.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t206.t2 t206.t5 a6))
(step t206.t7 (cl @p_113) :rule resolution :premises (t206.t1 t206.t6))
(step t206 (cl @p_93 @p_113) :rule subproof :discharge (t206.a0))
(step t207 (cl @p_114 @p_113) :rule resolution :premises (t205 t206))
(step t208 (cl @p_114 (not @p_113)) :rule implies_neg2)
(step t209 (cl @p_114 @p_114) :rule resolution :premises (t207 t208))
(step t210 (cl @p_114) :rule contraction :premises (t209))
(step t211 (cl @p_94) :rule resolution :premises (t160 t204 t210))
(step t212 (cl @p_93 @p_44) :rule implies :premises (t211))
(step t213 (cl (not @p_45) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1))))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule equiv_pos2)
(anchor :step t214 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t214.t0 (cl (= @p_83 @p_92)) :rule rare_rewrite :args ("arith-elim-lt" @p_61 @p_60))
(step t214.t1 (cl (= (* 1/1 (- @p_61 @p_60)) (* 1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t214.t2 (cl (= @p_91 @p_63)) :rule poly_simp_rel :premises (t214.t1))
(step t214.t3 (cl (= @p_92 @p_64)) :rule cong :premises (t214.t2))
(step t214.t4 (cl (= @p_83 @p_64)) :rule trans :premises (t214.t0 t214.t3))
(step t214.t5 (cl (= @p_82 @p_84)) :rule aci_simp)
(step t214.t6 (cl (= @p_80 @p_90)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v1))
(step t214.t7 (cl (= (* -1/1 (- 0/1 ?v1)) (* -1/1 (- @p_56 0/1)))) :rule poly_simp)
(step t214.t8 (cl (= @p_89 @p_57)) :rule poly_simp_rel :premises (t214.t7))
(step t214.t9 (cl (= @p_90 @p_67)) :rule cong :premises (t214.t8))
(step t214.t10 (cl (= @p_80 @p_67)) :rule trans :premises (t214.t6 t214.t9))
(step t214.t11 (cl (= @p_79 @p_88)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v2))
(step t214.t12 (cl (= (* 1/1 (- ?v0 ?v2)) (* 1/1 (- @p_53 0/1)))) :rule poly_simp)
(step t214.t13 (cl (= @p_87 @p_54)) :rule poly_simp_rel :premises (t214.t12))
(step t214.t14 (cl (= @p_88 @p_55)) :rule cong :premises (t214.t13))
(step t214.t15 (cl (= @p_79 @p_55)) :rule trans :premises (t214.t11 t214.t14))
(step t214.t16 (cl (= @p_81 @p_68)) :rule cong :premises (t214.t10 t214.t15))
(step t214.t17 (cl (= @p_77 @p_65)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0/1))
(step t214.t18 (cl (= @p_76 @p_86)) :rule rare_rewrite :args ("arith-elim-lt" ?v2 ?v0))
(step t214.t19 (cl (= (* -1/1 (- ?v2 ?v0)) (* -1/1 (- @p_48 0/1)))) :rule poly_simp)
(step t214.t20 (cl (= @p_85 @p_49)) :rule poly_simp_rel :premises (t214.t19))
(step t214.t21 (cl (= @p_86 @p_50)) :rule cong :premises (t214.t20))
(step t214.t22 (cl (= @p_76 @p_50)) :rule trans :premises (t214.t18 t214.t21))
(step t214.t23 (cl (= @p_78 @p_66)) :rule cong :premises (t214.t17 t214.t22))
(step t214.t24 (cl @p_71) :rule refl)
(step t214.t25 (cl (= @p_84 @p_69)) :rule cong :premises (t214.t16 t214.t23 t214.t24))
(step t214.t26 (cl (= @p_82 @p_69)) :rule trans :premises (t214.t5 t214.t25))
(step t214.t27 (cl (= (= @p_83 @p_82) @p_70)) :rule cong :premises (t214.t4 t214.t26))
(step t214 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (< (divide$ ?v0 ?v1) (divide$ ?v2 ?v1)) (and (=> (< 0/1 ?v1) (< ?v0 ?v2)) (and (=> (< ?v1 0/1) (< ?v2 ?v0)) (not (= ?v1 0/1)))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(anchor :step t215 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t215.t0 (cl (= @p_68 @p_75)) :rule rare_rewrite :args ("bool-impl-elim" @p_67 @p_55))
(step t215.t1 (cl (= @p_74 @p_57)) :rule rare_rewrite :args ("bool-double-not-elim" @p_57))
(step t215.t2 (cl (= @p_55 @p_55)) :rule refl)
(step t215.t3 (cl (= @p_75 @p_58)) :rule cong :premises (t215.t1 t215.t2))
(step t215.t4 (cl (= @p_68 @p_58)) :rule trans :premises (t215.t0 t215.t3))
(step t215.t5 (cl (= @p_66 @p_73)) :rule rare_rewrite :args ("bool-impl-elim" @p_65 @p_50))
(step t215.t6 (cl (= @p_72 @p_51)) :rule rare_rewrite :args ("bool-double-not-elim" @p_51))
(step t215.t7 (cl (= @p_50 @p_50)) :rule refl)
(step t215.t8 (cl (= @p_73 @p_52)) :rule cong :premises (t215.t6 t215.t7))
(step t215.t9 (cl (= @p_66 @p_52)) :rule trans :premises (t215.t5 t215.t8))
(step t215.t10 (cl @p_71) :rule refl)
(step t215.t11 (cl (= @p_69 @p_59)) :rule cong :premises (t215.t4 t215.t9 t215.t10))
(step t215.t12 (cl (= @p_70 (= @p_64 @p_59))) :rule cong :premises (t215.t11))
(step t215 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (=> (not (>= (* -1/1 ?v1) 0/1)) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (=> (not (>= ?v1 0/1)) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1))))))) :rule bind)
(step t216 (cl @p_45) :rule trans :premises (t214 t215))
(step t217 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (not (>= (+ (divide$ ?v0 ?v1) (* -1/1 (divide$ ?v2 ?v1))) 0/1)) (and (or (>= (* -1/1 ?v1) 0/1) (not (>= (+ ?v0 (* -1/1 ?v2)) 0/1))) (or (>= ?v1 0/1) (not (>= (+ (* -1/1 ?v0) ?v2) 0/1))) (not (= ?v1 0/1)))))) :rule resolution :premises (t213 t216 a6))
(step t218 (cl @p_44) :rule resolution :premises (t212 t217))
(step t219 (cl @p_41) :rule resolution :premises (t152 t159 t218))
(step t220 (cl @p_36) :rule resolution :premises (t133 t139 t219))
(step t221 (cl (not @p_29) (not @p_28) @p_23) :rule equiv_pos2)
(step t222 (cl @p_32) :rule evaluate)
(step t223 (cl (= @p_25 @p_6)) :rule cong :premises (t222 t47))
(step t224 (cl (= @p_26 @p_30)) :rule cong :premises (t223))
(step t225 (cl (= @p_27 @p_31)) :rule cong :premises (t224))
(step t226 (cl (= (* 1/1 (- @p_6 @p_30)) (* 2/1 (- @p_6 0/1)))) :rule poly_simp)
(step t227 (cl (= @p_31 @p_7)) :rule poly_simp_rel :premises (t226))
(step t228 (cl (= @p_27 @p_7)) :rule trans :premises (t225 t227))
(step t229 (cl @p_29) :rule cong :premises (t228))
(step t230 (cl @p_28 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t231)
(assume t231.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1)))))
(step t231.t0 (cl (or @p_22 @p_27)) :rule forall_inst :args (0/1 d$))
(step t231.t1 (cl @p_22 @p_27) :rule or :premises (t231.t0))
(step t231.t2 (cl (not @p_8) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t231.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t231.t3.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t231.t3.t1 (cl @p_10) :rule refl)
(step t231.t3.t2 (cl (= @p_18 @p_12)) :rule cong :premises (t231.t3.t0 t231.t3.t1))
(step t231.t3.t3 (cl (= @p_16 @p_20)) :rule poly_simp)
(step t231.t3.t4 (cl (= @p_19 @p_21)) :rule cong :premises (t231.t3.t2 t231.t3.t3))
(step t231.t3.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 @p_13)))) :rule poly_simp)
(step t231.t3.t6 (cl (= @p_21 @p_15)) :rule poly_simp_rel :premises (t231.t3.t5))
(step t231.t3.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t231.t3.t4 t231.t3.t6))
(step t231.t3 (cl @p_8) :rule bind)
(step t231.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t231.t2 t231.t3 a9))
(step t231.t5 (cl @p_27) :rule resolution :premises (t231.t1 t231.t4))
(step t231 (cl @p_22 @p_27) :rule subproof :discharge (t231.a0))
(step t232 (cl @p_28 @p_27) :rule resolution :premises (t230 t231))
(step t233 (cl @p_28 (not @p_27)) :rule implies_neg2)
(step t234 (cl @p_28 @p_28) :rule resolution :premises (t232 t233))
(step t235 (cl @p_28) :rule contraction :premises (t234))
(step t236 (cl @p_23) :rule resolution :premises (t221 t229 t235))
(step t237 (cl @p_22 @p_7) :rule implies :premises (t236))
(step t238 (cl (not @p_8) (not (forall ((?v0 Real) (?v1 Real)) (= (times$ (- ?v0) ?v1) (- (times$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t239 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t239.t0 (cl (= @p_17 @p_11)) :rule poly_simp)
(step t239.t1 (cl @p_10) :rule refl)
(step t239.t2 (cl (= @p_18 @p_12)) :rule cong :premises (t239.t0 t239.t1))
(step t239.t3 (cl (= @p_16 @p_20)) :rule poly_simp)
(step t239.t4 (cl (= @p_19 @p_21)) :rule cong :premises (t239.t2 t239.t3))
(step t239.t5 (cl (= (* 1/1 (- @p_12 @p_20)) (* 1/1 (- @p_14 @p_13)))) :rule poly_simp)
(step t239.t6 (cl (= @p_21 @p_15)) :rule poly_simp_rel :premises (t239.t5))
(step t239.t7 (cl (= @p_19 @p_15)) :rule trans :premises (t239.t4 t239.t6))
(step t239 (cl @p_8) :rule bind)
(step t240 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$ ?v0 ?v1) (* -1/1 (times$ (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t238 t239 a9))
(step t241 (cl @p_7) :rule resolution :premises (t237 t240))
(step t242 (cl) :rule resolution :premises (t40 t92 t220 t241))
)
1c0cae6106f9de06dd98f11bfd754436efedf8ad 2347 0
unsat
(
(define-fun @quantifiers_skolemize_32 () A$ (choice ((?v2 A$)) (not (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))))
(define-fun @quantifiers_skolemize_34 () A$ (choice ((?v0 A$)) (not (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))))
(assume a0 (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1))))
(assume a1 (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (< 0 (of_nat$ (fun_app$b card$ top$))) (= (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))) (of_nat$ (fun_app$b card$ top$)))))))
(assume a2 (forall ((?v0 A$) (?v1 A_set$)) (=> (member$ ?v0 (uminus$ ?v1)) (not (member$ ?v0 ?v1)))))
(assume a3 (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))))
(assume a4 (forall ((?v0 A_list$)) (finite$ (set$ ?v0))))
(assume a6 (! (not (= top$ bot$)) :named @p_1))
(assume a10 (! (= (! (of_nat$ (fun_app$b card$a (! (set$ xs$) :named @p_4))) :named @p_5) (! (of_nat$ (size$ (! (remdups$ xs$) :named @p_2))) :named @p_3)) :named @p_6))
(assume a11 (! (= card$a card$) :named @p_7))
(assume a12 (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))
(assume a13 (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0))))))
(assume a16 (forall ((?v0 A_list$)) (= (uminus$ (set$ ?v0)) (coset$ ?v0))))
(assume a17 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= (inf$ ?v0 ?v1) bot$) (forall ((?v2 A$)) (=> (member$ ?v2 ?v0) (not (member$ ?v2 ?v1)))))))
(assume a18 (! (= eq_set$ uu$) :named @p_8))
(assume a19 (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ (uminus$ ?v0)) (finite$ top$)))))
(assume a20 (! (= rhs$ (! (ite (! (= (! (of_nat$ (! (fun_app$b card$ top$) :named @p_9)) :named @p_10) 0) :named @p_16) false (! (and (! (= (! (+ @p_3 (! (of_nat$ (size$ (! (remdups$ ys$) :named @p_11))) :named @p_12)) :named @p_13) @p_10) :named @p_14) (and (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ xs$))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ ys$))) (not (member$ ?v0 (set$ (remdups$ xs$)))))))) :named @p_15)) :named @p_17)) :named @p_18))
(assume a21 (forall ((?v0 A_list$) (?v1 A_list$)) (= (set$ (append$ ?v0 ?v1)) (sup$ (set$ ?v0) (set$ ?v1)))))
(assume a22 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))))
(assume a23 (forall ((?v0 A_list$)) (= (set$ (remdups$ ?v0)) (set$ ?v0))))
(assume a24 (! (= subset$ less_eq$) :named @p_19))
(assume a27 (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0)))))))
(assume a28 (! (not (! (= (! (fun_app$ (fun_app$a eq_set$ (! (coset$ xs$) :named @p_21)) (! (set$ ys$) :named @p_20)) :named @p_22) rhs$) :named @p_23)) :named @p_24))
(assume a29 (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0))))
(step t0 (cl (! (not (! (or (! (not (! (member$ @quantifiers_skolemize_32 (! (set$ @p_2) :named @p_28)) :named @p_29)) :named @p_30) (! (not (! (member$ @quantifiers_skolemize_32 (! (set$ @p_11) :named @p_25)) :named @p_26)) :named @p_27)) :named @p_31)) :named @p_557) @p_30 @p_27) :rule or_pos)
(step t1 (cl @p_30 @p_27 @p_557) :rule reordering :premises (t0))
(step t2 (cl (! (and (! (= @p_4 @p_28) :named @p_486) (! (member$ @quantifiers_skolemize_32 @p_4) :named @p_89)) :named @p_683) (! (not @p_486) :named @p_487) (! (not @p_89) :named @p_90)) :rule and_neg)
(step t3 (cl (! (=> @p_683 @p_29) :named @p_685) @p_683) :rule implies_neg1)
(anchor :step t4)
(assume t4.a0 @p_486)
(assume t4.a1 @p_89)
(step t4.t0 (cl (! (=> (! (and @p_89 @p_486) :named @p_686) @p_29) :named @p_688) @p_686) :rule implies_neg1)
(anchor :step t4.t1)
(assume t4.t1.a0 @p_89)
(assume t4.t1.a1 @p_486)
(step t4.t1.t0 (cl (= (! (= @p_29 true) :named @p_689) @p_29)) :rule equiv_simplify)
(step t4.t1.t1 (cl (not @p_689) @p_29) :rule equiv1 :premises (t4.t1.t0))
(step t4.t1.t2 (cl (or (! (not (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :named @p_175) @p_486)) :rule forall_inst :args (xs$))
(step t4.t1.t3 (cl @p_175 @p_486) :rule or :premises (t4.t1.t2))
(step t4.t1.t4 (cl (not (! (= (forall ((?v0 A_list$)) (= (set$ (remdups$ ?v0)) (set$ ?v0))) (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :named @p_172)) (not (forall ((?v0 A_list$)) (= (set$ (remdups$ ?v0)) (set$ ?v0)))) (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule equiv_pos2)
(anchor :step t4.t1.t5 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t4.t1.t5.t0 (cl (= (= (! (set$ (! (remdups$ ?v0) :named @p_173)) :named @p_174) (! (set$ ?v0) :named @p_113)) (= @p_113 @p_174))) :rule rare_rewrite :args ("eq-symm" @p_174 @p_113))
(step t4.t1.t5 (cl @p_172) :rule bind)
(step t4.t1.t6 (cl (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule resolution :premises (t4.t1.t4 t4.t1.t5 a23))
(step t4.t1.t7 (cl @p_486) :rule resolution :premises (t4.t1.t3 t4.t1.t6))
(step t4.t1.t8 (cl (= @p_28 @p_4)) :rule symm :premises (t4.t1.t7))
(step t4.t1.t9 (cl (= @p_29 @p_89)) :rule cong :premises (t4.t1.t8))
(step t4.t1.t10 (cl (= (! (= @p_89 true) :named @p_690) @p_89)) :rule equiv_simplify)
(step t4.t1.t11 (cl @p_690 @p_90) :rule equiv2 :premises (t4.t1.t10))
(step t4.t1.t12 (cl @p_690) :rule resolution :premises (t4.t1.t11 t4.t1.a0))
(step t4.t1.t13 (cl @p_689) :rule trans :premises (t4.t1.t9 t4.t1.t12))
(step t4.t1.t14 (cl @p_29) :rule resolution :premises (t4.t1.t1 t4.t1.t13))
(step t4.t1 (cl @p_90 @p_487 @p_29) :rule subproof :discharge (t4.t1.a0 t4.t1.a1))
(step t4.t2 (cl (! (not @p_686) :named @p_687) @p_89) :rule and_pos :args (0))
(step t4.t3 (cl @p_687 @p_486) :rule and_pos :args (1))
(step t4.t4 (cl @p_29 @p_687 @p_687) :rule resolution :premises (t4.t1 t4.t2 t4.t3))
(step t4.t5 (cl @p_687 @p_687 @p_29) :rule reordering :premises (t4.t4))
(step t4.t6 (cl @p_687 @p_29) :rule contraction :premises (t4.t5))
(step t4.t7 (cl @p_688 @p_29) :rule resolution :premises (t4.t0 t4.t6))
(step t4.t8 (cl @p_688 @p_30) :rule implies_neg2)
(step t4.t9 (cl @p_688 @p_688) :rule resolution :premises (t4.t7 t4.t8))
(step t4.t10 (cl @p_688) :rule contraction :premises (t4.t9))
(step t4.t11 (cl @p_687 @p_29) :rule implies :premises (t4.t10))
(step t4.t12 (cl (or @p_175 @p_486)) :rule forall_inst :args (xs$))
(step t4.t13 (cl @p_175 @p_486) :rule or :premises (t4.t12))
(step t4.t14 (cl (not @p_172) (not (forall ((?v0 A_list$)) (= (set$ (remdups$ ?v0)) (set$ ?v0)))) (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule equiv_pos2)
(anchor :step t4.t15 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t4.t15.t0 (cl (= (= @p_174 @p_113) (= @p_113 @p_174))) :rule rare_rewrite :args ("eq-symm" @p_174 @p_113))
(step t4.t15 (cl @p_172) :rule bind)
(step t4.t16 (cl (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule resolution :premises (t4.t14 t4.t15 a23))
(step t4.t17 (cl @p_486) :rule resolution :premises (t4.t13 t4.t16))
(step t4.t18 (cl @p_686) :rule and_intro :premises (t4.a1 t4.t17))
(step t4.t19 (cl @p_29) :rule resolution :premises (t4.t11 t4.t18))
(step t4 (cl @p_487 @p_90 @p_29) :rule subproof :discharge (t4.a0 t4.a1))
(step t5 (cl (! (not @p_683) :named @p_684) @p_486) :rule and_pos :args (0))
(step t6 (cl @p_684 @p_89) :rule and_pos :args (1))
(step t7 (cl @p_29 @p_684 @p_684) :rule resolution :premises (t4 t5 t6))
(step t8 (cl @p_684 @p_684 @p_29) :rule reordering :premises (t7))
(step t9 (cl @p_684 @p_29) :rule contraction :premises (t8))
(step t10 (cl @p_685 @p_29) :rule resolution :premises (t3 t9))
(step t11 (cl @p_685 @p_30) :rule implies_neg2)
(step t12 (cl @p_685 @p_685) :rule resolution :premises (t10 t11))
(step t13 (cl @p_685) :rule contraction :premises (t12))
(step t14 (cl @p_684 @p_29) :rule implies :premises (t13))
(step t15 (cl @p_487 @p_90 @p_29) :rule resolution :premises (t2 t14))
(step t16 (cl (or @p_175 @p_486)) :rule forall_inst :args (xs$))
(step t17 (cl @p_175 @p_486) :rule or :premises (t16))
(step t18 (cl (not @p_172) (not (forall ((?v0 A_list$)) (= (set$ (remdups$ ?v0)) (set$ ?v0)))) (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule equiv_pos2)
(anchor :step t19 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t19.t0 (cl (= (= @p_174 @p_113) (= @p_113 @p_174))) :rule rare_rewrite :args ("eq-symm" @p_174 @p_113))
(step t19 (cl @p_172) :rule bind)
(step t20 (cl (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule resolution :premises (t18 t19 a23))
(step t21 (cl @p_486) :rule resolution :premises (t17 t20))
(step t22 (cl (not (! (= (! (or (! (or @p_90 (! (not (! (member$ @quantifiers_skolemize_32 @p_20) :named @p_87)) :named @p_88)) :named @p_91) (! (not @p_90) :named @p_93)) :named @p_94) (! (or @p_91 @p_89) :named @p_92)) :named @p_96)) (not @p_94) @p_92) :rule equiv_pos2)
(step t23 (cl (= @p_93 @p_89)) :rule rare_rewrite :args ("bool-double-not-elim" @p_89))
(step t24 (cl @p_96) :rule cong :premises (t23))
(step t25 (cl @p_91 @p_93) :rule or_neg :args (0))
(step t26 (cl @p_94 (! (not @p_91) :named @p_95)) :rule or_neg :args (0))
(step t27 (cl @p_94 (not @p_93)) :rule or_neg :args (1))
(step t28 (cl @p_94 @p_94) :rule resolution :premises (t25 t26 t27))
(step t29 (cl @p_94) :rule contraction :premises (t28))
(step t30 (cl @p_92) :rule resolution :premises (t22 t24 t29))
(step t31 (cl @p_91 @p_89) :rule or :premises (t30))
(step t32 (cl @p_89 @p_91) :rule reordering :premises (t31))
(step t33 (cl (not (! (= (! (or (! (not (! (not (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))) :named @p_129)) :named @p_130) @p_95) :named @p_131) (! (or (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))) @p_95) :named @p_128)) :named @p_135)) (not @p_131) @p_128) :rule equiv_pos2)
(step t34 (cl (= @p_130 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))))
(step t35 (cl (= @p_95 @p_95)) :rule refl)
(step t36 (cl @p_135) :rule cong :premises (t34 t35))
(step t37 (cl (! (=> @p_129 @p_95) :named @p_133) @p_129) :rule implies_neg1)
(anchor :step t38)
(assume t38.a0 @p_129)
(step t38.t0 (cl (not (! (= @p_129 @p_95) :named @p_134)) @p_130 @p_95) :rule equiv_pos2)
(anchor :step t38.t1 :args ((:= (?v2 A$) @quantifiers_skolemize_32)))
(step t38.t1.t0 (cl (= (or (not (member$ ?v2 @p_4)) (not (member$ ?v2 @p_20))) @p_91)) :rule refl)
(step t38.t1 (cl (= (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))) @p_91)) :rule sko_forall)
(step t38.t2 (cl @p_134) :rule cong :premises (t38.t1))
(step t38.t3 (cl @p_95) :rule resolution :premises (t38.t0 t38.t2 t38.a0))
(step t38 (cl @p_130 @p_95) :rule subproof :discharge (t38.a0))
(step t39 (cl @p_133 @p_95) :rule resolution :premises (t37 t38))
(step t40 (cl @p_133 (! (not @p_95) :named @p_132)) :rule implies_neg2)
(step t41 (cl @p_133 @p_133) :rule resolution :premises (t39 t40))
(step t42 (cl @p_133) :rule contraction :premises (t41))
(step t43 (cl @p_130 @p_95) :rule implies :premises (t42))
(step t44 (cl @p_131 (not @p_130)) :rule or_neg :args (0))
(step t45 (cl @p_131 @p_132) :rule or_neg :args (1))
(step t46 (cl @p_131 @p_131) :rule resolution :premises (t43 t44 t45))
(step t47 (cl @p_131) :rule contraction :premises (t46))
(step t48 (cl @p_128) :rule resolution :premises (t33 t36 t47))
(step t49 (cl (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))) @p_95) :rule or :premises (t48))
(step t50 (cl (not (! (= (! (or (! (not (! (not (! (= (! (of_nat$ (! (fun_app$b card$a top$) :named @p_32)) :named @p_33) (! (of_nat$ (! (fun_app$b card$a (! (set$ (append$ xs$ ys$)) :named @p_262)) :named @p_387)) :named @p_388)) :named @p_575)) :named @p_605)) :named @p_654) (! (not (! (= @p_262 (! (sup$ @p_4 @p_20) :named @p_261)) :named @p_263)) :named @p_333) (! (not (! (not (! (>= (! (+ (! (of_nat$ (! (fun_app$b card$a top$) :named @p_32)) :named @p_33) (! (* -1 (! (of_nat$ (! (fun_app$b card$a @p_261) :named @p_265)) :named @p_266)) :named @p_314)) :named @p_351) 1) :named @p_612)) :named @p_613)) :named @p_616) (! (not (! (>= @p_351 0) :named @p_632)) :named @p_635)) :named @p_655) (! (or @p_575 @p_333 @p_612 @p_635) :named @p_653)) :named @p_675)) (not @p_655) @p_653) :rule equiv_pos2)
(step t51 (cl (= @p_654 @p_575)) :rule rare_rewrite :args ("bool-double-not-elim" @p_575))
(step t52 (cl (= @p_333 @p_333)) :rule refl)
(step t53 (cl (= @p_616 @p_612)) :rule rare_rewrite :args ("bool-double-not-elim" @p_612))
(step t54 (cl (= @p_635 @p_635)) :rule refl)
(step t55 (cl @p_675) :rule cong :premises (t51 t52 t53 t54))
(step t56 (cl (! (=> (! (and @p_605 @p_263 @p_613 @p_632) :named @p_657) (! (and (! (not (! (= @p_33 @p_266) :named @p_340)) :named @p_345) @p_613 @p_632) :named @p_659)) :named @p_669) @p_657) :rule implies_neg1)
(anchor :step t57)
(assume t57.a0 @p_605)
(assume t57.a1 @p_263)
(assume t57.a2 @p_613)
(assume t57.a3 @p_632)
(step t57.t0 (cl (! (=> (! (and @p_605 @p_263) :named @p_670) @p_345) :named @p_672) @p_670) :rule implies_neg1)
(anchor :step t57.t1)
(assume t57.t1.a0 @p_605)
(assume t57.t1.a1 @p_263)
(step t57.t1.t0 (cl (= (! (= @p_340 false) :named @p_673) @p_345)) :rule equiv_simplify)
(step t57.t1.t1 (cl (not @p_673) @p_345) :rule equiv1 :premises (t57.t1.t0))
(step t57.t1.t2 (cl (or (! (not (forall ((?v0 A_list$) (?v1 A_list$)) (= (set$ (append$ ?v0 ?v1)) (sup$ (set$ ?v0) (set$ ?v1))))) :named @p_264) @p_263)) :rule forall_inst :args (xs$ ys$))
(step t57.t1.t3 (cl @p_264 @p_263) :rule or :premises (t57.t1.t2))
(step t57.t1.t4 (cl @p_263) :rule resolution :premises (t57.t1.t3 a21))
(step t57.t1.t5 (cl (= @p_261 @p_262)) :rule symm :premises (t57.t1.t4))
(step t57.t1.t6 (cl (= @p_265 @p_387)) :rule cong :premises (t57.t1.t5))
(step t57.t1.t7 (cl (= @p_266 @p_388)) :rule cong :premises (t57.t1.t6))
(step t57.t1.t8 (cl (= @p_340 @p_575)) :rule cong :premises (t57.t1.t7))
(step t57.t1.t9 (cl (= (! (= @p_575 false) :named @p_674) @p_605)) :rule equiv_simplify)
(step t57.t1.t10 (cl @p_674 @p_654) :rule equiv2 :premises (t57.t1.t9))
(step t57.t1.t11 (cl (! (not @p_654) :named @p_656) @p_575) :rule not_not)
(step t57.t1.t12 (cl @p_674 @p_575) :rule resolution :premises (t57.t1.t10 t57.t1.t11))
(step t57.t1.t13 (cl @p_674) :rule resolution :premises (t57.t1.t12 t57.t1.a0))
(step t57.t1.t14 (cl @p_673) :rule trans :premises (t57.t1.t8 t57.t1.t13))
(step t57.t1.t15 (cl @p_345) :rule resolution :premises (t57.t1.t1 t57.t1.t14))
(step t57.t1 (cl @p_654 @p_333 @p_345) :rule subproof :discharge (t57.t1.a0 t57.t1.a1))
(step t57.t2 (cl (! (not @p_670) :named @p_671) @p_605) :rule and_pos :args (0))
(step t57.t3 (cl @p_671 @p_263) :rule and_pos :args (1))
(step t57.t4 (cl @p_345 @p_671 @p_671) :rule resolution :premises (t57.t1 t57.t2 t57.t3))
(step t57.t5 (cl @p_671 @p_671 @p_345) :rule reordering :premises (t57.t4))
(step t57.t6 (cl @p_671 @p_345) :rule contraction :premises (t57.t5))
(step t57.t7 (cl @p_672 @p_345) :rule resolution :premises (t57.t0 t57.t6))
(step t57.t8 (cl @p_672 (! (not @p_345) :named @p_398)) :rule implies_neg2)
(step t57.t9 (cl @p_672 @p_672) :rule resolution :premises (t57.t7 t57.t8))
(step t57.t10 (cl @p_672) :rule contraction :premises (t57.t9))
(step t57.t11 (cl @p_671 @p_345) :rule implies :premises (t57.t10))
(step t57.t12 (cl (or @p_264 @p_263)) :rule forall_inst :args (xs$ ys$))
(step t57.t13 (cl @p_264 @p_263) :rule or :premises (t57.t12))
(step t57.t14 (cl @p_263) :rule resolution :premises (t57.t13 a21))
(step t57.t15 (cl @p_670) :rule and_intro :premises (t57.a0 t57.t14))
(step t57.t16 (cl @p_345) :rule resolution :premises (t57.t11 t57.t15))
(step t57.t17 (cl @p_659) :rule and_intro :premises (t57.t16 t57.a2 t57.a3))
(step t57 (cl @p_654 @p_333 @p_616 @p_635 @p_659) :rule subproof :discharge (t57.a0 t57.a1 t57.a2 t57.a3))
(step t58 (cl (! (not @p_657) :named @p_658) @p_605) :rule and_pos :args (0))
(step t59 (cl @p_658 @p_263) :rule and_pos :args (1))
(step t60 (cl @p_658 @p_613) :rule and_pos :args (2))
(step t61 (cl @p_658 @p_632) :rule and_pos :args (3))
(step t62 (cl @p_659 @p_658 @p_658 @p_658 @p_658) :rule resolution :premises (t57 t58 t59 t60 t61))
(step t63 (cl @p_658 @p_658 @p_658 @p_658 @p_659) :rule reordering :premises (t62))
(step t64 (cl @p_658 @p_659) :rule contraction :premises (t63))
(step t65 (cl @p_669 @p_659) :rule resolution :premises (t56 t64))
(step t66 (cl @p_669 (! (not @p_659) :named @p_660)) :rule implies_neg2)
(step t67 (cl @p_669 @p_669) :rule resolution :premises (t65 t66))
(step t68 (cl @p_669) :rule contraction :premises (t67))
(step t69 (cl @p_658 @p_659) :rule implies :premises (t68))
(step t70 (cl (! (=> @p_659 false) :named @p_661) @p_659) :rule implies_neg1)
(anchor :step t71)
(assume t71.a0 @p_345)
(assume t71.a1 @p_613)
(assume t71.a2 @p_632)
(step t71.t0 (cl (not (! (= (! (< @p_351 0) :named @p_644) @p_635) :named @p_646)) (! (not @p_644) :named @p_647) @p_635) :rule equiv_pos2)
(step t71.t1 (cl @p_646) :rule rare_rewrite :args ("arith-elim-lt" @p_351 0))
(step t71.t2 (cl (or (! (= @p_351 0) :named @p_360) (! (not (! (<= @p_351 0) :named @p_664)) :named @p_668) (! (not (<= 0 @p_351)) :named @p_662))) :rule la_disequality)
(step t71.t3 (cl @p_360 @p_668 @p_662) :rule or :premises (t71.t2))
(step t71.t4 (cl (not (! (= @p_345 (! (not @p_360) :named @p_424)) :named @p_667)) @p_398 @p_424) :rule equiv_pos2)
(step t71.t5 (cl (= (* 1 (- @p_351 0)) (* 1 (- @p_33 @p_266)))) :rule poly_simp)
(step t71.t6 (cl (= @p_360 @p_340)) :rule poly_simp_rel :premises (t71.t5))
(step t71.t7 (cl (= @p_424 @p_345)) :rule cong :premises (t71.t6))
(step t71.t8 (cl @p_667) :rule symm :premises (t71.t7))
(step t71.t9 (cl @p_424) :rule resolution :premises (t71.t4 t71.t8 t71.a0))
(step t71.t10 (cl (not (! (< @p_351 1) :named @p_665)) @p_664) :rule la_generic :args (1/1 1/1))
(step t71.t11 (cl (not (! (= @p_613 @p_665) :named @p_666)) @p_616 @p_665) :rule equiv_pos2)
(step t71.t12 (cl (= @p_665 @p_613)) :rule rare_rewrite :args ("arith-elim-lt" @p_351 1))
(step t71.t13 (cl @p_666) :rule symm :premises (t71.t12))
(step t71.t14 (cl @p_665) :rule resolution :premises (t71.t11 t71.t13 t71.a1))
(step t71.t15 (cl @p_664) :rule resolution :premises (t71.t10 t71.t14))
(step t71.t16 (cl (not (! (= @p_644 @p_662) :named @p_663)) @p_644 (not @p_662)) :rule equiv_pos1)
(step t71.t17 (cl @p_663) :rule comp_simplify)
(step t71.t18 (cl @p_644) :rule resolution :premises (t71.t3 t71.t9 t71.t15 t71.t16 t71.t17))
(step t71.t19 (cl @p_635) :rule resolution :premises (t71.t0 t71.t1 t71.t18))
(step t71.t20 (cl) :rule resolution :premises (t71.a2 t71.t19))
(step t71 (cl @p_398 @p_616 @p_635 false) :rule subproof :discharge (t71.a0 t71.a1 t71.a2))
(step t72 (cl @p_660 @p_345) :rule and_pos :args (0))
(step t73 (cl @p_660 @p_613) :rule and_pos :args (1))
(step t74 (cl @p_660 @p_632) :rule and_pos :args (2))
(step t75 (cl false @p_660 @p_660 @p_660) :rule resolution :premises (t71 t72 t73 t74))
(step t76 (cl @p_660 @p_660 @p_660 false) :rule reordering :premises (t75))
(step t77 (cl @p_660 false) :rule contraction :premises (t76))
(step t78 (cl @p_661 false) :rule resolution :premises (t70 t77))
(step t79 (cl @p_661 (! (not false) :named @p_344)) :rule implies_neg2)
(step t80 (cl @p_661 @p_661) :rule resolution :premises (t78 t79))
(step t81 (cl @p_661) :rule contraction :premises (t80))
(step t82 (cl (= @p_661 @p_660)) :rule implies_simplify)
(step t83 (cl (not @p_661) @p_660) :rule equiv1 :premises (t82))
(step t84 (cl @p_660) :rule resolution :premises (t81 t83))
(step t85 (cl @p_658) :rule resolution :premises (t69 t84))
(step t86 (cl @p_654 @p_333 @p_616 @p_635) :rule not_and :premises (t85))
(step t87 (cl @p_655 @p_656) :rule or_neg :args (0))
(step t88 (cl @p_655 (not @p_333)) :rule or_neg :args (1))
(step t89 (cl @p_655 (not @p_616)) :rule or_neg :args (2))
(step t90 (cl @p_655 (! (not @p_635) :named @p_636)) :rule or_neg :args (3))
(step t91 (cl @p_655 @p_655 @p_655 @p_655) :rule resolution :premises (t86 t87 t88 t89 t90))
(step t92 (cl @p_655) :rule contraction :premises (t91))
(step t93 (cl @p_653) :rule resolution :premises (t50 t55 t92))
(step t94 (cl @p_575 @p_333 @p_612 @p_635) :rule or :premises (t93))
(step t95 (cl (or @p_264 @p_263)) :rule forall_inst :args (xs$ ys$))
(step t96 (cl @p_264 @p_263) :rule or :premises (t95))
(step t97 (cl @p_263) :rule resolution :premises (t96 a21))
(step t98 (cl (not (! (= (! (or (! (not (! (= 0 (! (of_nat$ (fun_app$b card$a (! (inf$ @p_4 @p_20) :named @p_136))) :named @p_150)) :named @p_339)) :named @p_346) (! (not (! (= @p_5 (! (+ (! (* -1 (! (of_nat$ (fun_app$b card$a @p_20)) :named @p_251)) :named @p_267) (! (of_nat$ (fun_app$b card$a (! (inf$ @p_4 @p_20) :named @p_136))) :named @p_150) @p_266) :named @p_268)) :named @p_269)) :named @p_332) (! (not (! (= @p_5 (! (+ (* -1 @p_12) @p_33) :named @p_34)) :named @p_446)) :named @p_447) (! (not (! (= @p_12 @p_251) :named @p_252)) :named @p_327) @p_632) :named @p_634) (! (or (! (not (! (= @p_150 0) :named @p_151)) :named @p_335) (! (not (! (= @p_5 (! (+ (! (* -1 (! (of_nat$ (fun_app$b card$a @p_20)) :named @p_251)) :named @p_267) (! (of_nat$ (fun_app$b card$a (! (inf$ @p_4 @p_20) :named @p_136))) :named @p_150) @p_266) :named @p_268)) :named @p_269)) :named @p_332) (! (not (! (= @p_5 (! (+ (* -1 @p_12) @p_33) :named @p_34)) :named @p_446)) :named @p_447) (! (not (! (= @p_12 @p_251) :named @p_252)) :named @p_327) @p_632) :named @p_633)) :named @p_652)) (not @p_634) @p_633) :rule equiv_pos2)
(step t99 (cl (= (* 1 (- 0 @p_150)) (* -1 (- @p_150 0)))) :rule poly_simp)
(step t100 (cl (= @p_339 @p_151)) :rule poly_simp_rel :premises (t99))
(step t101 (cl (= @p_346 @p_335)) :rule cong :premises (t100))
(step t102 (cl (= @p_332 @p_332)) :rule refl)
(step t103 (cl (= @p_447 @p_447)) :rule refl)
(step t104 (cl (= @p_327 @p_327)) :rule refl)
(step t105 (cl (= @p_632 @p_632)) :rule refl)
(step t106 (cl @p_652) :rule cong :premises (t101 t102 t103 t104 t105))
(step t107 (cl (not (! (= (! (or @p_346 @p_332 @p_447 @p_327 @p_636) :named @p_637) @p_634) :named @p_651)) (not @p_637) @p_634) :rule equiv_pos2)
(step t108 (cl (= @p_636 @p_632)) :rule rare_rewrite :args ("bool-double-not-elim" @p_632))
(step t109 (cl (= @p_637 @p_633)) :rule cong :premises (t101 t102 t103 t104 t108))
(step t110 (cl (= @p_633 @p_634)) :rule symm :premises (t106))
(step t111 (cl @p_651) :rule trans :premises (t109 t110))
(step t112 (cl (! (=> (! (and @p_339 @p_269 @p_446 @p_252 @p_635) :named @p_638) false) :named @p_640) @p_638) :rule implies_neg1)
(anchor :step t113)
(assume t113.a0 @p_339)
(assume t113.a1 @p_269)
(assume t113.a2 @p_446)
(assume t113.a3 @p_252)
(assume t113.a4 @p_635)
(step t113.t0 (cl (not (! (= (! (< (! (+ @p_351 (! (* -1 @p_150) :named @p_355) (! (* -1 (! (+ @p_5 @p_251 @p_355 @p_314) :named @p_356)) :named @p_407) (! (+ @p_5 @p_12 (! (* -1 @p_33) :named @p_328)) :named @p_329) (! (* -1 (! (+ @p_12 @p_267) :named @p_353)) :named @p_406)) :named @p_642) (! (+ 0 (! (* -1 0) :named @p_348) @p_348 0 @p_348) :named @p_641)) :named @p_643) false) :named @p_648)) (not @p_643) false) :rule equiv_pos2)
(step t113.t1 (cl (= @p_643 (! (not (! (>= @p_642 @p_641) :named @p_649)) :named @p_650))) :rule rare_rewrite :args ("arith-elim-lt" @p_642 @p_641))
(step t113.t2 (cl (= @p_642 (! (+ (! (* 0 @p_150) :named @p_431) (! (* 0 @p_266) :named @p_379) @p_251 @p_328 @p_267 @p_33 (! (* 0 @p_12) :named @p_378) (! (* 0 @p_5) :named @p_377)) :named @p_432))) :rule poly_simp)
(step t113.t3 (cl (= @p_431 0)) :rule poly_simp)
(step t113.t4 (cl (= @p_379 0)) :rule poly_simp)
(step t113.t5 (cl (= @p_251 @p_251)) :rule refl)
(step t113.t6 (cl (= @p_328 @p_328)) :rule refl)
(step t113.t7 (cl (= @p_267 @p_267)) :rule refl)
(step t113.t8 (cl (= @p_33 @p_33)) :rule refl)
(step t113.t9 (cl (= @p_378 0)) :rule poly_simp)
(step t113.t10 (cl (= @p_377 0)) :rule poly_simp)
(step t113.t11 (cl (= @p_432 (! (+ 0 0 @p_251 @p_328 @p_267 @p_33 0 0) :named @p_433))) :rule cong :premises (t113.t3 t113.t4 t113.t5 t113.t6 t113.t7 t113.t8 t113.t9 t113.t10))
(step t113.t12 (cl (= @p_433 0)) :rule poly_simp)
(step t113.t13 (cl (= @p_432 0)) :rule trans :premises (t113.t11 t113.t12))
(step t113.t14 (cl (= @p_642 0)) :rule trans :premises (t113.t2 t113.t13))
(step t113.t15 (cl (= @p_348 0)) :rule evaluate)
(step t113.t16 (cl (= 0 0)) :rule refl)
(step t113.t17 (cl (= @p_641 (! (+ 0 0 0 0 0) :named @p_430))) :rule cong :premises (t113.t15 t113.t15 t113.t16 t113.t15))
(step t113.t18 (cl (= @p_430 0)) :rule evaluate)
(step t113.t19 (cl (= @p_641 0)) :rule trans :premises (t113.t17 t113.t18))
(step t113.t20 (cl (= @p_649 (! (>= 0 0) :named @p_429))) :rule cong :premises (t113.t14 t113.t19))
(step t113.t21 (cl (= @p_429 true)) :rule evaluate)
(step t113.t22 (cl (= @p_649 true)) :rule trans :premises (t113.t20 t113.t21))
(step t113.t23 (cl (= @p_650 (! (not true) :named @p_428))) :rule cong :premises (t113.t22))
(step t113.t24 (cl (= @p_428 false)) :rule evaluate)
(step t113.t25 (cl (= @p_650 false)) :rule trans :premises (t113.t23 t113.t24))
(step t113.t26 (cl @p_648) :rule trans :premises (t113.t1 t113.t25))
(step t113.t27 (cl @p_647 (! (not (! (= @p_355 @p_348) :named @p_414)) :named @p_421) (! (not (! (= @p_407 @p_348) :named @p_412)) :named @p_422) (! (not (! (= @p_329 0) :named @p_462)) :named @p_463) (! (not (! (= @p_406 @p_348) :named @p_410)) :named @p_423) @p_643) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t113.t28 (cl (not (! (= @p_635 @p_644) :named @p_645)) @p_636 @p_644) :rule equiv_pos2)
(step t113.t29 (cl @p_646) :rule rare_rewrite :args ("arith-elim-lt" @p_351 0))
(step t113.t30 (cl @p_645) :rule symm :premises (t113.t29))
(step t113.t31 (cl @p_644) :rule resolution :premises (t113.t28 t113.t30 t113.a4))
(step t113.t32 (cl (=> (! (and (! (< -1 0) :named @p_361) @p_151) :named @p_415) @p_414)) :rule la_mult_neg)
(step t113.t33 (cl (! (not @p_415) :named @p_416) @p_414) :rule implies :premises (t113.t32))
(step t113.t34 (cl (= (! (= @p_361 true) :named @p_365) @p_361)) :rule equiv_simplify)
(step t113.t35 (cl (not @p_365) @p_361) :rule equiv1 :premises (t113.t34))
(step t113.t36 (cl @p_365) :rule evaluate)
(step t113.t37 (cl @p_361) :rule resolution :premises (t113.t35 t113.t36))
(step t113.t38 (cl @p_151) :rule symm :premises (t113.a0))
(step t113.t39 (cl @p_415) :rule and_intro :premises (t113.t37 t113.t38))
(step t113.t40 (cl @p_414) :rule resolution :premises (t113.t33 t113.t39))
(step t113.t41 (cl (=> (! (and @p_361 (! (= @p_356 0) :named @p_370)) :named @p_413) @p_412)) :rule la_mult_neg)
(step t113.t42 (cl (not @p_413) @p_412) :rule implies :premises (t113.t41))
(step t113.t43 (cl (not (! (= @p_269 @p_370) :named @p_371)) @p_332 @p_370) :rule equiv_pos2)
(step t113.t44 (cl (= (* 1 (- @p_356 0)) (* 1 (! (- @p_5 @p_268) :named @p_322)))) :rule poly_simp)
(step t113.t45 (cl (= @p_370 @p_269)) :rule poly_simp_rel :premises (t113.t44))
(step t113.t46 (cl @p_371) :rule symm :premises (t113.t45))
(step t113.t47 (cl (! (not (! (or (! (not (! (finite$ @p_4) :named @p_272)) :named @p_273) (! (not (! (finite$ @p_20) :named @p_270)) :named @p_271) @p_269) :named @p_274)) :named @p_324) @p_273 @p_271 @p_269) :rule or_pos)
(step t113.t48 (cl @p_273 @p_271 @p_269 @p_324) :rule reordering :premises (t113.t47))
(step t113.t49 (cl (or (! (not (forall ((?v0 A_list$)) (finite$ (set$ ?v0)))) :named @p_323) @p_272)) :rule forall_inst :args (xs$))
(step t113.t50 (cl @p_323 @p_272) :rule or :premises (t113.t49))
(step t113.t51 (cl @p_272) :rule resolution :premises (t113.t50 a4))
(step t113.t52 (cl (or @p_323 @p_270)) :rule forall_inst :args (ys$))
(step t113.t53 (cl @p_323 @p_270) :rule or :premises (t113.t52))
(step t113.t54 (cl @p_270) :rule resolution :premises (t113.t53 a4))
(step t113.t55 (cl (not (! (= (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))) (! (or @p_273 @p_271 (! (= @p_150 (! (+ @p_314 @p_251 @p_5) :named @p_315)) :named @p_316)) :named @p_317)) :named @p_318) (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))) @p_274) :named @p_313)) :named @p_319)) (not @p_318) @p_313) :rule equiv_pos2)
(step t113.t56 (cl (= @p_315 (! (+ @p_5 @p_251 @p_314) :named @p_320))) :rule poly_simp)
(step t113.t57 (cl (= @p_316 (! (= @p_150 @p_320) :named @p_321))) :rule cong :premises (t113.t56))
(step t113.t58 (cl (= (* 1 (- @p_150 @p_320)) (* -1 @p_322))) :rule poly_simp)
(step t113.t59 (cl (= @p_321 @p_269)) :rule poly_simp_rel :premises (t113.t58))
(step t113.t60 (cl (= @p_316 @p_269)) :rule trans :premises (t113.t57 t113.t59))
(step t113.t61 (cl (= @p_317 @p_274)) :rule cong :premises (t113.t60))
(step t113.t62 (cl @p_319) :rule cong :premises (t113.t61))
(step t113.t63 (cl @p_318 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule implies_neg1)
(anchor :step t113.t64)
(assume t113.t64.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))
(step t113.t64.t0 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :named @p_312) @p_317)) :rule forall_inst :args (@p_4 @p_20))
(step t113.t64.t1 (cl @p_312 @p_317) :rule or :premises (t113.t64.t0))
(step t113.t64.t2 (cl (not (! (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :named @p_275)) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t113.t64.t3 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t64.t3.t0 (cl (= (* 1 (- (! (+ (! (of_nat$ (! (fun_app$b card$ ?v0) :named @p_162)) :named @p_163) (! (of_nat$ (! (fun_app$b card$ ?v1) :named @p_297)) :named @p_298)) :named @p_310) (! (+ (! (of_nat$ (! (fun_app$b card$ (! (sup$ ?v0 ?v1) :named @p_278)) :named @p_295)) :named @p_296) (! (of_nat$ (! (fun_app$b card$ (! (inf$ ?v0 ?v1) :named @p_140)) :named @p_293)) :named @p_294)) :named @p_309))) (* 1 (- (! (of_nat$ (! (fun_app$b card$ ?v0) :named @p_162)) :named @p_163) (! (+ (! (* -1 @p_298) :named @p_299) @p_296 @p_294) :named @p_300))))) :rule poly_simp)
(step t113.t64.t3.t1 (cl (= (! (= @p_310 @p_309) :named @p_311) (! (= @p_163 @p_300) :named @p_301))) :rule poly_simp_rel :premises (t113.t64.t3.t0))
(step t113.t64.t3.t2 (cl (= (=> (! (and (! (finite$ ?v0) :named @p_157) (! (finite$ ?v1) :named @p_285)) :named @p_303) @p_311) (! (=> @p_303 @p_301) :named @p_304))) :rule cong :premises (t113.t64.t3.t1))
(step t113.t64.t3 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t113.t64.t4 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t64.t4.t0 (cl (= @p_304 (! (or (! (not @p_303) :named @p_305) @p_301) :named @p_306))) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t113.t64.t4.t1 (cl (= @p_305 (! (or (! (not @p_157) :named @p_158) (! (not @p_285) :named @p_286)) :named @p_307))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t113.t64.t4.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t113.t64.t4.t3 (cl (= @p_306 (! (or @p_307 @p_301) :named @p_308))) :rule cong :premises (t113.t64.t4.t1 t113.t64.t4.t2))
(step t113.t64.t4.t4 (cl (= @p_308 (! (or @p_158 @p_286 @p_301) :named @p_302))) :rule aci_simp)
(step t113.t64.t4.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t113.t64.t4.t3 t113.t64.t4.t4))
(step t113.t64.t4.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t113.t64.t4.t0 t113.t64.t4.t5))
(step t113.t64.t4 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t113.t64.t5 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t113.t64.t3 t113.t64.t4))
(anchor :step t113.t64.t6 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t64.t6.t0 (cl (= card$ card$a)) :rule symm :premises (a11))
(step t113.t64.t6.t1 (cl (! (= ?v0 ?v0) :named @p_72)) :rule refl)
(step t113.t64.t6.t2 (cl (= @p_162 (! (fun_app$b card$a ?v0) :named @p_154))) :rule cong :premises (t113.t64.t6.t0 t113.t64.t6.t1))
(step t113.t64.t6.t3 (cl (= @p_163 (! (of_nat$ @p_154) :named @p_155))) :rule cong :premises (t113.t64.t6.t2))
(step t113.t64.t6.t4 (cl (! (= ?v1 ?v1) :named @p_73)) :rule refl)
(step t113.t64.t6.t5 (cl (= @p_297 (! (fun_app$b card$a ?v1) :named @p_276))) :rule cong :premises (t113.t64.t6.t0 t113.t64.t6.t4))
(step t113.t64.t6.t6 (cl (= @p_298 (! (of_nat$ @p_276) :named @p_277))) :rule cong :premises (t113.t64.t6.t5))
(step t113.t64.t6.t7 (cl (= @p_299 (! (* -1 @p_277) :named @p_287))) :rule cong :premises (t113.t64.t6.t6))
(step t113.t64.t6.t8 (cl (= @p_278 @p_278)) :rule refl)
(step t113.t64.t6.t9 (cl (= @p_295 (! (fun_app$b card$a @p_278) :named @p_279))) :rule cong :premises (t113.t64.t6.t0 t113.t64.t6.t8))
(step t113.t64.t6.t10 (cl (= @p_296 (! (of_nat$ @p_279) :named @p_280))) :rule cong :premises (t113.t64.t6.t9))
(step t113.t64.t6.t11 (cl (= @p_140 @p_140)) :rule refl)
(step t113.t64.t6.t12 (cl (= @p_293 (! (fun_app$b card$a @p_140) :named @p_282))) :rule cong :premises (t113.t64.t6.t0 t113.t64.t6.t11))
(step t113.t64.t6.t13 (cl (= @p_294 (! (of_nat$ @p_282) :named @p_283))) :rule cong :premises (t113.t64.t6.t12))
(step t113.t64.t6.t14 (cl (= @p_300 (! (+ @p_287 @p_280 @p_283) :named @p_288))) :rule cong :premises (t113.t64.t6.t7 t113.t64.t6.t10 t113.t64.t6.t13))
(step t113.t64.t6.t15 (cl (= @p_301 (! (= @p_155 @p_288) :named @p_289))) :rule cong :premises (t113.t64.t6.t3 t113.t64.t6.t14))
(step t113.t64.t6.t16 (cl (= @p_302 (! (or @p_158 @p_286 @p_289) :named @p_290))) :rule cong :premises (t113.t64.t6.t15))
(step t113.t64.t6 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t113.t64.t7 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t64.t7.t0 (cl (= @p_288 (! (+ @p_283 @p_280 @p_287) :named @p_291))) :rule poly_simp)
(step t113.t64.t7.t1 (cl (= @p_289 (! (= @p_155 @p_291) :named @p_292))) :rule cong :premises (t113.t64.t7.t0))
(step t113.t64.t7.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 (! (+ (* -1 @p_280) @p_277 @p_155) :named @p_281))))) :rule poly_simp)
(step t113.t64.t7.t3 (cl (= @p_292 (! (= @p_283 @p_281) :named @p_284))) :rule poly_simp_rel :premises (t113.t64.t7.t2))
(step t113.t64.t7.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t113.t64.t7.t1 t113.t64.t7.t3))
(step t113.t64.t7.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t113.t64.t7.t4))
(step t113.t64.t7 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t113.t64.t8 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t113.t64.t6 t113.t64.t7))
(step t113.t64.t9 (cl @p_275) :rule trans :premises (t113.t64.t5 t113.t64.t8))
(step t113.t64.t10 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t113.t64.t2 t113.t64.t9 a12))
(step t113.t64.t11 (cl @p_317) :rule resolution :premises (t113.t64.t1 t113.t64.t10))
(step t113.t64 (cl @p_312 @p_317) :rule subproof :discharge (t113.t64.a0))
(step t113.t65 (cl @p_318 @p_317) :rule resolution :premises (t113.t63 t113.t64))
(step t113.t66 (cl @p_318 (not @p_317)) :rule implies_neg2)
(step t113.t67 (cl @p_318 @p_318) :rule resolution :premises (t113.t65 t113.t66))
(step t113.t68 (cl @p_318) :rule contraction :premises (t113.t67))
(step t113.t69 (cl @p_313) :rule resolution :premises (t113.t55 t113.t62 t113.t68))
(step t113.t70 (cl @p_312 @p_274) :rule implies :premises (t113.t69))
(step t113.t71 (cl (not @p_275) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t113.t72 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t72.t0 (cl (= (* 1 (- @p_310 @p_309)) (* 1 (- @p_163 @p_300)))) :rule poly_simp)
(step t113.t72.t1 (cl (= @p_311 @p_301)) :rule poly_simp_rel :premises (t113.t72.t0))
(step t113.t72.t2 (cl (= (=> @p_303 @p_311) @p_304)) :rule cong :premises (t113.t72.t1))
(step t113.t72 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t113.t73 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t73.t0 (cl (= @p_304 @p_306)) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t113.t73.t1 (cl (= @p_305 @p_307)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t113.t73.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t113.t73.t3 (cl (= @p_306 @p_308)) :rule cong :premises (t113.t73.t1 t113.t73.t2))
(step t113.t73.t4 (cl (= @p_308 @p_302)) :rule aci_simp)
(step t113.t73.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t113.t73.t3 t113.t73.t4))
(step t113.t73.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t113.t73.t0 t113.t73.t5))
(step t113.t73 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t113.t74 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t113.t72 t113.t73))
(anchor :step t113.t75 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t75.t0 (cl (= card$ card$a)) :rule symm :premises (a11))
(step t113.t75.t1 (cl @p_72) :rule refl)
(step t113.t75.t2 (cl (= @p_162 @p_154)) :rule cong :premises (t113.t75.t0 t113.t75.t1))
(step t113.t75.t3 (cl (= @p_163 @p_155)) :rule cong :premises (t113.t75.t2))
(step t113.t75.t4 (cl @p_73) :rule refl)
(step t113.t75.t5 (cl (= @p_297 @p_276)) :rule cong :premises (t113.t75.t0 t113.t75.t4))
(step t113.t75.t6 (cl (= @p_298 @p_277)) :rule cong :premises (t113.t75.t5))
(step t113.t75.t7 (cl (= @p_299 @p_287)) :rule cong :premises (t113.t75.t6))
(step t113.t75.t8 (cl (= @p_278 @p_278)) :rule refl)
(step t113.t75.t9 (cl (= @p_295 @p_279)) :rule cong :premises (t113.t75.t0 t113.t75.t8))
(step t113.t75.t10 (cl (= @p_296 @p_280)) :rule cong :premises (t113.t75.t9))
(step t113.t75.t11 (cl (= @p_140 @p_140)) :rule refl)
(step t113.t75.t12 (cl (= @p_293 @p_282)) :rule cong :premises (t113.t75.t0 t113.t75.t11))
(step t113.t75.t13 (cl (= @p_294 @p_283)) :rule cong :premises (t113.t75.t12))
(step t113.t75.t14 (cl (= @p_300 @p_288)) :rule cong :premises (t113.t75.t7 t113.t75.t10 t113.t75.t13))
(step t113.t75.t15 (cl (= @p_301 @p_289)) :rule cong :premises (t113.t75.t3 t113.t75.t14))
(step t113.t75.t16 (cl (= @p_302 @p_290)) :rule cong :premises (t113.t75.t15))
(step t113.t75 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t113.t76 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t113.t76.t0 (cl (= @p_288 @p_291)) :rule poly_simp)
(step t113.t76.t1 (cl (= @p_289 @p_292)) :rule cong :premises (t113.t76.t0))
(step t113.t76.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 @p_281)))) :rule poly_simp)
(step t113.t76.t3 (cl (= @p_292 @p_284)) :rule poly_simp_rel :premises (t113.t76.t2))
(step t113.t76.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t113.t76.t1 t113.t76.t3))
(step t113.t76.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t113.t76.t4))
(step t113.t76 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t113.t77 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t113.t75 t113.t76))
(step t113.t78 (cl @p_275) :rule trans :premises (t113.t74 t113.t77))
(step t113.t79 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t113.t71 t113.t78 a12))
(step t113.t80 (cl @p_274) :rule resolution :premises (t113.t70 t113.t79))
(step t113.t81 (cl @p_269) :rule resolution :premises (t113.t48 t113.t51 t113.t54 t113.t80))
(step t113.t82 (cl @p_370) :rule resolution :premises (t113.t43 t113.t46 t113.t81))
(step t113.t83 (cl @p_413) :rule and_intro :premises (t113.t37 t113.t82))
(step t113.t84 (cl @p_412) :rule resolution :premises (t113.t42 t113.t83))
(step t113.t85 (cl (! (not (! (= @p_446 @p_462) :named @p_625)) :named @p_626) @p_447 @p_462) :rule equiv_pos2)
(step t113.t86 (cl (= (* 1 (- @p_329 0)) (* 1 (- @p_5 @p_34)))) :rule poly_simp)
(step t113.t87 (cl (= @p_462 @p_446)) :rule poly_simp_rel :premises (t113.t86))
(step t113.t88 (cl @p_625) :rule symm :premises (t113.t87))
(step t113.t89 (cl @p_462) :rule resolution :premises (t113.t85 t113.t88 t113.a2))
(step t113.t90 (cl (=> (! (and @p_361 (! (= @p_353 0) :named @p_366)) :named @p_411) @p_410)) :rule la_mult_neg)
(step t113.t91 (cl (not @p_411) @p_410) :rule implies :premises (t113.t90))
(step t113.t92 (cl (not (! (= @p_252 @p_366) :named @p_367)) @p_327 @p_366) :rule equiv_pos2)
(step t113.t93 (cl (= (* 1 (- @p_353 0)) (* 1 (- @p_12 @p_251)))) :rule poly_simp)
(step t113.t94 (cl (= @p_366 @p_252)) :rule poly_simp_rel :premises (t113.t93))
(step t113.t95 (cl @p_367) :rule symm :premises (t113.t94))
(step t113.t96 (cl (or (! (not (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :named @p_260) @p_252)) :rule forall_inst :args (ys$))
(step t113.t97 (cl @p_260 @p_252) :rule or :premises (t113.t96))
(step t113.t98 (cl (not (! (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :named @p_253)) (not (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0)))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule equiv_pos2)
(anchor :step t113.t99 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t113.t99.t0 (cl (= card$ card$a)) :rule symm :premises (a11))
(step t113.t99.t1 (cl (= @p_113 @p_113)) :rule refl)
(step t113.t99.t2 (cl (= (! (fun_app$b card$ @p_113) :named @p_258) (! (fun_app$b card$a @p_113) :named @p_254))) :rule cong :premises (t113.t99.t0 t113.t99.t1))
(step t113.t99.t3 (cl (= (! (of_nat$ @p_258) :named @p_259) (! (of_nat$ @p_254) :named @p_255))) :rule cong :premises (t113.t99.t2))
(step t113.t99.t4 (cl (= (! (of_nat$ (size$ @p_173)) :named @p_256) @p_256)) :rule refl)
(step t113.t99.t5 (cl (= (= @p_259 @p_256) (! (= @p_255 @p_256) :named @p_257))) :rule cong :premises (t113.t99.t3 t113.t99.t4))
(step t113.t99 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))))) :rule bind)
(anchor :step t113.t100 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t113.t100.t0 (cl (= (* 1 (- @p_255 @p_256)) (* -1 (- @p_256 @p_255)))) :rule poly_simp)
(step t113.t100.t1 (cl (= @p_257 (= @p_256 @p_255))) :rule poly_simp_rel :premises (t113.t100.t0))
(step t113.t100 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0))))))) :rule bind)
(step t113.t101 (cl @p_253) :rule trans :premises (t113.t99 t113.t100))
(step t113.t102 (cl (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule resolution :premises (t113.t98 t113.t101 a3))
(step t113.t103 (cl @p_252) :rule resolution :premises (t113.t97 t113.t102))
(step t113.t104 (cl @p_366) :rule resolution :premises (t113.t92 t113.t95 t113.t103))
(step t113.t105 (cl @p_411) :rule and_intro :premises (t113.t37 t113.t104))
(step t113.t106 (cl @p_410) :rule resolution :premises (t113.t91 t113.t105))
(step t113.t107 (cl @p_643) :rule resolution :premises (t113.t27 t113.t31 t113.t40 t113.t84 t113.t89 t113.t106))
(step t113.t108 (cl false) :rule resolution :premises (t113.t0 t113.t26 t113.t107))
(step t113 (cl @p_346 @p_332 @p_447 @p_327 @p_636 false) :rule subproof :discharge (t113.a0 t113.a1 t113.a2 t113.a3 t113.a4))
(step t114 (cl (! (not @p_638) :named @p_639) @p_339) :rule and_pos :args (0))
(step t115 (cl @p_639 @p_269) :rule and_pos :args (1))
(step t116 (cl @p_639 @p_446) :rule and_pos :args (2))
(step t117 (cl @p_639 @p_252) :rule and_pos :args (3))
(step t118 (cl @p_639 @p_635) :rule and_pos :args (4))
(step t119 (cl false @p_639 @p_639 @p_639 @p_639 @p_639) :rule resolution :premises (t113 t114 t115 t116 t117 t118))
(step t120 (cl @p_639 @p_639 @p_639 @p_639 @p_639 false) :rule reordering :premises (t119))
(step t121 (cl @p_639 false) :rule contraction :premises (t120))
(step t122 (cl @p_640 false) :rule resolution :premises (t112 t121))
(step t123 (cl @p_640 @p_344) :rule implies_neg2)
(step t124 (cl @p_640 @p_640) :rule resolution :premises (t122 t123))
(step t125 (cl @p_640) :rule contraction :premises (t124))
(step t126 (cl (= @p_640 @p_639)) :rule implies_simplify)
(step t127 (cl (not @p_640) @p_639) :rule equiv1 :premises (t126))
(step t128 (cl @p_639) :rule resolution :premises (t125 t127))
(step t129 (cl @p_346 @p_332 @p_447 @p_327 @p_636) :rule not_and :premises (t128))
(step t130 (cl @p_637 (! (not @p_346) :named @p_401)) :rule or_neg :args (0))
(step t131 (cl @p_637 (! (not @p_332) :named @p_400)) :rule or_neg :args (1))
(step t132 (cl @p_637 (! (not @p_447) :named @p_452)) :rule or_neg :args (2))
(step t133 (cl @p_637 (! (not @p_327) :named @p_399)) :rule or_neg :args (3))
(step t134 (cl @p_637 (not @p_636)) :rule or_neg :args (4))
(step t135 (cl @p_637 @p_637 @p_637 @p_637 @p_637) :rule resolution :premises (t129 t130 t131 t132 t133 t134))
(step t136 (cl @p_637) :rule contraction :premises (t135))
(step t137 (cl @p_634) :rule resolution :premises (t107 t111 t136))
(step t138 (cl @p_633) :rule resolution :premises (t98 t106 t137))
(step t139 (cl @p_335 @p_332 @p_447 @p_327 @p_632) :rule or :premises (t138))
(step t140 (cl @p_327 @p_447 @p_332 @p_335 @p_632) :rule reordering :premises (t139))
(step t141 (cl (! (and @p_6 (! (= @p_3 @p_34) :named @p_35)) :named @p_606) (! (not @p_6) :named @p_436) (! (not @p_35) :named @p_439)) :rule and_neg)
(step t142 (cl (! (=> @p_606 @p_446) :named @p_608) @p_606) :rule implies_neg1)
(anchor :step t143)
(assume t143.a0 @p_6)
(assume t143.a1 @p_35)
(step t143.t0 (cl (! (=> (! (and @p_35 @p_6) :named @p_609) @p_446) :named @p_611) @p_609) :rule implies_neg1)
(anchor :step t143.t1)
(assume t143.t1.a0 @p_35)
(assume t143.t1.a1 @p_6)
(step t143.t1.t0 (cl @p_446) :rule trans :premises (t143.t1.a1 t143.t1.a0))
(step t143.t1 (cl @p_439 @p_436 @p_446) :rule subproof :discharge (t143.t1.a0 t143.t1.a1))
(step t143.t2 (cl (! (not @p_609) :named @p_610) @p_35) :rule and_pos :args (0))
(step t143.t3 (cl @p_610 @p_6) :rule and_pos :args (1))
(step t143.t4 (cl @p_446 @p_610 @p_610) :rule resolution :premises (t143.t1 t143.t2 t143.t3))
(step t143.t5 (cl @p_610 @p_610 @p_446) :rule reordering :premises (t143.t4))
(step t143.t6 (cl @p_610 @p_446) :rule contraction :premises (t143.t5))
(step t143.t7 (cl @p_611 @p_446) :rule resolution :premises (t143.t0 t143.t6))
(step t143.t8 (cl @p_611 @p_447) :rule implies_neg2)
(step t143.t9 (cl @p_611 @p_611) :rule resolution :premises (t143.t7 t143.t8))
(step t143.t10 (cl @p_611) :rule contraction :premises (t143.t9))
(step t143.t11 (cl @p_610 @p_446) :rule implies :premises (t143.t10))
(step t143.t12 (cl @p_609) :rule and_intro :premises (t143.a1 t143.a0))
(step t143.t13 (cl @p_446) :rule resolution :premises (t143.t11 t143.t12))
(step t143 (cl @p_436 @p_439 @p_446) :rule subproof :discharge (t143.a0 t143.a1))
(step t144 (cl (! (not @p_606) :named @p_607) @p_6) :rule and_pos :args (0))
(step t145 (cl @p_607 @p_35) :rule and_pos :args (1))
(step t146 (cl @p_446 @p_607 @p_607) :rule resolution :premises (t143 t144 t145))
(step t147 (cl @p_607 @p_607 @p_446) :rule reordering :premises (t146))
(step t148 (cl @p_607 @p_446) :rule contraction :premises (t147))
(step t149 (cl @p_608 @p_446) :rule resolution :premises (t142 t148))
(step t150 (cl @p_608 @p_447) :rule implies_neg2)
(step t151 (cl @p_608 @p_608) :rule resolution :premises (t149 t150))
(step t152 (cl @p_608) :rule contraction :premises (t151))
(step t153 (cl @p_607 @p_446) :rule implies :premises (t152))
(step t154 (cl @p_436 @p_439 @p_446) :rule resolution :premises (t141 t153))
(step t155 (cl (! (not (! (and (! (not (! (= @p_33 0) :named @p_36)) :named @p_37) @p_35 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_38)) :named @p_40) @p_35) :rule and_pos :args (1))
(step t156 (cl @p_35 @p_40) :rule reordering :premises (t155))
(step t157 (cl (not (! (= @p_24 (! (not (! (= @p_22 @p_38) :named @p_41)) :named @p_42)) :named @p_43)) (not @p_24) @p_42) :rule equiv_pos2)
(step t158 (cl (= @p_23 (! (= rhs$ @p_22) :named @p_44))) :rule rare_rewrite :args ("eq-symm" @p_22 rhs$))
(step t159 (cl (= @p_24 (! (not @p_44) :named @p_45))) :rule cong :premises (t158))
(step t160 (cl (not (! (= (! (= rhs$ (! (and (! (not @p_16) :named @p_50) (! (= @p_10 @p_13) :named @p_49) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_51)) :named @p_52) (! (= rhs$ @p_38) :named @p_48)) :named @p_65)) (not @p_52) @p_48) :rule equiv_pos2)
(step t161 (cl (= card$ card$a)) :rule symm :premises (a11))
(step t162 (cl (= top$ top$)) :rule refl)
(step t163 (cl (= @p_9 @p_32)) :rule cong :premises (t161 t162))
(step t164 (cl (= @p_10 @p_33)) :rule cong :premises (t163))
(step t165 (cl (= 0 0)) :rule refl)
(step t166 (cl (= @p_16 @p_36)) :rule cong :premises (t164 t165))
(step t167 (cl (= @p_50 @p_37)) :rule cong :premises (t166))
(step t168 (cl (= @p_13 @p_13)) :rule refl)
(step t169 (cl (= @p_49 (! (= @p_33 @p_13) :named @p_66))) :rule cong :premises (t164 t168))
(step t170 (cl (= (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))))) :rule refl)
(step t171 (cl (= (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$)))))))) :rule refl)
(step t172 (cl (= @p_51 (! (and @p_37 @p_66 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_67))) :rule cong :premises (t167 t169 t170 t171))
(step t173 (cl (= @p_52 (! (= rhs$ @p_67) :named @p_68))) :rule cong :premises (t172))
(step t174 (cl (= (* 1 (- @p_33 @p_13)) (* -1 (- @p_3 @p_34)))) :rule poly_simp)
(step t175 (cl (= @p_66 @p_35)) :rule poly_simp_rel :premises (t174))
(step t176 (cl (= @p_67 @p_38)) :rule cong :premises (t175 t170 t171))
(step t177 (cl (= @p_68 @p_48)) :rule cong :premises (t176))
(step t178 (cl @p_65) :rule trans :premises (t173 t177))
(step t179 (cl (not (! (= @p_18 @p_52) :named @p_53)) (not @p_18) @p_52) :rule equiv_pos2)
(step t180 (cl (= @p_17 (! (and @p_50 @p_15) :named @p_54))) :rule rare_rewrite :args ("ite-then-false" @p_16 @p_15))
(step t181 (cl (= @p_15 (! (and @p_14 (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ xs$))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ ys$))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_63))) :rule aci_simp)
(step t182 (cl (= @p_54 (! (and @p_50 @p_63) :named @p_64))) :rule cong :premises (t181))
(step t183 (cl (= @p_64 (! (and @p_50 @p_14 (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ xs$))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ ys$))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_55))) :rule aci_simp)
(step t184 (cl (= @p_54 @p_55)) :rule trans :premises (t182 t183))
(step t185 (cl (= (* 1 (- @p_13 @p_10)) (* -1 (- @p_10 @p_13)))) :rule poly_simp)
(step t186 (cl (= @p_14 @p_49)) :rule poly_simp_rel :premises (t185))
(anchor :step t187 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t187.t0 (cl (= (=> (! (member$ ?v0 @p_28) :named @p_57) (! (not (! (member$ ?v0 @p_25) :named @p_59)) :named @p_60)) (! (or (! (not @p_57) :named @p_58) (! (not (! (member$ ?v0 @p_25) :named @p_59)) :named @p_60)) :named @p_62))) :rule rare_rewrite :args ("bool-impl-elim" @p_57 @p_60))
(step t187 (cl (= (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ xs$))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))))) :rule bind)
(anchor :step t188 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t188.t0 (cl (= (=> @p_59 @p_58) (! (or @p_60 @p_58) :named @p_61))) :rule rare_rewrite :args ("bool-impl-elim" @p_59 @p_58))
(step t188 (cl (= (forall ((?v0 A$)) (=> (member$ ?v0 (set$ (remdups$ ys$))) (not (member$ ?v0 (set$ (remdups$ xs$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$)))))))) :rule bind)
(step t189 (cl (= @p_55 @p_51)) :rule cong :premises (t186 t187 t188))
(step t190 (cl (= @p_54 @p_51)) :rule trans :premises (t184 t189))
(step t191 (cl (= @p_17 @p_51)) :rule trans :premises (t180 t190))
(step t192 (cl @p_53) :rule cong :premises (t191))
(step t193 (cl @p_52) :rule resolution :premises (t179 t192 a20))
(step t194 (cl @p_48) :rule resolution :premises (t160 t178 t193))
(step t195 (cl (= @p_22 @p_22)) :rule refl)
(step t196 (cl (= @p_44 (! (= @p_38 @p_22) :named @p_46))) :rule cong :premises (t194 t195))
(step t197 (cl (= @p_45 (! (not @p_46) :named @p_47))) :rule cong :premises (t196))
(step t198 (cl (= @p_46 @p_41)) :rule rare_rewrite :args ("eq-symm" @p_38 @p_22))
(step t199 (cl (= @p_47 @p_42)) :rule cong :premises (t198))
(step t200 (cl (= @p_45 @p_42)) :rule trans :premises (t197 t199))
(step t201 (cl @p_43) :rule trans :premises (t159 t200))
(step t202 (cl @p_42) :rule resolution :premises (t157 t201 a28))
(step t203 (cl @p_22 @p_38) :rule not_equiv1 :premises (t202))
(step t204 (cl (not (! (= (! (or @p_38 (! (not @p_37) :named @p_552) @p_439 (! (not (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))) :named @p_497) (! (not (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_550)) :named @p_553) (! (or @p_38 @p_36 @p_439 @p_497 @p_550) :named @p_551)) :named @p_555)) (not @p_553) @p_551) :rule equiv_pos2)
(step t205 (cl (= @p_552 @p_36)) :rule rare_rewrite :args ("bool-double-not-elim" @p_36))
(step t206 (cl (= @p_439 @p_439)) :rule refl)
(step t207 (cl (= @p_497 @p_497)) :rule refl)
(step t208 (cl (= @p_550 @p_550)) :rule refl)
(step t209 (cl @p_555) :rule cong :premises (t205 t206 t207 t208))
(step t210 (cl @p_38 @p_552 @p_439 @p_497 @p_550) :rule and_neg)
(step t211 (cl @p_553 @p_40) :rule or_neg :args (0))
(step t212 (cl @p_553 (! (not @p_552) :named @p_554)) :rule or_neg :args (1))
(step t213 (cl @p_553 (! (not @p_439) :named @p_440)) :rule or_neg :args (2))
(step t214 (cl @p_553 (! (not @p_497) :named @p_498)) :rule or_neg :args (3))
(step t215 (cl @p_553 (not @p_550)) :rule or_neg :args (4))
(step t216 (cl @p_553 @p_553 @p_553 @p_553 @p_553) :rule resolution :premises (t210 t211 t212 t213 t214 t215))
(step t217 (cl @p_553) :rule contraction :premises (t216))
(step t218 (cl @p_551) :rule resolution :premises (t204 t209 t217))
(step t219 (cl @p_38 @p_36 @p_439 @p_497 @p_550) :rule or :premises (t218))
(step t220 (cl @p_36 @p_38 @p_439 @p_497 @p_550) :rule reordering :premises (t219))
(step t221 (cl (! (not (! (= @p_36 (! (or (! (= bot$ top$) :named @p_510) (! (not (! (finite$ top$) :named @p_508)) :named @p_509)) :named @p_511)) :named @p_512)) :named @p_549) @p_37 @p_511) :rule equiv_pos2)
(step t222 (cl @p_37 @p_511 @p_549) :rule reordering :premises (t221))
(step t223 (cl (! (not @p_511) :named @p_517) @p_510 @p_509) :rule or_pos)
(step t224 (cl @p_510 @p_509 @p_517) :rule reordering :premises (t223))
(step t225 (cl (not @p_510)) :rule not_symm :premises (a6))
(step t226 (cl @p_40 @p_37) :rule and_pos :args (0))
(step t227 (cl @p_37 @p_40) :rule reordering :premises (t226))
(step t228 (cl (! (not (! (= @p_22 (! (= @p_21 @p_20) :named @p_69)) :named @p_70)) :named @p_85) (! (not @p_22) :named @p_39) @p_69) :rule equiv_pos2)
(step t229 (cl @p_39 @p_69 @p_85) :rule reordering :premises (t228))
(step t230 (cl (not (! (= (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1))) (! (= @p_69 @p_22) :named @p_82)) :named @p_83) (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1))) @p_70) :named @p_81)) :named @p_84)) (not @p_83) @p_81) :rule equiv_pos2)
(step t231 (cl (= @p_82 @p_70)) :rule rare_rewrite :args ("eq-symm" @p_69 @p_22))
(step t232 (cl @p_84) :rule cong :premises (t231))
(step t233 (cl @p_83 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :rule implies_neg1)
(anchor :step t234)
(assume t234.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1))))
(step t234.t0 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :named @p_80) @p_82)) :rule forall_inst :args (@p_21 @p_20))
(step t234.t1 (cl @p_80 @p_82) :rule or :premises (t234.t0))
(step t234.t2 (cl (not (! (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :named @p_71)) (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1)))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :rule equiv_pos2)
(anchor :step t234.t3 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t234.t3.t0 (cl (= uu$ eq_set$)) :rule symm :premises (a18))
(step t234.t3.t1 (cl @p_72) :rule refl)
(step t234.t3.t2 (cl (= (! (fun_app$a uu$ ?v0) :named @p_78) (! (fun_app$a eq_set$ ?v0) :named @p_74))) :rule cong :premises (t234.t3.t0 t234.t3.t1))
(step t234.t3.t3 (cl @p_73) :rule refl)
(step t234.t3.t4 (cl (= (! (fun_app$ @p_78 ?v1) :named @p_79) (! (fun_app$ @p_74 ?v1) :named @p_75))) :rule cong :premises (t234.t3.t2 t234.t3.t3))
(step t234.t3.t5 (cl (= (! (= ?v0 ?v1) :named @p_76) @p_76)) :rule refl)
(step t234.t3.t6 (cl (= (= @p_79 @p_76) (! (= @p_75 @p_76) :named @p_77))) :rule cong :premises (t234.t3.t4 t234.t3.t5))
(step t234.t3 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a eq_set$ ?v0) ?v1) (= ?v0 ?v1))))) :rule bind)
(anchor :step t234.t4 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t234.t4.t0 (cl (= @p_77 (= @p_76 @p_75))) :rule rare_rewrite :args ("eq-symm" @p_75 @p_76))
(step t234.t4 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a eq_set$ ?v0) ?v1) (= ?v0 ?v1))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1))))) :rule bind)
(step t234.t5 (cl @p_71) :rule trans :premises (t234.t3 t234.t4))
(step t234.t6 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :rule resolution :premises (t234.t2 t234.t5 a0))
(step t234.t7 (cl @p_82) :rule resolution :premises (t234.t1 t234.t6))
(step t234 (cl @p_80 @p_82) :rule subproof :discharge (t234.a0))
(step t235 (cl @p_83 @p_82) :rule resolution :premises (t233 t234))
(step t236 (cl @p_83 (not @p_82)) :rule implies_neg2)
(step t237 (cl @p_83 @p_83) :rule resolution :premises (t235 t236))
(step t238 (cl @p_83) :rule contraction :premises (t237))
(step t239 (cl @p_81) :rule resolution :premises (t230 t232 t238))
(step t240 (cl @p_80 @p_70) :rule implies :premises (t239))
(step t241 (cl (not @p_71) (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1)))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :rule equiv_pos2)
(anchor :step t242 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t242.t0 (cl (= uu$ eq_set$)) :rule symm :premises (a18))
(step t242.t1 (cl @p_72) :rule refl)
(step t242.t2 (cl (= @p_78 @p_74)) :rule cong :premises (t242.t0 t242.t1))
(step t242.t3 (cl @p_73) :rule refl)
(step t242.t4 (cl (= @p_79 @p_75)) :rule cong :premises (t242.t2 t242.t3))
(step t242.t5 (cl (= @p_76 @p_76)) :rule refl)
(step t242.t6 (cl (= (= @p_79 @p_76) @p_77)) :rule cong :premises (t242.t4 t242.t5))
(step t242 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (= ?v0 ?v1))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a eq_set$ ?v0) ?v1) (= ?v0 ?v1))))) :rule bind)
(anchor :step t243 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t243.t0 (cl (= @p_77 (= @p_76 @p_75))) :rule rare_rewrite :args ("eq-symm" @p_75 @p_76))
(step t243 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (fun_app$ (fun_app$a eq_set$ ?v0) ?v1) (= ?v0 ?v1))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1))))) :rule bind)
(step t244 (cl @p_71) :rule trans :premises (t242 t243))
(step t245 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (fun_app$ (fun_app$a eq_set$ ?v0) ?v1)))) :rule resolution :premises (t241 t244 a0))
(step t246 (cl @p_70) :rule resolution :premises (t240 t245))
(step t247 (cl @p_549 @p_36 @p_517) :rule equiv_pos1)
(step t248 (cl @p_36 @p_517 @p_549) :rule reordering :premises (t247))
(step t249 (cl (not (! (= (! (=> (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))) (! (= @p_511 @p_36) :named @p_514)) :named @p_515) (! (=> (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))) @p_512) :named @p_513)) :named @p_516)) (not @p_515) @p_513) :rule equiv_pos2)
(step t250 (cl (= @p_514 @p_512)) :rule rare_rewrite :args ("eq-symm" @p_511 @p_36))
(step t251 (cl @p_516) :rule cong :premises (t250))
(step t252 (cl @p_515 (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :rule implies_neg1)
(anchor :step t253)
(assume t253.a0 (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))))
(step t253.t0 (cl (or (! (not (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :named @p_168) @p_514)) :rule forall_inst :args (top$))
(step t253.t1 (cl @p_168 @p_514) :rule or :premises (t253.t0))
(step t253.t2 (cl (not (! (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :named @p_153)) (not (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0)))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :rule equiv_pos2)
(anchor :step t253.t3 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t253.t3.t0 (cl (= (! (= ?v0 bot$) :named @p_166) (! (= bot$ ?v0) :named @p_159))) :rule rare_rewrite :args ("eq-symm" ?v0 bot$))
(step t253.t3.t1 (cl (= @p_158 @p_158)) :rule refl)
(step t253.t3.t2 (cl (= (! (or @p_166 @p_158) :named @p_167) (! (or @p_159 @p_158) :named @p_160))) :rule cong :premises (t253.t3.t0 t253.t3.t1))
(step t253.t3.t3 (cl (= (= (! (= @p_163 0) :named @p_164) @p_167) (! (= @p_164 @p_160) :named @p_165))) :rule cong :premises (t253.t3.t2))
(step t253.t3 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))))) :rule bind)
(anchor :step t253.t4 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t253.t4.t0 (cl @p_72) :rule refl)
(step t253.t4.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t253.t4.t0))
(step t253.t4.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t253.t4.t1))
(step t253.t4.t3 (cl (= @p_164 (! (= @p_155 0) :named @p_156))) :rule cong :premises (t253.t4.t2 t165))
(step t253.t4.t4 (cl (= @p_160 @p_160)) :rule refl)
(step t253.t4.t5 (cl (= @p_165 (! (= @p_156 @p_160) :named @p_161))) :rule cong :premises (t253.t4.t3 t253.t4.t4))
(step t253.t4 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$a ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))))) :rule bind)
(anchor :step t253.t5 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t253.t5.t0 (cl (= @p_161 (= @p_160 @p_156))) :rule rare_rewrite :args ("eq-symm" @p_156 @p_160))
(step t253.t5 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$a ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))))) :rule bind)
(step t253.t6 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))))) :rule trans :premises (t253.t4 t253.t5))
(step t253.t7 (cl @p_153) :rule trans :premises (t253.t3 t253.t6))
(step t253.t8 (cl (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :rule resolution :premises (t253.t2 t253.t7 a13))
(step t253.t9 (cl @p_514) :rule resolution :premises (t253.t1 t253.t8))
(step t253 (cl @p_168 @p_514) :rule subproof :discharge (t253.a0))
(step t254 (cl @p_515 @p_514) :rule resolution :premises (t252 t253))
(step t255 (cl @p_515 (not @p_514)) :rule implies_neg2)
(step t256 (cl @p_515 @p_515) :rule resolution :premises (t254 t255))
(step t257 (cl @p_515) :rule contraction :premises (t256))
(step t258 (cl @p_513) :rule resolution :premises (t249 t251 t257))
(step t259 (cl @p_168 @p_512) :rule implies :premises (t258))
(step t260 (cl (not @p_153) (not (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0)))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :rule equiv_pos2)
(anchor :step t261 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t261.t0 (cl (= @p_166 @p_159)) :rule rare_rewrite :args ("eq-symm" ?v0 bot$))
(step t261.t1 (cl (= @p_158 @p_158)) :rule refl)
(step t261.t2 (cl (= @p_167 @p_160)) :rule cong :premises (t261.t0 t261.t1))
(step t261.t3 (cl (= (= @p_164 @p_167) @p_165)) :rule cong :premises (t261.t2))
(step t261 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= ?v0 bot$) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))))) :rule bind)
(anchor :step t262 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t262.t0 (cl @p_72) :rule refl)
(step t262.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t262.t0))
(step t262.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t262.t1))
(step t262.t3 (cl (= @p_164 @p_156)) :rule cong :premises (t262.t2 t165))
(step t262.t4 (cl (= @p_160 @p_160)) :rule refl)
(step t262.t5 (cl (= @p_165 @p_161)) :rule cong :premises (t262.t3 t262.t4))
(step t262 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$a ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))))) :rule bind)
(anchor :step t263 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t263.t0 (cl (= @p_161 (= @p_160 @p_156))) :rule rare_rewrite :args ("eq-symm" @p_156 @p_160))
(step t263 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$a ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))))) :rule bind)
(step t264 (cl (= (forall ((?v0 A_set$)) (= (= (of_nat$ (fun_app$b card$ ?v0)) 0) (or (= bot$ ?v0) (not (finite$ ?v0))))) (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0))))) :rule trans :premises (t262 t263))
(step t265 (cl @p_153) :rule trans :premises (t261 t264))
(step t266 (cl (forall ((?v0 A_set$)) (= (or (= bot$ ?v0) (not (finite$ ?v0))) (= (of_nat$ (fun_app$b card$a ?v0)) 0)))) :rule resolution :premises (t260 t265 a13))
(step t267 (cl @p_512) :rule resolution :premises (t259 t266))
(step t268 (cl (not (! (= (! (or (! (not @p_69) :named @p_86) @p_271 (! (not (! (= @p_21 (! (uminus$ @p_4) :named @p_101)) :named @p_110)) :named @p_117) (! (not (! (not (! (finite$ @p_101) :named @p_518)) :named @p_528)) :named @p_535)) :named @p_536) (! (or @p_86 @p_271 @p_117 @p_518) :named @p_534)) :named @p_548)) (not @p_536) @p_534) :rule equiv_pos2)
(step t269 (cl (= @p_535 @p_518)) :rule rare_rewrite :args ("bool-double-not-elim" @p_518))
(step t270 (cl @p_548) :rule cong :premises (t269))
(step t271 (cl (! (=> (! (and @p_69 @p_270 @p_110 @p_528) :named @p_538) (! (and @p_270 @p_69 @p_110 @p_528) :named @p_540)) :named @p_547) @p_538) :rule implies_neg1)
(anchor :step t272)
(assume t272.a0 @p_69)
(assume t272.a1 @p_270)
(assume t272.a2 @p_110)
(assume t272.a3 @p_528)
(step t272.t0 (cl (or @p_323 @p_270)) :rule forall_inst :args (ys$))
(step t272.t1 (cl @p_323 @p_270) :rule or :premises (t272.t0))
(step t272.t2 (cl @p_270) :rule resolution :premises (t272.t1 a4))
(step t272.t3 (cl (or (! (not (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :named @p_116) @p_110)) :rule forall_inst :args (xs$))
(step t272.t4 (cl @p_116 @p_110) :rule or :premises (t272.t3))
(step t272.t5 (cl (not (! (= (forall ((?v0 A_list$)) (= (uminus$ (set$ ?v0)) (coset$ ?v0))) (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :named @p_111)) (not (forall ((?v0 A_list$)) (= (uminus$ (set$ ?v0)) (coset$ ?v0)))) (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule equiv_pos2)
(anchor :step t272.t6 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t272.t6.t0 (cl (= (= (! (uminus$ @p_113) :named @p_114) (! (coset$ ?v0) :named @p_115)) (= @p_115 @p_114))) :rule rare_rewrite :args ("eq-symm" @p_114 @p_115))
(step t272.t6 (cl @p_111) :rule bind)
(step t272.t7 (cl (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule resolution :premises (t272.t5 t272.t6 a16))
(step t272.t8 (cl @p_110) :rule resolution :premises (t272.t4 t272.t7))
(step t272.t9 (cl @p_540) :rule and_intro :premises (t272.t2 t272.a0 t272.t8 t272.a3))
(step t272 (cl @p_86 @p_271 @p_117 @p_535 @p_540) :rule subproof :discharge (t272.a0 t272.a1 t272.a2 t272.a3))
(step t273 (cl (! (not @p_538) :named @p_539) @p_69) :rule and_pos :args (0))
(step t274 (cl @p_539 @p_270) :rule and_pos :args (1))
(step t275 (cl @p_539 @p_110) :rule and_pos :args (2))
(step t276 (cl @p_539 @p_528) :rule and_pos :args (3))
(step t277 (cl @p_540 @p_539 @p_539 @p_539 @p_539) :rule resolution :premises (t272 t273 t274 t275 t276))
(step t278 (cl @p_539 @p_539 @p_539 @p_539 @p_540) :rule reordering :premises (t277))
(step t279 (cl @p_539 @p_540) :rule contraction :premises (t278))
(step t280 (cl @p_547 @p_540) :rule resolution :premises (t271 t279))
(step t281 (cl @p_547 (! (not @p_540) :named @p_541)) :rule implies_neg2)
(step t282 (cl @p_547 @p_547) :rule resolution :premises (t280 t281))
(step t283 (cl @p_547) :rule contraction :premises (t282))
(step t284 (cl @p_539 @p_540) :rule implies :premises (t283))
(step t285 (cl (! (=> @p_540 false) :named @p_542) @p_540) :rule implies_neg1)
(anchor :step t286)
(assume t286.a0 @p_270)
(assume t286.a1 @p_69)
(assume t286.a2 @p_110)
(assume t286.a3 @p_528)
(step t286.t0 (cl (not (! (= (! (= false true) :named @p_543) false) :named @p_546)) (not @p_543) false) :rule equiv_pos2)
(step t286.t1 (cl @p_546) :rule evaluate)
(step t286.t2 (cl (= (! (= @p_518 false) :named @p_545) @p_528)) :rule equiv_simplify)
(step t286.t3 (cl @p_545 @p_535) :rule equiv2 :premises (t286.t2))
(step t286.t4 (cl (! (not @p_535) :named @p_537) @p_518) :rule not_not)
(step t286.t5 (cl @p_545 @p_518) :rule resolution :premises (t286.t3 t286.t4))
(step t286.t6 (cl @p_545) :rule resolution :premises (t286.t5 t286.a3))
(step t286.t7 (cl (= false @p_518)) :rule symm :premises (t286.t6))
(step t286.t8 (cl (or @p_116 @p_110)) :rule forall_inst :args (xs$))
(step t286.t9 (cl @p_116 @p_110) :rule or :premises (t286.t8))
(step t286.t10 (cl (not @p_111) (not (forall ((?v0 A_list$)) (= (uminus$ (set$ ?v0)) (coset$ ?v0)))) (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule equiv_pos2)
(anchor :step t286.t11 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t286.t11.t0 (cl (= (= @p_114 @p_115) (= @p_115 @p_114))) :rule rare_rewrite :args ("eq-symm" @p_114 @p_115))
(step t286.t11 (cl @p_111) :rule bind)
(step t286.t12 (cl (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule resolution :premises (t286.t10 t286.t11 a16))
(step t286.t13 (cl @p_110) :rule resolution :premises (t286.t9 t286.t12))
(step t286.t14 (cl (= @p_101 @p_21)) :rule symm :premises (t286.t13))
(step t286.t15 (cl (! (= @p_101 @p_20) :named @p_127)) :rule trans :premises (t286.t14 t286.a1))
(step t286.t16 (cl (= @p_518 @p_270)) :rule cong :premises (t286.t15))
(step t286.t17 (cl (= (! (= @p_270 true) :named @p_544) @p_270)) :rule equiv_simplify)
(step t286.t18 (cl @p_544 @p_271) :rule equiv2 :premises (t286.t17))
(step t286.t19 (cl (or @p_323 @p_270)) :rule forall_inst :args (ys$))
(step t286.t20 (cl @p_323 @p_270) :rule or :premises (t286.t19))
(step t286.t21 (cl @p_270) :rule resolution :premises (t286.t20 a4))
(step t286.t22 (cl @p_544) :rule resolution :premises (t286.t18 t286.t21))
(step t286.t23 (cl @p_543) :rule trans :premises (t286.t7 t286.t16 t286.t22))
(step t286.t24 (cl false) :rule resolution :premises (t286.t0 t286.t1 t286.t23))
(step t286 (cl @p_271 @p_86 @p_117 @p_535 false) :rule subproof :discharge (t286.a0 t286.a1 t286.a2 t286.a3))
(step t287 (cl @p_541 @p_270) :rule and_pos :args (0))
(step t288 (cl @p_541 @p_69) :rule and_pos :args (1))
(step t289 (cl @p_541 @p_110) :rule and_pos :args (2))
(step t290 (cl @p_541 @p_528) :rule and_pos :args (3))
(step t291 (cl false @p_541 @p_541 @p_541 @p_541) :rule resolution :premises (t286 t287 t288 t289 t290))
(step t292 (cl @p_541 @p_541 @p_541 @p_541 false) :rule reordering :premises (t291))
(step t293 (cl @p_541 false) :rule contraction :premises (t292))
(step t294 (cl @p_542 false) :rule resolution :premises (t285 t293))
(step t295 (cl @p_542 @p_344) :rule implies_neg2)
(step t296 (cl @p_542 @p_542) :rule resolution :premises (t294 t295))
(step t297 (cl @p_542) :rule contraction :premises (t296))
(step t298 (cl (= @p_542 @p_541)) :rule implies_simplify)
(step t299 (cl (not @p_542) @p_541) :rule equiv1 :premises (t298))
(step t300 (cl @p_541) :rule resolution :premises (t297 t299))
(step t301 (cl @p_539) :rule resolution :premises (t284 t300))
(step t302 (cl @p_86 @p_271 @p_117 @p_535) :rule not_and :premises (t301))
(step t303 (cl @p_536 (not @p_86)) :rule or_neg :args (0))
(step t304 (cl @p_536 (not @p_271)) :rule or_neg :args (1))
(step t305 (cl @p_536 (not @p_117)) :rule or_neg :args (2))
(step t306 (cl @p_536 @p_537) :rule or_neg :args (3))
(step t307 (cl @p_536 @p_536 @p_536 @p_536) :rule resolution :premises (t302 t303 t304 t305 t306))
(step t308 (cl @p_536) :rule contraction :premises (t307))
(step t309 (cl @p_534) :rule resolution :premises (t268 t270 t308))
(step t310 (cl @p_86 @p_271 @p_117 @p_518) :rule or :premises (t309))
(step t311 (cl (or @p_116 @p_110)) :rule forall_inst :args (xs$))
(step t312 (cl @p_116 @p_110) :rule or :premises (t311))
(step t313 (cl (not @p_111) (not (forall ((?v0 A_list$)) (= (uminus$ (set$ ?v0)) (coset$ ?v0)))) (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule equiv_pos2)
(anchor :step t314 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t314.t0 (cl (= (= @p_114 @p_115) (= @p_115 @p_114))) :rule rare_rewrite :args ("eq-symm" @p_114 @p_115))
(step t314 (cl @p_111) :rule bind)
(step t315 (cl (forall ((?v0 A_list$)) (= (coset$ ?v0) (uminus$ (set$ ?v0))))) :rule resolution :premises (t313 t314 a16))
(step t316 (cl @p_110) :rule resolution :premises (t312 t315))
(step t317 (cl (or @p_323 @p_270)) :rule forall_inst :args (ys$))
(step t318 (cl @p_323 @p_270) :rule or :premises (t317))
(step t319 (cl @p_270) :rule resolution :premises (t318 a4))
(step t320 (cl (not (! (= (! (or @p_511 (! (not @p_509) :named @p_531)) :named @p_532) (! (or @p_511 @p_508) :named @p_530)) :named @p_533)) (not @p_532) @p_530) :rule equiv_pos2)
(step t321 (cl (= @p_531 @p_508)) :rule rare_rewrite :args ("bool-double-not-elim" @p_508))
(step t322 (cl @p_533) :rule cong :premises (t321))
(step t323 (cl @p_511 @p_531) :rule or_neg :args (1))
(step t324 (cl @p_532 @p_517) :rule or_neg :args (0))
(step t325 (cl @p_532 (not @p_531)) :rule or_neg :args (1))
(step t326 (cl @p_532 @p_532) :rule resolution :premises (t323 t324 t325))
(step t327 (cl @p_532) :rule contraction :premises (t326))
(step t328 (cl @p_530) :rule resolution :premises (t320 t322 t327))
(step t329 (cl @p_511 @p_508) :rule or :premises (t328))
(step t330 (cl @p_508 @p_511) :rule reordering :premises (t329))
(step t331 (cl (! (not (! (= @p_508 @p_518) :named @p_519)) :named @p_529) @p_508 @p_528) :rule equiv_pos1)
(step t332 (cl @p_508 @p_528 @p_529) :rule reordering :premises (t331))
(step t333 (cl (! (not (! (or @p_273 @p_519) :named @p_520)) :named @p_527) @p_273 @p_519) :rule or_pos)
(step t334 (cl @p_273 @p_519 @p_527) :rule reordering :premises (t333))
(step t335 (cl (or @p_323 @p_272)) :rule forall_inst :args (xs$))
(step t336 (cl @p_323 @p_272) :rule or :premises (t335))
(step t337 (cl @p_272) :rule resolution :premises (t336 a4))
(step t338 (cl (or (! (not (forall ((?v0 A_set$)) (or (not (finite$ ?v0)) (= (finite$ top$) (finite$ (uminus$ ?v0)))))) :named @p_526) @p_520)) :rule forall_inst :args (@p_4))
(step t339 (cl @p_526 @p_520) :rule or :premises (t338))
(step t340 (cl (not (! (= (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ (uminus$ ?v0)) (finite$ top$)))) (forall ((?v0 A_set$)) (or (not (finite$ ?v0)) (= (finite$ top$) (finite$ (uminus$ ?v0)))))) :named @p_521)) (not (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ (uminus$ ?v0)) (finite$ top$))))) (forall ((?v0 A_set$)) (or (not (finite$ ?v0)) (= (finite$ top$) (finite$ (uminus$ ?v0)))))) :rule equiv_pos2)
(anchor :step t341 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t341.t0 (cl (= (! (= (! (finite$ (uminus$ ?v0)) :named @p_522) @p_508) :named @p_525) (! (= @p_508 @p_522) :named @p_523))) :rule rare_rewrite :args ("eq-symm" @p_522 @p_508))
(step t341.t1 (cl (= (=> @p_157 @p_525) (! (=> @p_157 @p_523) :named @p_524))) :rule cong :premises (t341.t0))
(step t341 (cl (= (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ (uminus$ ?v0)) (finite$ top$)))) (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ top$) (finite$ (uminus$ ?v0))))))) :rule bind)
(anchor :step t342 :args ((?v0 A_set$) (:= (?v0 A_set$) ?v0)))
(step t342.t0 (cl (= @p_524 (or @p_158 @p_523))) :rule rare_rewrite :args ("bool-impl-elim" @p_157 @p_523))
(step t342 (cl (= (forall ((?v0 A_set$)) (=> (finite$ ?v0) (= (finite$ top$) (finite$ (uminus$ ?v0))))) (forall ((?v0 A_set$)) (or (not (finite$ ?v0)) (= (finite$ top$) (finite$ (uminus$ ?v0))))))) :rule bind)
(step t343 (cl @p_521) :rule trans :premises (t341 t342))
(step t344 (cl (forall ((?v0 A_set$)) (or (not (finite$ ?v0)) (= (finite$ top$) (finite$ (uminus$ ?v0)))))) :rule resolution :premises (t340 t343 a19))
(step t345 (cl @p_520) :rule resolution :premises (t339 t344))
(step t346 (cl @p_519) :rule resolution :premises (t334 t337 t345))
(step t347 (cl @p_508) :rule resolution :premises (t203 t227 t229 t246 t248 t267 t310 t316 t319 t330 t332 t346))
(step t348 (cl @p_517) :rule resolution :premises (t224 t225 t347))
(step t349 (cl @p_37) :rule resolution :premises (t222 t348 t267))
(step t350 (cl (= (! (= (! (= (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :named @p_504) true) :named @p_505) @p_504)) :rule equiv_simplify)
(step t351 (cl (not @p_505) @p_504) :rule equiv1 :premises (t350))
(step t352 (cl (= @p_504 (! (= (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))) :named @p_506))) :rule rare_rewrite :args ("eq-symm" (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))))
(step t353 (cl (= (! (= @p_506 true) :named @p_507) @p_506)) :rule equiv_simplify)
(step t354 (cl @p_507 (not @p_506)) :rule equiv2 :premises (t353))
(anchor :step t355 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t355.t0 (cl (= @p_61 @p_62)) :rule aci_simp)
(step t355 (cl @p_506) :rule bind)
(step t356 (cl @p_507) :rule resolution :premises (t354 t355))
(step t357 (cl @p_505) :rule trans :premises (t352 t356))
(step t358 (cl @p_504) :rule resolution :premises (t351 t357))
(step t359 (cl @p_497 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$))))))) :rule equiv1 :premises (t358))
(step t360 (cl (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ ys$)))) (not (member$ ?v0 (set$ (remdups$ xs$)))))) @p_497) :rule reordering :premises (t359))
(step t361 (cl (not (! (= (! (or @p_498 (! (not (! (or (! (not (! (member$ @quantifiers_skolemize_34 @p_28) :named @p_469)) :named @p_470) (! (not (! (member$ @quantifiers_skolemize_34 @p_25) :named @p_467)) :named @p_468)) :named @p_471)) :named @p_475)) :named @p_499) (! (or (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) @p_475) :named @p_496)) :named @p_503)) (not @p_499) @p_496) :rule equiv_pos2)
(step t362 (cl (= @p_498 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))))
(step t363 (cl (= @p_475 @p_475)) :rule refl)
(step t364 (cl @p_503) :rule cong :premises (t362 t363))
(step t365 (cl (! (=> @p_497 @p_475) :named @p_501) @p_497) :rule implies_neg1)
(anchor :step t366)
(assume t366.a0 @p_497)
(step t366.t0 (cl (not (! (= @p_497 @p_475) :named @p_502)) @p_498 @p_475) :rule equiv_pos2)
(anchor :step t366.t1 :args ((:= (?v0 A$) @quantifiers_skolemize_34)))
(step t366.t1.t0 (cl (= @p_62 @p_471)) :rule refl)
(step t366.t1 (cl (= (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) @p_471)) :rule sko_forall)
(step t366.t2 (cl @p_502) :rule cong :premises (t366.t1))
(step t366.t3 (cl @p_475) :rule resolution :premises (t366.t0 t366.t2 t366.a0))
(step t366 (cl @p_498 @p_475) :rule subproof :discharge (t366.a0))
(step t367 (cl @p_501 @p_475) :rule resolution :premises (t365 t366))
(step t368 (cl @p_501 (! (not @p_475) :named @p_500)) :rule implies_neg2)
(step t369 (cl @p_501 @p_501) :rule resolution :premises (t367 t368))
(step t370 (cl @p_501) :rule contraction :premises (t369))
(step t371 (cl @p_498 @p_475) :rule implies :premises (t370))
(step t372 (cl @p_499 (not @p_498)) :rule or_neg :args (0))
(step t373 (cl @p_499 @p_500) :rule or_neg :args (1))
(step t374 (cl @p_499 @p_499) :rule resolution :premises (t371 t372 t373))
(step t375 (cl @p_499) :rule contraction :premises (t374))
(step t376 (cl @p_496) :rule resolution :premises (t361 t364 t375))
(step t377 (cl (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) @p_475) :rule or :premises (t376))
(step t378 (cl (! (and @p_69 @p_110 @p_486 (! (= @p_25 @p_20) :named @p_171) @p_467) :named @p_488) @p_86 @p_117 @p_487 (! (not @p_171) :named @p_201) @p_468) :rule and_neg)
(step t379 (cl (! (=> @p_488 (! (member$ @quantifiers_skolemize_34 (! (uminus$ @p_28) :named @p_481)) :named @p_482)) :named @p_490) @p_488) :rule implies_neg1)
(anchor :step t380)
(assume t380.a0 @p_69)
(assume t380.a1 @p_110)
(assume t380.a2 @p_486)
(assume t380.a3 @p_171)
(assume t380.a4 @p_467)
(step t380.t0 (cl (! (=> (! (and @p_467 @p_171 @p_69 @p_110 @p_486) :named @p_491) @p_482) :named @p_493) @p_491) :rule implies_neg1)
(anchor :step t380.t1)
(assume t380.t1.a0 @p_467)
(assume t380.t1.a1 @p_171)
(assume t380.t1.a2 @p_69)
(assume t380.t1.a3 @p_110)
(assume t380.t1.a4 @p_486)
(step t380.t1.t0 (cl (= (! (= @p_482 true) :named @p_494) @p_482)) :rule equiv_simplify)
(step t380.t1.t1 (cl (not @p_494) @p_482) :rule equiv1 :premises (t380.t1.t0))
(step t380.t1.t2 (cl (= @p_28 @p_4)) :rule symm :premises (t21))
(step t380.t1.t3 (cl (= @p_481 @p_101)) :rule cong :premises (t380.t1.t2))
(step t380.t1.t4 (cl (= @p_101 @p_21)) :rule symm :premises (t316))
(step t380.t1.t5 (cl (or @p_175 (! (= @p_20 @p_25) :named @p_177))) :rule forall_inst :args (ys$))
(step t380.t1.t6 (cl @p_175 @p_177) :rule or :premises (t380.t1.t5))
(step t380.t1.t7 (cl @p_177) :rule resolution :premises (t380.t1.t6 t20))
(step t380.t1.t8 (cl (= @p_481 @p_25)) :rule trans :premises (t380.t1.t3 t380.t1.t4 t380.t1.a2 t380.t1.t7))
(step t380.t1.t9 (cl (= @p_482 @p_467)) :rule cong :premises (t380.t1.t8))
(step t380.t1.t10 (cl (= (! (= @p_467 true) :named @p_495) @p_467)) :rule equiv_simplify)
(step t380.t1.t11 (cl @p_495 @p_468) :rule equiv2 :premises (t380.t1.t10))
(step t380.t1.t12 (cl @p_495) :rule resolution :premises (t380.t1.t11 t380.t1.a0))
(step t380.t1.t13 (cl @p_494) :rule trans :premises (t380.t1.t9 t380.t1.t12))
(step t380.t1.t14 (cl @p_482) :rule resolution :premises (t380.t1.t1 t380.t1.t13))
(step t380.t1 (cl @p_468 @p_201 @p_86 @p_117 @p_487 @p_482) :rule subproof :discharge (t380.t1.a0 t380.t1.a1 t380.t1.a2 t380.t1.a3 t380.t1.a4))
(step t380.t2 (cl (! (not @p_491) :named @p_492) @p_467) :rule and_pos :args (0))
(step t380.t3 (cl @p_492 @p_171) :rule and_pos :args (1))
(step t380.t4 (cl @p_492 @p_69) :rule and_pos :args (2))
(step t380.t5 (cl @p_492 @p_110) :rule and_pos :args (3))
(step t380.t6 (cl @p_492 @p_486) :rule and_pos :args (4))
(step t380.t7 (cl @p_482 @p_492 @p_492 @p_492 @p_492 @p_492) :rule resolution :premises (t380.t1 t380.t2 t380.t3 t380.t4 t380.t5 t380.t6))
(step t380.t8 (cl @p_492 @p_492 @p_492 @p_492 @p_492 @p_482) :rule reordering :premises (t380.t7))
(step t380.t9 (cl @p_492 @p_482) :rule contraction :premises (t380.t8))
(step t380.t10 (cl @p_493 @p_482) :rule resolution :premises (t380.t0 t380.t9))
(step t380.t11 (cl @p_493 (! (not @p_482) :named @p_483)) :rule implies_neg2)
(step t380.t12 (cl @p_493 @p_493) :rule resolution :premises (t380.t10 t380.t11))
(step t380.t13 (cl @p_493) :rule contraction :premises (t380.t12))
(step t380.t14 (cl @p_492 @p_482) :rule implies :premises (t380.t13))
(step t380.t15 (cl (not (! (= (! (=> (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0)))) @p_177) :named @p_178) (! (=> (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0)))) @p_171) :named @p_176)) :named @p_179)) (not @p_178) @p_176) :rule equiv_pos2)
(step t380.t16 (cl (= @p_177 @p_171)) :rule rare_rewrite :args ("eq-symm" @p_20 @p_25))
(step t380.t17 (cl @p_179) :rule cong :premises (t380.t16))
(step t380.t18 (cl @p_178 (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule implies_neg1)
(anchor :step t380.t19)
(assume t380.t19.a0 (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0)))))
(step t380.t19.t0 (cl (or @p_175 @p_177)) :rule forall_inst :args (ys$))
(step t380.t19.t1 (cl @p_175 @p_177) :rule or :premises (t380.t19.t0))
(step t380.t19.t2 (cl @p_177) :rule resolution :premises (t380.t19.t1 t20))
(step t380.t19 (cl @p_175 @p_177) :rule subproof :discharge (t380.t19.a0))
(step t380.t20 (cl @p_178 @p_177) :rule resolution :premises (t380.t18 t380.t19))
(step t380.t21 (cl @p_178 (not @p_177)) :rule implies_neg2)
(step t380.t22 (cl @p_178 @p_178) :rule resolution :premises (t380.t20 t380.t21))
(step t380.t23 (cl @p_178) :rule contraction :premises (t380.t22))
(step t380.t24 (cl @p_176) :rule resolution :premises (t380.t15 t380.t17 t380.t23))
(step t380.t25 (cl @p_175 @p_171) :rule implies :premises (t380.t24))
(step t380.t26 (cl @p_171) :rule resolution :premises (t380.t25 t20))
(step t380.t27 (cl @p_491) :rule and_intro :premises (t380.a4 t380.t26 t380.a0 t316 t21))
(step t380.t28 (cl @p_482) :rule resolution :premises (t380.t14 t380.t27))
(step t380 (cl @p_86 @p_117 @p_487 @p_201 @p_468 @p_482) :rule subproof :discharge (t380.a0 t380.a1 t380.a2 t380.a3 t380.a4))
(step t381 (cl (! (not @p_488) :named @p_489) @p_69) :rule and_pos :args (0))
(step t382 (cl @p_489 @p_110) :rule and_pos :args (1))
(step t383 (cl @p_489 @p_486) :rule and_pos :args (2))
(step t384 (cl @p_489 @p_171) :rule and_pos :args (3))
(step t385 (cl @p_489 @p_467) :rule and_pos :args (4))
(step t386 (cl @p_482 @p_489 @p_489 @p_489 @p_489 @p_489) :rule resolution :premises (t380 t381 t382 t383 t384 t385))
(step t387 (cl @p_489 @p_489 @p_489 @p_489 @p_489 @p_482) :rule reordering :premises (t386))
(step t388 (cl @p_489 @p_482) :rule contraction :premises (t387))
(step t389 (cl @p_490 @p_482) :rule resolution :premises (t379 t388))
(step t390 (cl @p_490 @p_483) :rule implies_neg2)
(step t391 (cl @p_490 @p_490) :rule resolution :premises (t389 t390))
(step t392 (cl @p_490) :rule contraction :premises (t391))
(step t393 (cl @p_489 @p_482) :rule implies :premises (t392))
(step t394 (cl @p_86 @p_117 @p_487 @p_201 @p_468 @p_482) :rule resolution :premises (t378 t393))
(step t395 (cl (not @p_179) (not @p_178) @p_176) :rule equiv_pos2)
(step t396 (cl (= @p_177 @p_171)) :rule rare_rewrite :args ("eq-symm" @p_20 @p_25))
(step t397 (cl @p_179) :rule cong :premises (t396))
(step t398 (cl @p_178 (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0))))) :rule implies_neg1)
(anchor :step t399)
(assume t399.a0 (forall ((?v0 A_list$)) (= (set$ ?v0) (set$ (remdups$ ?v0)))))
(step t399.t0 (cl (or @p_175 @p_177)) :rule forall_inst :args (ys$))
(step t399.t1 (cl @p_175 @p_177) :rule or :premises (t399.t0))
(step t399.t2 (cl @p_177) :rule resolution :premises (t399.t1 t20))
(step t399 (cl @p_175 @p_177) :rule subproof :discharge (t399.a0))
(step t400 (cl @p_178 @p_177) :rule resolution :premises (t398 t399))
(step t401 (cl @p_178 (not @p_177)) :rule implies_neg2)
(step t402 (cl @p_178 @p_178) :rule resolution :premises (t400 t401))
(step t403 (cl @p_178) :rule contraction :premises (t402))
(step t404 (cl @p_176) :rule resolution :premises (t395 t397 t403))
(step t405 (cl @p_175 @p_171) :rule implies :premises (t404))
(step t406 (cl @p_171) :rule resolution :premises (t405 t20))
(step t407 (cl (! (not (! (or @p_483 @p_470) :named @p_484)) :named @p_485) @p_483 @p_470) :rule or_pos)
(step t408 (cl @p_470 @p_483 @p_485) :rule reordering :premises (t407))
(step t409 (cl (or (! (not (forall ((?v0 A$) (?v1 A_set$)) (or (not (member$ ?v0 (uminus$ ?v1))) (not (member$ ?v0 ?v1))))) :named @p_108) @p_484)) :rule forall_inst :args (@quantifiers_skolemize_34 @p_28))
(step t410 (cl @p_108 @p_484) :rule or :premises (t409))
(step t411 (cl (not (! (= (forall ((?v0 A$) (?v1 A_set$)) (=> (member$ ?v0 (uminus$ ?v1)) (not (member$ ?v0 ?v1)))) (forall ((?v0 A$) (?v1 A_set$)) (or (not (member$ ?v0 (uminus$ ?v1))) (not (member$ ?v0 ?v1))))) :named @p_105)) (not (forall ((?v0 A$) (?v1 A_set$)) (=> (member$ ?v0 (uminus$ ?v1)) (not (member$ ?v0 ?v1))))) (forall ((?v0 A$) (?v1 A_set$)) (or (not (member$ ?v0 (uminus$ ?v1))) (not (member$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t412 :args ((?v0 A$) (?v1 A_set$) (:= (?v0 A$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t412.t0 (cl (= (=> (! (member$ ?v0 (uminus$ ?v1)) :named @p_107) (! (not (member$ ?v0 ?v1)) :named @p_106)) (or (not @p_107) @p_106))) :rule rare_rewrite :args ("bool-impl-elim" @p_107 @p_106))
(step t412 (cl @p_105) :rule bind)
(step t413 (cl (forall ((?v0 A$) (?v1 A_set$)) (or (not (member$ ?v0 (uminus$ ?v1))) (not (member$ ?v0 ?v1))))) :rule resolution :premises (t411 t412 a2))
(step t414 (cl @p_484) :rule resolution :premises (t410 t413))
(step t415 (cl (not (! (= (! (or @p_471 (! (not @p_468) :named @p_478)) :named @p_479) (! (or @p_471 @p_467) :named @p_477)) :named @p_480)) (not @p_479) @p_477) :rule equiv_pos2)
(step t416 (cl (= @p_478 @p_467)) :rule rare_rewrite :args ("bool-double-not-elim" @p_467))
(step t417 (cl @p_480) :rule cong :premises (t416))
(step t418 (cl @p_471 @p_478) :rule or_neg :args (1))
(step t419 (cl @p_479 @p_475) :rule or_neg :args (0))
(step t420 (cl @p_479 (not @p_478)) :rule or_neg :args (1))
(step t421 (cl @p_479 @p_479) :rule resolution :premises (t418 t419 t420))
(step t422 (cl @p_479) :rule contraction :premises (t421))
(step t423 (cl @p_477) :rule resolution :premises (t415 t417 t422))
(step t424 (cl @p_471 @p_467) :rule or :premises (t423))
(step t425 (cl @p_467 @p_471) :rule reordering :premises (t424))
(step t426 (cl (not (! (= (! (or @p_471 (! (not @p_470) :named @p_473)) :named @p_474) (! (or @p_471 @p_469) :named @p_472)) :named @p_476)) (not @p_474) @p_472) :rule equiv_pos2)
(step t427 (cl (= @p_473 @p_469)) :rule rare_rewrite :args ("bool-double-not-elim" @p_469))
(step t428 (cl @p_476) :rule cong :premises (t427))
(step t429 (cl @p_471 @p_473) :rule or_neg :args (0))
(step t430 (cl @p_474 @p_475) :rule or_neg :args (0))
(step t431 (cl @p_474 (not @p_473)) :rule or_neg :args (1))
(step t432 (cl @p_474 @p_474) :rule resolution :premises (t429 t430 t431))
(step t433 (cl @p_474) :rule contraction :premises (t432))
(step t434 (cl @p_472) :rule resolution :premises (t426 t428 t433))
(step t435 (cl @p_471 @p_469) :rule or :premises (t434))
(step t436 (cl @p_469 @p_471) :rule reordering :premises (t435))
(step t437 (cl @p_86 @p_471) :rule resolution :premises (t394 t406 t21 t316 t408 t414 t425 t436))
(step t438 (cl (not (! (= (! (or @p_436 @p_440 (! (not (! (not (! (>= @p_329 1) :named @p_330)) :named @p_331)) :named @p_438) (! (not (! (>= @p_329 0) :named @p_392)) :named @p_395)) :named @p_441) (! (or @p_436 @p_35 @p_330 @p_395) :named @p_437)) :named @p_466)) (not @p_441) @p_437) :rule equiv_pos2)
(step t439 (cl (= @p_440 @p_35)) :rule rare_rewrite :args ("bool-double-not-elim" @p_35))
(step t440 (cl (= @p_438 @p_330)) :rule rare_rewrite :args ("bool-double-not-elim" @p_330))
(step t441 (cl (= @p_395 @p_395)) :rule refl)
(step t442 (cl @p_466) :rule cong :premises (t439 t440 t441))
(step t443 (cl (! (and @p_6 @p_439 @p_331) :named @p_443) @p_436 @p_440 @p_438) :rule and_neg)
(step t444 (cl (! (=> @p_443 @p_395) :named @p_445) @p_443) :rule implies_neg1)
(anchor :step t445)
(assume t445.a0 @p_6)
(assume t445.a1 @p_439)
(assume t445.a2 @p_331)
(step t445.t0 (cl (! (=> (! (and @p_447 @p_331) :named @p_448) @p_395) :named @p_456) @p_448) :rule implies_neg1)
(anchor :step t445.t1)
(assume t445.t1.a0 @p_447)
(assume t445.t1.a1 @p_331)
(step t445.t1.t0 (cl (not (! (= (! (< @p_329 0) :named @p_417) @p_395) :named @p_419)) (! (not @p_417) :named @p_420) @p_395) :rule equiv_pos2)
(step t445.t1.t1 (cl @p_419) :rule rare_rewrite :args ("arith-elim-lt" @p_329 0))
(step t445.t1.t2 (cl (or @p_462 (! (not (! (<= @p_329 0) :named @p_459)) :named @p_465) (! (not (<= 0 @p_329)) :named @p_457))) :rule la_disequality)
(step t445.t1.t3 (cl @p_462 @p_465 @p_457) :rule or :premises (t445.t1.t2))
(step t445.t1.t4 (cl (not (! (= @p_447 @p_463) :named @p_464)) @p_452 @p_463) :rule equiv_pos2)
(step t445.t1.t5 (cl (= (* 1 (- @p_329 0)) (* 1 (- @p_5 @p_34)))) :rule poly_simp)
(step t445.t1.t6 (cl (= @p_462 @p_446)) :rule poly_simp_rel :premises (t445.t1.t5))
(step t445.t1.t7 (cl (= @p_463 @p_447)) :rule cong :premises (t445.t1.t6))
(step t445.t1.t8 (cl @p_464) :rule symm :premises (t445.t1.t7))
(step t445.t1.t9 (cl @p_463) :rule resolution :premises (t445.t1.t4 t445.t1.t8 t445.t1.a0))
(step t445.t1.t10 (cl (not (! (< @p_329 1) :named @p_460)) @p_459) :rule la_generic :args (1/1 1/1))
(step t445.t1.t11 (cl (not (! (= @p_331 @p_460) :named @p_461)) @p_438 @p_460) :rule equiv_pos2)
(step t445.t1.t12 (cl (= @p_460 @p_331)) :rule rare_rewrite :args ("arith-elim-lt" @p_329 1))
(step t445.t1.t13 (cl @p_461) :rule symm :premises (t445.t1.t12))
(step t445.t1.t14 (cl @p_460) :rule resolution :premises (t445.t1.t11 t445.t1.t13 t445.t1.a1))
(step t445.t1.t15 (cl @p_459) :rule resolution :premises (t445.t1.t10 t445.t1.t14))
(step t445.t1.t16 (cl (not (! (= @p_417 @p_457) :named @p_458)) @p_417 (not @p_457)) :rule equiv_pos1)
(step t445.t1.t17 (cl @p_458) :rule comp_simplify)
(step t445.t1.t18 (cl @p_417) :rule resolution :premises (t445.t1.t3 t445.t1.t9 t445.t1.t15 t445.t1.t16 t445.t1.t17))
(step t445.t1.t19 (cl @p_395) :rule resolution :premises (t445.t1.t0 t445.t1.t1 t445.t1.t18))
(step t445.t1 (cl @p_452 @p_438 @p_395) :rule subproof :discharge (t445.t1.a0 t445.t1.a1))
(step t445.t2 (cl (! (not @p_448) :named @p_455) @p_447) :rule and_pos :args (0))
(step t445.t3 (cl @p_455 @p_331) :rule and_pos :args (1))
(step t445.t4 (cl @p_395 @p_455 @p_455) :rule resolution :premises (t445.t1 t445.t2 t445.t3))
(step t445.t5 (cl @p_455 @p_455 @p_395) :rule reordering :premises (t445.t4))
(step t445.t6 (cl @p_455 @p_395) :rule contraction :premises (t445.t5))
(step t445.t7 (cl @p_456 @p_395) :rule resolution :premises (t445.t0 t445.t6))
(step t445.t8 (cl @p_456 (! (not @p_395) :named @p_396)) :rule implies_neg2)
(step t445.t9 (cl @p_456 @p_456) :rule resolution :premises (t445.t7 t445.t8))
(step t445.t10 (cl @p_456) :rule contraction :premises (t445.t9))
(step t445.t11 (cl @p_455 @p_395) :rule implies :premises (t445.t10))
(step t445.t12 (cl (! (=> (! (and @p_6 @p_439) :named @p_449) @p_447) :named @p_451) @p_449) :rule implies_neg1)
(anchor :step t445.t13)
(assume t445.t13.a0 @p_6)
(assume t445.t13.a1 @p_439)
(step t445.t13.t0 (cl (= (! (= @p_446 false) :named @p_453) @p_447)) :rule equiv_simplify)
(step t445.t13.t1 (cl (not @p_453) @p_447) :rule equiv1 :premises (t445.t13.t0))
(step t445.t13.t2 (cl (= @p_34 @p_34)) :rule refl)
(step t445.t13.t3 (cl (= @p_446 @p_35)) :rule cong :premises (t445.t13.a0 t445.t13.t2))
(step t445.t13.t4 (cl (= (! (= @p_35 false) :named @p_454) @p_439)) :rule equiv_simplify)
(step t445.t13.t5 (cl @p_454 @p_440) :rule equiv2 :premises (t445.t13.t4))
(step t445.t13.t6 (cl (! (not @p_440) :named @p_442) @p_35) :rule not_not)
(step t445.t13.t7 (cl @p_454 @p_35) :rule resolution :premises (t445.t13.t5 t445.t13.t6))
(step t445.t13.t8 (cl @p_454) :rule resolution :premises (t445.t13.t7 t445.t13.a1))
(step t445.t13.t9 (cl @p_453) :rule trans :premises (t445.t13.t3 t445.t13.t8))
(step t445.t13.t10 (cl @p_447) :rule resolution :premises (t445.t13.t1 t445.t13.t9))
(step t445.t13 (cl @p_436 @p_440 @p_447) :rule subproof :discharge (t445.t13.a0 t445.t13.a1))
(step t445.t14 (cl (! (not @p_449) :named @p_450) @p_6) :rule and_pos :args (0))
(step t445.t15 (cl @p_450 @p_439) :rule and_pos :args (1))
(step t445.t16 (cl @p_447 @p_450 @p_450) :rule resolution :premises (t445.t13 t445.t14 t445.t15))
(step t445.t17 (cl @p_450 @p_450 @p_447) :rule reordering :premises (t445.t16))
(step t445.t18 (cl @p_450 @p_447) :rule contraction :premises (t445.t17))
(step t445.t19 (cl @p_451 @p_447) :rule resolution :premises (t445.t12 t445.t18))
(step t445.t20 (cl @p_451 @p_452) :rule implies_neg2)
(step t445.t21 (cl @p_451 @p_451) :rule resolution :premises (t445.t19 t445.t20))
(step t445.t22 (cl @p_451) :rule contraction :premises (t445.t21))
(step t445.t23 (cl @p_450 @p_447) :rule implies :premises (t445.t22))
(step t445.t24 (cl @p_449) :rule and_intro :premises (t445.a0 t445.a1))
(step t445.t25 (cl @p_447) :rule resolution :premises (t445.t23 t445.t24))
(step t445.t26 (cl @p_448) :rule and_intro :premises (t445.t25 t445.a2))
(step t445.t27 (cl @p_395) :rule resolution :premises (t445.t11 t445.t26))
(step t445 (cl @p_436 @p_440 @p_438 @p_395) :rule subproof :discharge (t445.a0 t445.a1 t445.a2))
(step t446 (cl (! (not @p_443) :named @p_444) @p_6) :rule and_pos :args (0))
(step t447 (cl @p_444 @p_439) :rule and_pos :args (1))
(step t448 (cl @p_444 @p_331) :rule and_pos :args (2))
(step t449 (cl @p_395 @p_444 @p_444 @p_444) :rule resolution :premises (t445 t446 t447 t448))
(step t450 (cl @p_444 @p_444 @p_444 @p_395) :rule reordering :premises (t449))
(step t451 (cl @p_444 @p_395) :rule contraction :premises (t450))
(step t452 (cl @p_445 @p_395) :rule resolution :premises (t444 t451))
(step t453 (cl @p_445 @p_396) :rule implies_neg2)
(step t454 (cl @p_445 @p_445) :rule resolution :premises (t452 t453))
(step t455 (cl @p_445) :rule contraction :premises (t454))
(step t456 (cl @p_444 @p_395) :rule implies :premises (t455))
(step t457 (cl @p_436 @p_440 @p_438 @p_395) :rule resolution :premises (t443 t456))
(step t458 (cl @p_441 (not @p_436)) :rule or_neg :args (0))
(step t459 (cl @p_441 @p_442) :rule or_neg :args (1))
(step t460 (cl @p_441 (not @p_438)) :rule or_neg :args (2))
(step t461 (cl @p_441 @p_396) :rule or_neg :args (3))
(step t462 (cl @p_441 @p_441 @p_441 @p_441) :rule resolution :premises (t457 t458 t459 t460 t461))
(step t463 (cl @p_441) :rule contraction :premises (t462))
(step t464 (cl @p_437) :rule resolution :premises (t438 t442 t463))
(step t465 (cl @p_436 @p_35 @p_330 @p_395) :rule or :premises (t464))
(step t466 (cl @p_35 @p_436 @p_330 @p_395) :rule reordering :premises (t465))
(step t467 (cl (not (! (= (! (or @p_346 @p_332 @p_327 @p_345 @p_392) :named @p_394) (! (or @p_335 @p_332 @p_327 @p_345 @p_392) :named @p_393)) :named @p_435)) (not @p_394) @p_393) :rule equiv_pos2)
(step t468 (cl (= @p_345 @p_345)) :rule refl)
(step t469 (cl (= @p_392 @p_392)) :rule refl)
(step t470 (cl @p_435) :rule cong :premises (t101 t102 t104 t468 t469))
(step t471 (cl (not (! (= (! (or @p_346 @p_332 @p_327 @p_345 @p_396) :named @p_397) @p_394) :named @p_434)) (not @p_397) @p_394) :rule equiv_pos2)
(step t472 (cl (= @p_396 @p_392)) :rule rare_rewrite :args ("bool-double-not-elim" @p_392))
(step t473 (cl (= @p_397 @p_393)) :rule cong :premises (t101 t102 t104 t468 t472))
(step t474 (cl (= @p_393 @p_394)) :rule symm :premises (t470))
(step t475 (cl @p_434) :rule trans :premises (t473 t474))
(step t476 (cl (! (=> (! (and @p_339 @p_269 @p_252 @p_340 @p_395) :named @p_402) false) :named @p_404) @p_402) :rule implies_neg1)
(anchor :step t477)
(assume t477.a0 @p_339)
(assume t477.a1 @p_269)
(assume t477.a2 @p_252)
(assume t477.a3 @p_340)
(assume t477.a4 @p_395)
(step t477.t0 (cl (not (! (= (! (< (! (+ @p_329 @p_355 @p_407 @p_406 @p_351) :named @p_408) (! (+ 0 @p_348 @p_348 @p_348 0) :named @p_405)) :named @p_409) false) :named @p_425)) (not @p_409) false) :rule equiv_pos2)
(step t477.t1 (cl (= @p_409 (! (not (! (>= @p_408 @p_405) :named @p_426)) :named @p_427))) :rule rare_rewrite :args ("arith-elim-lt" @p_408 @p_405))
(step t477.t2 (cl (= @p_408 @p_432)) :rule poly_simp)
(step t477.t3 (cl (= @p_431 0)) :rule poly_simp)
(step t477.t4 (cl (= @p_379 0)) :rule poly_simp)
(step t477.t5 (cl (= @p_251 @p_251)) :rule refl)
(step t477.t6 (cl (= @p_328 @p_328)) :rule refl)
(step t477.t7 (cl (= @p_267 @p_267)) :rule refl)
(step t477.t8 (cl (= @p_33 @p_33)) :rule refl)
(step t477.t9 (cl (= @p_378 0)) :rule poly_simp)
(step t477.t10 (cl (= @p_377 0)) :rule poly_simp)
(step t477.t11 (cl (= @p_432 @p_433)) :rule cong :premises (t477.t3 t477.t4 t477.t5 t477.t6 t477.t7 t477.t8 t477.t9 t477.t10))
(step t477.t12 (cl (= @p_433 0)) :rule poly_simp)
(step t477.t13 (cl (= @p_432 0)) :rule trans :premises (t477.t11 t477.t12))
(step t477.t14 (cl (= @p_408 0)) :rule trans :premises (t477.t2 t477.t13))
(step t477.t15 (cl (= @p_348 0)) :rule evaluate)
(step t477.t16 (cl (= @p_405 @p_430)) :rule cong :premises (t477.t15 t477.t15 t477.t15 t165))
(step t477.t17 (cl (= @p_430 0)) :rule evaluate)
(step t477.t18 (cl (= @p_405 0)) :rule trans :premises (t477.t16 t477.t17))
(step t477.t19 (cl (= @p_426 @p_429)) :rule cong :premises (t477.t14 t477.t18))
(step t477.t20 (cl (= @p_429 true)) :rule evaluate)
(step t477.t21 (cl (= @p_426 true)) :rule trans :premises (t477.t19 t477.t20))
(step t477.t22 (cl (= @p_427 @p_428)) :rule cong :premises (t477.t21))
(step t477.t23 (cl (= @p_428 false)) :rule evaluate)
(step t477.t24 (cl (= @p_427 false)) :rule trans :premises (t477.t22 t477.t23))
(step t477.t25 (cl @p_425) :rule trans :premises (t477.t1 t477.t24))
(step t477.t26 (cl @p_420 @p_421 @p_422 @p_423 @p_424 @p_409) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t477.t27 (cl (not (! (= @p_395 @p_417) :named @p_418)) @p_396 @p_417) :rule equiv_pos2)
(step t477.t28 (cl @p_419) :rule rare_rewrite :args ("arith-elim-lt" @p_329 0))
(step t477.t29 (cl @p_418) :rule symm :premises (t477.t28))
(step t477.t30 (cl @p_417) :rule resolution :premises (t477.t27 t477.t29 t477.a4))
(step t477.t31 (cl (=> @p_415 @p_414)) :rule la_mult_neg)
(step t477.t32 (cl @p_416 @p_414) :rule implies :premises (t477.t31))
(step t477.t33 (cl (= @p_365 @p_361)) :rule equiv_simplify)
(step t477.t34 (cl (not @p_365) @p_361) :rule equiv1 :premises (t477.t33))
(step t477.t35 (cl @p_365) :rule evaluate)
(step t477.t36 (cl @p_361) :rule resolution :premises (t477.t34 t477.t35))
(step t477.t37 (cl @p_151) :rule symm :premises (t477.a0))
(step t477.t38 (cl @p_415) :rule and_intro :premises (t477.t36 t477.t37))
(step t477.t39 (cl @p_414) :rule resolution :premises (t477.t32 t477.t38))
(step t477.t40 (cl (=> @p_413 @p_412)) :rule la_mult_neg)
(step t477.t41 (cl (not @p_413) @p_412) :rule implies :premises (t477.t40))
(step t477.t42 (cl (not @p_371) @p_332 @p_370) :rule equiv_pos2)
(step t477.t43 (cl (= (* 1 (- @p_356 0)) (* 1 @p_322))) :rule poly_simp)
(step t477.t44 (cl (= @p_370 @p_269)) :rule poly_simp_rel :premises (t477.t43))
(step t477.t45 (cl @p_371) :rule symm :premises (t477.t44))
(step t477.t46 (cl @p_324 @p_273 @p_271 @p_269) :rule or_pos)
(step t477.t47 (cl @p_273 @p_271 @p_269 @p_324) :rule reordering :premises (t477.t46))
(step t477.t48 (cl (not @p_319) (not @p_318) @p_313) :rule equiv_pos2)
(step t477.t49 (cl (= @p_315 @p_320)) :rule poly_simp)
(step t477.t50 (cl (= @p_316 @p_321)) :rule cong :premises (t477.t49))
(step t477.t51 (cl (= (* 1 (- @p_150 @p_320)) (* -1 @p_322))) :rule poly_simp)
(step t477.t52 (cl (= @p_321 @p_269)) :rule poly_simp_rel :premises (t477.t51))
(step t477.t53 (cl (= @p_316 @p_269)) :rule trans :premises (t477.t50 t477.t52))
(step t477.t54 (cl (= @p_317 @p_274)) :rule cong :premises (t477.t53))
(step t477.t55 (cl @p_319) :rule cong :premises (t477.t54))
(step t477.t56 (cl @p_318 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule implies_neg1)
(anchor :step t477.t57)
(assume t477.t57.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))
(step t477.t57.t0 (cl (or @p_312 @p_317)) :rule forall_inst :args (@p_4 @p_20))
(step t477.t57.t1 (cl @p_312 @p_317) :rule or :premises (t477.t57.t0))
(step t477.t57.t2 (cl (not @p_275) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t477.t57.t3 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t57.t3.t0 (cl (= (* 1 (- @p_310 @p_309)) (* 1 (- @p_163 @p_300)))) :rule poly_simp)
(step t477.t57.t3.t1 (cl (= @p_311 @p_301)) :rule poly_simp_rel :premises (t477.t57.t3.t0))
(step t477.t57.t3.t2 (cl (= (=> @p_303 @p_311) @p_304)) :rule cong :premises (t477.t57.t3.t1))
(step t477.t57.t3 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t477.t57.t4 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t57.t4.t0 (cl (= @p_304 @p_306)) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t477.t57.t4.t1 (cl (= @p_305 @p_307)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t477.t57.t4.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t477.t57.t4.t3 (cl (= @p_306 @p_308)) :rule cong :premises (t477.t57.t4.t1 t477.t57.t4.t2))
(step t477.t57.t4.t4 (cl (= @p_308 @p_302)) :rule aci_simp)
(step t477.t57.t4.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t477.t57.t4.t3 t477.t57.t4.t4))
(step t477.t57.t4.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t477.t57.t4.t0 t477.t57.t4.t5))
(step t477.t57.t4 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t477.t57.t5 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t477.t57.t3 t477.t57.t4))
(anchor :step t477.t57.t6 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t57.t6.t0 (cl @p_72) :rule refl)
(step t477.t57.t6.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t477.t57.t6.t0))
(step t477.t57.t6.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t477.t57.t6.t1))
(step t477.t57.t6.t3 (cl @p_73) :rule refl)
(step t477.t57.t6.t4 (cl (= @p_297 @p_276)) :rule cong :premises (t161 t477.t57.t6.t3))
(step t477.t57.t6.t5 (cl (= @p_298 @p_277)) :rule cong :premises (t477.t57.t6.t4))
(step t477.t57.t6.t6 (cl (= @p_299 @p_287)) :rule cong :premises (t477.t57.t6.t5))
(step t477.t57.t6.t7 (cl (= @p_278 @p_278)) :rule refl)
(step t477.t57.t6.t8 (cl (= @p_295 @p_279)) :rule cong :premises (t161 t477.t57.t6.t7))
(step t477.t57.t6.t9 (cl (= @p_296 @p_280)) :rule cong :premises (t477.t57.t6.t8))
(step t477.t57.t6.t10 (cl (= @p_140 @p_140)) :rule refl)
(step t477.t57.t6.t11 (cl (= @p_293 @p_282)) :rule cong :premises (t161 t477.t57.t6.t10))
(step t477.t57.t6.t12 (cl (= @p_294 @p_283)) :rule cong :premises (t477.t57.t6.t11))
(step t477.t57.t6.t13 (cl (= @p_300 @p_288)) :rule cong :premises (t477.t57.t6.t6 t477.t57.t6.t9 t477.t57.t6.t12))
(step t477.t57.t6.t14 (cl (= @p_301 @p_289)) :rule cong :premises (t477.t57.t6.t2 t477.t57.t6.t13))
(step t477.t57.t6.t15 (cl (= @p_302 @p_290)) :rule cong :premises (t477.t57.t6.t14))
(step t477.t57.t6 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t477.t57.t7 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t57.t7.t0 (cl (= @p_288 @p_291)) :rule poly_simp)
(step t477.t57.t7.t1 (cl (= @p_289 @p_292)) :rule cong :premises (t477.t57.t7.t0))
(step t477.t57.t7.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 @p_281)))) :rule poly_simp)
(step t477.t57.t7.t3 (cl (= @p_292 @p_284)) :rule poly_simp_rel :premises (t477.t57.t7.t2))
(step t477.t57.t7.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t477.t57.t7.t1 t477.t57.t7.t3))
(step t477.t57.t7.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t477.t57.t7.t4))
(step t477.t57.t7 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t477.t57.t8 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t477.t57.t6 t477.t57.t7))
(step t477.t57.t9 (cl @p_275) :rule trans :premises (t477.t57.t5 t477.t57.t8))
(step t477.t57.t10 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t477.t57.t2 t477.t57.t9 a12))
(step t477.t57.t11 (cl @p_317) :rule resolution :premises (t477.t57.t1 t477.t57.t10))
(step t477.t57 (cl @p_312 @p_317) :rule subproof :discharge (t477.t57.a0))
(step t477.t58 (cl @p_318 @p_317) :rule resolution :premises (t477.t56 t477.t57))
(step t477.t59 (cl @p_318 (not @p_317)) :rule implies_neg2)
(step t477.t60 (cl @p_318 @p_318) :rule resolution :premises (t477.t58 t477.t59))
(step t477.t61 (cl @p_318) :rule contraction :premises (t477.t60))
(step t477.t62 (cl @p_313) :rule resolution :premises (t477.t48 t477.t55 t477.t61))
(step t477.t63 (cl @p_312 @p_274) :rule implies :premises (t477.t62))
(step t477.t64 (cl (not @p_275) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t477.t65 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t65.t0 (cl (= (* 1 (- @p_310 @p_309)) (* 1 (- @p_163 @p_300)))) :rule poly_simp)
(step t477.t65.t1 (cl (= @p_311 @p_301)) :rule poly_simp_rel :premises (t477.t65.t0))
(step t477.t65.t2 (cl (= (=> @p_303 @p_311) @p_304)) :rule cong :premises (t477.t65.t1))
(step t477.t65 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t477.t66 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t66.t0 (cl (= @p_304 @p_306)) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t477.t66.t1 (cl (= @p_305 @p_307)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t477.t66.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t477.t66.t3 (cl (= @p_306 @p_308)) :rule cong :premises (t477.t66.t1 t477.t66.t2))
(step t477.t66.t4 (cl (= @p_308 @p_302)) :rule aci_simp)
(step t477.t66.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t477.t66.t3 t477.t66.t4))
(step t477.t66.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t477.t66.t0 t477.t66.t5))
(step t477.t66 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t477.t67 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t477.t65 t477.t66))
(anchor :step t477.t68 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t68.t0 (cl @p_72) :rule refl)
(step t477.t68.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t477.t68.t0))
(step t477.t68.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t477.t68.t1))
(step t477.t68.t3 (cl @p_73) :rule refl)
(step t477.t68.t4 (cl (= @p_297 @p_276)) :rule cong :premises (t161 t477.t68.t3))
(step t477.t68.t5 (cl (= @p_298 @p_277)) :rule cong :premises (t477.t68.t4))
(step t477.t68.t6 (cl (= @p_299 @p_287)) :rule cong :premises (t477.t68.t5))
(step t477.t68.t7 (cl (= @p_278 @p_278)) :rule refl)
(step t477.t68.t8 (cl (= @p_295 @p_279)) :rule cong :premises (t161 t477.t68.t7))
(step t477.t68.t9 (cl (= @p_296 @p_280)) :rule cong :premises (t477.t68.t8))
(step t477.t68.t10 (cl (= @p_140 @p_140)) :rule refl)
(step t477.t68.t11 (cl (= @p_293 @p_282)) :rule cong :premises (t161 t477.t68.t10))
(step t477.t68.t12 (cl (= @p_294 @p_283)) :rule cong :premises (t477.t68.t11))
(step t477.t68.t13 (cl (= @p_300 @p_288)) :rule cong :premises (t477.t68.t6 t477.t68.t9 t477.t68.t12))
(step t477.t68.t14 (cl (= @p_301 @p_289)) :rule cong :premises (t477.t68.t2 t477.t68.t13))
(step t477.t68.t15 (cl (= @p_302 @p_290)) :rule cong :premises (t477.t68.t14))
(step t477.t68 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t477.t69 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t477.t69.t0 (cl (= @p_288 @p_291)) :rule poly_simp)
(step t477.t69.t1 (cl (= @p_289 @p_292)) :rule cong :premises (t477.t69.t0))
(step t477.t69.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 @p_281)))) :rule poly_simp)
(step t477.t69.t3 (cl (= @p_292 @p_284)) :rule poly_simp_rel :premises (t477.t69.t2))
(step t477.t69.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t477.t69.t1 t477.t69.t3))
(step t477.t69.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t477.t69.t4))
(step t477.t69 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t477.t70 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t477.t68 t477.t69))
(step t477.t71 (cl @p_275) :rule trans :premises (t477.t67 t477.t70))
(step t477.t72 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t477.t64 t477.t71 a12))
(step t477.t73 (cl @p_274) :rule resolution :premises (t477.t63 t477.t72))
(step t477.t74 (cl @p_269) :rule resolution :premises (t477.t47 t337 t319 t477.t73))
(step t477.t75 (cl @p_370) :rule resolution :premises (t477.t42 t477.t45 t477.t74))
(step t477.t76 (cl @p_413) :rule and_intro :premises (t477.t36 t477.t75))
(step t477.t77 (cl @p_412) :rule resolution :premises (t477.t41 t477.t76))
(step t477.t78 (cl (=> @p_411 @p_410)) :rule la_mult_neg)
(step t477.t79 (cl (not @p_411) @p_410) :rule implies :premises (t477.t78))
(step t477.t80 (cl (not @p_367) @p_327 @p_366) :rule equiv_pos2)
(step t477.t81 (cl (= (* 1 (- @p_353 0)) (* 1 (- @p_12 @p_251)))) :rule poly_simp)
(step t477.t82 (cl (= @p_366 @p_252)) :rule poly_simp_rel :premises (t477.t81))
(step t477.t83 (cl @p_367) :rule symm :premises (t477.t82))
(step t477.t84 (cl (or @p_260 @p_252)) :rule forall_inst :args (ys$))
(step t477.t85 (cl @p_260 @p_252) :rule or :premises (t477.t84))
(step t477.t86 (cl (not @p_253) (not (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0)))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule equiv_pos2)
(anchor :step t477.t87 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t477.t87.t0 (cl (= @p_113 @p_113)) :rule refl)
(step t477.t87.t1 (cl (= @p_258 @p_254)) :rule cong :premises (t161 t477.t87.t0))
(step t477.t87.t2 (cl (= @p_259 @p_255)) :rule cong :premises (t477.t87.t1))
(step t477.t87.t3 (cl (= @p_256 @p_256)) :rule refl)
(step t477.t87.t4 (cl (= (= @p_259 @p_256) @p_257)) :rule cong :premises (t477.t87.t2 t477.t87.t3))
(step t477.t87 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))))) :rule bind)
(anchor :step t477.t88 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t477.t88.t0 (cl (= (* 1 (- @p_255 @p_256)) (* -1 (- @p_256 @p_255)))) :rule poly_simp)
(step t477.t88.t1 (cl (= @p_257 (= @p_256 @p_255))) :rule poly_simp_rel :premises (t477.t88.t0))
(step t477.t88 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0))))))) :rule bind)
(step t477.t89 (cl @p_253) :rule trans :premises (t477.t87 t477.t88))
(step t477.t90 (cl (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule resolution :premises (t477.t86 t477.t89 a3))
(step t477.t91 (cl @p_252) :rule resolution :premises (t477.t85 t477.t90))
(step t477.t92 (cl @p_366) :rule resolution :premises (t477.t80 t477.t83 t477.t91))
(step t477.t93 (cl @p_411) :rule and_intro :premises (t477.t36 t477.t92))
(step t477.t94 (cl @p_410) :rule resolution :premises (t477.t79 t477.t93))
(step t477.t95 (cl (! (not (! (= @p_340 @p_360) :named @p_363)) :named @p_364) @p_345 @p_360) :rule equiv_pos2)
(step t477.t96 (cl (= (* 1 (- @p_351 0)) (* 1 (- @p_33 @p_266)))) :rule poly_simp)
(step t477.t97 (cl (= @p_360 @p_340)) :rule poly_simp_rel :premises (t477.t96))
(step t477.t98 (cl @p_363) :rule symm :premises (t477.t97))
(step t477.t99 (cl @p_360) :rule resolution :premises (t477.t95 t477.t98 t477.a3))
(step t477.t100 (cl @p_409) :rule resolution :premises (t477.t26 t477.t30 t477.t39 t477.t77 t477.t94 t477.t99))
(step t477.t101 (cl false) :rule resolution :premises (t477.t0 t477.t25 t477.t100))
(step t477 (cl @p_346 @p_332 @p_327 @p_345 @p_396 false) :rule subproof :discharge (t477.a0 t477.a1 t477.a2 t477.a3 t477.a4))
(step t478 (cl (! (not @p_402) :named @p_403) @p_339) :rule and_pos :args (0))
(step t479 (cl @p_403 @p_269) :rule and_pos :args (1))
(step t480 (cl @p_403 @p_252) :rule and_pos :args (2))
(step t481 (cl @p_403 @p_340) :rule and_pos :args (3))
(step t482 (cl @p_403 @p_395) :rule and_pos :args (4))
(step t483 (cl false @p_403 @p_403 @p_403 @p_403 @p_403) :rule resolution :premises (t477 t478 t479 t480 t481 t482))
(step t484 (cl @p_403 @p_403 @p_403 @p_403 @p_403 false) :rule reordering :premises (t483))
(step t485 (cl @p_403 false) :rule contraction :premises (t484))
(step t486 (cl @p_404 false) :rule resolution :premises (t476 t485))
(step t487 (cl @p_404 @p_344) :rule implies_neg2)
(step t488 (cl @p_404 @p_404) :rule resolution :premises (t486 t487))
(step t489 (cl @p_404) :rule contraction :premises (t488))
(step t490 (cl (= @p_404 @p_403)) :rule implies_simplify)
(step t491 (cl (not @p_404) @p_403) :rule equiv1 :premises (t490))
(step t492 (cl @p_403) :rule resolution :premises (t489 t491))
(step t493 (cl @p_346 @p_332 @p_327 @p_345 @p_396) :rule not_and :premises (t492))
(step t494 (cl @p_397 @p_401) :rule or_neg :args (0))
(step t495 (cl @p_397 @p_400) :rule or_neg :args (1))
(step t496 (cl @p_397 @p_399) :rule or_neg :args (2))
(step t497 (cl @p_397 @p_398) :rule or_neg :args (3))
(step t498 (cl @p_397 (not @p_396)) :rule or_neg :args (4))
(step t499 (cl @p_397 @p_397 @p_397 @p_397 @p_397) :rule resolution :premises (t493 t494 t495 t496 t497 t498))
(step t500 (cl @p_397) :rule contraction :premises (t499))
(step t501 (cl @p_394) :rule resolution :premises (t471 t475 t500))
(step t502 (cl @p_393) :rule resolution :premises (t467 t470 t501))
(step t503 (cl @p_335 @p_332 @p_327 @p_345 @p_392) :rule or :premises (t502))
(step t504 (cl @p_327 @p_392 @p_332 @p_345 @p_335) :rule reordering :premises (t503))
(step t505 (cl @p_324 @p_273 @p_271 @p_269) :rule or_pos)
(step t506 (cl @p_273 @p_271 @p_269 @p_324) :rule reordering :premises (t505))
(step t507 (cl (not @p_319) (not @p_318) @p_313) :rule equiv_pos2)
(step t508 (cl (= @p_315 @p_320)) :rule poly_simp)
(step t509 (cl (= @p_316 @p_321)) :rule cong :premises (t508))
(step t510 (cl (= (* 1 (- @p_150 @p_320)) (* -1 @p_322))) :rule poly_simp)
(step t511 (cl (= @p_321 @p_269)) :rule poly_simp_rel :premises (t510))
(step t512 (cl (= @p_316 @p_269)) :rule trans :premises (t509 t511))
(step t513 (cl (= @p_317 @p_274)) :rule cong :premises (t512))
(step t514 (cl @p_319) :rule cong :premises (t513))
(step t515 (cl @p_318 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule implies_neg1)
(anchor :step t516)
(assume t516.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))
(step t516.t0 (cl (or @p_312 @p_317)) :rule forall_inst :args (@p_4 @p_20))
(step t516.t1 (cl @p_312 @p_317) :rule or :premises (t516.t0))
(step t516.t2 (cl (not @p_275) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t516.t3 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t516.t3.t0 (cl (= (* 1 (- @p_310 @p_309)) (* 1 (- @p_163 @p_300)))) :rule poly_simp)
(step t516.t3.t1 (cl (= @p_311 @p_301)) :rule poly_simp_rel :premises (t516.t3.t0))
(step t516.t3.t2 (cl (= (=> @p_303 @p_311) @p_304)) :rule cong :premises (t516.t3.t1))
(step t516.t3 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t516.t4 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t516.t4.t0 (cl (= @p_304 @p_306)) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t516.t4.t1 (cl (= @p_305 @p_307)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t516.t4.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t516.t4.t3 (cl (= @p_306 @p_308)) :rule cong :premises (t516.t4.t1 t516.t4.t2))
(step t516.t4.t4 (cl (= @p_308 @p_302)) :rule aci_simp)
(step t516.t4.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t516.t4.t3 t516.t4.t4))
(step t516.t4.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t516.t4.t0 t516.t4.t5))
(step t516.t4 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t516.t5 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t516.t3 t516.t4))
(anchor :step t516.t6 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t516.t6.t0 (cl @p_72) :rule refl)
(step t516.t6.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t516.t6.t0))
(step t516.t6.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t516.t6.t1))
(step t516.t6.t3 (cl @p_73) :rule refl)
(step t516.t6.t4 (cl (= @p_297 @p_276)) :rule cong :premises (t161 t516.t6.t3))
(step t516.t6.t5 (cl (= @p_298 @p_277)) :rule cong :premises (t516.t6.t4))
(step t516.t6.t6 (cl (= @p_299 @p_287)) :rule cong :premises (t516.t6.t5))
(step t516.t6.t7 (cl (= @p_278 @p_278)) :rule refl)
(step t516.t6.t8 (cl (= @p_295 @p_279)) :rule cong :premises (t161 t516.t6.t7))
(step t516.t6.t9 (cl (= @p_296 @p_280)) :rule cong :premises (t516.t6.t8))
(step t516.t6.t10 (cl (= @p_140 @p_140)) :rule refl)
(step t516.t6.t11 (cl (= @p_293 @p_282)) :rule cong :premises (t161 t516.t6.t10))
(step t516.t6.t12 (cl (= @p_294 @p_283)) :rule cong :premises (t516.t6.t11))
(step t516.t6.t13 (cl (= @p_300 @p_288)) :rule cong :premises (t516.t6.t6 t516.t6.t9 t516.t6.t12))
(step t516.t6.t14 (cl (= @p_301 @p_289)) :rule cong :premises (t516.t6.t2 t516.t6.t13))
(step t516.t6.t15 (cl (= @p_302 @p_290)) :rule cong :premises (t516.t6.t14))
(step t516.t6 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t516.t7 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t516.t7.t0 (cl (= @p_288 @p_291)) :rule poly_simp)
(step t516.t7.t1 (cl (= @p_289 @p_292)) :rule cong :premises (t516.t7.t0))
(step t516.t7.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 @p_281)))) :rule poly_simp)
(step t516.t7.t3 (cl (= @p_292 @p_284)) :rule poly_simp_rel :premises (t516.t7.t2))
(step t516.t7.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t516.t7.t1 t516.t7.t3))
(step t516.t7.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t516.t7.t4))
(step t516.t7 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t516.t8 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t516.t6 t516.t7))
(step t516.t9 (cl @p_275) :rule trans :premises (t516.t5 t516.t8))
(step t516.t10 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t516.t2 t516.t9 a12))
(step t516.t11 (cl @p_317) :rule resolution :premises (t516.t1 t516.t10))
(step t516 (cl @p_312 @p_317) :rule subproof :discharge (t516.a0))
(step t517 (cl @p_318 @p_317) :rule resolution :premises (t515 t516))
(step t518 (cl @p_318 (not @p_317)) :rule implies_neg2)
(step t519 (cl @p_318 @p_318) :rule resolution :premises (t517 t518))
(step t520 (cl @p_318) :rule contraction :premises (t519))
(step t521 (cl @p_313) :rule resolution :premises (t507 t514 t520))
(step t522 (cl @p_312 @p_274) :rule implies :premises (t521))
(step t523 (cl (not @p_275) (not (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1)))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule equiv_pos2)
(anchor :step t524 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t524.t0 (cl (= (* 1 (- @p_310 @p_309)) (* 1 (- @p_163 @p_300)))) :rule poly_simp)
(step t524.t1 (cl (= @p_311 @p_301)) :rule poly_simp_rel :premises (t524.t0))
(step t524.t2 (cl (= (=> @p_303 @p_311) @p_304)) :rule cong :premises (t524.t1))
(step t524 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t525 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t525.t0 (cl (= @p_304 @p_306)) :rule rare_rewrite :args ("bool-impl-elim" @p_303 @p_301))
(step t525.t1 (cl (= @p_305 @p_307)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_157 @p_285 rare-list))
(step t525.t2 (cl (= @p_301 @p_301)) :rule refl)
(step t525.t3 (cl (= @p_306 @p_308)) :rule cong :premises (t525.t1 t525.t2))
(step t525.t4 (cl (= @p_308 @p_302)) :rule aci_simp)
(step t525.t5 (cl (= @p_306 @p_302)) :rule trans :premises (t525.t3 t525.t4))
(step t525.t6 (cl (= @p_304 @p_302)) :rule trans :premises (t525.t0 t525.t5))
(step t525 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule bind)
(step t526 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (=> (and (finite$ ?v0) (finite$ ?v1)) (= (+ (of_nat$ (fun_app$b card$ ?v0)) (of_nat$ (fun_app$b card$ ?v1))) (+ (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))))) :rule trans :premises (t524 t525))
(anchor :step t527 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t527.t0 (cl @p_72) :rule refl)
(step t527.t1 (cl (= @p_162 @p_154)) :rule cong :premises (t161 t527.t0))
(step t527.t2 (cl (= @p_163 @p_155)) :rule cong :premises (t527.t1))
(step t527.t3 (cl @p_73) :rule refl)
(step t527.t4 (cl (= @p_297 @p_276)) :rule cong :premises (t161 t527.t3))
(step t527.t5 (cl (= @p_298 @p_277)) :rule cong :premises (t527.t4))
(step t527.t6 (cl (= @p_299 @p_287)) :rule cong :premises (t527.t5))
(step t527.t7 (cl (= @p_278 @p_278)) :rule refl)
(step t527.t8 (cl (= @p_295 @p_279)) :rule cong :premises (t161 t527.t7))
(step t527.t9 (cl (= @p_296 @p_280)) :rule cong :premises (t527.t8))
(step t527.t10 (cl (= @p_140 @p_140)) :rule refl)
(step t527.t11 (cl (= @p_293 @p_282)) :rule cong :premises (t161 t527.t10))
(step t527.t12 (cl (= @p_294 @p_283)) :rule cong :premises (t527.t11))
(step t527.t13 (cl (= @p_300 @p_288)) :rule cong :premises (t527.t6 t527.t9 t527.t12))
(step t527.t14 (cl (= @p_301 @p_289)) :rule cong :premises (t527.t2 t527.t13))
(step t527.t15 (cl (= @p_302 @p_290)) :rule cong :premises (t527.t14))
(step t527 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))))) :rule bind)
(anchor :step t528 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t528.t0 (cl (= @p_288 @p_291)) :rule poly_simp)
(step t528.t1 (cl (= @p_289 @p_292)) :rule cong :premises (t528.t0))
(step t528.t2 (cl (= (* 1 (- @p_155 @p_291)) (* -1 (- @p_283 @p_281)))) :rule poly_simp)
(step t528.t3 (cl (= @p_292 @p_284)) :rule poly_simp_rel :premises (t528.t2))
(step t528.t4 (cl (= @p_289 @p_284)) :rule trans :premises (t528.t1 t528.t3))
(step t528.t5 (cl (= @p_290 (or @p_158 @p_286 @p_284))) :rule cong :premises (t528.t4))
(step t528 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$a ?v1))) (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule bind)
(step t529 (cl (= (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$ ?v0)) (+ (* -1 (of_nat$ (fun_app$b card$ ?v1))) (of_nat$ (fun_app$b card$ (sup$ ?v0 ?v1))) (of_nat$ (fun_app$b card$ (inf$ ?v0 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0)))))))) :rule trans :premises (t527 t528))
(step t530 (cl @p_275) :rule trans :premises (t526 t529))
(step t531 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (or (not (finite$ ?v0)) (not (finite$ ?v1)) (= (of_nat$ (fun_app$b card$a (inf$ ?v0 ?v1))) (+ (* -1 (of_nat$ (fun_app$b card$a (sup$ ?v0 ?v1)))) (of_nat$ (fun_app$b card$a ?v1)) (of_nat$ (fun_app$b card$a ?v0))))))) :rule resolution :premises (t523 t530 a12))
(step t532 (cl @p_274) :rule resolution :premises (t522 t531))
(step t533 (cl @p_269) :rule resolution :premises (t506 t337 t319 t532))
(step t534 (cl (or @p_260 @p_252)) :rule forall_inst :args (ys$))
(step t535 (cl @p_260 @p_252) :rule or :premises (t534))
(step t536 (cl (not @p_253) (not (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0)))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule equiv_pos2)
(anchor :step t537 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t537.t0 (cl (= @p_113 @p_113)) :rule refl)
(step t537.t1 (cl (= @p_258 @p_254)) :rule cong :premises (t161 t537.t0))
(step t537.t2 (cl (= @p_259 @p_255)) :rule cong :premises (t537.t1))
(step t537.t3 (cl (= @p_256 @p_256)) :rule refl)
(step t537.t4 (cl (= (= @p_259 @p_256) @p_257)) :rule cong :premises (t537.t2 t537.t3))
(step t537 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$ (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))))) :rule bind)
(anchor :step t538 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t538.t0 (cl (= (* 1 (- @p_255 @p_256)) (* -1 (- @p_256 @p_255)))) :rule poly_simp)
(step t538.t1 (cl (= @p_257 (= @p_256 @p_255))) :rule poly_simp_rel :premises (t538.t0))
(step t538 (cl (= (forall ((?v0 A_list$)) (= (of_nat$ (fun_app$b card$a (set$ ?v0))) (of_nat$ (size$ (remdups$ ?v0))))) (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0))))))) :rule bind)
(step t539 (cl @p_253) :rule trans :premises (t537 t538))
(step t540 (cl (forall ((?v0 A_list$)) (= (of_nat$ (size$ (remdups$ ?v0))) (of_nat$ (fun_app$b card$a (set$ ?v0)))))) :rule resolution :premises (t536 t539 a3))
(step t541 (cl @p_252) :rule resolution :premises (t535 t540))
(step t542 (cl (! (and @p_171 (! (= @p_25 (! (set$ (! (remdups$ @p_11) :named @p_180)) :named @p_181)) :named @p_182) (! (= @p_181 (! (set$ (! (remdups$ @p_180) :named @p_195)) :named @p_196)) :named @p_197) @p_263 (! (= @p_196 (! (set$ (! (remdups$ @p_195) :named @p_198)) :named @p_199)) :named @p_200) (! (= (! (set$ (append$ xs$ @p_198)) :named @p_216) (! (sup$ @p_4 @p_199) :named @p_325)) :named @p_326) (! (= @p_33 (! (of_nat$ (! (fun_app$b card$a @p_216) :named @p_217)) :named @p_218)) :named @p_219)) :named @p_389) @p_201 (! (not @p_182) :named @p_202) (! (not @p_197) :named @p_204) @p_333 (! (not @p_200) :named @p_205) (! (not @p_326) :named @p_334) (! (not @p_219) :named @p_336)) :rule and_neg)
(step t543 (cl (! (=> @p_389 @p_340) :named @p_391) @p_389) :rule implies_neg1)
(anchor :step t544)
(assume t544.a0 @p_171)
(assume t544.a1 @p_182)
(assume t544.a2 @p_197)
(assume t544.a3 @p_263)
(assume t544.a4 @p_200)
(assume t544.a5 @p_326)
(assume t544.a6 @p_219)
(step t544.t0 (cl (! (=> (! (and @p_263 @p_171 @p_182 @p_197 @p_200 @p_326 @p_219) :named @p_384) @p_340) :named @p_386) @p_384) :rule implies_neg1)
(anchor :step t544.t1)
(assume t544.t1.a0 @p_263)
(assume t544.t1.a1 @p_171)
(assume t544.t1.a2 @p_182)
(assume t544.t1.a3 @p_197)
(assume t544.t1.a4 @p_200)
(assume t544.t1.a5 @p_326)
(assume t544.t1.a6 @p_219)
(step t544.t1.t0 (cl (or @p_264 @p_326)) :rule forall_inst :args (xs$ @p_198))
(step t544.t1.t1 (cl @p_264 @p_326) :rule or :premises (t544.t1.t0))
(step t544.t1.t2 (cl @p_326) :rule resolution :premises (t544.t1.t1 a21))
(step t544.t1.t3 (cl (or @p_175 @p_200)) :rule forall_inst :args (@p_195))
(step t544.t1.t4 (cl @p_175 @p_200) :rule or :premises (t544.t1.t3))
(step t544.t1.t5 (cl @p_200) :rule resolution :premises (t544.t1.t4 t20))
(step t544.t1.t6 (cl (= @p_199 @p_196)) :rule symm :premises (t544.t1.t5))
(step t544.t1.t7 (cl (or @p_175 @p_197)) :rule forall_inst :args (@p_180))
(step t544.t1.t8 (cl @p_175 @p_197) :rule or :premises (t544.t1.t7))
(step t544.t1.t9 (cl @p_197) :rule resolution :premises (t544.t1.t8 t20))
(step t544.t1.t10 (cl (= @p_196 @p_181)) :rule symm :premises (t544.t1.t9))
(step t544.t1.t11 (cl (or @p_175 @p_182)) :rule forall_inst :args (@p_11))
(step t544.t1.t12 (cl @p_175 @p_182) :rule or :premises (t544.t1.t11))
(step t544.t1.t13 (cl @p_182) :rule resolution :premises (t544.t1.t12 t20))
(step t544.t1.t14 (cl (= @p_181 @p_25)) :rule symm :premises (t544.t1.t13))
(step t544.t1.t15 (cl (= @p_199 @p_20)) :rule trans :premises (t544.t1.t6 t544.t1.t10 t544.t1.t14 t406))
(step t544.t1.t16 (cl (= @p_325 @p_261)) :rule cong :premises (t544.t1.t15))
(step t544.t1.t17 (cl (= @p_261 @p_262)) :rule symm :premises (t97))
(step t544.t1.t18 (cl (= @p_216 @p_262)) :rule trans :premises (t544.t1.t2 t544.t1.t16 t544.t1.t17))
(step t544.t1.t19 (cl (= @p_217 @p_387)) :rule cong :premises (t544.t1.t18))
(step t544.t1.t20 (cl (= @p_218 @p_388)) :rule cong :premises (t544.t1.t19))
(step t544.t1.t21 (cl (= @p_387 @p_265)) :rule cong :premises (t97))
(step t544.t1.t22 (cl (= @p_388 @p_266)) :rule cong :premises (t544.t1.t21))
(step t544.t1.t23 (cl @p_340) :rule trans :premises (t544.t1.a6 t544.t1.t20 t544.t1.t22))
(step t544.t1 (cl @p_333 @p_201 @p_202 @p_204 @p_205 @p_334 @p_336 @p_340) :rule subproof :discharge (t544.t1.a0 t544.t1.a1 t544.t1.a2 t544.t1.a3 t544.t1.a4 t544.t1.a5 t544.t1.a6))
(step t544.t2 (cl (! (not @p_384) :named @p_385) @p_263) :rule and_pos :args (0))
(step t544.t3 (cl @p_385 @p_171) :rule and_pos :args (1))
(step t544.t4 (cl @p_385 @p_182) :rule and_pos :args (2))
(step t544.t5 (cl @p_385 @p_197) :rule and_pos :args (3))
(step t544.t6 (cl @p_385 @p_200) :rule and_pos :args (4))
(step t544.t7 (cl @p_385 @p_326) :rule and_pos :args (5))
(step t544.t8 (cl @p_385 @p_219) :rule and_pos :args (6))
(step t544.t9 (cl @p_340 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385) :rule resolution :premises (t544.t1 t544.t2 t544.t3 t544.t4 t544.t5 t544.t6 t544.t7 t544.t8))
(step t544.t10 (cl @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_340) :rule reordering :premises (t544.t9))
(step t544.t11 (cl @p_385 @p_340) :rule contraction :premises (t544.t10))
(step t544.t12 (cl @p_386 @p_340) :rule resolution :premises (t544.t0 t544.t11))
(step t544.t13 (cl @p_386 @p_345) :rule implies_neg2)
(step t544.t14 (cl @p_386 @p_386) :rule resolution :premises (t544.t12 t544.t13))
(step t544.t15 (cl @p_386) :rule contraction :premises (t544.t14))
(step t544.t16 (cl @p_385 @p_340) :rule implies :premises (t544.t15))
(step t544.t17 (cl (or @p_175 @p_182)) :rule forall_inst :args (@p_11))
(step t544.t18 (cl @p_175 @p_182) :rule or :premises (t544.t17))
(step t544.t19 (cl @p_182) :rule resolution :premises (t544.t18 t20))
(step t544.t20 (cl (or @p_175 @p_197)) :rule forall_inst :args (@p_180))
(step t544.t21 (cl @p_175 @p_197) :rule or :premises (t544.t20))
(step t544.t22 (cl @p_197) :rule resolution :premises (t544.t21 t20))
(step t544.t23 (cl (or @p_175 @p_200)) :rule forall_inst :args (@p_195))
(step t544.t24 (cl @p_175 @p_200) :rule or :premises (t544.t23))
(step t544.t25 (cl @p_200) :rule resolution :premises (t544.t24 t20))
(step t544.t26 (cl (or @p_264 @p_326)) :rule forall_inst :args (xs$ @p_198))
(step t544.t27 (cl @p_264 @p_326) :rule or :premises (t544.t26))
(step t544.t28 (cl @p_326) :rule resolution :premises (t544.t27 a21))
(step t544.t29 (cl @p_384) :rule and_intro :premises (t97 t406 t544.t19 t544.t22 t544.t25 t544.t28 t544.a6))
(step t544.t30 (cl @p_340) :rule resolution :premises (t544.t16 t544.t29))
(step t544 (cl @p_201 @p_202 @p_204 @p_333 @p_205 @p_334 @p_336 @p_340) :rule subproof :discharge (t544.a0 t544.a1 t544.a2 t544.a3 t544.a4 t544.a5 t544.a6))
(step t545 (cl (! (not @p_389) :named @p_390) @p_171) :rule and_pos :args (0))
(step t546 (cl @p_390 @p_182) :rule and_pos :args (1))
(step t547 (cl @p_390 @p_197) :rule and_pos :args (2))
(step t548 (cl @p_390 @p_263) :rule and_pos :args (3))
(step t549 (cl @p_390 @p_200) :rule and_pos :args (4))
(step t550 (cl @p_390 @p_326) :rule and_pos :args (5))
(step t551 (cl @p_390 @p_219) :rule and_pos :args (6))
(step t552 (cl @p_340 @p_390 @p_390 @p_390 @p_390 @p_390 @p_390 @p_390) :rule resolution :premises (t544 t545 t546 t547 t548 t549 t550 t551))
(step t553 (cl @p_390 @p_390 @p_390 @p_390 @p_390 @p_390 @p_390 @p_340) :rule reordering :premises (t552))
(step t554 (cl @p_390 @p_340) :rule contraction :premises (t553))
(step t555 (cl @p_391 @p_340) :rule resolution :premises (t543 t554))
(step t556 (cl @p_391 @p_345) :rule implies_neg2)
(step t557 (cl @p_391 @p_391) :rule resolution :premises (t555 t556))
(step t558 (cl @p_391) :rule contraction :premises (t557))
(step t559 (cl @p_390 @p_340) :rule implies :premises (t558))
(step t560 (cl @p_201 @p_202 @p_204 @p_333 @p_205 @p_334 @p_336 @p_340) :rule resolution :premises (t542 t559))
(step t561 (cl @p_201 @p_202 @p_204 @p_333 @p_205 @p_340 @p_334 @p_336) :rule reordering :premises (t560))
(step t562 (cl (or @p_264 @p_326)) :rule forall_inst :args (xs$ @p_198))
(step t563 (cl @p_264 @p_326) :rule or :premises (t562))
(step t564 (cl @p_326) :rule resolution :premises (t563 a21))
(step t565 (cl (or @p_175 @p_200)) :rule forall_inst :args (@p_195))
(step t566 (cl @p_175 @p_200) :rule or :premises (t565))
(step t567 (cl @p_200) :rule resolution :premises (t566 t20))
(step t568 (cl (or @p_175 @p_197)) :rule forall_inst :args (@p_180))
(step t569 (cl @p_175 @p_197) :rule or :premises (t568))
(step t570 (cl @p_197) :rule resolution :premises (t569 t20))
(step t571 (cl (or @p_175 @p_182)) :rule forall_inst :args (@p_11))
(step t572 (cl @p_175 @p_182) :rule or :premises (t571))
(step t573 (cl @p_182) :rule resolution :premises (t572 t20))
(step t574 (cl (! (=> (! (and @p_252 @p_171 @p_330 @p_182 @p_197 @p_269 @p_263 @p_200 @p_326 @p_151 @p_219) :named @p_337) (! (and @p_340 @p_252 @p_330 @p_269 @p_339) :named @p_341)) :named @p_382) @p_337) :rule implies_neg1)
(anchor :step t575)
(assume t575.a0 @p_252)
(assume t575.a1 @p_171)
(assume t575.a2 @p_330)
(assume t575.a3 @p_182)
(assume t575.a4 @p_197)
(assume t575.a5 @p_269)
(assume t575.a6 @p_263)
(assume t575.a7 @p_200)
(assume t575.a8 @p_326)
(assume t575.a9 @p_151)
(assume t575.a10 @p_219)
(step t575.t0 (cl @p_386 @p_384) :rule implies_neg1)
(anchor :step t575.t1)
(assume t575.t1.a0 @p_263)
(assume t575.t1.a1 @p_171)
(assume t575.t1.a2 @p_182)
(assume t575.t1.a3 @p_197)
(assume t575.t1.a4 @p_200)
(assume t575.t1.a5 @p_326)
(assume t575.t1.a6 @p_219)
(step t575.t1.t0 (cl (= @p_199 @p_196)) :rule symm :premises (t567))
(step t575.t1.t1 (cl (= @p_196 @p_181)) :rule symm :premises (t570))
(step t575.t1.t2 (cl (= @p_181 @p_25)) :rule symm :premises (t573))
(step t575.t1.t3 (cl (= @p_199 @p_20)) :rule trans :premises (t575.t1.t0 t575.t1.t1 t575.t1.t2 t406))
(step t575.t1.t4 (cl (= @p_325 @p_261)) :rule cong :premises (t575.t1.t3))
(step t575.t1.t5 (cl (= @p_261 @p_262)) :rule symm :premises (t97))
(step t575.t1.t6 (cl (= @p_216 @p_262)) :rule trans :premises (t564 t575.t1.t4 t575.t1.t5))
(step t575.t1.t7 (cl (= @p_217 @p_387)) :rule cong :premises (t575.t1.t6))
(step t575.t1.t8 (cl (= @p_218 @p_388)) :rule cong :premises (t575.t1.t7))
(step t575.t1.t9 (cl (= @p_387 @p_265)) :rule cong :premises (t97))
(step t575.t1.t10 (cl (= @p_388 @p_266)) :rule cong :premises (t575.t1.t9))
(step t575.t1.t11 (cl @p_340) :rule trans :premises (t575.t1.a6 t575.t1.t8 t575.t1.t10))
(step t575.t1 (cl @p_333 @p_201 @p_202 @p_204 @p_205 @p_334 @p_336 @p_340) :rule subproof :discharge (t575.t1.a0 t575.t1.a1 t575.t1.a2 t575.t1.a3 t575.t1.a4 t575.t1.a5 t575.t1.a6))
(step t575.t2 (cl @p_385 @p_263) :rule and_pos :args (0))
(step t575.t3 (cl @p_385 @p_171) :rule and_pos :args (1))
(step t575.t4 (cl @p_385 @p_182) :rule and_pos :args (2))
(step t575.t5 (cl @p_385 @p_197) :rule and_pos :args (3))
(step t575.t6 (cl @p_385 @p_200) :rule and_pos :args (4))
(step t575.t7 (cl @p_385 @p_326) :rule and_pos :args (5))
(step t575.t8 (cl @p_385 @p_219) :rule and_pos :args (6))
(step t575.t9 (cl @p_340 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385) :rule resolution :premises (t575.t1 t575.t2 t575.t3 t575.t4 t575.t5 t575.t6 t575.t7 t575.t8))
(step t575.t10 (cl @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_340) :rule reordering :premises (t575.t9))
(step t575.t11 (cl @p_385 @p_340) :rule contraction :premises (t575.t10))
(step t575.t12 (cl @p_386 @p_340) :rule resolution :premises (t575.t0 t575.t11))
(step t575.t13 (cl @p_386 @p_345) :rule implies_neg2)
(step t575.t14 (cl @p_386 @p_386) :rule resolution :premises (t575.t12 t575.t13))
(step t575.t15 (cl @p_386) :rule contraction :premises (t575.t14))
(step t575.t16 (cl @p_385 @p_340) :rule implies :premises (t575.t15))
(step t575.t17 (cl @p_384) :rule and_intro :premises (t97 t406 t573 t570 t567 t564 t575.a10))
(step t575.t18 (cl @p_340) :rule resolution :premises (t575.t16 t575.t17))
(step t575.t19 (cl (! (=> @p_151 @p_339) :named @p_383) @p_151) :rule implies_neg1)
(anchor :step t575.t20)
(assume t575.t20.a0 @p_151)
(step t575.t20.t0 (cl @p_339) :rule symm :premises (t575.t20.a0))
(step t575.t20 (cl @p_335 @p_339) :rule subproof :discharge (t575.t20.a0))
(step t575.t21 (cl @p_383 @p_339) :rule resolution :premises (t575.t19 t575.t20))
(step t575.t22 (cl @p_383 @p_346) :rule implies_neg2)
(step t575.t23 (cl @p_383 @p_383) :rule resolution :premises (t575.t21 t575.t22))
(step t575.t24 (cl @p_383) :rule contraction :premises (t575.t23))
(step t575.t25 (cl @p_335 @p_339) :rule implies :premises (t575.t24))
(step t575.t26 (cl @p_339) :rule resolution :premises (t575.t25 t575.a9))
(step t575.t27 (cl @p_341) :rule and_intro :premises (t575.t18 t541 t575.a2 t533 t575.t26))
(step t575 (cl @p_327 @p_201 @p_331 @p_202 @p_204 @p_332 @p_333 @p_205 @p_334 @p_335 @p_336 @p_341) :rule subproof :discharge (t575.a0 t575.a1 t575.a2 t575.a3 t575.a4 t575.a5 t575.a6 t575.a7 t575.a8 t575.a9 t575.a10))
(step t576 (cl (! (not @p_337) :named @p_338) @p_252) :rule and_pos :args (0))
(step t577 (cl @p_338 @p_171) :rule and_pos :args (1))
(step t578 (cl @p_338 @p_330) :rule and_pos :args (2))
(step t579 (cl @p_338 @p_182) :rule and_pos :args (3))
(step t580 (cl @p_338 @p_197) :rule and_pos :args (4))
(step t581 (cl @p_338 @p_269) :rule and_pos :args (5))
(step t582 (cl @p_338 @p_263) :rule and_pos :args (6))
(step t583 (cl @p_338 @p_200) :rule and_pos :args (7))
(step t584 (cl @p_338 @p_326) :rule and_pos :args (8))
(step t585 (cl @p_338 @p_151) :rule and_pos :args (9))
(step t586 (cl @p_338 @p_219) :rule and_pos :args (10))
(step t587 (cl @p_341 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338) :rule resolution :premises (t575 t576 t577 t578 t579 t580 t581 t582 t583 t584 t585 t586))
(step t588 (cl @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_338 @p_341) :rule reordering :premises (t587))
(step t589 (cl @p_338 @p_341) :rule contraction :premises (t588))
(step t590 (cl @p_382 @p_341) :rule resolution :premises (t574 t589))
(step t591 (cl @p_382 (! (not @p_341) :named @p_342)) :rule implies_neg2)
(step t592 (cl @p_382 @p_382) :rule resolution :premises (t590 t591))
(step t593 (cl @p_382) :rule contraction :premises (t592))
(step t594 (cl @p_338 @p_341) :rule implies :premises (t593))
(step t595 (cl (! (=> @p_341 false) :named @p_343) @p_341) :rule implies_neg1)
(anchor :step t596)
(assume t596.a0 @p_340)
(assume t596.a1 @p_252)
(assume t596.a2 @p_330)
(assume t596.a3 @p_269)
(assume t596.a4 @p_339)
(step t596.t0 (cl @p_151) :rule symm :premises (t596.a4))
(step t596.t1 (cl (! (=> @p_151 false) :named @p_347) @p_151) :rule implies_neg1)
(anchor :step t596.t2)
(assume t596.t2.a0 @p_151)
(step t596.t2.t0 (cl (not (! (= (! (<= (! (+ @p_150 @p_356 (! (* -1 @p_329) :named @p_354) @p_353 (! (* -1 @p_351) :named @p_352)) :named @p_357) (! (+ 0 0 (! (* -1 1) :named @p_349) 0 @p_348) :named @p_350)) :named @p_358) false) :named @p_374)) (not @p_358) false) :rule equiv_pos2)
(step t596.t2.t1 (cl (= @p_357 (! (+ @p_355 @p_379 @p_150 @p_267 @p_33 @p_251 @p_328 @p_378 @p_377) :named @p_380))) :rule poly_simp)
(step t596.t2.t2 (cl (= @p_379 0)) :rule poly_simp)
(step t596.t2.t3 (cl (= @p_150 @p_150)) :rule refl)
(step t596.t2.t4 (cl (= @p_267 @p_267)) :rule refl)
(step t596.t2.t5 (cl (= @p_33 @p_33)) :rule refl)
(step t596.t2.t6 (cl (= @p_251 @p_251)) :rule refl)
(step t596.t2.t7 (cl (= @p_328 @p_328)) :rule refl)
(step t596.t2.t8 (cl (= @p_378 0)) :rule poly_simp)
(step t596.t2.t9 (cl (= @p_377 0)) :rule poly_simp)
(step t596.t2.t10 (cl (= @p_380 (! (+ @p_355 0 @p_150 @p_267 @p_33 @p_251 @p_328 0 0) :named @p_381))) :rule cong :premises (t596.t2.t2 t596.t2.t3 t596.t2.t4 t596.t2.t5 t596.t2.t6 t596.t2.t7 t596.t2.t8 t596.t2.t9))
(step t596.t2.t11 (cl (= @p_381 0)) :rule poly_simp)
(step t596.t2.t12 (cl (= @p_380 0)) :rule trans :premises (t596.t2.t10 t596.t2.t11))
(step t596.t2.t13 (cl (= @p_357 0)) :rule trans :premises (t596.t2.t1 t596.t2.t12))
(step t596.t2.t14 (cl (= @p_349 -1)) :rule evaluate)
(step t596.t2.t15 (cl (= @p_348 0)) :rule evaluate)
(step t596.t2.t16 (cl (= @p_350 (! (+ 0 0 -1 0 0) :named @p_376))) :rule cong :premises (t596.t2.t14 t165 t596.t2.t15))
(step t596.t2.t17 (cl (= @p_376 -1)) :rule evaluate)
(step t596.t2.t18 (cl (= @p_350 -1)) :rule trans :premises (t596.t2.t16 t596.t2.t17))
(step t596.t2.t19 (cl (= @p_358 (! (<= 0 -1) :named @p_375))) :rule cong :premises (t596.t2.t13 t596.t2.t18))
(step t596.t2.t20 (cl (= @p_375 false)) :rule evaluate)
(step t596.t2.t21 (cl @p_374) :rule trans :premises (t596.t2.t19 t596.t2.t20))
(step t596.t2.t22 (cl @p_335 (! (not @p_370) :named @p_372) (not (! (<= @p_354 @p_349) :named @p_368)) (! (not @p_366) :named @p_373) (not (! (= @p_352 @p_348) :named @p_359)) @p_358) :rule la_generic :args (-1/1 -1/1 1/1 -1/1 -1/1 1/1))
(step t596.t2.t23 (cl (not @p_371) @p_332 @p_370) :rule equiv_pos2)
(step t596.t2.t24 (cl (= (* 1 (- @p_356 0)) (* 1 @p_322))) :rule poly_simp)
(step t596.t2.t25 (cl (= @p_370 @p_269)) :rule poly_simp_rel :premises (t596.t2.t24))
(step t596.t2.t26 (cl @p_371) :rule symm :premises (t596.t2.t25))
(step t596.t2.t27 (cl @p_370) :rule resolution :premises (t596.t2.t23 t596.t2.t26 t533))
(step t596.t2.t28 (cl (=> (! (and @p_361 @p_330) :named @p_369) @p_368)) :rule la_mult_neg)
(step t596.t2.t29 (cl (not @p_369) @p_368) :rule implies :premises (t596.t2.t28))
(step t596.t2.t30 (cl (= @p_365 @p_361)) :rule equiv_simplify)
(step t596.t2.t31 (cl (not @p_365) @p_361) :rule equiv1 :premises (t596.t2.t30))
(step t596.t2.t32 (cl @p_365) :rule evaluate)
(step t596.t2.t33 (cl @p_361) :rule resolution :premises (t596.t2.t31 t596.t2.t32))
(step t596.t2.t34 (cl @p_369) :rule and_intro :premises (t596.t2.t33 t596.a2))
(step t596.t2.t35 (cl @p_368) :rule resolution :premises (t596.t2.t29 t596.t2.t34))
(step t596.t2.t36 (cl (not @p_367) @p_327 @p_366) :rule equiv_pos2)
(step t596.t2.t37 (cl (= (* 1 (- @p_353 0)) (* 1 (- @p_12 @p_251)))) :rule poly_simp)
(step t596.t2.t38 (cl (= @p_366 @p_252)) :rule poly_simp_rel :premises (t596.t2.t37))
(step t596.t2.t39 (cl @p_367) :rule symm :premises (t596.t2.t38))
(step t596.t2.t40 (cl @p_366) :rule resolution :premises (t596.t2.t36 t596.t2.t39 t541))
(step t596.t2.t41 (cl (=> (! (and @p_361 @p_360) :named @p_362) @p_359)) :rule la_mult_neg)
(step t596.t2.t42 (cl (not @p_362) @p_359) :rule implies :premises (t596.t2.t41))
(step t596.t2.t43 (cl @p_364 @p_345 @p_360) :rule equiv_pos2)
(step t596.t2.t44 (cl (= (* 1 (- @p_351 0)) (* 1 (- @p_33 @p_266)))) :rule poly_simp)
(step t596.t2.t45 (cl (= @p_360 @p_340)) :rule poly_simp_rel :premises (t596.t2.t44))
(step t596.t2.t46 (cl @p_363) :rule symm :premises (t596.t2.t45))
(step t596.t2.t47 (cl @p_360) :rule resolution :premises (t596.t2.t43 t596.t2.t46 t596.a0))
(step t596.t2.t48 (cl @p_362) :rule and_intro :premises (t596.t2.t33 t596.t2.t47))
(step t596.t2.t49 (cl @p_359) :rule resolution :premises (t596.t2.t42 t596.t2.t48))
(step t596.t2.t50 (cl @p_358) :rule resolution :premises (t596.t2.t22 t596.t2.a0 t596.t2.t27 t596.t2.t35 t596.t2.t40 t596.t2.t49))
(step t596.t2.t51 (cl false) :rule resolution :premises (t596.t2.t0 t596.t2.t21 t596.t2.t50))
(step t596.t2 (cl @p_335 false) :rule subproof :discharge (t596.t2.a0))
(step t596.t3 (cl @p_347 false) :rule resolution :premises (t596.t1 t596.t2))
(step t596.t4 (cl @p_347 @p_344) :rule implies_neg2)
(step t596.t5 (cl @p_347 @p_347) :rule resolution :premises (t596.t3 t596.t4))
(step t596.t6 (cl @p_347) :rule contraction :premises (t596.t5))
(step t596.t7 (cl (= @p_347 @p_335)) :rule implies_simplify)
(step t596.t8 (cl (not @p_347) @p_335) :rule equiv1 :premises (t596.t7))
(step t596.t9 (cl @p_335) :rule resolution :premises (t596.t6 t596.t8))
(step t596.t10 (cl) :rule resolution :premises (t596.t0 t596.t9))
(step t596 (cl @p_345 @p_327 @p_331 @p_332 @p_346 false) :rule subproof :discharge (t596.a0 t596.a1 t596.a2 t596.a3 t596.a4))
(step t597 (cl @p_342 @p_340) :rule and_pos :args (0))
(step t598 (cl @p_342 @p_252) :rule and_pos :args (1))
(step t599 (cl @p_342 @p_330) :rule and_pos :args (2))
(step t600 (cl @p_342 @p_269) :rule and_pos :args (3))
(step t601 (cl @p_342 @p_339) :rule and_pos :args (4))
(step t602 (cl false @p_342 @p_342 @p_342 @p_342 @p_342) :rule resolution :premises (t596 t597 t598 t599 t600 t601))
(step t603 (cl @p_342 @p_342 @p_342 @p_342 @p_342 false) :rule reordering :premises (t602))
(step t604 (cl @p_342 false) :rule contraction :premises (t603))
(step t605 (cl @p_343 false) :rule resolution :premises (t595 t604))
(step t606 (cl @p_343 @p_344) :rule implies_neg2)
(step t607 (cl @p_343 @p_343) :rule resolution :premises (t605 t606))
(step t608 (cl @p_343) :rule contraction :premises (t607))
(step t609 (cl (= @p_343 @p_342)) :rule implies_simplify)
(step t610 (cl (not @p_343) @p_342) :rule equiv1 :premises (t609))
(step t611 (cl @p_342) :rule resolution :premises (t608 t610))
(step t612 (cl @p_338) :rule resolution :premises (t594 t611))
(step t613 (cl @p_327 @p_201 @p_331 @p_202 @p_204 @p_332 @p_333 @p_205 @p_334 @p_335 @p_336) :rule not_and :premises (t612))
(step t614 (cl (! (not (! (and (! (>= @p_33 1) :named @p_220) @p_219) :named @p_221)) :named @p_250) @p_219) :rule and_pos :args (1))
(step t615 (cl @p_219 @p_250) :rule reordering :premises (t614))
(step t616 (cl (! (not (! (= @p_221 (! (fun_app$ (! (fun_app$a less_eq$ @p_21) :named @p_183) @p_199) :named @p_206)) :named @p_222)) :named @p_249) @p_221 (! (not @p_206) :named @p_210)) :rule equiv_pos1)
(step t617 (cl @p_221 @p_210 @p_249) :rule reordering :premises (t616))
(step t618 (cl (or (! (not (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0))))) :named @p_248) @p_222)) :rule forall_inst :args (@p_198))
(step t619 (cl @p_248 @p_222) :rule or :premises (t618))
(step t620 (cl (not (! (= (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (< 0 (of_nat$ (fun_app$b card$ top$))) (= (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))) (of_nat$ (fun_app$b card$ top$)))))) (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0))))) :named @p_223)) (not (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (< 0 (of_nat$ (fun_app$b card$ top$))) (= (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))) (of_nat$ (fun_app$b card$ top$))))))) (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0))))) :rule equiv_pos2)
(anchor :step t621 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t621.t0 (cl (= (! (< 0 @p_10) :named @p_240) (! (not (! (>= 0 @p_10) :named @p_242)) :named @p_243))) :rule rare_rewrite :args ("arith-elim-lt" 0 @p_10))
(step t621.t1 (cl (= (! (not (! (>= @p_10 1) :named @p_234)) :named @p_244) (! (>= 1 (! (+ @p_10 1) :named @p_246)) :named @p_247))) :rule rare_rewrite :args ("arith-geq-tighten" @p_10 1))
(step t621.t2 (cl (= (* -1 (- 1 @p_246)) (* -1 (- 0 @p_10)))) :rule poly_simp)
(step t621.t3 (cl (= @p_247 @p_242)) :rule poly_simp_rel :premises (t621.t2))
(step t621.t4 (cl (= @p_244 @p_242)) :rule trans :premises (t621.t1 t621.t3))
(step t621.t5 (cl (= @p_242 @p_244)) :rule symm :premises (t621.t4))
(step t621.t6 (cl (= @p_243 (! (not @p_244) :named @p_245))) :rule cong :premises (t621.t5))
(step t621.t7 (cl (= @p_245 @p_234)) :rule rare_rewrite :args ("bool-double-not-elim" @p_234))
(step t621.t8 (cl (= @p_243 @p_234)) :rule trans :premises (t621.t6 t621.t7))
(step t621.t9 (cl (= @p_240 @p_234)) :rule trans :premises (t621.t0 t621.t8))
(step t621.t10 (cl (= (* 1 (- (! (of_nat$ (! (fun_app$b card$ (! (set$ (append$ xs$ ?v0)) :named @p_225)) :named @p_231)) :named @p_232) @p_10)) (* -1 (- @p_10 @p_232)))) :rule poly_simp)
(step t621.t11 (cl (= (! (= @p_232 @p_10) :named @p_239) (! (= @p_10 @p_232) :named @p_233))) :rule poly_simp_rel :premises (t621.t10))
(step t621.t12 (cl (= (! (and @p_240 @p_239) :named @p_241) (! (and @p_234 @p_233) :named @p_235))) :rule cong :premises (t621.t9 t621.t11))
(step t621.t13 (cl (= (= (! (fun_app$ (! (fun_app$a subset$ @p_21) :named @p_236) @p_113) :named @p_237) @p_241) (! (= @p_237 @p_235) :named @p_238))) :rule cong :premises (t621.t12))
(step t621 (cl (= (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (< 0 (of_nat$ (fun_app$b card$ top$))) (= (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))) (of_nat$ (fun_app$b card$ top$)))))) (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (>= (of_nat$ (fun_app$b card$ top$)) 1) (= (of_nat$ (fun_app$b card$ top$)) (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))))))))) :rule bind)
(anchor :step t622 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t622.t0 (cl (! (= @p_21 @p_21) :named @p_188)) :rule refl)
(step t622.t1 (cl (= @p_236 @p_183)) :rule cong :premises (a24 t622.t0))
(step t622.t2 (cl (= @p_113 @p_113)) :rule refl)
(step t622.t3 (cl (= @p_237 (! (fun_app$ @p_183 @p_113) :named @p_224))) :rule cong :premises (t622.t1 t622.t2))
(step t622.t4 (cl (= 1 1)) :rule refl)
(step t622.t5 (cl (= @p_234 @p_220)) :rule cong :premises (t164 t622.t4))
(step t622.t6 (cl (= @p_225 @p_225)) :rule refl)
(step t622.t7 (cl (= @p_231 (! (fun_app$b card$a @p_225) :named @p_226))) :rule cong :premises (t161 t622.t6))
(step t622.t8 (cl (= @p_232 (! (of_nat$ @p_226) :named @p_227))) :rule cong :premises (t622.t7))
(step t622.t9 (cl (= @p_233 (! (= @p_33 @p_227) :named @p_228))) :rule cong :premises (t164 t622.t8))
(step t622.t10 (cl (= @p_235 (! (and @p_220 @p_228) :named @p_229))) :rule cong :premises (t622.t5 t622.t9))
(step t622.t11 (cl (= @p_238 (! (= @p_224 @p_229) :named @p_230))) :rule cong :premises (t622.t3 t622.t10))
(step t622 (cl (= (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (>= (of_nat$ (fun_app$b card$ top$)) 1) (= (of_nat$ (fun_app$b card$ top$)) (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))))))) (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0)) (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))))))) :rule bind)
(anchor :step t623 :args ((?v0 A_list$) (:= (?v0 A_list$) ?v0)))
(step t623.t0 (cl (= @p_230 (= @p_229 @p_224))) :rule rare_rewrite :args ("eq-symm" @p_224 @p_229))
(step t623 (cl (= (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0)) (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))))) (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0)))))) :rule bind)
(step t624 (cl (= (forall ((?v0 A_list$)) (= (fun_app$ (fun_app$a subset$ (coset$ xs$)) (set$ ?v0)) (and (>= (of_nat$ (fun_app$b card$ top$)) 1) (= (of_nat$ (fun_app$b card$ top$)) (of_nat$ (fun_app$b card$ (set$ (append$ xs$ ?v0)))))))) (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0)))))) :rule trans :premises (t622 t623))
(step t625 (cl @p_223) :rule trans :premises (t621 t624))
(step t626 (cl (forall ((?v0 A_list$)) (= (and (>= (of_nat$ (fun_app$b card$a top$)) 1) (= (of_nat$ (fun_app$b card$a top$)) (of_nat$ (fun_app$b card$a (set$ (append$ xs$ ?v0)))))) (fun_app$ (fun_app$a less_eq$ (coset$ xs$)) (set$ ?v0))))) :rule resolution :premises (t620 t625 a1))
(step t627 (cl @p_222) :rule resolution :premises (t619 t626))
(step t628 (cl (! (and @p_69 @p_171 @p_182 (! (fun_app$ @p_183 @p_21) :named @p_184) @p_197 @p_200) :named @p_207) @p_86 @p_201 @p_202 (! (not @p_184) :named @p_203) @p_204 @p_205) :rule and_neg)
(step t629 (cl (! (=> @p_207 @p_206) :named @p_209) @p_207) :rule implies_neg1)
(anchor :step t630)
(assume t630.a0 @p_69)
(assume t630.a1 @p_171)
(assume t630.a2 @p_182)
(assume t630.a3 @p_184)
(assume t630.a4 @p_197)
(assume t630.a5 @p_200)
(step t630.t0 (cl (! (=> (! (and @p_184 @p_69 @p_171 @p_182 @p_197 @p_200) :named @p_211) @p_206) :named @p_213) @p_211) :rule implies_neg1)
(anchor :step t630.t1)
(assume t630.t1.a0 @p_184)
(assume t630.t1.a1 @p_69)
(assume t630.t1.a2 @p_171)
(assume t630.t1.a3 @p_182)
(assume t630.t1.a4 @p_197)
(assume t630.t1.a5 @p_200)
(step t630.t1.t0 (cl (= (! (= @p_206 true) :named @p_214) @p_206)) :rule equiv_simplify)
(step t630.t1.t1 (cl (not @p_214) @p_206) :rule equiv1 :premises (t630.t1.t0))
(step t630.t1.t2 (cl (= @p_199 @p_196)) :rule symm :premises (t567))
(step t630.t1.t3 (cl (= @p_196 @p_181)) :rule symm :premises (t570))
(step t630.t1.t4 (cl (= @p_181 @p_25)) :rule symm :premises (t573))
(step t630.t1.t5 (cl (= @p_199 @p_20)) :rule trans :premises (t630.t1.t2 t630.t1.t3 t630.t1.t4 t406))
(step t630.t1.t6 (cl (= @p_206 (! (fun_app$ @p_183 @p_20) :named @p_215))) :rule cong :premises (t630.t1.t5))
(step t630.t1.t7 (cl (= @p_20 @p_21)) :rule symm :premises (t630.t1.a1))
(step t630.t1.t8 (cl (= @p_215 @p_184)) :rule cong :premises (t630.t1.t7))
(step t630.t1.t9 (cl (! (= (! (= @p_184 true) :named @p_193) @p_184) :named @p_194)) :rule equiv_simplify)
(step t630.t1.t10 (cl @p_193 @p_203) :rule equiv2 :premises (t630.t1.t9))
(step t630.t1.t11 (cl (not (! (= (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))) (! (= @p_188 (! (and @p_184 @p_184) :named @p_187)) :named @p_189)) :named @p_190) (! (=> (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))) @p_184) :named @p_186)) :named @p_191)) (not @p_190) @p_186) :rule equiv_pos2)
(step t630.t1.t12 (cl (= @p_188 true)) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t630.t1.t13 (cl (= @p_187 @p_184)) :rule aci_simp)
(step t630.t1.t14 (cl (= @p_189 (! (= true @p_184) :named @p_192))) :rule cong :premises (t630.t1.t12 t630.t1.t13))
(step t630.t1.t15 (cl (= @p_192 @p_193)) :rule rare_rewrite :args ("eq-symm" true @p_184))
(step t630.t1.t16 (cl @p_194) :rule rare_rewrite :args ("bool-eq-true" @p_184))
(step t630.t1.t17 (cl (= @p_192 @p_184)) :rule trans :premises (t630.t1.t15 t630.t1.t16))
(step t630.t1.t18 (cl (= @p_189 @p_184)) :rule trans :premises (t630.t1.t14 t630.t1.t17))
(step t630.t1.t19 (cl @p_191) :rule cong :premises (t630.t1.t18))
(step t630.t1.t20 (cl @p_190 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t630.t1.t21)
(assume t630.t1.t21.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))))
(step t630.t1.t21.t0 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0))))) :named @p_185) @p_189)) :rule forall_inst :args (@p_21 @p_21))
(step t630.t1.t21.t1 (cl @p_185 @p_189) :rule or :premises (t630.t1.t21.t0))
(step t630.t1.t21.t2 (cl @p_189) :rule resolution :premises (t630.t1.t21.t1 t630.t1.t21.a0))
(step t630.t1.t21 (cl @p_185 @p_189) :rule subproof :discharge (t630.t1.t21.a0))
(step t630.t1.t22 (cl @p_190 @p_189) :rule resolution :premises (t630.t1.t20 t630.t1.t21))
(step t630.t1.t23 (cl @p_190 (not @p_189)) :rule implies_neg2)
(step t630.t1.t24 (cl @p_190 @p_190) :rule resolution :premises (t630.t1.t22 t630.t1.t23))
(step t630.t1.t25 (cl @p_190) :rule contraction :premises (t630.t1.t24))
(step t630.t1.t26 (cl @p_186) :rule resolution :premises (t630.t1.t11 t630.t1.t19 t630.t1.t25))
(step t630.t1.t27 (cl @p_185 @p_184) :rule implies :premises (t630.t1.t26))
(step t630.t1.t28 (cl @p_184) :rule resolution :premises (t630.t1.t27 a22))
(step t630.t1.t29 (cl @p_193) :rule resolution :premises (t630.t1.t10 t630.t1.t28))
(step t630.t1.t30 (cl @p_214) :rule trans :premises (t630.t1.t6 t630.t1.t8 t630.t1.t29))
(step t630.t1.t31 (cl @p_206) :rule resolution :premises (t630.t1.t1 t630.t1.t30))
(step t630.t1 (cl @p_203 @p_86 @p_201 @p_202 @p_204 @p_205 @p_206) :rule subproof :discharge (t630.t1.a0 t630.t1.a1 t630.t1.a2 t630.t1.a3 t630.t1.a4 t630.t1.a5))
(step t630.t2 (cl (! (not @p_211) :named @p_212) @p_184) :rule and_pos :args (0))
(step t630.t3 (cl @p_212 @p_69) :rule and_pos :args (1))
(step t630.t4 (cl @p_212 @p_171) :rule and_pos :args (2))
(step t630.t5 (cl @p_212 @p_182) :rule and_pos :args (3))
(step t630.t6 (cl @p_212 @p_197) :rule and_pos :args (4))
(step t630.t7 (cl @p_212 @p_200) :rule and_pos :args (5))
(step t630.t8 (cl @p_206 @p_212 @p_212 @p_212 @p_212 @p_212 @p_212) :rule resolution :premises (t630.t1 t630.t2 t630.t3 t630.t4 t630.t5 t630.t6 t630.t7))
(step t630.t9 (cl @p_212 @p_212 @p_212 @p_212 @p_212 @p_212 @p_206) :rule reordering :premises (t630.t8))
(step t630.t10 (cl @p_212 @p_206) :rule contraction :premises (t630.t9))
(step t630.t11 (cl @p_213 @p_206) :rule resolution :premises (t630.t0 t630.t10))
(step t630.t12 (cl @p_213 @p_210) :rule implies_neg2)
(step t630.t13 (cl @p_213 @p_213) :rule resolution :premises (t630.t11 t630.t12))
(step t630.t14 (cl @p_213) :rule contraction :premises (t630.t13))
(step t630.t15 (cl @p_212 @p_206) :rule implies :premises (t630.t14))
(step t630.t16 (cl (not @p_191) (not @p_190) @p_186) :rule equiv_pos2)
(step t630.t17 (cl (= @p_188 true)) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t630.t18 (cl (= @p_187 @p_184)) :rule aci_simp)
(step t630.t19 (cl (= @p_189 @p_192)) :rule cong :premises (t630.t17 t630.t18))
(step t630.t20 (cl (= @p_192 @p_193)) :rule rare_rewrite :args ("eq-symm" true @p_184))
(step t630.t21 (cl @p_194) :rule rare_rewrite :args ("bool-eq-true" @p_184))
(step t630.t22 (cl (= @p_192 @p_184)) :rule trans :premises (t630.t20 t630.t21))
(step t630.t23 (cl (= @p_189 @p_184)) :rule trans :premises (t630.t19 t630.t22))
(step t630.t24 (cl @p_191) :rule cong :premises (t630.t23))
(step t630.t25 (cl @p_190 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t630.t26)
(assume t630.t26.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))))
(step t630.t26.t0 (cl (or @p_185 @p_189)) :rule forall_inst :args (@p_21 @p_21))
(step t630.t26.t1 (cl @p_185 @p_189) :rule or :premises (t630.t26.t0))
(step t630.t26.t2 (cl @p_189) :rule resolution :premises (t630.t26.t1 t630.t26.a0))
(step t630.t26 (cl @p_185 @p_189) :rule subproof :discharge (t630.t26.a0))
(step t630.t27 (cl @p_190 @p_189) :rule resolution :premises (t630.t25 t630.t26))
(step t630.t28 (cl @p_190 (not @p_189)) :rule implies_neg2)
(step t630.t29 (cl @p_190 @p_190) :rule resolution :premises (t630.t27 t630.t28))
(step t630.t30 (cl @p_190) :rule contraction :premises (t630.t29))
(step t630.t31 (cl @p_186) :rule resolution :premises (t630.t16 t630.t24 t630.t30))
(step t630.t32 (cl @p_185 @p_184) :rule implies :premises (t630.t31))
(step t630.t33 (cl @p_184) :rule resolution :premises (t630.t32 a22))
(step t630.t34 (cl @p_211) :rule and_intro :premises (t630.t33 t630.a0 t406 t573 t570 t567))
(step t630.t35 (cl @p_206) :rule resolution :premises (t630.t15 t630.t34))
(step t630 (cl @p_86 @p_201 @p_202 @p_203 @p_204 @p_205 @p_206) :rule subproof :discharge (t630.a0 t630.a1 t630.a2 t630.a3 t630.a4 t630.a5))
(step t631 (cl (! (not @p_207) :named @p_208) @p_69) :rule and_pos :args (0))
(step t632 (cl @p_208 @p_171) :rule and_pos :args (1))
(step t633 (cl @p_208 @p_182) :rule and_pos :args (2))
(step t634 (cl @p_208 @p_184) :rule and_pos :args (3))
(step t635 (cl @p_208 @p_197) :rule and_pos :args (4))
(step t636 (cl @p_208 @p_200) :rule and_pos :args (5))
(step t637 (cl @p_206 @p_208 @p_208 @p_208 @p_208 @p_208 @p_208) :rule resolution :premises (t630 t631 t632 t633 t634 t635 t636))
(step t638 (cl @p_208 @p_208 @p_208 @p_208 @p_208 @p_208 @p_206) :rule reordering :premises (t637))
(step t639 (cl @p_208 @p_206) :rule contraction :premises (t638))
(step t640 (cl @p_209 @p_206) :rule resolution :premises (t629 t639))
(step t641 (cl @p_209 @p_210) :rule implies_neg2)
(step t642 (cl @p_209 @p_209) :rule resolution :premises (t640 t641))
(step t643 (cl @p_209) :rule contraction :premises (t642))
(step t644 (cl @p_208 @p_206) :rule implies :premises (t643))
(step t645 (cl @p_86 @p_201 @p_202 @p_203 @p_204 @p_205 @p_206) :rule resolution :premises (t628 t644))
(step t646 (cl (not @p_191) (not @p_190) @p_186) :rule equiv_pos2)
(step t647 (cl (= @p_188 true)) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t648 (cl (= @p_187 @p_184)) :rule aci_simp)
(step t649 (cl (= @p_189 @p_192)) :rule cong :premises (t647 t648))
(step t650 (cl (= @p_192 @p_193)) :rule rare_rewrite :args ("eq-symm" true @p_184))
(step t651 (cl @p_194) :rule rare_rewrite :args ("bool-eq-true" @p_184))
(step t652 (cl (= @p_192 @p_184)) :rule trans :premises (t650 t651))
(step t653 (cl (= @p_189 @p_184)) :rule trans :premises (t649 t652))
(step t654 (cl @p_191) :rule cong :premises (t653))
(step t655 (cl @p_190 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t656)
(assume t656.a0 (forall ((?v0 A_set$) (?v1 A_set$)) (= (= ?v0 ?v1) (and (fun_app$ (fun_app$a less_eq$ ?v0) ?v1) (fun_app$ (fun_app$a less_eq$ ?v1) ?v0)))))
(step t656.t0 (cl (or @p_185 @p_189)) :rule forall_inst :args (@p_21 @p_21))
(step t656.t1 (cl @p_185 @p_189) :rule or :premises (t656.t0))
(step t656.t2 (cl @p_189) :rule resolution :premises (t656.t1 t656.a0))
(step t656 (cl @p_185 @p_189) :rule subproof :discharge (t656.a0))
(step t657 (cl @p_190 @p_189) :rule resolution :premises (t655 t656))
(step t658 (cl @p_190 (not @p_189)) :rule implies_neg2)
(step t659 (cl @p_190 @p_190) :rule resolution :premises (t657 t658))
(step t660 (cl @p_190) :rule contraction :premises (t659))
(step t661 (cl @p_186) :rule resolution :premises (t646 t654 t660))
(step t662 (cl @p_185 @p_184) :rule implies :premises (t661))
(step t663 (cl @p_184) :rule resolution :premises (t662 a22))
(step t664 (cl (! (not (! (= (! (or (! (= bot$ @p_136) :named @p_137) (not (finite$ @p_136))) :named @p_149) @p_151) :named @p_152)) :named @p_170) (! (not @p_149) :named @p_169) @p_151) :rule equiv_pos2)
(step t665 (cl @p_151 @p_169 @p_170) :rule reordering :premises (t664))
(step t666 (cl (or @p_168 @p_152)) :rule forall_inst :args (@p_136))
(step t667 (cl @p_168 @p_152) :rule or :premises (t666))
(step t668 (cl @p_152) :rule resolution :premises (t667 t266))
(step t669 (cl @p_149 (not @p_137)) :rule or_neg :args (0))
(step t670 (cl (! (not (! (= @p_137 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))) :named @p_138)) :named @p_148) @p_137 @p_129) :rule equiv_pos1)
(step t671 (cl @p_137 @p_129 @p_148) :rule reordering :premises (t670))
(step t672 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (= bot$ (inf$ ?v0 ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1))))))) :named @p_147) @p_138)) :rule forall_inst :args (@p_4 @p_20))
(step t673 (cl @p_147 @p_138) :rule or :premises (t672))
(step t674 (cl (not (! (= (forall ((?v0 A_set$) (?v1 A_set$)) (= (= (inf$ ?v0 ?v1) bot$) (forall ((?v2 A$)) (=> (member$ ?v2 ?v0) (not (member$ ?v2 ?v1)))))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= bot$ (inf$ ?v0 ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1))))))) :named @p_139)) (not (forall ((?v0 A_set$) (?v1 A_set$)) (= (= (inf$ ?v0 ?v1) bot$) (forall ((?v2 A$)) (=> (member$ ?v2 ?v0) (not (member$ ?v2 ?v1))))))) (forall ((?v0 A_set$) (?v1 A_set$)) (= (= bot$ (inf$ ?v0 ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1))))))) :rule equiv_pos2)
(anchor :step t675 :args ((?v0 A_set$) (?v1 A_set$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t675.t0 (cl (= (! (= @p_140 bot$) :named @p_142) (! (= bot$ @p_140) :named @p_141))) :rule rare_rewrite :args ("eq-symm" @p_140 bot$))
(anchor :step t675.t1 :args ((?v2 A$) (:= (?v2 A$) ?v2)))
(step t675.t1.t0 (cl (= (=> (! (member$ ?v2 ?v0) :named @p_145) (! (not (member$ ?v2 ?v1)) :named @p_144)) (or (! (not @p_145) :named @p_146) (! (not (member$ ?v2 ?v1)) :named @p_144)))) :rule rare_rewrite :args ("bool-impl-elim" @p_145 @p_144))
(step t675.t1 (cl (= (forall ((?v2 A$)) (=> (member$ ?v2 ?v0) (not (member$ ?v2 ?v1)))) (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1)))))) :rule bind)
(step t675.t2 (cl (= (= @p_142 (forall ((?v2 A$)) (=> (member$ ?v2 ?v0) (not (member$ ?v2 ?v1))))) (= @p_141 (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1))))))) :rule cong :premises (t675.t0 t675.t1))
(step t675 (cl @p_139) :rule bind)
(step t676 (cl (forall ((?v0 A_set$) (?v1 A_set$)) (= (= bot$ (inf$ ?v0 ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 ?v0)) (not (member$ ?v2 ?v1))))))) :rule resolution :premises (t674 t675 a17))
(step t677 (cl @p_138) :rule resolution :premises (t673 t676))
(step t678 (cl (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))) @p_95) :rule or :premises (t48))
(step t679 (cl (! (and @p_69 @p_110 @p_87) :named @p_118) @p_86 @p_117 @p_88) :rule and_neg)
(step t680 (cl (! (=> @p_118 (! (member$ @quantifiers_skolemize_32 @p_101) :named @p_102)) :named @p_120) @p_118) :rule implies_neg1)
(anchor :step t681)
(assume t681.a0 @p_69)
(assume t681.a1 @p_110)
(assume t681.a2 @p_87)
(step t681.t0 (cl (! (=> (! (and @p_87 @p_69 @p_110) :named @p_121) @p_102) :named @p_123) @p_121) :rule implies_neg1)
(anchor :step t681.t1)
(assume t681.t1.a0 @p_87)
(assume t681.t1.a1 @p_69)
(assume t681.t1.a2 @p_110)
(step t681.t1.t0 (cl (= (! (= @p_102 true) :named @p_124) @p_102)) :rule equiv_simplify)
(step t681.t1.t1 (cl (not @p_124) @p_102) :rule equiv1 :premises (t681.t1.t0))
(step t681.t1.t2 (cl (= @p_101 @p_21)) :rule symm :premises (t316))
(step t681.t1.t3 (cl @p_127) :rule trans :premises (t681.t1.t2 t681.t1.a1))
(step t681.t1.t4 (cl (= @p_102 @p_87)) :rule cong :premises (t681.t1.t3))
(step t681.t1.t5 (cl (! (= (! (= @p_87 true) :named @p_125) @p_87) :named @p_126)) :rule equiv_simplify)
(step t681.t1.t6 (cl @p_125 @p_88) :rule equiv2 :premises (t681.t1.t5))
(step t681.t1.t7 (cl @p_125) :rule resolution :premises (t681.t1.t6 t681.t1.a0))
(step t681.t1.t8 (cl @p_124) :rule trans :premises (t681.t1.t4 t681.t1.t7))
(step t681.t1.t9 (cl @p_102) :rule resolution :premises (t681.t1.t1 t681.t1.t8))
(step t681.t1 (cl @p_88 @p_86 @p_117 @p_102) :rule subproof :discharge (t681.t1.a0 t681.t1.a1 t681.t1.a2))
(step t681.t2 (cl (! (not @p_121) :named @p_122) @p_87) :rule and_pos :args (0))
(step t681.t3 (cl @p_122 @p_69) :rule and_pos :args (1))
(step t681.t4 (cl @p_122 @p_110) :rule and_pos :args (2))
(step t681.t5 (cl @p_102 @p_122 @p_122 @p_122) :rule resolution :premises (t681.t1 t681.t2 t681.t3 t681.t4))
(step t681.t6 (cl @p_122 @p_122 @p_122 @p_102) :rule reordering :premises (t681.t5))
(step t681.t7 (cl @p_122 @p_102) :rule contraction :premises (t681.t6))
(step t681.t8 (cl @p_123 @p_102) :rule resolution :premises (t681.t0 t681.t7))
(step t681.t9 (cl @p_123 (! (not @p_102) :named @p_103)) :rule implies_neg2)
(step t681.t10 (cl @p_123 @p_123) :rule resolution :premises (t681.t8 t681.t9))
(step t681.t11 (cl @p_123) :rule contraction :premises (t681.t10))
(step t681.t12 (cl @p_122 @p_102) :rule implies :premises (t681.t11))
(step t681.t13 (cl @p_121) :rule and_intro :premises (t681.a2 t681.a0 t316))
(step t681.t14 (cl @p_102) :rule resolution :premises (t681.t12 t681.t13))
(step t681 (cl @p_86 @p_117 @p_88 @p_102) :rule subproof :discharge (t681.a0 t681.a1 t681.a2))
(step t682 (cl (! (not @p_118) :named @p_119) @p_69) :rule and_pos :args (0))
(step t683 (cl @p_119 @p_110) :rule and_pos :args (1))
(step t684 (cl @p_119 @p_87) :rule and_pos :args (2))
(step t685 (cl @p_102 @p_119 @p_119 @p_119) :rule resolution :premises (t681 t682 t683 t684))
(step t686 (cl @p_119 @p_119 @p_119 @p_102) :rule reordering :premises (t685))
(step t687 (cl @p_119 @p_102) :rule contraction :premises (t686))
(step t688 (cl @p_120 @p_102) :rule resolution :premises (t680 t687))
(step t689 (cl @p_120 @p_103) :rule implies_neg2)
(step t690 (cl @p_120 @p_120) :rule resolution :premises (t688 t689))
(step t691 (cl @p_120) :rule contraction :premises (t690))
(step t692 (cl @p_119 @p_102) :rule implies :premises (t691))
(step t693 (cl @p_86 @p_117 @p_88 @p_102) :rule resolution :premises (t679 t692))
(step t694 (cl (! (not (! (or @p_103 @p_90) :named @p_104)) :named @p_109) @p_103 @p_90) :rule or_pos)
(step t695 (cl @p_90 @p_103 @p_109) :rule reordering :premises (t694))
(step t696 (cl (or @p_108 @p_104)) :rule forall_inst :args (@quantifiers_skolemize_32 @p_4))
(step t697 (cl @p_108 @p_104) :rule or :premises (t696))
(step t698 (cl @p_104) :rule resolution :premises (t697 t413))
(step t699 (cl (not (! (= (! (or @p_91 (! (not @p_88) :named @p_98)) :named @p_99) (! (or @p_91 @p_87) :named @p_97)) :named @p_100)) (not @p_99) @p_97) :rule equiv_pos2)
(step t700 (cl (= @p_98 @p_87)) :rule rare_rewrite :args ("bool-double-not-elim" @p_87))
(step t701 (cl @p_100) :rule cong :premises (t700))
(step t702 (cl @p_91 @p_98) :rule or_neg :args (1))
(step t703 (cl @p_99 @p_95) :rule or_neg :args (0))
(step t704 (cl @p_99 (not @p_98)) :rule or_neg :args (1))
(step t705 (cl @p_99 @p_99) :rule resolution :premises (t702 t703 t704))
(step t706 (cl @p_99) :rule contraction :premises (t705))
(step t707 (cl @p_97) :rule resolution :premises (t699 t701 t706))
(step t708 (cl @p_91 @p_87) :rule or :premises (t707))
(step t709 (cl @p_87 @p_91) :rule reordering :premises (t708))
(step t710 (cl @p_86 @p_91) :rule resolution :premises (t693 t316 t695 t698 t709 t32))
(step t711 (cl @p_39 @p_40) :rule not_equiv2 :premises (t202))
(step t712 (cl @p_39) :rule resolution :premises (t220 t349 t360 t377 t437 t466 a10 t504 t533 t541 t561 t564 t567 t97 t570 t573 t406 t613 t564 t533 t567 t97 t570 t573 t406 t541 t615 t617 t627 t645 t567 t570 t663 t573 t406 t665 t668 t669 t671 t677 t678 t710 t229 t246 t711))
(step t713 (cl @p_38) :rule resolution :premises (t203 t712))
(step t714 (cl @p_35) :rule resolution :premises (t156 t713))
(step t715 (cl @p_446) :rule resolution :premises (t154 a10 t714))
(step t716 (cl (not (! (= (! (or @p_346 @p_332 @p_447 @p_327 @p_613) :named @p_615) (! (or @p_335 @p_332 @p_447 @p_327 @p_613) :named @p_614)) :named @p_631)) (not @p_615) @p_614) :rule equiv_pos2)
(step t717 (cl (= @p_613 @p_613)) :rule refl)
(step t718 (cl @p_631) :rule cong :premises (t101 t102 t103 t104 t717))
(step t719 (cl (! (=> (! (and @p_339 @p_269 @p_446 @p_252 @p_612) :named @p_617) false) :named @p_619) @p_617) :rule implies_neg1)
(anchor :step t720)
(assume t720.a0 @p_339)
(assume t720.a1 @p_269)
(assume t720.a2 @p_446)
(assume t720.a3 @p_252)
(assume t720.a4 @p_612)
(step t720.t0 (cl (not (! (= (! (<= (! (+ @p_352 @p_150 @p_356 @p_354 @p_353) :named @p_621) (! (+ @p_349 0 0 @p_348 0) :named @p_620)) :named @p_622) false) :named @p_629)) (not @p_622) false) :rule equiv_pos2)
(step t720.t1 (cl (= @p_621 @p_380)) :rule poly_simp)
(step t720.t2 (cl (= @p_379 0)) :rule poly_simp)
(step t720.t3 (cl (= @p_150 @p_150)) :rule refl)
(step t720.t4 (cl (= @p_267 @p_267)) :rule refl)
(step t720.t5 (cl (= @p_33 @p_33)) :rule refl)
(step t720.t6 (cl (= @p_251 @p_251)) :rule refl)
(step t720.t7 (cl (= @p_328 @p_328)) :rule refl)
(step t720.t8 (cl (= @p_378 0)) :rule poly_simp)
(step t720.t9 (cl (= @p_377 0)) :rule poly_simp)
(step t720.t10 (cl (= @p_380 @p_381)) :rule cong :premises (t720.t2 t720.t3 t720.t4 t720.t5 t720.t6 t720.t7 t720.t8 t720.t9))
(step t720.t11 (cl (= @p_381 0)) :rule poly_simp)
(step t720.t12 (cl (= @p_380 0)) :rule trans :premises (t720.t10 t720.t11))
(step t720.t13 (cl (= @p_621 0)) :rule trans :premises (t720.t1 t720.t12))
(step t720.t14 (cl (= @p_349 -1)) :rule evaluate)
(step t720.t15 (cl (= @p_348 0)) :rule evaluate)
(step t720.t16 (cl (= @p_620 (! (+ -1 0 0 0 0) :named @p_630))) :rule cong :premises (t720.t14 t165 t165 t720.t15 t165))
(step t720.t17 (cl (= @p_630 -1)) :rule evaluate)
(step t720.t18 (cl (= @p_620 -1)) :rule trans :premises (t720.t16 t720.t17))
(step t720.t19 (cl (= @p_622 @p_375)) :rule cong :premises (t720.t13 t720.t18))
(step t720.t20 (cl (= @p_375 false)) :rule evaluate)
(step t720.t21 (cl @p_629) :rule trans :premises (t720.t19 t720.t20))
(step t720.t22 (cl (not (! (<= @p_352 @p_349) :named @p_627)) @p_335 @p_372 (not (! (= @p_354 @p_348) :named @p_623)) @p_373 @p_622) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t720.t23 (cl (=> (! (and @p_361 @p_612) :named @p_628) @p_627)) :rule la_mult_neg)
(step t720.t24 (cl (not @p_628) @p_627) :rule implies :premises (t720.t23))
(step t720.t25 (cl (= @p_365 @p_361)) :rule equiv_simplify)
(step t720.t26 (cl (not @p_365) @p_361) :rule equiv1 :premises (t720.t25))
(step t720.t27 (cl @p_365) :rule evaluate)
(step t720.t28 (cl @p_361) :rule resolution :premises (t720.t26 t720.t27))
(step t720.t29 (cl @p_628) :rule and_intro :premises (t720.t28 t720.a4))
(step t720.t30 (cl @p_627) :rule resolution :premises (t720.t24 t720.t29))
(step t720.t31 (cl @p_151) :rule symm :premises (t720.a0))
(step t720.t32 (cl (not @p_371) @p_332 @p_370) :rule equiv_pos2)
(step t720.t33 (cl (= (* 1 (- @p_356 0)) (* 1 @p_322))) :rule poly_simp)
(step t720.t34 (cl (= @p_370 @p_269)) :rule poly_simp_rel :premises (t720.t33))
(step t720.t35 (cl @p_371) :rule symm :premises (t720.t34))
(step t720.t36 (cl @p_370) :rule resolution :premises (t720.t32 t720.t35 t533))
(step t720.t37 (cl (=> (! (and @p_361 @p_462) :named @p_624) @p_623)) :rule la_mult_neg)
(step t720.t38 (cl (not @p_624) @p_623) :rule implies :premises (t720.t37))
(step t720.t39 (cl @p_626 @p_447 @p_462) :rule equiv_pos2)
(step t720.t40 (cl (= (* 1 (- @p_329 0)) (* 1 (- @p_5 @p_34)))) :rule poly_simp)
(step t720.t41 (cl (= @p_462 @p_446)) :rule poly_simp_rel :premises (t720.t40))
(step t720.t42 (cl @p_625) :rule symm :premises (t720.t41))
(step t720.t43 (cl @p_462) :rule resolution :premises (t720.t39 t720.t42 t720.a2))
(step t720.t44 (cl @p_624) :rule and_intro :premises (t720.t28 t720.t43))
(step t720.t45 (cl @p_623) :rule resolution :premises (t720.t38 t720.t44))
(step t720.t46 (cl (not @p_367) @p_327 @p_366) :rule equiv_pos2)
(step t720.t47 (cl (= (* 1 (- @p_353 0)) (* 1 (- @p_12 @p_251)))) :rule poly_simp)
(step t720.t48 (cl (= @p_366 @p_252)) :rule poly_simp_rel :premises (t720.t47))
(step t720.t49 (cl @p_367) :rule symm :premises (t720.t48))
(step t720.t50 (cl @p_366) :rule resolution :premises (t720.t46 t720.t49 t541))
(step t720.t51 (cl @p_622) :rule resolution :premises (t720.t22 t720.t30 t720.t31 t720.t36 t720.t45 t720.t50))
(step t720.t52 (cl false) :rule resolution :premises (t720.t0 t720.t21 t720.t51))
(step t720 (cl @p_346 @p_332 @p_447 @p_327 @p_613 false) :rule subproof :discharge (t720.a0 t720.a1 t720.a2 t720.a3 t720.a4))
(step t721 (cl (! (not @p_617) :named @p_618) @p_339) :rule and_pos :args (0))
(step t722 (cl @p_618 @p_269) :rule and_pos :args (1))
(step t723 (cl @p_618 @p_446) :rule and_pos :args (2))
(step t724 (cl @p_618 @p_252) :rule and_pos :args (3))
(step t725 (cl @p_618 @p_612) :rule and_pos :args (4))
(step t726 (cl false @p_618 @p_618 @p_618 @p_618 @p_618) :rule resolution :premises (t720 t721 t722 t723 t724 t725))
(step t727 (cl @p_618 @p_618 @p_618 @p_618 @p_618 false) :rule reordering :premises (t726))
(step t728 (cl @p_618 false) :rule contraction :premises (t727))
(step t729 (cl @p_619 false) :rule resolution :premises (t719 t728))
(step t730 (cl @p_619 @p_344) :rule implies_neg2)
(step t731 (cl @p_619 @p_619) :rule resolution :premises (t729 t730))
(step t732 (cl @p_619) :rule contraction :premises (t731))
(step t733 (cl (= @p_619 @p_618)) :rule implies_simplify)
(step t734 (cl (not @p_619) @p_618) :rule equiv1 :premises (t733))
(step t735 (cl @p_618) :rule resolution :premises (t732 t734))
(step t736 (cl @p_346 @p_332 @p_447 @p_327 @p_613) :rule not_and :premises (t735))
(step t737 (cl @p_615 @p_401) :rule or_neg :args (0))
(step t738 (cl @p_615 @p_400) :rule or_neg :args (1))
(step t739 (cl @p_615 @p_452) :rule or_neg :args (2))
(step t740 (cl @p_615 @p_399) :rule or_neg :args (3))
(step t741 (cl @p_615 @p_616) :rule or_neg :args (4))
(step t742 (cl @p_615 @p_615 @p_615 @p_615 @p_615) :rule resolution :premises (t736 t737 t738 t739 t740 t741))
(step t743 (cl @p_615) :rule contraction :premises (t742))
(step t744 (cl @p_614) :rule resolution :premises (t716 t718 t743))
(step t745 (cl @p_335 @p_332 @p_447 @p_327 @p_613) :rule or :premises (t744))
(step t746 (cl @p_327 @p_447 @p_332 @p_335 @p_613) :rule reordering :premises (t745))
(step t747 (cl (! (and @p_220 @p_575) :named @p_576) (! (not @p_220) :named @p_587) @p_605) :rule and_neg)
(step t748 (cl @p_587 @p_576 @p_605) :rule reordering :premises (t747))
(step t749 (cl (not (! (= (! (or @p_552 (! (not (! (>= @p_33 0) :named @p_580)) :named @p_584) @p_220) :named @p_586) (! (or @p_36 @p_584 @p_220) :named @p_585)) :named @p_604)) (not @p_586) @p_585) :rule equiv_pos2)
(step t750 (cl (= @p_584 @p_584)) :rule refl)
(step t751 (cl (= @p_220 @p_220)) :rule refl)
(step t752 (cl @p_604) :rule cong :premises (t205 t750 t751))
(step t753 (cl (! (and @p_37 @p_580) :named @p_588) @p_552 @p_584) :rule and_neg)
(step t754 (cl (! (=> @p_588 @p_220) :named @p_590) @p_588) :rule implies_neg1)
(anchor :step t755)
(assume t755.a0 @p_37)
(assume t755.a1 @p_580)
(step t755.t0 (cl (! (=> (! (and (! (not (= 0 @p_33)) :named @p_591) @p_580) :named @p_592) @p_220) :named @p_596) @p_592) :rule implies_neg1)
(anchor :step t755.t1)
(assume t755.t1.a0 @p_591)
(assume t755.t1.a1 @p_580)
(step t755.t1.t0 (cl (not (! (> @p_33 0) :named @p_597)) @p_220) :rule la_generic :args (1/1 1/1))
(step t755.t1.t1 (cl @p_37) :rule not_symm :premises (t755.t1.a0))
(step t755.t1.t2 (cl (or @p_36 (! (not (<= @p_33 0)) :named @p_598) (! (not (! (<= 0 @p_33) :named @p_601)) :named @p_603))) :rule la_disequality)
(step t755.t1.t3 (cl @p_36 @p_598 @p_603) :rule or :premises (t755.t1.t2))
(step t755.t1.t4 (cl (! (= @p_580 @p_601) :named @p_602)) :rule comp_simplify)
(step t755.t1.t5 (cl (not @p_602) @p_584 @p_601) :rule equiv_pos2)
(step t755.t1.t6 (cl (or (! (not (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :named @p_583) @p_580)) :rule forall_inst :args (@p_32))
(step t755.t1.t7 (cl @p_583 @p_580) :rule or :premises (t755.t1.t6))
(step t755.t1.t8 (cl (not (! (= (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :named @p_581)) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t755.t1.t9 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t755.t1.t9.t0 (cl (= (<= 0 (! (of_nat$ ?v0) :named @p_582)) (>= @p_582 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_582))
(step t755.t1.t9 (cl @p_581) :rule bind)
(step t755.t1.t10 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t755.t1.t8 t755.t1.t9 a29))
(step t755.t1.t11 (cl @p_580) :rule resolution :premises (t755.t1.t7 t755.t1.t10))
(step t755.t1.t12 (cl @p_601) :rule resolution :premises (t755.t1.t4 t755.t1.t5 t755.t1.t11))
(step t755.t1.t13 (cl (! (= @p_597 @p_598) :named @p_600)) :rule comp_simplify)
(step t755.t1.t14 (cl (not @p_600) @p_597 (! (not @p_598) :named @p_599)) :rule equiv_pos1)
(step t755.t1.t15 (cl @p_597 @p_599) :rule resolution :premises (t755.t1.t13 t755.t1.t14))
(step t755.t1.t16 (cl @p_597) :rule resolution :premises (t755.t1.t1 t755.t1.t3 t755.t1.t12 t755.t1.t15))
(step t755.t1.t17 (cl @p_220) :rule resolution :premises (t755.t1.t0 t755.t1.t16))
(step t755.t1 (cl (! (not @p_591) :named @p_594) @p_584 @p_220) :rule subproof :discharge (t755.t1.a0 t755.t1.a1))
(step t755.t2 (cl (! (not @p_592) :named @p_595) @p_591) :rule and_pos :args (0))
(step t755.t3 (cl @p_595 @p_580) :rule and_pos :args (1))
(step t755.t4 (cl @p_220 @p_595 @p_595) :rule resolution :premises (t755.t1 t755.t2 t755.t3))
(step t755.t5 (cl @p_595 @p_595 @p_220) :rule reordering :premises (t755.t4))
(step t755.t6 (cl @p_595 @p_220) :rule contraction :premises (t755.t5))
(step t755.t7 (cl @p_596 @p_220) :rule resolution :premises (t755.t0 t755.t6))
(step t755.t8 (cl @p_596 @p_587) :rule implies_neg2)
(step t755.t9 (cl @p_596 @p_596) :rule resolution :premises (t755.t7 t755.t8))
(step t755.t10 (cl @p_596) :rule contraction :premises (t755.t9))
(step t755.t11 (cl @p_595 @p_220) :rule implies :premises (t755.t10))
(step t755.t12 (cl (! (=> @p_37 @p_591) :named @p_593) @p_37) :rule implies_neg1)
(anchor :step t755.t13)
(assume t755.t13.a0 @p_37)
(step t755.t13.t0 (cl @p_591) :rule not_symm :premises (t755.t13.a0))
(step t755.t13 (cl @p_552 @p_591) :rule subproof :discharge (t755.t13.a0))
(step t755.t14 (cl @p_593 @p_591) :rule resolution :premises (t755.t12 t755.t13))
(step t755.t15 (cl @p_593 @p_594) :rule implies_neg2)
(step t755.t16 (cl @p_593 @p_593) :rule resolution :premises (t755.t14 t755.t15))
(step t755.t17 (cl @p_593) :rule contraction :premises (t755.t16))
(step t755.t18 (cl @p_552 @p_591) :rule implies :premises (t755.t17))
(step t755.t19 (cl @p_591) :rule resolution :premises (t755.t18 t755.a0))
(step t755.t20 (cl (or @p_583 @p_580)) :rule forall_inst :args (@p_32))
(step t755.t21 (cl @p_583 @p_580) :rule or :premises (t755.t20))
(step t755.t22 (cl (not @p_581) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t755.t23 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t755.t23.t0 (cl (= (<= 0 @p_582) (>= @p_582 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_582))
(step t755.t23 (cl @p_581) :rule bind)
(step t755.t24 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t755.t22 t755.t23 a29))
(step t755.t25 (cl @p_580) :rule resolution :premises (t755.t21 t755.t24))
(step t755.t26 (cl @p_592) :rule and_intro :premises (t755.t19 t755.t25))
(step t755.t27 (cl @p_220) :rule resolution :premises (t755.t11 t755.t26))
(step t755 (cl @p_552 @p_584 @p_220) :rule subproof :discharge (t755.a0 t755.a1))
(step t756 (cl (! (not @p_588) :named @p_589) @p_37) :rule and_pos :args (0))
(step t757 (cl @p_589 @p_580) :rule and_pos :args (1))
(step t758 (cl @p_220 @p_589 @p_589) :rule resolution :premises (t755 t756 t757))
(step t759 (cl @p_589 @p_589 @p_220) :rule reordering :premises (t758))
(step t760 (cl @p_589 @p_220) :rule contraction :premises (t759))
(step t761 (cl @p_590 @p_220) :rule resolution :premises (t754 t760))
(step t762 (cl @p_590 @p_587) :rule implies_neg2)
(step t763 (cl @p_590 @p_590) :rule resolution :premises (t761 t762))
(step t764 (cl @p_590) :rule contraction :premises (t763))
(step t765 (cl @p_589 @p_220) :rule implies :premises (t764))
(step t766 (cl @p_552 @p_584 @p_220) :rule resolution :premises (t753 t765))
(step t767 (cl @p_586 @p_554) :rule or_neg :args (0))
(step t768 (cl @p_586 (not @p_584)) :rule or_neg :args (1))
(step t769 (cl @p_586 @p_587) :rule or_neg :args (2))
(step t770 (cl @p_586 @p_586 @p_586) :rule resolution :premises (t766 t767 t768 t769))
(step t771 (cl @p_586) :rule contraction :premises (t770))
(step t772 (cl @p_585) :rule resolution :premises (t749 t752 t771))
(step t773 (cl @p_36 @p_584 @p_220) :rule or :premises (t772))
(step t774 (cl @p_36 @p_220 @p_584) :rule reordering :premises (t773))
(step t775 (cl (or @p_583 @p_580)) :rule forall_inst :args (@p_32))
(step t776 (cl @p_583 @p_580) :rule or :premises (t775))
(step t777 (cl (not @p_581) (not (forall ((?v0 Nat$)) (<= 0 (of_nat$ ?v0)))) (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule equiv_pos2)
(anchor :step t778 :args ((?v0 Nat$) (:= (?v0 Nat$) ?v0)))
(step t778.t0 (cl (= (<= 0 @p_582) (>= @p_582 0))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_582))
(step t778 (cl @p_581) :rule bind)
(step t779 (cl (forall ((?v0 Nat$)) (>= (of_nat$ ?v0) 0))) :rule resolution :premises (t777 t778 a29))
(step t780 (cl @p_580) :rule resolution :premises (t776 t779))
(step t781 (cl @p_220) :rule resolution :premises (t774 t349 t780))
(step t782 (cl (! (not (! (= @p_576 @p_215) :named @p_577)) :named @p_579) (! (not @p_576) :named @p_578) @p_215) :rule equiv_pos2)
(step t783 (cl @p_215 @p_578 @p_579) :rule reordering :premises (t782))
(step t784 (cl (or @p_248 @p_577)) :rule forall_inst :args (ys$))
(step t785 (cl @p_248 @p_577) :rule or :premises (t784))
(step t786 (cl @p_577) :rule resolution :premises (t785 t626))
(step t787 (cl (! (and @p_215 (! (fun_app$ (fun_app$a less_eq$ @p_20) @p_21) :named @p_558)) :named @p_569) (! (not @p_215) :named @p_573) (! (not @p_558) :named @p_574)) :rule and_neg)
(step t788 (cl @p_573 @p_569 @p_574) :rule reordering :premises (t787))
(step t789 (cl (! (not (! (= @p_69 @p_569) :named @p_571)) :named @p_572) @p_69 (! (not @p_569) :named @p_570)) :rule equiv_pos1)
(step t790 (cl @p_69 @p_570 @p_572) :rule reordering :premises (t789))
(step t791 (cl @p_85 @p_22 @p_86) :rule equiv_pos1)
(step t792 (cl @p_22 @p_86 @p_85) :rule reordering :premises (t791))
(step t793 (cl @p_86) :rule resolution :premises (t792 t712 t246))
(step t794 (cl (or @p_185 @p_571)) :rule forall_inst :args (@p_21 @p_20))
(step t795 (cl @p_185 @p_571) :rule or :premises (t794))
(step t796 (cl @p_571) :rule resolution :premises (t795 a22))
(step t797 (cl @p_570) :rule resolution :premises (t790 t793 t796))
(step t798 (cl (! (not (! (= (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$))))) @p_558) :named @p_559)) :named @p_568) @p_129 @p_558) :rule equiv_pos2)
(step t799 (cl @p_129 @p_558 @p_568) :rule reordering :premises (t798))
(step t800 (cl (not (! (= (! (=> (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0)))))) (! (= @p_558 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))) :named @p_565)) :named @p_566) (! (=> (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0)))))) @p_559) :named @p_564)) :named @p_567)) (not @p_566) @p_564) :rule equiv_pos2)
(step t801 (cl (= @p_565 @p_559)) :rule rare_rewrite :args ("eq-symm" @p_558 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ xs$))) (not (member$ ?v2 (set$ ys$)))))))
(step t802 (cl @p_567) :rule cong :premises (t801))
(step t803 (cl @p_566 (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule implies_neg1)
(anchor :step t804)
(assume t804.a0 (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0)))))))
(step t804.t0 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :named @p_563) @p_565)) :rule forall_inst :args (@p_20 xs$))
(step t804.t1 (cl @p_563 @p_565) :rule or :premises (t804.t0))
(step t804.t2 (cl (not (! (= (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0)))))) (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :named @p_560)) (not (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0))))))) (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule equiv_pos2)
(anchor :step t804.t3 :args ((?v0 A_set$) (?v1 A_list$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_list$) ?v1)))
(anchor :step t804.t3.t0 :args ((?v2 A$) (:= (?v2 A$) ?v2)))
(step t804.t3.t0.t0 (cl (= (=> (! (member$ ?v2 (set$ ?v1)) :named @p_562) @p_146) (or (not @p_562) @p_146))) :rule rare_rewrite :args ("bool-impl-elim" @p_562 @p_146))
(step t804.t3.t0 (cl (= (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0)))) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0)))))) :rule bind)
(step t804.t3.t1 (cl (= (= (! (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) :named @p_561) (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0))))) (= @p_561 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule cong :premises (t804.t3.t0))
(step t804.t3 (cl @p_560) :rule bind)
(step t804.t4 (cl (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule resolution :premises (t804.t2 t804.t3 a27))
(step t804.t5 (cl @p_565) :rule resolution :premises (t804.t1 t804.t4))
(step t804 (cl @p_563 @p_565) :rule subproof :discharge (t804.a0))
(step t805 (cl @p_566 @p_565) :rule resolution :premises (t803 t804))
(step t806 (cl @p_566 (not @p_565)) :rule implies_neg2)
(step t807 (cl @p_566 @p_566) :rule resolution :premises (t805 t806))
(step t808 (cl @p_566) :rule contraction :premises (t807))
(step t809 (cl @p_564) :rule resolution :premises (t800 t802 t808))
(step t810 (cl @p_563 @p_559) :rule implies :premises (t809))
(step t811 (cl (not @p_560) (not (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0))))))) (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule equiv_pos2)
(anchor :step t812 :args ((?v0 A_set$) (?v1 A_list$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_list$) ?v1)))
(anchor :step t812.t0 :args ((?v2 A$) (:= (?v2 A$) ?v2)))
(step t812.t0.t0 (cl (= (=> @p_562 @p_146) (or (not @p_562) @p_146))) :rule rare_rewrite :args ("bool-impl-elim" @p_562 @p_146))
(step t812.t0 (cl (= (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0)))) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0)))))) :rule bind)
(step t812.t1 (cl (= (= @p_561 (forall ((?v2 A$)) (=> (member$ ?v2 (set$ ?v1)) (not (member$ ?v2 ?v0))))) (= @p_561 (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule cong :premises (t812.t0))
(step t812 (cl @p_560) :rule bind)
(step t813 (cl (forall ((?v0 A_set$) (?v1 A_list$)) (= (fun_app$ (fun_app$a less_eq$ ?v0) (coset$ ?v1)) (forall ((?v2 A$)) (or (not (member$ ?v2 (set$ ?v1))) (not (member$ ?v2 ?v0))))))) :rule resolution :premises (t811 t812 a27))
(step t814 (cl @p_559) :rule resolution :premises (t810 t813))
(step t815 (cl @p_129) :rule resolution :premises (t94 t97 t140 t715 t533 t541 t746 t715 t533 t541 t748 t781 t783 t786 t665 t668 t788 t797 t669 t799 t814 t671 t677))
(step t816 (cl @p_95) :rule resolution :premises (t49 t815))
(step t817 (cl @p_89) :rule resolution :premises (t32 t816))
(step t818 (cl @p_29) :rule resolution :premises (t15 t21 t817))
(step t819 (cl (! (and @p_171 @p_87) :named @p_676) @p_201 @p_88) :rule and_neg)
(step t820 (cl (! (=> @p_676 @p_26) :named @p_678) @p_676) :rule implies_neg1)
(anchor :step t821)
(assume t821.a0 @p_171)
(assume t821.a1 @p_87)
(step t821.t0 (cl (! (=> (! (and @p_87 @p_171) :named @p_679) @p_26) :named @p_681) @p_679) :rule implies_neg1)
(anchor :step t821.t1)
(assume t821.t1.a0 @p_87)
(assume t821.t1.a1 @p_171)
(step t821.t1.t0 (cl (= (! (= @p_26 true) :named @p_682) @p_26)) :rule equiv_simplify)
(step t821.t1.t1 (cl (not @p_682) @p_26) :rule equiv1 :premises (t821.t1.t0))
(step t821.t1.t2 (cl (= @p_26 @p_87)) :rule cong :premises (t406))
(step t821.t1.t3 (cl @p_126) :rule equiv_simplify)
(step t821.t1.t4 (cl @p_125 @p_88) :rule equiv2 :premises (t821.t1.t3))
(step t821.t1.t5 (cl @p_125) :rule resolution :premises (t821.t1.t4 t821.t1.a0))
(step t821.t1.t6 (cl @p_682) :rule trans :premises (t821.t1.t2 t821.t1.t5))
(step t821.t1.t7 (cl @p_26) :rule resolution :premises (t821.t1.t1 t821.t1.t6))
(step t821.t1 (cl @p_88 @p_201 @p_26) :rule subproof :discharge (t821.t1.a0 t821.t1.a1))
(step t821.t2 (cl (! (not @p_679) :named @p_680) @p_87) :rule and_pos :args (0))
(step t821.t3 (cl @p_680 @p_171) :rule and_pos :args (1))
(step t821.t4 (cl @p_26 @p_680 @p_680) :rule resolution :premises (t821.t1 t821.t2 t821.t3))
(step t821.t5 (cl @p_680 @p_680 @p_26) :rule reordering :premises (t821.t4))
(step t821.t6 (cl @p_680 @p_26) :rule contraction :premises (t821.t5))
(step t821.t7 (cl @p_681 @p_26) :rule resolution :premises (t821.t0 t821.t6))
(step t821.t8 (cl @p_681 @p_27) :rule implies_neg2)
(step t821.t9 (cl @p_681 @p_681) :rule resolution :premises (t821.t7 t821.t8))
(step t821.t10 (cl @p_681) :rule contraction :premises (t821.t9))
(step t821.t11 (cl @p_680 @p_26) :rule implies :premises (t821.t10))
(step t821.t12 (cl @p_679) :rule and_intro :premises (t821.a1 t406))
(step t821.t13 (cl @p_26) :rule resolution :premises (t821.t11 t821.t12))
(step t821 (cl @p_201 @p_88 @p_26) :rule subproof :discharge (t821.a0 t821.a1))
(step t822 (cl (! (not @p_676) :named @p_677) @p_171) :rule and_pos :args (0))
(step t823 (cl @p_677 @p_87) :rule and_pos :args (1))
(step t824 (cl @p_26 @p_677 @p_677) :rule resolution :premises (t821 t822 t823))
(step t825 (cl @p_677 @p_677 @p_26) :rule reordering :premises (t824))
(step t826 (cl @p_677 @p_26) :rule contraction :premises (t825))
(step t827 (cl @p_678 @p_26) :rule resolution :premises (t820 t826))
(step t828 (cl @p_678 @p_27) :rule implies_neg2)
(step t829 (cl @p_678 @p_678) :rule resolution :premises (t827 t828))
(step t830 (cl @p_678) :rule contraction :premises (t829))
(step t831 (cl @p_677 @p_26) :rule implies :premises (t830))
(step t832 (cl @p_201 @p_88 @p_26) :rule resolution :premises (t819 t831))
(step t833 (cl @p_87) :rule resolution :premises (t709 t816))
(step t834 (cl @p_26) :rule resolution :premises (t832 t406 t833))
(step t835 (cl (! (=> (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) @p_31) :named @p_556) (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))) :rule implies_neg1)
(anchor :step t836)
(assume t836.a0 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))))
(step t836.t0 (cl (or @p_497 @p_31)) :rule forall_inst :args (@quantifiers_skolemize_32))
(step t836.t1 (cl @p_497 @p_31) :rule or :premises (t836.t0))
(step t836.t2 (cl @p_31) :rule resolution :premises (t836.t1 t836.a0))
(step t836 (cl @p_497 @p_31) :rule subproof :discharge (t836.a0))
(step t837 (cl @p_556 @p_31) :rule resolution :premises (t835 t836))
(step t838 (cl @p_556 @p_557) :rule implies_neg2)
(step t839 (cl @p_556 @p_556) :rule resolution :premises (t837 t838))
(step t840 (cl @p_556) :rule contraction :premises (t839))
(step t841 (cl @p_497 @p_31) :rule implies :premises (t840))
(step t842 (cl @p_40 (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))) :rule and_pos :args (2))
(step t843 (cl (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$)))))) @p_40) :rule reordering :premises (t842))
(step t844 (cl (forall ((?v0 A$)) (or (not (member$ ?v0 (set$ (remdups$ xs$)))) (not (member$ ?v0 (set$ (remdups$ ys$))))))) :rule resolution :premises (t843 t713))
(step t845 (cl @p_31) :rule resolution :premises (t841 t844))
(step t846 (cl) :rule resolution :premises (t1 t818 t834 t845))
)
8458adc5a961e219a9e02a11b184875e66b2dc7c 28 0
unsat
(
(assume a0 (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (p$ ?v0 ?v1)))
(assume a1 (! (=> (! (p$ z$ y$) :named @p_1) false) :named @p_2))
(step t0 (cl (! (=> (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1)) @p_1) :named @p_7) (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1)))
(step t1.t0 (cl (or (! (not (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :named @p_6) @p_1)) :rule forall_inst :args (z$ y$))
(step t1.t1 (cl @p_6 @p_1) :rule or :premises (t1.t0))
(step t1.t2 (cl (not (! (= (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (p$ ?v0 ?v1)) (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :named @p_3)) (not (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (p$ ?v0 ?v1))) (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :rule equiv_pos2)
(step t1.t3 (cl @p_3) :rule qnt_rm_unused)
(step t1.t4 (cl (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :rule resolution :premises (t1.t2 t1.t3 a0))
(step t1.t5 (cl @p_1) :rule resolution :premises (t1.t1 t1.t4))
(step t1 (cl @p_6 @p_1) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_7 @p_1) :rule resolution :premises (t0 t1))
(step t3 (cl @p_7 (! (not @p_1) :named @p_4)) :rule implies_neg2)
(step t4 (cl @p_7 @p_7) :rule resolution :premises (t2 t3))
(step t5 (cl @p_7) :rule contraction :premises (t4))
(step t6 (cl @p_6 @p_1) :rule implies :premises (t5))
(step t7 (cl @p_1 @p_6) :rule reordering :premises (t6))
(step t8 (cl (not (! (= @p_2 @p_4) :named @p_5)) (not @p_2) @p_4) :rule equiv_pos2)
(step t9 (cl @p_5) :rule rare_rewrite :args ("bool-impl-false1" @p_1))
(step t10 (cl @p_4) :rule resolution :premises (t8 t9 a1))
(step t11 (cl (not @p_3) (not (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (p$ ?v0 ?v1))) (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :rule equiv_pos2)
(step t12 (cl @p_3) :rule qnt_rm_unused)
(step t13 (cl (forall ((?v0 A$) (?v1 B$)) (p$ ?v0 ?v1))) :rule resolution :premises (t11 t12 a0))
(step t14 (cl) :rule resolution :premises (t7 t10 t13))
)
d0515077aa52dd2b73217c747d0dd7bbd9331935 279 0
unsat
(
(assume a0 (! (not (! (<= y$ (! (ite (! (<= x$ y$) :named @p_1) y$ x$) :named @p_2)) :named @p_3)) :named @p_4))
(step t0 (cl (! (=> (! (and (! (>= (! (+ x$ (! (* -1 y$) :named @p_5)) :named @p_6) 1) :named @p_7) (! (>= (! (+ y$ (! (* -1 (! (ite @p_7 x$ y$) :named @p_8)) :named @p_9)) :named @p_10) 1) :named @p_11) (! (= x$ @p_8) :named @p_54)) :named @p_64) false) :named @p_66) @p_64) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 @p_7)
(assume t1.a1 @p_11)
(assume t1.a2 @p_54)
(step t1.t0 (cl (not (! (= @p_54 (! (= (! (+ x$ @p_9) :named @p_67) 0) :named @p_68)) :named @p_84)) (! (not @p_54) :named @p_63) @p_68) :rule equiv_pos2)
(step t1.t1 (cl (= (* 1 (- @p_67 0)) (* 1 (! (- x$ @p_8) :named @p_62)))) :rule poly_simp)
(step t1.t2 (cl (= @p_68 @p_54)) :rule poly_simp_rel :premises (t1.t1))
(step t1.t3 (cl @p_84) :rule symm :premises (t1.t2))
(step t1.t4 (cl @p_68) :rule resolution :premises (t1.t0 t1.t3 t1.a2))
(step t1.t5 (cl (! (=> @p_68 false) :named @p_70) @p_68) :rule implies_neg1)
(anchor :step t1.t6)
(assume t1.t6.a0 @p_68)
(step t1.t6.t0 (cl (not (! (= (! (<= (! (+ @p_67 (! (* -1 @p_10) :named @p_36) (! (* -1 @p_6) :named @p_72)) :named @p_73) (! (+ 0 (! (* -1 1) :named @p_34) @p_34) :named @p_71)) :named @p_74) false) :named @p_77)) (not @p_74) false) :rule equiv_pos2)
(step t1.t6.t1 (cl (= @p_73 (! (+ (! (* 0 @p_8) :named @p_81) y$ @p_5 (! (* 0 x$) :named @p_80)) :named @p_82))) :rule poly_simp)
(step t1.t6.t2 (cl (= @p_81 0)) :rule poly_simp)
(step t1.t6.t3 (cl (= y$ y$)) :rule refl)
(step t1.t6.t4 (cl (= @p_5 @p_5)) :rule refl)
(step t1.t6.t5 (cl (= @p_80 0)) :rule poly_simp)
(step t1.t6.t6 (cl (= @p_82 (! (+ 0 y$ @p_5 0) :named @p_83))) :rule cong :premises (t1.t6.t2 t1.t6.t3 t1.t6.t4 t1.t6.t5))
(step t1.t6.t7 (cl (= @p_83 0)) :rule poly_simp)
(step t1.t6.t8 (cl (= @p_82 0)) :rule trans :premises (t1.t6.t6 t1.t6.t7))
(step t1.t6.t9 (cl (= @p_73 0)) :rule trans :premises (t1.t6.t1 t1.t6.t8))
(step t1.t6.t10 (cl (= @p_34 -1)) :rule evaluate)
(step t1.t6.t11 (cl (= @p_71 (! (+ 0 -1 -1) :named @p_79))) :rule cong :premises (t1.t6.t10 t1.t6.t10))
(step t1.t6.t12 (cl (= @p_79 -2)) :rule evaluate)
(step t1.t6.t13 (cl (= @p_71 -2)) :rule trans :premises (t1.t6.t11 t1.t6.t12))
(step t1.t6.t14 (cl (= @p_74 (! (<= 0 -2) :named @p_78))) :rule cong :premises (t1.t6.t9 t1.t6.t13))
(step t1.t6.t15 (cl (= @p_78 false)) :rule evaluate)
(step t1.t6.t16 (cl @p_77) :rule trans :premises (t1.t6.t14 t1.t6.t15))
(step t1.t6.t17 (cl (! (not @p_68) :named @p_69) (! (not (! (<= @p_36 @p_34) :named @p_39)) :named @p_43) (not (! (<= @p_72 @p_34) :named @p_75)) @p_74) :rule la_generic :args (-1/1 1/1 1/1 1/1))
(step t1.t6.t18 (cl (=> (! (and (! (< -1 0) :named @p_40) @p_11) :named @p_41) @p_39)) :rule la_mult_neg)
(step t1.t6.t19 (cl (not @p_41) @p_39) :rule implies :premises (t1.t6.t18))
(step t1.t6.t20 (cl (= (! (= @p_40 true) :named @p_42) @p_40)) :rule equiv_simplify)
(step t1.t6.t21 (cl (not @p_42) @p_40) :rule equiv1 :premises (t1.t6.t20))
(step t1.t6.t22 (cl @p_42) :rule evaluate)
(step t1.t6.t23 (cl @p_40) :rule resolution :premises (t1.t6.t21 t1.t6.t22))
(step t1.t6.t24 (cl (not (! (= @p_4 @p_11) :named @p_12)) (not @p_4) @p_11) :rule equiv_pos2)
(step t1.t6.t25 (cl (= @p_1 (! (not (! (>= x$ (! (+ y$ 1) :named @p_25)) :named @p_26)) :named @p_27))) :rule rare_rewrite :args ("arith-leq-norm" x$ y$))
(step t1.t6.t26 (cl (= (* -1 (- x$ @p_25)) (* -1 (- @p_6 1)))) :rule poly_simp)
(step t1.t6.t27 (cl (= @p_26 @p_7)) :rule poly_simp_rel :premises (t1.t6.t26))
(step t1.t6.t28 (cl (= @p_27 (! (not @p_7) :named @p_23))) :rule cong :premises (t1.t6.t27))
(step t1.t6.t29 (cl (= @p_1 @p_23)) :rule trans :premises (t1.t6.t25 t1.t6.t28))
(step t1.t6.t30 (cl (= x$ x$)) :rule refl)
(step t1.t6.t31 (cl (= @p_2 (! (ite @p_23 y$ x$) :named @p_24))) :rule cong :premises (t1.t6.t29 t1.t6.t3 t1.t6.t30))
(step t1.t6.t32 (cl (= @p_24 @p_8)) :rule rare_rewrite :args ("ite-not-cond" @p_7 y$ x$))
(step t1.t6.t33 (cl (= @p_2 @p_8)) :rule trans :premises (t1.t6.t31 t1.t6.t32))
(step t1.t6.t34 (cl (= @p_3 (! (<= y$ @p_8) :named @p_19))) :rule cong :premises (t1.t6.t33))
(step t1.t6.t35 (cl (= @p_19 (! (not (! (>= y$ (! (+ @p_8 1) :named @p_20)) :named @p_21)) :named @p_22))) :rule rare_rewrite :args ("arith-leq-norm" y$ @p_8))
(step t1.t6.t36 (cl (= (* -1 (- y$ @p_20)) (* -1 (- @p_10 1)))) :rule poly_simp)
(step t1.t6.t37 (cl (= @p_21 @p_11)) :rule poly_simp_rel :premises (t1.t6.t36))
(step t1.t6.t38 (cl (= @p_22 (! (not @p_11) :named @p_17))) :rule cong :premises (t1.t6.t37))
(step t1.t6.t39 (cl (= @p_19 @p_17)) :rule trans :premises (t1.t6.t35 t1.t6.t38))
(step t1.t6.t40 (cl (= @p_3 @p_17)) :rule trans :premises (t1.t6.t34 t1.t6.t39))
(step t1.t6.t41 (cl (= @p_4 (! (not @p_17) :named @p_18))) :rule cong :premises (t1.t6.t40))
(step t1.t6.t42 (cl (= @p_18 @p_11)) :rule rare_rewrite :args ("bool-double-not-elim" @p_11))
(step t1.t6.t43 (cl @p_12) :rule trans :premises (t1.t6.t41 t1.t6.t42))
(step t1.t6.t44 (cl (= (! (= (! (= @p_8 @p_8) :named @p_13) true) :named @p_14) @p_13)) :rule equiv_simplify)
(step t1.t6.t45 (cl (not @p_14) @p_13) :rule equiv1 :premises (t1.t6.t44))
(step t1.t6.t46 (cl (= (* -1 (! (- @p_8 @p_8) :named @p_16)) (* 1 @p_16))) :rule poly_simp)
(step t1.t6.t47 (cl (! (= @p_13 @p_13) :named @p_15)) :rule poly_simp_rel :premises (t1.t6.t46))
(step t1.t6.t48 (cl @p_13) :rule refl)
(step t1.t6.t49 (cl @p_13) :rule refl)
(step t1.t6.t50 (cl @p_15) :rule cong :premises (t1.t6.t48 t1.t6.t49))
(step t1.t6.t51 (cl @p_14) :rule rare_rewrite :args ("eq-refl" @p_8))
(step t1.t6.t52 (cl @p_14) :rule trans :premises (t1.t6.t47 t1.t6.t50 t1.t6.t51))
(step t1.t6.t53 (cl @p_13) :rule resolution :premises (t1.t6.t45 t1.t6.t52))
(step t1.t6.t54 (cl (= @p_9 @p_9)) :rule cong :premises (t1.t6.t53))
(step t1.t6.t55 (cl (= @p_10 @p_10)) :rule cong :premises (t1.t6.t54))
(step t1.t6.t56 (cl (= 1 1)) :rule refl)
(step t1.t6.t57 (cl (= @p_11 @p_11)) :rule cong :premises (t1.t6.t55 t1.t6.t56))
(step t1.t6.t58 (cl @p_12) :rule trans :premises (t1.t6.t43 t1.t6.t57))
(step t1.t6.t59 (cl @p_11) :rule resolution :premises (t1.t6.t24 t1.t6.t58 a0))
(step t1.t6.t60 (cl @p_41) :rule and_intro :premises (t1.t6.t23 t1.t6.t59))
(step t1.t6.t61 (cl @p_39) :rule resolution :premises (t1.t6.t19 t1.t6.t60))
(step t1.t6.t62 (cl (=> (! (and @p_40 @p_7) :named @p_76) @p_75)) :rule la_mult_neg)
(step t1.t6.t63 (cl (not @p_76) @p_75) :rule implies :premises (t1.t6.t62))
(step t1.t6.t64 (cl @p_76) :rule and_intro :premises (t1.t6.t23 t1.a0))
(step t1.t6.t65 (cl @p_75) :rule resolution :premises (t1.t6.t63 t1.t6.t64))
(step t1.t6.t66 (cl @p_74) :rule resolution :premises (t1.t6.t17 t1.t6.a0 t1.t6.t61 t1.t6.t65))
(step t1.t6.t67 (cl false) :rule resolution :premises (t1.t6.t0 t1.t6.t16 t1.t6.t66))
(step t1.t6 (cl @p_69 false) :rule subproof :discharge (t1.t6.a0))
(step t1.t7 (cl @p_70 false) :rule resolution :premises (t1.t5 t1.t6))
(step t1.t8 (cl @p_70 (! (not false) :named @p_33)) :rule implies_neg2)
(step t1.t9 (cl @p_70 @p_70) :rule resolution :premises (t1.t7 t1.t8))
(step t1.t10 (cl @p_70) :rule contraction :premises (t1.t9))
(step t1.t11 (cl (= @p_70 @p_69)) :rule implies_simplify)
(step t1.t12 (cl (not @p_70) @p_69) :rule equiv1 :premises (t1.t11))
(step t1.t13 (cl @p_69) :rule resolution :premises (t1.t10 t1.t12))
(step t1.t14 (cl) :rule resolution :premises (t1.t4 t1.t13))
(step t1 (cl @p_23 @p_17 @p_63 false) :rule subproof :discharge (t1.a0 t1.a1 t1.a2))
(step t2 (cl (! (not @p_64) :named @p_65) @p_7) :rule and_pos :args (0))
(step t3 (cl @p_65 @p_11) :rule and_pos :args (1))
(step t4 (cl @p_65 @p_54) :rule and_pos :args (2))
(step t5 (cl false @p_65 @p_65 @p_65) :rule resolution :premises (t1 t2 t3 t4))
(step t6 (cl @p_65 @p_65 @p_65 false) :rule reordering :premises (t5))
(step t7 (cl @p_65 false) :rule contraction :premises (t6))
(step t8 (cl @p_66 false) :rule resolution :premises (t0 t7))
(step t9 (cl @p_66 @p_33) :rule implies_neg2)
(step t10 (cl @p_66 @p_66) :rule resolution :premises (t8 t9))
(step t11 (cl @p_66) :rule contraction :premises (t10))
(step t12 (cl (= @p_66 @p_65)) :rule implies_simplify)
(step t13 (cl (not @p_66) @p_65) :rule equiv1 :premises (t12))
(step t14 (cl @p_65) :rule resolution :premises (t11 t13))
(step t15 (cl @p_23 @p_17 @p_63) :rule not_and :premises (t14))
(step t16 (cl (not (! (= (! (ite @p_7 (! (= @p_8 x$) :named @p_57) (! (= @p_8 y$) :named @p_56)) :named @p_58) (! (ite @p_7 @p_54 (! (= y$ @p_8) :named @p_28)) :named @p_55)) :named @p_61)) (! (not @p_58) :named @p_60) @p_55) :rule equiv_pos2)
(step t17 (cl (= (* 1 (- @p_8 x$)) (* -1 @p_62))) :rule poly_simp)
(step t18 (cl (= @p_57 @p_54)) :rule poly_simp_rel :premises (t17))
(step t19 (cl (= (* 1 (- @p_8 y$)) (* -1 (- y$ @p_8)))) :rule poly_simp)
(step t20 (cl (= @p_56 @p_28)) :rule poly_simp_rel :premises (t19))
(step t21 (cl @p_61) :rule cong :premises (t18 t20))
(step t22 (cl (not (! (= @p_58 @p_58) :named @p_59)) @p_60 @p_58) :rule equiv_pos2)
(step t23 (cl (= @p_14 @p_13)) :rule equiv_simplify)
(step t24 (cl (not @p_14) @p_13) :rule equiv1 :premises (t23))
(step t25 (cl (= (* -1 @p_16) (* 1 @p_16))) :rule poly_simp)
(step t26 (cl @p_15) :rule poly_simp_rel :premises (t25))
(step t27 (cl @p_13) :rule refl)
(step t28 (cl @p_13) :rule refl)
(step t29 (cl @p_15) :rule cong :premises (t27 t28))
(step t30 (cl @p_14) :rule rare_rewrite :args ("eq-refl" @p_8))
(step t31 (cl @p_14) :rule trans :premises (t26 t29 t30))
(step t32 (cl @p_13) :rule resolution :premises (t24 t31))
(step t33 (cl (= x$ x$)) :rule refl)
(step t34 (cl (= @p_57 @p_57)) :rule cong :premises (t32 t33))
(step t35 (cl (= y$ y$)) :rule refl)
(step t36 (cl (= @p_56 @p_56)) :rule cong :premises (t32 t35))
(step t37 (cl @p_59) :rule cong :premises (t34 t36))
(step t38 (cl (= @p_58 true)) :rule rare_rewrite :args ("ite-eq" @p_7 x$ y$))
(step t39 (cl @p_58 (not true)) :rule equiv2 :premises (t38))
(step t40 (cl true) :rule true)
(step t41 (cl @p_58) :rule resolution :premises (t39 t40))
(step t42 (cl @p_58) :rule resolution :premises (t22 t37 t41))
(step t43 (cl @p_55) :rule resolution :premises (t16 t21 t42))
(step t44 (cl @p_23 @p_54) :rule ite2 :premises (t43))
(step t45 (cl @p_7 @p_28) :rule ite1 :premises (t43))
(step t46 (cl (! (=> @p_11 (! (not @p_28) :named @p_29)) :named @p_30) @p_11) :rule implies_neg1)
(anchor :step t47)
(assume t47.a0 @p_11)
(step t47.t0 (cl @p_30 @p_11) :rule implies_neg1)
(anchor :step t47.t1)
(assume t47.t1.a0 @p_11)
(step t47.t1.t0 (cl (! (=> @p_28 false) :named @p_32) @p_28) :rule implies_neg1)
(anchor :step t47.t1.t1)
(assume t47.t1.t1.a0 @p_28)
(step t47.t1.t1.t0 (cl (not (! (= (! (<= (! (+ y$ @p_36) :named @p_37) (! (+ @p_8 @p_34) :named @p_35)) :named @p_38) false) :named @p_44)) (not @p_38) false) :rule equiv_pos2)
(step t47.t1.t1.t1 (cl (= @p_36 (! (+ @p_5 @p_8) :named @p_52))) :rule poly_simp)
(step t47.t1.t1.t2 (cl (= @p_37 (! (+ y$ @p_52) :named @p_53))) :rule cong :premises (t47.t1.t1.t1))
(step t47.t1.t1.t3 (cl (= @p_53 @p_8)) :rule poly_simp)
(step t47.t1.t1.t4 (cl (= @p_37 @p_8)) :rule trans :premises (t47.t1.t1.t2 t47.t1.t1.t3))
(step t47.t1.t1.t5 (cl (= @p_34 -1)) :rule evaluate)
(step t47.t1.t1.t6 (cl (= @p_35 (! (+ @p_8 -1) :named @p_51))) :rule cong :premises (t47.t1.t1.t5))
(step t47.t1.t1.t7 (cl (= @p_51 (! (+ -1 @p_8) :named @p_45))) :rule poly_simp)
(step t47.t1.t1.t8 (cl (= @p_35 @p_45)) :rule trans :premises (t47.t1.t1.t6 t47.t1.t1.t7))
(step t47.t1.t1.t9 (cl (= @p_38 (! (<= @p_8 @p_45) :named @p_46))) :rule cong :premises (t47.t1.t1.t4 t47.t1.t1.t8))
(step t47.t1.t1.t10 (cl (= @p_46 (! (>= @p_45 @p_8) :named @p_47))) :rule rare_rewrite :args ("arith-elim-leq" @p_8 @p_45))
(step t47.t1.t1.t11 (cl (= @p_47 (! (>= (! (- @p_45 @p_8) :named @p_48) 0) :named @p_49))) :rule rare_rewrite :args ("arith-geq-norm1-int" @p_45 @p_8))
(step t47.t1.t1.t12 (cl (= @p_48 -1)) :rule poly_simp)
(step t47.t1.t1.t13 (cl (= 0 0)) :rule refl)
(step t47.t1.t1.t14 (cl (= @p_49 (! (>= -1 0) :named @p_50))) :rule cong :premises (t47.t1.t1.t12 t47.t1.t1.t13))
(step t47.t1.t1.t15 (cl (= @p_50 false)) :rule evaluate)
(step t47.t1.t1.t16 (cl (= @p_49 false)) :rule trans :premises (t47.t1.t1.t14 t47.t1.t1.t15))
(step t47.t1.t1.t17 (cl (= @p_47 false)) :rule trans :premises (t47.t1.t1.t11 t47.t1.t1.t16))
(step t47.t1.t1.t18 (cl (= @p_46 false)) :rule trans :premises (t47.t1.t1.t10 t47.t1.t1.t17))
(step t47.t1.t1.t19 (cl @p_44) :rule trans :premises (t47.t1.t1.t9 t47.t1.t1.t18))
(step t47.t1.t1.t20 (cl @p_29 @p_43 @p_38) :rule la_generic :args (-1/1 1/1 1/1))
(step t47.t1.t1.t21 (cl (=> @p_41 @p_39)) :rule la_mult_neg)
(step t47.t1.t1.t22 (cl (not @p_41) @p_39) :rule implies :premises (t47.t1.t1.t21))
(step t47.t1.t1.t23 (cl (= @p_42 @p_40)) :rule equiv_simplify)
(step t47.t1.t1.t24 (cl (not @p_42) @p_40) :rule equiv1 :premises (t47.t1.t1.t23))
(step t47.t1.t1.t25 (cl @p_42) :rule evaluate)
(step t47.t1.t1.t26 (cl @p_40) :rule resolution :premises (t47.t1.t1.t24 t47.t1.t1.t25))
(step t47.t1.t1.t27 (cl (not @p_12) (not @p_4) @p_11) :rule equiv_pos2)
(step t47.t1.t1.t28 (cl (= @p_1 @p_27)) :rule rare_rewrite :args ("arith-leq-norm" x$ y$))
(step t47.t1.t1.t29 (cl (= (* -1 (- x$ @p_25)) (* -1 (- @p_6 1)))) :rule poly_simp)
(step t47.t1.t1.t30 (cl (= @p_26 @p_7)) :rule poly_simp_rel :premises (t47.t1.t1.t29))
(step t47.t1.t1.t31 (cl (= @p_27 @p_23)) :rule cong :premises (t47.t1.t1.t30))
(step t47.t1.t1.t32 (cl (= @p_1 @p_23)) :rule trans :premises (t47.t1.t1.t28 t47.t1.t1.t31))
(step t47.t1.t1.t33 (cl (= @p_2 @p_24)) :rule cong :premises (t47.t1.t1.t32 t35 t33))
(step t47.t1.t1.t34 (cl (= @p_24 @p_8)) :rule rare_rewrite :args ("ite-not-cond" @p_7 y$ x$))
(step t47.t1.t1.t35 (cl (= @p_2 @p_8)) :rule trans :premises (t47.t1.t1.t33 t47.t1.t1.t34))
(step t47.t1.t1.t36 (cl (= @p_3 @p_19)) :rule cong :premises (t47.t1.t1.t35))
(step t47.t1.t1.t37 (cl (= @p_19 @p_22)) :rule rare_rewrite :args ("arith-leq-norm" y$ @p_8))
(step t47.t1.t1.t38 (cl (= (* -1 (- y$ @p_20)) (* -1 (- @p_10 1)))) :rule poly_simp)
(step t47.t1.t1.t39 (cl (= @p_21 @p_11)) :rule poly_simp_rel :premises (t47.t1.t1.t38))
(step t47.t1.t1.t40 (cl (= @p_22 @p_17)) :rule cong :premises (t47.t1.t1.t39))
(step t47.t1.t1.t41 (cl (= @p_19 @p_17)) :rule trans :premises (t47.t1.t1.t37 t47.t1.t1.t40))
(step t47.t1.t1.t42 (cl (= @p_3 @p_17)) :rule trans :premises (t47.t1.t1.t36 t47.t1.t1.t41))
(step t47.t1.t1.t43 (cl (= @p_4 @p_18)) :rule cong :premises (t47.t1.t1.t42))
(step t47.t1.t1.t44 (cl (= @p_18 @p_11)) :rule rare_rewrite :args ("bool-double-not-elim" @p_11))
(step t47.t1.t1.t45 (cl @p_12) :rule trans :premises (t47.t1.t1.t43 t47.t1.t1.t44))
(step t47.t1.t1.t46 (cl (= @p_9 @p_9)) :rule cong :premises (t32))
(step t47.t1.t1.t47 (cl (= @p_10 @p_10)) :rule cong :premises (t47.t1.t1.t46))
(step t47.t1.t1.t48 (cl (= 1 1)) :rule refl)
(step t47.t1.t1.t49 (cl (= @p_11 @p_11)) :rule cong :premises (t47.t1.t1.t47 t47.t1.t1.t48))
(step t47.t1.t1.t50 (cl @p_12) :rule trans :premises (t47.t1.t1.t45 t47.t1.t1.t49))
(step t47.t1.t1.t51 (cl @p_11) :rule resolution :premises (t47.t1.t1.t27 t47.t1.t1.t50 a0))
(step t47.t1.t1.t52 (cl @p_41) :rule and_intro :premises (t47.t1.t1.t26 t47.t1.t1.t51))
(step t47.t1.t1.t53 (cl @p_39) :rule resolution :premises (t47.t1.t1.t22 t47.t1.t1.t52))
(step t47.t1.t1.t54 (cl @p_38) :rule resolution :premises (t47.t1.t1.t20 t47.t1.t1.a0 t47.t1.t1.t53))
(step t47.t1.t1.t55 (cl false) :rule resolution :premises (t47.t1.t1.t0 t47.t1.t1.t19 t47.t1.t1.t54))
(step t47.t1.t1 (cl @p_29 false) :rule subproof :discharge (t47.t1.t1.a0))
(step t47.t1.t2 (cl @p_32 false) :rule resolution :premises (t47.t1.t0 t47.t1.t1))
(step t47.t1.t3 (cl @p_32 @p_33) :rule implies_neg2)
(step t47.t1.t4 (cl @p_32 @p_32) :rule resolution :premises (t47.t1.t2 t47.t1.t3))
(step t47.t1.t5 (cl @p_32) :rule contraction :premises (t47.t1.t4))
(step t47.t1.t6 (cl (= @p_32 @p_29)) :rule implies_simplify)
(step t47.t1.t7 (cl (not @p_32) @p_29) :rule equiv1 :premises (t47.t1.t6))
(step t47.t1.t8 (cl @p_29) :rule resolution :premises (t47.t1.t5 t47.t1.t7))
(step t47.t1 (cl @p_17 @p_29) :rule subproof :discharge (t47.t1.a0))
(step t47.t2 (cl @p_30 @p_29) :rule resolution :premises (t47.t0 t47.t1))
(step t47.t3 (cl @p_30 (! (not @p_29) :named @p_31)) :rule implies_neg2)
(step t47.t4 (cl @p_30 @p_30) :rule resolution :premises (t47.t2 t47.t3))
(step t47.t5 (cl @p_30) :rule contraction :premises (t47.t4))
(step t47.t6 (cl @p_17 @p_29) :rule implies :premises (t47.t5))
(step t47.t7 (cl (not @p_12) (not @p_4) @p_11) :rule equiv_pos2)
(step t47.t8 (cl (= @p_1 @p_27)) :rule rare_rewrite :args ("arith-leq-norm" x$ y$))
(step t47.t9 (cl (= (* -1 (- x$ @p_25)) (* -1 (- @p_6 1)))) :rule poly_simp)
(step t47.t10 (cl (= @p_26 @p_7)) :rule poly_simp_rel :premises (t47.t9))
(step t47.t11 (cl (= @p_27 @p_23)) :rule cong :premises (t47.t10))
(step t47.t12 (cl (= @p_1 @p_23)) :rule trans :premises (t47.t8 t47.t11))
(step t47.t13 (cl (= @p_2 @p_24)) :rule cong :premises (t47.t12 t35 t33))
(step t47.t14 (cl (= @p_24 @p_8)) :rule rare_rewrite :args ("ite-not-cond" @p_7 y$ x$))
(step t47.t15 (cl (= @p_2 @p_8)) :rule trans :premises (t47.t13 t47.t14))
(step t47.t16 (cl (= @p_3 @p_19)) :rule cong :premises (t47.t15))
(step t47.t17 (cl (= @p_19 @p_22)) :rule rare_rewrite :args ("arith-leq-norm" y$ @p_8))
(step t47.t18 (cl (= (* -1 (- y$ @p_20)) (* -1 (- @p_10 1)))) :rule poly_simp)
(step t47.t19 (cl (= @p_21 @p_11)) :rule poly_simp_rel :premises (t47.t18))
(step t47.t20 (cl (= @p_22 @p_17)) :rule cong :premises (t47.t19))
(step t47.t21 (cl (= @p_19 @p_17)) :rule trans :premises (t47.t17 t47.t20))
(step t47.t22 (cl (= @p_3 @p_17)) :rule trans :premises (t47.t16 t47.t21))
(step t47.t23 (cl (= @p_4 @p_18)) :rule cong :premises (t47.t22))
(step t47.t24 (cl (= @p_18 @p_11)) :rule rare_rewrite :args ("bool-double-not-elim" @p_11))
(step t47.t25 (cl @p_12) :rule trans :premises (t47.t23 t47.t24))
(step t47.t26 (cl (= @p_9 @p_9)) :rule cong :premises (t32))
(step t47.t27 (cl (= @p_10 @p_10)) :rule cong :premises (t47.t26))
(step t47.t28 (cl (= 1 1)) :rule refl)
(step t47.t29 (cl (= @p_11 @p_11)) :rule cong :premises (t47.t27 t47.t28))
(step t47.t30 (cl @p_12) :rule trans :premises (t47.t25 t47.t29))
(step t47.t31 (cl @p_11) :rule resolution :premises (t47.t7 t47.t30 a0))
(step t47.t32 (cl @p_29) :rule resolution :premises (t47.t6 t47.t31))
(step t47 (cl @p_17 @p_29) :rule subproof :discharge (t47.a0))
(step t48 (cl @p_30 @p_29) :rule resolution :premises (t46 t47))
(step t49 (cl @p_30 @p_31) :rule implies_neg2)
(step t50 (cl @p_30 @p_30) :rule resolution :premises (t48 t49))
(step t51 (cl @p_30) :rule contraction :premises (t50))
(step t52 (cl @p_17 @p_29) :rule implies :premises (t51))
(step t53 (cl (not @p_12) (not @p_4) @p_11) :rule equiv_pos2)
(step t54 (cl (= @p_1 @p_27)) :rule rare_rewrite :args ("arith-leq-norm" x$ y$))
(step t55 (cl (= (* -1 (- x$ @p_25)) (* -1 (- @p_6 1)))) :rule poly_simp)
(step t56 (cl (= @p_26 @p_7)) :rule poly_simp_rel :premises (t55))
(step t57 (cl (= @p_27 @p_23)) :rule cong :premises (t56))
(step t58 (cl (= @p_1 @p_23)) :rule trans :premises (t54 t57))
(step t59 (cl (= @p_2 @p_24)) :rule cong :premises (t58 t35 t33))
(step t60 (cl (= @p_24 @p_8)) :rule rare_rewrite :args ("ite-not-cond" @p_7 y$ x$))
(step t61 (cl (= @p_2 @p_8)) :rule trans :premises (t59 t60))
(step t62 (cl (= @p_3 @p_19)) :rule cong :premises (t61))
(step t63 (cl (= @p_19 @p_22)) :rule rare_rewrite :args ("arith-leq-norm" y$ @p_8))
(step t64 (cl (= (* -1 (- y$ @p_20)) (* -1 (- @p_10 1)))) :rule poly_simp)
(step t65 (cl (= @p_21 @p_11)) :rule poly_simp_rel :premises (t64))
(step t66 (cl (= @p_22 @p_17)) :rule cong :premises (t65))
(step t67 (cl (= @p_19 @p_17)) :rule trans :premises (t63 t66))
(step t68 (cl (= @p_3 @p_17)) :rule trans :premises (t62 t67))
(step t69 (cl (= @p_4 @p_18)) :rule cong :premises (t68))
(step t70 (cl (= @p_18 @p_11)) :rule rare_rewrite :args ("bool-double-not-elim" @p_11))
(step t71 (cl @p_12) :rule trans :premises (t69 t70))
(step t72 (cl (= @p_9 @p_9)) :rule cong :premises (t32))
(step t73 (cl (= @p_10 @p_10)) :rule cong :premises (t72))
(step t74 (cl (= 1 1)) :rule refl)
(step t75 (cl (= @p_11 @p_11)) :rule cong :premises (t73 t74))
(step t76 (cl @p_12) :rule trans :premises (t71 t75))
(step t77 (cl @p_11) :rule resolution :premises (t53 t76 a0))
(step t78 (cl @p_29) :rule resolution :premises (t52 t77))
(step t79 (cl @p_7) :rule resolution :premises (t45 t78))
(step t80 (cl @p_54) :rule resolution :premises (t44 t79))
(step t81 (cl) :rule resolution :premises (t15 t80 t79 t77))
)
cfe5008698bd36b58a9f74dd8b585bd55b1514f8 364 0
unsat
(
(define-fun @quantifiers_skolemize_3 () A$ (choice ((?v3 A$)) (not (or (not (= (arg_min_on$ f$ (image$b g$ b$)) (fun_app$b g$ ?v3))) (not (member$a ?v3 b$))))))
(assume a0 (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= ?v0 bot$))) (member$ (arg_min_on$ ?v1 ?v0) ?v0))))
(assume a2 (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (and (not (= ?v0 bot$)) (member$ ?v1 ?v0))) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))))
(assume a4 (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (= (fun_app$a (comp$ ?v0 ?v1) ?v2) (fun_app$ ?v0 (fun_app$b ?v1 ?v2)))))
(assume a7 (forall ((?v0 A_set$) (?v1 A_b_fun$)) (=> (finite$a ?v0) (finite$ (image$b ?v1 ?v0)))))
(assume a11 (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (=> (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false))) false)))
(assume a15 (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v2)) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))
(assume a19 (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= (image$b ?v0 ?v1) bot$) (= ?v1 bot$a))))
(assume a21 (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (and (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (and (member$ ?v2 ?v1) (member$ ?v3 ?v1)))) (= ?v2 ?v3))))
(assume a22 (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1))))))
(assume a23 (! (inj_on$ f$ (! (image$b g$ b$) :named @p_1)) :named @p_2))
(assume a24 (! (finite$a b$) :named @p_3))
(assume a25 (! (not (! (= b$ bot$a) :named @p_4)) :named @p_5))
(assume a26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_6) b$) :named @p_7) b$) :named @p_8))
(assume a27 (! (not (exists ((?v0 A$)) (and (member$a ?v0 b$) (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$)))))) :named @p_9))
(assume a52 (! (not (! (= (! (arg_min_on$ f$ @p_1) :named @p_11) (! (fun_app$b g$ @p_7) :named @p_10)) :named @p_12)) :named @p_13))
(step t0 (cl (not (! (= (! (or (! (and (! (less_eq$ (! (fun_app$a @p_6 @quantifiers_skolemize_3) :named @p_14) (! (fun_app$a @p_6 @p_7) :named @p_15)) :named @p_18) (! (not (! (= @p_15 @p_14) :named @p_16)) :named @p_17)) :named @p_19) (! (not @p_18) :named @p_242) (! (not @p_17) :named @p_244)) :named @p_245) (! (or @p_19 @p_242 @p_16) :named @p_243)) :named @p_246)) (not @p_245) @p_243) :rule equiv_pos2)
(step t1 (cl (= @p_244 @p_16)) :rule rare_rewrite :args ("bool-double-not-elim" @p_16))
(step t2 (cl @p_246) :rule cong :premises (t1))
(step t3 (cl @p_19 @p_242 @p_244) :rule and_neg)
(step t4 (cl @p_245 (! (not @p_19) :named @p_20)) :rule or_neg :args (0))
(step t5 (cl @p_245 (not @p_242)) :rule or_neg :args (1))
(step t6 (cl @p_245 (not @p_244)) :rule or_neg :args (2))
(step t7 (cl @p_245 @p_245 @p_245) :rule resolution :premises (t3 t4 t5 t6))
(step t8 (cl @p_245) :rule contraction :premises (t7))
(step t9 (cl @p_243) :rule resolution :premises (t0 t2 t8))
(step t10 (cl @p_19 @p_242 @p_16) :rule or :premises (t9))
(step t11 (cl @p_16 @p_19 @p_242) :rule reordering :premises (t10))
(step t12 (cl (= (! (= @p_16 false) :named @p_199) @p_17)) :rule equiv_simplify)
(step t13 (cl (not @p_199) @p_17) :rule equiv1 :premises (t12))
(step t14 (cl (or (! (not (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (= (fun_app$a (comp$ ?v0 ?v1) ?v2) (fun_app$ ?v0 (fun_app$b ?v1 ?v2))))) :named @p_192) (! (= @p_15 (! (fun_app$ f$ @p_10) :named @p_125)) :named @p_191))) :rule forall_inst :args (f$ g$ @p_7))
(step t15 (cl @p_192 @p_191) :rule or :premises (t14))
(step t16 (cl @p_191) :rule resolution :premises (t15 a4))
(step t17 (cl (or @p_192 (! (= @p_14 (! (fun_app$ f$ (! (fun_app$b g$ @quantifiers_skolemize_3) :named @p_41)) :named @p_193)) :named @p_198))) :rule forall_inst :args (f$ g$ @quantifiers_skolemize_3))
(step t18 (cl @p_192 @p_198) :rule or :premises (t17))
(step t19 (cl @p_198) :rule resolution :premises (t18 a4))
(step t20 (cl (not (! (= (! (or (! (or (! (not (! (= @p_11 @p_41) :named @p_42)) :named @p_43) (! (not (! (member$a @quantifiers_skolemize_3 b$) :named @p_32)) :named @p_33)) :named @p_44) (! (not @p_43) :named @p_195)) :named @p_196) (! (or @p_44 @p_42) :named @p_194)) :named @p_197)) (not @p_196) @p_194) :rule equiv_pos2)
(step t21 (cl (= @p_195 @p_42)) :rule rare_rewrite :args ("bool-double-not-elim" @p_42))
(step t22 (cl @p_197) :rule cong :premises (t21))
(step t23 (cl @p_44 @p_195) :rule or_neg :args (0))
(step t24 (cl @p_196 (! (not @p_44) :named @p_45)) :rule or_neg :args (0))
(step t25 (cl @p_196 (not @p_195)) :rule or_neg :args (1))
(step t26 (cl @p_196 @p_196) :rule resolution :premises (t23 t24 t25))
(step t27 (cl @p_196) :rule contraction :premises (t26))
(step t28 (cl @p_194) :rule resolution :premises (t20 t22 t27))
(step t29 (cl @p_44 @p_42) :rule or :premises (t28))
(step t30 (cl @p_42 @p_44) :rule reordering :premises (t29))
(step t31 (cl (not (! (= (! (not (forall ((?v3 A$)) (or (not (= (arg_min_on$ f$ (image$b g$ b$)) (fun_app$b g$ ?v3))) (not (member$a ?v3 b$))))) :named @p_46) @p_45) :named @p_117)) (not @p_46) @p_45) :rule equiv_pos2)
(anchor :step t32 :args ((:= (?v3 A$) @quantifiers_skolemize_3)))
(step t32.t0 (cl (= (or (not (= @p_11 (fun_app$b g$ ?v3))) (not (member$a ?v3 b$))) @p_44)) :rule refl)
(step t32 (cl (= (forall ((?v3 A$)) (or (not (= (arg_min_on$ f$ (image$b g$ b$)) (fun_app$b g$ ?v3))) (not (member$a ?v3 b$)))) @p_44)) :rule sko_forall)
(step t33 (cl @p_117) :rule cong :premises (t32))
(step t34 (cl (! (not (! (or (! (not (! (member$ @p_11 @p_1) :named @p_47)) :named @p_48) @p_46) :named @p_49)) :named @p_116) @p_48 @p_46) :rule or_pos)
(step t35 (cl @p_48 @p_46 @p_116) :rule reordering :premises (t34))
(step t36 (cl (! (not (! (or (! (not (! (finite$ @p_1) :named @p_67)) :named @p_68) (! (= bot$ @p_1) :named @p_66) @p_47) :named @p_69)) :named @p_115) @p_68 @p_66 @p_47) :rule or_pos)
(step t37 (cl @p_68 @p_66 @p_47 @p_115) :rule reordering :premises (t36))
(step t38 (cl (! (not (! (or (! (not @p_3) :named @p_108) @p_67) :named @p_109)) :named @p_114) @p_108 @p_67) :rule or_pos)
(step t39 (cl @p_108 @p_67 @p_114) :rule reordering :premises (t38))
(step t40 (cl (or (! (not (forall ((?v0 A_set$) (?v1 A_b_fun$)) (or (not (finite$a ?v0)) (finite$ (image$b ?v1 ?v0))))) :named @p_113) @p_109)) :rule forall_inst :args (b$ g$))
(step t41 (cl @p_113 @p_109) :rule or :premises (t40))
(step t42 (cl (not (! (= (forall ((?v0 A_set$) (?v1 A_b_fun$)) (=> (finite$a ?v0) (finite$ (image$b ?v1 ?v0)))) (forall ((?v0 A_set$) (?v1 A_b_fun$)) (or (not (finite$a ?v0)) (finite$ (image$b ?v1 ?v0))))) :named @p_110)) (not (forall ((?v0 A_set$) (?v1 A_b_fun$)) (=> (finite$a ?v0) (finite$ (image$b ?v1 ?v0))))) (forall ((?v0 A_set$) (?v1 A_b_fun$)) (or (not (finite$a ?v0)) (finite$ (image$b ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t43 :args ((?v0 A_set$) (?v1 A_b_fun$) (:= (?v0 A_set$) ?v0) (:= (?v1 A_b_fun$) ?v1)))
(step t43.t0 (cl (= (=> (! (finite$a ?v0) :named @p_112) (! (finite$ (image$b ?v1 ?v0)) :named @p_111)) (or (not @p_112) @p_111))) :rule rare_rewrite :args ("bool-impl-elim" @p_112 @p_111))
(step t43 (cl @p_110) :rule bind)
(step t44 (cl (forall ((?v0 A_set$) (?v1 A_b_fun$)) (or (not (finite$a ?v0)) (finite$ (image$b ?v1 ?v0))))) :rule resolution :premises (t42 t43 a7))
(step t45 (cl @p_109) :rule resolution :premises (t41 t44))
(step t46 (cl @p_67) :rule resolution :premises (t39 a24 t45))
(step t47 (cl (! (not (! (= @p_4 @p_66) :named @p_93)) :named @p_107) @p_4 (! (not @p_66) :named @p_92)) :rule equiv_pos1)
(step t48 (cl @p_4 @p_92 @p_107) :rule reordering :premises (t47))
(step t49 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1))) (! (= @p_66 (! (= bot$a b$) :named @p_102)) :named @p_103)) :named @p_104) (! (=> (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1))) @p_93) :named @p_101)) :named @p_105)) (not @p_104) @p_101) :rule equiv_pos2)
(step t50 (cl (= @p_102 @p_4)) :rule rare_rewrite :args ("eq-symm" bot$a b$))
(step t51 (cl (= @p_103 (! (= @p_66 @p_4) :named @p_106))) :rule cong :premises (t50))
(step t52 (cl (= @p_106 @p_93)) :rule rare_rewrite :args ("eq-symm" @p_66 @p_4))
(step t53 (cl (= @p_103 @p_93)) :rule trans :premises (t51 t52))
(step t54 (cl @p_105) :rule cong :premises (t53))
(step t55 (cl @p_104 (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :rule implies_neg1)
(anchor :step t56)
(assume t56.a0 (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1))))
(step t56.t0 (cl (or (! (not (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :named @p_100) @p_103)) :rule forall_inst :args (g$ b$))
(step t56.t1 (cl @p_100 @p_103) :rule or :premises (t56.t0))
(step t56.t2 (cl (not (! (= (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= (image$b ?v0 ?v1) bot$) (= ?v1 bot$a))) (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :named @p_94)) (not (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= (image$b ?v0 ?v1) bot$) (= ?v1 bot$a)))) (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :rule equiv_pos2)
(anchor :step t56.t3 :args ((?v0 A_b_fun$) (?v1 A_set$) (:= (?v0 A_b_fun$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t56.t3.t0 (cl (= (! (= (! (image$b ?v0 ?v1) :named @p_96) bot$) :named @p_99) (! (= bot$ @p_96) :named @p_97))) :rule rare_rewrite :args ("eq-symm" @p_96 bot$))
(step t56.t3.t1 (cl (= (! (= ?v1 bot$a) :named @p_98) (! (= bot$a ?v1) :named @p_95))) :rule rare_rewrite :args ("eq-symm" ?v1 bot$a))
(step t56.t3.t2 (cl (= (= @p_99 @p_98) (= @p_97 @p_95))) :rule cong :premises (t56.t3.t0 t56.t3.t1))
(step t56.t3 (cl @p_94) :rule bind)
(step t56.t4 (cl (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :rule resolution :premises (t56.t2 t56.t3 a19))
(step t56.t5 (cl @p_103) :rule resolution :premises (t56.t1 t56.t4))
(step t56 (cl @p_100 @p_103) :rule subproof :discharge (t56.a0))
(step t57 (cl @p_104 @p_103) :rule resolution :premises (t55 t56))
(step t58 (cl @p_104 (not @p_103)) :rule implies_neg2)
(step t59 (cl @p_104 @p_104) :rule resolution :premises (t57 t58))
(step t60 (cl @p_104) :rule contraction :premises (t59))
(step t61 (cl @p_101) :rule resolution :premises (t49 t54 t60))
(step t62 (cl @p_100 @p_93) :rule implies :premises (t61))
(step t63 (cl (not @p_94) (not (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= (image$b ?v0 ?v1) bot$) (= ?v1 bot$a)))) (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :rule equiv_pos2)
(anchor :step t64 :args ((?v0 A_b_fun$) (?v1 A_set$) (:= (?v0 A_b_fun$) ?v0) (:= (?v1 A_set$) ?v1)))
(step t64.t0 (cl (= @p_99 @p_97)) :rule rare_rewrite :args ("eq-symm" @p_96 bot$))
(step t64.t1 (cl (= @p_98 @p_95)) :rule rare_rewrite :args ("eq-symm" ?v1 bot$a))
(step t64.t2 (cl (= (= @p_99 @p_98) (= @p_97 @p_95))) :rule cong :premises (t64.t0 t64.t1))
(step t64 (cl @p_94) :rule bind)
(step t65 (cl (forall ((?v0 A_b_fun$) (?v1 A_set$)) (= (= bot$ (image$b ?v0 ?v1)) (= bot$a ?v1)))) :rule resolution :premises (t63 t64 a19))
(step t66 (cl @p_93) :rule resolution :premises (t62 t65))
(step t67 (cl @p_92) :rule resolution :premises (t48 a25 t66))
(step t68 (cl (or (! (not (forall ((?v0 B_set$) (?v1 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (member$ (arg_min_on$ ?v1 ?v0) ?v0)))) :named @p_91) @p_69)) :rule forall_inst :args (@p_1 f$))
(step t69 (cl @p_91 @p_69) :rule or :premises (t68))
(step t70 (cl (not (! (= (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= ?v0 bot$))) (member$ (arg_min_on$ ?v1 ?v0) ?v0))) (forall ((?v0 B_set$) (?v1 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (member$ (arg_min_on$ ?v1 ?v0) ?v0)))) :named @p_70)) (not (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= ?v0 bot$))) (member$ (arg_min_on$ ?v1 ?v0) ?v0)))) (forall ((?v0 B_set$) (?v1 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (member$ (arg_min_on$ ?v1 ?v0) ?v0)))) :rule equiv_pos2)
(anchor :step t71 :args ((?v0 B_set$) (?v1 B_c_fun$) (:= (?v0 B_set$) ?v0) (:= (?v1 B_c_fun$) ?v1)))
(step t71.t0 (cl (= (! (= ?v0 bot$) :named @p_88) (! (= bot$ ?v0) :named @p_74))) :rule rare_rewrite :args ("eq-symm" ?v0 bot$))
(step t71.t1 (cl (= (! (not @p_88) :named @p_89) (! (not @p_74) :named @p_78))) :rule cong :premises (t71.t0))
(step t71.t2 (cl (= (! (and (! (finite$ ?v0) :named @p_75) @p_89) :named @p_90) (! (and @p_75 @p_78) :named @p_79))) :rule cong :premises (t71.t1))
(step t71.t3 (cl (! (= (! (member$ (arg_min_on$ ?v1 ?v0) ?v0) :named @p_73) @p_73) :named @p_85)) :rule refl)
(step t71.t4 (cl (= (=> @p_90 @p_73) (! (=> @p_79 @p_73) :named @p_80))) :rule cong :premises (t71.t2 t71.t3))
(step t71 (cl (= (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= ?v0 bot$))) (member$ (arg_min_on$ ?v1 ?v0) ?v0))) (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= bot$ ?v0))) (member$ (arg_min_on$ ?v1 ?v0) ?v0))))) :rule bind)
(anchor :step t72 :args ((?v0 B_set$) (?v1 B_c_fun$) (:= (?v0 B_set$) ?v0) (:= (?v1 B_c_fun$) ?v1)))
(step t72.t0 (cl (= @p_80 (! (or (! (not @p_79) :named @p_81) @p_73) :named @p_82))) :rule rare_rewrite :args ("bool-impl-elim" @p_79 @p_73))
(step t72.t1 (cl (= @p_81 (! (or (! (not @p_75) :named @p_76) (! (not @p_78) :named @p_86)) :named @p_87))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_75 @p_78 rare-list))
(step t72.t2 (cl (= @p_86 @p_74)) :rule rare_rewrite :args ("bool-double-not-elim" @p_74))
(step t72.t3 (cl (= @p_87 (! (or @p_76 @p_74) :named @p_83))) :rule cong :premises (t72.t2))
(step t72.t4 (cl (= @p_81 @p_83)) :rule trans :premises (t72.t1 t72.t3))
(step t72.t5 (cl @p_85) :rule refl)
(step t72.t6 (cl (= @p_82 (! (or @p_83 @p_73) :named @p_84))) :rule cong :premises (t72.t4 t72.t5))
(step t72.t7 (cl (= @p_84 (! (or @p_76 @p_74 @p_73) :named @p_77))) :rule aci_simp)
(step t72.t8 (cl (= @p_82 @p_77)) :rule trans :premises (t72.t6 t72.t7))
(step t72.t9 (cl (= @p_80 @p_77)) :rule trans :premises (t72.t0 t72.t8))
(step t72 (cl (= (forall ((?v0 B_set$) (?v1 B_c_fun$)) (=> (and (finite$ ?v0) (not (= bot$ ?v0))) (member$ (arg_min_on$ ?v1 ?v0) ?v0))) (forall ((?v0 B_set$) (?v1 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (member$ (arg_min_on$ ?v1 ?v0) ?v0))))) :rule bind)
(step t73 (cl @p_70) :rule trans :premises (t71 t72))
(step t74 (cl (forall ((?v0 B_set$) (?v1 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (member$ (arg_min_on$ ?v1 ?v0) ?v0)))) :rule resolution :premises (t70 t73 a0))
(step t75 (cl @p_69) :rule resolution :premises (t69 t74))
(step t76 (cl @p_47) :rule resolution :premises (t37 t46 t67 t75))
(step t77 (cl (or (! (not (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (or (not (member$ ?v0 (image$b ?v1 ?v2))) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))))) :named @p_65) @p_49)) :rule forall_inst :args (@p_11 g$ b$))
(step t78 (cl @p_65 @p_49) :rule or :premises (t77))
(step t79 (cl (not (! (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (=> (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false))) false)) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (or (not (member$ ?v0 (image$b ?v1 ?v2))) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))))) :named @p_50)) (not (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (=> (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false))) false))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (or (not (member$ ?v0 (image$b ?v1 ?v2))) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))))) :rule equiv_pos2)
(anchor :step t80 :args ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$) (:= (?v0 B$) ?v0) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A_set$) ?v2)))
(step t80.t0 (cl (= (! (=> (! (and (! (member$ ?v0 (image$b ?v1 ?v2)) :named @p_54) (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false))) :named @p_57) false) :named @p_58) (! (not @p_57) :named @p_59))) :rule rare_rewrite :args ("bool-impl-false1" @p_57))
(anchor :step t80.t1 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t80.t1.t0 (cl (= (=> (! (and (! (= ?v0 (fun_app$b ?v1 ?v3)) :named @p_62) (! (member$a ?v3 ?v2) :named @p_61)) :named @p_63) false) (! (not @p_63) :named @p_64))) :rule rare_rewrite :args ("bool-impl-false1" @p_63))
(step t80.t1 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false)) (forall ((?v3 A$)) (not (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)))))) :rule bind)
(anchor :step t80.t2 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t80.t2.t0 (cl (= @p_64 (or (not @p_62) (not @p_61)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_62 @p_61 rare-list))
(step t80.t2 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)))) (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))) :rule bind)
(step t80.t3 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false)) (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))) :rule trans :premises (t80.t1 t80.t2))
(step t80.t4 (cl (= @p_57 (! (and @p_54 (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2))))) :named @p_55))) :rule cong :premises (t80.t3))
(step t80.t5 (cl (= @p_59 (! (not @p_55) :named @p_56))) :rule cong :premises (t80.t4))
(step t80.t6 (cl (= @p_58 @p_56)) :rule trans :premises (t80.t0 t80.t5))
(step t80 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (=> (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v3)) (member$a ?v3 ?v2)) false))) false)) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (not (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2))))))))) :rule bind)
(anchor :step t81 :args ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$) (:= (?v0 B$) ?v0) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A_set$) ?v2)))
(step t81.t0 (cl (= @p_56 (or (not @p_54) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_54 (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))) rare-list))
(step t81 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (not (and (member$ ?v0 (image$b ?v1 ?v2)) (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2))))))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (or (not (member$ ?v0 (image$b ?v1 ?v2))) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2))))))))) :rule bind)
(step t82 (cl @p_50) :rule trans :premises (t80 t81))
(step t83 (cl (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (or (not (member$ ?v0 (image$b ?v1 ?v2))) (not (forall ((?v3 A$)) (or (not (= ?v0 (fun_app$b ?v1 ?v3))) (not (member$a ?v3 ?v2)))))))) :rule resolution :premises (t79 t82 a11))
(step t84 (cl @p_49) :rule resolution :premises (t78 t83))
(step t85 (cl @p_46) :rule resolution :premises (t35 t76 t84))
(step t86 (cl @p_45) :rule resolution :premises (t31 t33 t85))
(step t87 (cl @p_42) :rule resolution :premises (t30 t86))
(step t88 (cl (= @p_41 @p_11)) :rule symm :premises (t87))
(step t89 (cl (= @p_193 (! (fun_app$ f$ @p_11) :named @p_126))) :rule cong :premises (t88))
(step t90 (cl (= @p_14 @p_126)) :rule trans :premises (t19 t89))
(step t91 (cl (= @p_16 (! (= @p_125 @p_126) :named @p_200))) :rule cong :premises (t16 t90))
(step t92 (cl (= (! (= @p_200 false) :named @p_201) (! (not @p_200) :named @p_202))) :rule equiv_simplify)
(step t93 (cl @p_201 (! (not @p_202) :named @p_241)) :rule equiv2 :premises (t92))
(step t94 (cl (not @p_241) @p_200) :rule not_not)
(step t95 (cl @p_201 @p_200) :rule resolution :premises (t93 t94))
(step t96 (cl (! (not (! (or (! (not @p_2) :named @p_203) @p_202 (! (not (! (member$ @p_10 @p_1) :named @p_129)) :named @p_130) @p_48 @p_12) :named @p_204)) :named @p_240) @p_203 @p_202 @p_130 @p_48 @p_12) :rule or_pos)
(step t97 (cl @p_12 @p_203 @p_48 @p_130 @p_202 @p_240) :rule reordering :premises (t96))
(step t98 (cl (! (not (! (or (! (not @p_8) :named @p_154) @p_129) :named @p_155)) :named @p_189) @p_154 @p_129) :rule or_pos)
(step t99 (cl @p_154 @p_129 @p_189) :rule reordering :premises (t98))
(step t100 (cl (or (! (not (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3))))) :named @p_188) @p_155)) :rule forall_inst :args (g$ @p_7 b$))
(step t101 (cl @p_188 @p_155) :rule or :premises (t100))
(step t102 (cl (not (! (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v2)) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3))))) :named @p_156)) (not (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v2)) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3))))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3))))) :rule equiv_pos2)
(anchor :step t103 :args ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (:= (?v0 B$) ?v0) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A$) ?v2) (:= (?v3 A_set$) ?v3)))
(step t103.t0 (cl (= (! (= ?v0 (! (fun_app$b ?v1 ?v2) :named @p_160)) :named @p_171) (! (= @p_160 ?v0) :named @p_173))) :rule rare_rewrite :args ("eq-symm" ?v0 @p_160))
(step t103.t1 (cl (= (! (member$a ?v2 ?v3) :named @p_162) @p_162)) :rule refl)
(step t103.t2 (cl (= (! (and @p_171 @p_162) :named @p_187) (! (and @p_173 @p_162) :named @p_181))) :rule cong :premises (t103.t0 t103.t1))
(step t103.t3 (cl (! (= (! (member$ ?v0 (! (image$b ?v1 ?v3) :named @p_159)) :named @p_172) @p_172) :named @p_180)) :rule refl)
(step t103.t4 (cl (= (=> @p_187 @p_172) (! (=> @p_181 @p_172) :named @p_182))) :rule cong :premises (t103.t2 t103.t3))
(step t103 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= ?v0 (fun_app$b ?v1 ?v2)) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= (fun_app$b ?v1 ?v2) ?v0) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule bind)
(anchor :step t104 :args ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (:= (?v0 B$) ?v0) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A$) ?v2) (:= (?v3 A_set$) ?v3)))
(step t104.t0 (cl (= @p_182 (! (or (! (not @p_181) :named @p_183) @p_172) :named @p_184))) :rule rare_rewrite :args ("bool-impl-elim" @p_181 @p_172))
(step t104.t1 (cl (= @p_183 (! (or (! (not @p_173) :named @p_174) (! (not @p_162) :named @p_163)) :named @p_185))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_173 @p_162 rare-list))
(step t104.t2 (cl @p_180) :rule refl)
(step t104.t3 (cl (= @p_184 (! (or @p_185 @p_172) :named @p_186))) :rule cong :premises (t104.t1 t104.t2))
(step t104.t4 (cl (= @p_186 (! (or @p_174 @p_163 @p_172) :named @p_178))) :rule aci_simp)
(step t104.t5 (cl (= @p_184 @p_178)) :rule trans :premises (t104.t3 t104.t4))
(step t104.t6 (cl (= @p_182 @p_178)) :rule trans :premises (t104.t0 t104.t5))
(step t104 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= (fun_app$b ?v1 ?v2) ?v0) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule bind)
(step t105 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule qnt_rm_unused)
(step t106 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule symm :premises (t105))
(step t107 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule qnt_rm_unused)
(step t108 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule trans :premises (t106 t107))
(step t109 (cl (= (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (forall ((?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3))))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule qnt_join)
(step t110 (cl (= (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (forall ((?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3))))))) :rule symm :premises (t109))
(anchor :step t111 :args ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A$) ?v2) (:= (?v3 A_set$) ?v3)))
(anchor :step t111.t0 :args ((?v0 B$) (:= (?v0 B$) ?v0)))
(step t111.t0.t0 (cl (= @p_178 (! (or @p_174 @p_174 @p_163 @p_172) :named @p_179))) :rule aci_simp)
(step t111.t0.t1 (cl (= @p_173 @p_171)) :rule rare_rewrite :args ("eq-symm" @p_160 ?v0))
(step t111.t0.t2 (cl (= @p_174 (! (not @p_171) :named @p_175))) :rule cong :premises (t111.t0.t1))
(step t111.t0.t3 (cl (= @p_174 @p_174)) :rule refl)
(step t111.t0.t4 (cl (! (= @p_163 @p_163) :named @p_169)) :rule refl)
(step t111.t0.t5 (cl @p_180) :rule refl)
(step t111.t0.t6 (cl (= @p_179 (! (or @p_175 @p_174 @p_163 @p_172) :named @p_176))) :rule cong :premises (t111.t0.t2 t111.t0.t3 t111.t0.t4 t111.t0.t5))
(step t111.t0.t7 (cl (= @p_178 @p_176)) :rule trans :premises (t111.t0.t0 t111.t0.t6))
(step t111.t0 (cl (= (forall ((?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v0 B$)) (or (not (= ?v0 (fun_app$b ?v1 ?v2))) (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))))) :rule bind)
(anchor :step t111.t1 :args ((:= (?v0 B$) @p_160)))
(step t111.t1.t0 (cl (= @p_176 (! (or (! (not (! (= @p_160 @p_160) :named @p_165)) :named @p_166) @p_166 @p_163 (! (member$ @p_160 @p_159) :named @p_161)) :named @p_177))) :rule refl)
(step t111.t1.t1 (cl (= @p_177 (! (or @p_166 @p_163 @p_161) :named @p_167))) :rule rare_rewrite :args ("or-not-refl" @p_160 (rare-list @p_166 @p_163 @p_161)))
(step t111.t1.t2 (cl (= @p_176 @p_167)) :rule trans :premises (t111.t1.t0 t111.t1.t1))
(step t111.t1 (cl (= (forall ((?v0 B$)) (or (not (= ?v0 (fun_app$b ?v1 ?v2))) (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) @p_167)) :rule onepoint)
(step t111.t2 (cl (= (forall ((?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) @p_167)) :rule trans :premises (t111.t0 t111.t1))
(step t111 (cl (= (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (forall ((?v0 B$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3))))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) (fun_app$b ?v1 ?v2))) (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))))) :rule bind)
(step t112 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) (fun_app$b ?v1 ?v2))) (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))))) :rule trans :premises (t108 t110 t111))
(anchor :step t113 :args ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$) (:= (?v1 A_b_fun$) ?v1) (:= (?v2 A$) ?v2) (:= (?v3 A_set$) ?v3)))
(step t113.t0 (cl (= @p_165 true)) :rule rare_rewrite :args ("eq-refl" @p_160))
(step t113.t1 (cl (= @p_166 (! (not true) :named @p_170))) :rule cong :premises (t113.t0))
(step t113.t2 (cl (= @p_170 false)) :rule evaluate)
(step t113.t3 (cl (= @p_166 false)) :rule trans :premises (t113.t1 t113.t2))
(step t113.t4 (cl @p_169) :rule refl)
(step t113.t5 (cl (= @p_161 @p_161)) :rule refl)
(step t113.t6 (cl (= @p_167 (! (or false @p_163 @p_161) :named @p_168))) :rule cong :premises (t113.t3 t113.t4 t113.t5))
(step t113.t7 (cl (= @p_168 (! (or @p_163 @p_161) :named @p_164))) :rule aci_simp)
(step t113.t8 (cl (= @p_167 @p_164)) :rule trans :premises (t113.t6 t113.t7))
(step t113 (cl (= (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) (fun_app$b ?v1 ?v2))) (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))))) :rule bind)
(step t114 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (= (fun_app$b ?v1 ?v2) ?v0)) (not (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))))) :rule trans :premises (t112 t113))
(step t115 (cl (= (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (=> (and (= (fun_app$b ?v1 ?v2) ?v0) (member$a ?v2 ?v3)) (member$ ?v0 (image$b ?v1 ?v3)))) (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3)))))) :rule trans :premises (t104 t114))
(step t116 (cl @p_156) :rule trans :premises (t103 t115))
(step t117 (cl (forall ((?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (or (not (member$a ?v2 ?v3)) (member$ (fun_app$b ?v1 ?v2) (image$b ?v1 ?v3))))) :rule resolution :premises (t102 t116 a15))
(step t118 (cl @p_155) :rule resolution :premises (t101 t117))
(step t119 (cl @p_129) :rule resolution :premises (t99 a26 t118))
(step t120 (cl (or (! (not (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (or (not (inj_on$ ?v0 ?v1)) (not (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3))) (not (member$ ?v2 ?v1)) (not (member$ ?v3 ?v1)) (= ?v3 ?v2)))) :named @p_239) @p_204)) :rule forall_inst :args (f$ @p_1 @p_10 @p_11))
(step t121 (cl @p_239 @p_204) :rule or :premises (t120))
(step t122 (cl (not (! (= (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (and (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (and (member$ ?v2 ?v1) (member$ ?v3 ?v1)))) (= ?v2 ?v3))) (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (or (not (inj_on$ ?v0 ?v1)) (not (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3))) (not (member$ ?v2 ?v1)) (not (member$ ?v3 ?v1)) (= ?v3 ?v2)))) :named @p_205)) (not (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (and (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (and (member$ ?v2 ?v1) (member$ ?v3 ?v1)))) (= ?v2 ?v3)))) (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (or (not (inj_on$ ?v0 ?v1)) (not (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3))) (not (member$ ?v2 ?v1)) (not (member$ ?v3 ?v1)) (= ?v3 ?v2)))) :rule equiv_pos2)
(anchor :step t123 :args ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$) (:= (?v0 B_c_fun$) ?v0) (:= (?v1 B_set$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3)))
(step t123.t0 (cl (= (! (and (! (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) :named @p_215) (! (and (! (member$ ?v2 ?v1) :named @p_213) (! (member$ ?v3 ?v1) :named @p_211)) :named @p_232)) :named @p_236) (! (and @p_215 @p_213 @p_211) :named @p_229))) :rule aci_simp)
(step t123.t1 (cl (= (! (and (! (inj_on$ ?v0 ?v1) :named @p_217) @p_236) :named @p_237) (! (and @p_217 @p_229) :named @p_238))) :rule cong :premises (t123.t0))
(step t123.t2 (cl (= @p_238 (! (and @p_217 @p_215 @p_213 @p_211) :named @p_220))) :rule aci_simp)
(step t123.t3 (cl (= @p_237 @p_220)) :rule trans :premises (t123.t1 t123.t2))
(step t123.t4 (cl (= (! (= ?v2 ?v3) :named @p_235) (! (= ?v3 ?v2) :named @p_210))) :rule rare_rewrite :args ("eq-symm" ?v2 ?v3))
(step t123.t5 (cl (= (=> @p_237 @p_235) (! (=> @p_220 @p_210) :named @p_221))) :rule cong :premises (t123.t3 t123.t4))
(step t123 (cl (= (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (and (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (and (member$ ?v2 ?v1) (member$ ?v3 ?v1)))) (= ?v2 ?v3))) (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (member$ ?v2 ?v1) (member$ ?v3 ?v1)) (= ?v3 ?v2))))) :rule bind)
(anchor :step t124 :args ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$) (:= (?v0 B_c_fun$) ?v0) (:= (?v1 B_set$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3)))
(step t124.t0 (cl (= @p_221 (! (or (! (not @p_220) :named @p_222) @p_210) :named @p_223))) :rule rare_rewrite :args ("bool-impl-elim" @p_220 @p_210))
(step t124.t1 (cl (= @p_222 (! (or (! (not @p_217) :named @p_218) (! (not @p_229) :named @p_230)) :named @p_231))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_217 @p_215 (rare-list @p_213 @p_211)))
(step t124.t2 (cl (= @p_230 (! (or (! (not @p_215) :named @p_216) (! (not @p_232) :named @p_233)) :named @p_234))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_215 @p_213 (rare-list @p_211)))
(step t124.t3 (cl (= @p_233 (! (or (! (not @p_213) :named @p_214) (! (not @p_211) :named @p_212)) :named @p_226))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_213 @p_211 rare-list))
(step t124.t4 (cl (= @p_234 (! (or @p_216 @p_226) :named @p_227))) :rule cong :premises (t124.t3))
(step t124.t5 (cl (= @p_230 @p_227)) :rule trans :premises (t124.t2 t124.t4))
(step t124.t6 (cl (= @p_231 (! (or @p_218 @p_227) :named @p_228))) :rule cong :premises (t124.t5))
(step t124.t7 (cl (= @p_222 @p_228)) :rule trans :premises (t124.t1 t124.t6))
(step t124.t8 (cl (= @p_228 (! (or @p_218 @p_216 @p_214 @p_212) :named @p_224))) :rule aci_simp)
(step t124.t9 (cl (= @p_222 @p_224)) :rule trans :premises (t124.t7 t124.t8))
(step t124.t10 (cl (= @p_210 @p_210)) :rule refl)
(step t124.t11 (cl (= @p_223 (! (or @p_224 @p_210) :named @p_225))) :rule cong :premises (t124.t9 t124.t10))
(step t124.t12 (cl (= @p_225 (! (or @p_218 @p_216 @p_214 @p_212 @p_210) :named @p_219))) :rule aci_simp)
(step t124.t13 (cl (= @p_223 @p_219)) :rule trans :premises (t124.t11 t124.t12))
(step t124.t14 (cl (= @p_221 @p_219)) :rule trans :premises (t124.t0 t124.t13))
(step t124 (cl (= (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (=> (and (inj_on$ ?v0 ?v1) (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3)) (member$ ?v2 ?v1) (member$ ?v3 ?v1)) (= ?v3 ?v2))) (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (or (not (inj_on$ ?v0 ?v1)) (not (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3))) (not (member$ ?v2 ?v1)) (not (member$ ?v3 ?v1)) (= ?v3 ?v2))))) :rule bind)
(step t125 (cl @p_205) :rule trans :premises (t123 t124))
(step t126 (cl (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (or (not (inj_on$ ?v0 ?v1)) (not (= (fun_app$ ?v0 ?v2) (fun_app$ ?v0 ?v3))) (not (member$ ?v2 ?v1)) (not (member$ ?v3 ?v1)) (= ?v3 ?v2)))) :rule resolution :premises (t122 t125 a21))
(step t127 (cl @p_204) :rule resolution :premises (t121 t126))
(step t128 (cl @p_202) :rule resolution :premises (t97 a52 a23 t76 t119 t127))
(step t129 (cl @p_201) :rule resolution :premises (t95 t128))
(step t130 (cl @p_199) :rule trans :premises (t91 t129))
(step t131 (cl @p_17) :rule resolution :premises (t13 t130))
(step t132 (cl (= (! (= @p_18 true) :named @p_124) @p_18)) :rule equiv_simplify)
(step t133 (cl (not @p_124) @p_18) :rule equiv1 :premises (t132))
(step t134 (cl (= @p_18 (! (less_eq$ @p_126 @p_125) :named @p_127))) :rule cong :premises (t90 t16))
(step t135 (cl (= (! (= @p_127 true) :named @p_128) @p_127)) :rule equiv_simplify)
(step t136 (cl @p_128 (not @p_127)) :rule equiv2 :premises (t135))
(step t137 (cl (! (not (! (or @p_68 @p_66 @p_130 @p_127) :named @p_131)) :named @p_190) @p_68 @p_66 @p_130 @p_127) :rule or_pos)
(step t138 (cl @p_68 @p_66 @p_130 @p_127 @p_190) :rule reordering :premises (t137))
(step t139 (cl (or (! (not (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (not (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1))))) :named @p_153) @p_131)) :rule forall_inst :args (@p_1 @p_10 f$))
(step t140 (cl @p_153 @p_131) :rule or :premises (t139))
(step t141 (cl (not (! (= (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (and (not (= ?v0 bot$)) (member$ ?v1 ?v0))) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))) (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (not (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1))))) :named @p_132)) (not (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (and (not (= ?v0 bot$)) (member$ ?v1 ?v0))) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1))))) (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (not (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1))))) :rule equiv_pos2)
(anchor :step t142 :args ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$) (:= (?v0 B_set$) ?v0) (:= (?v1 B$) ?v1) (:= (?v2 B_c_fun$) ?v2)))
(step t142.t0 (cl (= (! (and @p_75 (and @p_89 (! (member$ ?v1 ?v0) :named @p_136))) :named @p_151) (! (and @p_75 @p_89 @p_136) :named @p_152))) :rule aci_simp)
(step t142.t1 (cl (= @p_88 @p_74)) :rule rare_rewrite :args ("eq-symm" ?v0 bot$))
(step t142.t2 (cl (= @p_89 @p_78)) :rule cong :premises (t142.t1))
(step t142.t3 (cl (= @p_136 @p_136)) :rule refl)
(step t142.t4 (cl (= @p_152 (! (and @p_75 @p_78 @p_136) :named @p_139))) :rule cong :premises (t142.t2 t142.t3))
(step t142.t5 (cl (= @p_151 @p_139)) :rule trans :premises (t142.t0 t142.t4))
(step t142.t6 (cl (! (= (! (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)) :named @p_135) @p_135) :named @p_145)) :rule refl)
(step t142.t7 (cl (= (=> @p_151 @p_135) (! (=> @p_139 @p_135) :named @p_140))) :rule cong :premises (t142.t5 t142.t6))
(step t142 (cl (= (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (and (not (= ?v0 bot$)) (member$ ?v1 ?v0))) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))) (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (not (= bot$ ?v0)) (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))))) :rule bind)
(anchor :step t143 :args ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$) (:= (?v0 B_set$) ?v0) (:= (?v1 B$) ?v1) (:= (?v2 B_c_fun$) ?v2)))
(step t143.t0 (cl (= @p_140 (! (or (! (not @p_139) :named @p_141) @p_135) :named @p_142))) :rule rare_rewrite :args ("bool-impl-elim" @p_139 @p_135))
(step t143.t1 (cl (= @p_141 (! (or @p_76 (! (not (and @p_78 @p_136)) :named @p_149)) :named @p_150))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_75 @p_78 (rare-list @p_136)))
(step t143.t2 (cl (= @p_149 (! (or @p_86 (! (not @p_136) :named @p_137)) :named @p_146))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_78 @p_136 rare-list))
(step t143.t3 (cl (= @p_150 (! (or @p_76 @p_146) :named @p_147))) :rule cong :premises (t143.t2))
(step t143.t4 (cl (= @p_141 @p_147)) :rule trans :premises (t143.t1 t143.t3))
(step t143.t5 (cl (= @p_147 (! (or @p_76 @p_86 @p_137) :named @p_148))) :rule aci_simp)
(step t143.t6 (cl (= @p_86 @p_74)) :rule rare_rewrite :args ("bool-double-not-elim" @p_74))
(step t143.t7 (cl (= @p_137 @p_137)) :rule refl)
(step t143.t8 (cl (= @p_148 (! (or @p_76 @p_74 @p_137) :named @p_143))) :rule cong :premises (t143.t6 t143.t7))
(step t143.t9 (cl (= @p_147 @p_143)) :rule trans :premises (t143.t5 t143.t8))
(step t143.t10 (cl (= @p_141 @p_143)) :rule trans :premises (t143.t4 t143.t9))
(step t143.t11 (cl @p_145) :rule refl)
(step t143.t12 (cl (= @p_142 (! (or @p_143 @p_135) :named @p_144))) :rule cong :premises (t143.t10 t143.t11))
(step t143.t13 (cl (= @p_144 (! (or @p_76 @p_74 @p_137 @p_135) :named @p_138))) :rule aci_simp)
(step t143.t14 (cl (= @p_142 @p_138)) :rule trans :premises (t143.t12 t143.t13))
(step t143.t15 (cl (= @p_140 @p_138)) :rule trans :premises (t143.t0 t143.t14))
(step t143 (cl (= (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (=> (and (finite$ ?v0) (not (= bot$ ?v0)) (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))) (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (not (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1)))))) :rule bind)
(step t144 (cl @p_132) :rule trans :premises (t142 t143))
(step t145 (cl (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (or (not (finite$ ?v0)) (= bot$ ?v0) (not (member$ ?v1 ?v0)) (less_eq$ (fun_app$ ?v2 (arg_min_on$ ?v2 ?v0)) (fun_app$ ?v2 ?v1))))) :rule resolution :premises (t141 t144 a2))
(step t146 (cl @p_131) :rule resolution :premises (t140 t145))
(step t147 (cl @p_127) :rule resolution :premises (t138 t46 t67 t119 t146))
(step t148 (cl @p_128) :rule resolution :premises (t136 t147))
(step t149 (cl @p_124) :rule trans :premises (t134 t148))
(step t150 (cl @p_18) :rule resolution :premises (t133 t149))
(step t151 (cl (! (not (! (= (! (less$ @p_14 @p_15) :named @p_21) @p_19) :named @p_22)) :named @p_123) @p_21 @p_20) :rule equiv_pos1)
(step t152 (cl @p_21 @p_20 @p_123) :rule reordering :premises (t151))
(step t153 (cl (! (not (! (or @p_33 (! (not @p_21) :named @p_31)) :named @p_34)) :named @p_122) @p_33 @p_31) :rule or_pos)
(step t154 (cl @p_33 @p_31 @p_122) :rule reordering :premises (t153))
(step t155 (cl (not (! (= (! (or @p_44 (! (not @p_33) :named @p_119)) :named @p_120) (! (or @p_44 @p_32) :named @p_118)) :named @p_121)) (not @p_120) @p_118) :rule equiv_pos2)
(step t156 (cl (= @p_119 @p_32)) :rule rare_rewrite :args ("bool-double-not-elim" @p_32))
(step t157 (cl @p_121) :rule cong :premises (t156))
(step t158 (cl @p_44 @p_119) :rule or_neg :args (1))
(step t159 (cl @p_120 @p_45) :rule or_neg :args (0))
(step t160 (cl @p_120 (not @p_119)) :rule or_neg :args (1))
(step t161 (cl @p_120 @p_120) :rule resolution :premises (t158 t159 t160))
(step t162 (cl @p_120) :rule contraction :premises (t161))
(step t163 (cl @p_118) :rule resolution :premises (t155 t157 t162))
(step t164 (cl @p_44 @p_32) :rule or :premises (t163))
(step t165 (cl @p_32 @p_44) :rule reordering :premises (t164))
(step t166 (cl @p_32) :rule resolution :premises (t165 t86))
(step t167 (cl (or (! (not (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))) :named @p_36) @p_34)) :rule forall_inst :args (@quantifiers_skolemize_3))
(step t168 (cl @p_36 @p_34) :rule or :premises (t167))
(step t169 (cl (not (! (= @p_9 (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))) :named @p_35)) (not @p_9) (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))) :rule equiv_pos2)
(step t170 (cl (= (exists ((?v0 A$)) (and (member$a ?v0 b$) (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))) (! (not (forall ((?v0 A$)) (not (and (member$a ?v0 b$) (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))) :named @p_38))) :rule connective_def)
(anchor :step t171 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t171.t0 (cl (= (not (and (! (member$a ?v0 b$) :named @p_40) (! (less$ (fun_app$a @p_6 ?v0) @p_15) :named @p_39))) (or (not @p_40) (not @p_39)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_40 @p_39 rare-list))
(step t171 (cl (= (forall ((?v0 A$)) (not (and (member$a ?v0 b$) (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$)))))) (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$)))))))) :rule bind)
(step t172 (cl (= @p_38 @p_36)) :rule cong :premises (t171))
(step t173 (cl (= (exists ((?v0 A$)) (and (member$a ?v0 b$) (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))) @p_36)) :rule trans :premises (t170 t172))
(step t174 (cl (= @p_9 (! (not @p_36) :named @p_37))) :rule cong :premises (t173))
(step t175 (cl (= @p_37 (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$)))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))))
(step t176 (cl @p_35) :rule trans :premises (t174 t175))
(step t177 (cl (forall ((?v0 A$)) (or (not (member$a ?v0 b$)) (not (less$ (fun_app$a (comp$ f$ g$) ?v0) (fun_app$a (comp$ f$ g$) (arg_min_on$a (comp$ f$ g$) b$))))))) :rule resolution :premises (t169 t176 a27))
(step t178 (cl @p_34) :rule resolution :premises (t168 t177))
(step t179 (cl @p_31) :rule resolution :premises (t154 t166 t178))
(step t180 (cl (not (! (= (! (=> (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1))))) (! (= @p_21 (! (and @p_18 (! (not (! (= @p_14 @p_15) :named @p_25)) :named @p_26)) :named @p_27)) :named @p_28)) :named @p_29) (! (=> (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1))))) @p_22) :named @p_24)) :named @p_30)) (not @p_29) @p_24) :rule equiv_pos2)
(step t181 (cl (= @p_25 @p_16)) :rule rare_rewrite :args ("eq-symm" @p_14 @p_15))
(step t182 (cl (= @p_26 @p_17)) :rule cong :premises (t181))
(step t183 (cl (= @p_27 @p_19)) :rule cong :premises (t182))
(step t184 (cl (= @p_28 @p_22)) :rule cong :premises (t183))
(step t185 (cl @p_30) :rule cong :premises (t184))
(step t186 (cl @p_29 (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1)))))) :rule implies_neg1)
(anchor :step t187)
(assume t187.a0 (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1))))))
(step t187.t0 (cl (or (! (not (forall ((?v0 C$) (?v1 C$)) (= (less$ ?v0 ?v1) (and (less_eq$ ?v0 ?v1) (not (= ?v0 ?v1)))))) :named @p_23) @p_28)) :rule forall_inst :args (@p_14 @p_15))
(step t187.t1 (cl @p_23 @p_28) :rule or :premises (t187.t0))
(step t187.t2 (cl @p_28) :rule resolution :premises (t187.t1 t187.a0))
(step t187 (cl @p_23 @p_28) :rule subproof :discharge (t187.a0))
(step t188 (cl @p_29 @p_28) :rule resolution :premises (t186 t187))
(step t189 (cl @p_29 (not @p_28)) :rule implies_neg2)
(step t190 (cl @p_29 @p_29) :rule resolution :premises (t188 t189))
(step t191 (cl @p_29) :rule contraction :premises (t190))
(step t192 (cl @p_24) :rule resolution :premises (t180 t185 t191))
(step t193 (cl @p_23 @p_22) :rule implies :premises (t192))
(step t194 (cl @p_22) :rule resolution :premises (t193 a22))
(step t195 (cl @p_20) :rule resolution :premises (t152 t179 t194))
(step t196 (cl) :rule resolution :premises (t11 t131 t150 t195))
)
12e5976a14d2e73cabcffaf4ee91fb0bcdd74daf 433 0
unsat
(
(define-fun @quantifiers_skolemize_4 () B_list$ (choice ((?v0 B_list$)) (not (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0))))))))))
(define-fun @quantifiers_skolemize_3 () B_list$ (choice ((?v0 B_list$)) (not (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))))
(assume a1 (! (not (! (=> (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (=> (and (= (rec_join$ ?v1) ?v0) (and (=> (and (= ?v1 nil$) (= uu$ ?v0)) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false) (=> (and (= (rec_join$ ?v1) (rec_join$ ?v1)) (and (=> (and (= ?v1 nil$) (= uu$ (rec_join$ ?v1))) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false))) (! (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (=> (and (= (rec_join$ ?v0) ?v1) (and (=> (and (= ?v0 nil$) (= uu$ ?v1)) false) (and (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false)) (forall ((?v0 B_list$)) (=> (and (= (rec_join$ ?v0) (rec_join$ ?v0)) (and (=> (and (= ?v0 nil$) (= uu$ (rec_join$ ?v0))) false) (and (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false))))) false))) :named @p_1)) :named @p_2)) :named @p_3))
(step t0 (cl (! (not (! (or (! (and (= nil$ @quantifiers_skolemize_4) (= uu$ (! (rec_join$ @quantifiers_skolemize_4) :named @p_4))) :named @p_5) (! (not (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_254) (! (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_253)) :named @p_255)) :named @p_290) @p_5 @p_254 @p_253) :rule or_pos)
(step t1 (cl @p_5 @p_254 @p_253 @p_290) :rule reordering :premises (t0))
(anchor :step t2 :args ((BOUND_VARIABLE_8143 B$) (BOUND_VARIABLE_8145 B$) (BOUND_VARIABLE_8144 B_list$) (:= (?v2 B$) BOUND_VARIABLE_8143) (:= (?v3 B$) BOUND_VARIABLE_8145) (:= (?v4 B_list$) BOUND_VARIABLE_8144)))
(step t2.t0 (cl (= (or (not (= (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_98)) :named @p_102) @quantifiers_skolemize_4)) (not (= (! (joinpaths$ (! (coeff_cube_to_path$ ?v2) :named @p_99) (rec_join$ @p_98)) :named @p_100) @p_4))) (! (or (not (= (cons$ BOUND_VARIABLE_8143 (! (cons$ BOUND_VARIABLE_8145 BOUND_VARIABLE_8144) :named @p_288)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_8143) (rec_join$ @p_288)) @p_4))) :named @p_289))) :rule refl)
(step t2 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4))))) (forall ((BOUND_VARIABLE_8143 B$) (BOUND_VARIABLE_8145 B$) (BOUND_VARIABLE_8144 B_list$)) (or (not (= (cons$ BOUND_VARIABLE_8143 (cons$ BOUND_VARIABLE_8145 BOUND_VARIABLE_8144)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_8143) (rec_join$ (cons$ BOUND_VARIABLE_8145 BOUND_VARIABLE_8144))) (rec_join$ @quantifiers_skolemize_4))))))) :rule bind)
(anchor :step t3 :args ((?v1 B$) (?v2 B$) (?v3 B_list$) (:= (BOUND_VARIABLE_8143 B$) ?v1) (:= (BOUND_VARIABLE_8145 B$) ?v2) (:= (BOUND_VARIABLE_8144 B_list$) ?v3)))
(step t3.t0 (cl (= @p_289 (! (or (! (not (! (= (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_46)) :named @p_50) @quantifiers_skolemize_4) :named @p_264)) :named @p_265) (! (not (! (= (! (joinpaths$ (! (coeff_cube_to_path$ ?v1) :named @p_47) (rec_join$ @p_46)) :named @p_48) @p_4) :named @p_262)) :named @p_263)) :named @p_266))) :rule refl)
(step t3 (cl (= (forall ((BOUND_VARIABLE_8143 B$) (BOUND_VARIABLE_8145 B$) (BOUND_VARIABLE_8144 B_list$)) (or (not (= (cons$ BOUND_VARIABLE_8143 (cons$ BOUND_VARIABLE_8145 BOUND_VARIABLE_8144)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_8143) (rec_join$ (cons$ BOUND_VARIABLE_8145 BOUND_VARIABLE_8144))) (rec_join$ @quantifiers_skolemize_4))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4))))))) :rule bind)
(step t4 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4))))))) :rule trans :premises (t2 t3))
(step t5 (cl (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_7) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4)))))) :rule equiv1 :premises (t4))
(step t6 (cl (not (! (= (! (or (! (or @p_5 (! (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_8) @p_7) :named @p_9) (! (not @p_7) :named @p_285)) :named @p_286) (! (or @p_9 (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_284)) :named @p_287)) (not @p_286) @p_284) :rule equiv_pos2)
(step t7 (cl (= @p_285 (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4)))))))
(step t8 (cl @p_287) :rule cong :premises (t7))
(step t9 (cl @p_9 @p_285) :rule or_neg :args (2))
(step t10 (cl @p_286 (! (not @p_9) :named @p_10)) :rule or_neg :args (0))
(step t11 (cl @p_286 (not @p_285)) :rule or_neg :args (1))
(step t12 (cl @p_286 @p_286) :rule resolution :premises (t9 t10 t11))
(step t13 (cl @p_286) :rule contraction :premises (t12))
(step t14 (cl @p_284) :rule resolution :premises (t6 t8 t13))
(step t15 (cl @p_9 (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4)))))) :rule or :premises (t14))
(step t16 (cl (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4))))) @p_9) :rule reordering :premises (t15))
(step t17 (cl (not (! (= (! (or (! (not (! (not (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0))))))))) :named @p_11)) :named @p_247) @p_10) :named @p_248) (! (or (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) @p_10) :named @p_246)) :named @p_252)) (not @p_248) @p_246) :rule equiv_pos2)
(step t18 (cl (= @p_247 (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0))))))))))
(step t19 (cl (= @p_10 @p_10)) :rule refl)
(step t20 (cl @p_252) :rule cong :premises (t18 t19))
(step t21 (cl (! (=> @p_11 @p_10) :named @p_250) @p_11) :rule implies_neg1)
(anchor :step t22)
(assume t22.a0 @p_11)
(step t22.t0 (cl (not (! (= @p_11 @p_10) :named @p_251)) @p_247 @p_10) :rule equiv_pos2)
(anchor :step t22.t1 :args ((:= (?v0 B_list$) @quantifiers_skolemize_4)))
(step t22.t1.t0 (cl (= (! (or (! (and (! (= nil$ ?v0) :named @p_22) (! (= uu$ (! (rec_join$ ?v0) :named @p_20)) :named @p_21)) :named @p_23) (! (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) :named @p_61) (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))) :named @p_60)) :named @p_62) @p_9)) :rule refl)
(step t22.t1 (cl (= (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) @p_9)) :rule sko_forall)
(step t22.t2 (cl @p_251) :rule cong :premises (t22.t1))
(step t22.t3 (cl @p_10) :rule resolution :premises (t22.t0 t22.t2 t22.a0))
(step t22 (cl @p_247 @p_10) :rule subproof :discharge (t22.a0))
(step t23 (cl @p_250 @p_10) :rule resolution :premises (t21 t22))
(step t24 (cl @p_250 (! (not @p_10) :named @p_249)) :rule implies_neg2)
(step t25 (cl @p_250 @p_250) :rule resolution :premises (t23 t24))
(step t26 (cl @p_250) :rule contraction :premises (t25))
(step t27 (cl @p_247 @p_10) :rule implies :premises (t26))
(step t28 (cl @p_248 (not @p_247)) :rule or_neg :args (0))
(step t29 (cl @p_248 @p_249) :rule or_neg :args (1))
(step t30 (cl @p_248 @p_248) :rule resolution :premises (t27 t28 t29))
(step t31 (cl @p_248) :rule contraction :premises (t30))
(step t32 (cl @p_246) :rule resolution :premises (t17 t20 t31))
(step t33 (cl (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) @p_10) :rule or :premises (t32))
(step t34 (cl (! (not (! (or (! (and (= nil$ @quantifiers_skolemize_3) (= uu$ (! (rec_join$ @quantifiers_skolemize_3) :named @p_197))) :named @p_198) (! (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_242) (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_241)) :named @p_243)) :named @p_245) @p_198 @p_242 @p_241) :rule or_pos)
(step t35 (cl @p_198 @p_242 @p_241 @p_245) :rule reordering :premises (t34))
(step t36 (cl (! (=> (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) @p_243) :named @p_244) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0))))))))) :rule implies_neg1)
(anchor :step t37)
(assume t37.a0 (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))
(step t37.t0 (cl (or @p_11 @p_243)) :rule forall_inst :args (@quantifiers_skolemize_3))
(step t37.t1 (cl @p_11 @p_243) :rule or :premises (t37.t0))
(step t37.t2 (cl @p_243) :rule resolution :premises (t37.t1 t37.a0))
(step t37 (cl @p_11 @p_243) :rule subproof :discharge (t37.a0))
(step t38 (cl @p_244 @p_243) :rule resolution :premises (t36 t37))
(step t39 (cl @p_244 @p_245) :rule implies_neg2)
(step t40 (cl @p_244 @p_244) :rule resolution :premises (t38 t39))
(step t41 (cl @p_244) :rule contraction :premises (t40))
(step t42 (cl @p_11 @p_243) :rule implies :premises (t41))
(anchor :step t43 :args ((BOUND_VARIABLE_7931 B$) (BOUND_VARIABLE_7933 B$) (BOUND_VARIABLE_7932 B_list$) (:= (?v1 B$) BOUND_VARIABLE_7931) (:= (?v2 B$) BOUND_VARIABLE_7933) (:= (?v3 B_list$) BOUND_VARIABLE_7932)))
(step t43.t0 (cl (= (! (or (! (not (! (= @p_50 @quantifiers_skolemize_3) :named @p_214)) :named @p_215) (! (not (! (= @p_48 @p_197) :named @p_212)) :named @p_213)) :named @p_216) (! (or (not (= (cons$ BOUND_VARIABLE_7931 (! (cons$ BOUND_VARIABLE_7933 BOUND_VARIABLE_7932) :named @p_239)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_7931) (rec_join$ @p_239)) @p_197))) :named @p_240))) :rule refl)
(step t43 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3))))) (forall ((BOUND_VARIABLE_7931 B$) (BOUND_VARIABLE_7933 B$) (BOUND_VARIABLE_7932 B_list$)) (or (not (= (cons$ BOUND_VARIABLE_7931 (cons$ BOUND_VARIABLE_7933 BOUND_VARIABLE_7932)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_7931) (rec_join$ (cons$ BOUND_VARIABLE_7933 BOUND_VARIABLE_7932))) (rec_join$ @quantifiers_skolemize_3))))))) :rule bind)
(anchor :step t44 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (BOUND_VARIABLE_7931 B$) ?v2) (:= (BOUND_VARIABLE_7933 B$) ?v3) (:= (BOUND_VARIABLE_7932 B_list$) ?v4)))
(step t44.t0 (cl (= @p_240 (or (not (= @p_102 @quantifiers_skolemize_3)) (not (= @p_100 @p_197))))) :rule refl)
(step t44 (cl (= (forall ((BOUND_VARIABLE_7931 B$) (BOUND_VARIABLE_7933 B$) (BOUND_VARIABLE_7932 B_list$)) (or (not (= (cons$ BOUND_VARIABLE_7931 (cons$ BOUND_VARIABLE_7933 BOUND_VARIABLE_7932)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ BOUND_VARIABLE_7931) (rec_join$ (cons$ BOUND_VARIABLE_7933 BOUND_VARIABLE_7932))) (rec_join$ @quantifiers_skolemize_3))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_3))))))) :rule bind)
(step t45 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_3))))))) :rule trans :premises (t43 t44))
(step t46 (cl (! (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_195) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_3)))))) :rule equiv1 :premises (t45))
(anchor :step t47 :args ((?v2 B$) (:= (?v1 B$) ?v2)))
(step t47.t0 (cl (= (! (or (! (not (! (= (! (cons$ ?v1 nil$) :named @p_55) @quantifiers_skolemize_3) :named @p_223)) :named @p_224) (! (not (! (= @p_47 @p_197) :named @p_221)) :named @p_222)) :named @p_225) (or (not (= (! (cons$ ?v2 nil$) :named @p_112) @quantifiers_skolemize_3)) (not (= @p_99 @p_197))))) :rule refl)
(step t47 (cl (= (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3))))) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_3))))))) :rule bind)
(step t48 (cl (! (not (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_196) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_3)))))) :rule equiv1 :premises (t47))
(step t49 (cl (not (! (= (! (or (! (or @p_198 @p_196 @p_195) :named @p_199) (! (not @p_195) :named @p_236)) :named @p_237) (! (or @p_199 (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_235)) :named @p_238)) (not @p_237) @p_235) :rule equiv_pos2)
(step t50 (cl (= @p_236 (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3)))))))
(step t51 (cl @p_238) :rule cong :premises (t50))
(step t52 (cl @p_199 @p_236) :rule or_neg :args (2))
(step t53 (cl @p_237 (! (not @p_199) :named @p_200)) :rule or_neg :args (0))
(step t54 (cl @p_237 (not @p_236)) :rule or_neg :args (1))
(step t55 (cl @p_237 @p_237) :rule resolution :premises (t52 t53 t54))
(step t56 (cl @p_237) :rule contraction :premises (t55))
(step t57 (cl @p_235) :rule resolution :premises (t49 t51 t56))
(step t58 (cl @p_199 (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3)))))) :rule or :premises (t57))
(step t59 (cl (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3))))) @p_199) :rule reordering :premises (t58))
(step t60 (cl (not (! (= (! (or @p_199 (! (not @p_196) :named @p_232)) :named @p_233) (! (or @p_199 (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3)))))) :named @p_231)) :named @p_234)) (not @p_233) @p_231) :rule equiv_pos2)
(step t61 (cl (= @p_232 (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3)))))))
(step t62 (cl @p_234) :rule cong :premises (t61))
(step t63 (cl @p_199 @p_232) :rule or_neg :args (1))
(step t64 (cl @p_233 @p_200) :rule or_neg :args (0))
(step t65 (cl @p_233 (not @p_232)) :rule or_neg :args (1))
(step t66 (cl @p_233 @p_233) :rule resolution :premises (t63 t64 t65))
(step t67 (cl @p_233) :rule contraction :premises (t66))
(step t68 (cl @p_231) :rule resolution :premises (t60 t62 t67))
(step t69 (cl @p_199 (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3)))))) :rule or :premises (t68))
(step t70 (cl (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3))))) @p_199) :rule reordering :premises (t69))
(step t71 (cl @p_199 (not @p_198)) :rule or_neg :args (0))
(step t72 (cl (not (! (= (! (or (! (not (! (not (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))) :named @p_12)) :named @p_202) @p_200) :named @p_203) (! (or (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) @p_200) :named @p_201)) :named @p_230)) (not @p_203) @p_201) :rule equiv_pos2)
(step t73 (cl (= @p_202 (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))))
(step t74 (cl (= @p_200 @p_200)) :rule refl)
(step t75 (cl @p_230) :rule cong :premises (t73 t74))
(step t76 (cl (not (! (= (! (=> @p_12 (! (not (! (or @p_198 (! (not (forall ((?v1 B$)) (or (not (= @quantifiers_skolemize_3 (cons$ ?v1 nil$))) (not (= (rec_join$ @quantifiers_skolemize_3) (coeff_cube_to_path$ ?v1)))))) :named @p_206) (! (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= @quantifiers_skolemize_3 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ @quantifiers_skolemize_3) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))) :named @p_205)) :named @p_207)) :named @p_208)) :named @p_209) (! (=> @p_12 @p_200) :named @p_204)) :named @p_211)) (not @p_209) @p_204) :rule equiv_pos2)
(anchor :step t77 :args ((?v1 B$) (:= (?v1 B$) ?v1)))
(step t77.t0 (cl (= (! (= @quantifiers_skolemize_3 @p_55) :named @p_228) @p_223)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_3 @p_55))
(step t77.t1 (cl (= (! (not @p_228) :named @p_229) @p_224)) :rule cong :premises (t77.t0))
(step t77.t2 (cl (= (! (= @p_197 @p_47) :named @p_226) @p_221)) :rule rare_rewrite :args ("eq-symm" @p_197 @p_47))
(step t77.t3 (cl (= (! (not @p_226) :named @p_227) @p_222)) :rule cong :premises (t77.t2))
(step t77.t4 (cl (= (or @p_229 @p_227) @p_225)) :rule cong :premises (t77.t1 t77.t3))
(step t77 (cl (= (forall ((?v1 B$)) (or (not (= @quantifiers_skolemize_3 (cons$ ?v1 nil$))) (not (= (rec_join$ @quantifiers_skolemize_3) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_3)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_3))))))) :rule bind)
(step t78 (cl (= @p_206 @p_196)) :rule cong :premises (t77))
(anchor :step t79 :args ((?v1 B$) (?v2 B$) (?v3 B_list$) (:= (?v1 B$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B_list$) ?v3)))
(step t79.t0 (cl (= (! (= @quantifiers_skolemize_3 @p_50) :named @p_219) @p_214)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_3 @p_50))
(step t79.t1 (cl (= (! (not @p_219) :named @p_220) @p_215)) :rule cong :premises (t79.t0))
(step t79.t2 (cl (= (! (= @p_197 @p_48) :named @p_217) @p_212)) :rule rare_rewrite :args ("eq-symm" @p_197 @p_48))
(step t79.t3 (cl (= (! (not @p_217) :named @p_218) @p_213)) :rule cong :premises (t79.t2))
(step t79.t4 (cl (= (or @p_220 @p_218) @p_216)) :rule cong :premises (t79.t1 t79.t3))
(step t79 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= @quantifiers_skolemize_3 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ @quantifiers_skolemize_3) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_3)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_3))))))) :rule bind)
(step t80 (cl (= @p_205 @p_195)) :rule cong :premises (t79))
(step t81 (cl (= @p_207 @p_199)) :rule cong :premises (t78 t80))
(step t82 (cl (= @p_208 @p_200)) :rule cong :premises (t81))
(step t83 (cl @p_211) :rule cong :premises (t82))
(step t84 (cl @p_209 @p_12) :rule implies_neg1)
(anchor :step t85)
(assume t85.a0 @p_12)
(step t85.t0 (cl (not (! (= @p_12 @p_208) :named @p_210)) @p_202 @p_208) :rule equiv_pos2)
(anchor :step t85.t1 :args ((:= (?v0 B_list$) @quantifiers_skolemize_3)))
(step t85.t1.t0 (cl (= (! (or @p_23 (! (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) :named @p_19) (! (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))) :named @p_18)) :named @p_24) @p_207)) :rule refl)
(step t85.t1 (cl (= (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) @p_207)) :rule sko_forall)
(step t85.t2 (cl @p_210) :rule cong :premises (t85.t1))
(step t85.t3 (cl @p_208) :rule resolution :premises (t85.t0 t85.t2 t85.a0))
(step t85 (cl @p_202 @p_208) :rule subproof :discharge (t85.a0))
(step t86 (cl @p_209 @p_208) :rule resolution :premises (t84 t85))
(step t87 (cl @p_209 (not @p_208)) :rule implies_neg2)
(step t88 (cl @p_209 @p_209) :rule resolution :premises (t86 t87))
(step t89 (cl @p_209) :rule contraction :premises (t88))
(step t90 (cl @p_204) :rule resolution :premises (t76 t83 t89))
(step t91 (cl @p_202 @p_200) :rule implies :premises (t90))
(step t92 (cl @p_203 (not @p_202)) :rule or_neg :args (0))
(step t93 (cl @p_203 (not @p_200)) :rule or_neg :args (1))
(step t94 (cl @p_203 @p_203) :rule resolution :premises (t91 t92 t93))
(step t95 (cl @p_203) :rule contraction :premises (t94))
(step t96 (cl @p_201) :rule resolution :premises (t72 t75 t95))
(step t97 (cl (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) @p_200) :rule or :premises (t96))
(step t98 (cl (not (! (= @p_3 (! (not (! (=> (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))) (! (= (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))) :named @p_13)) :named @p_14)) :named @p_15)) :named @p_16)) (not @p_3) @p_15) :rule equiv_pos2)
(anchor :step t99 :args ((?v0 Real_a_fun$) (?v1 B_list$) (:= (?v0 Real_a_fun$) ?v0) (:= (?v1 B_list$) ?v1)))
(step t99.t0 (cl (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_129) ?v0) :named @p_169) (and (! (=> (! (and (! (= ?v1 nil$) :named @p_161) (! (= uu$ ?v0) :named @p_126)) :named @p_167) false) :named @p_168) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) :named @p_170) false) :named @p_171) (! (not @p_170) :named @p_186))) :rule rare_rewrite :args ("bool-impl-false1" @p_170))
(step t99.t1 (cl (= @p_170 (! (and @p_169 @p_168 (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))) :named @p_187))) :rule aci_simp)
(step t99.t2 (cl (= @p_169 (! (= ?v0 @p_129) :named @p_130))) :rule rare_rewrite :args ("eq-symm" @p_129 ?v0))
(step t99.t3 (cl (= @p_168 (! (not @p_167) :named @p_194))) :rule rare_rewrite :args ("bool-impl-false1" @p_167))
(step t99.t4 (cl (= @p_161 (! (= nil$ ?v1) :named @p_127))) :rule rare_rewrite :args ("eq-symm" ?v1 nil$))
(step t99.t5 (cl (= @p_126 @p_126)) :rule refl)
(step t99.t6 (cl (= @p_167 (! (and @p_127 @p_126) :named @p_128))) :rule cong :premises (t99.t4 t99.t5))
(step t99.t7 (cl (= @p_194 (! (not @p_128) :named @p_142))) :rule cong :premises (t99.t6))
(step t99.t8 (cl (= @p_168 @p_142)) :rule trans :premises (t99.t3 t99.t7))
(anchor :step t99.t9 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t99.t9.t0 (cl (= (=> (! (and (! (= ?v1 @p_112) :named @p_181) (! (= ?v0 @p_99) :named @p_191)) :named @p_192) false) (! (not @p_192) :named @p_193))) :rule rare_rewrite :args ("bool-impl-false1" @p_192))
(step t99.t9 (cl (= (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (not (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))))))) :rule bind)
(anchor :step t99.t10 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t99.t10.t0 (cl (= @p_193 (or (! (not @p_181) :named @p_182) (not @p_191)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_191 rare-list))
(step t99.t10 (cl (= (forall ((?v2 B$)) (not (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))))) :rule bind)
(step t99.t11 (cl (= (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))))) :rule trans :premises (t99.t9 t99.t10))
(anchor :step t99.t12 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t99.t12.t0 (cl (= (=> (! (and (! (= ?v1 @p_102) :named @p_176) (! (= ?v0 @p_100) :named @p_188)) :named @p_189) false) (! (not @p_189) :named @p_190))) :rule rare_rewrite :args ("bool-impl-false1" @p_189))
(step t99.t12 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule bind)
(anchor :step t99.t13 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t99.t13.t0 (cl (= @p_190 (or (! (not @p_176) :named @p_177) (not @p_188)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_176 @p_188 rare-list))
(step t99.t13 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule bind)
(step t99.t14 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule trans :premises (t99.t12 t99.t13))
(step t99.t15 (cl (= @p_187 (! (and @p_130 @p_142 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4)))))))) :named @p_143))) :rule cong :premises (t99.t2 t99.t8 t99.t11 t99.t14))
(step t99.t16 (cl (= @p_170 @p_143)) :rule trans :premises (t99.t1 t99.t15))
(step t99.t17 (cl (= @p_186 (! (not @p_143) :named @p_144))) :rule cong :premises (t99.t16))
(step t99.t18 (cl (= @p_171 @p_144)) :rule trans :premises (t99.t0 t99.t17))
(step t99.t19 (cl (= (! (=> (! (and (! (= @p_129 @p_129) :named @p_164) (and (! (=> (! (and @p_161 (! (= uu$ @p_129) :named @p_135)) :named @p_162) false) :named @p_163) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) :named @p_165) false) :named @p_166) (! (not @p_165) :named @p_172))) :rule rare_rewrite :args ("bool-impl-false1" @p_165))
(step t99.t20 (cl (= @p_165 (! (and @p_164 @p_163 (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))) :named @p_173))) :rule aci_simp)
(step t99.t21 (cl (= @p_164 true)) :rule rare_rewrite :args ("eq-refl" @p_129))
(step t99.t22 (cl (= @p_163 (! (not @p_162) :named @p_185))) :rule rare_rewrite :args ("bool-impl-false1" @p_162))
(step t99.t23 (cl (= @p_135 @p_135)) :rule refl)
(step t99.t24 (cl (= @p_162 (! (and @p_127 @p_135) :named @p_136))) :rule cong :premises (t99.t4 t99.t23))
(step t99.t25 (cl (= @p_185 (! (not @p_136) :named @p_139))) :rule cong :premises (t99.t24))
(step t99.t26 (cl (= @p_163 @p_139)) :rule trans :premises (t99.t22 t99.t25))
(anchor :step t99.t27 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t99.t27.t0 (cl (= (=> (! (and @p_181 (! (= @p_129 @p_99) :named @p_180)) :named @p_183) false) (! (not @p_183) :named @p_184))) :rule rare_rewrite :args ("bool-impl-false1" @p_183))
(step t99.t27 (cl (= (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (not (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))))) :rule bind)
(anchor :step t99.t28 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t99.t28.t0 (cl (= @p_184 (or @p_182 (not @p_180)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_180 rare-list))
(step t99.t28 (cl (= (forall ((?v2 B$)) (not (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))))) :rule bind)
(step t99.t29 (cl (= (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))))) :rule trans :premises (t99.t27 t99.t28))
(anchor :step t99.t30 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t99.t30.t0 (cl (= (=> (! (and @p_176 (! (= @p_129 @p_100) :named @p_175)) :named @p_178) false) (! (not @p_178) :named @p_179))) :rule rare_rewrite :args ("bool-impl-false1" @p_178))
(step t99.t30 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule bind)
(anchor :step t99.t31 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t99.t31.t0 (cl (= @p_179 (or @p_177 (not @p_175)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_176 @p_175 rare-list))
(step t99.t31 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule bind)
(step t99.t32 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :rule trans :premises (t99.t30 t99.t31))
(step t99.t33 (cl (= @p_173 (! (and true @p_139 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4)))))))) :named @p_174))) :rule cong :premises (t99.t21 t99.t26 t99.t29 t99.t32))
(step t99.t34 (cl (= @p_174 (! (and @p_139 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4)))))))) :named @p_140))) :rule aci_simp)
(step t99.t35 (cl (= @p_173 @p_140)) :rule trans :premises (t99.t33 t99.t34))
(step t99.t36 (cl (= @p_165 @p_140)) :rule trans :premises (t99.t20 t99.t35))
(step t99.t37 (cl (= @p_172 (! (not @p_140) :named @p_141))) :rule cong :premises (t99.t36))
(step t99.t38 (cl (= @p_166 @p_141)) :rule trans :premises (t99.t19 t99.t37))
(step t99.t39 (cl (= (= @p_171 @p_166) (! (= @p_144 @p_141) :named @p_145))) :rule cong :premises (t99.t18 t99.t38))
(step t99 (cl (= (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (=> (and (= (rec_join$ ?v1) ?v0) (and (=> (and (= ?v1 nil$) (= uu$ ?v0)) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false) (=> (and (= (rec_join$ ?v1) (rec_join$ ?v1)) (and (=> (and (= ?v1 nil$) (= uu$ (rec_join$ ?v1))) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false))) (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (not (and (= ?v0 (rec_join$ ?v1)) (not (and (= nil$ ?v1) (= uu$ ?v0))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (not (and (not (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1)))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))))) :rule bind)
(anchor :step t100 :args ((?v0 Real_a_fun$) (?v1 B_list$) (:= (?v0 Real_a_fun$) ?v0) (:= (?v1 B_list$) ?v1)))
(step t100.t0 (cl (= @p_144 (! (or (! (not @p_130) :named @p_131) (! (not (and @p_142 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :named @p_157)) :named @p_158))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_130 @p_142 (rare-list (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))
(step t100.t1 (cl (= @p_157 (! (or (! (not @p_142) :named @p_153) (! (not (and (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :named @p_159)) :named @p_160))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_142 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (rare-list (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))
(step t100.t2 (cl (= @p_159 (! (or (! (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) :named @p_125) (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4)))))))) :named @p_124)) :named @p_152))) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))) rare-list))
(step t100.t3 (cl (= @p_160 (! (or @p_153 @p_152) :named @p_154))) :rule cong :premises (t100.t2))
(step t100.t4 (cl (= @p_157 @p_154)) :rule trans :premises (t100.t1 t100.t3))
(step t100.t5 (cl (= @p_158 (! (or @p_131 @p_154) :named @p_155))) :rule cong :premises (t100.t4))
(step t100.t6 (cl (= @p_144 @p_155)) :rule trans :premises (t100.t0 t100.t5))
(step t100.t7 (cl (= @p_155 (! (or @p_131 @p_153 @p_125 @p_124) :named @p_156))) :rule aci_simp)
(step t100.t8 (cl (= @p_153 @p_128)) :rule rare_rewrite :args ("bool-double-not-elim" @p_128))
(step t100.t9 (cl (= @p_125 @p_125)) :rule refl)
(step t100.t10 (cl (= @p_124 @p_124)) :rule refl)
(step t100.t11 (cl (= @p_156 (! (or @p_131 @p_128 @p_125 @p_124) :named @p_132))) :rule cong :premises (t100.t8 t100.t9 t100.t10))
(step t100.t12 (cl (= @p_155 @p_132)) :rule trans :premises (t100.t7 t100.t11))
(step t100.t13 (cl (= @p_144 @p_132)) :rule trans :premises (t100.t6 t100.t12))
(step t100.t14 (cl (= @p_141 (! (or (! (not @p_139) :named @p_147) (! (not (and (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) :named @p_150)) :named @p_151))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_139 (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (rare-list (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))
(step t100.t15 (cl (= @p_150 (! (or (! (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) :named @p_134) (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4)))))))) :named @p_133)) :named @p_146))) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))) rare-list))
(step t100.t16 (cl (= @p_151 (! (or @p_147 @p_146) :named @p_148))) :rule cong :premises (t100.t15))
(step t100.t17 (cl (= @p_141 @p_148)) :rule trans :premises (t100.t14 t100.t16))
(step t100.t18 (cl (= @p_148 (! (or @p_147 @p_134 @p_133) :named @p_149))) :rule aci_simp)
(step t100.t19 (cl (= @p_147 @p_136)) :rule rare_rewrite :args ("bool-double-not-elim" @p_136))
(step t100.t20 (cl (= @p_134 @p_134)) :rule refl)
(step t100.t21 (cl (= @p_133 @p_133)) :rule refl)
(step t100.t22 (cl (= @p_149 (! (or @p_136 @p_134 @p_133) :named @p_137))) :rule cong :premises (t100.t19 t100.t20 t100.t21))
(step t100.t23 (cl (= @p_148 @p_137)) :rule trans :premises (t100.t18 t100.t22))
(step t100.t24 (cl (= @p_141 @p_137)) :rule trans :premises (t100.t17 t100.t23))
(step t100.t25 (cl (= @p_145 (! (= @p_132 @p_137) :named @p_138))) :rule cong :premises (t100.t13 t100.t24))
(step t100 (cl (= (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (not (and (= ?v0 (rec_join$ ?v1)) (not (and (= nil$ ?v1) (= uu$ ?v0))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (not (and (not (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1)))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))) (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))))) :rule bind)
(anchor :step t101 :args ((?v0 Real_a_fun$) (?v1 B_list$) (:= (?v0 Real_a_fun$) ?v0) (:= (?v1 B_list$) ?v1)))
(step t101.t0 (cl (= @p_138 (= @p_137 @p_132))) :rule rare_rewrite :args ("eq-symm" @p_132 @p_137))
(step t101 (cl (= (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))) (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))))) :rule bind)
(step t102 (cl (= (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (not (and (= ?v0 (rec_join$ ?v1)) (not (and (= nil$ ?v1) (= uu$ ?v0))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (not (and (not (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1)))) (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))) (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))))) :rule trans :premises (t100 t101))
(step t103 (cl (= (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (=> (and (= (rec_join$ ?v1) ?v0) (and (=> (and (= ?v1 nil$) (= uu$ ?v0)) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= ?v0 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false) (=> (and (= (rec_join$ ?v1) (rec_join$ ?v1)) (and (=> (and (= ?v1 nil$) (= uu$ (rec_join$ ?v1))) false) (and (forall ((?v2 B$)) (=> (and (= ?v1 (cons$ ?v2 nil$)) (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4))) (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false))) (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (= (or (and (= nil$ ?v1) (= uu$ (rec_join$ ?v1))) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= (rec_join$ ?v1) (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= (rec_join$ ?v1) (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))) (or (not (= ?v0 (rec_join$ ?v1))) (and (= nil$ ?v1) (= uu$ ?v0)) (not (forall ((?v2 B$)) (or (not (= ?v1 (cons$ ?v2 nil$))) (not (= ?v0 (coeff_cube_to_path$ ?v2)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= ?v1 (cons$ ?v2 (cons$ ?v3 ?v4)))) (not (= ?v0 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))))))))))) :rule trans :premises (t99 t102))
(anchor :step t104 :args ((?v0 B_list$) (?v1 Real_a_fun$) (:= (?v0 B_list$) ?v0) (:= (?v1 Real_a_fun$) ?v1)))
(step t104.t0 (cl (= (! (=> (! (and (! (= @p_20 ?v1) :named @p_91) (and (! (=> (! (and (! (= ?v0 nil$) :named @p_34) (! (= uu$ ?v1) :named @p_70)) :named @p_89) false) :named @p_90) (and (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) :named @p_92) false) :named @p_93) (! (not @p_92) :named @p_94))) :rule rare_rewrite :args ("bool-impl-false1" @p_92))
(step t104.t1 (cl (= @p_92 (! (and @p_91 @p_90 (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))) :named @p_95))) :rule aci_simp)
(step t104.t2 (cl (= @p_91 (! (= ?v1 @p_20) :named @p_67))) :rule rare_rewrite :args ("eq-symm" @p_20 ?v1))
(step t104.t3 (cl (= @p_90 (! (not @p_89) :named @p_121))) :rule rare_rewrite :args ("bool-impl-false1" @p_89))
(step t104.t4 (cl (= @p_34 @p_22)) :rule rare_rewrite :args ("eq-symm" ?v0 nil$))
(step t104.t5 (cl (= @p_70 @p_70)) :rule refl)
(step t104.t6 (cl (= @p_89 (! (and @p_22 @p_70) :named @p_71))) :rule cong :premises (t104.t4 t104.t5))
(step t104.t7 (cl (= @p_121 (! (not @p_71) :named @p_77))) :rule cong :premises (t104.t6))
(step t104.t8 (cl (= @p_90 @p_77)) :rule trans :premises (t104.t3 t104.t7))
(anchor :step t104.t9 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t104.t9.t0 (cl (= (! (=> (! (and (! (= ?v0 @p_112) :named @p_117) (! (= ?v1 @p_99) :named @p_116)) :named @p_118) false) :named @p_119) (! (not @p_118) :named @p_120))) :rule rare_rewrite :args ("bool-impl-false1" @p_118))
(step t104.t9.t1 (cl (= @p_117 (! (= @p_112 ?v0) :named @p_113))) :rule rare_rewrite :args ("eq-symm" ?v0 @p_112))
(step t104.t9.t2 (cl (= @p_116 (! (= @p_99 ?v1) :named @p_111))) :rule rare_rewrite :args ("eq-symm" ?v1 @p_99))
(step t104.t9.t3 (cl (= @p_118 (! (and @p_113 @p_111) :named @p_114))) :rule cong :premises (t104.t9.t1 t104.t9.t2))
(step t104.t9.t4 (cl (= @p_120 (! (not @p_114) :named @p_115))) :rule cong :premises (t104.t9.t3))
(step t104.t9.t5 (cl (= @p_119 @p_115)) :rule trans :premises (t104.t9.t0 t104.t9.t4))
(step t104.t9 (cl (= (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (not (and (= (cons$ ?v2 nil$) ?v0) (= (coeff_cube_to_path$ ?v2) ?v1)))))) :rule bind)
(anchor :step t104.t10 :args ((?v2 B$) (:= (?v2 B$) ?v2)))
(step t104.t10.t0 (cl (= @p_115 (or (not @p_113) (not @p_111)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_113 @p_111 rare-list))
(step t104.t10 (cl (= (forall ((?v2 B$)) (not (and (= (cons$ ?v2 nil$) ?v0) (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))))) :rule bind)
(step t104.t11 (cl (= (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))))) :rule trans :premises (t104.t9 t104.t10))
(anchor :step t104.t12 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t104.t12.t0 (cl (= (! (=> (! (and (! (= ?v0 @p_102) :named @p_107) (! (= ?v1 @p_100) :named @p_106)) :named @p_108) false) :named @p_109) (! (not @p_108) :named @p_110))) :rule rare_rewrite :args ("bool-impl-false1" @p_108))
(step t104.t12.t1 (cl (= @p_107 (! (= @p_102 ?v0) :named @p_103))) :rule rare_rewrite :args ("eq-symm" ?v0 @p_102))
(step t104.t12.t2 (cl (= @p_106 (! (= @p_100 ?v1) :named @p_101))) :rule rare_rewrite :args ("eq-symm" ?v1 @p_100))
(step t104.t12.t3 (cl (= @p_108 (! (and @p_103 @p_101) :named @p_104))) :rule cong :premises (t104.t12.t1 t104.t12.t2))
(step t104.t12.t4 (cl (= @p_110 (! (not @p_104) :named @p_105))) :rule cong :premises (t104.t12.t3))
(step t104.t12.t5 (cl (= @p_109 @p_105)) :rule trans :premises (t104.t12.t0 t104.t12.t4))
(step t104.t12 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0) (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))) :rule bind)
(anchor :step t104.t13 :args ((?v2 B$) (?v3 B$) (?v4 B_list$) (:= (?v2 B$) ?v2) (:= (?v3 B$) ?v3) (:= (?v4 B_list$) ?v4)))
(step t104.t13.t0 (cl (= @p_105 (or (not @p_103) (not @p_101)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_103 @p_101 rare-list))
(step t104.t13 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (not (and (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0) (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))) :rule bind)
(step t104.t14 (cl (= (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))) :rule trans :premises (t104.t12 t104.t13))
(step t104.t15 (cl (= @p_95 (! (and @p_67 @p_77 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))) :named @p_78))) :rule cong :premises (t104.t2 t104.t8 t104.t11 t104.t14))
(step t104.t16 (cl (= @p_92 @p_78)) :rule trans :premises (t104.t1 t104.t15))
(step t104.t17 (cl (= @p_94 (! (not @p_78) :named @p_79))) :rule cong :premises (t104.t16))
(step t104.t18 (cl (= @p_93 @p_79)) :rule trans :premises (t104.t0 t104.t17))
(step t104 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (=> (and (= (rec_join$ ?v0) ?v1) (and (=> (and (= ?v0 nil$) (= uu$ ?v1)) false) (and (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false)) (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (not (and (= ?v1 (rec_join$ ?v0)) (not (and (= nil$ ?v0) (= uu$ ?v1))) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))))) :rule bind)
(anchor :step t105 :args ((?v0 B_list$) (?v1 Real_a_fun$) (:= (?v0 B_list$) ?v0) (:= (?v1 Real_a_fun$) ?v1)))
(step t105.t0 (cl (= @p_79 (! (or (! (not @p_67) :named @p_72) (! (not (and @p_77 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))) :named @p_85)) :named @p_86))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_67 @p_77 (rare-list (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))))
(step t105.t1 (cl (= @p_85 (! (or (! (not @p_77) :named @p_81) (! (not (and (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))) :named @p_87)) :named @p_88))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_77 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (rare-list (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))))
(step t105.t2 (cl (= @p_87 (! (or (! (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) :named @p_69) (! (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))) :named @p_68)) :named @p_80))) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))) rare-list))
(step t105.t3 (cl (= @p_88 (! (or @p_81 @p_80) :named @p_82))) :rule cong :premises (t105.t2))
(step t105.t4 (cl (= @p_85 @p_82)) :rule trans :premises (t105.t1 t105.t3))
(step t105.t5 (cl (= @p_86 (! (or @p_72 @p_82) :named @p_83))) :rule cong :premises (t105.t4))
(step t105.t6 (cl (= @p_79 @p_83)) :rule trans :premises (t105.t0 t105.t5))
(step t105.t7 (cl (= @p_83 (! (or @p_72 @p_81 @p_69 @p_68) :named @p_84))) :rule aci_simp)
(step t105.t8 (cl (= @p_81 @p_71)) :rule rare_rewrite :args ("bool-double-not-elim" @p_71))
(step t105.t9 (cl (= @p_69 @p_69)) :rule refl)
(step t105.t10 (cl (= @p_68 @p_68)) :rule refl)
(step t105.t11 (cl (= @p_84 (! (or @p_72 @p_71 @p_69 @p_68) :named @p_76))) :rule cong :premises (t105.t8 t105.t9 t105.t10))
(step t105.t12 (cl (= @p_83 @p_76)) :rule trans :premises (t105.t7 t105.t11))
(step t105.t13 (cl (= @p_79 @p_76)) :rule trans :premises (t105.t6 t105.t12))
(step t105 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (not (and (= ?v1 (rec_join$ ?v0)) (not (and (= nil$ ?v0) (= uu$ ?v1))) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))))) :rule bind)
(step t106 (cl (= (forall ((?v0 B_list$)) (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))))) (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))))) :rule qnt_join)
(step t107 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v0 B_list$)) (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))))))) :rule symm :premises (t106))
(anchor :step t108 :args ((?v0 B_list$) (:= (?v0 B_list$) ?v0)))
(anchor :step t108.t0 :args ((?v1 Real_a_fun$) (:= (?v1 Real_a_fun$) ?v1)))
(step t108.t0.t0 (cl (= @p_76 (! (or @p_72 @p_72 @p_71 @p_69 @p_68) :named @p_73))) :rule aci_simp)
(step t108.t0 (cl (= (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))))) :rule bind)
(anchor :step t108.t1 :args ((:= (?v1 Real_a_fun$) @p_20)))
(step t108.t1.t0 (cl (= @p_73 (! (or (! (not (! (= @p_20 @p_20) :named @p_37)) :named @p_63) @p_63 @p_23 @p_61 @p_60) :named @p_74))) :rule refl)
(step t108.t1.t1 (cl (= @p_74 (! (or @p_63 @p_23 @p_61 @p_60) :named @p_64))) :rule rare_rewrite :args ("or-not-refl" @p_20 (rare-list @p_63 @p_23 @p_61 @p_60)))
(step t108.t1.t2 (cl (= @p_73 @p_64)) :rule trans :premises (t108.t1.t0 t108.t1.t1))
(step t108.t1 (cl (= (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) @p_64)) :rule onepoint)
(step t108.t2 (cl (= (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) @p_64)) :rule trans :premises (t108.t0 t108.t1))
(step t108 (cl (= (forall ((?v0 B_list$)) (forall ((?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1)))))))) (forall ((?v0 B_list$)) (or (not (= (rec_join$ ?v0) (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule bind)
(step t109 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v0 B_list$)) (or (not (= (rec_join$ ?v0) (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule trans :premises (t107 t108))
(anchor :step t110 :args ((?v0 B_list$) (:= (?v0 B_list$) ?v0)))
(step t110.t0 (cl (= @p_37 true)) :rule rare_rewrite :args ("eq-refl" @p_20))
(step t110.t1 (cl (= @p_63 (! (not true) :named @p_66))) :rule cong :premises (t110.t0))
(step t110.t2 (cl (= @p_66 false)) :rule evaluate)
(step t110.t3 (cl (= @p_63 false)) :rule trans :premises (t110.t1 t110.t2))
(step t110.t4 (cl (= @p_23 @p_23)) :rule refl)
(step t110.t5 (cl (= @p_61 @p_61)) :rule refl)
(step t110.t6 (cl (= @p_60 @p_60)) :rule refl)
(step t110.t7 (cl (= @p_64 (! (or false @p_23 @p_61 @p_60) :named @p_65))) :rule cong :premises (t110.t3 t110.t4 t110.t5 t110.t6))
(step t110.t8 (cl (= @p_65 @p_62)) :rule aci_simp)
(step t110.t9 (cl (= @p_64 @p_62)) :rule trans :premises (t110.t7 t110.t8))
(step t110 (cl (= (forall ((?v0 B_list$)) (or (not (= (rec_join$ ?v0) (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule bind)
(step t111 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (or (not (= ?v1 (rec_join$ ?v0))) (and (= nil$ ?v0) (= uu$ ?v1)) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule trans :premises (t109 t110))
(step t112 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (not (and (= ?v1 (rec_join$ ?v0)) (not (and (= nil$ ?v0) (= uu$ ?v1))) (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) ?v1)))) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) ?v1))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule trans :premises (t105 t111))
(step t113 (cl (= (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (=> (and (= (rec_join$ ?v0) ?v1) (and (=> (and (= ?v0 nil$) (= uu$ ?v1)) false) (and (forall ((?v2 B$)) (=> (and (= ?v0 (cons$ ?v2 nil$)) (= ?v1 (coeff_cube_to_path$ ?v2))) false)) (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (=> (and (= ?v0 (cons$ ?v2 (cons$ ?v3 ?v4))) (= ?v1 (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))))) false))))) false)) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))))) :rule trans :premises (t104 t112))
(anchor :step t114 :args ((?v0 B_list$) (:= (?v0 B_list$) ?v0)))
(step t114.t0 (cl (= (! (=> (! (and @p_37 (and (! (=> (! (and @p_34 @p_21) :named @p_35) false) :named @p_36) (and (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false))))) :named @p_38) false) :named @p_39) (! (not @p_38) :named @p_40))) :rule rare_rewrite :args ("bool-impl-false1" @p_38))
(step t114.t1 (cl (= @p_38 (! (and @p_37 @p_36 (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false))) :named @p_41))) :rule aci_simp)
(step t114.t2 (cl (= @p_37 true)) :rule rare_rewrite :args ("eq-refl" @p_20))
(step t114.t3 (cl (= @p_36 (! (not @p_35) :named @p_59))) :rule rare_rewrite :args ("bool-impl-false1" @p_35))
(step t114.t4 (cl (= @p_34 @p_22)) :rule rare_rewrite :args ("eq-symm" ?v0 nil$))
(step t114.t5 (cl (= @p_21 @p_21)) :rule refl)
(step t114.t6 (cl (= @p_35 @p_23)) :rule cong :premises (t114.t4 t114.t5))
(step t114.t7 (cl (= @p_59 (! (not @p_23) :named @p_25))) :rule cong :premises (t114.t6))
(step t114.t8 (cl (= @p_36 @p_25)) :rule trans :premises (t114.t3 t114.t7))
(anchor :step t114.t9 :args ((?v1 B$) (:= (?v1 B$) ?v1)))
(step t114.t9.t0 (cl (= (=> (! (and (! (= ?v0 @p_55) :named @p_56) (! (= @p_20 @p_47) :named @p_54)) :named @p_57) false) (! (not @p_57) :named @p_58))) :rule rare_rewrite :args ("bool-impl-false1" @p_57))
(step t114.t9 (cl (= (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$)) (not (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))))) :rule bind)
(anchor :step t114.t10 :args ((?v1 B$) (:= (?v1 B$) ?v1)))
(step t114.t10.t0 (cl (= @p_58 (or (not @p_56) (not @p_54)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_56 @p_54 rare-list))
(step t114.t10 (cl (= (forall ((?v1 B$)) (not (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))))) :rule bind)
(step t114.t11 (cl (= (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))))) :rule trans :premises (t114.t9 t114.t10))
(anchor :step t114.t12 :args ((?v1 B$) (?v2 B$) (?v3 B_list$) (:= (?v1 B$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B_list$) ?v3)))
(step t114.t12.t0 (cl (= (=> (! (and (! (= ?v0 @p_50) :named @p_51) (! (= @p_20 @p_48) :named @p_49)) :named @p_52) false) (! (not @p_52) :named @p_53))) :rule rare_rewrite :args ("bool-impl-false1" @p_52))
(step t114.t12 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (not (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))) :rule bind)
(anchor :step t114.t13 :args ((?v1 B$) (?v2 B$) (?v3 B_list$) (:= (?v1 B$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B_list$) ?v3)))
(step t114.t13.t0 (cl (= @p_53 (or (not @p_51) (not @p_49)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_51 @p_49 rare-list))
(step t114.t13 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (not (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))) :rule bind)
(step t114.t14 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))) :rule trans :premises (t114.t12 t114.t13))
(step t114.t15 (cl (= @p_41 (! (and true @p_25 (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))) :named @p_42))) :rule cong :premises (t114.t2 t114.t8 t114.t11 t114.t14))
(step t114.t16 (cl (= @p_42 (! (and @p_25 (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))) :named @p_26))) :rule aci_simp)
(step t114.t17 (cl (= @p_41 @p_26)) :rule trans :premises (t114.t15 t114.t16))
(step t114.t18 (cl (= @p_38 @p_26)) :rule trans :premises (t114.t1 t114.t17))
(step t114.t19 (cl (= @p_40 (! (not @p_26) :named @p_27))) :rule cong :premises (t114.t18))
(step t114.t20 (cl (= @p_39 @p_27)) :rule trans :premises (t114.t0 t114.t19))
(step t114 (cl (= (forall ((?v0 B_list$)) (=> (and (= (rec_join$ ?v0) (rec_join$ ?v0)) (and (=> (and (= ?v0 nil$) (= uu$ (rec_join$ ?v0))) false) (and (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false))))) false)) (forall ((?v0 B_list$)) (not (and (not (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0)))) (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))))) :rule bind)
(anchor :step t115 :args ((?v0 B_list$) (:= (?v0 B_list$) ?v0)))
(step t115.t0 (cl (= @p_27 (! (or (! (not @p_25) :named @p_29) (! (not (and (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))) :named @p_32)) :named @p_33))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_25 (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (rare-list (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))
(step t115.t1 (cl (= @p_32 (! (or @p_19 @p_18) :named @p_28))) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))) rare-list))
(step t115.t2 (cl (= @p_33 (! (or @p_29 @p_28) :named @p_30))) :rule cong :premises (t115.t1))
(step t115.t3 (cl (= @p_27 @p_30)) :rule trans :premises (t115.t0 t115.t2))
(step t115.t4 (cl (= @p_30 (! (or @p_29 @p_19 @p_18) :named @p_31))) :rule aci_simp)
(step t115.t5 (cl (= @p_29 @p_23)) :rule rare_rewrite :args ("bool-double-not-elim" @p_23))
(step t115.t6 (cl (= @p_19 @p_19)) :rule refl)
(step t115.t7 (cl (= @p_18 @p_18)) :rule refl)
(step t115.t8 (cl (= @p_31 @p_24)) :rule cong :premises (t115.t5 t115.t6 t115.t7))
(step t115.t9 (cl (= @p_30 @p_24)) :rule trans :premises (t115.t4 t115.t8))
(step t115.t10 (cl (= @p_27 @p_24)) :rule trans :premises (t115.t3 t115.t9))
(step t115 (cl (= (forall ((?v0 B_list$)) (not (and (not (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0)))) (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))))) :rule bind)
(step t116 (cl (= (forall ((?v0 B_list$)) (=> (and (= (rec_join$ ?v0) (rec_join$ ?v0)) (and (=> (and (= ?v0 nil$) (= uu$ (rec_join$ ?v0))) false) (and (forall ((?v1 B$)) (=> (and (= ?v0 (cons$ ?v1 nil$)) (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1))) false)) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (=> (and (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3))) (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))) false))))) false)) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))))) :rule trans :premises (t114 t115))
(step t117 (cl (= @p_1 @p_13)) :rule cong :premises (t113 t116))
(step t118 (cl (= @p_2 @p_14)) :rule cong :premises (t103 t117))
(step t119 (cl @p_16) :rule cong :premises (t118))
(step t120 (cl @p_15) :rule resolution :premises (t98 t119 a1))
(step t121 (cl (not @p_13)) :rule not_implies2 :premises (t120))
(step t122 (cl @p_11 @p_12) :rule not_equiv2 :premises (t121))
(step t123 (cl @p_11) :rule resolution :premises (t35 t42 t46 t48 t59 t70 t71 t97 t122))
(step t124 (cl @p_10) :rule resolution :premises (t33 t123))
(step t125 (cl (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ @quantifiers_skolemize_4)))))) :rule resolution :premises (t16 t124))
(step t126 (cl (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4)))))) :rule resolution :premises (t5 t125))
(anchor :step t127 :args ((?v1 B$) (:= (?v2 B$) ?v1)))
(step t127.t0 (cl (= (or (not (= @p_112 @quantifiers_skolemize_4)) (not (= @p_99 @p_4))) (! (or (! (not (! (= @p_55 @quantifiers_skolemize_4) :named @p_273)) :named @p_274) (! (not (! (= @p_47 @p_4) :named @p_271)) :named @p_272)) :named @p_275))) :rule refl)
(step t127 (cl (= (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4))))) (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_4))))))) :rule bind)
(step t128 (cl @p_8 (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_4)))))) :rule equiv1 :premises (t127))
(step t129 (cl (not (! (= (! (or @p_9 (! (not @p_8) :named @p_281)) :named @p_282) (! (or @p_9 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4)))))) :named @p_280)) :named @p_283)) (not @p_282) @p_280) :rule equiv_pos2)
(step t130 (cl (= @p_281 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4)))))))
(step t131 (cl @p_283) :rule cong :premises (t130))
(step t132 (cl @p_9 @p_281) :rule or_neg :args (1))
(step t133 (cl @p_282 @p_10) :rule or_neg :args (0))
(step t134 (cl @p_282 (not @p_281)) :rule or_neg :args (1))
(step t135 (cl @p_282 @p_282) :rule resolution :premises (t132 t133 t134))
(step t136 (cl @p_282) :rule contraction :premises (t135))
(step t137 (cl @p_280) :rule resolution :premises (t129 t131 t136))
(step t138 (cl @p_9 (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4)))))) :rule or :premises (t137))
(step t139 (cl (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4))))) @p_9) :rule reordering :premises (t138))
(step t140 (cl (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ @quantifiers_skolemize_4)))))) :rule resolution :premises (t139 t124))
(step t141 (cl (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_4)))))) :rule resolution :premises (t128 t140))
(step t142 (cl (not (! (= (! (=> (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) (! (or @p_5 (! (not (forall ((?v1 B$)) (or (not (= @quantifiers_skolemize_4 (cons$ ?v1 nil$))) (not (= (rec_join$ @quantifiers_skolemize_4) (coeff_cube_to_path$ ?v1)))))) :named @p_258) (! (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= @quantifiers_skolemize_4 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ @quantifiers_skolemize_4) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))) :named @p_257)) :named @p_259)) :named @p_260) (! (=> (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))) @p_255) :named @p_256)) :named @p_261)) (not @p_260) @p_256) :rule equiv_pos2)
(anchor :step t143 :args ((?v1 B$) (:= (?v1 B$) ?v1)))
(step t143.t0 (cl (= (! (= @quantifiers_skolemize_4 @p_55) :named @p_278) @p_273)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_4 @p_55))
(step t143.t1 (cl (= (! (not @p_278) :named @p_279) @p_274)) :rule cong :premises (t143.t0))
(step t143.t2 (cl (= (! (= @p_4 @p_47) :named @p_276) @p_271)) :rule rare_rewrite :args ("eq-symm" @p_4 @p_47))
(step t143.t3 (cl (= (! (not @p_276) :named @p_277) @p_272)) :rule cong :premises (t143.t2))
(step t143.t4 (cl (= (or @p_279 @p_277) @p_275)) :rule cong :premises (t143.t1 t143.t3))
(step t143 (cl (= (forall ((?v1 B$)) (or (not (= @quantifiers_skolemize_4 (cons$ ?v1 nil$))) (not (= (rec_join$ @quantifiers_skolemize_4) (coeff_cube_to_path$ ?v1))))) (forall ((?v1 B$)) (or (not (= (cons$ ?v1 nil$) @quantifiers_skolemize_4)) (not (= (coeff_cube_to_path$ ?v1) (rec_join$ @quantifiers_skolemize_4))))))) :rule bind)
(step t144 (cl (= @p_258 @p_254)) :rule cong :premises (t143))
(anchor :step t145 :args ((?v1 B$) (?v2 B$) (?v3 B_list$) (:= (?v1 B$) ?v1) (:= (?v2 B$) ?v2) (:= (?v3 B_list$) ?v3)))
(step t145.t0 (cl (= (! (= @quantifiers_skolemize_4 @p_50) :named @p_269) @p_264)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_4 @p_50))
(step t145.t1 (cl (= (! (not @p_269) :named @p_270) @p_265)) :rule cong :premises (t145.t0))
(step t145.t2 (cl (= (! (= @p_4 @p_48) :named @p_267) @p_262)) :rule rare_rewrite :args ("eq-symm" @p_4 @p_48))
(step t145.t3 (cl (= (! (not @p_267) :named @p_268) @p_263)) :rule cong :premises (t145.t2))
(step t145.t4 (cl (= (or @p_270 @p_268) @p_266)) :rule cong :premises (t145.t1 t145.t3))
(step t145 (cl (= (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= @quantifiers_skolemize_4 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ @quantifiers_skolemize_4) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))) (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= (cons$ ?v1 (cons$ ?v2 ?v3)) @quantifiers_skolemize_4)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))) (rec_join$ @quantifiers_skolemize_4))))))) :rule bind)
(step t146 (cl (= @p_257 @p_253)) :rule cong :premises (t145))
(step t147 (cl (= @p_259 @p_255)) :rule cong :premises (t144 t146))
(step t148 (cl @p_261) :rule cong :premises (t147))
(step t149 (cl @p_260 (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))) :rule implies_neg1)
(anchor :step t150)
(assume t150.a0 (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3)))))))))))
(step t150.t0 (cl (or @p_12 @p_259)) :rule forall_inst :args (@quantifiers_skolemize_4))
(step t150.t1 (cl @p_12 @p_259) :rule or :premises (t150.t0))
(step t150.t2 (cl @p_259) :rule resolution :premises (t150.t1 t150.a0))
(step t150 (cl @p_12 @p_259) :rule subproof :discharge (t150.a0))
(step t151 (cl @p_260 @p_259) :rule resolution :premises (t149 t150))
(step t152 (cl @p_260 (not @p_259)) :rule implies_neg2)
(step t153 (cl @p_260 @p_260) :rule resolution :premises (t151 t152))
(step t154 (cl @p_260) :rule contraction :premises (t153))
(step t155 (cl @p_256) :rule resolution :premises (t142 t148 t154))
(step t156 (cl @p_12 @p_255) :rule implies :premises (t155))
(step t157 (cl (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v2 B$)) (or (not (= (cons$ ?v2 nil$) ?v0)) (not (= (coeff_cube_to_path$ ?v2) (rec_join$ ?v0)))))) (not (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (or (not (= (cons$ ?v2 (cons$ ?v3 ?v4)) ?v0)) (not (= (joinpaths$ (coeff_cube_to_path$ ?v2) (rec_join$ (cons$ ?v3 ?v4))) (rec_join$ ?v0)))))))) (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))) :rule not_equiv1 :premises (t121))
(step t158 (cl (forall ((?v0 B_list$)) (or (and (= nil$ ?v0) (= uu$ (rec_join$ ?v0))) (not (forall ((?v1 B$)) (or (not (= ?v0 (cons$ ?v1 nil$))) (not (= (rec_join$ ?v0) (coeff_cube_to_path$ ?v1)))))) (not (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (or (not (= ?v0 (cons$ ?v1 (cons$ ?v2 ?v3)))) (not (= (rec_join$ ?v0) (joinpaths$ (coeff_cube_to_path$ ?v1) (rec_join$ (cons$ ?v2 ?v3))))))))))) :rule resolution :premises (t157 t123))
(step t159 (cl @p_255) :rule resolution :premises (t156 t158))
(step t160 (cl @p_9 (! (not @p_5) :named @p_6)) :rule or_neg :args (0))
(step t161 (cl @p_6) :rule resolution :premises (t160 t124))
(step t162 (cl) :rule resolution :premises (t1 t126 t141 t159 t161))
)
6c9fc05a380fc8237fe8afde986344855428e9e3 7168 0
unsat
(
(assume a0 (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))))
(assume a1 (forall ((?v0 Int)) (= (centered_divide$ ?v0 0) 0)))
(assume a2 (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0)))
(assume a3 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)))))
(assume a4 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(assume a5 (forall ((?v0 Int)) (= (dvd$ 2 ?v0) (= (modulo$ ?v0 2) 0))))
(assume a6 (forall ((?v0 Int)) (= (<= 0 (divide$ ?v0 2)) (<= 0 ?v0))))
(assume a7 (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0))))
(assume a8 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(assume a9 (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))))
(assume a10 (forall ((?v0 Int)) (= (not (dvd$ 2 ?v0)) (= (modulo$ ?v0 2) 1))))
(assume a11 (! (not (! (= (! (centered_divide$ 0 k$) :named @p_1) 0) :named @p_2)) :named @p_3))
(step t0 (cl (! (not (! (or (! (not (! (>= (! (times$ (! (divide$ (! (ite (! (>= k$ 0) :named @p_5) k$ (! (* -1 k$) :named @p_4)) :named @p_6) 2) :named @p_7) 2) :named @p_8) 0) :named @p_15)) :named @p_16) (! (not (! (>= (! (+ (! (divide$ (! (ite (! (>= k$ 0) :named @p_5) k$ (! (* -1 k$) :named @p_4)) :named @p_6) 2) :named @p_7) (! (* -1 @p_8) :named @p_11)) :named @p_12) 1) :named @p_13)) :named @p_14) (! (= (! (times$ (! (divide$ (! (ite (! (>= k$ 0) :named @p_5) k$ (! (* -1 k$) :named @p_4)) :named @p_6) 2) :named @p_7) 2) :named @p_8) (! (modulo$ @p_8 @p_7) :named @p_9)) :named @p_10)) :named @p_17)) :named @p_1097) @p_16 @p_14 @p_10) :rule or_pos)
(step t1 (cl @p_16 @p_10 @p_14 @p_1097) :rule reordering :premises (t0))
(step t2 (cl (! (=> (! (and (! (= (! (divide$ @p_8 @p_7) :named @p_742) 2) :named @p_743) (! (= @p_8 (! (+ (! (times$ @p_7 @p_742) :named @p_1076) @p_9) :named @p_1098)) :named @p_1099) @p_10 (! (>= @p_8 1) :named @p_1049)) :named @p_1102) (! (and @p_10 (! (= @p_8 (! (+ (! (times$ @p_7 @p_742) :named @p_1076) @p_9) :named @p_1098)) :named @p_1099) @p_1049 (! (= @p_8 @p_1076) :named @p_1077)) :named @p_1104)) :named @p_1135) @p_1102) :rule implies_neg1)
(anchor :step t3)
(assume t3.a0 @p_743)
(assume t3.a1 @p_1099)
(assume t3.a2 @p_10)
(assume t3.a3 @p_1049)
(step t3.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :named @p_190) @p_1099)) :rule forall_inst :args (@p_7 @p_8))
(step t3.t1 (cl @p_190 @p_1099) :rule or :premises (t3.t0))
(step t3.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :named @p_179)) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t3.t3 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t3.t3.t0 (cl (= (! (+ (! (+ (! (times$ ?v0 (divide$ ?v1 ?v0)) :named @p_181) (! (modulo$ ?v1 ?v0) :named @p_180)) :named @p_182) ?v2) :named @p_185) (! (+ @p_180 @p_181 ?v2) :named @p_189))) :rule poly_simp)
(step t3.t3.t1 (cl (= @p_189 (! (+ ?v2 @p_181 @p_180) :named @p_187))) :rule poly_simp)
(step t3.t3.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t3.t3.t0 t3.t3.t1))
(step t3.t3.t3 (cl (= (! (+ ?v1 ?v2) :named @p_184) @p_184)) :rule refl)
(step t3.t3.t4 (cl (= (! (= @p_185 @p_184) :named @p_186) (! (= @p_187 @p_184) :named @p_188))) :rule cong :premises (t3.t3.t2 t3.t3.t3))
(step t3.t3.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t3.t3.t6 (cl (= @p_188 (! (= ?v1 @p_182) :named @p_183))) :rule poly_simp_rel :premises (t3.t3.t5))
(step t3.t3.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t3.t3.t4 t3.t3.t6))
(step t3.t3 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t3.t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t3.t5 (cl @p_179) :rule trans :premises (t3.t3 t3.t4))
(step t3.t6 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t3.t2 t3.t5 a0))
(step t3.t7 (cl @p_1099) :rule resolution :premises (t3.t1 t3.t6))
(step t3.t8 (cl (! (=> @p_743 @p_1077) :named @p_1082) @p_743) :rule implies_neg1)
(anchor :step t3.t9)
(assume t3.t9.a0 @p_743)
(step t3.t9.t0 (cl (! (= 2 @p_742) :named @p_746)) :rule symm :premises (t3.t9.a0))
(step t3.t9.t1 (cl @p_1077) :rule cong :premises (t3.t9.t0))
(step t3.t9 (cl (! (not @p_743) :named @p_794) @p_1077) :rule subproof :discharge (t3.t9.a0))
(step t3.t10 (cl @p_1082 @p_1077) :rule resolution :premises (t3.t8 t3.t9))
(step t3.t11 (cl @p_1082 (! (not @p_1077) :named @p_1083)) :rule implies_neg2)
(step t3.t12 (cl @p_1082 @p_1082) :rule resolution :premises (t3.t10 t3.t11))
(step t3.t13 (cl @p_1082) :rule contraction :premises (t3.t12))
(step t3.t14 (cl @p_794 @p_1077) :rule implies :premises (t3.t13))
(step t3.t15 (cl @p_1077) :rule resolution :premises (t3.t14 t3.a0))
(step t3.t16 (cl @p_1104) :rule and_intro :premises (t3.a2 t3.t7 t3.a3 t3.t15))
(step t3 (cl @p_794 (! (not @p_1099) :named @p_1100) (! (not @p_10) :named @p_1101) (! (not @p_1049) :named @p_1051) @p_1104) :rule subproof :discharge (t3.a0 t3.a1 t3.a2 t3.a3))
(step t4 (cl (! (not @p_1102) :named @p_1103) @p_743) :rule and_pos :args (0))
(step t5 (cl @p_1103 @p_1099) :rule and_pos :args (1))
(step t6 (cl @p_1103 @p_10) :rule and_pos :args (2))
(step t7 (cl @p_1103 @p_1049) :rule and_pos :args (3))
(step t8 (cl @p_1104 @p_1103 @p_1103 @p_1103 @p_1103) :rule resolution :premises (t3 t4 t5 t6 t7))
(step t9 (cl @p_1103 @p_1103 @p_1103 @p_1103 @p_1104) :rule reordering :premises (t8))
(step t10 (cl @p_1103 @p_1104) :rule contraction :premises (t9))
(step t11 (cl @p_1135 @p_1104) :rule resolution :premises (t2 t10))
(step t12 (cl @p_1135 (! (not @p_1104) :named @p_1105)) :rule implies_neg2)
(step t13 (cl @p_1135 @p_1135) :rule resolution :premises (t11 t12))
(step t14 (cl @p_1135) :rule contraction :premises (t13))
(step t15 (cl @p_1103 @p_1104) :rule implies :premises (t14))
(step t16 (cl (! (=> @p_1104 false) :named @p_1106) @p_1104) :rule implies_neg1)
(anchor :step t17)
(assume t17.a0 @p_10)
(assume t17.a1 @p_1099)
(assume t17.a2 @p_1049)
(assume t17.a3 @p_1077)
(step t17.t0 (cl (not (! (= @p_1077 (! (= (! (+ @p_8 (! (* -1 @p_1076) :named @p_1107)) :named @p_1108) 0) :named @p_1109)) :named @p_1134)) @p_1083 @p_1109) :rule equiv_pos2)
(step t17.t1 (cl (= (* 1 (- @p_1108 0)) (* 1 (- @p_8 @p_1076)))) :rule poly_simp)
(step t17.t2 (cl (= @p_1109 @p_1077)) :rule poly_simp_rel :premises (t17.t1))
(step t17.t3 (cl @p_1134) :rule symm :premises (t17.t2))
(step t17.t4 (cl @p_1109) :rule resolution :premises (t17.t0 t17.t3 t17.a3))
(step t17.t5 (cl (! (=> @p_1109 false) :named @p_1111) @p_1109) :rule implies_neg1)
(anchor :step t17.t6)
(assume t17.t6.a0 @p_1109)
(step t17.t6.t0 (cl (not (! (= (! (<= (! (+ @p_1108 @p_11 (! (* -1 (! (+ @p_8 @p_1107 (! (* -1 @p_9) :named @p_1113)) :named @p_1115)) :named @p_1116) (! (+ @p_8 @p_1113) :named @p_1114)) :named @p_1117) (! (+ 0 (! (* -1 1) :named @p_298) (! (* -1 0) :named @p_297) 0) :named @p_1112)) :named @p_1118) false) :named @p_1128)) (not @p_1118) false) :rule equiv_pos2)
(step t17.t6.t1 (cl (= @p_1117 (! (+ (! (* 0 @p_9) :named @p_1131) (! (* 0 @p_1076) :named @p_1130) @p_11 @p_8) :named @p_1132))) :rule poly_simp)
(step t17.t6.t2 (cl (= @p_1131 0)) :rule poly_simp)
(step t17.t6.t3 (cl (= @p_1130 0)) :rule poly_simp)
(step t17.t6.t4 (cl (= @p_11 @p_11)) :rule refl)
(step t17.t6.t5 (cl (= @p_8 @p_8)) :rule refl)
(step t17.t6.t6 (cl (= @p_1132 (! (+ 0 0 @p_11 @p_8) :named @p_1133))) :rule cong :premises (t17.t6.t2 t17.t6.t3 t17.t6.t4 t17.t6.t5))
(step t17.t6.t7 (cl (= @p_1133 0)) :rule poly_simp)
(step t17.t6.t8 (cl (= @p_1132 0)) :rule trans :premises (t17.t6.t6 t17.t6.t7))
(step t17.t6.t9 (cl (= @p_1117 0)) :rule trans :premises (t17.t6.t1 t17.t6.t8))
(step t17.t6.t10 (cl (= @p_298 -1)) :rule evaluate)
(step t17.t6.t11 (cl (= @p_297 0)) :rule evaluate)
(step t17.t6.t12 (cl (! (= 0 0) :named @p_56)) :rule refl)
(step t17.t6.t13 (cl (= @p_1112 (! (+ 0 -1 0 0) :named @p_1129))) :rule cong :premises (t17.t6.t10 t17.t6.t11 t17.t6.t12))
(step t17.t6.t14 (cl (= @p_1129 -1)) :rule evaluate)
(step t17.t6.t15 (cl (= @p_1112 -1)) :rule trans :premises (t17.t6.t13 t17.t6.t14))
(step t17.t6.t16 (cl (= @p_1118 (! (<= 0 -1) :named @p_323))) :rule cong :premises (t17.t6.t9 t17.t6.t15))
(step t17.t6.t17 (cl (= @p_323 false)) :rule evaluate)
(step t17.t6.t18 (cl @p_1128) :rule trans :premises (t17.t6.t16 t17.t6.t17))
(step t17.t6.t19 (cl (! (not @p_1109) :named @p_1110) (not (! (<= @p_11 @p_298) :named @p_1126)) (not (! (= @p_1116 @p_297) :named @p_1122)) (not (! (= @p_1114 0) :named @p_1119)) @p_1118) :rule la_generic :args (-1/1 1/1 -1/1 -1/1 1/1))
(step t17.t6.t20 (cl (=> (! (and (! (< -1 0) :named @p_308) @p_1049) :named @p_1127) @p_1126)) :rule la_mult_neg)
(step t17.t6.t21 (cl (not @p_1127) @p_1126) :rule implies :premises (t17.t6.t20))
(step t17.t6.t22 (cl (= (! (= @p_308 true) :named @p_310) @p_308)) :rule equiv_simplify)
(step t17.t6.t23 (cl (not @p_310) @p_308) :rule equiv1 :premises (t17.t6.t22))
(step t17.t6.t24 (cl @p_310) :rule evaluate)
(step t17.t6.t25 (cl @p_308) :rule resolution :premises (t17.t6.t23 t17.t6.t24))
(step t17.t6.t26 (cl @p_1127) :rule and_intro :premises (t17.t6.t25 t17.a2))
(step t17.t6.t27 (cl @p_1126) :rule resolution :premises (t17.t6.t21 t17.t6.t26))
(step t17.t6.t28 (cl (=> (! (and @p_308 (! (= @p_1115 0) :named @p_1123)) :named @p_1124) @p_1122)) :rule la_mult_neg)
(step t17.t6.t29 (cl (not @p_1124) @p_1122) :rule implies :premises (t17.t6.t28))
(step t17.t6.t30 (cl (not (! (= @p_1099 @p_1123) :named @p_1125)) @p_1100 @p_1123) :rule equiv_pos2)
(step t17.t6.t31 (cl (= (* 1 (- @p_1115 0)) (* 1 (- @p_8 @p_1098)))) :rule poly_simp)
(step t17.t6.t32 (cl (= @p_1123 @p_1099)) :rule poly_simp_rel :premises (t17.t6.t31))
(step t17.t6.t33 (cl @p_1125) :rule symm :premises (t17.t6.t32))
(step t17.t6.t34 (cl (or @p_190 @p_1099)) :rule forall_inst :args (@p_7 @p_8))
(step t17.t6.t35 (cl @p_190 @p_1099) :rule or :premises (t17.t6.t34))
(step t17.t6.t36 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t17.t6.t37 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t17.t6.t37.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t17.t6.t37.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t17.t6.t37.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t17.t6.t37.t0 t17.t6.t37.t1))
(step t17.t6.t37.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t17.t6.t37.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t17.t6.t37.t2 t17.t6.t37.t3))
(step t17.t6.t37.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t17.t6.t37.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t17.t6.t37.t5))
(step t17.t6.t37.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t17.t6.t37.t4 t17.t6.t37.t6))
(step t17.t6.t37 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t17.t6.t38 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t17.t6.t39 (cl @p_179) :rule trans :premises (t17.t6.t37 t17.t6.t38))
(step t17.t6.t40 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t17.t6.t36 t17.t6.t39 a0))
(step t17.t6.t41 (cl @p_1099) :rule resolution :premises (t17.t6.t35 t17.t6.t40))
(step t17.t6.t42 (cl @p_1123) :rule resolution :premises (t17.t6.t30 t17.t6.t33 t17.t6.t41))
(step t17.t6.t43 (cl @p_1124) :rule and_intro :premises (t17.t6.t25 t17.t6.t42))
(step t17.t6.t44 (cl @p_1122) :rule resolution :premises (t17.t6.t29 t17.t6.t43))
(step t17.t6.t45 (cl (not (! (= @p_10 @p_1119) :named @p_1121)) @p_1101 @p_1119) :rule equiv_pos2)
(step t17.t6.t46 (cl (= (* 1 (- @p_1114 0)) (* 1 (- @p_8 @p_9)))) :rule poly_simp)
(step t17.t6.t47 (cl (= @p_1119 @p_10)) :rule poly_simp_rel :premises (t17.t6.t46))
(step t17.t6.t48 (cl @p_1121) :rule symm :premises (t17.t6.t47))
(step t17.t6.t49 (cl @p_1119) :rule resolution :premises (t17.t6.t45 t17.t6.t48 t17.a0))
(step t17.t6.t50 (cl @p_1118) :rule resolution :premises (t17.t6.t19 t17.t6.a0 t17.t6.t27 t17.t6.t44 t17.t6.t49))
(step t17.t6.t51 (cl false) :rule resolution :premises (t17.t6.t0 t17.t6.t18 t17.t6.t50))
(step t17.t6 (cl @p_1110 false) :rule subproof :discharge (t17.t6.a0))
(step t17.t7 (cl @p_1111 false) :rule resolution :premises (t17.t5 t17.t6))
(step t17.t8 (cl @p_1111 (! (not false) :named @p_212)) :rule implies_neg2)
(step t17.t9 (cl @p_1111 @p_1111) :rule resolution :premises (t17.t7 t17.t8))
(step t17.t10 (cl @p_1111) :rule contraction :premises (t17.t9))
(step t17.t11 (cl (= @p_1111 @p_1110)) :rule implies_simplify)
(step t17.t12 (cl (not @p_1111) @p_1110) :rule equiv1 :premises (t17.t11))
(step t17.t13 (cl @p_1110) :rule resolution :premises (t17.t10 t17.t12))
(step t17.t14 (cl) :rule resolution :premises (t17.t4 t17.t13))
(step t17 (cl @p_1101 @p_1100 @p_1051 @p_1083 false) :rule subproof :discharge (t17.a0 t17.a1 t17.a2 t17.a3))
(step t18 (cl @p_1105 @p_10) :rule and_pos :args (0))
(step t19 (cl @p_1105 @p_1099) :rule and_pos :args (1))
(step t20 (cl @p_1105 @p_1049) :rule and_pos :args (2))
(step t21 (cl @p_1105 @p_1077) :rule and_pos :args (3))
(step t22 (cl false @p_1105 @p_1105 @p_1105 @p_1105) :rule resolution :premises (t17 t18 t19 t20 t21))
(step t23 (cl @p_1105 @p_1105 @p_1105 @p_1105 false) :rule reordering :premises (t22))
(step t24 (cl @p_1105 false) :rule contraction :premises (t23))
(step t25 (cl @p_1106 false) :rule resolution :premises (t16 t24))
(step t26 (cl @p_1106 @p_212) :rule implies_neg2)
(step t27 (cl @p_1106 @p_1106) :rule resolution :premises (t25 t26))
(step t28 (cl @p_1106) :rule contraction :premises (t27))
(step t29 (cl (= @p_1106 @p_1105)) :rule implies_simplify)
(step t30 (cl (not @p_1106) @p_1105) :rule equiv1 :premises (t29))
(step t31 (cl @p_1105) :rule resolution :premises (t28 t30))
(step t32 (cl @p_1103) :rule resolution :premises (t15 t31))
(step t33 (cl @p_794 @p_1100 @p_1101 @p_1051) :rule not_and :premises (t32))
(step t34 (cl (! (not (! (or (! (= @p_7 0) :named @p_101) @p_743) :named @p_744)) :named @p_750) @p_101 @p_743) :rule or_pos)
(step t35 (cl @p_101 @p_743 @p_750) :rule reordering :premises (t34))
(step t36 (cl (not (! (= (! (or (! (not (! (= k$ (! (* -1 @p_6) :named @p_120)) :named @p_522)) :named @p_1440) (! (not (! (not @p_5) :named @p_523)) :named @p_539) (! (not (! (not (! (>= (! (+ @p_6 (! (* -1 @p_7) :named @p_46)) :named @p_111) 1) :named @p_112)) :named @p_113)) :named @p_673) (! (not @p_101) :named @p_102) (! (not (! (= k$ (! (+ (! (times$ (centered_divide$ k$ 0) 0) :named @p_104) (! (centered_modulo$ k$ 0) :named @p_103)) :named @p_105)) :named @p_106)) :named @p_532)) :named @p_1493) (! (or @p_1440 @p_5 @p_112 @p_102 @p_532) :named @p_1492)) :named @p_1510)) (not @p_1493) @p_1492) :rule equiv_pos2)
(step t37 (cl (= @p_539 @p_5)) :rule rare_rewrite :args ("bool-double-not-elim" @p_5))
(step t38 (cl (= @p_673 @p_112)) :rule rare_rewrite :args ("bool-double-not-elim" @p_112))
(step t39 (cl (= @p_102 @p_102)) :rule refl)
(step t40 (cl (= @p_532 @p_532)) :rule refl)
(step t41 (cl @p_1510) :rule cong :premises (t37 t38 t39 t40))
(step t42 (cl (! (=> (! (and @p_522 @p_523 @p_113 @p_101 @p_106) :named @p_1494) (! (and (! (= @p_120 @p_105) :named @p_1447) (! (= 0 @p_7) :named @p_680) @p_106 @p_523 @p_113) :named @p_1496)) :named @p_1509) @p_1494) :rule implies_neg1)
(anchor :step t43)
(assume t43.a0 @p_522)
(assume t43.a1 @p_523)
(assume t43.a2 @p_113)
(assume t43.a3 @p_101)
(assume t43.a4 @p_106)
(step t43.t0 (cl (! (=> (! (and @p_106 @p_522) :named @p_1487) @p_1447) :named @p_1490) @p_1487) :rule implies_neg1)
(anchor :step t43.t1)
(assume t43.t1.a0 @p_106)
(assume t43.t1.a1 @p_522)
(step t43.t1.t0 (cl (= @p_120 k$)) :rule symm :premises (t43.t1.a1))
(step t43.t1.t1 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :named @p_110) @p_106)) :rule forall_inst :args (k$ 0))
(step t43.t1.t2 (cl @p_110 @p_106) :rule or :premises (t43.t1.t1))
(step t43.t1.t3 (cl (not (! (= (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0)) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :named @p_107)) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t43.t1.t4 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t43.t1.t4.t0 (cl (= (* 1 (- (! (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (! (centered_modulo$ ?v0 ?v1) :named @p_108)) :named @p_109) ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t43.t1.t4.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t43.t1.t4.t0))
(step t43.t1.t4 (cl @p_107) :rule bind)
(step t43.t1.t5 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t43.t1.t3 t43.t1.t4 a2))
(step t43.t1.t6 (cl @p_106) :rule resolution :premises (t43.t1.t2 t43.t1.t5))
(step t43.t1.t7 (cl @p_1447) :rule trans :premises (t43.t1.t0 t43.t1.t6))
(step t43.t1 (cl @p_532 @p_1440 @p_1447) :rule subproof :discharge (t43.t1.a0 t43.t1.a1))
(step t43.t2 (cl (! (not @p_1487) :named @p_1489) @p_106) :rule and_pos :args (0))
(step t43.t3 (cl @p_1489 @p_522) :rule and_pos :args (1))
(step t43.t4 (cl @p_1447 @p_1489 @p_1489) :rule resolution :premises (t43.t1 t43.t2 t43.t3))
(step t43.t5 (cl @p_1489 @p_1489 @p_1447) :rule reordering :premises (t43.t4))
(step t43.t6 (cl @p_1489 @p_1447) :rule contraction :premises (t43.t5))
(step t43.t7 (cl @p_1490 @p_1447) :rule resolution :premises (t43.t0 t43.t6))
(step t43.t8 (cl @p_1490 (! (not @p_1447) :named @p_1451)) :rule implies_neg2)
(step t43.t9 (cl @p_1490 @p_1490) :rule resolution :premises (t43.t7 t43.t8))
(step t43.t10 (cl @p_1490) :rule contraction :premises (t43.t9))
(step t43.t11 (cl @p_1489 @p_1447) :rule implies :premises (t43.t10))
(step t43.t12 (cl (or @p_110 @p_106)) :rule forall_inst :args (k$ 0))
(step t43.t13 (cl @p_110 @p_106) :rule or :premises (t43.t12))
(step t43.t14 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t43.t15 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t43.t15.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t43.t15.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t43.t15.t0))
(step t43.t15 (cl @p_107) :rule bind)
(step t43.t16 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t43.t14 t43.t15 a2))
(step t43.t17 (cl @p_106) :rule resolution :premises (t43.t13 t43.t16))
(step t43.t18 (cl @p_1487) :rule and_intro :premises (t43.t17 t43.a0))
(step t43.t19 (cl @p_1447) :rule resolution :premises (t43.t11 t43.t18))
(step t43.t20 (cl (! (=> @p_101 @p_680) :named @p_727) @p_101) :rule implies_neg1)
(anchor :step t43.t21)
(assume t43.t21.a0 @p_101)
(step t43.t21.t0 (cl @p_680) :rule symm :premises (t43.t21.a0))
(step t43.t21 (cl @p_102 @p_680) :rule subproof :discharge (t43.t21.a0))
(step t43.t22 (cl @p_727 @p_680) :rule resolution :premises (t43.t20 t43.t21))
(step t43.t23 (cl @p_727 (! (not @p_680) :named @p_686)) :rule implies_neg2)
(step t43.t24 (cl @p_727 @p_727) :rule resolution :premises (t43.t22 t43.t23))
(step t43.t25 (cl @p_727) :rule contraction :premises (t43.t24))
(step t43.t26 (cl @p_102 @p_680) :rule implies :premises (t43.t25))
(step t43.t27 (cl @p_680) :rule resolution :premises (t43.t26 t43.a3))
(step t43.t28 (cl @p_1496) :rule and_intro :premises (t43.t19 t43.t27 t43.t17 t43.a1 t43.a2))
(step t43 (cl @p_1440 @p_539 @p_673 @p_102 @p_532 @p_1496) :rule subproof :discharge (t43.a0 t43.a1 t43.a2 t43.a3 t43.a4))
(step t44 (cl (! (not @p_1494) :named @p_1495) @p_522) :rule and_pos :args (0))
(step t45 (cl @p_1495 @p_523) :rule and_pos :args (1))
(step t46 (cl @p_1495 @p_113) :rule and_pos :args (2))
(step t47 (cl @p_1495 @p_101) :rule and_pos :args (3))
(step t48 (cl @p_1495 @p_106) :rule and_pos :args (4))
(step t49 (cl @p_1496 @p_1495 @p_1495 @p_1495 @p_1495 @p_1495) :rule resolution :premises (t43 t44 t45 t46 t47 t48))
(step t50 (cl @p_1495 @p_1495 @p_1495 @p_1495 @p_1495 @p_1496) :rule reordering :premises (t49))
(step t51 (cl @p_1495 @p_1496) :rule contraction :premises (t50))
(step t52 (cl @p_1509 @p_1496) :rule resolution :premises (t42 t51))
(step t53 (cl @p_1509 (! (not @p_1496) :named @p_1497)) :rule implies_neg2)
(step t54 (cl @p_1509 @p_1509) :rule resolution :premises (t52 t53))
(step t55 (cl @p_1509) :rule contraction :premises (t54))
(step t56 (cl @p_1495 @p_1496) :rule implies :premises (t55))
(step t57 (cl (! (=> @p_1496 false) :named @p_1498) @p_1496) :rule implies_neg1)
(anchor :step t58)
(assume t58.a0 @p_1447)
(assume t58.a1 @p_680)
(assume t58.a2 @p_106)
(assume t58.a3 @p_523)
(assume t58.a4 @p_113)
(step t58.t0 (cl (! (not (! (< @p_111 1) :named @p_700)) :named @p_715) (! (<= @p_111 0) :named @p_1396)) :rule la_generic :args (1/1 1/1))
(step t58.t1 (cl (! (not (! (= @p_113 @p_700) :named @p_703)) :named @p_704) @p_673 @p_700) :rule equiv_pos2)
(step t58.t2 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t58.t3 (cl @p_703) :rule symm :premises (t58.t2))
(step t58.t4 (cl @p_700) :rule resolution :premises (t58.t1 t58.t3 t58.a4))
(step t58.t5 (cl @p_1396) :rule resolution :premises (t58.t0 t58.t4))
(step t58.t6 (cl (! (not (! (= (! (> @p_111 0) :named @p_1398) (! (not @p_1396) :named @p_1397)) :named @p_1414)) :named @p_1419) (! (not @p_1398) :named @p_1420) @p_1397) :rule equiv_pos2)
(step t58.t7 (cl (= @p_1398 (! (not (! (>= 0 @p_111) :named @p_1415)) :named @p_1416))) :rule rare_rewrite :args ("arith-elim-gt" @p_111 0))
(step t58.t8 (cl (= @p_1396 @p_1415)) :rule rare_rewrite :args ("arith-elim-leq" @p_111 0))
(step t58.t9 (cl (= @p_1415 @p_1396)) :rule symm :premises (t58.t8))
(step t58.t10 (cl (= @p_1416 @p_1397)) :rule cong :premises (t58.t9))
(step t58.t11 (cl @p_1414) :rule trans :premises (t58.t7 t58.t10))
(step t58.t12 (cl (! (not (! (= @p_1397 @p_1398) :named @p_1410)) :named @p_1417) (! (not @p_1397) :named @p_1418) @p_1398) :rule equiv_pos2)
(step t58.t13 (cl (= @p_1396 (! (not (! (>= @p_111 (! (+ 0 1) :named @p_1411)) :named @p_1412)) :named @p_1413))) :rule rare_rewrite :args ("arith-leq-norm" @p_111 0))
(step t58.t14 (cl (= @p_1411 1)) :rule evaluate)
(step t58.t15 (cl (= @p_1412 @p_112)) :rule cong :premises (t58.t14))
(step t58.t16 (cl (= @p_1413 @p_113)) :rule cong :premises (t58.t15))
(step t58.t17 (cl (= @p_1396 @p_113)) :rule trans :premises (t58.t13 t58.t16))
(step t58.t18 (cl (= @p_1397 @p_673)) :rule cong :premises (t58.t17))
(step t58.t19 (cl (= @p_1397 @p_112)) :rule trans :premises (t58.t18 t38))
(step t58.t20 (cl (= @p_1398 @p_112)) :rule trans :premises (t58.t11 t58.t19))
(step t58.t21 (cl (= @p_112 @p_1398)) :rule symm :premises (t58.t20))
(step t58.t22 (cl @p_1410) :rule trans :premises (t58.t19 t58.t21))
(step t58.t23 (cl (! (=> @p_1396 false) :named @p_1399) @p_1396) :rule implies_neg1)
(anchor :step t58.t24)
(assume t58.t24.a0 @p_1396)
(step t58.t24.t0 (cl (not (! (= (! (< (! (+ @p_111 k$ (! (* -1 (! (+ k$ (! (* -1 @p_104) :named @p_545) (! (* -1 @p_103) :named @p_544)) :named @p_546)) :named @p_1456) @p_7 (! (* -1 (! (+ @p_6 @p_104 @p_103) :named @p_1457)) :named @p_1458)) :named @p_1500) (! (+ 0 0 @p_297 0 @p_297) :named @p_1499)) :named @p_1501) false) :named @p_1502)) (not @p_1501) false) :rule equiv_pos2)
(step t58.t24.t1 (cl (= @p_1501 (! (not (! (>= @p_1500 @p_1499) :named @p_1503)) :named @p_1504))) :rule rare_rewrite :args ("arith-elim-lt" @p_1500 @p_1499))
(step t58.t24.t2 (cl (= @p_1500 (! (+ @p_104 @p_103 @p_544 @p_545 @p_46 @p_7 (! (* 0 @p_6) :named @p_617) (! (* 0 k$) :named @p_1506)) :named @p_1507))) :rule poly_simp)
(step t58.t24.t3 (cl (= @p_617 0)) :rule poly_simp)
(step t58.t24.t4 (cl (= @p_1506 0)) :rule poly_simp)
(step t58.t24.t5 (cl (= @p_1507 (! (+ @p_104 @p_103 @p_544 @p_545 @p_46 @p_7 0 0) :named @p_1508))) :rule cong :premises (t58.t24.t3 t58.t24.t4))
(step t58.t24.t6 (cl (= @p_1508 0)) :rule poly_simp)
(step t58.t24.t7 (cl (= @p_1507 0)) :rule trans :premises (t58.t24.t5 t58.t24.t6))
(step t58.t24.t8 (cl (= @p_1500 0)) :rule trans :premises (t58.t24.t2 t58.t24.t7))
(step t58.t24.t9 (cl (= @p_297 0)) :rule evaluate)
(step t58.t24.t10 (cl @p_56) :rule refl)
(step t58.t24.t11 (cl (= @p_1499 (! (+ 0 0 0 0 0) :named @p_1505))) :rule cong :premises (t58.t24.t9 t58.t24.t10 t58.t24.t9))
(step t58.t24.t12 (cl (= @p_1505 0)) :rule evaluate)
(step t58.t24.t13 (cl (= @p_1499 0)) :rule trans :premises (t58.t24.t11 t58.t24.t12))
(step t58.t24.t14 (cl (= @p_1503 (! (>= 0 0) :named @p_366))) :rule cong :premises (t58.t24.t8 t58.t24.t13))
(step t58.t24.t15 (cl (= @p_366 true)) :rule evaluate)
(step t58.t24.t16 (cl (= @p_1503 true)) :rule trans :premises (t58.t24.t14 t58.t24.t15))
(step t58.t24.t17 (cl (= @p_1504 (! (not true) :named @p_365))) :rule cong :premises (t58.t24.t16))
(step t58.t24.t18 (cl (= @p_365 false)) :rule evaluate)
(step t58.t24.t19 (cl (= @p_1504 false)) :rule trans :premises (t58.t24.t17 t58.t24.t18))
(step t58.t24.t20 (cl @p_1502) :rule trans :premises (t58.t24.t1 t58.t24.t19))
(step t58.t24.t21 (cl @p_1397 (! (not (! (< k$ 0) :named @p_1452)) :named @p_1453) (! (not (! (= @p_1456 @p_297) :named @p_1461)) :named @p_1475) @p_102 (! (not (! (= @p_1458 @p_297) :named @p_1463)) :named @p_1474) @p_1501) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 1/1))
(step t58.t24.t22 (cl (! (not (! (= @p_523 @p_1452) :named @p_1484)) :named @p_1485) @p_539 @p_1452) :rule equiv_pos2)
(step t58.t24.t23 (cl (= @p_1452 @p_523)) :rule rare_rewrite :args ("arith-elim-lt" k$ 0))
(step t58.t24.t24 (cl @p_1484) :rule symm :premises (t58.t24.t23))
(step t58.t24.t25 (cl @p_1452) :rule resolution :premises (t58.t24.t22 t58.t24.t24 t58.a3))
(step t58.t24.t26 (cl (=> (! (and @p_308 (! (= @p_546 0) :named @p_549)) :named @p_1462) @p_1461)) :rule la_mult_neg)
(step t58.t24.t27 (cl (not @p_1462) @p_1461) :rule implies :premises (t58.t24.t26))
(step t58.t24.t28 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t58.t24.t29 (cl (not @p_310) @p_308) :rule equiv1 :premises (t58.t24.t28))
(step t58.t24.t30 (cl @p_310) :rule evaluate)
(step t58.t24.t31 (cl @p_308) :rule resolution :premises (t58.t24.t29 t58.t24.t30))
(step t58.t24.t32 (cl (not (! (= @p_106 @p_549) :named @p_550)) @p_532 @p_549) :rule equiv_pos2)
(step t58.t24.t33 (cl (= (* 1 (- @p_546 0)) (* 1 (- k$ @p_105)))) :rule poly_simp)
(step t58.t24.t34 (cl (= @p_549 @p_106)) :rule poly_simp_rel :premises (t58.t24.t33))
(step t58.t24.t35 (cl @p_550) :rule symm :premises (t58.t24.t34))
(step t58.t24.t36 (cl (or @p_110 @p_106)) :rule forall_inst :args (k$ 0))
(step t58.t24.t37 (cl @p_110 @p_106) :rule or :premises (t58.t24.t36))
(step t58.t24.t38 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t58.t24.t39 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t58.t24.t39.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t58.t24.t39.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t58.t24.t39.t0))
(step t58.t24.t39 (cl @p_107) :rule bind)
(step t58.t24.t40 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t58.t24.t38 t58.t24.t39 a2))
(step t58.t24.t41 (cl @p_106) :rule resolution :premises (t58.t24.t37 t58.t24.t40))
(step t58.t24.t42 (cl @p_549) :rule resolution :premises (t58.t24.t32 t58.t24.t35 t58.t24.t41))
(step t58.t24.t43 (cl @p_1462) :rule and_intro :premises (t58.t24.t31 t58.t24.t42))
(step t58.t24.t44 (cl @p_1461) :rule resolution :premises (t58.t24.t27 t58.t24.t43))
(step t58.t24.t45 (cl @p_101) :rule symm :premises (t58.a1))
(step t58.t24.t46 (cl (=> (! (and @p_308 (! (= @p_1457 0) :named @p_1464)) :named @p_1465) @p_1463)) :rule la_mult_neg)
(step t58.t24.t47 (cl (! (not @p_1465) :named @p_1473) @p_1463) :rule implies :premises (t58.t24.t46))
(step t58.t24.t48 (cl (! (not (! (= @p_1447 @p_1464) :named @p_1468)) :named @p_1472) @p_1451 @p_1464) :rule equiv_pos2)
(step t58.t24.t49 (cl (= (* 1 (- @p_120 @p_105)) (* -1 (! (- @p_6 (! (+ @p_545 @p_544) :named @p_1469)) :named @p_1471)))) :rule poly_simp)
(step t58.t24.t50 (cl (= @p_1447 (! (= @p_6 @p_1469) :named @p_1470))) :rule poly_simp_rel :premises (t58.t24.t49))
(step t58.t24.t51 (cl (= (* 1 (- @p_1457 0)) (* 1 @p_1471))) :rule poly_simp)
(step t58.t24.t52 (cl (= @p_1464 @p_1470)) :rule poly_simp_rel :premises (t58.t24.t51))
(step t58.t24.t53 (cl (= @p_1470 @p_1464)) :rule symm :premises (t58.t24.t52))
(step t58.t24.t54 (cl @p_1468) :rule trans :premises (t58.t24.t50 t58.t24.t53))
(step t58.t24.t55 (cl @p_1464) :rule resolution :premises (t58.t24.t48 t58.t24.t54 t58.a0))
(step t58.t24.t56 (cl @p_1465) :rule and_intro :premises (t58.t24.t31 t58.t24.t55))
(step t58.t24.t57 (cl @p_1463) :rule resolution :premises (t58.t24.t47 t58.t24.t56))
(step t58.t24.t58 (cl @p_1501) :rule resolution :premises (t58.t24.t21 t58.t24.a0 t58.t24.t25 t58.t24.t44 t58.t24.t45 t58.t24.t57))
(step t58.t24.t59 (cl false) :rule resolution :premises (t58.t24.t0 t58.t24.t20 t58.t24.t58))
(step t58.t24 (cl @p_1397 false) :rule subproof :discharge (t58.t24.a0))
(step t58.t25 (cl @p_1399 false) :rule resolution :premises (t58.t23 t58.t24))
(step t58.t26 (cl @p_1399 @p_212) :rule implies_neg2)
(step t58.t27 (cl @p_1399 @p_1399) :rule resolution :premises (t58.t25 t58.t26))
(step t58.t28 (cl @p_1399) :rule contraction :premises (t58.t27))
(step t58.t29 (cl (! (= @p_1399 @p_1397) :named @p_1401)) :rule implies_simplify)
(step t58.t30 (cl (! (not @p_1399) :named @p_1400) @p_1397) :rule equiv1 :premises (t58.t29))
(step t58.t31 (cl @p_1397) :rule resolution :premises (t58.t28 t58.t30))
(step t58.t32 (cl @p_1398) :rule resolution :premises (t58.t12 t58.t22 t58.t31))
(step t58.t33 (cl @p_1397) :rule resolution :premises (t58.t6 t58.t11 t58.t32))
(step t58.t34 (cl) :rule resolution :premises (t58.t5 t58.t33))
(step t58 (cl @p_1451 @p_686 @p_532 @p_539 @p_673 false) :rule subproof :discharge (t58.a0 t58.a1 t58.a2 t58.a3 t58.a4))
(step t59 (cl @p_1497 @p_1447) :rule and_pos :args (0))
(step t60 (cl @p_1497 @p_680) :rule and_pos :args (1))
(step t61 (cl @p_1497 @p_106) :rule and_pos :args (2))
(step t62 (cl @p_1497 @p_523) :rule and_pos :args (3))
(step t63 (cl @p_1497 @p_113) :rule and_pos :args (4))
(step t64 (cl false @p_1497 @p_1497 @p_1497 @p_1497 @p_1497) :rule resolution :premises (t58 t59 t60 t61 t62 t63))
(step t65 (cl @p_1497 @p_1497 @p_1497 @p_1497 @p_1497 false) :rule reordering :premises (t64))
(step t66 (cl @p_1497 false) :rule contraction :premises (t65))
(step t67 (cl @p_1498 false) :rule resolution :premises (t57 t66))
(step t68 (cl @p_1498 @p_212) :rule implies_neg2)
(step t69 (cl @p_1498 @p_1498) :rule resolution :premises (t67 t68))
(step t70 (cl @p_1498) :rule contraction :premises (t69))
(step t71 (cl (= @p_1498 @p_1497)) :rule implies_simplify)
(step t72 (cl (not @p_1498) @p_1497) :rule equiv1 :premises (t71))
(step t73 (cl @p_1497) :rule resolution :premises (t70 t72))
(step t74 (cl @p_1495) :rule resolution :premises (t56 t73))
(step t75 (cl @p_1440 @p_539 @p_673 @p_102 @p_532) :rule not_and :premises (t74))
(step t76 (cl @p_1493 (! (not @p_1440) :named @p_1444)) :rule or_neg :args (0))
(step t77 (cl @p_1493 (! (not @p_539) :named @p_1443)) :rule or_neg :args (1))
(step t78 (cl @p_1493 (! (not @p_673) :named @p_676)) :rule or_neg :args (2))
(step t79 (cl @p_1493 (! (not @p_102) :named @p_675)) :rule or_neg :args (3))
(step t80 (cl @p_1493 (! (not @p_532) :named @p_538)) :rule or_neg :args (4))
(step t81 (cl @p_1493 @p_1493 @p_1493 @p_1493 @p_1493) :rule resolution :premises (t75 t76 t77 t78 t79 t80))
(step t82 (cl @p_1493) :rule contraction :premises (t81))
(step t83 (cl @p_1492) :rule resolution :premises (t36 t41 t82))
(step t84 (cl @p_1440 @p_5 @p_112 @p_102 @p_532) :rule or :premises (t83))
(step t85 (cl @p_5 @p_1440 @p_112 @p_102 @p_532) :rule reordering :premises (t84))
(step t86 (cl (! (not (! (or (! (not (! (>= @p_7 0) :named @p_116)) :named @p_117) @p_113 (! (= @p_7 (! (modulo$ @p_7 @p_6) :named @p_114)) :named @p_115)) :named @p_118)) :named @p_1439) @p_117 @p_113 @p_115) :rule or_pos)
(step t87 (cl @p_117 @p_115 @p_113 @p_1439) :rule reordering :premises (t86))
(step t88 (cl (not (! (= (! (or (! (not (! (= k$ (! (divide$ (! (times$ @p_1 k$) :named @p_169) @p_1) :named @p_172)) :named @p_224)) :named @p_227) (! (not (! (= (! (centered_divide$ 0 0) :named @p_425) 0) :named @p_426)) :named @p_435) (! (not (! (= @p_1 (! (divide$ (! (times$ @p_172 @p_1) :named @p_249) (! (divide$ (! (times$ @p_1 k$) :named @p_169) @p_1) :named @p_172)) :named @p_428)) :named @p_429)) :named @p_485) (! (not (! (not (! (= @p_1 @p_249) :named @p_372)) :named @p_373)) :named @p_378) (! (not (! (not (! (>= @p_249 1) :named @p_284)) :named @p_285)) :named @p_288) (! (not (! (>= @p_249 0) :named @p_333)) :named @p_336) (! (not (! (= @p_1 (! (+ (! (modulo$ @p_1 2) :named @p_457) (! (times$ 2 (divide$ @p_1 2)) :named @p_456)) :named @p_458)) :named @p_459)) :named @p_486) (! (not (! (= (! (times$ k$ 0) :named @p_465) 0) :named @p_466)) :named @p_487) (! (not (! (= (! (divide$ @p_465 k$) :named @p_476) 0) :named @p_477)) :named @p_488)) :named @p_490) (! (or @p_227 @p_435 @p_485 @p_372 @p_284 @p_336 @p_486 @p_487 @p_488) :named @p_489)) :named @p_514)) (not @p_490) @p_489) :rule equiv_pos2)
(step t89 (cl (= @p_378 @p_372)) :rule rare_rewrite :args ("bool-double-not-elim" @p_372))
(step t90 (cl (= @p_288 @p_284)) :rule rare_rewrite :args ("bool-double-not-elim" @p_284))
(step t91 (cl (= @p_336 @p_336)) :rule refl)
(step t92 (cl (= @p_486 @p_486)) :rule refl)
(step t93 (cl (= @p_487 @p_487)) :rule refl)
(step t94 (cl (= @p_488 @p_488)) :rule refl)
(step t95 (cl @p_514) :rule cong :premises (t89 t90 t91 t92 t93 t94))
(step t96 (cl (! (=> (! (and @p_224 @p_426 @p_429 @p_373 @p_285 @p_333 @p_459 @p_466 @p_477) :named @p_492) (! (and @p_426 (! (= 0 @p_458) :named @p_494) @p_459 (! (= 0 @p_249) :named @p_382) @p_373) :named @p_495)) :named @p_505) @p_492) :rule implies_neg1)
(anchor :step t97)
(assume t97.a0 @p_224)
(assume t97.a1 @p_426)
(assume t97.a2 @p_429)
(assume t97.a3 @p_373)
(assume t97.a4 @p_285)
(assume t97.a5 @p_333)
(assume t97.a6 @p_459)
(assume t97.a7 @p_466)
(assume t97.a8 @p_477)
(step t97.t0 (cl (or (! (not (forall ((?v0 Int)) (= (centered_divide$ ?v0 0) 0))) :named @p_427) @p_426)) :rule forall_inst :args (0))
(step t97.t1 (cl @p_427 @p_426) :rule or :premises (t97.t0))
(step t97.t2 (cl @p_426) :rule resolution :premises (t97.t1 a1))
(step t97.t3 (cl (! (=> (! (and @p_459 @p_429 @p_382 @p_224 @p_466 @p_477) :named @p_510) @p_494) :named @p_512) @p_510) :rule implies_neg1)
(anchor :step t97.t4)
(assume t97.t4.a0 @p_459)
(assume t97.t4.a1 @p_429)
(assume t97.t4.a2 @p_382)
(assume t97.t4.a3 @p_224)
(assume t97.t4.a4 @p_466)
(assume t97.t4.a5 @p_477)
(step t97.t4.t0 (cl (! (= 0 @p_476) :named @p_480)) :rule symm :premises (t97.t4.a5))
(step t97.t4.t1 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) (! (= (! (= 0 @p_465) :named @p_470) (! (or @p_56 (! (= k$ 1) :named @p_468)) :named @p_469)) :named @p_471)) :named @p_472) (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) @p_466) :named @p_467)) :named @p_473)) (not @p_472) @p_467) :rule equiv_pos2)
(step t97.t4.t2 (cl (= (* 1 (- 0 @p_465)) (* -1 (- @p_465 0)))) :rule poly_simp)
(step t97.t4.t3 (cl (= @p_470 @p_466)) :rule poly_simp_rel :premises (t97.t4.t2))
(step t97.t4.t4 (cl (= @p_56 true)) :rule evaluate)
(step t97.t4.t5 (cl (= @p_468 @p_468)) :rule refl)
(step t97.t4.t6 (cl (= @p_469 (! (or true @p_468) :named @p_475))) :rule cong :premises (t97.t4.t4 t97.t4.t5))
(step t97.t4.t7 (cl (= @p_475 true)) :rule or_simplify)
(step t97.t4.t8 (cl (= @p_469 true)) :rule trans :premises (t97.t4.t6 t97.t4.t7))
(step t97.t4.t9 (cl (= @p_471 (! (= @p_466 true) :named @p_474))) :rule cong :premises (t97.t4.t3 t97.t4.t8))
(step t97.t4.t10 (cl (= @p_474 @p_466)) :rule rare_rewrite :args ("bool-eq-true" @p_466))
(step t97.t4.t11 (cl (= @p_471 @p_466)) :rule trans :premises (t97.t4.t9 t97.t4.t10))
(step t97.t4.t12 (cl @p_473) :rule cong :premises (t97.t4.t11))
(step t97.t4.t13 (cl @p_472 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t97.t4.t14)
(assume t97.t4.t14.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t97.t4.t14.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :named @p_91) @p_471)) :rule forall_inst :args (0 k$))
(step t97.t4.t14.t1 (cl @p_91 @p_471) :rule or :premises (t97.t4.t14.t0))
(step t97.t4.t14.t2 (cl @p_471) :rule resolution :premises (t97.t4.t14.t1 t97.t4.t14.a0))
(step t97.t4.t14 (cl @p_91 @p_471) :rule subproof :discharge (t97.t4.t14.a0))
(step t97.t4.t15 (cl @p_472 @p_471) :rule resolution :premises (t97.t4.t13 t97.t4.t14))
(step t97.t4.t16 (cl @p_472 (not @p_471)) :rule implies_neg2)
(step t97.t4.t17 (cl @p_472 @p_472) :rule resolution :premises (t97.t4.t15 t97.t4.t16))
(step t97.t4.t18 (cl @p_472) :rule contraction :premises (t97.t4.t17))
(step t97.t4.t19 (cl @p_467) :rule resolution :premises (t97.t4.t1 t97.t4.t12 t97.t4.t18))
(step t97.t4.t20 (cl @p_91 @p_466) :rule implies :premises (t97.t4.t19))
(step t97.t4.t21 (cl @p_466) :rule resolution :premises (t97.t4.t20 a8))
(step t97.t4.t22 (cl (= k$ k$)) :rule refl)
(step t97.t4.t23 (cl (= @p_476 (! (divide$ 0 k$) :named @p_513))) :rule cong :premises (t97.t4.t21 t97.t4.t22))
(step t97.t4.t24 (cl (! (not (! (or @p_2 @p_224) :named @p_225)) :named @p_226) @p_2 @p_224) :rule or_pos)
(step t97.t4.t25 (cl @p_2 @p_224 @p_226) :rule reordering :premises (t97.t4.t24))
(step t97.t4.t26 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :named @p_82) @p_225)) :rule forall_inst :args (@p_1 k$))
(step t97.t4.t27 (cl @p_82 @p_225) :rule or :premises (t97.t4.t26))
(step t97.t4.t28 (cl (not (! (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :named @p_72)) (not (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t97.t4.t29 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t97.t4.t29.t0 (cl (= (* 1 (- (! (divide$ (times$ ?v0 ?v1) ?v0) :named @p_73) ?v1)) (* -1 (- ?v1 @p_73)))) :rule poly_simp)
(step t97.t4.t29.t1 (cl (= (! (= @p_73 ?v1) :named @p_81) (! (= ?v1 @p_73) :named @p_74))) :rule poly_simp_rel :premises (t97.t4.t29.t0))
(step t97.t4.t29.t2 (cl (= (=> (! (not (! (= ?v0 0) :named @p_75)) :named @p_77) @p_81) (! (=> @p_77 @p_74) :named @p_78))) :rule cong :premises (t97.t4.t29.t1))
(step t97.t4.t29 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t97.t4.t30 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t97.t4.t30.t0 (cl (= @p_78 (! (or (! (not @p_77) :named @p_79) @p_74) :named @p_80))) :rule rare_rewrite :args ("bool-impl-elim" @p_77 @p_74))
(step t97.t4.t30.t1 (cl (= @p_79 @p_75)) :rule rare_rewrite :args ("bool-double-not-elim" @p_75))
(step t97.t4.t30.t2 (cl (= @p_74 @p_74)) :rule refl)
(step t97.t4.t30.t3 (cl (= @p_80 (! (or @p_75 @p_74) :named @p_76))) :rule cong :premises (t97.t4.t30.t1 t97.t4.t30.t2))
(step t97.t4.t30.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t97.t4.t30.t0 t97.t4.t30.t3))
(step t97.t4.t30 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(step t97.t4.t31 (cl @p_72) :rule trans :premises (t97.t4.t29 t97.t4.t30))
(step t97.t4.t32 (cl (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule resolution :premises (t97.t4.t28 t97.t4.t31 a9))
(step t97.t4.t33 (cl @p_225) :rule resolution :premises (t97.t4.t27 t97.t4.t32))
(step t97.t4.t34 (cl @p_224) :rule resolution :premises (t97.t4.t25 a11 t97.t4.t33))
(step t97.t4.t35 (cl (= @p_513 @p_428)) :rule cong :premises (t97.t4.a2 t97.t4.t34))
(step t97.t4.t36 (cl (= @p_428 @p_1)) :rule symm :premises (t97.t4.a1))
(step t97.t4.t37 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (! (= @p_1 (! (+ @p_456 @p_457) :named @p_461)) :named @p_462)) :named @p_463) (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) @p_459) :named @p_460)) :named @p_464)) (not @p_463) @p_460) :rule equiv_pos2)
(step t97.t4.t38 (cl (= @p_461 @p_458)) :rule poly_simp)
(step t97.t4.t39 (cl (= @p_462 @p_459)) :rule cong :premises (t97.t4.t38))
(step t97.t4.t40 (cl @p_464) :rule cong :premises (t97.t4.t39))
(step t97.t4.t41 (cl @p_463 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t97.t4.t42)
(assume t97.t4.t42.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t97.t4.t42.t0 (cl (or @p_190 @p_462)) :rule forall_inst :args (2 @p_1))
(step t97.t4.t42.t1 (cl @p_190 @p_462) :rule or :premises (t97.t4.t42.t0))
(step t97.t4.t42.t2 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t97.t4.t42.t3 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t97.t4.t42.t3.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t97.t4.t42.t3.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t97.t4.t42.t3.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t97.t4.t42.t3.t0 t97.t4.t42.t3.t1))
(step t97.t4.t42.t3.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t97.t4.t42.t3.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t97.t4.t42.t3.t2 t97.t4.t42.t3.t3))
(step t97.t4.t42.t3.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t97.t4.t42.t3.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t97.t4.t42.t3.t5))
(step t97.t4.t42.t3.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t97.t4.t42.t3.t4 t97.t4.t42.t3.t6))
(step t97.t4.t42.t3 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t97.t4.t42.t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t97.t4.t42.t5 (cl @p_179) :rule trans :premises (t97.t4.t42.t3 t97.t4.t42.t4))
(step t97.t4.t42.t6 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t97.t4.t42.t2 t97.t4.t42.t5 a0))
(step t97.t4.t42.t7 (cl @p_462) :rule resolution :premises (t97.t4.t42.t1 t97.t4.t42.t6))
(step t97.t4.t42 (cl @p_190 @p_462) :rule subproof :discharge (t97.t4.t42.a0))
(step t97.t4.t43 (cl @p_463 @p_462) :rule resolution :premises (t97.t4.t41 t97.t4.t42))
(step t97.t4.t44 (cl @p_463 (not @p_462)) :rule implies_neg2)
(step t97.t4.t45 (cl @p_463 @p_463) :rule resolution :premises (t97.t4.t43 t97.t4.t44))
(step t97.t4.t46 (cl @p_463) :rule contraction :premises (t97.t4.t45))
(step t97.t4.t47 (cl @p_460) :rule resolution :premises (t97.t4.t37 t97.t4.t40 t97.t4.t46))
(step t97.t4.t48 (cl @p_190 @p_459) :rule implies :premises (t97.t4.t47))
(step t97.t4.t49 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t97.t4.t50 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t97.t4.t50.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t97.t4.t50.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t97.t4.t50.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t97.t4.t50.t0 t97.t4.t50.t1))
(step t97.t4.t50.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t97.t4.t50.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t97.t4.t50.t2 t97.t4.t50.t3))
(step t97.t4.t50.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t97.t4.t50.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t97.t4.t50.t5))
(step t97.t4.t50.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t97.t4.t50.t4 t97.t4.t50.t6))
(step t97.t4.t50 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t97.t4.t51 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t97.t4.t52 (cl @p_179) :rule trans :premises (t97.t4.t50 t97.t4.t51))
(step t97.t4.t53 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t97.t4.t49 t97.t4.t52 a0))
(step t97.t4.t54 (cl @p_459) :rule resolution :premises (t97.t4.t48 t97.t4.t53))
(step t97.t4.t55 (cl @p_494) :rule trans :premises (t97.t4.t0 t97.t4.t23 t97.t4.t35 t97.t4.t36 t97.t4.t54))
(step t97.t4 (cl @p_486 @p_485 (! (not @p_382) :named @p_383) @p_227 @p_487 @p_488 @p_494) :rule subproof :discharge (t97.t4.a0 t97.t4.a1 t97.t4.a2 t97.t4.a3 t97.t4.a4 t97.t4.a5))
(step t97.t5 (cl (! (not @p_510) :named @p_511) @p_459) :rule and_pos :args (0))
(step t97.t6 (cl @p_511 @p_429) :rule and_pos :args (1))
(step t97.t7 (cl @p_511 @p_382) :rule and_pos :args (2))
(step t97.t8 (cl @p_511 @p_224) :rule and_pos :args (3))
(step t97.t9 (cl @p_511 @p_466) :rule and_pos :args (4))
(step t97.t10 (cl @p_511 @p_477) :rule and_pos :args (5))
(step t97.t11 (cl @p_494 @p_511 @p_511 @p_511 @p_511 @p_511 @p_511) :rule resolution :premises (t97.t4 t97.t5 t97.t6 t97.t7 t97.t8 t97.t9 t97.t10))
(step t97.t12 (cl @p_511 @p_511 @p_511 @p_511 @p_511 @p_511 @p_494) :rule reordering :premises (t97.t11))
(step t97.t13 (cl @p_511 @p_494) :rule contraction :premises (t97.t12))
(step t97.t14 (cl @p_512 @p_494) :rule resolution :premises (t97.t3 t97.t13))
(step t97.t15 (cl @p_512 (! (not @p_494) :named @p_498)) :rule implies_neg2)
(step t97.t16 (cl @p_512 @p_512) :rule resolution :premises (t97.t14 t97.t15))
(step t97.t17 (cl @p_512) :rule contraction :premises (t97.t16))
(step t97.t18 (cl @p_511 @p_494) :rule implies :premises (t97.t17))
(step t97.t19 (cl (not @p_464) (not @p_463) @p_460) :rule equiv_pos2)
(step t97.t20 (cl (= @p_461 @p_458)) :rule poly_simp)
(step t97.t21 (cl (= @p_462 @p_459)) :rule cong :premises (t97.t20))
(step t97.t22 (cl @p_464) :rule cong :premises (t97.t21))
(step t97.t23 (cl @p_463 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t97.t24)
(assume t97.t24.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t97.t24.t0 (cl (or @p_190 @p_462)) :rule forall_inst :args (2 @p_1))
(step t97.t24.t1 (cl @p_190 @p_462) :rule or :premises (t97.t24.t0))
(step t97.t24.t2 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t97.t24.t3 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t97.t24.t3.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t97.t24.t3.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t97.t24.t3.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t97.t24.t3.t0 t97.t24.t3.t1))
(step t97.t24.t3.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t97.t24.t3.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t97.t24.t3.t2 t97.t24.t3.t3))
(step t97.t24.t3.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t97.t24.t3.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t97.t24.t3.t5))
(step t97.t24.t3.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t97.t24.t3.t4 t97.t24.t3.t6))
(step t97.t24.t3 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t97.t24.t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t97.t24.t5 (cl @p_179) :rule trans :premises (t97.t24.t3 t97.t24.t4))
(step t97.t24.t6 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t97.t24.t2 t97.t24.t5 a0))
(step t97.t24.t7 (cl @p_462) :rule resolution :premises (t97.t24.t1 t97.t24.t6))
(step t97.t24 (cl @p_190 @p_462) :rule subproof :discharge (t97.t24.a0))
(step t97.t25 (cl @p_463 @p_462) :rule resolution :premises (t97.t23 t97.t24))
(step t97.t26 (cl @p_463 (not @p_462)) :rule implies_neg2)
(step t97.t27 (cl @p_463 @p_463) :rule resolution :premises (t97.t25 t97.t26))
(step t97.t28 (cl @p_463) :rule contraction :premises (t97.t27))
(step t97.t29 (cl @p_460) :rule resolution :premises (t97.t19 t97.t22 t97.t28))
(step t97.t30 (cl @p_190 @p_459) :rule implies :premises (t97.t29))
(step t97.t31 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t97.t32 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t97.t32.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t97.t32.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t97.t32.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t97.t32.t0 t97.t32.t1))
(step t97.t32.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t97.t32.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t97.t32.t2 t97.t32.t3))
(step t97.t32.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t97.t32.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t97.t32.t5))
(step t97.t32.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t97.t32.t4 t97.t32.t6))
(step t97.t32 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t97.t33 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t97.t34 (cl @p_179) :rule trans :premises (t97.t32 t97.t33))
(step t97.t35 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t97.t31 t97.t34 a0))
(step t97.t36 (cl @p_459) :rule resolution :premises (t97.t30 t97.t35))
(step t97.t37 (cl (! (=> (! (and @p_333 @p_285) :named @p_506) @p_382) :named @p_508) @p_506) :rule implies_neg1)
(anchor :step t97.t38)
(assume t97.t38.a0 @p_333)
(assume t97.t38.a1 @p_285)
(step t97.t38.t0 (cl (! (not (! (< @p_249 1) :named @p_407)) :named @p_410) (! (<= @p_249 0) :named @p_406)) :rule la_generic :args (1/1 1/1))
(step t97.t38.t1 (cl (! (not (! (= @p_285 @p_407) :named @p_408)) :named @p_409) @p_288 @p_407) :rule equiv_pos2)
(step t97.t38.t2 (cl (= @p_407 @p_285)) :rule rare_rewrite :args ("arith-elim-lt" @p_249 1))
(step t97.t38.t3 (cl @p_408) :rule symm :premises (t97.t38.t2))
(step t97.t38.t4 (cl @p_407) :rule resolution :premises (t97.t38.t1 t97.t38.t3 t97.t38.a1))
(step t97.t38.t5 (cl @p_406) :rule resolution :premises (t97.t38.t0 t97.t38.t4))
(step t97.t38.t6 (cl (! (or (! (= @p_249 0) :named @p_411) (! (not @p_406) :named @p_413) (! (not (! (<= 0 @p_249) :named @p_403)) :named @p_404)) :named @p_414)) :rule la_disequality)
(step t97.t38.t7 (cl @p_411 @p_413 @p_404) :rule or :premises (t97.t38.t6))
(step t97.t38.t8 (cl (! (= @p_333 @p_403) :named @p_509)) :rule comp_simplify)
(step t97.t38.t9 (cl (not @p_509) @p_336 @p_403) :rule equiv_pos2)
(step t97.t38.t10 (cl @p_403) :rule resolution :premises (t97.t38.t8 t97.t38.t9 t97.t38.a0))
(step t97.t38.t11 (cl @p_411) :rule resolution :premises (t97.t38.t5 t97.t38.t7 t97.t38.t10))
(step t97.t38.t12 (cl @p_382) :rule symm :premises (t97.t38.t11))
(step t97.t38 (cl @p_336 @p_288 @p_382) :rule subproof :discharge (t97.t38.a0 t97.t38.a1))
(step t97.t39 (cl (! (not @p_506) :named @p_507) @p_333) :rule and_pos :args (0))
(step t97.t40 (cl @p_507 @p_285) :rule and_pos :args (1))
(step t97.t41 (cl @p_382 @p_507 @p_507) :rule resolution :premises (t97.t38 t97.t39 t97.t40))
(step t97.t42 (cl @p_507 @p_507 @p_382) :rule reordering :premises (t97.t41))
(step t97.t43 (cl @p_507 @p_382) :rule contraction :premises (t97.t42))
(step t97.t44 (cl @p_508 @p_382) :rule resolution :premises (t97.t37 t97.t43))
(step t97.t45 (cl @p_508 @p_383) :rule implies_neg2)
(step t97.t46 (cl @p_508 @p_508) :rule resolution :premises (t97.t44 t97.t45))
(step t97.t47 (cl @p_508) :rule contraction :premises (t97.t46))
(step t97.t48 (cl @p_507 @p_382) :rule implies :premises (t97.t47))
(step t97.t49 (cl @p_506) :rule and_intro :premises (t97.a5 t97.a4))
(step t97.t50 (cl @p_382) :rule resolution :premises (t97.t48 t97.t49))
(step t97.t51 (cl @p_226 @p_2 @p_224) :rule or_pos)
(step t97.t52 (cl @p_2 @p_224 @p_226) :rule reordering :premises (t97.t51))
(step t97.t53 (cl (or @p_82 @p_225)) :rule forall_inst :args (@p_1 k$))
(step t97.t54 (cl @p_82 @p_225) :rule or :premises (t97.t53))
(step t97.t55 (cl (not @p_72) (not (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t97.t56 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t97.t56.t0 (cl (= (* 1 (- @p_73 ?v1)) (* -1 (- ?v1 @p_73)))) :rule poly_simp)
(step t97.t56.t1 (cl (= @p_81 @p_74)) :rule poly_simp_rel :premises (t97.t56.t0))
(step t97.t56.t2 (cl (= (=> @p_77 @p_81) @p_78)) :rule cong :premises (t97.t56.t1))
(step t97.t56 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t97.t57 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t97.t57.t0 (cl (= @p_78 @p_80)) :rule rare_rewrite :args ("bool-impl-elim" @p_77 @p_74))
(step t97.t57.t1 (cl (= @p_79 @p_75)) :rule rare_rewrite :args ("bool-double-not-elim" @p_75))
(step t97.t57.t2 (cl (= @p_74 @p_74)) :rule refl)
(step t97.t57.t3 (cl (= @p_80 @p_76)) :rule cong :premises (t97.t57.t1 t97.t57.t2))
(step t97.t57.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t97.t57.t0 t97.t57.t3))
(step t97.t57 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(step t97.t58 (cl @p_72) :rule trans :premises (t97.t56 t97.t57))
(step t97.t59 (cl (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule resolution :premises (t97.t55 t97.t58 a9))
(step t97.t60 (cl @p_225) :rule resolution :premises (t97.t54 t97.t59))
(step t97.t61 (cl @p_224) :rule resolution :premises (t97.t52 a11 t97.t60))
(step t97.t62 (cl (not @p_473) (not @p_472) @p_467) :rule equiv_pos2)
(step t97.t63 (cl (= (* 1 (- 0 @p_465)) (* -1 (- @p_465 0)))) :rule poly_simp)
(step t97.t64 (cl (= @p_470 @p_466)) :rule poly_simp_rel :premises (t97.t63))
(step t97.t65 (cl (= @p_56 true)) :rule evaluate)
(step t97.t66 (cl (= @p_468 @p_468)) :rule refl)
(step t97.t67 (cl (= @p_469 @p_475)) :rule cong :premises (t97.t65 t97.t66))
(step t97.t68 (cl (= @p_475 true)) :rule or_simplify)
(step t97.t69 (cl (= @p_469 true)) :rule trans :premises (t97.t67 t97.t68))
(step t97.t70 (cl (= @p_471 @p_474)) :rule cong :premises (t97.t64 t97.t69))
(step t97.t71 (cl (= @p_474 @p_466)) :rule rare_rewrite :args ("bool-eq-true" @p_466))
(step t97.t72 (cl (= @p_471 @p_466)) :rule trans :premises (t97.t70 t97.t71))
(step t97.t73 (cl @p_473) :rule cong :premises (t97.t72))
(step t97.t74 (cl @p_472 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t97.t75)
(assume t97.t75.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t97.t75.t0 (cl (or @p_91 @p_471)) :rule forall_inst :args (0 k$))
(step t97.t75.t1 (cl @p_91 @p_471) :rule or :premises (t97.t75.t0))
(step t97.t75.t2 (cl @p_471) :rule resolution :premises (t97.t75.t1 t97.t75.a0))
(step t97.t75 (cl @p_91 @p_471) :rule subproof :discharge (t97.t75.a0))
(step t97.t76 (cl @p_472 @p_471) :rule resolution :premises (t97.t74 t97.t75))
(step t97.t77 (cl @p_472 (not @p_471)) :rule implies_neg2)
(step t97.t78 (cl @p_472 @p_472) :rule resolution :premises (t97.t76 t97.t77))
(step t97.t79 (cl @p_472) :rule contraction :premises (t97.t78))
(step t97.t80 (cl @p_467) :rule resolution :premises (t97.t62 t97.t73 t97.t79))
(step t97.t81 (cl @p_91 @p_466) :rule implies :premises (t97.t80))
(step t97.t82 (cl @p_466) :rule resolution :premises (t97.t81 a8))
(step t97.t83 (cl @p_510) :rule and_intro :premises (t97.t36 t97.a2 t97.t50 t97.t61 t97.t82 t97.a8))
(step t97.t84 (cl @p_494) :rule resolution :premises (t97.t18 t97.t83))
(step t97.t85 (cl @p_495) :rule and_intro :premises (t97.t2 t97.t84 t97.t36 t97.t50 t97.a3))
(step t97 (cl @p_227 @p_435 @p_485 @p_378 @p_288 @p_336 @p_486 @p_487 @p_488 @p_495) :rule subproof :discharge (t97.a0 t97.a1 t97.a2 t97.a3 t97.a4 t97.a5 t97.a6 t97.a7 t97.a8))
(step t98 (cl (! (not @p_492) :named @p_493) @p_224) :rule and_pos :args (0))
(step t99 (cl @p_493 @p_426) :rule and_pos :args (1))
(step t100 (cl @p_493 @p_429) :rule and_pos :args (2))
(step t101 (cl @p_493 @p_373) :rule and_pos :args (3))
(step t102 (cl @p_493 @p_285) :rule and_pos :args (4))
(step t103 (cl @p_493 @p_333) :rule and_pos :args (5))
(step t104 (cl @p_493 @p_459) :rule and_pos :args (6))
(step t105 (cl @p_493 @p_466) :rule and_pos :args (7))
(step t106 (cl @p_493 @p_477) :rule and_pos :args (8))
(step t107 (cl @p_495 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493) :rule resolution :premises (t97 t98 t99 t100 t101 t102 t103 t104 t105 t106))
(step t108 (cl @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_493 @p_495) :rule reordering :premises (t107))
(step t109 (cl @p_493 @p_495) :rule contraction :premises (t108))
(step t110 (cl @p_505 @p_495) :rule resolution :premises (t96 t109))
(step t111 (cl @p_505 (! (not @p_495) :named @p_496)) :rule implies_neg2)
(step t112 (cl @p_505 @p_505) :rule resolution :premises (t110 t111))
(step t113 (cl @p_505) :rule contraction :premises (t112))
(step t114 (cl @p_493 @p_495) :rule implies :premises (t113))
(step t115 (cl (! (=> @p_495 false) :named @p_497) @p_495) :rule implies_neg1)
(anchor :step t116)
(assume t116.a0 @p_426)
(assume t116.a1 @p_494)
(assume t116.a2 @p_459)
(assume t116.a3 @p_382)
(assume t116.a4 @p_373)
(step t116.t0 (cl (! (not (! (= (! (= false true) :named @p_499) false) :named @p_502)) :named @p_503) (! (not @p_499) :named @p_504) false) :rule equiv_pos2)
(step t116.t1 (cl @p_502) :rule evaluate)
(step t116.t2 (cl (= (! (= @p_372 false) :named @p_501) @p_373)) :rule equiv_simplify)
(step t116.t3 (cl @p_501 @p_378) :rule equiv2 :premises (t116.t2))
(step t116.t4 (cl (! (not @p_378) :named @p_491) @p_372) :rule not_not)
(step t116.t5 (cl @p_501 @p_372) :rule resolution :premises (t116.t3 t116.t4))
(step t116.t6 (cl @p_501) :rule resolution :premises (t116.t5 t116.a4))
(step t116.t7 (cl (= false @p_372)) :rule symm :premises (t116.t6))
(step t116.t8 (cl (= (! (= @p_372 true) :named @p_500) @p_372)) :rule equiv_simplify)
(step t116.t9 (cl @p_500 @p_373) :rule equiv2 :premises (t116.t8))
(step t116.t10 (cl (not @p_464) (not @p_463) @p_460) :rule equiv_pos2)
(step t116.t11 (cl (= @p_461 @p_458)) :rule poly_simp)
(step t116.t12 (cl (= @p_462 @p_459)) :rule cong :premises (t116.t11))
(step t116.t13 (cl @p_464) :rule cong :premises (t116.t12))
(step t116.t14 (cl @p_463 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t116.t15)
(assume t116.t15.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t116.t15.t0 (cl (or @p_190 @p_462)) :rule forall_inst :args (2 @p_1))
(step t116.t15.t1 (cl @p_190 @p_462) :rule or :premises (t116.t15.t0))
(step t116.t15.t2 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t116.t15.t3 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t116.t15.t3.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t116.t15.t3.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t116.t15.t3.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t116.t15.t3.t0 t116.t15.t3.t1))
(step t116.t15.t3.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t116.t15.t3.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t116.t15.t3.t2 t116.t15.t3.t3))
(step t116.t15.t3.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t116.t15.t3.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t116.t15.t3.t5))
(step t116.t15.t3.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t116.t15.t3.t4 t116.t15.t3.t6))
(step t116.t15.t3 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t116.t15.t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t116.t15.t5 (cl @p_179) :rule trans :premises (t116.t15.t3 t116.t15.t4))
(step t116.t15.t6 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t116.t15.t2 t116.t15.t5 a0))
(step t116.t15.t7 (cl @p_462) :rule resolution :premises (t116.t15.t1 t116.t15.t6))
(step t116.t15 (cl @p_190 @p_462) :rule subproof :discharge (t116.t15.a0))
(step t116.t16 (cl @p_463 @p_462) :rule resolution :premises (t116.t14 t116.t15))
(step t116.t17 (cl @p_463 (not @p_462)) :rule implies_neg2)
(step t116.t18 (cl @p_463 @p_463) :rule resolution :premises (t116.t16 t116.t17))
(step t116.t19 (cl @p_463) :rule contraction :premises (t116.t18))
(step t116.t20 (cl @p_460) :rule resolution :premises (t116.t10 t116.t13 t116.t19))
(step t116.t21 (cl @p_190 @p_459) :rule implies :premises (t116.t20))
(step t116.t22 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t116.t23 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t116.t23.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t116.t23.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t116.t23.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t116.t23.t0 t116.t23.t1))
(step t116.t23.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t116.t23.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t116.t23.t2 t116.t23.t3))
(step t116.t23.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t116.t23.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t116.t23.t5))
(step t116.t23.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t116.t23.t4 t116.t23.t6))
(step t116.t23 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t116.t24 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t116.t25 (cl @p_179) :rule trans :premises (t116.t23 t116.t24))
(step t116.t26 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t116.t22 t116.t25 a0))
(step t116.t27 (cl @p_459) :rule resolution :premises (t116.t21 t116.t26))
(step t116.t28 (cl (= @p_458 0)) :rule symm :premises (t116.a1))
(step t116.t29 (cl (or @p_427 @p_426)) :rule forall_inst :args (0))
(step t116.t30 (cl @p_427 @p_426) :rule or :premises (t116.t29))
(step t116.t31 (cl @p_426) :rule resolution :premises (t116.t30 a1))
(step t116.t32 (cl (= 0 @p_425)) :rule symm :premises (t116.t31))
(step t116.t33 (cl (! (= @p_1 @p_425) :named @p_442)) :rule trans :premises (t116.t27 t116.t28 t116.t32))
(step t116.t34 (cl @p_372) :rule trans :premises (t116.t33 t116.t31 t116.a3))
(step t116.t35 (cl @p_500) :rule resolution :premises (t116.t9 t116.t34))
(step t116.t36 (cl @p_499) :rule trans :premises (t116.t7 t116.t35))
(step t116.t37 (cl false) :rule resolution :premises (t116.t0 t116.t1 t116.t36))
(step t116 (cl @p_435 @p_498 @p_486 @p_383 @p_378 false) :rule subproof :discharge (t116.a0 t116.a1 t116.a2 t116.a3 t116.a4))
(step t117 (cl @p_496 @p_426) :rule and_pos :args (0))
(step t118 (cl @p_496 @p_494) :rule and_pos :args (1))
(step t119 (cl @p_496 @p_459) :rule and_pos :args (2))
(step t120 (cl @p_496 @p_382) :rule and_pos :args (3))
(step t121 (cl @p_496 @p_373) :rule and_pos :args (4))
(step t122 (cl false @p_496 @p_496 @p_496 @p_496 @p_496) :rule resolution :premises (t116 t117 t118 t119 t120 t121))
(step t123 (cl @p_496 @p_496 @p_496 @p_496 @p_496 false) :rule reordering :premises (t122))
(step t124 (cl @p_496 false) :rule contraction :premises (t123))
(step t125 (cl @p_497 false) :rule resolution :premises (t115 t124))
(step t126 (cl @p_497 @p_212) :rule implies_neg2)
(step t127 (cl @p_497 @p_497) :rule resolution :premises (t125 t126))
(step t128 (cl @p_497) :rule contraction :premises (t127))
(step t129 (cl (= @p_497 @p_496)) :rule implies_simplify)
(step t130 (cl (not @p_497) @p_496) :rule equiv1 :premises (t129))
(step t131 (cl @p_496) :rule resolution :premises (t128 t130))
(step t132 (cl @p_493) :rule resolution :premises (t114 t131))
(step t133 (cl @p_227 @p_435 @p_485 @p_378 @p_288 @p_336 @p_486 @p_487 @p_488) :rule not_and :premises (t132))
(step t134 (cl @p_490 (! (not @p_227) :named @p_232)) :rule or_neg :args (0))
(step t135 (cl @p_490 (not @p_435)) :rule or_neg :args (1))
(step t136 (cl @p_490 (not @p_485)) :rule or_neg :args (2))
(step t137 (cl @p_490 @p_491) :rule or_neg :args (3))
(step t138 (cl @p_490 (! (not @p_288) :named @p_377)) :rule or_neg :args (4))
(step t139 (cl @p_490 (! (not @p_336) :named @p_337)) :rule or_neg :args (5))
(step t140 (cl @p_490 (not @p_486)) :rule or_neg :args (6))
(step t141 (cl @p_490 (not @p_487)) :rule or_neg :args (7))
(step t142 (cl @p_490 (not @p_488)) :rule or_neg :args (8))
(step t143 (cl @p_490 @p_490 @p_490 @p_490 @p_490 @p_490 @p_490 @p_490 @p_490) :rule resolution :premises (t133 t134 t135 t136 t137 t138 t139 t140 t141 t142))
(step t144 (cl @p_490) :rule contraction :premises (t143))
(step t145 (cl @p_489) :rule resolution :premises (t88 t95 t144))
(step t146 (cl @p_227 @p_435 @p_485 @p_372 @p_284 @p_336 @p_486 @p_487 @p_488) :rule or :premises (t145))
(step t147 (cl @p_227 @p_435 @p_372 @p_485 @p_284 @p_336 @p_486 @p_487 @p_488) :rule reordering :premises (t146))
(step t148 (cl (! (not (! (or (! (= k$ 0) :named @p_433) @p_477) :named @p_478)) :named @p_484) @p_433 @p_477) :rule or_pos)
(step t149 (cl @p_433 @p_477 @p_484) :rule reordering :premises (t148))
(step t150 (cl (! (and @p_433 @p_426) :named @p_436) (! (not @p_433) :named @p_434) @p_435) :rule and_neg)
(step t151 (cl (! (=> @p_436 @p_2) :named @p_438) @p_436) :rule implies_neg1)
(anchor :step t152)
(assume t152.a0 @p_433)
(assume t152.a1 @p_426)
(step t152.t0 (cl (! (=> (! (and @p_426 @p_433) :named @p_439) @p_2) :named @p_441) @p_439) :rule implies_neg1)
(anchor :step t152.t1)
(assume t152.t1.a0 @p_426)
(assume t152.t1.a1 @p_433)
(step t152.t1.t0 (cl @p_442) :rule cong :premises (t152.t1.a1))
(step t152.t1.t1 (cl (or @p_427 @p_426)) :rule forall_inst :args (0))
(step t152.t1.t2 (cl @p_427 @p_426) :rule or :premises (t152.t1.t1))
(step t152.t1.t3 (cl @p_426) :rule resolution :premises (t152.t1.t2 a1))
(step t152.t1.t4 (cl @p_2) :rule trans :premises (t152.t1.t0 t152.t1.t3))
(step t152.t1 (cl @p_435 @p_434 @p_2) :rule subproof :discharge (t152.t1.a0 t152.t1.a1))
(step t152.t2 (cl (! (not @p_439) :named @p_440) @p_426) :rule and_pos :args (0))
(step t152.t3 (cl @p_440 @p_433) :rule and_pos :args (1))
(step t152.t4 (cl @p_2 @p_440 @p_440) :rule resolution :premises (t152.t1 t152.t2 t152.t3))
(step t152.t5 (cl @p_440 @p_440 @p_2) :rule reordering :premises (t152.t4))
(step t152.t6 (cl @p_440 @p_2) :rule contraction :premises (t152.t5))
(step t152.t7 (cl @p_441 @p_2) :rule resolution :premises (t152.t0 t152.t6))
(step t152.t8 (cl @p_441 @p_3) :rule implies_neg2)
(step t152.t9 (cl @p_441 @p_441) :rule resolution :premises (t152.t7 t152.t8))
(step t152.t10 (cl @p_441) :rule contraction :premises (t152.t9))
(step t152.t11 (cl @p_440 @p_2) :rule implies :premises (t152.t10))
(step t152.t12 (cl (or @p_427 @p_426)) :rule forall_inst :args (0))
(step t152.t13 (cl @p_427 @p_426) :rule or :premises (t152.t12))
(step t152.t14 (cl @p_426) :rule resolution :premises (t152.t13 a1))
(step t152.t15 (cl @p_439) :rule and_intro :premises (t152.t14 t152.a0))
(step t152.t16 (cl @p_2) :rule resolution :premises (t152.t11 t152.t15))
(step t152 (cl @p_434 @p_435 @p_2) :rule subproof :discharge (t152.a0 t152.a1))
(step t153 (cl (! (not @p_436) :named @p_437) @p_433) :rule and_pos :args (0))
(step t154 (cl @p_437 @p_426) :rule and_pos :args (1))
(step t155 (cl @p_2 @p_437 @p_437) :rule resolution :premises (t152 t153 t154))
(step t156 (cl @p_437 @p_437 @p_2) :rule reordering :premises (t155))
(step t157 (cl @p_437 @p_2) :rule contraction :premises (t156))
(step t158 (cl @p_438 @p_2) :rule resolution :premises (t151 t157))
(step t159 (cl @p_438 @p_3) :rule implies_neg2)
(step t160 (cl @p_438 @p_438) :rule resolution :premises (t158 t159))
(step t161 (cl @p_438) :rule contraction :premises (t160))
(step t162 (cl @p_437 @p_2) :rule implies :premises (t161))
(step t163 (cl @p_434 @p_435 @p_2) :rule resolution :premises (t150 t162))
(step t164 (cl @p_2 @p_434 @p_435) :rule reordering :premises (t163))
(step t165 (cl (or @p_427 @p_426)) :rule forall_inst :args (0))
(step t166 (cl @p_427 @p_426) :rule or :premises (t165))
(step t167 (cl @p_426) :rule resolution :premises (t166 a1))
(step t168 (cl @p_434) :rule resolution :premises (t164 t167 a11))
(step t169 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (! (or @p_433 @p_480) :named @p_481)) :named @p_482) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) @p_478) :named @p_479)) :named @p_483)) (not @p_482) @p_479) :rule equiv_pos2)
(step t170 (cl (= (* 1 (- 0 @p_476)) (* -1 (- @p_476 0)))) :rule poly_simp)
(step t171 (cl (= @p_480 @p_477)) :rule poly_simp_rel :premises (t170))
(step t172 (cl (= @p_481 @p_478)) :rule cong :premises (t171))
(step t173 (cl @p_483) :rule cong :premises (t172))
(step t174 (cl @p_482 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t175)
(assume t175.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t175.t0 (cl (or @p_82 @p_481)) :rule forall_inst :args (k$ 0))
(step t175.t1 (cl @p_82 @p_481) :rule or :premises (t175.t0))
(step t175.t2 (cl (not @p_72) (not (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t175.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t175.t3.t0 (cl (= (* 1 (- @p_73 ?v1)) (* -1 (- ?v1 @p_73)))) :rule poly_simp)
(step t175.t3.t1 (cl (= @p_81 @p_74)) :rule poly_simp_rel :premises (t175.t3.t0))
(step t175.t3.t2 (cl (= (=> @p_77 @p_81) @p_78)) :rule cong :premises (t175.t3.t1))
(step t175.t3 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t175.t4 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t175.t4.t0 (cl (= @p_78 @p_80)) :rule rare_rewrite :args ("bool-impl-elim" @p_77 @p_74))
(step t175.t4.t1 (cl (= @p_79 @p_75)) :rule rare_rewrite :args ("bool-double-not-elim" @p_75))
(step t175.t4.t2 (cl (= @p_74 @p_74)) :rule refl)
(step t175.t4.t3 (cl (= @p_80 @p_76)) :rule cong :premises (t175.t4.t1 t175.t4.t2))
(step t175.t4.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t175.t4.t0 t175.t4.t3))
(step t175.t4 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(step t175.t5 (cl @p_72) :rule trans :premises (t175.t3 t175.t4))
(step t175.t6 (cl (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule resolution :premises (t175.t2 t175.t5 a9))
(step t175.t7 (cl @p_481) :rule resolution :premises (t175.t1 t175.t6))
(step t175 (cl @p_82 @p_481) :rule subproof :discharge (t175.a0))
(step t176 (cl @p_482 @p_481) :rule resolution :premises (t174 t175))
(step t177 (cl @p_482 (not @p_481)) :rule implies_neg2)
(step t178 (cl @p_482 @p_482) :rule resolution :premises (t176 t177))
(step t179 (cl @p_482) :rule contraction :premises (t178))
(step t180 (cl @p_479) :rule resolution :premises (t169 t173 t179))
(step t181 (cl @p_82 @p_478) :rule implies :premises (t180))
(step t182 (cl (not @p_72) (not (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t183 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t183.t0 (cl (= (* 1 (- @p_73 ?v1)) (* -1 (- ?v1 @p_73)))) :rule poly_simp)
(step t183.t1 (cl (= @p_81 @p_74)) :rule poly_simp_rel :premises (t183.t0))
(step t183.t2 (cl (= (=> @p_77 @p_81) @p_78)) :rule cong :premises (t183.t1))
(step t183 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= (divide$ (times$ ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t184 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t184.t0 (cl (= @p_78 @p_80)) :rule rare_rewrite :args ("bool-impl-elim" @p_77 @p_74))
(step t184.t1 (cl (= @p_79 @p_75)) :rule rare_rewrite :args ("bool-double-not-elim" @p_75))
(step t184.t2 (cl (= @p_74 @p_74)) :rule refl)
(step t184.t3 (cl (= @p_80 @p_76)) :rule cong :premises (t184.t1 t184.t2))
(step t184.t4 (cl (= @p_78 @p_76)) :rule trans :premises (t184.t0 t184.t3))
(step t184 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (not (= ?v0 0)) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))) :rule bind)
(step t185 (cl @p_72) :rule trans :premises (t183 t184))
(step t186 (cl (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule resolution :premises (t182 t185 a9))
(step t187 (cl @p_478) :rule resolution :premises (t181 t186))
(step t188 (cl @p_477) :rule resolution :premises (t149 t168 t187))
(step t189 (cl (not @p_473) (not @p_472) @p_467) :rule equiv_pos2)
(step t190 (cl (= (* 1 (- 0 @p_465)) (* -1 (- @p_465 0)))) :rule poly_simp)
(step t191 (cl (= @p_470 @p_466)) :rule poly_simp_rel :premises (t190))
(step t192 (cl (= @p_56 true)) :rule evaluate)
(step t193 (cl (= @p_468 @p_468)) :rule refl)
(step t194 (cl (= @p_469 @p_475)) :rule cong :premises (t192 t193))
(step t195 (cl (= @p_475 true)) :rule or_simplify)
(step t196 (cl (= @p_469 true)) :rule trans :premises (t194 t195))
(step t197 (cl (= @p_471 @p_474)) :rule cong :premises (t191 t196))
(step t198 (cl (= @p_474 @p_466)) :rule rare_rewrite :args ("bool-eq-true" @p_466))
(step t199 (cl (= @p_471 @p_466)) :rule trans :premises (t197 t198))
(step t200 (cl @p_473) :rule cong :premises (t199))
(step t201 (cl @p_472 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t202)
(assume t202.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t202.t0 (cl (or @p_91 @p_471)) :rule forall_inst :args (0 k$))
(step t202.t1 (cl @p_91 @p_471) :rule or :premises (t202.t0))
(step t202.t2 (cl @p_471) :rule resolution :premises (t202.t1 t202.a0))
(step t202 (cl @p_91 @p_471) :rule subproof :discharge (t202.a0))
(step t203 (cl @p_472 @p_471) :rule resolution :premises (t201 t202))
(step t204 (cl @p_472 (not @p_471)) :rule implies_neg2)
(step t205 (cl @p_472 @p_472) :rule resolution :premises (t203 t204))
(step t206 (cl @p_472) :rule contraction :premises (t205))
(step t207 (cl @p_467) :rule resolution :premises (t189 t200 t206))
(step t208 (cl @p_91 @p_466) :rule implies :premises (t207))
(step t209 (cl @p_466) :rule resolution :premises (t208 a8))
(step t210 (cl (not @p_464) (not @p_463) @p_460) :rule equiv_pos2)
(step t211 (cl (= @p_461 @p_458)) :rule poly_simp)
(step t212 (cl (= @p_462 @p_459)) :rule cong :premises (t211))
(step t213 (cl @p_464) :rule cong :premises (t212))
(step t214 (cl @p_463 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t215)
(assume t215.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t215.t0 (cl (or @p_190 @p_462)) :rule forall_inst :args (2 @p_1))
(step t215.t1 (cl @p_190 @p_462) :rule or :premises (t215.t0))
(step t215.t2 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t215.t3 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t215.t3.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t215.t3.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t215.t3.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t215.t3.t0 t215.t3.t1))
(step t215.t3.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t215.t3.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t215.t3.t2 t215.t3.t3))
(step t215.t3.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t215.t3.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t215.t3.t5))
(step t215.t3.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t215.t3.t4 t215.t3.t6))
(step t215.t3 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t215.t4 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t215.t5 (cl @p_179) :rule trans :premises (t215.t3 t215.t4))
(step t215.t6 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t215.t2 t215.t5 a0))
(step t215.t7 (cl @p_462) :rule resolution :premises (t215.t1 t215.t6))
(step t215 (cl @p_190 @p_462) :rule subproof :discharge (t215.a0))
(step t216 (cl @p_463 @p_462) :rule resolution :premises (t214 t215))
(step t217 (cl @p_463 (not @p_462)) :rule implies_neg2)
(step t218 (cl @p_463 @p_463) :rule resolution :premises (t216 t217))
(step t219 (cl @p_463) :rule contraction :premises (t218))
(step t220 (cl @p_460) :rule resolution :premises (t210 t213 t219))
(step t221 (cl @p_190 @p_459) :rule implies :premises (t220))
(step t222 (cl (not @p_179) (not (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule equiv_pos2)
(anchor :step t223 :args ((?v0 Int) (?v1 Int) (?v2 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1) (:= (?v2 Int) ?v2)))
(step t223.t0 (cl (= @p_185 @p_189)) :rule poly_simp)
(step t223.t1 (cl (= @p_189 @p_187)) :rule poly_simp)
(step t223.t2 (cl (= @p_185 @p_187)) :rule trans :premises (t223.t0 t223.t1))
(step t223.t3 (cl (= @p_184 @p_184)) :rule refl)
(step t223.t4 (cl (= @p_186 @p_188)) :rule cong :premises (t223.t2 t223.t3))
(step t223.t5 (cl (= (* 1 (- @p_187 @p_184)) (* -1 (- ?v1 @p_182)))) :rule poly_simp)
(step t223.t6 (cl (= @p_188 @p_183)) :rule poly_simp_rel :premises (t223.t5))
(step t223.t7 (cl (= @p_186 @p_183)) :rule trans :premises (t223.t4 t223.t6))
(step t223 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= (+ (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)) ?v2) (+ ?v1 ?v2))) (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule bind)
(step t224 (cl (= (forall ((?v0 Int) (?v1 Int) (?v2 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))) :rule qnt_rm_unused)
(step t225 (cl @p_179) :rule trans :premises (t223 t224))
(step t226 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule resolution :premises (t222 t225 a0))
(step t227 (cl @p_459) :rule resolution :premises (t221 t226))
(step t228 (cl (! (not (! (or (! (= @p_172 0) :named @p_430) @p_429) :named @p_431)) :named @p_455) @p_430 @p_429) :rule or_pos)
(step t229 (cl @p_430 @p_429 @p_455) :rule reordering :premises (t228))
(step t230 (cl (not (! (= (! (or @p_227 (! (not @p_434) :named @p_444) (! (not @p_430) :named @p_432)) :named @p_445) (! (or @p_227 @p_433 @p_432) :named @p_443)) :named @p_454)) (not @p_445) @p_443) :rule equiv_pos2)
(step t231 (cl (= @p_444 @p_433)) :rule rare_rewrite :args ("bool-double-not-elim" @p_433))
(step t232 (cl (= @p_432 @p_432)) :rule refl)
(step t233 (cl @p_454) :rule cong :premises (t231 t232))
(step t234 (cl (! (and @p_224 @p_434) :named @p_448) @p_227 @p_444) :rule and_neg)
(step t235 (cl (! (=> @p_448 @p_432) :named @p_450) @p_448) :rule implies_neg1)
(anchor :step t236)
(assume t236.a0 @p_224)
(assume t236.a1 @p_434)
(step t236.t0 (cl @p_450 @p_448) :rule implies_neg1)
(anchor :step t236.t1)
(assume t236.t1.a0 @p_224)
(assume t236.t1.a1 @p_434)
(step t236.t1.t0 (cl (= (! (= @p_430 false) :named @p_451) @p_432)) :rule equiv_simplify)
(step t236.t1.t1 (cl (not @p_451) @p_432) :rule equiv1 :premises (t236.t1.t0))
(step t236.t1.t2 (cl @p_226 @p_2 @p_224) :rule or_pos)
(step t236.t1.t3 (cl @p_2 @p_224 @p_226) :rule reordering :premises (t236.t1.t2))
(step t236.t1.t4 (cl (or @p_82 @p_225)) :rule forall_inst :args (@p_1 k$))
(step t236.t1.t5 (cl @p_82 @p_225) :rule or :premises (t236.t1.t4))
(step t236.t1.t6 (cl @p_225) :rule resolution :premises (t236.t1.t5 t186))
(step t236.t1.t7 (cl @p_224) :rule resolution :premises (t236.t1.t3 a11 t236.t1.t6))
(step t236.t1.t8 (cl (= @p_172 k$)) :rule symm :premises (t236.t1.t7))
(step t236.t1.t9 (cl @p_56) :rule refl)
(step t236.t1.t10 (cl (= @p_430 @p_433)) :rule cong :premises (t236.t1.t8 t236.t1.t9))
(step t236.t1.t11 (cl (! (= (! (= @p_433 false) :named @p_452) @p_434) :named @p_453)) :rule equiv_simplify)
(step t236.t1.t12 (cl @p_452 @p_444) :rule equiv2 :premises (t236.t1.t11))
(step t236.t1.t13 (cl (! (not @p_444) :named @p_447) @p_433) :rule not_not)
(step t236.t1.t14 (cl @p_452 @p_433) :rule resolution :premises (t236.t1.t12 t236.t1.t13))
(step t236.t1.t15 (cl @p_452) :rule resolution :premises (t236.t1.t14 t236.t1.a1))
(step t236.t1.t16 (cl @p_451) :rule trans :premises (t236.t1.t10 t236.t1.t15))
(step t236.t1.t17 (cl @p_432) :rule resolution :premises (t236.t1.t1 t236.t1.t16))
(step t236.t1 (cl @p_227 @p_444 @p_432) :rule subproof :discharge (t236.t1.a0 t236.t1.a1))
(step t236.t2 (cl (! (not @p_448) :named @p_449) @p_224) :rule and_pos :args (0))
(step t236.t3 (cl @p_449 @p_434) :rule and_pos :args (1))
(step t236.t4 (cl @p_432 @p_449 @p_449) :rule resolution :premises (t236.t1 t236.t2 t236.t3))
(step t236.t5 (cl @p_449 @p_449 @p_432) :rule reordering :premises (t236.t4))
(step t236.t6 (cl @p_449 @p_432) :rule contraction :premises (t236.t5))
(step t236.t7 (cl @p_450 @p_432) :rule resolution :premises (t236.t0 t236.t6))
(step t236.t8 (cl @p_450 (! (not @p_432) :named @p_446)) :rule implies_neg2)
(step t236.t9 (cl @p_450 @p_450) :rule resolution :premises (t236.t7 t236.t8))
(step t236.t10 (cl @p_450) :rule contraction :premises (t236.t9))
(step t236.t11 (cl @p_449 @p_432) :rule implies :premises (t236.t10))
(step t236.t12 (cl @p_226 @p_2 @p_224) :rule or_pos)
(step t236.t13 (cl @p_2 @p_224 @p_226) :rule reordering :premises (t236.t12))
(step t236.t14 (cl (or @p_82 @p_225)) :rule forall_inst :args (@p_1 k$))
(step t236.t15 (cl @p_82 @p_225) :rule or :premises (t236.t14))
(step t236.t16 (cl @p_225) :rule resolution :premises (t236.t15 t186))
(step t236.t17 (cl @p_224) :rule resolution :premises (t236.t13 a11 t236.t16))
(step t236.t18 (cl @p_448) :rule and_intro :premises (t236.t17 t236.a1))
(step t236.t19 (cl @p_432) :rule resolution :premises (t236.t11 t236.t18))
(step t236 (cl @p_227 @p_444 @p_432) :rule subproof :discharge (t236.a0 t236.a1))
(step t237 (cl @p_449 @p_224) :rule and_pos :args (0))
(step t238 (cl @p_449 @p_434) :rule and_pos :args (1))
(step t239 (cl @p_432 @p_449 @p_449) :rule resolution :premises (t236 t237 t238))
(step t240 (cl @p_449 @p_449 @p_432) :rule reordering :premises (t239))
(step t241 (cl @p_449 @p_432) :rule contraction :premises (t240))
(step t242 (cl @p_450 @p_432) :rule resolution :premises (t235 t241))
(step t243 (cl @p_450 @p_446) :rule implies_neg2)
(step t244 (cl @p_450 @p_450) :rule resolution :premises (t242 t243))
(step t245 (cl @p_450) :rule contraction :premises (t244))
(step t246 (cl @p_449 @p_432) :rule implies :premises (t245))
(step t247 (cl @p_227 @p_444 @p_432) :rule resolution :premises (t234 t246))
(step t248 (cl @p_445 @p_232) :rule or_neg :args (0))
(step t249 (cl @p_445 @p_447) :rule or_neg :args (1))
(step t250 (cl @p_445 @p_446) :rule or_neg :args (2))
(step t251 (cl @p_445 @p_445 @p_445) :rule resolution :premises (t247 t248 t249 t250))
(step t252 (cl @p_445) :rule contraction :premises (t251))
(step t253 (cl @p_443) :rule resolution :premises (t230 t233 t252))
(step t254 (cl @p_227 @p_433 @p_432) :rule or :premises (t253))
(step t255 (cl @p_433 @p_227 @p_432) :rule reordering :premises (t254))
(step t256 (cl @p_226 @p_2 @p_224) :rule or_pos)
(step t257 (cl @p_2 @p_224 @p_226) :rule reordering :premises (t256))
(step t258 (cl (or @p_82 @p_225)) :rule forall_inst :args (@p_1 k$))
(step t259 (cl @p_82 @p_225) :rule or :premises (t258))
(step t260 (cl @p_225) :rule resolution :premises (t259 t186))
(step t261 (cl @p_224) :rule resolution :premises (t257 a11 t260))
(step t262 (cl @p_432) :rule resolution :premises (t255 t168 t261))
(step t263 (cl (or @p_82 @p_431)) :rule forall_inst :args (@p_172 @p_1))
(step t264 (cl @p_82 @p_431) :rule or :premises (t263))
(step t265 (cl @p_431) :rule resolution :premises (t264 t186))
(step t266 (cl @p_429) :rule resolution :premises (t229 t262 t265))
(step t267 (cl (not (! (= (! (or (! (not @p_3) :named @p_375) (! (not (! (= @p_169 (! (* -1 (! (centered_modulo$ 0 k$) :named @p_132)) :named @p_191)) :named @p_192)) :named @p_198) @p_227 (! (not (! (= @p_132 (! (+ @p_46 @p_114) :named @p_131)) :named @p_133)) :named @p_283) (! (not (! (= @p_169 (! (+ (! (times$ @p_1 @p_172) :named @p_173) (! (modulo$ @p_169 @p_1) :named @p_170)) :named @p_177)) :named @p_178)) :named @p_199) (! (not (! (= @p_169 (! (+ @p_170 @p_249) :named @p_253)) :named @p_254)) :named @p_261) (! (not @p_115) :named @p_130) @p_373 @p_288) :named @p_376) (! (or @p_2 @p_198 @p_227 @p_283 @p_199 @p_261 @p_130 @p_373 @p_284) :named @p_374)) :named @p_424)) (not @p_376) @p_374) :rule equiv_pos2)
(step t268 (cl (= @p_375 @p_2)) :rule rare_rewrite :args ("bool-double-not-elim" @p_2))
(step t269 (cl (= @p_198 @p_198)) :rule refl)
(step t270 (cl (= @p_227 @p_227)) :rule refl)
(step t271 (cl (= @p_283 @p_283)) :rule refl)
(step t272 (cl (= @p_199 @p_199)) :rule refl)
(step t273 (cl (= @p_261 @p_261)) :rule refl)
(step t274 (cl (= @p_130 @p_130)) :rule refl)
(step t275 (cl (= @p_373 @p_373)) :rule refl)
(step t276 (cl @p_424) :rule cong :premises (t268 t269 t270 t271 t272 t273 t274 t275 t90))
(step t277 (cl (! (=> (! (and @p_3 @p_192 @p_224 @p_133 @p_178 @p_254 @p_115 @p_372 @p_285) :named @p_380) (! (and (! (= @p_191 @p_177) :named @p_208) (! (= @p_191 @p_173) :named @p_235) (! (= @p_191 @p_253) :named @p_269) @p_133 @p_115 @p_285 @p_383) :named @p_384)) :named @p_415) @p_380) :rule implies_neg1)
(anchor :step t278)
(assume t278.a0 @p_3)
(assume t278.a1 @p_192)
(assume t278.a2 @p_224)
(assume t278.a3 @p_133)
(assume t278.a4 @p_178)
(assume t278.a5 @p_254)
(assume t278.a6 @p_115)
(assume t278.a7 @p_372)
(assume t278.a8 @p_285)
(step t278.t0 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))) (! (= 0 (! (+ @p_169 @p_132) :named @p_194)) :named @p_195)) :named @p_196) (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))) @p_192) :named @p_193)) :named @p_197)) (not @p_196) @p_193) :rule equiv_pos2)
(step t278.t1 (cl (= (* 1 (- 0 @p_194)) (* -1 (- @p_169 @p_191)))) :rule poly_simp)
(step t278.t2 (cl (= @p_195 @p_192)) :rule poly_simp_rel :premises (t278.t1))
(step t278.t3 (cl @p_197) :rule cong :premises (t278.t2))
(step t278.t4 (cl @p_196 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t278.t5)
(assume t278.t5.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))))
(step t278.t5.t0 (cl (or @p_110 @p_195)) :rule forall_inst :args (0 k$))
(step t278.t5.t1 (cl @p_110 @p_195) :rule or :premises (t278.t5.t0))
(step t278.t5.t2 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t278.t5.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t278.t5.t3.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t278.t5.t3.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t278.t5.t3.t0))
(step t278.t5.t3 (cl @p_107) :rule bind)
(step t278.t5.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t278.t5.t2 t278.t5.t3 a2))
(step t278.t5.t5 (cl @p_195) :rule resolution :premises (t278.t5.t1 t278.t5.t4))
(step t278.t5 (cl @p_110 @p_195) :rule subproof :discharge (t278.t5.a0))
(step t278.t6 (cl @p_196 @p_195) :rule resolution :premises (t278.t4 t278.t5))
(step t278.t7 (cl @p_196 (not @p_195)) :rule implies_neg2)
(step t278.t8 (cl @p_196 @p_196) :rule resolution :premises (t278.t6 t278.t7))
(step t278.t9 (cl @p_196) :rule contraction :premises (t278.t8))
(step t278.t10 (cl @p_193) :rule resolution :premises (t278.t0 t278.t3 t278.t9))
(step t278.t11 (cl @p_110 @p_192) :rule implies :premises (t278.t10))
(step t278.t12 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t278.t13 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t278.t13.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t278.t13.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t278.t13.t0))
(step t278.t13 (cl @p_107) :rule bind)
(step t278.t14 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t278.t12 t278.t13 a2))
(step t278.t15 (cl @p_192) :rule resolution :premises (t278.t11 t278.t14))
(step t278.t16 (cl (= @p_191 @p_169)) :rule symm :premises (t278.t15))
(step t278.t17 (cl (or @p_190 @p_178)) :rule forall_inst :args (@p_1 @p_169))
(step t278.t18 (cl @p_190 @p_178) :rule or :premises (t278.t17))
(step t278.t19 (cl @p_178) :rule resolution :premises (t278.t18 t226))
(step t278.t20 (cl @p_208) :rule trans :premises (t278.t16 t278.t19))
(step t278.t21 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t278.t22 (cl @p_235) :rule trans :premises (t278.t16 t278.t21))
(step t278.t23 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))) (! (= @p_169 (! (+ @p_249 @p_170) :named @p_257)) :named @p_258)) :named @p_259) (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))) @p_254) :named @p_256)) :named @p_260)) (not @p_259) @p_256) :rule equiv_pos2)
(step t278.t24 (cl (= @p_257 @p_253)) :rule poly_simp)
(step t278.t25 (cl (= @p_258 @p_254)) :rule cong :premises (t278.t24))
(step t278.t26 (cl @p_260) :rule cong :premises (t278.t25))
(step t278.t27 (cl @p_259 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t278.t28)
(assume t278.t28.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t278.t28.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :named @p_255) @p_258)) :rule forall_inst :args (@p_169 @p_1))
(step t278.t28.t1 (cl @p_255 @p_258) :rule or :premises (t278.t28.t0))
(step t278.t28.t2 (cl @p_258) :rule resolution :premises (t278.t28.t1 t278.t28.a0))
(step t278.t28 (cl @p_255 @p_258) :rule subproof :discharge (t278.t28.a0))
(step t278.t29 (cl @p_259 @p_258) :rule resolution :premises (t278.t27 t278.t28))
(step t278.t30 (cl @p_259 (not @p_258)) :rule implies_neg2)
(step t278.t31 (cl @p_259 @p_259) :rule resolution :premises (t278.t29 t278.t30))
(step t278.t32 (cl @p_259) :rule contraction :premises (t278.t31))
(step t278.t33 (cl @p_256) :rule resolution :premises (t278.t23 t278.t26 t278.t32))
(step t278.t34 (cl @p_255 @p_254) :rule implies :premises (t278.t33))
(step t278.t35 (cl @p_254) :rule resolution :premises (t278.t34 a4))
(step t278.t36 (cl @p_269) :rule trans :premises (t278.t16 t278.t35))
(step t278.t37 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1)))))) @p_133) :named @p_155) @p_155) :named @p_163)) (not @p_155) @p_155) :rule equiv_pos2)
(step t278.t38 (cl (= (! (= (! (= @p_6 @p_6) :named @p_162) true) :named @p_164) @p_162)) :rule equiv_simplify)
(step t278.t39 (cl (not @p_164) @p_162) :rule equiv1 :premises (t278.t38))
(step t278.t40 (cl (= (* -1 (! (- @p_6 @p_6) :named @p_166)) (* 1 @p_166))) :rule poly_simp)
(step t278.t41 (cl (! (= @p_162 @p_162) :named @p_165)) :rule poly_simp_rel :premises (t278.t40))
(step t278.t42 (cl @p_162) :rule refl)
(step t278.t43 (cl @p_162) :rule refl)
(step t278.t44 (cl @p_165) :rule cong :premises (t278.t42 t278.t43))
(step t278.t45 (cl @p_164) :rule rare_rewrite :args ("eq-refl" @p_6))
(step t278.t46 (cl @p_164) :rule trans :premises (t278.t41 t278.t44 t278.t45))
(step t278.t47 (cl @p_162) :rule resolution :premises (t278.t39 t278.t46))
(step t278.t48 (cl (= 2 2)) :rule refl)
(step t278.t49 (cl (! (= @p_7 @p_7) :named @p_167)) :rule cong :premises (t278.t47 t278.t48))
(step t278.t50 (cl (! (= @p_46 @p_46) :named @p_168)) :rule cong :premises (t278.t49))
(step t278.t51 (cl (= @p_114 @p_114)) :rule cong :premises (t278.t49 t278.t47))
(step t278.t52 (cl (= @p_131 @p_131)) :rule cong :premises (t278.t50 t278.t51))
(step t278.t53 (cl (= @p_133 @p_133)) :rule cong :premises (t278.t52))
(step t278.t54 (cl @p_163) :rule cong :premises (t278.t53))
(step t278.t55 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1)))))) (! (= @p_132 (! (+ @p_46 (! (modulo$ (! (+ 0 @p_7) :named @p_156) @p_6) :named @p_157)) :named @p_158)) :named @p_159)) :named @p_160) @p_155) :named @p_161)) (not @p_160) @p_155) :rule equiv_pos2)
(step t278.t56 (cl (= @p_156 @p_7)) :rule poly_simp)
(step t278.t57 (cl (= @p_157 @p_114)) :rule cong :premises (t278.t56 t278.t43))
(step t278.t58 (cl (= @p_158 @p_131)) :rule cong :premises (t278.t57))
(step t278.t59 (cl (= @p_159 @p_133)) :rule cong :premises (t278.t58))
(step t278.t60 (cl @p_161) :rule cong :premises (t278.t59))
(step t278.t61 (cl @p_160 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule implies_neg1)
(anchor :step t278.t62)
(assume t278.t62.a0 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1)))))))
(step t278.t62.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :named @p_154) @p_159)) :rule forall_inst :args (0 k$))
(step t278.t62.t1 (cl @p_154 @p_159) :rule or :premises (t278.t62.t0))
(step t278.t62.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :named @p_134)) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t278.t62.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t278.t62.t3.t0 (cl (= (! (- (! (modulo$ (! (+ ?v0 (! (divide$ (! (ite (! (< ?v1 0) :named @p_143) (! (- ?v1) :named @p_142) ?v1) :named @p_144) 2) :named @p_145)) :named @p_146) @p_144) :named @p_147) (! (divide$ (! (ite (! (< ?v1 0) :named @p_143) (! (- ?v1) :named @p_142) ?v1) :named @p_144) 2) :named @p_145)) :named @p_148) (! (+ (! (modulo$ (! (+ ?v0 (! (divide$ (! (ite (! (< ?v1 0) :named @p_143) (! (- ?v1) :named @p_142) ?v1) :named @p_144) 2) :named @p_145)) :named @p_146) @p_144) :named @p_147) (! (* -1 @p_145) :named @p_149)) :named @p_150))) :rule poly_simp)
(step t278.t62.t3.t1 (cl (= @p_143 (! (not (! (>= ?v1 0) :named @p_135)) :named @p_152))) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t278.t62.t3.t2 (cl (= @p_142 (! (* -1 ?v1) :named @p_23))) :rule poly_simp)
(step t278.t62.t3.t3 (cl (! (= ?v1 ?v1) :named @p_20)) :rule refl)
(step t278.t62.t3.t4 (cl (= @p_144 (! (ite @p_152 @p_23 ?v1) :named @p_153))) :rule cong :premises (t278.t62.t3.t1 t278.t62.t3.t2 t278.t62.t3.t3))
(step t278.t62.t3.t5 (cl (= @p_153 (! (ite @p_135 ?v1 @p_23) :named @p_136))) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t278.t62.t3.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t278.t62.t3.t4 t278.t62.t3.t5))
(step t278.t62.t3.t7 (cl (= @p_145 (! (divide$ @p_136 2) :named @p_137))) :rule cong :premises (t278.t62.t3.t6 t278.t48))
(step t278.t62.t3.t8 (cl (= @p_146 (! (+ ?v0 @p_137) :named @p_138))) :rule cong :premises (t278.t62.t3.t7))
(step t278.t62.t3.t9 (cl (= @p_147 (! (modulo$ @p_138 @p_136) :named @p_139))) :rule cong :premises (t278.t62.t3.t8 t278.t62.t3.t6))
(step t278.t62.t3.t10 (cl (= @p_149 (! (* -1 @p_137) :named @p_140))) :rule cong :premises (t278.t62.t3.t7))
(step t278.t62.t3.t11 (cl (= @p_150 (! (+ @p_139 @p_140) :named @p_151))) :rule cong :premises (t278.t62.t3.t9 t278.t62.t3.t10))
(step t278.t62.t3.t12 (cl (= @p_151 (! (+ @p_140 @p_139) :named @p_141))) :rule poly_simp)
(step t278.t62.t3.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t278.t62.t3.t11 t278.t62.t3.t12))
(step t278.t62.t3.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t278.t62.t3.t0 t278.t62.t3.t13))
(step t278.t62.t3.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t278.t62.t3.t14))
(step t278.t62.t3 (cl @p_134) :rule bind)
(step t278.t62.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t278.t62.t2 t278.t62.t3 a3))
(step t278.t62.t5 (cl @p_159) :rule resolution :premises (t278.t62.t1 t278.t62.t4))
(step t278.t62 (cl @p_154 @p_159) :rule subproof :discharge (t278.t62.a0))
(step t278.t63 (cl @p_160 @p_159) :rule resolution :premises (t278.t61 t278.t62))
(step t278.t64 (cl @p_160 (not @p_159)) :rule implies_neg2)
(step t278.t65 (cl @p_160 @p_160) :rule resolution :premises (t278.t63 t278.t64))
(step t278.t66 (cl @p_160) :rule contraction :premises (t278.t65))
(step t278.t67 (cl @p_155) :rule resolution :premises (t278.t55 t278.t60 t278.t66))
(step t278.t68 (cl @p_155) :rule resolution :premises (t278.t37 t278.t54 t278.t67))
(step t278.t69 (cl @p_154 @p_133) :rule implies :premises (t278.t68))
(step t278.t70 (cl (not @p_134) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t278.t71 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t278.t71.t0 (cl (= @p_148 @p_150)) :rule poly_simp)
(step t278.t71.t1 (cl (= @p_143 @p_152)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t278.t71.t2 (cl (= @p_142 @p_23)) :rule poly_simp)
(step t278.t71.t3 (cl @p_20) :rule refl)
(step t278.t71.t4 (cl (= @p_144 @p_153)) :rule cong :premises (t278.t71.t1 t278.t71.t2 t278.t71.t3))
(step t278.t71.t5 (cl (= @p_153 @p_136)) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t278.t71.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t278.t71.t4 t278.t71.t5))
(step t278.t71.t7 (cl (= @p_145 @p_137)) :rule cong :premises (t278.t71.t6 t278.t48))
(step t278.t71.t8 (cl (= @p_146 @p_138)) :rule cong :premises (t278.t71.t7))
(step t278.t71.t9 (cl (= @p_147 @p_139)) :rule cong :premises (t278.t71.t8 t278.t71.t6))
(step t278.t71.t10 (cl (= @p_149 @p_140)) :rule cong :premises (t278.t71.t7))
(step t278.t71.t11 (cl (= @p_150 @p_151)) :rule cong :premises (t278.t71.t9 t278.t71.t10))
(step t278.t71.t12 (cl (= @p_151 @p_141)) :rule poly_simp)
(step t278.t71.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t278.t71.t11 t278.t71.t12))
(step t278.t71.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t278.t71.t0 t278.t71.t13))
(step t278.t71.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t278.t71.t14))
(step t278.t71 (cl @p_134) :rule bind)
(step t278.t72 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t278.t70 t278.t71 a3))
(step t278.t73 (cl @p_133) :rule resolution :premises (t278.t69 t278.t72))
(step t278.t74 (cl (! (=> (! (and @p_372 @p_3) :named @p_416) @p_383) :named @p_418) @p_416) :rule implies_neg1)
(anchor :step t278.t75)
(assume t278.t75.a0 @p_372)
(assume t278.t75.a1 @p_3)
(step t278.t75.t0 (cl (! (= (! (= @p_382 false) :named @p_419) @p_383) :named @p_423)) :rule equiv_simplify)
(step t278.t75.t1 (cl (not @p_419) @p_383) :rule equiv1 :premises (t278.t75.t0))
(step t278.t75.t2 (cl (not (! (= (! (= @p_411 false) :named @p_420) @p_419) :named @p_422)) (not @p_420) @p_419) :rule equiv_pos2)
(step t278.t75.t3 (cl (= @p_420 (! (not @p_411) :named @p_412))) :rule rare_rewrite :args ("bool-eq-false" @p_411))
(step t278.t75.t4 (cl @p_423) :rule rare_rewrite :args ("bool-eq-false" @p_382))
(step t278.t75.t5 (cl (= (* 1 (- 0 @p_249)) (* -1 (- @p_249 0)))) :rule poly_simp)
(step t278.t75.t6 (cl (= @p_382 @p_411)) :rule poly_simp_rel :premises (t278.t75.t5))
(step t278.t75.t7 (cl (= @p_383 @p_412)) :rule cong :premises (t278.t75.t6))
(step t278.t75.t8 (cl (= @p_419 @p_412)) :rule trans :premises (t278.t75.t4 t278.t75.t7))
(step t278.t75.t9 (cl (= @p_412 @p_419)) :rule symm :premises (t278.t75.t8))
(step t278.t75.t10 (cl @p_422) :rule trans :premises (t278.t75.t3 t278.t75.t9))
(step t278.t75.t11 (cl (= @p_249 @p_1)) :rule symm :premises (t278.t75.a0))
(step t278.t75.t12 (cl @p_56) :rule refl)
(step t278.t75.t13 (cl (= @p_411 @p_2)) :rule cong :premises (t278.t75.t11 t278.t75.t12))
(step t278.t75.t14 (cl (= (! (= @p_2 false) :named @p_421) @p_3)) :rule equiv_simplify)
(step t278.t75.t15 (cl @p_421 @p_375) :rule equiv2 :premises (t278.t75.t14))
(step t278.t75.t16 (cl (! (not @p_375) :named @p_379) @p_2) :rule not_not)
(step t278.t75.t17 (cl @p_421 @p_2) :rule resolution :premises (t278.t75.t15 t278.t75.t16))
(step t278.t75.t18 (cl @p_421) :rule resolution :premises (t278.t75.t17 t278.t75.a1))
(step t278.t75.t19 (cl @p_420) :rule trans :premises (t278.t75.t13 t278.t75.t18))
(step t278.t75.t20 (cl @p_419) :rule resolution :premises (t278.t75.t2 t278.t75.t10 t278.t75.t19))
(step t278.t75.t21 (cl @p_383) :rule resolution :premises (t278.t75.t1 t278.t75.t20))
(step t278.t75 (cl @p_373 @p_375 @p_383) :rule subproof :discharge (t278.t75.a0 t278.t75.a1))
(step t278.t76 (cl (! (not @p_416) :named @p_417) @p_372) :rule and_pos :args (0))
(step t278.t77 (cl @p_417 @p_3) :rule and_pos :args (1))
(step t278.t78 (cl @p_383 @p_417 @p_417) :rule resolution :premises (t278.t75 t278.t76 t278.t77))
(step t278.t79 (cl @p_417 @p_417 @p_383) :rule reordering :premises (t278.t78))
(step t278.t80 (cl @p_417 @p_383) :rule contraction :premises (t278.t79))
(step t278.t81 (cl @p_418 @p_383) :rule resolution :premises (t278.t74 t278.t80))
(step t278.t82 (cl @p_418 (! (not @p_383) :named @p_387)) :rule implies_neg2)
(step t278.t83 (cl @p_418 @p_418) :rule resolution :premises (t278.t81 t278.t82))
(step t278.t84 (cl @p_418) :rule contraction :premises (t278.t83))
(step t278.t85 (cl @p_417 @p_383) :rule implies :premises (t278.t84))
(step t278.t86 (cl @p_416) :rule and_intro :premises (t278.a7 t278.a0))
(step t278.t87 (cl @p_383) :rule resolution :premises (t278.t85 t278.t86))
(step t278.t88 (cl @p_384) :rule and_intro :premises (t278.t20 t278.t22 t278.t36 t278.t73 t278.a6 t278.a8 t278.t87))
(step t278 (cl @p_375 @p_198 @p_227 @p_283 @p_199 @p_261 @p_130 @p_373 @p_288 @p_384) :rule subproof :discharge (t278.a0 t278.a1 t278.a2 t278.a3 t278.a4 t278.a5 t278.a6 t278.a7 t278.a8))
(step t279 (cl (! (not @p_380) :named @p_381) @p_3) :rule and_pos :args (0))
(step t280 (cl @p_381 @p_192) :rule and_pos :args (1))
(step t281 (cl @p_381 @p_224) :rule and_pos :args (2))
(step t282 (cl @p_381 @p_133) :rule and_pos :args (3))
(step t283 (cl @p_381 @p_178) :rule and_pos :args (4))
(step t284 (cl @p_381 @p_254) :rule and_pos :args (5))
(step t285 (cl @p_381 @p_115) :rule and_pos :args (6))
(step t286 (cl @p_381 @p_372) :rule and_pos :args (7))
(step t287 (cl @p_381 @p_285) :rule and_pos :args (8))
(step t288 (cl @p_384 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381) :rule resolution :premises (t278 t279 t280 t281 t282 t283 t284 t285 t286 t287))
(step t289 (cl @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_381 @p_384) :rule reordering :premises (t288))
(step t290 (cl @p_381 @p_384) :rule contraction :premises (t289))
(step t291 (cl @p_415 @p_384) :rule resolution :premises (t277 t290))
(step t292 (cl @p_415 (! (not @p_384) :named @p_385)) :rule implies_neg2)
(step t293 (cl @p_415 @p_415) :rule resolution :premises (t291 t292))
(step t294 (cl @p_415) :rule contraction :premises (t293))
(step t295 (cl @p_381 @p_384) :rule implies :premises (t294))
(step t296 (cl (! (=> @p_384 false) :named @p_386) @p_384) :rule implies_neg1)
(anchor :step t297)
(assume t297.a0 @p_208)
(assume t297.a1 @p_235)
(assume t297.a2 @p_269)
(assume t297.a3 @p_133)
(assume t297.a4 @p_115)
(assume t297.a5 @p_285)
(assume t297.a6 @p_383)
(step t297.t0 (cl (! (not (! (< @p_249 0) :named @p_355)) :named @p_357) (! (<= @p_249 -1) :named @p_388)) :rule la_generic :args (1/1 1/1))
(step t297.t1 (cl @p_414) :rule la_disequality)
(step t297.t2 (cl @p_411 @p_413 @p_404) :rule or :premises (t297.t1))
(step t297.t3 (cl @p_412) :rule not_symm :premises (t297.a6))
(step t297.t4 (cl @p_410 @p_406) :rule la_generic :args (1/1 1/1))
(step t297.t5 (cl @p_409 @p_288 @p_407) :rule equiv_pos2)
(step t297.t6 (cl (= @p_407 @p_285)) :rule rare_rewrite :args ("arith-elim-lt" @p_249 1))
(step t297.t7 (cl @p_408) :rule symm :premises (t297.t6))
(step t297.t8 (cl @p_407) :rule resolution :premises (t297.t5 t297.t7 t297.a5))
(step t297.t9 (cl @p_406) :rule resolution :premises (t297.t4 t297.t8))
(step t297.t10 (cl (not (! (= @p_355 @p_404) :named @p_405)) @p_355 (not @p_404)) :rule equiv_pos1)
(step t297.t11 (cl @p_405) :rule comp_simplify)
(step t297.t12 (cl @p_355) :rule resolution :premises (t297.t2 t297.t3 t297.t9 t297.t10 t297.t11))
(step t297.t13 (cl @p_388) :rule resolution :premises (t297.t0 t297.t12))
(step t297.t14 (cl (not (! (= (! (> @p_249 -1) :named @p_390) (! (not @p_388) :named @p_389)) :named @p_400)) (not @p_390) @p_389) :rule equiv_pos2)
(step t297.t15 (cl (= @p_390 (! (not (! (>= -1 @p_249) :named @p_401)) :named @p_402))) :rule rare_rewrite :args ("arith-elim-gt" @p_249 -1))
(step t297.t16 (cl (= @p_388 @p_401)) :rule rare_rewrite :args ("arith-elim-leq" @p_249 -1))
(step t297.t17 (cl (= @p_401 @p_388)) :rule symm :premises (t297.t16))
(step t297.t18 (cl (= @p_402 @p_389)) :rule cong :premises (t297.t17))
(step t297.t19 (cl @p_400) :rule trans :premises (t297.t15 t297.t18))
(step t297.t20 (cl (not (! (= @p_389 @p_390) :named @p_396)) (not @p_389) @p_390) :rule equiv_pos2)
(step t297.t21 (cl (= @p_388 (! (not (! (>= @p_249 (! (+ -1 1) :named @p_397)) :named @p_398)) :named @p_399))) :rule rare_rewrite :args ("arith-leq-norm" @p_249 -1))
(step t297.t22 (cl (= @p_397 0)) :rule evaluate)
(step t297.t23 (cl (= @p_398 @p_333)) :rule cong :premises (t297.t22))
(step t297.t24 (cl (= @p_399 @p_336)) :rule cong :premises (t297.t23))
(step t297.t25 (cl (= @p_388 @p_336)) :rule trans :premises (t297.t21 t297.t24))
(step t297.t26 (cl (= @p_389 @p_337)) :rule cong :premises (t297.t25))
(step t297.t27 (cl (= @p_337 @p_333)) :rule rare_rewrite :args ("bool-double-not-elim" @p_333))
(step t297.t28 (cl (= @p_389 @p_333)) :rule trans :premises (t297.t26 t297.t27))
(step t297.t29 (cl (= @p_390 @p_333)) :rule trans :premises (t297.t19 t297.t28))
(step t297.t30 (cl (= @p_333 @p_390)) :rule symm :premises (t297.t29))
(step t297.t31 (cl @p_396) :rule trans :premises (t297.t28 t297.t30))
(step t297.t32 (cl (! (=> @p_388 false) :named @p_391) @p_388) :rule implies_neg1)
(anchor :step t297.t33)
(assume t297.t33.a0 @p_388)
(step t297.t33.t0 (cl (not (! (= (! (<= (! (+ @p_249 (! (* -1 (! (+ @p_7 (! (* -1 @p_114) :named @p_301)) :named @p_302)) :named @p_345) (! (+ @p_132 @p_7 @p_301) :named @p_303) (! (* -1 (! (+ @p_132 @p_170 @p_249) :named @p_274)) :named @p_344) (! (* -1 (! (+ @p_132 @p_173) :named @p_240)) :named @p_343) (! (+ @p_132 @p_173 @p_170) :named @p_214)) :named @p_393) (! (+ -1 @p_297 0 @p_297 @p_297 0) :named @p_392)) :named @p_394) false) :named @p_395)) (not @p_394) false) :rule equiv_pos2)
(step t297.t33.t1 (cl (= @p_393 (! (+ (! (* 0 @p_249) :named @p_368) (! (* 0 @p_170) :named @p_329) (! (* 0 @p_173) :named @p_328) (! (* 0 @p_114) :named @p_327) (! (* 0 @p_7) :named @p_326) (! (* 0 @p_132) :named @p_325)) :named @p_369))) :rule poly_simp)
(step t297.t33.t2 (cl (= @p_368 0)) :rule poly_simp)
(step t297.t33.t3 (cl (= @p_329 0)) :rule poly_simp)
(step t297.t33.t4 (cl (= @p_328 0)) :rule poly_simp)
(step t297.t33.t5 (cl (= @p_327 0)) :rule poly_simp)
(step t297.t33.t6 (cl (= @p_326 0)) :rule poly_simp)
(step t297.t33.t7 (cl (= @p_325 0)) :rule poly_simp)
(step t297.t33.t8 (cl (= @p_369 (! (+ 0 0 0 0 0 0) :named @p_367))) :rule cong :premises (t297.t33.t2 t297.t33.t3 t297.t33.t4 t297.t33.t5 t297.t33.t6 t297.t33.t7))
(step t297.t33.t9 (cl (= @p_367 0)) :rule evaluate)
(step t297.t33.t10 (cl (= @p_369 0)) :rule trans :premises (t297.t33.t8 t297.t33.t9))
(step t297.t33.t11 (cl (= @p_393 0)) :rule trans :premises (t297.t33.t1 t297.t33.t10))
(step t297.t33.t12 (cl (= @p_297 0)) :rule evaluate)
(step t297.t33.t13 (cl @p_56) :rule refl)
(step t297.t33.t14 (cl (= @p_392 (! (+ -1 0 0 0 0 0) :named @p_324))) :rule cong :premises (t297.t33.t12 t297.t33.t13 t297.t33.t12 t297.t33.t12 t297.t33.t13))
(step t297.t33.t15 (cl (= @p_324 -1)) :rule evaluate)
(step t297.t33.t16 (cl (= @p_392 -1)) :rule trans :premises (t297.t33.t14 t297.t33.t15))
(step t297.t33.t17 (cl (= @p_394 @p_323)) :rule cong :premises (t297.t33.t11 t297.t33.t16))
(step t297.t33.t18 (cl (= @p_323 false)) :rule evaluate)
(step t297.t33.t19 (cl @p_395) :rule trans :premises (t297.t33.t17 t297.t33.t18))
(step t297.t33.t20 (cl @p_389 (! (not (! (= @p_345 @p_297) :named @p_352)) :named @p_359) (! (not (! (= @p_303 0) :named @p_317)) :named @p_358) (! (not (! (= @p_344 @p_297) :named @p_350)) :named @p_360) (! (not (! (= @p_343 @p_297) :named @p_348)) :named @p_361) (! (not (! (= @p_214 0) :named @p_215)) :named @p_216) @p_394) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t297.t33.t21 (cl (=> (! (and @p_308 (! (= @p_302 0) :named @p_311)) :named @p_353) @p_352)) :rule la_mult_neg)
(step t297.t33.t22 (cl (! (not @p_353) :named @p_354) @p_352) :rule implies :premises (t297.t33.t21))
(step t297.t33.t23 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t297.t33.t24 (cl (not @p_310) @p_308) :rule equiv1 :premises (t297.t33.t23))
(step t297.t33.t25 (cl @p_310) :rule evaluate)
(step t297.t33.t26 (cl @p_308) :rule resolution :premises (t297.t33.t24 t297.t33.t25))
(step t297.t33.t27 (cl (! (not (! (= @p_115 @p_311) :named @p_314)) :named @p_315) @p_130 @p_311) :rule equiv_pos2)
(step t297.t33.t28 (cl (= (* 1 (- @p_302 0)) (* 1 (- @p_7 @p_114)))) :rule poly_simp)
(step t297.t33.t29 (cl (= @p_311 @p_115)) :rule poly_simp_rel :premises (t297.t33.t28))
(step t297.t33.t30 (cl @p_314) :rule symm :premises (t297.t33.t29))
(step t297.t33.t31 (cl @p_311) :rule resolution :premises (t297.t33.t27 t297.t33.t30 t297.a4))
(step t297.t33.t32 (cl @p_353) :rule and_intro :premises (t297.t33.t26 t297.t33.t31))
(step t297.t33.t33 (cl @p_352) :rule resolution :premises (t297.t33.t22 t297.t33.t32))
(step t297.t33.t34 (cl (not (! (= @p_133 @p_317) :named @p_319)) @p_283 @p_317) :rule equiv_pos2)
(step t297.t33.t35 (cl (= (* 1 (- @p_303 0)) (* 1 (- @p_132 @p_131)))) :rule poly_simp)
(step t297.t33.t36 (cl (= @p_317 @p_133)) :rule poly_simp_rel :premises (t297.t33.t35))
(step t297.t33.t37 (cl @p_319) :rule symm :premises (t297.t33.t36))
(step t297.t33.t38 (cl (not @p_163) (not @p_155) @p_155) :rule equiv_pos2)
(step t297.t33.t39 (cl (= @p_164 @p_162)) :rule equiv_simplify)
(step t297.t33.t40 (cl (not @p_164) @p_162) :rule equiv1 :premises (t297.t33.t39))
(step t297.t33.t41 (cl (= (* -1 @p_166) (* 1 @p_166))) :rule poly_simp)
(step t297.t33.t42 (cl @p_165) :rule poly_simp_rel :premises (t297.t33.t41))
(step t297.t33.t43 (cl @p_162) :rule refl)
(step t297.t33.t44 (cl @p_162) :rule refl)
(step t297.t33.t45 (cl @p_165) :rule cong :premises (t297.t33.t43 t297.t33.t44))
(step t297.t33.t46 (cl @p_164) :rule rare_rewrite :args ("eq-refl" @p_6))
(step t297.t33.t47 (cl @p_164) :rule trans :premises (t297.t33.t42 t297.t33.t45 t297.t33.t46))
(step t297.t33.t48 (cl @p_162) :rule resolution :premises (t297.t33.t40 t297.t33.t47))
(step t297.t33.t49 (cl (= 2 2)) :rule refl)
(step t297.t33.t50 (cl @p_167) :rule cong :premises (t297.t33.t48 t297.t33.t49))
(step t297.t33.t51 (cl @p_168) :rule cong :premises (t297.t33.t50))
(step t297.t33.t52 (cl (= @p_114 @p_114)) :rule cong :premises (t297.t33.t50 t297.t33.t48))
(step t297.t33.t53 (cl (= @p_131 @p_131)) :rule cong :premises (t297.t33.t51 t297.t33.t52))
(step t297.t33.t54 (cl (= @p_133 @p_133)) :rule cong :premises (t297.t33.t53))
(step t297.t33.t55 (cl @p_163) :rule cong :premises (t297.t33.t54))
(step t297.t33.t56 (cl (not @p_161) (not @p_160) @p_155) :rule equiv_pos2)
(step t297.t33.t57 (cl (= @p_156 @p_7)) :rule poly_simp)
(step t297.t33.t58 (cl (= @p_157 @p_114)) :rule cong :premises (t297.t33.t57 t297.t33.t44))
(step t297.t33.t59 (cl (= @p_158 @p_131)) :rule cong :premises (t297.t33.t58))
(step t297.t33.t60 (cl (= @p_159 @p_133)) :rule cong :premises (t297.t33.t59))
(step t297.t33.t61 (cl @p_161) :rule cong :premises (t297.t33.t60))
(step t297.t33.t62 (cl @p_160 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule implies_neg1)
(anchor :step t297.t33.t63)
(assume t297.t33.t63.a0 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1)))))))
(step t297.t33.t63.t0 (cl (or @p_154 @p_159)) :rule forall_inst :args (0 k$))
(step t297.t33.t63.t1 (cl @p_154 @p_159) :rule or :premises (t297.t33.t63.t0))
(step t297.t33.t63.t2 (cl (not @p_134) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t297.t33.t63.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t297.t33.t63.t3.t0 (cl (= @p_148 @p_150)) :rule poly_simp)
(step t297.t33.t63.t3.t1 (cl (= @p_143 @p_152)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t297.t33.t63.t3.t2 (cl (= @p_142 @p_23)) :rule poly_simp)
(step t297.t33.t63.t3.t3 (cl @p_20) :rule refl)
(step t297.t33.t63.t3.t4 (cl (= @p_144 @p_153)) :rule cong :premises (t297.t33.t63.t3.t1 t297.t33.t63.t3.t2 t297.t33.t63.t3.t3))
(step t297.t33.t63.t3.t5 (cl (= @p_153 @p_136)) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t297.t33.t63.t3.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t297.t33.t63.t3.t4 t297.t33.t63.t3.t5))
(step t297.t33.t63.t3.t7 (cl (= @p_145 @p_137)) :rule cong :premises (t297.t33.t63.t3.t6 t297.t33.t49))
(step t297.t33.t63.t3.t8 (cl (= @p_146 @p_138)) :rule cong :premises (t297.t33.t63.t3.t7))
(step t297.t33.t63.t3.t9 (cl (= @p_147 @p_139)) :rule cong :premises (t297.t33.t63.t3.t8 t297.t33.t63.t3.t6))
(step t297.t33.t63.t3.t10 (cl (= @p_149 @p_140)) :rule cong :premises (t297.t33.t63.t3.t7))
(step t297.t33.t63.t3.t11 (cl (= @p_150 @p_151)) :rule cong :premises (t297.t33.t63.t3.t9 t297.t33.t63.t3.t10))
(step t297.t33.t63.t3.t12 (cl (= @p_151 @p_141)) :rule poly_simp)
(step t297.t33.t63.t3.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t297.t33.t63.t3.t11 t297.t33.t63.t3.t12))
(step t297.t33.t63.t3.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t297.t33.t63.t3.t0 t297.t33.t63.t3.t13))
(step t297.t33.t63.t3.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t297.t33.t63.t3.t14))
(step t297.t33.t63.t3 (cl @p_134) :rule bind)
(step t297.t33.t63.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t297.t33.t63.t2 t297.t33.t63.t3 a3))
(step t297.t33.t63.t5 (cl @p_159) :rule resolution :premises (t297.t33.t63.t1 t297.t33.t63.t4))
(step t297.t33.t63 (cl @p_154 @p_159) :rule subproof :discharge (t297.t33.t63.a0))
(step t297.t33.t64 (cl @p_160 @p_159) :rule resolution :premises (t297.t33.t62 t297.t33.t63))
(step t297.t33.t65 (cl @p_160 (not @p_159)) :rule implies_neg2)
(step t297.t33.t66 (cl @p_160 @p_160) :rule resolution :premises (t297.t33.t64 t297.t33.t65))
(step t297.t33.t67 (cl @p_160) :rule contraction :premises (t297.t33.t66))
(step t297.t33.t68 (cl @p_155) :rule resolution :premises (t297.t33.t56 t297.t33.t61 t297.t33.t67))
(step t297.t33.t69 (cl @p_155) :rule resolution :premises (t297.t33.t38 t297.t33.t55 t297.t33.t68))
(step t297.t33.t70 (cl @p_154 @p_133) :rule implies :premises (t297.t33.t69))
(step t297.t33.t71 (cl (not @p_134) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t297.t33.t72 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t297.t33.t72.t0 (cl (= @p_148 @p_150)) :rule poly_simp)
(step t297.t33.t72.t1 (cl (= @p_143 @p_152)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t297.t33.t72.t2 (cl (= @p_142 @p_23)) :rule poly_simp)
(step t297.t33.t72.t3 (cl @p_20) :rule refl)
(step t297.t33.t72.t4 (cl (= @p_144 @p_153)) :rule cong :premises (t297.t33.t72.t1 t297.t33.t72.t2 t297.t33.t72.t3))
(step t297.t33.t72.t5 (cl (= @p_153 @p_136)) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t297.t33.t72.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t297.t33.t72.t4 t297.t33.t72.t5))
(step t297.t33.t72.t7 (cl (= @p_145 @p_137)) :rule cong :premises (t297.t33.t72.t6 t297.t33.t49))
(step t297.t33.t72.t8 (cl (= @p_146 @p_138)) :rule cong :premises (t297.t33.t72.t7))
(step t297.t33.t72.t9 (cl (= @p_147 @p_139)) :rule cong :premises (t297.t33.t72.t8 t297.t33.t72.t6))
(step t297.t33.t72.t10 (cl (= @p_149 @p_140)) :rule cong :premises (t297.t33.t72.t7))
(step t297.t33.t72.t11 (cl (= @p_150 @p_151)) :rule cong :premises (t297.t33.t72.t9 t297.t33.t72.t10))
(step t297.t33.t72.t12 (cl (= @p_151 @p_141)) :rule poly_simp)
(step t297.t33.t72.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t297.t33.t72.t11 t297.t33.t72.t12))
(step t297.t33.t72.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t297.t33.t72.t0 t297.t33.t72.t13))
(step t297.t33.t72.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t297.t33.t72.t14))
(step t297.t33.t72 (cl @p_134) :rule bind)
(step t297.t33.t73 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t297.t33.t71 t297.t33.t72 a3))
(step t297.t33.t74 (cl @p_133) :rule resolution :premises (t297.t33.t70 t297.t33.t73))
(step t297.t33.t75 (cl @p_317) :rule resolution :premises (t297.t33.t34 t297.t33.t37 t297.t33.t74))
(step t297.t33.t76 (cl (=> (! (and @p_308 (! (= @p_274 0) :named @p_275)) :named @p_351) @p_350)) :rule la_mult_neg)
(step t297.t33.t77 (cl (not @p_351) @p_350) :rule implies :premises (t297.t33.t76))
(step t297.t33.t78 (cl (! (not (! (= @p_269 @p_275) :named @p_279)) :named @p_280) (! (not @p_269) :named @p_273) @p_275) :rule equiv_pos2)
(step t297.t33.t79 (cl (= (* 1 (- @p_191 @p_253)) (* -1 (! (- @p_132 (! (+ (! (* -1 @p_170) :named @p_171) (! (* -1 @p_249) :named @p_250)) :named @p_251)) :named @p_278)))) :rule poly_simp)
(step t297.t33.t80 (cl (= @p_269 (! (= @p_132 @p_251) :named @p_252))) :rule poly_simp_rel :premises (t297.t33.t79))
(step t297.t33.t81 (cl (= (* 1 (- @p_274 0)) (* 1 @p_278))) :rule poly_simp)
(step t297.t33.t82 (cl (= @p_275 @p_252)) :rule poly_simp_rel :premises (t297.t33.t81))
(step t297.t33.t83 (cl (= @p_252 @p_275)) :rule symm :premises (t297.t33.t82))
(step t297.t33.t84 (cl @p_279) :rule trans :premises (t297.t33.t80 t297.t33.t83))
(step t297.t33.t85 (cl (not @p_197) (not @p_196) @p_193) :rule equiv_pos2)
(step t297.t33.t86 (cl (= (* 1 (- 0 @p_194)) (* -1 (- @p_169 @p_191)))) :rule poly_simp)
(step t297.t33.t87 (cl (= @p_195 @p_192)) :rule poly_simp_rel :premises (t297.t33.t86))
(step t297.t33.t88 (cl @p_197) :rule cong :premises (t297.t33.t87))
(step t297.t33.t89 (cl @p_196 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t297.t33.t90)
(assume t297.t33.t90.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))))
(step t297.t33.t90.t0 (cl (or @p_110 @p_195)) :rule forall_inst :args (0 k$))
(step t297.t33.t90.t1 (cl @p_110 @p_195) :rule or :premises (t297.t33.t90.t0))
(step t297.t33.t90.t2 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t297.t33.t90.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t297.t33.t90.t3.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t297.t33.t90.t3.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t297.t33.t90.t3.t0))
(step t297.t33.t90.t3 (cl @p_107) :rule bind)
(step t297.t33.t90.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t297.t33.t90.t2 t297.t33.t90.t3 a2))
(step t297.t33.t90.t5 (cl @p_195) :rule resolution :premises (t297.t33.t90.t1 t297.t33.t90.t4))
(step t297.t33.t90 (cl @p_110 @p_195) :rule subproof :discharge (t297.t33.t90.a0))
(step t297.t33.t91 (cl @p_196 @p_195) :rule resolution :premises (t297.t33.t89 t297.t33.t90))
(step t297.t33.t92 (cl @p_196 (not @p_195)) :rule implies_neg2)
(step t297.t33.t93 (cl @p_196 @p_196) :rule resolution :premises (t297.t33.t91 t297.t33.t92))
(step t297.t33.t94 (cl @p_196) :rule contraction :premises (t297.t33.t93))
(step t297.t33.t95 (cl @p_193) :rule resolution :premises (t297.t33.t85 t297.t33.t88 t297.t33.t94))
(step t297.t33.t96 (cl @p_110 @p_192) :rule implies :premises (t297.t33.t95))
(step t297.t33.t97 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t297.t33.t98 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t297.t33.t98.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t297.t33.t98.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t297.t33.t98.t0))
(step t297.t33.t98 (cl @p_107) :rule bind)
(step t297.t33.t99 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t297.t33.t97 t297.t33.t98 a2))
(step t297.t33.t100 (cl @p_192) :rule resolution :premises (t297.t33.t96 t297.t33.t99))
(step t297.t33.t101 (cl (= @p_191 @p_169)) :rule symm :premises (t297.t33.t100))
(step t297.t33.t102 (cl (not @p_260) (not @p_259) @p_256) :rule equiv_pos2)
(step t297.t33.t103 (cl (= @p_257 @p_253)) :rule poly_simp)
(step t297.t33.t104 (cl (= @p_258 @p_254)) :rule cong :premises (t297.t33.t103))
(step t297.t33.t105 (cl @p_260) :rule cong :premises (t297.t33.t104))
(step t297.t33.t106 (cl @p_259 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t297.t33.t107)
(assume t297.t33.t107.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t297.t33.t107.t0 (cl (or @p_255 @p_258)) :rule forall_inst :args (@p_169 @p_1))
(step t297.t33.t107.t1 (cl @p_255 @p_258) :rule or :premises (t297.t33.t107.t0))
(step t297.t33.t107.t2 (cl @p_258) :rule resolution :premises (t297.t33.t107.t1 t297.t33.t107.a0))
(step t297.t33.t107 (cl @p_255 @p_258) :rule subproof :discharge (t297.t33.t107.a0))
(step t297.t33.t108 (cl @p_259 @p_258) :rule resolution :premises (t297.t33.t106 t297.t33.t107))
(step t297.t33.t109 (cl @p_259 (not @p_258)) :rule implies_neg2)
(step t297.t33.t110 (cl @p_259 @p_259) :rule resolution :premises (t297.t33.t108 t297.t33.t109))
(step t297.t33.t111 (cl @p_259) :rule contraction :premises (t297.t33.t110))
(step t297.t33.t112 (cl @p_256) :rule resolution :premises (t297.t33.t102 t297.t33.t105 t297.t33.t111))
(step t297.t33.t113 (cl @p_255 @p_254) :rule implies :premises (t297.t33.t112))
(step t297.t33.t114 (cl @p_254) :rule resolution :premises (t297.t33.t113 a4))
(step t297.t33.t115 (cl @p_269) :rule trans :premises (t297.t33.t101 t297.t33.t114))
(step t297.t33.t116 (cl @p_275) :rule resolution :premises (t297.t33.t78 t297.t33.t84 t297.t33.t115))
(step t297.t33.t117 (cl @p_351) :rule and_intro :premises (t297.t33.t26 t297.t33.t116))
(step t297.t33.t118 (cl @p_350) :rule resolution :premises (t297.t33.t77 t297.t33.t117))
(step t297.t33.t119 (cl (=> (! (and @p_308 (! (= @p_240 0) :named @p_241)) :named @p_349) @p_348)) :rule la_mult_neg)
(step t297.t33.t120 (cl (not @p_349) @p_348) :rule implies :premises (t297.t33.t119))
(step t297.t33.t121 (cl (! (not (! (= @p_235 @p_241) :named @p_245)) :named @p_246) (! (not @p_235) :named @p_239) @p_241) :rule equiv_pos2)
(step t297.t33.t122 (cl (= (* 1 (- @p_191 @p_173)) (* -1 (! (- @p_132 (! (* -1 @p_173) :named @p_174)) :named @p_244)))) :rule poly_simp)
(step t297.t33.t123 (cl (= @p_235 (! (= @p_132 @p_174) :named @p_223))) :rule poly_simp_rel :premises (t297.t33.t122))
(step t297.t33.t124 (cl (= (* 1 (- @p_240 0)) (* 1 @p_244))) :rule poly_simp)
(step t297.t33.t125 (cl (= @p_241 @p_223)) :rule poly_simp_rel :premises (t297.t33.t124))
(step t297.t33.t126 (cl (= @p_223 @p_241)) :rule symm :premises (t297.t33.t125))
(step t297.t33.t127 (cl @p_245) :rule trans :premises (t297.t33.t123 t297.t33.t126))
(step t297.t33.t128 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t297.t33.t129 (cl @p_235) :rule trans :premises (t297.t33.t101 t297.t33.t128))
(step t297.t33.t130 (cl @p_241) :rule resolution :premises (t297.t33.t121 t297.t33.t127 t297.t33.t129))
(step t297.t33.t131 (cl @p_349) :rule and_intro :premises (t297.t33.t26 t297.t33.t130))
(step t297.t33.t132 (cl @p_348) :rule resolution :premises (t297.t33.t120 t297.t33.t131))
(step t297.t33.t133 (cl (! (not (! (= @p_208 @p_215) :named @p_219)) :named @p_220) (! (not @p_208) :named @p_213) @p_215) :rule equiv_pos2)
(step t297.t33.t134 (cl (= (* 1 (- @p_191 @p_177)) (* -1 (! (- @p_132 (! (+ @p_174 @p_171) :named @p_175)) :named @p_218)))) :rule poly_simp)
(step t297.t33.t135 (cl (= @p_208 (! (= @p_132 @p_175) :named @p_176))) :rule poly_simp_rel :premises (t297.t33.t134))
(step t297.t33.t136 (cl (= (* 1 (- @p_214 0)) (* 1 @p_218))) :rule poly_simp)
(step t297.t33.t137 (cl (= @p_215 @p_176)) :rule poly_simp_rel :premises (t297.t33.t136))
(step t297.t33.t138 (cl (= @p_176 @p_215)) :rule symm :premises (t297.t33.t137))
(step t297.t33.t139 (cl @p_219) :rule trans :premises (t297.t33.t135 t297.t33.t138))
(step t297.t33.t140 (cl (or @p_190 @p_178)) :rule forall_inst :args (@p_1 @p_169))
(step t297.t33.t141 (cl @p_190 @p_178) :rule or :premises (t297.t33.t140))
(step t297.t33.t142 (cl @p_178) :rule resolution :premises (t297.t33.t141 t226))
(step t297.t33.t143 (cl @p_208) :rule trans :premises (t297.t33.t101 t297.t33.t142))
(step t297.t33.t144 (cl @p_215) :rule resolution :premises (t297.t33.t133 t297.t33.t139 t297.t33.t143))
(step t297.t33.t145 (cl @p_394) :rule resolution :premises (t297.t33.t20 t297.t33.a0 t297.t33.t33 t297.t33.t75 t297.t33.t118 t297.t33.t132 t297.t33.t144))
(step t297.t33.t146 (cl false) :rule resolution :premises (t297.t33.t0 t297.t33.t19 t297.t33.t145))
(step t297.t33 (cl @p_389 false) :rule subproof :discharge (t297.t33.a0))
(step t297.t34 (cl @p_391 false) :rule resolution :premises (t297.t32 t297.t33))
(step t297.t35 (cl @p_391 @p_212) :rule implies_neg2)
(step t297.t36 (cl @p_391 @p_391) :rule resolution :premises (t297.t34 t297.t35))
(step t297.t37 (cl @p_391) :rule contraction :premises (t297.t36))
(step t297.t38 (cl (= @p_391 @p_389)) :rule implies_simplify)
(step t297.t39 (cl (not @p_391) @p_389) :rule equiv1 :premises (t297.t38))
(step t297.t40 (cl @p_389) :rule resolution :premises (t297.t37 t297.t39))
(step t297.t41 (cl @p_390) :rule resolution :premises (t297.t20 t297.t31 t297.t40))
(step t297.t42 (cl @p_389) :rule resolution :premises (t297.t14 t297.t19 t297.t41))
(step t297.t43 (cl) :rule resolution :premises (t297.t13 t297.t42))
(step t297 (cl @p_213 @p_239 @p_273 @p_283 @p_130 @p_288 @p_387 false) :rule subproof :discharge (t297.a0 t297.a1 t297.a2 t297.a3 t297.a4 t297.a5 t297.a6))
(step t298 (cl @p_385 @p_208) :rule and_pos :args (0))
(step t299 (cl @p_385 @p_235) :rule and_pos :args (1))
(step t300 (cl @p_385 @p_269) :rule and_pos :args (2))
(step t301 (cl @p_385 @p_133) :rule and_pos :args (3))
(step t302 (cl @p_385 @p_115) :rule and_pos :args (4))
(step t303 (cl @p_385 @p_285) :rule and_pos :args (5))
(step t304 (cl @p_385 @p_383) :rule and_pos :args (6))
(step t305 (cl false @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385) :rule resolution :premises (t297 t298 t299 t300 t301 t302 t303 t304))
(step t306 (cl @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 @p_385 false) :rule reordering :premises (t305))
(step t307 (cl @p_385 false) :rule contraction :premises (t306))
(step t308 (cl @p_386 false) :rule resolution :premises (t296 t307))
(step t309 (cl @p_386 @p_212) :rule implies_neg2)
(step t310 (cl @p_386 @p_386) :rule resolution :premises (t308 t309))
(step t311 (cl @p_386) :rule contraction :premises (t310))
(step t312 (cl (= @p_386 @p_385)) :rule implies_simplify)
(step t313 (cl (not @p_386) @p_385) :rule equiv1 :premises (t312))
(step t314 (cl @p_385) :rule resolution :premises (t311 t313))
(step t315 (cl @p_381) :rule resolution :premises (t295 t314))
(step t316 (cl @p_375 @p_198 @p_227 @p_283 @p_199 @p_261 @p_130 @p_373 @p_288) :rule not_and :premises (t315))
(step t317 (cl @p_376 @p_379) :rule or_neg :args (0))
(step t318 (cl @p_376 (! (not @p_198) :named @p_205)) :rule or_neg :args (1))
(step t319 (cl @p_376 @p_232) :rule or_neg :args (2))
(step t320 (cl @p_376 (! (not @p_283) :named @p_293)) :rule or_neg :args (3))
(step t321 (cl @p_376 (! (not @p_199) :named @p_204)) :rule or_neg :args (4))
(step t322 (cl @p_376 (! (not @p_261) :named @p_266)) :rule or_neg :args (5))
(step t323 (cl @p_376 (! (not @p_130) :named @p_292)) :rule or_neg :args (6))
(step t324 (cl @p_376 @p_378) :rule or_neg :args (7))
(step t325 (cl @p_376 @p_377) :rule or_neg :args (8))
(step t326 (cl @p_376 @p_376 @p_376 @p_376 @p_376 @p_376 @p_376 @p_376 @p_376) :rule resolution :premises (t316 t317 t318 t319 t320 t321 t322 t323 t324 t325))
(step t327 (cl @p_376) :rule contraction :premises (t326))
(step t328 (cl @p_374) :rule resolution :premises (t267 t276 t327))
(step t329 (cl @p_2 @p_198 @p_227 @p_283 @p_199 @p_261 @p_130 @p_373 @p_284) :rule or :premises (t328))
(step t330 (cl @p_2 @p_198 @p_283 @p_227 @p_199 @p_261 @p_130 @p_373 @p_284) :rule reordering :premises (t329))
(step t331 (cl (not @p_260) (not @p_259) @p_256) :rule equiv_pos2)
(step t332 (cl (= @p_257 @p_253)) :rule poly_simp)
(step t333 (cl (= @p_258 @p_254)) :rule cong :premises (t332))
(step t334 (cl @p_260) :rule cong :premises (t333))
(step t335 (cl @p_259 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t336)
(assume t336.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t336.t0 (cl (or @p_255 @p_258)) :rule forall_inst :args (@p_169 @p_1))
(step t336.t1 (cl @p_255 @p_258) :rule or :premises (t336.t0))
(step t336.t2 (cl @p_258) :rule resolution :premises (t336.t1 t336.a0))
(step t336 (cl @p_255 @p_258) :rule subproof :discharge (t336.a0))
(step t337 (cl @p_259 @p_258) :rule resolution :premises (t335 t336))
(step t338 (cl @p_259 (not @p_258)) :rule implies_neg2)
(step t339 (cl @p_259 @p_259) :rule resolution :premises (t337 t338))
(step t340 (cl @p_259) :rule contraction :premises (t339))
(step t341 (cl @p_256) :rule resolution :premises (t331 t334 t340))
(step t342 (cl @p_255 @p_254) :rule implies :premises (t341))
(step t343 (cl @p_254) :rule resolution :premises (t342 a4))
(step t344 (cl (or @p_190 @p_178)) :rule forall_inst :args (@p_1 @p_169))
(step t345 (cl @p_190 @p_178) :rule or :premises (t344))
(step t346 (cl @p_178) :rule resolution :premises (t345 t226))
(step t347 (cl (not @p_163) (not @p_155) @p_155) :rule equiv_pos2)
(step t348 (cl (= @p_164 @p_162)) :rule equiv_simplify)
(step t349 (cl (not @p_164) @p_162) :rule equiv1 :premises (t348))
(step t350 (cl (= (* -1 @p_166) (* 1 @p_166))) :rule poly_simp)
(step t351 (cl @p_165) :rule poly_simp_rel :premises (t350))
(step t352 (cl @p_162) :rule refl)
(step t353 (cl @p_162) :rule refl)
(step t354 (cl @p_165) :rule cong :premises (t352 t353))
(step t355 (cl @p_164) :rule rare_rewrite :args ("eq-refl" @p_6))
(step t356 (cl @p_164) :rule trans :premises (t351 t354 t355))
(step t357 (cl @p_162) :rule resolution :premises (t349 t356))
(step t358 (cl (= 2 2)) :rule refl)
(step t359 (cl @p_167) :rule cong :premises (t357 t358))
(step t360 (cl @p_168) :rule cong :premises (t359))
(step t361 (cl (= @p_114 @p_114)) :rule cong :premises (t359 t357))
(step t362 (cl (= @p_131 @p_131)) :rule cong :premises (t360 t361))
(step t363 (cl (= @p_133 @p_133)) :rule cong :premises (t362))
(step t364 (cl @p_163) :rule cong :premises (t363))
(step t365 (cl (not @p_161) (not @p_160) @p_155) :rule equiv_pos2)
(step t366 (cl (= @p_156 @p_7)) :rule poly_simp)
(step t367 (cl (= @p_157 @p_114)) :rule cong :premises (t366 t353))
(step t368 (cl (= @p_158 @p_131)) :rule cong :premises (t367))
(step t369 (cl (= @p_159 @p_133)) :rule cong :premises (t368))
(step t370 (cl @p_161) :rule cong :premises (t369))
(step t371 (cl @p_160 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule implies_neg1)
(anchor :step t372)
(assume t372.a0 (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1)))))))
(step t372.t0 (cl (or @p_154 @p_159)) :rule forall_inst :args (0 k$))
(step t372.t1 (cl @p_154 @p_159) :rule or :premises (t372.t0))
(step t372.t2 (cl (not @p_134) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t372.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t372.t3.t0 (cl (= @p_148 @p_150)) :rule poly_simp)
(step t372.t3.t1 (cl (= @p_143 @p_152)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t372.t3.t2 (cl (= @p_142 @p_23)) :rule poly_simp)
(step t372.t3.t3 (cl @p_20) :rule refl)
(step t372.t3.t4 (cl (= @p_144 @p_153)) :rule cong :premises (t372.t3.t1 t372.t3.t2 t372.t3.t3))
(step t372.t3.t5 (cl (= @p_153 @p_136)) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t372.t3.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t372.t3.t4 t372.t3.t5))
(step t372.t3.t7 (cl (= @p_145 @p_137)) :rule cong :premises (t372.t3.t6 t358))
(step t372.t3.t8 (cl (= @p_146 @p_138)) :rule cong :premises (t372.t3.t7))
(step t372.t3.t9 (cl (= @p_147 @p_139)) :rule cong :premises (t372.t3.t8 t372.t3.t6))
(step t372.t3.t10 (cl (= @p_149 @p_140)) :rule cong :premises (t372.t3.t7))
(step t372.t3.t11 (cl (= @p_150 @p_151)) :rule cong :premises (t372.t3.t9 t372.t3.t10))
(step t372.t3.t12 (cl (= @p_151 @p_141)) :rule poly_simp)
(step t372.t3.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t372.t3.t11 t372.t3.t12))
(step t372.t3.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t372.t3.t0 t372.t3.t13))
(step t372.t3.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t372.t3.t14))
(step t372.t3 (cl @p_134) :rule bind)
(step t372.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t372.t2 t372.t3 a3))
(step t372.t5 (cl @p_159) :rule resolution :premises (t372.t1 t372.t4))
(step t372 (cl @p_154 @p_159) :rule subproof :discharge (t372.a0))
(step t373 (cl @p_160 @p_159) :rule resolution :premises (t371 t372))
(step t374 (cl @p_160 (not @p_159)) :rule implies_neg2)
(step t375 (cl @p_160 @p_160) :rule resolution :premises (t373 t374))
(step t376 (cl @p_160) :rule contraction :premises (t375))
(step t377 (cl @p_155) :rule resolution :premises (t365 t370 t376))
(step t378 (cl @p_155) :rule resolution :premises (t347 t364 t377))
(step t379 (cl @p_154 @p_133) :rule implies :premises (t378))
(step t380 (cl (not @p_134) (not (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (- (modulo$ (+ ?v0 (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2)) (ite (< ?v1 0) (- ?v1) ?v1)) (divide$ (ite (< ?v1 0) (- ?v1) ?v1) 2))))) (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule equiv_pos2)
(anchor :step t381 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t381.t0 (cl (= @p_148 @p_150)) :rule poly_simp)
(step t381.t1 (cl (= @p_143 @p_152)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 0))
(step t381.t2 (cl (= @p_142 @p_23)) :rule poly_simp)
(step t381.t3 (cl @p_20) :rule refl)
(step t381.t4 (cl (= @p_144 @p_153)) :rule cong :premises (t381.t1 t381.t2 t381.t3))
(step t381.t5 (cl (= @p_153 @p_136)) :rule rare_rewrite :args ("ite-not-cond" @p_135 @p_23 ?v1))
(step t381.t6 (cl (= @p_144 @p_136)) :rule trans :premises (t381.t4 t381.t5))
(step t381.t7 (cl (= @p_145 @p_137)) :rule cong :premises (t381.t6 t358))
(step t381.t8 (cl (= @p_146 @p_138)) :rule cong :premises (t381.t7))
(step t381.t9 (cl (= @p_147 @p_139)) :rule cong :premises (t381.t8 t381.t6))
(step t381.t10 (cl (= @p_149 @p_140)) :rule cong :premises (t381.t7))
(step t381.t11 (cl (= @p_150 @p_151)) :rule cong :premises (t381.t9 t381.t10))
(step t381.t12 (cl (= @p_151 @p_141)) :rule poly_simp)
(step t381.t13 (cl (= @p_150 @p_141)) :rule trans :premises (t381.t11 t381.t12))
(step t381.t14 (cl (= @p_148 @p_141)) :rule trans :premises (t381.t0 t381.t13))
(step t381.t15 (cl (= (= @p_108 @p_148) (= @p_108 @p_141))) :rule cong :premises (t381.t14))
(step t381 (cl @p_134) :rule bind)
(step t382 (cl (forall ((?v0 Int) (?v1 Int)) (= (centered_modulo$ ?v0 ?v1) (+ (* -1 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (modulo$ (+ ?v0 (divide$ (ite (>= ?v1 0) ?v1 (* -1 ?v1)) 2)) (ite (>= ?v1 0) ?v1 (* -1 ?v1))))))) :rule resolution :premises (t380 t381 a3))
(step t383 (cl @p_133) :rule resolution :premises (t379 t382))
(step t384 (cl (not @p_197) (not @p_196) @p_193) :rule equiv_pos2)
(step t385 (cl (= (* 1 (- 0 @p_194)) (* -1 (- @p_169 @p_191)))) :rule poly_simp)
(step t386 (cl (= @p_195 @p_192)) :rule poly_simp_rel :premises (t385))
(step t387 (cl @p_197) :rule cong :premises (t386))
(step t388 (cl @p_196 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t389)
(assume t389.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))))
(step t389.t0 (cl (or @p_110 @p_195)) :rule forall_inst :args (0 k$))
(step t389.t1 (cl @p_110 @p_195) :rule or :premises (t389.t0))
(step t389.t2 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t389.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t389.t3.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t389.t3.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t389.t3.t0))
(step t389.t3 (cl @p_107) :rule bind)
(step t389.t4 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t389.t2 t389.t3 a2))
(step t389.t5 (cl @p_195) :rule resolution :premises (t389.t1 t389.t4))
(step t389 (cl @p_110 @p_195) :rule subproof :discharge (t389.a0))
(step t390 (cl @p_196 @p_195) :rule resolution :premises (t388 t389))
(step t391 (cl @p_196 (not @p_195)) :rule implies_neg2)
(step t392 (cl @p_196 @p_196) :rule resolution :premises (t390 t391))
(step t393 (cl @p_196) :rule contraction :premises (t392))
(step t394 (cl @p_193) :rule resolution :premises (t384 t387 t393))
(step t395 (cl @p_110 @p_192) :rule implies :premises (t394))
(step t396 (cl (not @p_107) (not (forall ((?v0 Int) (?v1 Int)) (= (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)) ?v0))) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t397 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t397.t0 (cl (= (* 1 (- @p_109 ?v0)) (* -1 (- ?v0 @p_109)))) :rule poly_simp)
(step t397.t1 (cl (= (= @p_109 ?v0) (= ?v0 @p_109))) :rule poly_simp_rel :premises (t397.t0))
(step t397 (cl @p_107) :rule bind)
(step t398 (cl (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule resolution :premises (t396 t397 a2))
(step t399 (cl @p_192) :rule resolution :premises (t395 t398))
(step t400 (cl (not (! (= (! (or @p_283 @p_130 @p_273 @p_239 @p_213 @p_333) :named @p_335) (! (or @p_283 @p_130 (! (not @p_252) :named @p_263) (! (not @p_223) :named @p_229) (! (not @p_176) :named @p_201) @p_333) :named @p_334)) :named @p_371)) (not @p_335) @p_334) :rule equiv_pos2)
(step t401 (cl (= (* 1 (- @p_191 @p_253)) (* -1 @p_278))) :rule poly_simp)
(step t402 (cl (= @p_269 @p_252)) :rule poly_simp_rel :premises (t401))
(step t403 (cl (= @p_273 @p_263)) :rule cong :premises (t402))
(step t404 (cl (= (* 1 (- @p_191 @p_173)) (* -1 @p_244))) :rule poly_simp)
(step t405 (cl (= @p_235 @p_223)) :rule poly_simp_rel :premises (t404))
(step t406 (cl (= @p_239 @p_229)) :rule cong :premises (t405))
(step t407 (cl (= (* 1 (- @p_191 @p_177)) (* -1 @p_218))) :rule poly_simp)
(step t408 (cl (= @p_208 @p_176)) :rule poly_simp_rel :premises (t407))
(step t409 (cl (= @p_213 @p_201)) :rule cong :premises (t408))
(step t410 (cl (= @p_333 @p_333)) :rule refl)
(step t411 (cl @p_371) :rule cong :premises (t403 t406 t409 t410))
(step t412 (cl (not (! (= (! (or @p_283 @p_130 @p_273 @p_239 @p_213 @p_337) :named @p_338) @p_335) :named @p_370)) (not @p_338) @p_335) :rule equiv_pos2)
(step t413 (cl (= @p_337 @p_333)) :rule rare_rewrite :args ("bool-double-not-elim" @p_333))
(step t414 (cl (= @p_338 @p_334)) :rule cong :premises (t403 t406 t409 t413))
(step t415 (cl (= @p_334 @p_335)) :rule symm :premises (t411))
(step t416 (cl @p_370) :rule trans :premises (t414 t415))
(step t417 (cl (! (=> (! (and @p_133 @p_115 @p_269 @p_235 @p_208 @p_336) :named @p_339) false) :named @p_341) @p_339) :rule implies_neg1)
(anchor :step t418)
(assume t418.a0 @p_133)
(assume t418.a1 @p_115)
(assume t418.a2 @p_269)
(assume t418.a3 @p_235)
(assume t418.a4 @p_208)
(assume t418.a5 @p_336)
(step t418.t0 (cl (not (! (= (! (< (! (+ @p_249 @p_303 @p_345 @p_344 @p_343 @p_214) :named @p_346) (! (+ 0 0 @p_297 @p_297 @p_297 0) :named @p_342)) :named @p_347) false) :named @p_362)) (not @p_347) false) :rule equiv_pos2)
(step t418.t1 (cl (= @p_347 (! (not (! (>= @p_346 @p_342) :named @p_363)) :named @p_364))) :rule rare_rewrite :args ("arith-elim-lt" @p_346 @p_342))
(step t418.t2 (cl (= @p_346 @p_369)) :rule poly_simp)
(step t418.t3 (cl (= @p_368 0)) :rule poly_simp)
(step t418.t4 (cl (= @p_329 0)) :rule poly_simp)
(step t418.t5 (cl (= @p_328 0)) :rule poly_simp)
(step t418.t6 (cl (= @p_327 0)) :rule poly_simp)
(step t418.t7 (cl (= @p_326 0)) :rule poly_simp)
(step t418.t8 (cl (= @p_325 0)) :rule poly_simp)
(step t418.t9 (cl (= @p_369 @p_367)) :rule cong :premises (t418.t3 t418.t4 t418.t5 t418.t6 t418.t7 t418.t8))
(step t418.t10 (cl (= @p_367 0)) :rule evaluate)
(step t418.t11 (cl (= @p_369 0)) :rule trans :premises (t418.t9 t418.t10))
(step t418.t12 (cl (= @p_346 0)) :rule trans :premises (t418.t2 t418.t11))
(step t418.t13 (cl (= @p_297 0)) :rule evaluate)
(step t418.t14 (cl @p_56) :rule refl)
(step t418.t15 (cl (= @p_342 @p_367)) :rule cong :premises (t418.t13 t418.t13 t418.t13 t418.t14))
(step t418.t16 (cl (= @p_342 0)) :rule trans :premises (t418.t15 t418.t10))
(step t418.t17 (cl (= @p_363 @p_366)) :rule cong :premises (t418.t12 t418.t16))
(step t418.t18 (cl (= @p_366 true)) :rule evaluate)
(step t418.t19 (cl (= @p_363 true)) :rule trans :premises (t418.t17 t418.t18))
(step t418.t20 (cl (= @p_364 @p_365)) :rule cong :premises (t418.t19))
(step t418.t21 (cl (= @p_365 false)) :rule evaluate)
(step t418.t22 (cl (= @p_364 false)) :rule trans :premises (t418.t20 t418.t21))
(step t418.t23 (cl @p_362) :rule trans :premises (t418.t1 t418.t22))
(step t418.t24 (cl @p_357 @p_358 @p_359 @p_360 @p_361 @p_216 @p_347) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t418.t25 (cl (not (! (= @p_336 @p_355) :named @p_356)) @p_337 @p_355) :rule equiv_pos2)
(step t418.t26 (cl (= @p_355 @p_336)) :rule rare_rewrite :args ("arith-elim-lt" @p_249 0))
(step t418.t27 (cl @p_356) :rule symm :premises (t418.t26))
(step t418.t28 (cl @p_355) :rule resolution :premises (t418.t25 t418.t27 t418.a5))
(step t418.t29 (cl (not @p_319) @p_283 @p_317) :rule equiv_pos2)
(step t418.t30 (cl (= (* 1 (- @p_303 0)) (* 1 (- @p_132 @p_131)))) :rule poly_simp)
(step t418.t31 (cl (= @p_317 @p_133)) :rule poly_simp_rel :premises (t418.t30))
(step t418.t32 (cl @p_319) :rule symm :premises (t418.t31))
(step t418.t33 (cl @p_317) :rule resolution :premises (t418.t29 t418.t32 t383))
(step t418.t34 (cl (=> @p_353 @p_352)) :rule la_mult_neg)
(step t418.t35 (cl @p_354 @p_352) :rule implies :premises (t418.t34))
(step t418.t36 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t418.t37 (cl (not @p_310) @p_308) :rule equiv1 :premises (t418.t36))
(step t418.t38 (cl @p_310) :rule evaluate)
(step t418.t39 (cl @p_308) :rule resolution :premises (t418.t37 t418.t38))
(step t418.t40 (cl @p_315 @p_130 @p_311) :rule equiv_pos2)
(step t418.t41 (cl (= (* 1 (- @p_302 0)) (* 1 (- @p_7 @p_114)))) :rule poly_simp)
(step t418.t42 (cl (= @p_311 @p_115)) :rule poly_simp_rel :premises (t418.t41))
(step t418.t43 (cl @p_314) :rule symm :premises (t418.t42))
(step t418.t44 (cl @p_311) :rule resolution :premises (t418.t40 t418.t43 t418.a1))
(step t418.t45 (cl @p_353) :rule and_intro :premises (t418.t39 t418.t44))
(step t418.t46 (cl @p_352) :rule resolution :premises (t418.t35 t418.t45))
(step t418.t47 (cl (=> @p_351 @p_350)) :rule la_mult_neg)
(step t418.t48 (cl (not @p_351) @p_350) :rule implies :premises (t418.t47))
(step t418.t49 (cl @p_280 @p_273 @p_275) :rule equiv_pos2)
(step t418.t50 (cl (= (* 1 (- @p_274 0)) (* 1 @p_278))) :rule poly_simp)
(step t418.t51 (cl (= @p_275 @p_252)) :rule poly_simp_rel :premises (t418.t50))
(step t418.t52 (cl (= @p_252 @p_275)) :rule symm :premises (t418.t51))
(step t418.t53 (cl @p_279) :rule trans :premises (t402 t418.t52))
(step t418.t54 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t418.t55 (cl @p_269) :rule trans :premises (t418.t54 t343))
(step t418.t56 (cl @p_275) :rule resolution :premises (t418.t49 t418.t53 t418.t55))
(step t418.t57 (cl @p_351) :rule and_intro :premises (t418.t39 t418.t56))
(step t418.t58 (cl @p_350) :rule resolution :premises (t418.t48 t418.t57))
(step t418.t59 (cl (=> @p_349 @p_348)) :rule la_mult_neg)
(step t418.t60 (cl (not @p_349) @p_348) :rule implies :premises (t418.t59))
(step t418.t61 (cl @p_246 @p_239 @p_241) :rule equiv_pos2)
(step t418.t62 (cl (= (* 1 (- @p_240 0)) (* 1 @p_244))) :rule poly_simp)
(step t418.t63 (cl (= @p_241 @p_223)) :rule poly_simp_rel :premises (t418.t62))
(step t418.t64 (cl (= @p_223 @p_241)) :rule symm :premises (t418.t63))
(step t418.t65 (cl @p_245) :rule trans :premises (t405 t418.t64))
(step t418.t66 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t418.t67 (cl @p_235) :rule trans :premises (t418.t54 t418.t66))
(step t418.t68 (cl @p_241) :rule resolution :premises (t418.t61 t418.t65 t418.t67))
(step t418.t69 (cl @p_349) :rule and_intro :premises (t418.t39 t418.t68))
(step t418.t70 (cl @p_348) :rule resolution :premises (t418.t60 t418.t69))
(step t418.t71 (cl @p_220 @p_213 @p_215) :rule equiv_pos2)
(step t418.t72 (cl (= (* 1 (- @p_214 0)) (* 1 @p_218))) :rule poly_simp)
(step t418.t73 (cl (= @p_215 @p_176)) :rule poly_simp_rel :premises (t418.t72))
(step t418.t74 (cl (= @p_176 @p_215)) :rule symm :premises (t418.t73))
(step t418.t75 (cl @p_219) :rule trans :premises (t408 t418.t74))
(step t418.t76 (cl @p_208) :rule trans :premises (t418.t54 t346))
(step t418.t77 (cl @p_215) :rule resolution :premises (t418.t71 t418.t75 t418.t76))
(step t418.t78 (cl @p_347) :rule resolution :premises (t418.t24 t418.t28 t418.t33 t418.t46 t418.t58 t418.t70 t418.t77))
(step t418.t79 (cl false) :rule resolution :premises (t418.t0 t418.t23 t418.t78))
(step t418 (cl @p_283 @p_130 @p_273 @p_239 @p_213 @p_337 false) :rule subproof :discharge (t418.a0 t418.a1 t418.a2 t418.a3 t418.a4 t418.a5))
(step t419 (cl (! (not @p_339) :named @p_340) @p_133) :rule and_pos :args (0))
(step t420 (cl @p_340 @p_115) :rule and_pos :args (1))
(step t421 (cl @p_340 @p_269) :rule and_pos :args (2))
(step t422 (cl @p_340 @p_235) :rule and_pos :args (3))
(step t423 (cl @p_340 @p_208) :rule and_pos :args (4))
(step t424 (cl @p_340 @p_336) :rule and_pos :args (5))
(step t425 (cl false @p_340 @p_340 @p_340 @p_340 @p_340 @p_340) :rule resolution :premises (t418 t419 t420 t421 t422 t423 t424))
(step t426 (cl @p_340 @p_340 @p_340 @p_340 @p_340 @p_340 false) :rule reordering :premises (t425))
(step t427 (cl @p_340 false) :rule contraction :premises (t426))
(step t428 (cl @p_341 false) :rule resolution :premises (t417 t427))
(step t429 (cl @p_341 @p_212) :rule implies_neg2)
(step t430 (cl @p_341 @p_341) :rule resolution :premises (t428 t429))
(step t431 (cl @p_341) :rule contraction :premises (t430))
(step t432 (cl (= @p_341 @p_340)) :rule implies_simplify)
(step t433 (cl (not @p_341) @p_340) :rule equiv1 :premises (t432))
(step t434 (cl @p_340) :rule resolution :premises (t431 t433))
(step t435 (cl @p_283 @p_130 @p_273 @p_239 @p_213 @p_337) :rule not_and :premises (t434))
(step t436 (cl @p_338 @p_293) :rule or_neg :args (0))
(step t437 (cl @p_338 @p_292) :rule or_neg :args (1))
(step t438 (cl @p_338 (! (not @p_273) :named @p_291)) :rule or_neg :args (2))
(step t439 (cl @p_338 (! (not @p_239) :named @p_290)) :rule or_neg :args (3))
(step t440 (cl @p_338 (! (not @p_213) :named @p_289)) :rule or_neg :args (4))
(step t441 (cl @p_338 (not @p_337)) :rule or_neg :args (5))
(step t442 (cl @p_338 @p_338 @p_338 @p_338 @p_338 @p_338) :rule resolution :premises (t435 t436 t437 t438 t439 t440 t441))
(step t443 (cl @p_338) :rule contraction :premises (t442))
(step t444 (cl @p_335) :rule resolution :premises (t412 t416 t443))
(step t445 (cl @p_334) :rule resolution :premises (t400 t411 t444))
(step t446 (cl @p_283 @p_130 @p_263 @p_229 @p_201 @p_333) :rule or :premises (t445))
(step t447 (cl @p_283 @p_130 @p_229 @p_201 @p_263 @p_333) :rule reordering :premises (t446))
(step t448 (cl (not (! (= (! (or @p_198 @p_261 (! (not @p_263) :named @p_264)) :named @p_265) (! (or @p_198 @p_261 @p_252) :named @p_262)) :named @p_282)) (not @p_265) @p_262) :rule equiv_pos2)
(step t449 (cl (= @p_264 @p_252)) :rule rare_rewrite :args ("bool-double-not-elim" @p_252))
(step t450 (cl @p_282) :rule cong :premises (t449))
(step t451 (cl (! (=> (! (and @p_192 @p_254 @p_263) :named @p_267) (! (and @p_269 @p_263) :named @p_270)) :named @p_281) @p_267) :rule implies_neg1)
(anchor :step t452)
(assume t452.a0 @p_192)
(assume t452.a1 @p_254)
(assume t452.a2 @p_263)
(step t452.t0 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t452.t1 (cl @p_269) :rule trans :premises (t452.t0 t343))
(step t452.t2 (cl @p_270) :rule and_intro :premises (t452.t1 t452.a2))
(step t452 (cl @p_198 @p_261 @p_264 @p_270) :rule subproof :discharge (t452.a0 t452.a1 t452.a2))
(step t453 (cl (! (not @p_267) :named @p_268) @p_192) :rule and_pos :args (0))
(step t454 (cl @p_268 @p_254) :rule and_pos :args (1))
(step t455 (cl @p_268 @p_263) :rule and_pos :args (2))
(step t456 (cl @p_270 @p_268 @p_268 @p_268) :rule resolution :premises (t452 t453 t454 t455))
(step t457 (cl @p_268 @p_268 @p_268 @p_270) :rule reordering :premises (t456))
(step t458 (cl @p_268 @p_270) :rule contraction :premises (t457))
(step t459 (cl @p_281 @p_270) :rule resolution :premises (t451 t458))
(step t460 (cl @p_281 (! (not @p_270) :named @p_271)) :rule implies_neg2)
(step t461 (cl @p_281 @p_281) :rule resolution :premises (t459 t460))
(step t462 (cl @p_281) :rule contraction :premises (t461))
(step t463 (cl @p_268 @p_270) :rule implies :premises (t462))
(step t464 (cl (! (=> @p_270 false) :named @p_272) @p_270) :rule implies_neg1)
(anchor :step t465)
(assume t465.a0 @p_269)
(assume t465.a1 @p_263)
(step t465.t0 (cl @p_280 @p_273 @p_275) :rule equiv_pos2)
(step t465.t1 (cl (= (* 1 (- @p_274 0)) (* 1 @p_278))) :rule poly_simp)
(step t465.t2 (cl (= @p_275 @p_252)) :rule poly_simp_rel :premises (t465.t1))
(step t465.t3 (cl (= @p_252 @p_275)) :rule symm :premises (t465.t2))
(step t465.t4 (cl @p_279) :rule trans :premises (t402 t465.t3))
(step t465.t5 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t465.t6 (cl @p_269) :rule trans :premises (t465.t5 t343))
(step t465.t7 (cl @p_275) :rule resolution :premises (t465.t0 t465.t4 t465.t6))
(step t465.t8 (cl (not (! (= @p_263 (! (not @p_275) :named @p_276)) :named @p_277)) @p_264 @p_276) :rule equiv_pos2)
(step t465.t9 (cl (= @p_276 @p_263)) :rule cong :premises (t465.t2))
(step t465.t10 (cl @p_277) :rule symm :premises (t465.t9))
(step t465.t11 (cl @p_276) :rule resolution :premises (t465.t8 t465.t10 t465.a1))
(step t465.t12 (cl) :rule resolution :premises (t465.t7 t465.t11))
(step t465 (cl @p_273 @p_264 false) :rule subproof :discharge (t465.a0 t465.a1))
(step t466 (cl @p_271 @p_269) :rule and_pos :args (0))
(step t467 (cl @p_271 @p_263) :rule and_pos :args (1))
(step t468 (cl false @p_271 @p_271) :rule resolution :premises (t465 t466 t467))
(step t469 (cl @p_271 @p_271 false) :rule reordering :premises (t468))
(step t470 (cl @p_271 false) :rule contraction :premises (t469))
(step t471 (cl @p_272 false) :rule resolution :premises (t464 t470))
(step t472 (cl @p_272 @p_212) :rule implies_neg2)
(step t473 (cl @p_272 @p_272) :rule resolution :premises (t471 t472))
(step t474 (cl @p_272) :rule contraction :premises (t473))
(step t475 (cl (= @p_272 @p_271)) :rule implies_simplify)
(step t476 (cl (not @p_272) @p_271) :rule equiv1 :premises (t475))
(step t477 (cl @p_271) :rule resolution :premises (t474 t476))
(step t478 (cl @p_268) :rule resolution :premises (t463 t477))
(step t479 (cl @p_198 @p_261 @p_264) :rule not_and :premises (t478))
(step t480 (cl @p_265 @p_205) :rule or_neg :args (0))
(step t481 (cl @p_265 @p_266) :rule or_neg :args (1))
(step t482 (cl @p_265 (not @p_264)) :rule or_neg :args (2))
(step t483 (cl @p_265 @p_265 @p_265) :rule resolution :premises (t479 t480 t481 t482))
(step t484 (cl @p_265) :rule contraction :premises (t483))
(step t485 (cl @p_262) :rule resolution :premises (t448 t450 t484))
(step t486 (cl @p_198 @p_261 @p_252) :rule or :premises (t485))
(step t487 (cl @p_252) :rule resolution :premises (t486 t399 t343))
(step t488 (cl (not (! (= (! (or @p_198 @p_227 (! (not @p_229) :named @p_230)) :named @p_231) (! (or @p_198 @p_227 @p_223) :named @p_228)) :named @p_248)) (not @p_231) @p_228) :rule equiv_pos2)
(step t489 (cl (= @p_230 @p_223)) :rule rare_rewrite :args ("bool-double-not-elim" @p_223))
(step t490 (cl @p_248) :rule cong :premises (t489))
(step t491 (cl (! (=> (! (and @p_192 @p_224 @p_229) :named @p_233) (! (and @p_235 @p_229) :named @p_236)) :named @p_247) @p_233) :rule implies_neg1)
(anchor :step t492)
(assume t492.a0 @p_192)
(assume t492.a1 @p_224)
(assume t492.a2 @p_229)
(step t492.t0 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t492.t1 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t492.t2 (cl @p_235) :rule trans :premises (t492.t0 t492.t1))
(step t492.t3 (cl @p_236) :rule and_intro :premises (t492.t2 t492.a2))
(step t492 (cl @p_198 @p_227 @p_230 @p_236) :rule subproof :discharge (t492.a0 t492.a1 t492.a2))
(step t493 (cl (! (not @p_233) :named @p_234) @p_192) :rule and_pos :args (0))
(step t494 (cl @p_234 @p_224) :rule and_pos :args (1))
(step t495 (cl @p_234 @p_229) :rule and_pos :args (2))
(step t496 (cl @p_236 @p_234 @p_234 @p_234) :rule resolution :premises (t492 t493 t494 t495))
(step t497 (cl @p_234 @p_234 @p_234 @p_236) :rule reordering :premises (t496))
(step t498 (cl @p_234 @p_236) :rule contraction :premises (t497))
(step t499 (cl @p_247 @p_236) :rule resolution :premises (t491 t498))
(step t500 (cl @p_247 (! (not @p_236) :named @p_237)) :rule implies_neg2)
(step t501 (cl @p_247 @p_247) :rule resolution :premises (t499 t500))
(step t502 (cl @p_247) :rule contraction :premises (t501))
(step t503 (cl @p_234 @p_236) :rule implies :premises (t502))
(step t504 (cl (! (=> @p_236 false) :named @p_238) @p_236) :rule implies_neg1)
(anchor :step t505)
(assume t505.a0 @p_235)
(assume t505.a1 @p_229)
(step t505.t0 (cl @p_246 @p_239 @p_241) :rule equiv_pos2)
(step t505.t1 (cl (= (* 1 (- @p_240 0)) (* 1 @p_244))) :rule poly_simp)
(step t505.t2 (cl (= @p_241 @p_223)) :rule poly_simp_rel :premises (t505.t1))
(step t505.t3 (cl (= @p_223 @p_241)) :rule symm :premises (t505.t2))
(step t505.t4 (cl @p_245) :rule trans :premises (t405 t505.t3))
(step t505.t5 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t505.t6 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t505.t7 (cl @p_235) :rule trans :premises (t505.t5 t505.t6))
(step t505.t8 (cl @p_241) :rule resolution :premises (t505.t0 t505.t4 t505.t7))
(step t505.t9 (cl (not (! (= @p_229 (! (not @p_241) :named @p_242)) :named @p_243)) @p_230 @p_242) :rule equiv_pos2)
(step t505.t10 (cl (= @p_242 @p_229)) :rule cong :premises (t505.t2))
(step t505.t11 (cl @p_243) :rule symm :premises (t505.t10))
(step t505.t12 (cl @p_242) :rule resolution :premises (t505.t9 t505.t11 t505.a1))
(step t505.t13 (cl) :rule resolution :premises (t505.t8 t505.t12))
(step t505 (cl @p_239 @p_230 false) :rule subproof :discharge (t505.a0 t505.a1))
(step t506 (cl @p_237 @p_235) :rule and_pos :args (0))
(step t507 (cl @p_237 @p_229) :rule and_pos :args (1))
(step t508 (cl false @p_237 @p_237) :rule resolution :premises (t505 t506 t507))
(step t509 (cl @p_237 @p_237 false) :rule reordering :premises (t508))
(step t510 (cl @p_237 false) :rule contraction :premises (t509))
(step t511 (cl @p_238 false) :rule resolution :premises (t504 t510))
(step t512 (cl @p_238 @p_212) :rule implies_neg2)
(step t513 (cl @p_238 @p_238) :rule resolution :premises (t511 t512))
(step t514 (cl @p_238) :rule contraction :premises (t513))
(step t515 (cl (= @p_238 @p_237)) :rule implies_simplify)
(step t516 (cl (not @p_238) @p_237) :rule equiv1 :premises (t515))
(step t517 (cl @p_237) :rule resolution :premises (t514 t516))
(step t518 (cl @p_234) :rule resolution :premises (t503 t517))
(step t519 (cl @p_198 @p_227 @p_230) :rule not_and :premises (t518))
(step t520 (cl @p_231 @p_205) :rule or_neg :args (0))
(step t521 (cl @p_231 @p_232) :rule or_neg :args (1))
(step t522 (cl @p_231 (not @p_230)) :rule or_neg :args (2))
(step t523 (cl @p_231 @p_231 @p_231) :rule resolution :premises (t519 t520 t521 t522))
(step t524 (cl @p_231) :rule contraction :premises (t523))
(step t525 (cl @p_228) :rule resolution :premises (t488 t490 t524))
(step t526 (cl @p_198 @p_227 @p_223) :rule or :premises (t525))
(step t527 (cl @p_223) :rule resolution :premises (t526 t399 t261))
(step t528 (cl (not (! (= (! (or @p_198 @p_199 (! (not @p_201) :named @p_202)) :named @p_203) (! (or @p_198 @p_199 @p_176) :named @p_200)) :named @p_222)) (not @p_203) @p_200) :rule equiv_pos2)
(step t529 (cl (= @p_202 @p_176)) :rule rare_rewrite :args ("bool-double-not-elim" @p_176))
(step t530 (cl @p_222) :rule cong :premises (t529))
(step t531 (cl (! (=> (! (and @p_192 @p_178 @p_201) :named @p_206) (! (and @p_208 @p_201) :named @p_209)) :named @p_221) @p_206) :rule implies_neg1)
(anchor :step t532)
(assume t532.a0 @p_192)
(assume t532.a1 @p_178)
(assume t532.a2 @p_201)
(step t532.t0 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t532.t1 (cl @p_208) :rule trans :premises (t532.t0 t346))
(step t532.t2 (cl @p_209) :rule and_intro :premises (t532.t1 t532.a2))
(step t532 (cl @p_198 @p_199 @p_202 @p_209) :rule subproof :discharge (t532.a0 t532.a1 t532.a2))
(step t533 (cl (! (not @p_206) :named @p_207) @p_192) :rule and_pos :args (0))
(step t534 (cl @p_207 @p_178) :rule and_pos :args (1))
(step t535 (cl @p_207 @p_201) :rule and_pos :args (2))
(step t536 (cl @p_209 @p_207 @p_207 @p_207) :rule resolution :premises (t532 t533 t534 t535))
(step t537 (cl @p_207 @p_207 @p_207 @p_209) :rule reordering :premises (t536))
(step t538 (cl @p_207 @p_209) :rule contraction :premises (t537))
(step t539 (cl @p_221 @p_209) :rule resolution :premises (t531 t538))
(step t540 (cl @p_221 (! (not @p_209) :named @p_210)) :rule implies_neg2)
(step t541 (cl @p_221 @p_221) :rule resolution :premises (t539 t540))
(step t542 (cl @p_221) :rule contraction :premises (t541))
(step t543 (cl @p_207 @p_209) :rule implies :premises (t542))
(step t544 (cl (! (=> @p_209 false) :named @p_211) @p_209) :rule implies_neg1)
(anchor :step t545)
(assume t545.a0 @p_208)
(assume t545.a1 @p_201)
(step t545.t0 (cl @p_220 @p_213 @p_215) :rule equiv_pos2)
(step t545.t1 (cl (= (* 1 (- @p_214 0)) (* 1 @p_218))) :rule poly_simp)
(step t545.t2 (cl (= @p_215 @p_176)) :rule poly_simp_rel :premises (t545.t1))
(step t545.t3 (cl (= @p_176 @p_215)) :rule symm :premises (t545.t2))
(step t545.t4 (cl @p_219) :rule trans :premises (t408 t545.t3))
(step t545.t5 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t545.t6 (cl @p_208) :rule trans :premises (t545.t5 t346))
(step t545.t7 (cl @p_215) :rule resolution :premises (t545.t0 t545.t4 t545.t6))
(step t545.t8 (cl (not (! (= @p_201 @p_216) :named @p_217)) @p_202 @p_216) :rule equiv_pos2)
(step t545.t9 (cl (= @p_216 @p_201)) :rule cong :premises (t545.t2))
(step t545.t10 (cl @p_217) :rule symm :premises (t545.t9))
(step t545.t11 (cl @p_216) :rule resolution :premises (t545.t8 t545.t10 t545.a1))
(step t545.t12 (cl) :rule resolution :premises (t545.t7 t545.t11))
(step t545 (cl @p_213 @p_202 false) :rule subproof :discharge (t545.a0 t545.a1))
(step t546 (cl @p_210 @p_208) :rule and_pos :args (0))
(step t547 (cl @p_210 @p_201) :rule and_pos :args (1))
(step t548 (cl false @p_210 @p_210) :rule resolution :premises (t545 t546 t547))
(step t549 (cl @p_210 @p_210 false) :rule reordering :premises (t548))
(step t550 (cl @p_210 false) :rule contraction :premises (t549))
(step t551 (cl @p_211 false) :rule resolution :premises (t544 t550))
(step t552 (cl @p_211 @p_212) :rule implies_neg2)
(step t553 (cl @p_211 @p_211) :rule resolution :premises (t551 t552))
(step t554 (cl @p_211) :rule contraction :premises (t553))
(step t555 (cl (= @p_211 @p_210)) :rule implies_simplify)
(step t556 (cl (not @p_211) @p_210) :rule equiv1 :premises (t555))
(step t557 (cl @p_210) :rule resolution :premises (t554 t556))
(step t558 (cl @p_207) :rule resolution :premises (t543 t557))
(step t559 (cl @p_198 @p_199 @p_202) :rule not_and :premises (t558))
(step t560 (cl @p_203 @p_205) :rule or_neg :args (0))
(step t561 (cl @p_203 @p_204) :rule or_neg :args (1))
(step t562 (cl @p_203 (not @p_202)) :rule or_neg :args (2))
(step t563 (cl @p_203 @p_203 @p_203) :rule resolution :premises (t559 t560 t561 t562))
(step t564 (cl @p_203) :rule contraction :premises (t563))
(step t565 (cl @p_200) :rule resolution :premises (t528 t530 t564))
(step t566 (cl @p_198 @p_199 @p_176) :rule or :premises (t565))
(step t567 (cl @p_176) :rule resolution :premises (t566 t399 t346))
(step t568 (cl (not (! (= (! (or @p_283 @p_130 @p_273 @p_239 @p_213 @p_285) :named @p_287) (! (or @p_283 @p_130 @p_263 @p_229 @p_201 @p_285) :named @p_286)) :named @p_332)) (not @p_287) @p_286) :rule equiv_pos2)
(step t569 (cl (= @p_285 @p_285)) :rule refl)
(step t570 (cl @p_332) :rule cong :premises (t403 t406 t409 t569))
(step t571 (cl (! (=> (! (and @p_133 @p_115 @p_269 @p_235 @p_208 @p_284) :named @p_294) false) :named @p_296) @p_294) :rule implies_neg1)
(anchor :step t572)
(assume t572.a0 @p_133)
(assume t572.a1 @p_115)
(assume t572.a2 @p_269)
(assume t572.a3 @p_235)
(assume t572.a4 @p_208)
(assume t572.a5 @p_284)
(step t572.t0 (cl (not (! (= (! (<= (! (+ @p_250 (! (* -1 @p_303) :named @p_304) @p_302 @p_274 @p_240 (! (* -1 @p_214) :named @p_300)) :named @p_305) (! (+ @p_298 @p_297 0 0 0 @p_297) :named @p_299)) :named @p_306) false) :named @p_322)) (not @p_306) false) :rule equiv_pos2)
(step t572.t1 (cl (= @p_305 (! (+ @p_250 @p_249 @p_329 @p_328 @p_327 @p_326 @p_325) :named @p_330))) :rule poly_simp)
(step t572.t2 (cl (= @p_329 0)) :rule poly_simp)
(step t572.t3 (cl (= @p_328 0)) :rule poly_simp)
(step t572.t4 (cl (= @p_327 0)) :rule poly_simp)
(step t572.t5 (cl (= @p_326 0)) :rule poly_simp)
(step t572.t6 (cl (= @p_325 0)) :rule poly_simp)
(step t572.t7 (cl (= @p_330 (! (+ @p_250 @p_249 0 0 0 0 0) :named @p_331))) :rule cong :premises (t572.t2 t572.t3 t572.t4 t572.t5 t572.t6))
(step t572.t8 (cl (= @p_331 0)) :rule poly_simp)
(step t572.t9 (cl (= @p_330 0)) :rule trans :premises (t572.t7 t572.t8))
(step t572.t10 (cl (= @p_305 0)) :rule trans :premises (t572.t1 t572.t9))
(step t572.t11 (cl (= @p_298 -1)) :rule evaluate)
(step t572.t12 (cl (= @p_297 0)) :rule evaluate)
(step t572.t13 (cl @p_56) :rule refl)
(step t572.t14 (cl (= @p_299 @p_324)) :rule cong :premises (t572.t11 t572.t12 t572.t13 t572.t13 t572.t13 t572.t12))
(step t572.t15 (cl (= @p_324 -1)) :rule evaluate)
(step t572.t16 (cl (= @p_299 -1)) :rule trans :premises (t572.t14 t572.t15))
(step t572.t17 (cl (= @p_306 @p_323)) :rule cong :premises (t572.t10 t572.t16))
(step t572.t18 (cl (= @p_323 false)) :rule evaluate)
(step t572.t19 (cl @p_322) :rule trans :premises (t572.t17 t572.t18))
(step t572.t20 (cl (not (! (<= @p_250 @p_298) :named @p_320)) (not (! (= @p_304 @p_297) :named @p_316)) (not @p_311) @p_276 @p_242 (not (! (= @p_300 @p_297) :named @p_307)) @p_306) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t572.t21 (cl (=> (! (and @p_308 @p_284) :named @p_321) @p_320)) :rule la_mult_neg)
(step t572.t22 (cl (not @p_321) @p_320) :rule implies :premises (t572.t21))
(step t572.t23 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t572.t24 (cl (not @p_310) @p_308) :rule equiv1 :premises (t572.t23))
(step t572.t25 (cl @p_310) :rule evaluate)
(step t572.t26 (cl @p_308) :rule resolution :premises (t572.t24 t572.t25))
(step t572.t27 (cl @p_321) :rule and_intro :premises (t572.t26 t572.a5))
(step t572.t28 (cl @p_320) :rule resolution :premises (t572.t22 t572.t27))
(step t572.t29 (cl (=> (! (and @p_308 @p_317) :named @p_318) @p_316)) :rule la_mult_neg)
(step t572.t30 (cl (not @p_318) @p_316) :rule implies :premises (t572.t29))
(step t572.t31 (cl (not @p_319) @p_283 @p_317) :rule equiv_pos2)
(step t572.t32 (cl (= (* 1 (- @p_303 0)) (* 1 (- @p_132 @p_131)))) :rule poly_simp)
(step t572.t33 (cl (= @p_317 @p_133)) :rule poly_simp_rel :premises (t572.t32))
(step t572.t34 (cl @p_319) :rule symm :premises (t572.t33))
(step t572.t35 (cl @p_317) :rule resolution :premises (t572.t31 t572.t34 t383))
(step t572.t36 (cl @p_318) :rule and_intro :premises (t572.t26 t572.t35))
(step t572.t37 (cl @p_316) :rule resolution :premises (t572.t30 t572.t36))
(step t572.t38 (cl @p_315 @p_130 @p_311) :rule equiv_pos2)
(step t572.t39 (cl (= (* 1 (- @p_302 0)) (* 1 (- @p_7 @p_114)))) :rule poly_simp)
(step t572.t40 (cl (= @p_311 @p_115)) :rule poly_simp_rel :premises (t572.t39))
(step t572.t41 (cl @p_314) :rule symm :premises (t572.t40))
(step t572.t42 (cl @p_311) :rule resolution :premises (t572.t38 t572.t41 t572.a1))
(step t572.t43 (cl @p_280 @p_273 @p_275) :rule equiv_pos2)
(step t572.t44 (cl (= (* 1 (- @p_274 0)) (* 1 @p_278))) :rule poly_simp)
(step t572.t45 (cl (= @p_275 @p_252)) :rule poly_simp_rel :premises (t572.t44))
(step t572.t46 (cl (= @p_252 @p_275)) :rule symm :premises (t572.t45))
(step t572.t47 (cl @p_279) :rule trans :premises (t402 t572.t46))
(step t572.t48 (cl (= @p_191 @p_169)) :rule symm :premises (t399))
(step t572.t49 (cl @p_269) :rule trans :premises (t572.t48 t343))
(step t572.t50 (cl @p_275) :rule resolution :premises (t572.t43 t572.t47 t572.t49))
(step t572.t51 (cl @p_246 @p_239 @p_241) :rule equiv_pos2)
(step t572.t52 (cl (= (* 1 (- @p_240 0)) (* 1 @p_244))) :rule poly_simp)
(step t572.t53 (cl (= @p_241 @p_223)) :rule poly_simp_rel :premises (t572.t52))
(step t572.t54 (cl (= @p_223 @p_241)) :rule symm :premises (t572.t53))
(step t572.t55 (cl @p_245) :rule trans :premises (t405 t572.t54))
(step t572.t56 (cl (= @p_169 @p_173)) :rule cong :premises (t261))
(step t572.t57 (cl @p_235) :rule trans :premises (t572.t48 t572.t56))
(step t572.t58 (cl @p_241) :rule resolution :premises (t572.t51 t572.t55 t572.t57))
(step t572.t59 (cl (=> (! (and @p_308 @p_215) :named @p_309) @p_307)) :rule la_mult_neg)
(step t572.t60 (cl (not @p_309) @p_307) :rule implies :premises (t572.t59))
(step t572.t61 (cl @p_220 @p_213 @p_215) :rule equiv_pos2)
(step t572.t62 (cl (= (* 1 (- @p_214 0)) (* 1 @p_218))) :rule poly_simp)
(step t572.t63 (cl (= @p_215 @p_176)) :rule poly_simp_rel :premises (t572.t62))
(step t572.t64 (cl (= @p_176 @p_215)) :rule symm :premises (t572.t63))
(step t572.t65 (cl @p_219) :rule trans :premises (t408 t572.t64))
(step t572.t66 (cl @p_208) :rule trans :premises (t572.t48 t346))
(step t572.t67 (cl @p_215) :rule resolution :premises (t572.t61 t572.t65 t572.t66))
(step t572.t68 (cl @p_309) :rule and_intro :premises (t572.t26 t572.t67))
(step t572.t69 (cl @p_307) :rule resolution :premises (t572.t60 t572.t68))
(step t572.t70 (cl @p_306) :rule resolution :premises (t572.t20 t572.t28 t572.t37 t572.t42 t572.t50 t572.t58 t572.t69))
(step t572.t71 (cl false) :rule resolution :premises (t572.t0 t572.t19 t572.t70))
(step t572 (cl @p_283 @p_130 @p_273 @p_239 @p_213 @p_285 false) :rule subproof :discharge (t572.a0 t572.a1 t572.a2 t572.a3 t572.a4 t572.a5))
(step t573 (cl (! (not @p_294) :named @p_295) @p_133) :rule and_pos :args (0))
(step t574 (cl @p_295 @p_115) :rule and_pos :args (1))
(step t575 (cl @p_295 @p_269) :rule and_pos :args (2))
(step t576 (cl @p_295 @p_235) :rule and_pos :args (3))
(step t577 (cl @p_295 @p_208) :rule and_pos :args (4))
(step t578 (cl @p_295 @p_284) :rule and_pos :args (5))
(step t579 (cl false @p_295 @p_295 @p_295 @p_295 @p_295 @p_295) :rule resolution :premises (t572 t573 t574 t575 t576 t577 t578))
(step t580 (cl @p_295 @p_295 @p_295 @p_295 @p_295 @p_295 false) :rule reordering :premises (t579))
(step t581 (cl @p_295 false) :rule contraction :premises (t580))
(step t582 (cl @p_296 false) :rule resolution :premises (t571 t581))
(step t583 (cl @p_296 @p_212) :rule implies_neg2)
(step t584 (cl @p_296 @p_296) :rule resolution :premises (t582 t583))
(step t585 (cl @p_296) :rule contraction :premises (t584))
(step t586 (cl (= @p_296 @p_295)) :rule implies_simplify)
(step t587 (cl (not @p_296) @p_295) :rule equiv1 :premises (t586))
(step t588 (cl @p_295) :rule resolution :premises (t585 t587))
(step t589 (cl @p_283 @p_130 @p_273 @p_239 @p_213 @p_285) :rule not_and :premises (t588))
(step t590 (cl @p_287 @p_293) :rule or_neg :args (0))
(step t591 (cl @p_287 @p_292) :rule or_neg :args (1))
(step t592 (cl @p_287 @p_291) :rule or_neg :args (2))
(step t593 (cl @p_287 @p_290) :rule or_neg :args (3))
(step t594 (cl @p_287 @p_289) :rule or_neg :args (4))
(step t595 (cl @p_287 @p_288) :rule or_neg :args (5))
(step t596 (cl @p_287 @p_287 @p_287 @p_287 @p_287 @p_287) :rule resolution :premises (t589 t590 t591 t592 t593 t594 t595))
(step t597 (cl @p_287) :rule contraction :premises (t596))
(step t598 (cl @p_286) :rule resolution :premises (t568 t570 t597))
(step t599 (cl @p_283 @p_130 @p_263 @p_229 @p_201 @p_285) :rule or :premises (t598))
(step t600 (cl @p_283 @p_130 @p_229 @p_201 @p_263 @p_285) :rule reordering :premises (t599))
(step t601 (cl @p_130) :rule resolution :premises (t147 t188 t209 t227 t266 t167 t261 t330 t343 t346 t261 t383 t399 a11 t447 t487 t527 t567 t383 t600 t487 t527 t567 t383))
(step t602 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) (! (or @p_117 (! (>= (! (+ @p_7 @p_120) :named @p_121) 0) :named @p_122) @p_115) :named @p_123)) :named @p_124) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) @p_118) :named @p_119)) :named @p_125)) (not @p_124) @p_119) :rule equiv_pos2)
(step t603 (cl (= @p_121 (! (+ @p_120 @p_7) :named @p_126))) :rule poly_simp)
(step t604 (cl @p_56) :rule refl)
(step t605 (cl (= @p_122 (! (>= @p_126 0) :named @p_127))) :rule cong :premises (t603 t604))
(step t606 (cl (= @p_113 (! (>= 1 (! (+ @p_111 1) :named @p_128)) :named @p_129))) :rule rare_rewrite :args ("arith-geq-tighten" @p_111 1))
(step t607 (cl (= (* -1 (- 1 @p_128)) (* -1 (- @p_126 0)))) :rule poly_simp)
(step t608 (cl (= @p_129 @p_127)) :rule poly_simp_rel :premises (t607))
(step t609 (cl (= @p_113 @p_127)) :rule trans :premises (t606 t608))
(step t610 (cl (= @p_127 @p_113)) :rule symm :premises (t609))
(step t611 (cl (= @p_122 @p_113)) :rule trans :premises (t605 t610))
(step t612 (cl (= @p_115 @p_115)) :rule refl)
(step t613 (cl (= @p_123 @p_118)) :rule cong :premises (t611 t612))
(step t614 (cl @p_125) :rule cong :premises (t613))
(step t615 (cl @p_124 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t616)
(assume t616.a0 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))))
(step t616.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :named @p_44) @p_123)) :rule forall_inst :args (@p_7 @p_6))
(step t616.t1 (cl @p_44 @p_123) :rule or :premises (t616.t0))
(step t616.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0))) (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :named @p_18)) (not (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t616.t3 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t616.t3.t0 (cl (= (! (<= 0 ?v0) :named @p_40) (! (>= ?v0 0) :named @p_26))) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t616.t3.t1 (cl (= (! (< ?v0 ?v1) :named @p_39) (! (not (! (>= ?v0 ?v1) :named @p_42)) :named @p_43))) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v1))
(step t616.t3.t2 (cl (= (* 1 (- ?v0 ?v1)) (* 1 (- (! (+ ?v0 @p_23) :named @p_24) 0)))) :rule poly_simp)
(step t616.t3.t3 (cl (= @p_42 (! (>= @p_24 0) :named @p_25))) :rule poly_simp_rel :premises (t616.t3.t2))
(step t616.t3.t4 (cl (= @p_43 (! (not @p_25) :named @p_29))) :rule cong :premises (t616.t3.t3))
(step t616.t3.t5 (cl (= @p_39 @p_29)) :rule trans :premises (t616.t3.t1 t616.t3.t4))
(step t616.t3.t6 (cl (= (! (and @p_40 @p_39) :named @p_41) (! (and @p_26 @p_29) :named @p_30))) :rule cong :premises (t616.t3.t0 t616.t3.t5))
(step t616.t3.t7 (cl (= (* 1 (- (! (modulo$ ?v0 ?v1) :named @p_21) ?v0)) (* -1 (- ?v0 @p_21)))) :rule poly_simp)
(step t616.t3.t8 (cl (= (! (= @p_21 ?v0) :named @p_38) (! (= ?v0 @p_21) :named @p_22))) :rule poly_simp_rel :premises (t616.t3.t7))
(step t616.t3.t9 (cl (= (=> @p_41 @p_38) (! (=> @p_30 @p_22) :named @p_31))) :rule cong :premises (t616.t3.t6 t616.t3.t8))
(step t616.t3 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0))) (forall ((?v0 Int) (?v1 Int)) (=> (and (>= ?v0 0) (not (>= (+ ?v0 (* -1 ?v1)) 0))) (= ?v0 (modulo$ ?v0 ?v1)))))) :rule bind)
(anchor :step t616.t4 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t616.t4.t0 (cl (= @p_31 (! (or (! (not @p_30) :named @p_32) @p_22) :named @p_33))) :rule rare_rewrite :args ("bool-impl-elim" @p_30 @p_22))
(step t616.t4.t1 (cl (= @p_32 (! (or (! (not @p_26) :named @p_27) (! (not @p_29) :named @p_36)) :named @p_37))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_26 @p_29 rare-list))
(step t616.t4.t2 (cl (= @p_36 @p_25)) :rule rare_rewrite :args ("bool-double-not-elim" @p_25))
(step t616.t4.t3 (cl (= @p_37 (! (or @p_27 @p_25) :named @p_34))) :rule cong :premises (t616.t4.t2))
(step t616.t4.t4 (cl (= @p_32 @p_34)) :rule trans :premises (t616.t4.t1 t616.t4.t3))
(step t616.t4.t5 (cl (= @p_22 @p_22)) :rule refl)
(step t616.t4.t6 (cl (= @p_33 (! (or @p_34 @p_22) :named @p_35))) :rule cong :premises (t616.t4.t4 t616.t4.t5))
(step t616.t4.t7 (cl (= @p_35 (! (or @p_27 @p_25 @p_22) :named @p_28))) :rule aci_simp)
(step t616.t4.t8 (cl (= @p_33 @p_28)) :rule trans :premises (t616.t4.t6 t616.t4.t7))
(step t616.t4.t9 (cl (= @p_31 @p_28)) :rule trans :premises (t616.t4.t0 t616.t4.t8))
(step t616.t4 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (>= ?v0 0) (not (>= (+ ?v0 (* -1 ?v1)) 0))) (= ?v0 (modulo$ ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))))) :rule bind)
(step t616.t5 (cl @p_18) :rule trans :premises (t616.t3 t616.t4))
(step t616.t6 (cl (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule resolution :premises (t616.t2 t616.t5 a7))
(step t616.t7 (cl @p_123) :rule resolution :premises (t616.t1 t616.t6))
(step t616 (cl @p_44 @p_123) :rule subproof :discharge (t616.a0))
(step t617 (cl @p_124 @p_123) :rule resolution :premises (t615 t616))
(step t618 (cl @p_124 (not @p_123)) :rule implies_neg2)
(step t619 (cl @p_124 @p_124) :rule resolution :premises (t617 t618))
(step t620 (cl @p_124) :rule contraction :premises (t619))
(step t621 (cl @p_119) :rule resolution :premises (t602 t614 t620))
(step t622 (cl @p_44 @p_118) :rule implies :premises (t621))
(step t623 (cl (not @p_18) (not (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0)))) (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t624 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t624.t0 (cl (= @p_40 @p_26)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t624.t1 (cl (= @p_39 @p_43)) :rule rare_rewrite :args ("arith-elim-lt" ?v0 ?v1))
(step t624.t2 (cl (= (* 1 (- ?v0 ?v1)) (* 1 (- @p_24 0)))) :rule poly_simp)
(step t624.t3 (cl (= @p_42 @p_25)) :rule poly_simp_rel :premises (t624.t2))
(step t624.t4 (cl (= @p_43 @p_29)) :rule cong :premises (t624.t3))
(step t624.t5 (cl (= @p_39 @p_29)) :rule trans :premises (t624.t1 t624.t4))
(step t624.t6 (cl (= @p_41 @p_30)) :rule cong :premises (t624.t0 t624.t5))
(step t624.t7 (cl (= (* 1 (- @p_21 ?v0)) (* -1 (- ?v0 @p_21)))) :rule poly_simp)
(step t624.t8 (cl (= @p_38 @p_22)) :rule poly_simp_rel :premises (t624.t7))
(step t624.t9 (cl (= (=> @p_41 @p_38) @p_31)) :rule cong :premises (t624.t6 t624.t8))
(step t624 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (<= 0 ?v0) (< ?v0 ?v1)) (= (modulo$ ?v0 ?v1) ?v0))) (forall ((?v0 Int) (?v1 Int)) (=> (and (>= ?v0 0) (not (>= (+ ?v0 (* -1 ?v1)) 0))) (= ?v0 (modulo$ ?v0 ?v1)))))) :rule bind)
(anchor :step t625 :args ((?v0 Int) (?v1 Int) (:= (?v0 Int) ?v0) (:= (?v1 Int) ?v1)))
(step t625.t0 (cl (= @p_31 @p_33)) :rule rare_rewrite :args ("bool-impl-elim" @p_30 @p_22))
(step t625.t1 (cl (= @p_32 @p_37)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_26 @p_29 rare-list))
(step t625.t2 (cl (= @p_36 @p_25)) :rule rare_rewrite :args ("bool-double-not-elim" @p_25))
(step t625.t3 (cl (= @p_37 @p_34)) :rule cong :premises (t625.t2))
(step t625.t4 (cl (= @p_32 @p_34)) :rule trans :premises (t625.t1 t625.t3))
(step t625.t5 (cl (= @p_22 @p_22)) :rule refl)
(step t625.t6 (cl (= @p_33 @p_35)) :rule cong :premises (t625.t4 t625.t5))
(step t625.t7 (cl (= @p_35 @p_28)) :rule aci_simp)
(step t625.t8 (cl (= @p_33 @p_28)) :rule trans :premises (t625.t6 t625.t7))
(step t625.t9 (cl (= @p_31 @p_28)) :rule trans :premises (t625.t0 t625.t8))
(step t625 (cl (= (forall ((?v0 Int) (?v1 Int)) (=> (and (>= ?v0 0) (not (>= (+ ?v0 (* -1 ?v1)) 0))) (= ?v0 (modulo$ ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))))) :rule bind)
(step t626 (cl @p_18) :rule trans :premises (t624 t625))
(step t627 (cl (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule resolution :premises (t623 t626 a7))
(step t628 (cl @p_118) :rule resolution :premises (t622 t627))
(step t629 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) (! (or @p_16 (! (>= (! (+ @p_8 @p_46) :named @p_47) 0) :named @p_48) @p_10) :named @p_49)) :named @p_50) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) @p_17) :named @p_45)) :named @p_51)) (not @p_50) @p_45) :rule equiv_pos2)
(step t630 (cl (= @p_47 (! (+ @p_46 @p_8) :named @p_52))) :rule poly_simp)
(step t631 (cl (= @p_48 (! (>= @p_52 0) :named @p_53))) :rule cong :premises (t630 t604))
(step t632 (cl (= @p_14 (! (>= 1 (! (+ @p_12 1) :named @p_54)) :named @p_55))) :rule rare_rewrite :args ("arith-geq-tighten" @p_12 1))
(step t633 (cl (= (* -1 (- 1 @p_54)) (* -1 (- @p_52 0)))) :rule poly_simp)
(step t634 (cl (= @p_55 @p_53)) :rule poly_simp_rel :premises (t633))
(step t635 (cl (= @p_14 @p_53)) :rule trans :premises (t632 t634))
(step t636 (cl (= @p_53 @p_14)) :rule symm :premises (t635))
(step t637 (cl (= @p_48 @p_14)) :rule trans :premises (t631 t636))
(step t638 (cl (= @p_10 @p_10)) :rule refl)
(step t639 (cl (= @p_49 @p_17)) :rule cong :premises (t637 t638))
(step t640 (cl @p_51) :rule cong :premises (t639))
(step t641 (cl @p_50 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t642)
(assume t642.a0 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))))
(step t642.t0 (cl (or @p_44 @p_49)) :rule forall_inst :args (@p_8 @p_7))
(step t642.t1 (cl @p_44 @p_49) :rule or :premises (t642.t0))
(step t642.t2 (cl @p_49) :rule resolution :premises (t642.t1 t627))
(step t642 (cl @p_44 @p_49) :rule subproof :discharge (t642.a0))
(step t643 (cl @p_50 @p_49) :rule resolution :premises (t641 t642))
(step t644 (cl @p_50 (not @p_49)) :rule implies_neg2)
(step t645 (cl @p_50 @p_50) :rule resolution :premises (t643 t644))
(step t646 (cl @p_50) :rule contraction :premises (t645))
(step t647 (cl @p_45) :rule resolution :premises (t629 t640 t646))
(step t648 (cl @p_44 @p_17) :rule implies :premises (t647))
(step t649 (cl @p_17) :rule resolution :premises (t648 t627))
(step t650 (cl (or @p_190 @p_1099)) :rule forall_inst :args (@p_7 @p_8))
(step t651 (cl @p_190 @p_1099) :rule or :premises (t650))
(step t652 (cl @p_1099) :rule resolution :premises (t651 t226))
(step t653 (cl (not (! (= (! (or (! (not (! (>= (! (+ @p_7 (! (* -1 (! (times$ 2 @p_7) :named @p_668)) :named @p_690)) :named @p_912) 1) :named @p_913)) :named @p_915) (! (not (! (= (! (+ @p_668 (! (modulo$ @p_6 2) :named @p_57)) :named @p_669) (! (+ @p_57 @p_8) :named @p_785)) :named @p_801)) :named @p_806) @p_13) :named @p_979) (! (or (! (not (! (>= (! (+ @p_7 (! (* -1 (! (times$ 2 @p_7) :named @p_668)) :named @p_690)) :named @p_912) 1) :named @p_913)) :named @p_915) (! (not (! (= @p_668 @p_8) :named @p_793)) :named @p_798) @p_13) :named @p_978)) :named @p_1011)) (not @p_979) @p_978) :rule equiv_pos2)
(step t654 (cl (= (* 1 (- @p_669 @p_785)) (! (* 1 (- @p_668 @p_8)) :named @p_804))) :rule poly_simp)
(step t655 (cl (= @p_801 @p_793)) :rule poly_simp_rel :premises (t654))
(step t656 (cl (= @p_806 @p_798)) :rule cong :premises (t655))
(step t657 (cl (= @p_13 @p_13)) :rule refl)
(step t658 (cl @p_1011) :rule cong :premises (t656 t657))
(step t659 (cl (not (! (= (! (or @p_915 @p_806 (! (not @p_14) :named @p_980)) :named @p_981) @p_979) :named @p_1010)) (not @p_981) @p_979) :rule equiv_pos2)
(step t660 (cl (= @p_980 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t661 (cl (= @p_981 @p_978)) :rule cong :premises (t656 t660))
(step t662 (cl (= @p_978 @p_979)) :rule symm :premises (t658))
(step t663 (cl @p_1010) :rule trans :premises (t661 t662))
(step t664 (cl (! (=> (! (and @p_913 @p_801 @p_14) :named @p_984) false) :named @p_986) @p_984) :rule implies_neg1)
(anchor :step t665)
(assume t665.a0 @p_913)
(assume t665.a1 @p_801)
(assume t665.a2 @p_14)
(step t665.t0 (cl (not (! (= (! (< (! (+ @p_12 (! (* -1 @p_912) :named @p_989) (! (* -1 (! (+ @p_668 @p_11) :named @p_799)) :named @p_988)) :named @p_990) (! (+ 1 @p_298 @p_297) :named @p_987)) :named @p_991) false) :named @p_1003)) (not @p_991) false) :rule equiv_pos2)
(step t665.t1 (cl (= @p_991 (! (not (! (>= @p_990 @p_987) :named @p_1004)) :named @p_1005))) :rule rare_rewrite :args ("arith-elim-lt" @p_990 @p_987))
(step t665.t2 (cl (= @p_990 (! (+ @p_668 (! (* 0 @p_8) :named @p_1007) @p_690 @p_326) :named @p_1008))) :rule poly_simp)
(step t665.t3 (cl (= @p_1007 0)) :rule poly_simp)
(step t665.t4 (cl (= @p_690 @p_690)) :rule refl)
(step t665.t5 (cl (= @p_326 0)) :rule poly_simp)
(step t665.t6 (cl (= @p_1008 (! (+ @p_668 0 @p_690 0) :named @p_1009))) :rule cong :premises (t665.t3 t665.t4 t665.t5))
(step t665.t7 (cl (= @p_1009 0)) :rule poly_simp)
(step t665.t8 (cl (= @p_1008 0)) :rule trans :premises (t665.t6 t665.t7))
(step t665.t9 (cl (= @p_990 0)) :rule trans :premises (t665.t2 t665.t8))
(step t665.t10 (cl (= @p_298 -1)) :rule evaluate)
(step t665.t11 (cl (= @p_297 0)) :rule evaluate)
(step t665.t12 (cl (= @p_987 (! (+ 1 -1 0) :named @p_1006))) :rule cong :premises (t665.t10 t665.t11))
(step t665.t13 (cl (= @p_1006 0)) :rule evaluate)
(step t665.t14 (cl (= @p_987 0)) :rule trans :premises (t665.t12 t665.t13))
(step t665.t15 (cl (= @p_1004 @p_366)) :rule cong :premises (t665.t9 t665.t14))
(step t665.t16 (cl (= @p_366 true)) :rule evaluate)
(step t665.t17 (cl (= @p_1004 true)) :rule trans :premises (t665.t15 t665.t16))
(step t665.t18 (cl (= @p_1005 @p_365)) :rule cong :premises (t665.t17))
(step t665.t19 (cl (= @p_365 false)) :rule evaluate)
(step t665.t20 (cl (= @p_1005 false)) :rule trans :premises (t665.t18 t665.t19))
(step t665.t21 (cl @p_1003) :rule trans :premises (t665.t1 t665.t20))
(step t665.t22 (cl (! (not (! (< @p_12 1) :named @p_996)) :named @p_1001) (not (! (<= @p_989 @p_298) :named @p_994)) (! (not (! (= @p_988 @p_297) :named @p_992)) :named @p_1002) @p_991) :rule la_generic :args (1/1 1/1 -1/1 1/1))
(step t665.t23 (cl (! (not (! (= @p_14 @p_996) :named @p_999)) :named @p_1000) @p_980 @p_996) :rule equiv_pos2)
(step t665.t24 (cl (= @p_996 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" @p_12 1))
(step t665.t25 (cl @p_999) :rule symm :premises (t665.t24))
(step t665.t26 (cl @p_996) :rule resolution :premises (t665.t23 t665.t25 t665.a2))
(step t665.t27 (cl (=> (! (and @p_308 @p_913) :named @p_995) @p_994)) :rule la_mult_neg)
(step t665.t28 (cl (not @p_995) @p_994) :rule implies :premises (t665.t27))
(step t665.t29 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t665.t30 (cl (not @p_310) @p_308) :rule equiv1 :premises (t665.t29))
(step t665.t31 (cl @p_310) :rule evaluate)
(step t665.t32 (cl @p_308) :rule resolution :premises (t665.t30 t665.t31))
(step t665.t33 (cl @p_995) :rule and_intro :premises (t665.t32 t665.a0))
(step t665.t34 (cl @p_994) :rule resolution :premises (t665.t28 t665.t33))
(step t665.t35 (cl (=> (! (and @p_308 (! (= @p_799 0) :named @p_800)) :named @p_993) @p_992)) :rule la_mult_neg)
(step t665.t36 (cl (not @p_993) @p_992) :rule implies :premises (t665.t35))
(step t665.t37 (cl (! (not (! (= @p_801 @p_800) :named @p_802)) :named @p_805) @p_806 @p_800) :rule equiv_pos2)
(step t665.t38 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t665.t39 (cl (! (= @p_800 @p_793) :named @p_803)) :rule poly_simp_rel :premises (t665.t38))
(step t665.t40 (cl (= @p_793 @p_800)) :rule symm :premises (t665.t39))
(step t665.t41 (cl @p_802) :rule trans :premises (t655 t665.t40))
(step t665.t42 (cl (or @p_190 (! (= @p_6 @p_669) :named @p_670))) :rule forall_inst :args (2 @p_6))
(step t665.t43 (cl @p_190 @p_670) :rule or :premises (t665.t42))
(step t665.t44 (cl @p_670) :rule resolution :premises (t665.t43 t226))
(step t665.t45 (cl (= @p_669 @p_6)) :rule symm :premises (t665.t44))
(step t665.t46 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))) (! (= @p_6 (! (+ @p_8 @p_57) :named @p_788)) :named @p_789)) :named @p_790) (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))) (! (= @p_6 @p_785) :named @p_786)) :named @p_787)) :named @p_791)) (not @p_790) @p_787) :rule equiv_pos2)
(step t665.t47 (cl (= @p_788 @p_785)) :rule poly_simp)
(step t665.t48 (cl (= @p_789 @p_786)) :rule cong :premises (t665.t47))
(step t665.t49 (cl @p_791) :rule cong :premises (t665.t48))
(step t665.t50 (cl @p_790 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t665.t51)
(assume t665.t51.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t665.t51.t0 (cl (or @p_255 @p_789)) :rule forall_inst :args (@p_6 2))
(step t665.t51.t1 (cl @p_255 @p_789) :rule or :premises (t665.t51.t0))
(step t665.t51.t2 (cl @p_789) :rule resolution :premises (t665.t51.t1 t665.t51.a0))
(step t665.t51 (cl @p_255 @p_789) :rule subproof :discharge (t665.t51.a0))
(step t665.t52 (cl @p_790 @p_789) :rule resolution :premises (t665.t50 t665.t51))
(step t665.t53 (cl @p_790 (not @p_789)) :rule implies_neg2)
(step t665.t54 (cl @p_790 @p_790) :rule resolution :premises (t665.t52 t665.t53))
(step t665.t55 (cl @p_790) :rule contraction :premises (t665.t54))
(step t665.t56 (cl @p_787) :rule resolution :premises (t665.t46 t665.t49 t665.t55))
(step t665.t57 (cl @p_255 @p_786) :rule implies :premises (t665.t56))
(step t665.t58 (cl @p_786) :rule resolution :premises (t665.t57 a4))
(step t665.t59 (cl @p_801) :rule trans :premises (t665.t45 t665.t58))
(step t665.t60 (cl @p_800) :rule resolution :premises (t665.t37 t665.t41 t665.t59))
(step t665.t61 (cl @p_993) :rule and_intro :premises (t665.t32 t665.t60))
(step t665.t62 (cl @p_992) :rule resolution :premises (t665.t36 t665.t61))
(step t665.t63 (cl @p_991) :rule resolution :premises (t665.t22 t665.t26 t665.t34 t665.t62))
(step t665.t64 (cl false) :rule resolution :premises (t665.t0 t665.t21 t665.t63))
(step t665 (cl @p_915 @p_806 @p_980 false) :rule subproof :discharge (t665.a0 t665.a1 t665.a2))
(step t666 (cl (! (not @p_984) :named @p_985) @p_913) :rule and_pos :args (0))
(step t667 (cl @p_985 @p_801) :rule and_pos :args (1))
(step t668 (cl @p_985 @p_14) :rule and_pos :args (2))
(step t669 (cl false @p_985 @p_985 @p_985) :rule resolution :premises (t665 t666 t667 t668))
(step t670 (cl @p_985 @p_985 @p_985 false) :rule reordering :premises (t669))
(step t671 (cl @p_985 false) :rule contraction :premises (t670))
(step t672 (cl @p_986 false) :rule resolution :premises (t664 t671))
(step t673 (cl @p_986 @p_212) :rule implies_neg2)
(step t674 (cl @p_986 @p_986) :rule resolution :premises (t672 t673))
(step t675 (cl @p_986) :rule contraction :premises (t674))
(step t676 (cl (= @p_986 @p_985)) :rule implies_simplify)
(step t677 (cl (not @p_986) @p_985) :rule equiv1 :premises (t676))
(step t678 (cl @p_985) :rule resolution :premises (t675 t677))
(step t679 (cl @p_915 @p_806 @p_980) :rule not_and :premises (t678))
(step t680 (cl @p_981 (! (not @p_915) :named @p_916)) :rule or_neg :args (0))
(step t681 (cl @p_981 (! (not @p_806) :named @p_983)) :rule or_neg :args (1))
(step t682 (cl @p_981 (! (not @p_980) :named @p_982)) :rule or_neg :args (2))
(step t683 (cl @p_981 @p_981 @p_981) :rule resolution :premises (t679 t680 t681 t682))
(step t684 (cl @p_981) :rule contraction :premises (t683))
(step t685 (cl @p_979) :rule resolution :premises (t659 t663 t684))
(step t686 (cl @p_978) :rule resolution :premises (t653 t658 t685))
(step t687 (cl @p_915 @p_798 @p_13) :rule or :premises (t686))
(step t688 (cl @p_798 @p_13 @p_915) :rule reordering :premises (t687))
(step t689 (cl (not (! (= (! (or (! (not (! (= k$ @p_6) :named @p_524)) :named @p_583) (! (not @p_670) :named @p_671) (! (not @p_786) :named @p_792) (! (not (! (= @p_57 1) :named @p_58)) :named @p_974) @p_532 (! (not @p_1051) :named @p_1052) (! (not (! (>= @p_105 2) :named @p_833)) :named @p_834)) :named @p_1424) (! (or @p_583 @p_671 @p_792 @p_974 @p_532 @p_1049 @p_834) :named @p_1423)) :named @p_1438)) (not @p_1424) @p_1423) :rule equiv_pos2)
(step t690 (cl (= @p_1052 @p_1049)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1049))
(step t691 (cl (= @p_834 @p_834)) :rule refl)
(step t692 (cl @p_1438) :rule cong :premises (t690 t691))
(step t693 (cl (! (=> (! (and @p_524 @p_670 @p_786 @p_58 @p_106 @p_1051 @p_833) :named @p_1425) (! (and (! (= 1 @p_57) :named @p_923) (! (= @p_669 @p_105) :named @p_924) @p_801 @p_1051 @p_833) :named @p_1427)) :named @p_1437) @p_1425) :rule implies_neg1)
(anchor :step t694)
(assume t694.a0 @p_524)
(assume t694.a1 @p_670)
(assume t694.a2 @p_786)
(assume t694.a3 @p_58)
(assume t694.a4 @p_106)
(assume t694.a5 @p_1051)
(assume t694.a6 @p_833)
(step t694.t0 (cl (! (=> @p_58 @p_923) :named @p_1047) @p_58) :rule implies_neg1)
(anchor :step t694.t1)
(assume t694.t1.a0 @p_58)
(step t694.t1.t0 (cl @p_923) :rule symm :premises (t694.t1.a0))
(step t694.t1 (cl @p_974 @p_923) :rule subproof :discharge (t694.t1.a0))
(step t694.t2 (cl @p_1047 @p_923) :rule resolution :premises (t694.t0 t694.t1))
(step t694.t3 (cl @p_1047 (! (not @p_923) :named @p_929)) :rule implies_neg2)
(step t694.t4 (cl @p_1047 @p_1047) :rule resolution :premises (t694.t2 t694.t3))
(step t694.t5 (cl @p_1047) :rule contraction :premises (t694.t4))
(step t694.t6 (cl @p_974 @p_923) :rule implies :premises (t694.t5))
(step t694.t7 (cl @p_923) :rule resolution :premises (t694.t6 t694.a3))
(step t694.t8 (cl (! (=> (! (and @p_106 @p_524 @p_670) :named @p_967) @p_924) :named @p_969) @p_967) :rule implies_neg1)
(anchor :step t694.t9)
(assume t694.t9.a0 @p_106)
(assume t694.t9.a1 @p_524)
(assume t694.t9.a2 @p_670)
(step t694.t9.t0 (cl (or @p_190 @p_670)) :rule forall_inst :args (2 @p_6))
(step t694.t9.t1 (cl @p_190 @p_670) :rule or :premises (t694.t9.t0))
(step t694.t9.t2 (cl @p_670) :rule resolution :premises (t694.t9.t1 t226))
(step t694.t9.t3 (cl (= @p_669 @p_6)) :rule symm :premises (t694.t9.t2))
(step t694.t9.t4 (cl (! (= @p_6 k$) :named @p_527)) :rule symm :premises (t694.t9.a1))
(step t694.t9.t5 (cl (or @p_110 @p_106)) :rule forall_inst :args (k$ 0))
(step t694.t9.t6 (cl @p_110 @p_106) :rule or :premises (t694.t9.t5))
(step t694.t9.t7 (cl @p_106) :rule resolution :premises (t694.t9.t6 t398))
(step t694.t9.t8 (cl @p_924) :rule trans :premises (t694.t9.t3 t694.t9.t4 t694.t9.t7))
(step t694.t9 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t694.t9.a0 t694.t9.a1 t694.t9.a2))
(step t694.t10 (cl (! (not @p_967) :named @p_968) @p_106) :rule and_pos :args (0))
(step t694.t11 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t694.t12 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t694.t13 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t694.t9 t694.t10 t694.t11 t694.t12))
(step t694.t14 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t694.t13))
(step t694.t15 (cl @p_968 @p_924) :rule contraction :premises (t694.t14))
(step t694.t16 (cl @p_969 @p_924) :rule resolution :premises (t694.t8 t694.t15))
(step t694.t17 (cl @p_969 (! (not @p_924) :named @p_928)) :rule implies_neg2)
(step t694.t18 (cl @p_969 @p_969) :rule resolution :premises (t694.t16 t694.t17))
(step t694.t19 (cl @p_969) :rule contraction :premises (t694.t18))
(step t694.t20 (cl @p_968 @p_924) :rule implies :premises (t694.t19))
(step t694.t21 (cl (or @p_110 @p_106)) :rule forall_inst :args (k$ 0))
(step t694.t22 (cl @p_110 @p_106) :rule or :premises (t694.t21))
(step t694.t23 (cl @p_106) :rule resolution :premises (t694.t22 t398))
(step t694.t24 (cl (or @p_190 @p_670)) :rule forall_inst :args (2 @p_6))
(step t694.t25 (cl @p_190 @p_670) :rule or :premises (t694.t24))
(step t694.t26 (cl @p_670) :rule resolution :premises (t694.t25 t226))
(step t694.t27 (cl @p_967) :rule and_intro :premises (t694.t23 t694.a0 t694.t26))
(step t694.t28 (cl @p_924) :rule resolution :premises (t694.t20 t694.t27))
(step t694.t29 (cl (= @p_669 @p_6)) :rule symm :premises (t694.t26))
(step t694.t30 (cl (not @p_791) (not @p_790) @p_787) :rule equiv_pos2)
(step t694.t31 (cl (= @p_788 @p_785)) :rule poly_simp)
(step t694.t32 (cl (= @p_789 @p_786)) :rule cong :premises (t694.t31))
(step t694.t33 (cl @p_791) :rule cong :premises (t694.t32))
(step t694.t34 (cl @p_790 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t694.t35)
(assume t694.t35.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t694.t35.t0 (cl (or @p_255 @p_789)) :rule forall_inst :args (@p_6 2))
(step t694.t35.t1 (cl @p_255 @p_789) :rule or :premises (t694.t35.t0))
(step t694.t35.t2 (cl @p_789) :rule resolution :premises (t694.t35.t1 t694.t35.a0))
(step t694.t35 (cl @p_255 @p_789) :rule subproof :discharge (t694.t35.a0))
(step t694.t36 (cl @p_790 @p_789) :rule resolution :premises (t694.t34 t694.t35))
(step t694.t37 (cl @p_790 (not @p_789)) :rule implies_neg2)
(step t694.t38 (cl @p_790 @p_790) :rule resolution :premises (t694.t36 t694.t37))
(step t694.t39 (cl @p_790) :rule contraction :premises (t694.t38))
(step t694.t40 (cl @p_787) :rule resolution :premises (t694.t30 t694.t33 t694.t39))
(step t694.t41 (cl @p_255 @p_786) :rule implies :premises (t694.t40))
(step t694.t42 (cl @p_786) :rule resolution :premises (t694.t41 a4))
(step t694.t43 (cl @p_801) :rule trans :premises (t694.t29 t694.t42))
(step t694.t44 (cl @p_1427) :rule and_intro :premises (t694.t7 t694.t28 t694.t43 t694.a5 t694.a6))
(step t694 (cl @p_583 @p_671 @p_792 @p_974 @p_532 @p_1052 @p_834 @p_1427) :rule subproof :discharge (t694.a0 t694.a1 t694.a2 t694.a3 t694.a4 t694.a5 t694.a6))
(step t695 (cl (! (not @p_1425) :named @p_1426) @p_524) :rule and_pos :args (0))
(step t696 (cl @p_1426 @p_670) :rule and_pos :args (1))
(step t697 (cl @p_1426 @p_786) :rule and_pos :args (2))
(step t698 (cl @p_1426 @p_58) :rule and_pos :args (3))
(step t699 (cl @p_1426 @p_106) :rule and_pos :args (4))
(step t700 (cl @p_1426 @p_1051) :rule and_pos :args (5))
(step t701 (cl @p_1426 @p_833) :rule and_pos :args (6))
(step t702 (cl @p_1427 @p_1426 @p_1426 @p_1426 @p_1426 @p_1426 @p_1426 @p_1426) :rule resolution :premises (t694 t695 t696 t697 t698 t699 t700 t701))
(step t703 (cl @p_1426 @p_1426 @p_1426 @p_1426 @p_1426 @p_1426 @p_1426 @p_1427) :rule reordering :premises (t702))
(step t704 (cl @p_1426 @p_1427) :rule contraction :premises (t703))
(step t705 (cl @p_1437 @p_1427) :rule resolution :premises (t693 t704))
(step t706 (cl @p_1437 (! (not @p_1427) :named @p_1428)) :rule implies_neg2)
(step t707 (cl @p_1437 @p_1437) :rule resolution :premises (t705 t706))
(step t708 (cl @p_1437) :rule contraction :premises (t707))
(step t709 (cl @p_1426 @p_1427) :rule implies :premises (t708))
(step t710 (cl (! (=> @p_1427 false) :named @p_1429) @p_1427) :rule implies_neg1)
(anchor :step t711)
(assume t711.a0 @p_923)
(assume t711.a1 @p_924)
(assume t711.a2 @p_801)
(assume t711.a3 @p_1051)
(assume t711.a4 @p_833)
(step t711.t0 (cl (! (not (! (= (! (< @p_105 2) :named @p_846) @p_834) :named @p_866)) :named @p_868) (! (not @p_846) :named @p_869) @p_834) :rule equiv_pos2)
(step t711.t1 (cl @p_866) :rule rare_rewrite :args ("arith-elim-lt" @p_105 2))
(step t711.t2 (cl (! (not (! (= @p_834 @p_846) :named @p_865)) :named @p_867) (! (not @p_834) :named @p_838) @p_846) :rule equiv_pos2)
(step t711.t3 (cl @p_865) :rule symm :premises (t711.t1))
(step t711.t4 (cl (! (=> @p_833 false) :named @p_847) @p_833) :rule implies_neg1)
(anchor :step t711.t5)
(assume t711.t5.a0 @p_833)
(step t711.t5.t0 (cl (not (! (= (! (< (! (+ (! (* -1 @p_105) :named @p_852) @p_8 @p_799 (! (* -1 (! (+ @p_668 @p_57 @p_545 @p_544) :named @p_932)) :named @p_1025) @p_57) :named @p_1431) (! (+ (! (* -1 2) :named @p_850) 1 0 @p_297 1) :named @p_1430)) :named @p_1432) false) :named @p_1433)) (not @p_1432) false) :rule equiv_pos2)
(step t711.t5.t1 (cl (= @p_1432 (! (not (! (>= @p_1431 @p_1430) :named @p_1434)) :named @p_1435))) :rule rare_rewrite :args ("arith-elim-lt" @p_1431 @p_1430))
(step t711.t5.t2 (cl (= @p_1431 (! (+ @p_104 @p_103 @p_544 @p_545 @p_11 @p_8 (! (* 0 @p_57) :named @p_722) (! (* 0 @p_668) :named @p_721)) :named @p_1290))) :rule poly_simp)
(step t711.t5.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t711.t5.t4 (cl (= @p_721 0)) :rule poly_simp)
(step t711.t5.t5 (cl (= @p_1290 (! (+ @p_104 @p_103 @p_544 @p_545 @p_11 @p_8 0 0) :named @p_1291))) :rule cong :premises (t711.t5.t3 t711.t5.t4))
(step t711.t5.t6 (cl (= @p_1291 0)) :rule poly_simp)
(step t711.t5.t7 (cl (= @p_1290 0)) :rule trans :premises (t711.t5.t5 t711.t5.t6))
(step t711.t5.t8 (cl (= @p_1431 0)) :rule trans :premises (t711.t5.t2 t711.t5.t7))
(step t711.t5.t9 (cl (= @p_850 -2)) :rule evaluate)
(step t711.t5.t10 (cl (= 1 1)) :rule refl)
(step t711.t5.t11 (cl (= @p_297 0)) :rule evaluate)
(step t711.t5.t12 (cl (= @p_1430 (! (+ -2 1 0 0 1) :named @p_1436))) :rule cong :premises (t711.t5.t9 t711.t5.t10 t604 t711.t5.t11 t711.t5.t10))
(step t711.t5.t13 (cl (= @p_1436 0)) :rule evaluate)
(step t711.t5.t14 (cl (= @p_1430 0)) :rule trans :premises (t711.t5.t12 t711.t5.t13))
(step t711.t5.t15 (cl (= @p_1434 @p_366)) :rule cong :premises (t711.t5.t8 t711.t5.t14))
(step t711.t5.t16 (cl (= @p_366 true)) :rule evaluate)
(step t711.t5.t17 (cl (= @p_1434 true)) :rule trans :premises (t711.t5.t15 t711.t5.t16))
(step t711.t5.t18 (cl (= @p_1435 @p_365)) :rule cong :premises (t711.t5.t17))
(step t711.t5.t19 (cl (= @p_365 false)) :rule evaluate)
(step t711.t5.t20 (cl (= @p_1435 false)) :rule trans :premises (t711.t5.t18 t711.t5.t19))
(step t711.t5.t21 (cl @p_1433) :rule trans :premises (t711.t5.t1 t711.t5.t20))
(step t711.t5.t22 (cl (! (not (! (<= @p_852 @p_850) :named @p_856)) :named @p_859) (! (not (! (< @p_8 1) :named @p_1066)) :named @p_1071) (! (not @p_800) :named @p_808) (! (not (! (= @p_1025 @p_297) :named @p_1028)) :named @p_1038) @p_974 @p_1432) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 1/1))
(step t711.t5.t23 (cl (=> (! (and @p_308 @p_833) :named @p_857) @p_856)) :rule la_mult_neg)
(step t711.t5.t24 (cl (! (not @p_857) :named @p_858) @p_856) :rule implies :premises (t711.t5.t23))
(step t711.t5.t25 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t711.t5.t26 (cl (not @p_310) @p_308) :rule equiv1 :premises (t711.t5.t25))
(step t711.t5.t27 (cl @p_310) :rule evaluate)
(step t711.t5.t28 (cl @p_308) :rule resolution :premises (t711.t5.t26 t711.t5.t27))
(step t711.t5.t29 (cl @p_857) :rule and_intro :premises (t711.t5.t28 t711.t5.a0))
(step t711.t5.t30 (cl @p_856) :rule resolution :premises (t711.t5.t24 t711.t5.t29))
(step t711.t5.t31 (cl (! (not (! (= @p_1051 @p_1066) :named @p_1069)) :named @p_1070) @p_1052 @p_1066) :rule equiv_pos2)
(step t711.t5.t32 (cl (= @p_1066 @p_1051)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 1))
(step t711.t5.t33 (cl @p_1069) :rule symm :premises (t711.t5.t32))
(step t711.t5.t34 (cl @p_1066) :rule resolution :premises (t711.t5.t31 t711.t5.t33 t711.a3))
(step t711.t5.t35 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t711.t5.t36 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t711.t5.t37 (cl @p_803) :rule poly_simp_rel :premises (t711.t5.t36))
(step t711.t5.t38 (cl (= @p_793 @p_800)) :rule symm :premises (t711.t5.t37))
(step t711.t5.t39 (cl @p_802) :rule trans :premises (t655 t711.t5.t38))
(step t711.t5.t40 (cl (or @p_190 @p_670)) :rule forall_inst :args (2 @p_6))
(step t711.t5.t41 (cl @p_190 @p_670) :rule or :premises (t711.t5.t40))
(step t711.t5.t42 (cl @p_670) :rule resolution :premises (t711.t5.t41 t226))
(step t711.t5.t43 (cl (= @p_669 @p_6)) :rule symm :premises (t711.t5.t42))
(step t711.t5.t44 (cl (not @p_791) (not @p_790) @p_787) :rule equiv_pos2)
(step t711.t5.t45 (cl (= @p_788 @p_785)) :rule poly_simp)
(step t711.t5.t46 (cl (= @p_789 @p_786)) :rule cong :premises (t711.t5.t45))
(step t711.t5.t47 (cl @p_791) :rule cong :premises (t711.t5.t46))
(step t711.t5.t48 (cl @p_790 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t711.t5.t49)
(assume t711.t5.t49.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t711.t5.t49.t0 (cl (or @p_255 @p_789)) :rule forall_inst :args (@p_6 2))
(step t711.t5.t49.t1 (cl @p_255 @p_789) :rule or :premises (t711.t5.t49.t0))
(step t711.t5.t49.t2 (cl @p_789) :rule resolution :premises (t711.t5.t49.t1 t711.t5.t49.a0))
(step t711.t5.t49 (cl @p_255 @p_789) :rule subproof :discharge (t711.t5.t49.a0))
(step t711.t5.t50 (cl @p_790 @p_789) :rule resolution :premises (t711.t5.t48 t711.t5.t49))
(step t711.t5.t51 (cl @p_790 (not @p_789)) :rule implies_neg2)
(step t711.t5.t52 (cl @p_790 @p_790) :rule resolution :premises (t711.t5.t50 t711.t5.t51))
(step t711.t5.t53 (cl @p_790) :rule contraction :premises (t711.t5.t52))
(step t711.t5.t54 (cl @p_787) :rule resolution :premises (t711.t5.t44 t711.t5.t47 t711.t5.t53))
(step t711.t5.t55 (cl @p_255 @p_786) :rule implies :premises (t711.t5.t54))
(step t711.t5.t56 (cl @p_786) :rule resolution :premises (t711.t5.t55 a4))
(step t711.t5.t57 (cl @p_801) :rule trans :premises (t711.t5.t43 t711.t5.t56))
(step t711.t5.t58 (cl @p_800) :rule resolution :premises (t711.t5.t35 t711.t5.t39 t711.t5.t57))
(step t711.t5.t59 (cl (=> (! (and @p_308 (! (= @p_932 0) :named @p_940)) :named @p_1029) @p_1028)) :rule la_mult_neg)
(step t711.t5.t60 (cl (! (not @p_1029) :named @p_1030) @p_1028) :rule implies :premises (t711.t5.t59))
(step t711.t5.t61 (cl (! (not (! (= @p_924 @p_940) :named @p_942)) :named @p_946) @p_928 @p_940) :rule equiv_pos2)
(step t711.t5.t62 (cl (= (* 1 (- @p_669 @p_105)) (! (* 1 (- @p_668 (! (+ (! (* -1 @p_57) :named @p_689) @p_104 @p_103) :named @p_943))) :named @p_945))) :rule poly_simp)
(step t711.t5.t63 (cl (= @p_924 (! (= @p_668 @p_943) :named @p_944))) :rule poly_simp_rel :premises (t711.t5.t62))
(step t711.t5.t64 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t711.t5.t65 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t711.t5.t64))
(step t711.t5.t66 (cl (= @p_944 @p_940)) :rule symm :premises (t711.t5.t65))
(step t711.t5.t67 (cl @p_942) :rule trans :premises (t711.t5.t63 t711.t5.t66))
(step t711.t5.t68 (cl @p_940) :rule resolution :premises (t711.t5.t61 t711.t5.t67 t711.a1))
(step t711.t5.t69 (cl @p_1029) :rule and_intro :premises (t711.t5.t28 t711.t5.t68))
(step t711.t5.t70 (cl @p_1028) :rule resolution :premises (t711.t5.t60 t711.t5.t69))
(step t711.t5.t71 (cl @p_58) :rule symm :premises (t711.a0))
(step t711.t5.t72 (cl @p_1432) :rule resolution :premises (t711.t5.t22 t711.t5.t30 t711.t5.t34 t711.t5.t58 t711.t5.t70 t711.t5.t71))
(step t711.t5.t73 (cl false) :rule resolution :premises (t711.t5.t0 t711.t5.t21 t711.t5.t72))
(step t711.t5 (cl @p_834 false) :rule subproof :discharge (t711.t5.a0))
(step t711.t6 (cl @p_847 false) :rule resolution :premises (t711.t4 t711.t5))
(step t711.t7 (cl @p_847 @p_212) :rule implies_neg2)
(step t711.t8 (cl @p_847 @p_847) :rule resolution :premises (t711.t6 t711.t7))
(step t711.t9 (cl @p_847) :rule contraction :premises (t711.t8))
(step t711.t10 (cl (! (= @p_847 @p_834) :named @p_849)) :rule implies_simplify)
(step t711.t11 (cl (! (not @p_847) :named @p_848) @p_834) :rule equiv1 :premises (t711.t10))
(step t711.t12 (cl @p_834) :rule resolution :premises (t711.t9 t711.t11))
(step t711.t13 (cl @p_846) :rule resolution :premises (t711.t2 t711.t3 t711.t12))
(step t711.t14 (cl @p_834) :rule resolution :premises (t711.t0 t711.t1 t711.t13))
(step t711.t15 (cl) :rule resolution :premises (t711.a4 t711.t14))
(step t711 (cl @p_929 @p_928 @p_806 @p_1052 @p_834 false) :rule subproof :discharge (t711.a0 t711.a1 t711.a2 t711.a3 t711.a4))
(step t712 (cl @p_1428 @p_923) :rule and_pos :args (0))
(step t713 (cl @p_1428 @p_924) :rule and_pos :args (1))
(step t714 (cl @p_1428 @p_801) :rule and_pos :args (2))
(step t715 (cl @p_1428 @p_1051) :rule and_pos :args (3))
(step t716 (cl @p_1428 @p_833) :rule and_pos :args (4))
(step t717 (cl false @p_1428 @p_1428 @p_1428 @p_1428 @p_1428) :rule resolution :premises (t711 t712 t713 t714 t715 t716))
(step t718 (cl @p_1428 @p_1428 @p_1428 @p_1428 @p_1428 false) :rule reordering :premises (t717))
(step t719 (cl @p_1428 false) :rule contraction :premises (t718))
(step t720 (cl @p_1429 false) :rule resolution :premises (t710 t719))
(step t721 (cl @p_1429 @p_212) :rule implies_neg2)
(step t722 (cl @p_1429 @p_1429) :rule resolution :premises (t720 t721))
(step t723 (cl @p_1429) :rule contraction :premises (t722))
(step t724 (cl (= @p_1429 @p_1428)) :rule implies_simplify)
(step t725 (cl (not @p_1429) @p_1428) :rule equiv1 :premises (t724))
(step t726 (cl @p_1428) :rule resolution :premises (t723 t725))
(step t727 (cl @p_1426) :rule resolution :premises (t709 t726))
(step t728 (cl @p_583 @p_671 @p_792 @p_974 @p_532 @p_1052 @p_834) :rule not_and :premises (t727))
(step t729 (cl @p_1424 (! (not @p_583) :named @p_589)) :rule or_neg :args (0))
(step t730 (cl @p_1424 (! (not @p_671) :named @p_677)) :rule or_neg :args (1))
(step t731 (cl @p_1424 (! (not @p_792) :named @p_1017)) :rule or_neg :args (2))
(step t732 (cl @p_1424 (! (not @p_974) :named @p_1016)) :rule or_neg :args (3))
(step t733 (cl @p_1424 @p_538) :rule or_neg :args (4))
(step t734 (cl @p_1424 (! (not @p_1052) :named @p_1054)) :rule or_neg :args (5))
(step t735 (cl @p_1424 @p_838) :rule or_neg :args (6))
(step t736 (cl @p_1424 @p_1424 @p_1424 @p_1424 @p_1424 @p_1424 @p_1424) :rule resolution :premises (t728 t729 t730 t731 t732 t733 t734 t735))
(step t737 (cl @p_1424) :rule contraction :premises (t736))
(step t738 (cl @p_1423) :rule resolution :premises (t689 t692 t737))
(step t739 (cl @p_583 @p_671 @p_792 @p_974 @p_532 @p_1049 @p_834) :rule or :premises (t738))
(step t740 (cl (or @p_110 @p_106)) :rule forall_inst :args (k$ 0))
(step t741 (cl @p_110 @p_106) :rule or :premises (t740))
(step t742 (cl @p_106) :rule resolution :premises (t741 t398))
(step t743 (cl (not @p_791) (not @p_790) @p_787) :rule equiv_pos2)
(step t744 (cl (= @p_788 @p_785)) :rule poly_simp)
(step t745 (cl (= @p_789 @p_786)) :rule cong :premises (t744))
(step t746 (cl @p_791) :rule cong :premises (t745))
(step t747 (cl @p_790 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t748)
(assume t748.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (divide$ ?v0 ?v1) ?v1) (modulo$ ?v0 ?v1)))))
(step t748.t0 (cl (or @p_255 @p_789)) :rule forall_inst :args (@p_6 2))
(step t748.t1 (cl @p_255 @p_789) :rule or :premises (t748.t0))
(step t748.t2 (cl @p_789) :rule resolution :premises (t748.t1 t748.a0))
(step t748 (cl @p_255 @p_789) :rule subproof :discharge (t748.a0))
(step t749 (cl @p_790 @p_789) :rule resolution :premises (t747 t748))
(step t750 (cl @p_790 (not @p_789)) :rule implies_neg2)
(step t751 (cl @p_790 @p_790) :rule resolution :premises (t749 t750))
(step t752 (cl @p_790) :rule contraction :premises (t751))
(step t753 (cl @p_787) :rule resolution :premises (t743 t746 t752))
(step t754 (cl @p_255 @p_786) :rule implies :premises (t753))
(step t755 (cl @p_786) :rule resolution :premises (t754 a4))
(step t756 (cl (or @p_190 @p_670)) :rule forall_inst :args (2 @p_6))
(step t757 (cl @p_190 @p_670) :rule or :premises (t756))
(step t758 (cl @p_670) :rule resolution :premises (t757 t226))
(step t759 (cl (not (! (= (! (or @p_583 @p_671 @p_673 @p_974 @p_532 @p_916) :named @p_1390) (! (or @p_583 @p_671 @p_112 @p_974 @p_532 @p_913) :named @p_1389)) :named @p_1422)) (not @p_1390) @p_1389) :rule equiv_pos2)
(step t760 (cl (= @p_974 @p_974)) :rule refl)
(step t761 (cl (= @p_916 @p_913)) :rule rare_rewrite :args ("bool-double-not-elim" @p_913))
(step t762 (cl @p_1422) :rule cong :premises (t38 t760 t40 t761))
(step t763 (cl (! (=> (! (and @p_524 @p_670 @p_113 @p_58 @p_106 @p_915) :named @p_1391) (! (and (! (= @p_6 @p_105) :named @p_592) @p_924 @p_923 @p_915 @p_113) :named @p_1393)) :named @p_1421) @p_1391) :rule implies_neg1)
(anchor :step t764)
(assume t764.a0 @p_524)
(assume t764.a1 @p_670)
(assume t764.a2 @p_113)
(assume t764.a3 @p_58)
(assume t764.a4 @p_106)
(assume t764.a5 @p_915)
(step t764.t0 (cl (! (=> (! (and @p_106 @p_524) :named @p_628) @p_592) :named @p_631) @p_628) :rule implies_neg1)
(anchor :step t764.t1)
(assume t764.t1.a0 @p_106)
(assume t764.t1.a1 @p_524)
(step t764.t1.t0 (cl @p_527) :rule symm :premises (t764.t1.a1))
(step t764.t1.t1 (cl @p_592) :rule trans :premises (t764.t1.t0 t742))
(step t764.t1 (cl @p_532 @p_583 @p_592) :rule subproof :discharge (t764.t1.a0 t764.t1.a1))
(step t764.t2 (cl (! (not @p_628) :named @p_630) @p_106) :rule and_pos :args (0))
(step t764.t3 (cl @p_630 @p_524) :rule and_pos :args (1))
(step t764.t4 (cl @p_592 @p_630 @p_630) :rule resolution :premises (t764.t1 t764.t2 t764.t3))
(step t764.t5 (cl @p_630 @p_630 @p_592) :rule reordering :premises (t764.t4))
(step t764.t6 (cl @p_630 @p_592) :rule contraction :premises (t764.t5))
(step t764.t7 (cl @p_631 @p_592) :rule resolution :premises (t764.t0 t764.t6))
(step t764.t8 (cl @p_631 (! (not @p_592) :named @p_596)) :rule implies_neg2)
(step t764.t9 (cl @p_631 @p_631) :rule resolution :premises (t764.t7 t764.t8))
(step t764.t10 (cl @p_631) :rule contraction :premises (t764.t9))
(step t764.t11 (cl @p_630 @p_592) :rule implies :premises (t764.t10))
(step t764.t12 (cl @p_628) :rule and_intro :premises (t742 t764.a0))
(step t764.t13 (cl @p_592) :rule resolution :premises (t764.t11 t764.t12))
(step t764.t14 (cl @p_969 @p_967) :rule implies_neg1)
(anchor :step t764.t15)
(assume t764.t15.a0 @p_106)
(assume t764.t15.a1 @p_524)
(assume t764.t15.a2 @p_670)
(step t764.t15.t0 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t764.t15.t1 (cl @p_527) :rule symm :premises (t764.t15.a1))
(step t764.t15.t2 (cl @p_924) :rule trans :premises (t764.t15.t0 t764.t15.t1 t742))
(step t764.t15 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t764.t15.a0 t764.t15.a1 t764.t15.a2))
(step t764.t16 (cl @p_968 @p_106) :rule and_pos :args (0))
(step t764.t17 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t764.t18 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t764.t19 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t764.t15 t764.t16 t764.t17 t764.t18))
(step t764.t20 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t764.t19))
(step t764.t21 (cl @p_968 @p_924) :rule contraction :premises (t764.t20))
(step t764.t22 (cl @p_969 @p_924) :rule resolution :premises (t764.t14 t764.t21))
(step t764.t23 (cl @p_969 @p_928) :rule implies_neg2)
(step t764.t24 (cl @p_969 @p_969) :rule resolution :premises (t764.t22 t764.t23))
(step t764.t25 (cl @p_969) :rule contraction :premises (t764.t24))
(step t764.t26 (cl @p_968 @p_924) :rule implies :premises (t764.t25))
(step t764.t27 (cl @p_967) :rule and_intro :premises (t742 t764.a0 t758))
(step t764.t28 (cl @p_924) :rule resolution :premises (t764.t26 t764.t27))
(step t764.t29 (cl @p_1047 @p_58) :rule implies_neg1)
(anchor :step t764.t30)
(assume t764.t30.a0 @p_58)
(step t764.t30.t0 (cl @p_923) :rule symm :premises (t764.t30.a0))
(step t764.t30 (cl @p_974 @p_923) :rule subproof :discharge (t764.t30.a0))
(step t764.t31 (cl @p_1047 @p_923) :rule resolution :premises (t764.t29 t764.t30))
(step t764.t32 (cl @p_1047 @p_929) :rule implies_neg2)
(step t764.t33 (cl @p_1047 @p_1047) :rule resolution :premises (t764.t31 t764.t32))
(step t764.t34 (cl @p_1047) :rule contraction :premises (t764.t33))
(step t764.t35 (cl @p_974 @p_923) :rule implies :premises (t764.t34))
(step t764.t36 (cl @p_923) :rule resolution :premises (t764.t35 t764.a3))
(step t764.t37 (cl @p_1393) :rule and_intro :premises (t764.t13 t764.t28 t764.t36 t764.a5 t764.a2))
(step t764 (cl @p_583 @p_671 @p_673 @p_974 @p_532 @p_916 @p_1393) :rule subproof :discharge (t764.a0 t764.a1 t764.a2 t764.a3 t764.a4 t764.a5))
(step t765 (cl (! (not @p_1391) :named @p_1392) @p_524) :rule and_pos :args (0))
(step t766 (cl @p_1392 @p_670) :rule and_pos :args (1))
(step t767 (cl @p_1392 @p_113) :rule and_pos :args (2))
(step t768 (cl @p_1392 @p_58) :rule and_pos :args (3))
(step t769 (cl @p_1392 @p_106) :rule and_pos :args (4))
(step t770 (cl @p_1392 @p_915) :rule and_pos :args (5))
(step t771 (cl @p_1393 @p_1392 @p_1392 @p_1392 @p_1392 @p_1392 @p_1392) :rule resolution :premises (t764 t765 t766 t767 t768 t769 t770))
(step t772 (cl @p_1392 @p_1392 @p_1392 @p_1392 @p_1392 @p_1392 @p_1393) :rule reordering :premises (t771))
(step t773 (cl @p_1392 @p_1393) :rule contraction :premises (t772))
(step t774 (cl @p_1421 @p_1393) :rule resolution :premises (t763 t773))
(step t775 (cl @p_1421 (! (not @p_1393) :named @p_1394)) :rule implies_neg2)
(step t776 (cl @p_1421 @p_1421) :rule resolution :premises (t774 t775))
(step t777 (cl @p_1421) :rule contraction :premises (t776))
(step t778 (cl @p_1392 @p_1393) :rule implies :premises (t777))
(step t779 (cl (! (=> @p_1393 false) :named @p_1395) @p_1393) :rule implies_neg1)
(anchor :step t780)
(assume t780.a0 @p_592)
(assume t780.a1 @p_924)
(assume t780.a2 @p_923)
(assume t780.a3 @p_915)
(assume t780.a4 @p_113)
(step t780.t0 (cl @p_715 @p_1396) :rule la_generic :args (1/1 1/1))
(step t780.t1 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t780.t2 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t780.t3 (cl @p_703) :rule symm :premises (t780.t2))
(step t780.t4 (cl @p_700) :rule resolution :premises (t780.t1 t780.t3 t780.a4))
(step t780.t5 (cl @p_1396) :rule resolution :premises (t780.t0 t780.t4))
(step t780.t6 (cl @p_1419 @p_1420 @p_1397) :rule equiv_pos2)
(step t780.t7 (cl (= @p_1398 @p_1416)) :rule rare_rewrite :args ("arith-elim-gt" @p_111 0))
(step t780.t8 (cl (= @p_1396 @p_1415)) :rule rare_rewrite :args ("arith-elim-leq" @p_111 0))
(step t780.t9 (cl (= @p_1415 @p_1396)) :rule symm :premises (t780.t8))
(step t780.t10 (cl (= @p_1416 @p_1397)) :rule cong :premises (t780.t9))
(step t780.t11 (cl @p_1414) :rule trans :premises (t780.t7 t780.t10))
(step t780.t12 (cl @p_1417 @p_1418 @p_1398) :rule equiv_pos2)
(step t780.t13 (cl (= @p_1396 @p_1413)) :rule rare_rewrite :args ("arith-leq-norm" @p_111 0))
(step t780.t14 (cl (= @p_1411 1)) :rule evaluate)
(step t780.t15 (cl (= @p_1412 @p_112)) :rule cong :premises (t780.t14))
(step t780.t16 (cl (= @p_1413 @p_113)) :rule cong :premises (t780.t15))
(step t780.t17 (cl (= @p_1396 @p_113)) :rule trans :premises (t780.t13 t780.t16))
(step t780.t18 (cl (= @p_1397 @p_673)) :rule cong :premises (t780.t17))
(step t780.t19 (cl (= @p_1397 @p_112)) :rule trans :premises (t780.t18 t38))
(step t780.t20 (cl (= @p_1398 @p_112)) :rule trans :premises (t780.t11 t780.t19))
(step t780.t21 (cl (= @p_112 @p_1398)) :rule symm :premises (t780.t20))
(step t780.t22 (cl @p_1410) :rule trans :premises (t780.t19 t780.t21))
(step t780.t23 (cl @p_1399 @p_1396) :rule implies_neg1)
(anchor :step t780.t24)
(assume t780.t24.a0 @p_1396)
(step t780.t24.t0 (cl (not (! (= (! (< (! (+ @p_111 @p_912 @p_689 @p_932 (! (* -1 (! (+ @p_6 @p_545 @p_544) :named @p_601)) :named @p_602)) :named @p_1403) (! (+ 0 1 @p_298 0 @p_297) :named @p_1402)) :named @p_1404) false) :named @p_1406)) (not @p_1404) false) :rule equiv_pos2)
(step t780.t24.t1 (cl (= @p_1404 (! (not (! (>= @p_1403 @p_1402) :named @p_1407)) :named @p_1408))) :rule rare_rewrite :args ("arith-elim-lt" @p_1403 @p_1402))
(step t780.t24.t2 (cl (= @p_1403 (! (+ (! (* 0 @p_104) :named @p_619) (! (* 0 @p_103) :named @p_618) @p_689 @p_690 @p_57 @p_668 @p_46 @p_7 @p_617) :named @p_1385))) :rule poly_simp)
(step t780.t24.t3 (cl (= @p_619 0)) :rule poly_simp)
(step t780.t24.t4 (cl (= @p_618 0)) :rule poly_simp)
(step t780.t24.t5 (cl (= @p_689 @p_689)) :rule refl)
(step t780.t24.t6 (cl (= @p_690 @p_690)) :rule refl)
(step t780.t24.t7 (cl (= @p_57 @p_57)) :rule refl)
(step t780.t24.t8 (cl (= @p_668 @p_668)) :rule refl)
(step t780.t24.t9 (cl @p_168) :rule refl)
(step t780.t24.t10 (cl @p_167) :rule refl)
(step t780.t24.t11 (cl (= @p_617 0)) :rule poly_simp)
(step t780.t24.t12 (cl (= @p_1385 (! (+ 0 0 @p_689 @p_690 @p_57 @p_668 @p_46 @p_7 0) :named @p_1386))) :rule cong :premises (t780.t24.t3 t780.t24.t4 t780.t24.t5 t780.t24.t6 t780.t24.t7 t780.t24.t8 t780.t24.t9 t780.t24.t10 t780.t24.t11))
(step t780.t24.t13 (cl (= @p_1386 0)) :rule poly_simp)
(step t780.t24.t14 (cl (= @p_1385 0)) :rule trans :premises (t780.t24.t12 t780.t24.t13))
(step t780.t24.t15 (cl (= @p_1403 0)) :rule trans :premises (t780.t24.t2 t780.t24.t14))
(step t780.t24.t16 (cl (= @p_298 -1)) :rule evaluate)
(step t780.t24.t17 (cl (= @p_297 0)) :rule evaluate)
(step t780.t24.t18 (cl (= @p_1402 (! (+ 0 1 -1 0 0) :named @p_1409))) :rule cong :premises (t780.t24.t16 t604 t780.t24.t17))
(step t780.t24.t19 (cl (= @p_1409 0)) :rule evaluate)
(step t780.t24.t20 (cl (= @p_1402 0)) :rule trans :premises (t780.t24.t18 t780.t24.t19))
(step t780.t24.t21 (cl (= @p_1407 @p_366)) :rule cong :premises (t780.t24.t15 t780.t24.t20))
(step t780.t24.t22 (cl (= @p_366 true)) :rule evaluate)
(step t780.t24.t23 (cl (= @p_1407 true)) :rule trans :premises (t780.t24.t21 t780.t24.t22))
(step t780.t24.t24 (cl (= @p_1408 @p_365)) :rule cong :premises (t780.t24.t23))
(step t780.t24.t25 (cl (= @p_365 false)) :rule evaluate)
(step t780.t24.t26 (cl (= @p_1408 false)) :rule trans :premises (t780.t24.t24 t780.t24.t25))
(step t780.t24.t27 (cl @p_1406) :rule trans :premises (t780.t24.t1 t780.t24.t26))
(step t780.t24.t28 (cl @p_1397 (! (not (! (< @p_912 1) :named @p_935)) :named @p_956) (! (not (! (= @p_689 @p_298) :named @p_947)) :named @p_954) (! (not @p_940) :named @p_955) (! (not (! (= @p_602 @p_297) :named @p_605)) :named @p_612) @p_1404) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 1/1))
(step t780.t24.t29 (cl (! (not (! (= @p_915 @p_935) :named @p_938)) :named @p_939) @p_916 @p_935) :rule equiv_pos2)
(step t780.t24.t30 (cl (= @p_935 @p_915)) :rule rare_rewrite :args ("arith-elim-lt" @p_912 1))
(step t780.t24.t31 (cl @p_938) :rule symm :premises (t780.t24.t30))
(step t780.t24.t32 (cl @p_935) :rule resolution :premises (t780.t24.t29 t780.t24.t31 t780.a3))
(step t780.t24.t33 (cl (=> (! (and @p_308 @p_58) :named @p_948) @p_947)) :rule la_mult_neg)
(step t780.t24.t34 (cl (! (not @p_948) :named @p_950) @p_947) :rule implies :premises (t780.t24.t33))
(step t780.t24.t35 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t780.t24.t36 (cl (not @p_310) @p_308) :rule equiv1 :premises (t780.t24.t35))
(step t780.t24.t37 (cl @p_310) :rule evaluate)
(step t780.t24.t38 (cl @p_308) :rule resolution :premises (t780.t24.t36 t780.t24.t37))
(step t780.t24.t39 (cl @p_58) :rule symm :premises (t780.a2))
(step t780.t24.t40 (cl @p_948) :rule and_intro :premises (t780.t24.t38 t780.t24.t39))
(step t780.t24.t41 (cl @p_947) :rule resolution :premises (t780.t24.t34 t780.t24.t40))
(step t780.t24.t42 (cl @p_946 @p_928 @p_940) :rule equiv_pos2)
(step t780.t24.t43 (cl (= (* 1 (- @p_669 @p_105)) @p_945)) :rule poly_simp)
(step t780.t24.t44 (cl (= @p_924 @p_944)) :rule poly_simp_rel :premises (t780.t24.t43))
(step t780.t24.t45 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t780.t24.t46 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t780.t24.t45))
(step t780.t24.t47 (cl (= @p_944 @p_940)) :rule symm :premises (t780.t24.t46))
(step t780.t24.t48 (cl @p_942) :rule trans :premises (t780.t24.t44 t780.t24.t47))
(step t780.t24.t49 (cl @p_940) :rule resolution :premises (t780.t24.t42 t780.t24.t48 t780.a1))
(step t780.t24.t50 (cl (=> (! (and @p_308 (! (= @p_601 0) :named @p_606)) :named @p_607) @p_605)) :rule la_mult_neg)
(step t780.t24.t51 (cl (! (not @p_607) :named @p_611) @p_605) :rule implies :premises (t780.t24.t50))
(step t780.t24.t52 (cl (! (not (! (= @p_592 @p_606) :named @p_609)) :named @p_610) @p_596 @p_606) :rule equiv_pos2)
(step t780.t24.t53 (cl (= (* 1 (- @p_601 0)) (* 1 (- @p_6 @p_105)))) :rule poly_simp)
(step t780.t24.t54 (cl (= @p_606 @p_592)) :rule poly_simp_rel :premises (t780.t24.t53))
(step t780.t24.t55 (cl @p_609) :rule symm :premises (t780.t24.t54))
(step t780.t24.t56 (cl @p_606) :rule resolution :premises (t780.t24.t52 t780.t24.t55 t780.a0))
(step t780.t24.t57 (cl @p_607) :rule and_intro :premises (t780.t24.t38 t780.t24.t56))
(step t780.t24.t58 (cl @p_605) :rule resolution :premises (t780.t24.t51 t780.t24.t57))
(step t780.t24.t59 (cl @p_1404) :rule resolution :premises (t780.t24.t28 t780.t24.a0 t780.t24.t32 t780.t24.t41 t780.t24.t49 t780.t24.t58))
(step t780.t24.t60 (cl false) :rule resolution :premises (t780.t24.t0 t780.t24.t27 t780.t24.t59))
(step t780.t24 (cl @p_1397 false) :rule subproof :discharge (t780.t24.a0))
(step t780.t25 (cl @p_1399 false) :rule resolution :premises (t780.t23 t780.t24))
(step t780.t26 (cl @p_1399 @p_212) :rule implies_neg2)
(step t780.t27 (cl @p_1399 @p_1399) :rule resolution :premises (t780.t25 t780.t26))
(step t780.t28 (cl @p_1399) :rule contraction :premises (t780.t27))
(step t780.t29 (cl @p_1401) :rule implies_simplify)
(step t780.t30 (cl @p_1400 @p_1397) :rule equiv1 :premises (t780.t29))
(step t780.t31 (cl @p_1397) :rule resolution :premises (t780.t28 t780.t30))
(step t780.t32 (cl @p_1398) :rule resolution :premises (t780.t12 t780.t22 t780.t31))
(step t780.t33 (cl @p_1397) :rule resolution :premises (t780.t6 t780.t11 t780.t32))
(step t780.t34 (cl) :rule resolution :premises (t780.t5 t780.t33))
(step t780 (cl @p_596 @p_928 @p_929 @p_916 @p_673 false) :rule subproof :discharge (t780.a0 t780.a1 t780.a2 t780.a3 t780.a4))
(step t781 (cl @p_1394 @p_592) :rule and_pos :args (0))
(step t782 (cl @p_1394 @p_924) :rule and_pos :args (1))
(step t783 (cl @p_1394 @p_923) :rule and_pos :args (2))
(step t784 (cl @p_1394 @p_915) :rule and_pos :args (3))
(step t785 (cl @p_1394 @p_113) :rule and_pos :args (4))
(step t786 (cl false @p_1394 @p_1394 @p_1394 @p_1394 @p_1394) :rule resolution :premises (t780 t781 t782 t783 t784 t785))
(step t787 (cl @p_1394 @p_1394 @p_1394 @p_1394 @p_1394 false) :rule reordering :premises (t786))
(step t788 (cl @p_1394 false) :rule contraction :premises (t787))
(step t789 (cl @p_1395 false) :rule resolution :premises (t779 t788))
(step t790 (cl @p_1395 @p_212) :rule implies_neg2)
(step t791 (cl @p_1395 @p_1395) :rule resolution :premises (t789 t790))
(step t792 (cl @p_1395) :rule contraction :premises (t791))
(step t793 (cl (= @p_1395 @p_1394)) :rule implies_simplify)
(step t794 (cl (not @p_1395) @p_1394) :rule equiv1 :premises (t793))
(step t795 (cl @p_1394) :rule resolution :premises (t792 t794))
(step t796 (cl @p_1392) :rule resolution :premises (t778 t795))
(step t797 (cl @p_583 @p_671 @p_673 @p_974 @p_532 @p_916) :rule not_and :premises (t796))
(step t798 (cl @p_1390 @p_589) :rule or_neg :args (0))
(step t799 (cl @p_1390 @p_677) :rule or_neg :args (1))
(step t800 (cl @p_1390 @p_676) :rule or_neg :args (2))
(step t801 (cl @p_1390 @p_1016) :rule or_neg :args (3))
(step t802 (cl @p_1390 @p_538) :rule or_neg :args (4))
(step t803 (cl @p_1390 (! (not @p_916) :named @p_918)) :rule or_neg :args (5))
(step t804 (cl @p_1390 @p_1390 @p_1390 @p_1390 @p_1390 @p_1390) :rule resolution :premises (t797 t798 t799 t800 t801 t802 t803))
(step t805 (cl @p_1390) :rule contraction :premises (t804))
(step t806 (cl @p_1389) :rule resolution :premises (t759 t762 t805))
(step t807 (cl @p_583 @p_671 @p_112 @p_974 @p_532 @p_913) :rule or :premises (t806))
(step t808 (cl @p_583 @p_112 @p_671 @p_974 @p_532 @p_913) :rule reordering :premises (t807))
(step t809 (cl (not (! (= (! (or @p_583 (! (not (! (>= k$ 1) :named @p_564)) :named @p_566) @p_671 @p_792 @p_974 (! (not @p_16) :named @p_1013) @p_532) :named @p_1014) (! (or @p_583 @p_566 @p_671 @p_792 @p_974 @p_15 @p_532) :named @p_1012)) :named @p_1048)) (not @p_1014) @p_1012) :rule equiv_pos2)
(step t810 (cl (= @p_1013 @p_15)) :rule rare_rewrite :args ("bool-double-not-elim" @p_15))
(step t811 (cl @p_1048) :rule cong :premises (t810 t40))
(step t812 (cl (! (=> (! (and @p_524 @p_564 @p_670 @p_786 @p_58 @p_16 @p_106) :named @p_1018) (! (and @p_106 @p_801 @p_924 @p_923 @p_16 @p_564) :named @p_1020)) :named @p_1045) @p_1018) :rule implies_neg1)
(anchor :step t813)
(assume t813.a0 @p_524)
(assume t813.a1 @p_564)
(assume t813.a2 @p_670)
(assume t813.a3 @p_786)
(assume t813.a4 @p_58)
(assume t813.a5 @p_16)
(assume t813.a6 @p_106)
(step t813.t0 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t813.t1 (cl @p_801) :rule trans :premises (t813.t0 t755))
(step t813.t2 (cl @p_969 @p_967) :rule implies_neg1)
(anchor :step t813.t3)
(assume t813.t3.a0 @p_106)
(assume t813.t3.a1 @p_524)
(assume t813.t3.a2 @p_670)
(step t813.t3.t0 (cl @p_527) :rule symm :premises (t813.t3.a1))
(step t813.t3.t1 (cl @p_924) :rule trans :premises (t813.t0 t813.t3.t0 t742))
(step t813.t3 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t813.t3.a0 t813.t3.a1 t813.t3.a2))
(step t813.t4 (cl @p_968 @p_106) :rule and_pos :args (0))
(step t813.t5 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t813.t6 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t813.t7 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t813.t3 t813.t4 t813.t5 t813.t6))
(step t813.t8 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t813.t7))
(step t813.t9 (cl @p_968 @p_924) :rule contraction :premises (t813.t8))
(step t813.t10 (cl @p_969 @p_924) :rule resolution :premises (t813.t2 t813.t9))
(step t813.t11 (cl @p_969 @p_928) :rule implies_neg2)
(step t813.t12 (cl @p_969 @p_969) :rule resolution :premises (t813.t10 t813.t11))
(step t813.t13 (cl @p_969) :rule contraction :premises (t813.t12))
(step t813.t14 (cl @p_968 @p_924) :rule implies :premises (t813.t13))
(step t813.t15 (cl @p_967) :rule and_intro :premises (t742 t813.a0 t758))
(step t813.t16 (cl @p_924) :rule resolution :premises (t813.t14 t813.t15))
(step t813.t17 (cl @p_1047 @p_58) :rule implies_neg1)
(anchor :step t813.t18)
(assume t813.t18.a0 @p_58)
(step t813.t18.t0 (cl @p_923) :rule symm :premises (t813.t18.a0))
(step t813.t18 (cl @p_974 @p_923) :rule subproof :discharge (t813.t18.a0))
(step t813.t19 (cl @p_1047 @p_923) :rule resolution :premises (t813.t17 t813.t18))
(step t813.t20 (cl @p_1047 @p_929) :rule implies_neg2)
(step t813.t21 (cl @p_1047 @p_1047) :rule resolution :premises (t813.t19 t813.t20))
(step t813.t22 (cl @p_1047) :rule contraction :premises (t813.t21))
(step t813.t23 (cl @p_974 @p_923) :rule implies :premises (t813.t22))
(step t813.t24 (cl @p_923) :rule resolution :premises (t813.t23 t813.a4))
(step t813.t25 (cl @p_1020) :rule and_intro :premises (t742 t813.t1 t813.t16 t813.t24 t813.a5 t813.a1))
(step t813 (cl @p_583 @p_566 @p_671 @p_792 @p_974 @p_1013 @p_532 @p_1020) :rule subproof :discharge (t813.a0 t813.a1 t813.a2 t813.a3 t813.a4 t813.a5 t813.a6))
(step t814 (cl (! (not @p_1018) :named @p_1019) @p_524) :rule and_pos :args (0))
(step t815 (cl @p_1019 @p_564) :rule and_pos :args (1))
(step t816 (cl @p_1019 @p_670) :rule and_pos :args (2))
(step t817 (cl @p_1019 @p_786) :rule and_pos :args (3))
(step t818 (cl @p_1019 @p_58) :rule and_pos :args (4))
(step t819 (cl @p_1019 @p_16) :rule and_pos :args (5))
(step t820 (cl @p_1019 @p_106) :rule and_pos :args (6))
(step t821 (cl @p_1020 @p_1019 @p_1019 @p_1019 @p_1019 @p_1019 @p_1019 @p_1019) :rule resolution :premises (t813 t814 t815 t816 t817 t818 t819 t820))
(step t822 (cl @p_1019 @p_1019 @p_1019 @p_1019 @p_1019 @p_1019 @p_1019 @p_1020) :rule reordering :premises (t821))
(step t823 (cl @p_1019 @p_1020) :rule contraction :premises (t822))
(step t824 (cl @p_1045 @p_1020) :rule resolution :premises (t812 t823))
(step t825 (cl @p_1045 (! (not @p_1020) :named @p_1021)) :rule implies_neg2)
(step t826 (cl @p_1045 @p_1045) :rule resolution :premises (t824 t825))
(step t827 (cl @p_1045) :rule contraction :premises (t826))
(step t828 (cl @p_1019 @p_1020) :rule implies :premises (t827))
(step t829 (cl (! (=> @p_1020 false) :named @p_1022) @p_1020) :rule implies_neg1)
(anchor :step t830)
(assume t830.a0 @p_106)
(assume t830.a1 @p_801)
(assume t830.a2 @p_924)
(assume t830.a3 @p_923)
(assume t830.a4 @p_16)
(assume t830.a5 @p_564)
(step t830.t0 (cl (not (! (= (! (< k$ 1) :named @p_577) @p_566) :named @p_579)) (! (not @p_577) :named @p_581) @p_566) :rule equiv_pos2)
(step t830.t1 (cl @p_579) :rule rare_rewrite :args ("arith-elim-lt" k$ 1))
(step t830.t2 (cl (! (not (! (= @p_566 @p_577) :named @p_578)) :named @p_580) (! (not @p_566) :named @p_567) @p_577) :rule equiv_pos2)
(step t830.t3 (cl @p_578) :rule symm :premises (t830.t1))
(step t830.t4 (cl (! (=> @p_564 false) :named @p_1023) @p_564) :rule implies_neg1)
(anchor :step t830.t5)
(assume t830.t5.a0 @p_564)
(step t830.t5.t0 (cl (not (! (= (! (< (! (+ @p_4 @p_8 @p_57 @p_1025 @p_799 @p_546) :named @p_1026) (! (+ @p_298 0 1 @p_297 0 0) :named @p_1024)) :named @p_1027) false) :named @p_1039)) (not @p_1027) false) :rule equiv_pos2)
(step t830.t5.t1 (cl (= @p_1027 (! (not (! (>= @p_1026 @p_1024) :named @p_1040)) :named @p_1041))) :rule rare_rewrite :args ("arith-elim-lt" @p_1026 @p_1024))
(step t830.t5.t2 (cl (= @p_1026 (! (+ @p_619 @p_618 @p_11 @p_8 @p_722 @p_721 @p_4 k$) :named @p_1043))) :rule poly_simp)
(step t830.t5.t3 (cl (= @p_619 0)) :rule poly_simp)
(step t830.t5.t4 (cl (= @p_618 0)) :rule poly_simp)
(step t830.t5.t5 (cl (= @p_11 @p_11)) :rule refl)
(step t830.t5.t6 (cl (= @p_8 @p_8)) :rule refl)
(step t830.t5.t7 (cl (= @p_722 0)) :rule poly_simp)
(step t830.t5.t8 (cl (= @p_721 0)) :rule poly_simp)
(step t830.t5.t9 (cl (= @p_4 @p_4)) :rule refl)
(step t830.t5.t10 (cl (= k$ k$)) :rule refl)
(step t830.t5.t11 (cl (= @p_1043 (! (+ 0 0 @p_11 @p_8 0 0 @p_4 k$) :named @p_1044))) :rule cong :premises (t830.t5.t3 t830.t5.t4 t830.t5.t5 t830.t5.t6 t830.t5.t7 t830.t5.t8 t830.t5.t9 t830.t5.t10))
(step t830.t5.t12 (cl (= @p_1044 0)) :rule poly_simp)
(step t830.t5.t13 (cl (= @p_1043 0)) :rule trans :premises (t830.t5.t11 t830.t5.t12))
(step t830.t5.t14 (cl (= @p_1026 0)) :rule trans :premises (t830.t5.t2 t830.t5.t13))
(step t830.t5.t15 (cl (= @p_298 -1)) :rule evaluate)
(step t830.t5.t16 (cl (= 1 1)) :rule refl)
(step t830.t5.t17 (cl (= @p_297 0)) :rule evaluate)
(step t830.t5.t18 (cl (= @p_1024 (! (+ -1 0 1 0 0 0) :named @p_1042))) :rule cong :premises (t830.t5.t15 t604 t830.t5.t16 t830.t5.t17 t604 t604))
(step t830.t5.t19 (cl (= @p_1042 0)) :rule evaluate)
(step t830.t5.t20 (cl (= @p_1024 0)) :rule trans :premises (t830.t5.t18 t830.t5.t19))
(step t830.t5.t21 (cl (= @p_1040 @p_366)) :rule cong :premises (t830.t5.t14 t830.t5.t20))
(step t830.t5.t22 (cl (= @p_366 true)) :rule evaluate)
(step t830.t5.t23 (cl (= @p_1040 true)) :rule trans :premises (t830.t5.t21 t830.t5.t22))
(step t830.t5.t24 (cl (= @p_1041 @p_365)) :rule cong :premises (t830.t5.t23))
(step t830.t5.t25 (cl (= @p_365 false)) :rule evaluate)
(step t830.t5.t26 (cl (= @p_1041 false)) :rule trans :premises (t830.t5.t24 t830.t5.t25))
(step t830.t5.t27 (cl @p_1039) :rule trans :premises (t830.t5.t1 t830.t5.t26))
(step t830.t5.t28 (cl (! (not (! (<= @p_4 @p_298) :named @p_705)) :named @p_714) (! (not (! (< @p_8 0) :named @p_1031)) :named @p_1037) @p_974 @p_1038 @p_808 (! (not @p_549) :named @p_557) @p_1027) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t830.t5.t29 (cl (=> (! (and @p_308 @p_564) :named @p_706) @p_705)) :rule la_mult_neg)
(step t830.t5.t30 (cl (! (not @p_706) :named @p_707) @p_705) :rule implies :premises (t830.t5.t29))
(step t830.t5.t31 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t830.t5.t32 (cl (not @p_310) @p_308) :rule equiv1 :premises (t830.t5.t31))
(step t830.t5.t33 (cl @p_310) :rule evaluate)
(step t830.t5.t34 (cl @p_308) :rule resolution :premises (t830.t5.t32 t830.t5.t33))
(step t830.t5.t35 (cl @p_706) :rule and_intro :premises (t830.t5.t34 t830.t5.a0))
(step t830.t5.t36 (cl @p_705) :rule resolution :premises (t830.t5.t30 t830.t5.t35))
(step t830.t5.t37 (cl (! (not (! (= @p_16 @p_1031) :named @p_1034)) :named @p_1036) @p_1013 @p_1031) :rule equiv_pos2)
(step t830.t5.t38 (cl (! (= @p_1031 @p_16) :named @p_1035)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0))
(step t830.t5.t39 (cl @p_1034) :rule symm :premises (t830.t5.t38))
(step t830.t5.t40 (cl @p_1031) :rule resolution :premises (t830.t5.t37 t830.t5.t39 t830.a4))
(step t830.t5.t41 (cl @p_58) :rule symm :premises (t830.a3))
(step t830.t5.t42 (cl (=> @p_1029 @p_1028)) :rule la_mult_neg)
(step t830.t5.t43 (cl @p_1030 @p_1028) :rule implies :premises (t830.t5.t42))
(step t830.t5.t44 (cl @p_946 @p_928 @p_940) :rule equiv_pos2)
(step t830.t5.t45 (cl (= (* 1 (- @p_669 @p_105)) @p_945)) :rule poly_simp)
(step t830.t5.t46 (cl (= @p_924 @p_944)) :rule poly_simp_rel :premises (t830.t5.t45))
(step t830.t5.t47 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t830.t5.t48 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t830.t5.t47))
(step t830.t5.t49 (cl (= @p_944 @p_940)) :rule symm :premises (t830.t5.t48))
(step t830.t5.t50 (cl @p_942) :rule trans :premises (t830.t5.t46 t830.t5.t49))
(step t830.t5.t51 (cl @p_940) :rule resolution :premises (t830.t5.t44 t830.t5.t50 t830.a2))
(step t830.t5.t52 (cl @p_1029) :rule and_intro :premises (t830.t5.t34 t830.t5.t51))
(step t830.t5.t53 (cl @p_1028) :rule resolution :premises (t830.t5.t43 t830.t5.t52))
(step t830.t5.t54 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t830.t5.t55 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t830.t5.t56 (cl @p_803) :rule poly_simp_rel :premises (t830.t5.t55))
(step t830.t5.t57 (cl (= @p_793 @p_800)) :rule symm :premises (t830.t5.t56))
(step t830.t5.t58 (cl @p_802) :rule trans :premises (t655 t830.t5.t57))
(step t830.t5.t59 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t830.t5.t60 (cl @p_801) :rule trans :premises (t830.t5.t59 t755))
(step t830.t5.t61 (cl @p_800) :rule resolution :premises (t830.t5.t54 t830.t5.t58 t830.t5.t60))
(step t830.t5.t62 (cl (not @p_550) @p_532 @p_549) :rule equiv_pos2)
(step t830.t5.t63 (cl (= (* 1 (- @p_546 0)) (* 1 (- k$ @p_105)))) :rule poly_simp)
(step t830.t5.t64 (cl (= @p_549 @p_106)) :rule poly_simp_rel :premises (t830.t5.t63))
(step t830.t5.t65 (cl @p_550) :rule symm :premises (t830.t5.t64))
(step t830.t5.t66 (cl @p_549) :rule resolution :premises (t830.t5.t62 t830.t5.t65 t742))
(step t830.t5.t67 (cl @p_1027) :rule resolution :premises (t830.t5.t28 t830.t5.t36 t830.t5.t40 t830.t5.t41 t830.t5.t53 t830.t5.t61 t830.t5.t66))
(step t830.t5.t68 (cl false) :rule resolution :premises (t830.t5.t0 t830.t5.t27 t830.t5.t67))
(step t830.t5 (cl @p_566 false) :rule subproof :discharge (t830.t5.a0))
(step t830.t6 (cl @p_1023 false) :rule resolution :premises (t830.t4 t830.t5))
(step t830.t7 (cl @p_1023 @p_212) :rule implies_neg2)
(step t830.t8 (cl @p_1023 @p_1023) :rule resolution :premises (t830.t6 t830.t7))
(step t830.t9 (cl @p_1023) :rule contraction :premises (t830.t8))
(step t830.t10 (cl (= @p_1023 @p_566)) :rule implies_simplify)
(step t830.t11 (cl (not @p_1023) @p_566) :rule equiv1 :premises (t830.t10))
(step t830.t12 (cl @p_566) :rule resolution :premises (t830.t9 t830.t11))
(step t830.t13 (cl @p_577) :rule resolution :premises (t830.t2 t830.t3 t830.t12))
(step t830.t14 (cl @p_566) :rule resolution :premises (t830.t0 t830.t1 t830.t13))
(step t830.t15 (cl) :rule resolution :premises (t830.a5 t830.t14))
(step t830 (cl @p_532 @p_806 @p_928 @p_929 @p_1013 @p_566 false) :rule subproof :discharge (t830.a0 t830.a1 t830.a2 t830.a3 t830.a4 t830.a5))
(step t831 (cl @p_1021 @p_106) :rule and_pos :args (0))
(step t832 (cl @p_1021 @p_801) :rule and_pos :args (1))
(step t833 (cl @p_1021 @p_924) :rule and_pos :args (2))
(step t834 (cl @p_1021 @p_923) :rule and_pos :args (3))
(step t835 (cl @p_1021 @p_16) :rule and_pos :args (4))
(step t836 (cl @p_1021 @p_564) :rule and_pos :args (5))
(step t837 (cl false @p_1021 @p_1021 @p_1021 @p_1021 @p_1021 @p_1021) :rule resolution :premises (t830 t831 t832 t833 t834 t835 t836))
(step t838 (cl @p_1021 @p_1021 @p_1021 @p_1021 @p_1021 @p_1021 false) :rule reordering :premises (t837))
(step t839 (cl @p_1021 false) :rule contraction :premises (t838))
(step t840 (cl @p_1022 false) :rule resolution :premises (t829 t839))
(step t841 (cl @p_1022 @p_212) :rule implies_neg2)
(step t842 (cl @p_1022 @p_1022) :rule resolution :premises (t840 t841))
(step t843 (cl @p_1022) :rule contraction :premises (t842))
(step t844 (cl (= @p_1022 @p_1021)) :rule implies_simplify)
(step t845 (cl (not @p_1022) @p_1021) :rule equiv1 :premises (t844))
(step t846 (cl @p_1021) :rule resolution :premises (t843 t845))
(step t847 (cl @p_1019) :rule resolution :premises (t828 t846))
(step t848 (cl @p_583 @p_566 @p_671 @p_792 @p_974 @p_1013 @p_532) :rule not_and :premises (t847))
(step t849 (cl @p_1014 @p_589) :rule or_neg :args (0))
(step t850 (cl @p_1014 @p_567) :rule or_neg :args (1))
(step t851 (cl @p_1014 @p_677) :rule or_neg :args (2))
(step t852 (cl @p_1014 @p_1017) :rule or_neg :args (3))
(step t853 (cl @p_1014 @p_1016) :rule or_neg :args (4))
(step t854 (cl @p_1014 (! (not @p_1013) :named @p_1015)) :rule or_neg :args (5))
(step t855 (cl @p_1014 @p_538) :rule or_neg :args (6))
(step t856 (cl @p_1014 @p_1014 @p_1014 @p_1014 @p_1014 @p_1014 @p_1014) :rule resolution :premises (t848 t849 t850 t851 t852 t853 t854 t855))
(step t857 (cl @p_1014) :rule contraction :premises (t856))
(step t858 (cl @p_1012) :rule resolution :premises (t809 t811 t857))
(step t859 (cl @p_583 @p_566 @p_671 @p_792 @p_974 @p_15 @p_532) :rule or :premises (t858))
(step t860 (cl (not (! (= (! (or (! (not (! (= (! (not (! (dvd$ 2 @p_6) :named @p_59)) :named @p_60) @p_58) :named @p_61)) :named @p_1243) (! (not @p_60) :named @p_1245) @p_58) :named @p_1246) (! (or @p_1243 @p_59 @p_58) :named @p_1244)) :named @p_1247)) (not @p_1246) @p_1244) :rule equiv_pos2)
(step t861 (cl (= @p_1245 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t862 (cl (= @p_58 @p_58)) :rule refl)
(step t863 (cl @p_1247) :rule cong :premises (t861 t862))
(step t864 (cl @p_1243 @p_1245 @p_58) :rule equiv_pos2)
(step t865 (cl @p_1246 (not @p_1243)) :rule or_neg :args (0))
(step t866 (cl @p_1246 (not @p_1245)) :rule or_neg :args (1))
(step t867 (cl @p_1246 @p_974) :rule or_neg :args (2))
(step t868 (cl @p_1246 @p_1246 @p_1246) :rule resolution :premises (t864 t865 t866 t867))
(step t869 (cl @p_1246) :rule contraction :premises (t868))
(step t870 (cl @p_1244) :rule resolution :premises (t860 t863 t869))
(step t871 (cl @p_1243 @p_59 @p_58) :rule or :premises (t870))
(step t872 (cl @p_59 @p_58 @p_1243) :rule reordering :premises (t871))
(step t873 (cl (or (! (not (forall ((?v0 Int)) (= (not (dvd$ 2 ?v0)) (= (modulo$ ?v0 2) 1)))) :named @p_62) @p_61)) :rule forall_inst :args (@p_6))
(step t874 (cl @p_62 @p_61) :rule or :premises (t873))
(step t875 (cl @p_61) :rule resolution :premises (t874 a10))
(step t876 (cl (! (not (! (= @p_59 (! (= @p_57 0) :named @p_63)) :named @p_64)) :named @p_1242) @p_60 @p_63) :rule equiv_pos2)
(step t877 (cl @p_63 @p_60 @p_1242) :rule reordering :premises (t876))
(step t878 (cl (or (! (not (forall ((?v0 Int)) (= (dvd$ 2 ?v0) (= (modulo$ ?v0 2) 0)))) :named @p_65) @p_64)) :rule forall_inst :args (@p_6))
(step t879 (cl @p_65 @p_64) :rule or :premises (t878))
(step t880 (cl @p_64) :rule resolution :premises (t879 a5))
(step t881 (cl (not (! (= (! (or @p_583 @p_671 @p_673 (! (not @p_63) :named @p_66) (! (not (! (not (! (= @p_7 @p_668) :named @p_732)) :named @p_740)) :named @p_1353) @p_532 @p_916) :named @p_1354) (! (or @p_583 @p_671 @p_112 @p_66 @p_732 @p_532 @p_913) :named @p_1352)) :named @p_1388)) (not @p_1354) @p_1352) :rule equiv_pos2)
(step t882 (cl (= @p_66 @p_66)) :rule refl)
(step t883 (cl (= @p_1353 @p_732)) :rule rare_rewrite :args ("bool-double-not-elim" @p_732))
(step t884 (cl @p_1388) :rule cong :premises (t38 t882 t883 t40 t761))
(step t885 (cl (! (=> (! (and @p_524 @p_670 @p_113 @p_63 @p_740 @p_106 @p_915) :named @p_1356) (! (and @p_740 @p_915 @p_924 (! (= 0 @p_57) :named @p_1188) @p_113 @p_592) :named @p_1358)) :named @p_1387) @p_1356) :rule implies_neg1)
(anchor :step t886)
(assume t886.a0 @p_524)
(assume t886.a1 @p_670)
(assume t886.a2 @p_113)
(assume t886.a3 @p_63)
(assume t886.a4 @p_740)
(assume t886.a5 @p_106)
(assume t886.a6 @p_915)
(step t886.t0 (cl @p_969 @p_967) :rule implies_neg1)
(anchor :step t886.t1)
(assume t886.t1.a0 @p_106)
(assume t886.t1.a1 @p_524)
(assume t886.t1.a2 @p_670)
(step t886.t1.t0 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t886.t1.t1 (cl @p_527) :rule symm :premises (t886.t1.a1))
(step t886.t1.t2 (cl @p_924) :rule trans :premises (t886.t1.t0 t886.t1.t1 t742))
(step t886.t1 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t886.t1.a0 t886.t1.a1 t886.t1.a2))
(step t886.t2 (cl @p_968 @p_106) :rule and_pos :args (0))
(step t886.t3 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t886.t4 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t886.t5 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t886.t1 t886.t2 t886.t3 t886.t4))
(step t886.t6 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t886.t5))
(step t886.t7 (cl @p_968 @p_924) :rule contraction :premises (t886.t6))
(step t886.t8 (cl @p_969 @p_924) :rule resolution :premises (t886.t0 t886.t7))
(step t886.t9 (cl @p_969 @p_928) :rule implies_neg2)
(step t886.t10 (cl @p_969 @p_969) :rule resolution :premises (t886.t8 t886.t9))
(step t886.t11 (cl @p_969) :rule contraction :premises (t886.t10))
(step t886.t12 (cl @p_968 @p_924) :rule implies :premises (t886.t11))
(step t886.t13 (cl @p_967) :rule and_intro :premises (t742 t886.a0 t758))
(step t886.t14 (cl @p_924) :rule resolution :premises (t886.t12 t886.t13))
(step t886.t15 (cl (! (=> @p_63 @p_1188) :named @p_1224) @p_63) :rule implies_neg1)
(anchor :step t886.t16)
(assume t886.t16.a0 @p_63)
(step t886.t16.t0 (cl @p_1188) :rule symm :premises (t886.t16.a0))
(step t886.t16 (cl @p_66 @p_1188) :rule subproof :discharge (t886.t16.a0))
(step t886.t17 (cl @p_1224 @p_1188) :rule resolution :premises (t886.t15 t886.t16))
(step t886.t18 (cl @p_1224 (! (not @p_1188) :named @p_1192)) :rule implies_neg2)
(step t886.t19 (cl @p_1224 @p_1224) :rule resolution :premises (t886.t17 t886.t18))
(step t886.t20 (cl @p_1224) :rule contraction :premises (t886.t19))
(step t886.t21 (cl @p_66 @p_1188) :rule implies :premises (t886.t20))
(step t886.t22 (cl @p_1188) :rule resolution :premises (t886.t21 t886.a3))
(step t886.t23 (cl @p_631 @p_628) :rule implies_neg1)
(anchor :step t886.t24)
(assume t886.t24.a0 @p_106)
(assume t886.t24.a1 @p_524)
(step t886.t24.t0 (cl @p_527) :rule symm :premises (t886.t24.a1))
(step t886.t24.t1 (cl @p_592) :rule trans :premises (t886.t24.t0 t742))
(step t886.t24 (cl @p_532 @p_583 @p_592) :rule subproof :discharge (t886.t24.a0 t886.t24.a1))
(step t886.t25 (cl @p_630 @p_106) :rule and_pos :args (0))
(step t886.t26 (cl @p_630 @p_524) :rule and_pos :args (1))
(step t886.t27 (cl @p_592 @p_630 @p_630) :rule resolution :premises (t886.t24 t886.t25 t886.t26))
(step t886.t28 (cl @p_630 @p_630 @p_592) :rule reordering :premises (t886.t27))
(step t886.t29 (cl @p_630 @p_592) :rule contraction :premises (t886.t28))
(step t886.t30 (cl @p_631 @p_592) :rule resolution :premises (t886.t23 t886.t29))
(step t886.t31 (cl @p_631 @p_596) :rule implies_neg2)
(step t886.t32 (cl @p_631 @p_631) :rule resolution :premises (t886.t30 t886.t31))
(step t886.t33 (cl @p_631) :rule contraction :premises (t886.t32))
(step t886.t34 (cl @p_630 @p_592) :rule implies :premises (t886.t33))
(step t886.t35 (cl @p_628) :rule and_intro :premises (t742 t886.a0))
(step t886.t36 (cl @p_592) :rule resolution :premises (t886.t34 t886.t35))
(step t886.t37 (cl @p_1358) :rule and_intro :premises (t886.a4 t886.a6 t886.t14 t886.t22 t886.a2 t886.t36))
(step t886 (cl @p_583 @p_671 @p_673 @p_66 @p_1353 @p_532 @p_916 @p_1358) :rule subproof :discharge (t886.a0 t886.a1 t886.a2 t886.a3 t886.a4 t886.a5 t886.a6))
(step t887 (cl (! (not @p_1356) :named @p_1357) @p_524) :rule and_pos :args (0))
(step t888 (cl @p_1357 @p_670) :rule and_pos :args (1))
(step t889 (cl @p_1357 @p_113) :rule and_pos :args (2))
(step t890 (cl @p_1357 @p_63) :rule and_pos :args (3))
(step t891 (cl @p_1357 @p_740) :rule and_pos :args (4))
(step t892 (cl @p_1357 @p_106) :rule and_pos :args (5))
(step t893 (cl @p_1357 @p_915) :rule and_pos :args (6))
(step t894 (cl @p_1358 @p_1357 @p_1357 @p_1357 @p_1357 @p_1357 @p_1357 @p_1357) :rule resolution :premises (t886 t887 t888 t889 t890 t891 t892 t893))
(step t895 (cl @p_1357 @p_1357 @p_1357 @p_1357 @p_1357 @p_1357 @p_1357 @p_1358) :rule reordering :premises (t894))
(step t896 (cl @p_1357 @p_1358) :rule contraction :premises (t895))
(step t897 (cl @p_1387 @p_1358) :rule resolution :premises (t885 t896))
(step t898 (cl @p_1387 (! (not @p_1358) :named @p_1359)) :rule implies_neg2)
(step t899 (cl @p_1387 @p_1387) :rule resolution :premises (t897 t898))
(step t900 (cl @p_1387) :rule contraction :premises (t899))
(step t901 (cl @p_1357 @p_1358) :rule implies :premises (t900))
(step t902 (cl (! (=> @p_1358 false) :named @p_1360) @p_1358) :rule implies_neg1)
(anchor :step t903)
(assume t903.a0 @p_740)
(assume t903.a1 @p_915)
(assume t903.a2 @p_924)
(assume t903.a3 @p_1188)
(assume t903.a4 @p_113)
(assume t903.a5 @p_592)
(step t903.t0 (cl @p_610 @p_596 @p_606) :rule equiv_pos2)
(step t903.t1 (cl (= (* 1 (- @p_601 0)) (* 1 (- @p_6 @p_105)))) :rule poly_simp)
(step t903.t2 (cl (= @p_606 @p_592)) :rule poly_simp_rel :premises (t903.t1))
(step t903.t3 (cl @p_609) :rule symm :premises (t903.t2))
(step t903.t4 (cl @p_606) :rule resolution :premises (t903.t0 t903.t3 t903.a5))
(step t903.t5 (cl (! (=> @p_606 false) :named @p_1361) @p_606) :rule implies_neg1)
(anchor :step t903.t6)
(assume t903.t6.a0 @p_606)
(step t903.t6.t0 (cl (not (! (= (! (< (! (+ @p_602 @p_111 @p_689 @p_932 @p_912) :named @p_1363) (! (+ @p_297 1 @p_297 0 -1) :named @p_1362)) :named @p_1364) false) :named @p_1381)) (not @p_1364) false) :rule equiv_pos2)
(step t903.t6.t1 (cl (= @p_1364 (! (not (! (>= @p_1363 @p_1362) :named @p_1382)) :named @p_1383))) :rule rare_rewrite :args ("arith-elim-lt" @p_1363 @p_1362))
(step t903.t6.t2 (cl (= @p_1363 @p_1385)) :rule poly_simp)
(step t903.t6.t3 (cl (= @p_619 0)) :rule poly_simp)
(step t903.t6.t4 (cl (= @p_618 0)) :rule poly_simp)
(step t903.t6.t5 (cl (= @p_689 @p_689)) :rule refl)
(step t903.t6.t6 (cl (= @p_690 @p_690)) :rule refl)
(step t903.t6.t7 (cl (= @p_57 @p_57)) :rule refl)
(step t903.t6.t8 (cl (= @p_668 @p_668)) :rule refl)
(step t903.t6.t9 (cl @p_168) :rule refl)
(step t903.t6.t10 (cl @p_167) :rule refl)
(step t903.t6.t11 (cl (= @p_617 0)) :rule poly_simp)
(step t903.t6.t12 (cl (= @p_1385 @p_1386)) :rule cong :premises (t903.t6.t3 t903.t6.t4 t903.t6.t5 t903.t6.t6 t903.t6.t7 t903.t6.t8 t903.t6.t9 t903.t6.t10 t903.t6.t11))
(step t903.t6.t13 (cl (= @p_1386 0)) :rule poly_simp)
(step t903.t6.t14 (cl (= @p_1385 0)) :rule trans :premises (t903.t6.t12 t903.t6.t13))
(step t903.t6.t15 (cl (= @p_1363 0)) :rule trans :premises (t903.t6.t2 t903.t6.t14))
(step t903.t6.t16 (cl (= @p_297 0)) :rule evaluate)
(step t903.t6.t17 (cl (= 1 1)) :rule refl)
(step t903.t6.t18 (cl (= -1 -1)) :rule refl)
(step t903.t6.t19 (cl (= @p_1362 (! (+ 0 1 0 0 -1) :named @p_1384))) :rule cong :premises (t903.t6.t16 t903.t6.t17 t903.t6.t16 t604 t903.t6.t18))
(step t903.t6.t20 (cl (= @p_1384 0)) :rule evaluate)
(step t903.t6.t21 (cl (= @p_1362 0)) :rule trans :premises (t903.t6.t19 t903.t6.t20))
(step t903.t6.t22 (cl (= @p_1382 @p_366)) :rule cong :premises (t903.t6.t15 t903.t6.t21))
(step t903.t6.t23 (cl (= @p_366 true)) :rule evaluate)
(step t903.t6.t24 (cl (= @p_1382 true)) :rule trans :premises (t903.t6.t22 t903.t6.t23))
(step t903.t6.t25 (cl (= @p_1383 @p_365)) :rule cong :premises (t903.t6.t24))
(step t903.t6.t26 (cl (= @p_365 false)) :rule evaluate)
(step t903.t6.t27 (cl (= @p_1383 false)) :rule trans :premises (t903.t6.t25 t903.t6.t26))
(step t903.t6.t28 (cl @p_1381) :rule trans :premises (t903.t6.t1 t903.t6.t27))
(step t903.t6.t29 (cl @p_612 @p_715 (! (not (! (= @p_689 @p_297) :named @p_1201)) :named @p_1211) @p_955 (! (not (! (<= @p_912 -1) :named @p_1365)) :named @p_1380) @p_1364) :rule la_generic :args (-1/1 1/1 -1/1 -1/1 1/1 1/1))
(step t903.t6.t30 (cl (=> @p_607 @p_605)) :rule la_mult_neg)
(step t903.t6.t31 (cl @p_611 @p_605) :rule implies :premises (t903.t6.t30))
(step t903.t6.t32 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t903.t6.t33 (cl (not @p_310) @p_308) :rule equiv1 :premises (t903.t6.t32))
(step t903.t6.t34 (cl @p_310) :rule evaluate)
(step t903.t6.t35 (cl @p_308) :rule resolution :premises (t903.t6.t33 t903.t6.t34))
(step t903.t6.t36 (cl @p_607) :rule and_intro :premises (t903.t6.t35 t903.t6.a0))
(step t903.t6.t37 (cl @p_605) :rule resolution :premises (t903.t6.t31 t903.t6.t36))
(step t903.t6.t38 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t903.t6.t39 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t903.t6.t40 (cl @p_703) :rule symm :premises (t903.t6.t39))
(step t903.t6.t41 (cl @p_700) :rule resolution :premises (t903.t6.t38 t903.t6.t40 t903.a4))
(step t903.t6.t42 (cl (=> (! (and @p_308 @p_63) :named @p_1202) @p_1201)) :rule la_mult_neg)
(step t903.t6.t43 (cl (! (not @p_1202) :named @p_1204) @p_1201) :rule implies :premises (t903.t6.t42))
(step t903.t6.t44 (cl @p_63) :rule symm :premises (t903.a3))
(step t903.t6.t45 (cl @p_1202) :rule and_intro :premises (t903.t6.t35 t903.t6.t44))
(step t903.t6.t46 (cl @p_1201) :rule resolution :premises (t903.t6.t43 t903.t6.t45))
(step t903.t6.t47 (cl @p_946 @p_928 @p_940) :rule equiv_pos2)
(step t903.t6.t48 (cl (= (* 1 (- @p_669 @p_105)) @p_945)) :rule poly_simp)
(step t903.t6.t49 (cl (= @p_924 @p_944)) :rule poly_simp_rel :premises (t903.t6.t48))
(step t903.t6.t50 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t903.t6.t51 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t903.t6.t50))
(step t903.t6.t52 (cl (= @p_944 @p_940)) :rule symm :premises (t903.t6.t51))
(step t903.t6.t53 (cl @p_942) :rule trans :premises (t903.t6.t49 t903.t6.t52))
(step t903.t6.t54 (cl @p_940) :rule resolution :premises (t903.t6.t47 t903.t6.t53 t903.a2))
(step t903.t6.t55 (cl (! (not (! (< @p_912 0) :named @p_1366)) :named @p_1379) @p_1365) :rule la_generic :args (1/1 1/1))
(step t903.t6.t56 (cl (! (or (! (= @p_912 0) :named @p_1372) (! (not (! (<= @p_912 0) :named @p_1371)) :named @p_1377) (! (not (<= 0 @p_912)) :named @p_1367)) :named @p_1378)) :rule la_disequality)
(step t903.t6.t57 (cl @p_1372 @p_1377 @p_1367) :rule or :premises (t903.t6.t56))
(step t903.t6.t58 (cl (! (not (! (= @p_740 (! (not @p_1372) :named @p_1373)) :named @p_1375)) :named @p_1376) @p_1353 @p_1373) :rule equiv_pos2)
(step t903.t6.t59 (cl (= (* 1 (- @p_912 0)) (* 1 (- @p_7 @p_668)))) :rule poly_simp)
(step t903.t6.t60 (cl (= @p_1372 @p_732)) :rule poly_simp_rel :premises (t903.t6.t59))
(step t903.t6.t61 (cl (= @p_1373 @p_740)) :rule cong :premises (t903.t6.t60))
(step t903.t6.t62 (cl @p_1375) :rule symm :premises (t903.t6.t61))
(step t903.t6.t63 (cl @p_1373) :rule resolution :premises (t903.t6.t58 t903.t6.t62 t903.a0))
(step t903.t6.t64 (cl @p_956 @p_1371) :rule la_generic :args (1/1 1/1))
(step t903.t6.t65 (cl @p_939 @p_916 @p_935) :rule equiv_pos2)
(step t903.t6.t66 (cl (= @p_935 @p_915)) :rule rare_rewrite :args ("arith-elim-lt" @p_912 1))
(step t903.t6.t67 (cl @p_938) :rule symm :premises (t903.t6.t66))
(step t903.t6.t68 (cl @p_935) :rule resolution :premises (t903.t6.t65 t903.t6.t67 t903.a1))
(step t903.t6.t69 (cl @p_1371) :rule resolution :premises (t903.t6.t64 t903.t6.t68))
(step t903.t6.t70 (cl (! (not (! (= @p_1366 @p_1367) :named @p_1368)) :named @p_1369) @p_1366 (! (not @p_1367) :named @p_1370)) :rule equiv_pos1)
(step t903.t6.t71 (cl @p_1368) :rule comp_simplify)
(step t903.t6.t72 (cl @p_1366) :rule resolution :premises (t903.t6.t57 t903.t6.t63 t903.t6.t69 t903.t6.t70 t903.t6.t71))
(step t903.t6.t73 (cl @p_1365) :rule resolution :premises (t903.t6.t55 t903.t6.t72))
(step t903.t6.t74 (cl @p_1364) :rule resolution :premises (t903.t6.t29 t903.t6.t37 t903.t6.t41 t903.t6.t46 t903.t6.t54 t903.t6.t73))
(step t903.t6.t75 (cl false) :rule resolution :premises (t903.t6.t0 t903.t6.t28 t903.t6.t74))
(step t903.t6 (cl (! (not @p_606) :named @p_888) false) :rule subproof :discharge (t903.t6.a0))
(step t903.t7 (cl @p_1361 false) :rule resolution :premises (t903.t5 t903.t6))
(step t903.t8 (cl @p_1361 @p_212) :rule implies_neg2)
(step t903.t9 (cl @p_1361 @p_1361) :rule resolution :premises (t903.t7 t903.t8))
(step t903.t10 (cl @p_1361) :rule contraction :premises (t903.t9))
(step t903.t11 (cl (= @p_1361 @p_888)) :rule implies_simplify)
(step t903.t12 (cl (not @p_1361) @p_888) :rule equiv1 :premises (t903.t11))
(step t903.t13 (cl @p_888) :rule resolution :premises (t903.t10 t903.t12))
(step t903.t14 (cl) :rule resolution :premises (t903.t4 t903.t13))
(step t903 (cl @p_1353 @p_916 @p_928 @p_1192 @p_673 @p_596 false) :rule subproof :discharge (t903.a0 t903.a1 t903.a2 t903.a3 t903.a4 t903.a5))
(step t904 (cl @p_1359 @p_740) :rule and_pos :args (0))
(step t905 (cl @p_1359 @p_915) :rule and_pos :args (1))
(step t906 (cl @p_1359 @p_924) :rule and_pos :args (2))
(step t907 (cl @p_1359 @p_1188) :rule and_pos :args (3))
(step t908 (cl @p_1359 @p_113) :rule and_pos :args (4))
(step t909 (cl @p_1359 @p_592) :rule and_pos :args (5))
(step t910 (cl false @p_1359 @p_1359 @p_1359 @p_1359 @p_1359 @p_1359) :rule resolution :premises (t903 t904 t905 t906 t907 t908 t909))
(step t911 (cl @p_1359 @p_1359 @p_1359 @p_1359 @p_1359 @p_1359 false) :rule reordering :premises (t910))
(step t912 (cl @p_1359 false) :rule contraction :premises (t911))
(step t913 (cl @p_1360 false) :rule resolution :premises (t902 t912))
(step t914 (cl @p_1360 @p_212) :rule implies_neg2)
(step t915 (cl @p_1360 @p_1360) :rule resolution :premises (t913 t914))
(step t916 (cl @p_1360) :rule contraction :premises (t915))
(step t917 (cl (= @p_1360 @p_1359)) :rule implies_simplify)
(step t918 (cl (not @p_1360) @p_1359) :rule equiv1 :premises (t917))
(step t919 (cl @p_1359) :rule resolution :premises (t916 t918))
(step t920 (cl @p_1357) :rule resolution :premises (t901 t919))
(step t921 (cl @p_583 @p_671 @p_673 @p_66 @p_1353 @p_532 @p_916) :rule not_and :premises (t920))
(step t922 (cl @p_1354 @p_589) :rule or_neg :args (0))
(step t923 (cl @p_1354 @p_677) :rule or_neg :args (1))
(step t924 (cl @p_1354 @p_676) :rule or_neg :args (2))
(step t925 (cl @p_1354 (! (not @p_66) :named @p_1182)) :rule or_neg :args (3))
(step t926 (cl @p_1354 (! (not @p_1353) :named @p_1355)) :rule or_neg :args (4))
(step t927 (cl @p_1354 @p_538) :rule or_neg :args (5))
(step t928 (cl @p_1354 @p_918) :rule or_neg :args (6))
(step t929 (cl @p_1354 @p_1354 @p_1354 @p_1354 @p_1354 @p_1354 @p_1354) :rule resolution :premises (t921 t922 t923 t924 t925 t926 t927 t928))
(step t930 (cl @p_1354) :rule contraction :premises (t929))
(step t931 (cl @p_1352) :rule resolution :premises (t881 t884 t930))
(step t932 (cl @p_583 @p_671 @p_112 @p_66 @p_732 @p_532 @p_913) :rule or :premises (t931))
(step t933 (cl @p_583 @p_112 @p_671 @p_732 @p_66 @p_532 @p_913) :rule reordering :premises (t932))
(step t934 (cl (! (=> (! (>= @p_8 3) :named @p_1267) @p_15) :named @p_1337) @p_1267) :rule implies_neg1)
(anchor :step t935)
(assume t935.a0 @p_1267)
(step t935.t0 (cl @p_1337 @p_1267) :rule implies_neg1)
(anchor :step t935.t1)
(assume t935.t1.a0 @p_1267)
(step t935.t1.t0 (cl (! (not (! (= @p_1037 @p_15) :named @p_1349)) :named @p_1350) (! (not @p_1037) :named @p_1351) @p_15) :rule equiv_pos2)
(step t935.t1.t1 (cl @p_1035) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0))
(step t935.t1.t2 (cl (= @p_1037 @p_1013)) :rule cong :premises (t935.t1.t1))
(step t935.t1.t3 (cl @p_1349) :rule trans :premises (t935.t1.t2 t810))
(step t935.t1.t4 (cl (! (=> @p_1031 false) :named @p_1338) @p_1031) :rule implies_neg1)
(anchor :step t935.t1.t5)
(assume t935.t1.t5.a0 @p_1031)
(step t935.t1.t5.t0 (cl (not (! (= (! (< (! (+ @p_8 @p_11) :named @p_1322) (! (+ 0 (! (* -1 3) :named @p_1320)) :named @p_1341)) :named @p_1342) false) :named @p_1344)) (not @p_1342) false) :rule equiv_pos2)
(step t935.t1.t5.t1 (cl (= @p_1342 (! (not (! (>= @p_1322 @p_1341) :named @p_1345)) :named @p_1346))) :rule rare_rewrite :args ("arith-elim-lt" @p_1322 @p_1341))
(step t935.t1.t5.t2 (cl (= @p_1322 0)) :rule poly_simp)
(step t935.t1.t5.t3 (cl (= @p_1320 -3)) :rule evaluate)
(step t935.t1.t5.t4 (cl (= @p_1341 (! (+ 0 -3) :named @p_1348))) :rule cong :premises (t935.t1.t5.t3))
(step t935.t1.t5.t5 (cl (= @p_1348 -3)) :rule evaluate)
(step t935.t1.t5.t6 (cl (= @p_1341 -3)) :rule trans :premises (t935.t1.t5.t4 t935.t1.t5.t5))
(step t935.t1.t5.t7 (cl (= @p_1345 (! (>= 0 -3) :named @p_1347))) :rule cong :premises (t935.t1.t5.t2 t935.t1.t5.t6))
(step t935.t1.t5.t8 (cl (= @p_1347 true)) :rule evaluate)
(step t935.t1.t5.t9 (cl (= @p_1345 true)) :rule trans :premises (t935.t1.t5.t7 t935.t1.t5.t8))
(step t935.t1.t5.t10 (cl (= @p_1346 @p_365)) :rule cong :premises (t935.t1.t5.t9))
(step t935.t1.t5.t11 (cl (= @p_365 false)) :rule evaluate)
(step t935.t1.t5.t12 (cl (= @p_1346 false)) :rule trans :premises (t935.t1.t5.t10 t935.t1.t5.t11))
(step t935.t1.t5.t13 (cl @p_1344) :rule trans :premises (t935.t1.t5.t1 t935.t1.t5.t12))
(step t935.t1.t5.t14 (cl @p_1037 (! (not (! (<= @p_11 @p_1320) :named @p_1324)) :named @p_1328) @p_1342) :rule la_generic :args (1/1 1/1 1/1))
(step t935.t1.t5.t15 (cl (=> (! (and @p_308 @p_1267) :named @p_1325) @p_1324)) :rule la_mult_neg)
(step t935.t1.t5.t16 (cl (! (not @p_1325) :named @p_1326) @p_1324) :rule implies :premises (t935.t1.t5.t15))
(step t935.t1.t5.t17 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t935.t1.t5.t18 (cl (not @p_310) @p_308) :rule equiv1 :premises (t935.t1.t5.t17))
(step t935.t1.t5.t19 (cl @p_310) :rule evaluate)
(step t935.t1.t5.t20 (cl @p_308) :rule resolution :premises (t935.t1.t5.t18 t935.t1.t5.t19))
(step t935.t1.t5.t21 (cl @p_1325) :rule and_intro :premises (t935.t1.t5.t20 t935.t1.a0))
(step t935.t1.t5.t22 (cl @p_1324) :rule resolution :premises (t935.t1.t5.t16 t935.t1.t5.t21))
(step t935.t1.t5.t23 (cl @p_1342) :rule resolution :premises (t935.t1.t5.t14 t935.t1.t5.a0 t935.t1.t5.t22))
(step t935.t1.t5.t24 (cl false) :rule resolution :premises (t935.t1.t5.t0 t935.t1.t5.t13 t935.t1.t5.t23))
(step t935.t1.t5 (cl @p_1037 false) :rule subproof :discharge (t935.t1.t5.a0))
(step t935.t1.t6 (cl @p_1338 false) :rule resolution :premises (t935.t1.t4 t935.t1.t5))
(step t935.t1.t7 (cl @p_1338 @p_212) :rule implies_neg2)
(step t935.t1.t8 (cl @p_1338 @p_1338) :rule resolution :premises (t935.t1.t6 t935.t1.t7))
(step t935.t1.t9 (cl @p_1338) :rule contraction :premises (t935.t1.t8))
(step t935.t1.t10 (cl (! (= @p_1338 @p_1037) :named @p_1340)) :rule implies_simplify)
(step t935.t1.t11 (cl (! (not @p_1338) :named @p_1339) @p_1037) :rule equiv1 :premises (t935.t1.t10))
(step t935.t1.t12 (cl @p_1037) :rule resolution :premises (t935.t1.t9 t935.t1.t11))
(step t935.t1.t13 (cl @p_15) :rule resolution :premises (t935.t1.t0 t935.t1.t3 t935.t1.t12))
(step t935.t1 (cl (! (not @p_1267) :named @p_1269) @p_15) :rule subproof :discharge (t935.t1.a0))
(step t935.t2 (cl @p_1337 @p_15) :rule resolution :premises (t935.t0 t935.t1))
(step t935.t3 (cl @p_1337 @p_16) :rule implies_neg2)
(step t935.t4 (cl @p_1337 @p_1337) :rule resolution :premises (t935.t2 t935.t3))
(step t935.t5 (cl @p_1337) :rule contraction :premises (t935.t4))
(step t935.t6 (cl @p_1269 @p_15) :rule implies :premises (t935.t5))
(step t935.t7 (cl @p_15) :rule resolution :premises (t935.t6 t935.a0))
(step t935 (cl @p_1269 @p_15) :rule subproof :discharge (t935.a0))
(step t936 (cl @p_1337 @p_15) :rule resolution :premises (t934 t935))
(step t937 (cl @p_1337 @p_16) :rule implies_neg2)
(step t938 (cl @p_1337 @p_1337) :rule resolution :premises (t936 t937))
(step t939 (cl @p_1337) :rule contraction :premises (t938))
(step t940 (cl @p_1269 @p_15) :rule implies :premises (t939))
(step t941 (cl (! (=> @p_1267 @p_1049) :named @p_1316) @p_1267) :rule implies_neg1)
(anchor :step t942)
(assume t942.a0 @p_1267)
(step t942.t0 (cl @p_1316 @p_1267) :rule implies_neg1)
(anchor :step t942.t1)
(assume t942.t1.a0 @p_1267)
(step t942.t1.t0 (cl (! (not (! (= @p_1071 @p_1049) :named @p_1334)) :named @p_1335) (! (not @p_1071) :named @p_1336) @p_1049) :rule equiv_pos2)
(step t942.t1.t1 (cl (= @p_1066 @p_1051)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 1))
(step t942.t1.t2 (cl (= @p_1071 @p_1052)) :rule cong :premises (t942.t1.t1))
(step t942.t1.t3 (cl @p_1334) :rule trans :premises (t942.t1.t2 t690))
(step t942.t1.t4 (cl (! (=> @p_1066 false) :named @p_1317) @p_1066) :rule implies_neg1)
(anchor :step t942.t1.t5)
(assume t942.t1.t5.a0 @p_1066)
(step t942.t1.t5.t0 (cl (not (! (= (! (< @p_1322 (! (+ 1 @p_1320) :named @p_1321)) :named @p_1323) false) :named @p_1329)) (not @p_1323) false) :rule equiv_pos2)
(step t942.t1.t5.t1 (cl (= @p_1323 (! (not (! (>= @p_1322 @p_1321) :named @p_1330)) :named @p_1331))) :rule rare_rewrite :args ("arith-elim-lt" @p_1322 @p_1321))
(step t942.t1.t5.t2 (cl (= @p_1322 0)) :rule poly_simp)
(step t942.t1.t5.t3 (cl (= @p_1320 -3)) :rule evaluate)
(step t942.t1.t5.t4 (cl (= @p_1321 (! (+ 1 -3) :named @p_1333))) :rule cong :premises (t942.t1.t5.t3))
(step t942.t1.t5.t5 (cl (= @p_1333 -2)) :rule evaluate)
(step t942.t1.t5.t6 (cl (= @p_1321 -2)) :rule trans :premises (t942.t1.t5.t4 t942.t1.t5.t5))
(step t942.t1.t5.t7 (cl (= @p_1330 (! (>= 0 -2) :named @p_1332))) :rule cong :premises (t942.t1.t5.t2 t942.t1.t5.t6))
(step t942.t1.t5.t8 (cl (= @p_1332 true)) :rule evaluate)
(step t942.t1.t5.t9 (cl (= @p_1330 true)) :rule trans :premises (t942.t1.t5.t7 t942.t1.t5.t8))
(step t942.t1.t5.t10 (cl (= @p_1331 @p_365)) :rule cong :premises (t942.t1.t5.t9))
(step t942.t1.t5.t11 (cl (= @p_365 false)) :rule evaluate)
(step t942.t1.t5.t12 (cl (= @p_1331 false)) :rule trans :premises (t942.t1.t5.t10 t942.t1.t5.t11))
(step t942.t1.t5.t13 (cl @p_1329) :rule trans :premises (t942.t1.t5.t1 t942.t1.t5.t12))
(step t942.t1.t5.t14 (cl @p_1071 @p_1328 @p_1323) :rule la_generic :args (1/1 1/1 1/1))
(step t942.t1.t5.t15 (cl (=> @p_1325 @p_1324)) :rule la_mult_neg)
(step t942.t1.t5.t16 (cl @p_1326 @p_1324) :rule implies :premises (t942.t1.t5.t15))
(step t942.t1.t5.t17 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t942.t1.t5.t18 (cl (not @p_310) @p_308) :rule equiv1 :premises (t942.t1.t5.t17))
(step t942.t1.t5.t19 (cl @p_310) :rule evaluate)
(step t942.t1.t5.t20 (cl @p_308) :rule resolution :premises (t942.t1.t5.t18 t942.t1.t5.t19))
(step t942.t1.t5.t21 (cl @p_1325) :rule and_intro :premises (t942.t1.t5.t20 t942.t1.a0))
(step t942.t1.t5.t22 (cl @p_1324) :rule resolution :premises (t942.t1.t5.t16 t942.t1.t5.t21))
(step t942.t1.t5.t23 (cl @p_1323) :rule resolution :premises (t942.t1.t5.t14 t942.t1.t5.a0 t942.t1.t5.t22))
(step t942.t1.t5.t24 (cl false) :rule resolution :premises (t942.t1.t5.t0 t942.t1.t5.t13 t942.t1.t5.t23))
(step t942.t1.t5 (cl @p_1071 false) :rule subproof :discharge (t942.t1.t5.a0))
(step t942.t1.t6 (cl @p_1317 false) :rule resolution :premises (t942.t1.t4 t942.t1.t5))
(step t942.t1.t7 (cl @p_1317 @p_212) :rule implies_neg2)
(step t942.t1.t8 (cl @p_1317 @p_1317) :rule resolution :premises (t942.t1.t6 t942.t1.t7))
(step t942.t1.t9 (cl @p_1317) :rule contraction :premises (t942.t1.t8))
(step t942.t1.t10 (cl (! (= @p_1317 @p_1071) :named @p_1319)) :rule implies_simplify)
(step t942.t1.t11 (cl (! (not @p_1317) :named @p_1318) @p_1071) :rule equiv1 :premises (t942.t1.t10))
(step t942.t1.t12 (cl @p_1071) :rule resolution :premises (t942.t1.t9 t942.t1.t11))
(step t942.t1.t13 (cl @p_1049) :rule resolution :premises (t942.t1.t0 t942.t1.t3 t942.t1.t12))
(step t942.t1 (cl @p_1269 @p_1049) :rule subproof :discharge (t942.t1.a0))
(step t942.t2 (cl @p_1316 @p_1049) :rule resolution :premises (t942.t0 t942.t1))
(step t942.t3 (cl @p_1316 @p_1051) :rule implies_neg2)
(step t942.t4 (cl @p_1316 @p_1316) :rule resolution :premises (t942.t2 t942.t3))
(step t942.t5 (cl @p_1316) :rule contraction :premises (t942.t4))
(step t942.t6 (cl @p_1269 @p_1049) :rule implies :premises (t942.t5))
(step t942.t7 (cl @p_1049) :rule resolution :premises (t942.t6 t942.a0))
(step t942 (cl @p_1269 @p_1049) :rule subproof :discharge (t942.a0))
(step t943 (cl @p_1316 @p_1049) :rule resolution :premises (t941 t942))
(step t944 (cl @p_1316 @p_1051) :rule implies_neg2)
(step t945 (cl @p_1316 @p_1316) :rule resolution :premises (t943 t944))
(step t946 (cl @p_1316) :rule contraction :premises (t945))
(step t947 (cl @p_1269 @p_1049) :rule implies :premises (t946))
(step t948 (cl (not (! (= (! (or @p_583 @p_671 @p_792 (! (not (! (not (! (= @p_8 2) :named @p_1168)) :named @p_1179)) :named @p_1183) (! (not (! (not (! (>= @p_57 1) :named @p_1248)) :named @p_1249)) :named @p_1251) (! (not @p_1269) :named @p_1270) @p_532 @p_834) :named @p_1271) (! (or @p_583 @p_671 @p_792 @p_1168 @p_1248 @p_1267 @p_532 @p_834) :named @p_1268)) :named @p_1315)) (not @p_1271) @p_1268) :rule equiv_pos2)
(step t949 (cl (= @p_1183 @p_1168)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1168))
(step t950 (cl (= @p_1251 @p_1248)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1248))
(step t951 (cl (= @p_1270 @p_1267)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1267))
(step t952 (cl @p_1315) :rule cong :premises (t949 t950 t951 t40 t691))
(step t953 (cl (! (=> (! (and @p_524 @p_670 @p_786 @p_1179 @p_1249 @p_1269 @p_106 @p_833) :named @p_1272) (! (and @p_833 @p_801 @p_1249 @p_924 (! (not (! (= 2 @p_8) :named @p_1172)) :named @p_1193) @p_1269) :named @p_1274)) :named @p_1312) @p_1272) :rule implies_neg1)
(anchor :step t954)
(assume t954.a0 @p_524)
(assume t954.a1 @p_670)
(assume t954.a2 @p_786)
(assume t954.a3 @p_1179)
(assume t954.a4 @p_1249)
(assume t954.a5 @p_1269)
(assume t954.a6 @p_106)
(assume t954.a7 @p_833)
(step t954.t0 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t954.t1 (cl @p_801) :rule trans :premises (t954.t0 t755))
(step t954.t2 (cl @p_969 @p_967) :rule implies_neg1)
(anchor :step t954.t3)
(assume t954.t3.a0 @p_106)
(assume t954.t3.a1 @p_524)
(assume t954.t3.a2 @p_670)
(step t954.t3.t0 (cl @p_527) :rule symm :premises (t954.t3.a1))
(step t954.t3.t1 (cl @p_924) :rule trans :premises (t954.t0 t954.t3.t0 t742))
(step t954.t3 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t954.t3.a0 t954.t3.a1 t954.t3.a2))
(step t954.t4 (cl @p_968 @p_106) :rule and_pos :args (0))
(step t954.t5 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t954.t6 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t954.t7 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t954.t3 t954.t4 t954.t5 t954.t6))
(step t954.t8 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t954.t7))
(step t954.t9 (cl @p_968 @p_924) :rule contraction :premises (t954.t8))
(step t954.t10 (cl @p_969 @p_924) :rule resolution :premises (t954.t2 t954.t9))
(step t954.t11 (cl @p_969 @p_928) :rule implies_neg2)
(step t954.t12 (cl @p_969 @p_969) :rule resolution :premises (t954.t10 t954.t11))
(step t954.t13 (cl @p_969) :rule contraction :premises (t954.t12))
(step t954.t14 (cl @p_968 @p_924) :rule implies :premises (t954.t13))
(step t954.t15 (cl @p_967) :rule and_intro :premises (t742 t954.a0 t758))
(step t954.t16 (cl @p_924) :rule resolution :premises (t954.t14 t954.t15))
(step t954.t17 (cl (! (=> @p_1179 @p_1193) :named @p_1314) @p_1179) :rule implies_neg1)
(anchor :step t954.t18)
(assume t954.t18.a0 @p_1179)
(step t954.t18.t0 (cl @p_1193) :rule not_symm :premises (t954.t18.a0))
(step t954.t18 (cl @p_1183 @p_1193) :rule subproof :discharge (t954.t18.a0))
(step t954.t19 (cl @p_1314 @p_1193) :rule resolution :premises (t954.t17 t954.t18))
(step t954.t20 (cl @p_1314 (! (not @p_1193) :named @p_1277)) :rule implies_neg2)
(step t954.t21 (cl @p_1314 @p_1314) :rule resolution :premises (t954.t19 t954.t20))
(step t954.t22 (cl @p_1314) :rule contraction :premises (t954.t21))
(step t954.t23 (cl @p_1183 @p_1193) :rule implies :premises (t954.t22))
(step t954.t24 (cl @p_1193) :rule resolution :premises (t954.t23 t954.a3))
(step t954.t25 (cl @p_1274) :rule and_intro :premises (t954.a7 t954.t1 t954.a4 t954.t16 t954.t24 t954.a5))
(step t954 (cl @p_583 @p_671 @p_792 @p_1183 @p_1251 @p_1270 @p_532 @p_834 @p_1274) :rule subproof :discharge (t954.a0 t954.a1 t954.a2 t954.a3 t954.a4 t954.a5 t954.a6 t954.a7))
(step t955 (cl (! (not @p_1272) :named @p_1273) @p_524) :rule and_pos :args (0))
(step t956 (cl @p_1273 @p_670) :rule and_pos :args (1))
(step t957 (cl @p_1273 @p_786) :rule and_pos :args (2))
(step t958 (cl @p_1273 @p_1179) :rule and_pos :args (3))
(step t959 (cl @p_1273 @p_1249) :rule and_pos :args (4))
(step t960 (cl @p_1273 @p_1269) :rule and_pos :args (5))
(step t961 (cl @p_1273 @p_106) :rule and_pos :args (6))
(step t962 (cl @p_1273 @p_833) :rule and_pos :args (7))
(step t963 (cl @p_1274 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273) :rule resolution :premises (t954 t955 t956 t957 t958 t959 t960 t961 t962))
(step t964 (cl @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1273 @p_1274) :rule reordering :premises (t963))
(step t965 (cl @p_1273 @p_1274) :rule contraction :premises (t964))
(step t966 (cl @p_1312 @p_1274) :rule resolution :premises (t953 t965))
(step t967 (cl @p_1312 (! (not @p_1274) :named @p_1275)) :rule implies_neg2)
(step t968 (cl @p_1312 @p_1312) :rule resolution :premises (t966 t967))
(step t969 (cl @p_1312) :rule contraction :premises (t968))
(step t970 (cl @p_1273 @p_1274) :rule implies :premises (t969))
(step t971 (cl (! (=> @p_1274 false) :named @p_1276) @p_1274) :rule implies_neg1)
(anchor :step t972)
(assume t972.a0 @p_833)
(assume t972.a1 @p_801)
(assume t972.a2 @p_1249)
(assume t972.a3 @p_924)
(assume t972.a4 @p_1193)
(assume t972.a5 @p_1269)
(step t972.t0 (cl (! (not (! (< @p_8 2) :named @p_1302)) :named @p_1311) (! (<= @p_8 1) :named @p_1278)) :rule la_generic :args (1/1 1/1))
(step t972.t1 (cl (or @p_1168 (! (not (! (<= @p_8 2) :named @p_1305)) :named @p_1310) (! (not (<= 2 @p_8)) :named @p_1303))) :rule la_disequality)
(step t972.t2 (cl @p_1168 @p_1310 @p_1303) :rule or :premises (t972.t1))
(step t972.t3 (cl @p_1179) :rule not_symm :premises (t972.a4))
(step t972.t4 (cl (not (! (< @p_8 3) :named @p_1306)) @p_1305) :rule la_generic :args (1/1 1/1))
(step t972.t5 (cl (not (! (= @p_1269 @p_1306) :named @p_1309)) @p_1270 @p_1306) :rule equiv_pos2)
(step t972.t6 (cl (= @p_1306 @p_1269)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 3))
(step t972.t7 (cl @p_1309) :rule symm :premises (t972.t6))
(step t972.t8 (cl @p_1306) :rule resolution :premises (t972.t5 t972.t7 t972.a5))
(step t972.t9 (cl @p_1305) :rule resolution :premises (t972.t4 t972.t8))
(step t972.t10 (cl (not (! (= @p_1302 @p_1303) :named @p_1304)) @p_1302 (not @p_1303)) :rule equiv_pos1)
(step t972.t11 (cl @p_1304) :rule comp_simplify)
(step t972.t12 (cl @p_1302) :rule resolution :premises (t972.t2 t972.t3 t972.t9 t972.t10 t972.t11))
(step t972.t13 (cl @p_1278) :rule resolution :premises (t972.t0 t972.t12))
(step t972.t14 (cl (not (! (= (! (> @p_8 1) :named @p_1280) (! (not @p_1278) :named @p_1279)) :named @p_1299)) (not @p_1280) @p_1279) :rule equiv_pos2)
(step t972.t15 (cl (= @p_1280 (! (not (! (>= 1 @p_8) :named @p_1300)) :named @p_1301))) :rule rare_rewrite :args ("arith-elim-gt" @p_8 1))
(step t972.t16 (cl (= @p_1278 @p_1300)) :rule rare_rewrite :args ("arith-elim-leq" @p_8 1))
(step t972.t17 (cl (= @p_1300 @p_1278)) :rule symm :premises (t972.t16))
(step t972.t18 (cl (= @p_1301 @p_1279)) :rule cong :premises (t972.t17))
(step t972.t19 (cl @p_1299) :rule trans :premises (t972.t15 t972.t18))
(step t972.t20 (cl (not (! (= @p_1279 @p_1280) :named @p_1292)) (not @p_1279) @p_1280) :rule equiv_pos2)
(step t972.t21 (cl (= @p_1278 (! (not (! (>= @p_8 (! (+ 1 1) :named @p_1296)) :named @p_1297)) :named @p_1298))) :rule rare_rewrite :args ("arith-leq-norm" @p_8 1))
(step t972.t22 (cl (= @p_1296 2)) :rule evaluate)
(step t972.t23 (cl (= @p_1297 (! (>= @p_8 2) :named @p_1293))) :rule cong :premises (t972.t22))
(step t972.t24 (cl (= @p_1298 (! (not @p_1293) :named @p_1294))) :rule cong :premises (t972.t23))
(step t972.t25 (cl (= @p_1278 @p_1294)) :rule trans :premises (t972.t21 t972.t24))
(step t972.t26 (cl (= @p_1279 (! (not @p_1294) :named @p_1295))) :rule cong :premises (t972.t25))
(step t972.t27 (cl (= @p_1295 @p_1293)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1293))
(step t972.t28 (cl (= @p_1279 @p_1293)) :rule trans :premises (t972.t26 t972.t27))
(step t972.t29 (cl (= @p_1280 @p_1293)) :rule trans :premises (t972.t19 t972.t28))
(step t972.t30 (cl (= @p_1293 @p_1280)) :rule symm :premises (t972.t29))
(step t972.t31 (cl @p_1292) :rule trans :premises (t972.t28 t972.t30))
(step t972.t32 (cl (! (=> @p_1278 false) :named @p_1281) @p_1278) :rule implies_neg1)
(anchor :step t972.t33)
(assume t972.t33.a0 @p_1278)
(step t972.t33.t0 (cl (not (! (= (! (< (! (+ @p_8 @p_1025 @p_57 @p_799 @p_852) :named @p_1283) (! (+ 1 @p_297 1 0 @p_850) :named @p_1282)) :named @p_1284) false) :named @p_1286)) (not @p_1284) false) :rule equiv_pos2)
(step t972.t33.t1 (cl (= @p_1284 (! (not (! (>= @p_1283 @p_1282) :named @p_1287)) :named @p_1288))) :rule rare_rewrite :args ("arith-elim-lt" @p_1283 @p_1282))
(step t972.t33.t2 (cl (= @p_1283 @p_1290)) :rule poly_simp)
(step t972.t33.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t972.t33.t4 (cl (= @p_721 0)) :rule poly_simp)
(step t972.t33.t5 (cl (= @p_1290 @p_1291)) :rule cong :premises (t972.t33.t3 t972.t33.t4))
(step t972.t33.t6 (cl (= @p_1291 0)) :rule poly_simp)
(step t972.t33.t7 (cl (= @p_1290 0)) :rule trans :premises (t972.t33.t5 t972.t33.t6))
(step t972.t33.t8 (cl (= @p_1283 0)) :rule trans :premises (t972.t33.t2 t972.t33.t7))
(step t972.t33.t9 (cl (= @p_297 0)) :rule evaluate)
(step t972.t33.t10 (cl (= 1 1)) :rule refl)
(step t972.t33.t11 (cl (= @p_850 -2)) :rule evaluate)
(step t972.t33.t12 (cl (= @p_1282 (! (+ 1 0 1 0 -2) :named @p_1289))) :rule cong :premises (t972.t33.t9 t972.t33.t10 t604 t972.t33.t11))
(step t972.t33.t13 (cl (= @p_1289 0)) :rule evaluate)
(step t972.t33.t14 (cl (= @p_1282 0)) :rule trans :premises (t972.t33.t12 t972.t33.t13))
(step t972.t33.t15 (cl (= @p_1287 @p_366)) :rule cong :premises (t972.t33.t8 t972.t33.t14))
(step t972.t33.t16 (cl (= @p_366 true)) :rule evaluate)
(step t972.t33.t17 (cl (= @p_1287 true)) :rule trans :premises (t972.t33.t15 t972.t33.t16))
(step t972.t33.t18 (cl (= @p_1288 @p_365)) :rule cong :premises (t972.t33.t17))
(step t972.t33.t19 (cl (= @p_365 false)) :rule evaluate)
(step t972.t33.t20 (cl (= @p_1288 false)) :rule trans :premises (t972.t33.t18 t972.t33.t19))
(step t972.t33.t21 (cl @p_1286) :rule trans :premises (t972.t33.t1 t972.t33.t20))
(step t972.t33.t22 (cl @p_1279 @p_1038 (! (not (! (< @p_57 1) :named @p_1253)) :named @p_1266) @p_808 @p_859 @p_1284) :rule la_generic :args (1/1 -1/1 1/1 -1/1 1/1 1/1))
(step t972.t33.t23 (cl (=> @p_1029 @p_1028)) :rule la_mult_neg)
(step t972.t33.t24 (cl @p_1030 @p_1028) :rule implies :premises (t972.t33.t23))
(step t972.t33.t25 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t972.t33.t26 (cl (not @p_310) @p_308) :rule equiv1 :premises (t972.t33.t25))
(step t972.t33.t27 (cl @p_310) :rule evaluate)
(step t972.t33.t28 (cl @p_308) :rule resolution :premises (t972.t33.t26 t972.t33.t27))
(step t972.t33.t29 (cl @p_946 @p_928 @p_940) :rule equiv_pos2)
(step t972.t33.t30 (cl (= (* 1 (- @p_669 @p_105)) @p_945)) :rule poly_simp)
(step t972.t33.t31 (cl (= @p_924 @p_944)) :rule poly_simp_rel :premises (t972.t33.t30))
(step t972.t33.t32 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t972.t33.t33 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t972.t33.t32))
(step t972.t33.t34 (cl (= @p_944 @p_940)) :rule symm :premises (t972.t33.t33))
(step t972.t33.t35 (cl @p_942) :rule trans :premises (t972.t33.t31 t972.t33.t34))
(step t972.t33.t36 (cl @p_940) :rule resolution :premises (t972.t33.t29 t972.t33.t35 t972.a3))
(step t972.t33.t37 (cl @p_1029) :rule and_intro :premises (t972.t33.t28 t972.t33.t36))
(step t972.t33.t38 (cl @p_1028) :rule resolution :premises (t972.t33.t24 t972.t33.t37))
(step t972.t33.t39 (cl (! (not (! (= @p_1249 @p_1253) :named @p_1263)) :named @p_1265) @p_1251 @p_1253) :rule equiv_pos2)
(step t972.t33.t40 (cl (! (= @p_1253 @p_1249) :named @p_1264)) :rule rare_rewrite :args ("arith-elim-lt" @p_57 1))
(step t972.t33.t41 (cl @p_1263) :rule symm :premises (t972.t33.t40))
(step t972.t33.t42 (cl @p_1253) :rule resolution :premises (t972.t33.t39 t972.t33.t41 t972.a2))
(step t972.t33.t43 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t972.t33.t44 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t972.t33.t45 (cl @p_803) :rule poly_simp_rel :premises (t972.t33.t44))
(step t972.t33.t46 (cl (= @p_793 @p_800)) :rule symm :premises (t972.t33.t45))
(step t972.t33.t47 (cl @p_802) :rule trans :premises (t655 t972.t33.t46))
(step t972.t33.t48 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t972.t33.t49 (cl @p_801) :rule trans :premises (t972.t33.t48 t755))
(step t972.t33.t50 (cl @p_800) :rule resolution :premises (t972.t33.t43 t972.t33.t47 t972.t33.t49))
(step t972.t33.t51 (cl (=> @p_857 @p_856)) :rule la_mult_neg)
(step t972.t33.t52 (cl @p_858 @p_856) :rule implies :premises (t972.t33.t51))
(step t972.t33.t53 (cl @p_857) :rule and_intro :premises (t972.t33.t28 t972.a0))
(step t972.t33.t54 (cl @p_856) :rule resolution :premises (t972.t33.t52 t972.t33.t53))
(step t972.t33.t55 (cl @p_1284) :rule resolution :premises (t972.t33.t22 t972.t33.a0 t972.t33.t38 t972.t33.t42 t972.t33.t50 t972.t33.t54))
(step t972.t33.t56 (cl false) :rule resolution :premises (t972.t33.t0 t972.t33.t21 t972.t33.t55))
(step t972.t33 (cl @p_1279 false) :rule subproof :discharge (t972.t33.a0))
(step t972.t34 (cl @p_1281 false) :rule resolution :premises (t972.t32 t972.t33))
(step t972.t35 (cl @p_1281 @p_212) :rule implies_neg2)
(step t972.t36 (cl @p_1281 @p_1281) :rule resolution :premises (t972.t34 t972.t35))
(step t972.t37 (cl @p_1281) :rule contraction :premises (t972.t36))
(step t972.t38 (cl (= @p_1281 @p_1279)) :rule implies_simplify)
(step t972.t39 (cl (not @p_1281) @p_1279) :rule equiv1 :premises (t972.t38))
(step t972.t40 (cl @p_1279) :rule resolution :premises (t972.t37 t972.t39))
(step t972.t41 (cl @p_1280) :rule resolution :premises (t972.t20 t972.t31 t972.t40))
(step t972.t42 (cl @p_1279) :rule resolution :premises (t972.t14 t972.t19 t972.t41))
(step t972.t43 (cl) :rule resolution :premises (t972.t13 t972.t42))
(step t972 (cl @p_834 @p_806 @p_1251 @p_928 @p_1277 @p_1270 false) :rule subproof :discharge (t972.a0 t972.a1 t972.a2 t972.a3 t972.a4 t972.a5))
(step t973 (cl @p_1275 @p_833) :rule and_pos :args (0))
(step t974 (cl @p_1275 @p_801) :rule and_pos :args (1))
(step t975 (cl @p_1275 @p_1249) :rule and_pos :args (2))
(step t976 (cl @p_1275 @p_924) :rule and_pos :args (3))
(step t977 (cl @p_1275 @p_1193) :rule and_pos :args (4))
(step t978 (cl @p_1275 @p_1269) :rule and_pos :args (5))
(step t979 (cl false @p_1275 @p_1275 @p_1275 @p_1275 @p_1275 @p_1275) :rule resolution :premises (t972 t973 t974 t975 t976 t977 t978))
(step t980 (cl @p_1275 @p_1275 @p_1275 @p_1275 @p_1275 @p_1275 false) :rule reordering :premises (t979))
(step t981 (cl @p_1275 false) :rule contraction :premises (t980))
(step t982 (cl @p_1276 false) :rule resolution :premises (t971 t981))
(step t983 (cl @p_1276 @p_212) :rule implies_neg2)
(step t984 (cl @p_1276 @p_1276) :rule resolution :premises (t982 t983))
(step t985 (cl @p_1276) :rule contraction :premises (t984))
(step t986 (cl (= @p_1276 @p_1275)) :rule implies_simplify)
(step t987 (cl (not @p_1276) @p_1275) :rule equiv1 :premises (t986))
(step t988 (cl @p_1275) :rule resolution :premises (t985 t987))
(step t989 (cl @p_1273) :rule resolution :premises (t970 t988))
(step t990 (cl @p_583 @p_671 @p_792 @p_1183 @p_1251 @p_1270 @p_532 @p_834) :rule not_and :premises (t989))
(step t991 (cl @p_1271 @p_589) :rule or_neg :args (0))
(step t992 (cl @p_1271 @p_677) :rule or_neg :args (1))
(step t993 (cl @p_1271 @p_1017) :rule or_neg :args (2))
(step t994 (cl @p_1271 (not @p_1183)) :rule or_neg :args (3))
(step t995 (cl @p_1271 (not @p_1251)) :rule or_neg :args (4))
(step t996 (cl @p_1271 (not @p_1270)) :rule or_neg :args (5))
(step t997 (cl @p_1271 @p_538) :rule or_neg :args (6))
(step t998 (cl @p_1271 @p_838) :rule or_neg :args (7))
(step t999 (cl @p_1271 @p_1271 @p_1271 @p_1271 @p_1271 @p_1271 @p_1271 @p_1271) :rule resolution :premises (t990 t991 t992 t993 t994 t995 t996 t997 t998))
(step t1000 (cl @p_1271) :rule contraction :premises (t999))
(step t1001 (cl @p_1268) :rule resolution :premises (t948 t952 t1000))
(step t1002 (cl @p_583 @p_671 @p_792 @p_1168 @p_1248 @p_1267 @p_532 @p_834) :rule or :premises (t1001))
(step t1003 (cl (! (=> @p_63 @p_1249) :named @p_1250) @p_63) :rule implies_neg1)
(anchor :step t1004)
(assume t1004.a0 @p_63)
(step t1004.t0 (cl (! (=> @p_1188 @p_1249) :named @p_1252) @p_1188) :rule implies_neg1)
(anchor :step t1004.t1)
(assume t1004.t1.a0 @p_1188)
(step t1004.t1.t0 (cl (not @p_1264) @p_1266 @p_1249) :rule equiv_pos2)
(step t1004.t1.t1 (cl @p_1264) :rule rare_rewrite :args ("arith-elim-lt" @p_57 1))
(step t1004.t1.t2 (cl @p_1265 @p_1251 @p_1253) :rule equiv_pos2)
(step t1004.t1.t3 (cl @p_1263) :rule symm :premises (t1004.t1.t1))
(step t1004.t1.t4 (cl (! (=> @p_1248 false) :named @p_1254) @p_1248) :rule implies_neg1)
(anchor :step t1004.t1.t5)
(assume t1004.t1.t5.a0 @p_1248)
(step t1004.t1.t5.t0 (cl (not (! (= (! (<= (! (+ @p_689 @p_57) :named @p_1256) (! (+ @p_298 0) :named @p_1255)) :named @p_1257) false) :named @p_1261)) (not @p_1257) false) :rule equiv_pos2)
(step t1004.t1.t5.t1 (cl (= @p_1256 0)) :rule poly_simp)
(step t1004.t1.t5.t2 (cl (= @p_298 -1)) :rule evaluate)
(step t1004.t1.t5.t3 (cl (= @p_1255 (! (+ -1 0) :named @p_1262))) :rule cong :premises (t1004.t1.t5.t2 t604))
(step t1004.t1.t5.t4 (cl (= @p_1262 -1)) :rule evaluate)
(step t1004.t1.t5.t5 (cl (= @p_1255 -1)) :rule trans :premises (t1004.t1.t5.t3 t1004.t1.t5.t4))
(step t1004.t1.t5.t6 (cl (= @p_1257 @p_323)) :rule cong :premises (t1004.t1.t5.t1 t1004.t1.t5.t5))
(step t1004.t1.t5.t7 (cl (= @p_323 false)) :rule evaluate)
(step t1004.t1.t5.t8 (cl @p_1261) :rule trans :premises (t1004.t1.t5.t6 t1004.t1.t5.t7))
(step t1004.t1.t5.t9 (cl (not (! (<= @p_689 @p_298) :named @p_1258)) @p_66 @p_1257) :rule la_generic :args (1/1 -1/1 1/1))
(step t1004.t1.t5.t10 (cl (=> (! (and @p_308 @p_1248) :named @p_1259) @p_1258)) :rule la_mult_neg)
(step t1004.t1.t5.t11 (cl (not @p_1259) @p_1258) :rule implies :premises (t1004.t1.t5.t10))
(step t1004.t1.t5.t12 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1004.t1.t5.t13 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1004.t1.t5.t12))
(step t1004.t1.t5.t14 (cl @p_310) :rule evaluate)
(step t1004.t1.t5.t15 (cl @p_308) :rule resolution :premises (t1004.t1.t5.t13 t1004.t1.t5.t14))
(step t1004.t1.t5.t16 (cl @p_1259) :rule and_intro :premises (t1004.t1.t5.t15 t1004.t1.t5.a0))
(step t1004.t1.t5.t17 (cl @p_1258) :rule resolution :premises (t1004.t1.t5.t11 t1004.t1.t5.t16))
(step t1004.t1.t5.t18 (cl @p_63) :rule symm :premises (t1004.t1.a0))
(step t1004.t1.t5.t19 (cl @p_1257) :rule resolution :premises (t1004.t1.t5.t9 t1004.t1.t5.t17 t1004.t1.t5.t18))
(step t1004.t1.t5.t20 (cl false) :rule resolution :premises (t1004.t1.t5.t0 t1004.t1.t5.t8 t1004.t1.t5.t19))
(step t1004.t1.t5 (cl @p_1249 false) :rule subproof :discharge (t1004.t1.t5.a0))
(step t1004.t1.t6 (cl @p_1254 false) :rule resolution :premises (t1004.t1.t4 t1004.t1.t5))
(step t1004.t1.t7 (cl @p_1254 @p_212) :rule implies_neg2)
(step t1004.t1.t8 (cl @p_1254 @p_1254) :rule resolution :premises (t1004.t1.t6 t1004.t1.t7))
(step t1004.t1.t9 (cl @p_1254) :rule contraction :premises (t1004.t1.t8))
(step t1004.t1.t10 (cl (= @p_1254 @p_1249)) :rule implies_simplify)
(step t1004.t1.t11 (cl (not @p_1254) @p_1249) :rule equiv1 :premises (t1004.t1.t10))
(step t1004.t1.t12 (cl @p_1249) :rule resolution :premises (t1004.t1.t9 t1004.t1.t11))
(step t1004.t1.t13 (cl @p_1253) :rule resolution :premises (t1004.t1.t2 t1004.t1.t3 t1004.t1.t12))
(step t1004.t1.t14 (cl @p_1249) :rule resolution :premises (t1004.t1.t0 t1004.t1.t1 t1004.t1.t13))
(step t1004.t1 (cl @p_1192 @p_1249) :rule subproof :discharge (t1004.t1.a0))
(step t1004.t2 (cl @p_1252 @p_1249) :rule resolution :premises (t1004.t0 t1004.t1))
(step t1004.t3 (cl @p_1252 @p_1251) :rule implies_neg2)
(step t1004.t4 (cl @p_1252 @p_1252) :rule resolution :premises (t1004.t2 t1004.t3))
(step t1004.t5 (cl @p_1252) :rule contraction :premises (t1004.t4))
(step t1004.t6 (cl @p_1192 @p_1249) :rule implies :premises (t1004.t5))
(step t1004.t7 (cl @p_1224 @p_63) :rule implies_neg1)
(anchor :step t1004.t8)
(assume t1004.t8.a0 @p_63)
(step t1004.t8.t0 (cl @p_1188) :rule symm :premises (t1004.t8.a0))
(step t1004.t8 (cl @p_66 @p_1188) :rule subproof :discharge (t1004.t8.a0))
(step t1004.t9 (cl @p_1224 @p_1188) :rule resolution :premises (t1004.t7 t1004.t8))
(step t1004.t10 (cl @p_1224 @p_1192) :rule implies_neg2)
(step t1004.t11 (cl @p_1224 @p_1224) :rule resolution :premises (t1004.t9 t1004.t10))
(step t1004.t12 (cl @p_1224) :rule contraction :premises (t1004.t11))
(step t1004.t13 (cl @p_66 @p_1188) :rule implies :premises (t1004.t12))
(step t1004.t14 (cl @p_1188) :rule resolution :premises (t1004.t13 t1004.a0))
(step t1004.t15 (cl @p_1249) :rule resolution :premises (t1004.t6 t1004.t14))
(step t1004 (cl @p_66 @p_1249) :rule subproof :discharge (t1004.a0))
(step t1005 (cl @p_1250 @p_1249) :rule resolution :premises (t1003 t1004))
(step t1006 (cl @p_1250 @p_1251) :rule implies_neg2)
(step t1007 (cl @p_1250 @p_1250) :rule resolution :premises (t1005 t1006))
(step t1008 (cl @p_1250) :rule contraction :premises (t1007))
(step t1009 (cl @p_66 @p_1249) :rule implies :premises (t1008))
(step t1010 (cl (! (not (! (= (! (= @p_7 1) :named @p_1166) @p_1168) :named @p_1169)) :named @p_1178) @p_1166 @p_1179) :rule equiv_pos1)
(step t1011 (cl @p_1166 @p_1179 @p_1178) :rule reordering :premises (t1010))
(step t1012 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) (! (= @p_1172 (! (or (! (= 2 0) :named @p_85) @p_1166) :named @p_1171)) :named @p_1173)) :named @p_1174) (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) @p_1169) :named @p_1170)) :named @p_1175)) (not @p_1174) @p_1170) :rule equiv_pos2)
(step t1013 (cl (= (* -2 (- 2 @p_8)) (* 2 (- @p_8 2)))) :rule poly_simp)
(step t1014 (cl (= @p_1172 @p_1168)) :rule poly_simp_rel :premises (t1013))
(step t1015 (cl (= @p_85 false)) :rule evaluate)
(step t1016 (cl (= @p_1166 @p_1166)) :rule refl)
(step t1017 (cl (= @p_1171 (! (or false @p_1166) :named @p_1177))) :rule cong :premises (t1015 t1016))
(step t1018 (cl (= @p_1177 @p_1166)) :rule aci_simp)
(step t1019 (cl (= @p_1171 @p_1166)) :rule trans :premises (t1017 t1018))
(step t1020 (cl (= @p_1173 (! (= @p_1168 @p_1166) :named @p_1176))) :rule cong :premises (t1014 t1019))
(step t1021 (cl (= @p_1176 @p_1169)) :rule rare_rewrite :args ("eq-symm" @p_1168 @p_1166))
(step t1022 (cl (= @p_1173 @p_1169)) :rule trans :premises (t1020 t1021))
(step t1023 (cl @p_1175) :rule cong :premises (t1022))
(step t1024 (cl @p_1174 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t1025)
(assume t1025.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t1025.t0 (cl (or @p_91 @p_1173)) :rule forall_inst :args (2 @p_7))
(step t1025.t1 (cl @p_91 @p_1173) :rule or :premises (t1025.t0))
(step t1025.t2 (cl @p_1173) :rule resolution :premises (t1025.t1 t1025.a0))
(step t1025 (cl @p_91 @p_1173) :rule subproof :discharge (t1025.a0))
(step t1026 (cl @p_1174 @p_1173) :rule resolution :premises (t1024 t1025))
(step t1027 (cl @p_1174 (not @p_1173)) :rule implies_neg2)
(step t1028 (cl @p_1174 @p_1174) :rule resolution :premises (t1026 t1027))
(step t1029 (cl @p_1174) :rule contraction :premises (t1028))
(step t1030 (cl @p_1170) :rule resolution :premises (t1012 t1023 t1029))
(step t1031 (cl @p_91 @p_1169) :rule implies :premises (t1030))
(step t1032 (cl (not (! (= (! (or @p_671 @p_792 @p_673 (! (not @p_1166) :named @p_1167) @p_1179 @p_974) :named @p_1227) (! (or @p_671 @p_792 @p_112 @p_1167 @p_1179 @p_974) :named @p_1226)) :named @p_1241)) (not @p_1227) @p_1226) :rule equiv_pos2)
(step t1033 (cl (= @p_1167 @p_1167)) :rule refl)
(step t1034 (cl (= @p_1179 @p_1179)) :rule refl)
(step t1035 (cl @p_1241) :rule cong :premises (t38 t1033 t1034 t760))
(step t1036 (cl (! (=> (! (and @p_670 @p_786 @p_113 @p_1166 @p_1168 @p_58) :named @p_1228) (! (and @p_923 @p_113 @p_670 @p_1172 @p_801 (! (= 1 @p_7) :named @p_1187)) :named @p_1230)) :named @p_1240) @p_1228) :rule implies_neg1)
(anchor :step t1037)
(assume t1037.a0 @p_670)
(assume t1037.a1 @p_786)
(assume t1037.a2 @p_113)
(assume t1037.a3 @p_1166)
(assume t1037.a4 @p_1168)
(assume t1037.a5 @p_58)
(step t1037.t0 (cl @p_1047 @p_58) :rule implies_neg1)
(anchor :step t1037.t1)
(assume t1037.t1.a0 @p_58)
(step t1037.t1.t0 (cl @p_923) :rule symm :premises (t1037.t1.a0))
(step t1037.t1 (cl @p_974 @p_923) :rule subproof :discharge (t1037.t1.a0))
(step t1037.t2 (cl @p_1047 @p_923) :rule resolution :premises (t1037.t0 t1037.t1))
(step t1037.t3 (cl @p_1047 @p_929) :rule implies_neg2)
(step t1037.t4 (cl @p_1047 @p_1047) :rule resolution :premises (t1037.t2 t1037.t3))
(step t1037.t5 (cl @p_1047) :rule contraction :premises (t1037.t4))
(step t1037.t6 (cl @p_974 @p_923) :rule implies :premises (t1037.t5))
(step t1037.t7 (cl @p_923) :rule resolution :premises (t1037.t6 t1037.a5))
(step t1037.t8 (cl (! (=> @p_1168 @p_1172) :named @p_1222) @p_1168) :rule implies_neg1)
(anchor :step t1037.t9)
(assume t1037.t9.a0 @p_1168)
(step t1037.t9.t0 (cl @p_1172) :rule symm :premises (t1037.t9.a0))
(step t1037.t9 (cl @p_1179 @p_1172) :rule subproof :discharge (t1037.t9.a0))
(step t1037.t10 (cl @p_1222 @p_1172) :rule resolution :premises (t1037.t8 t1037.t9))
(step t1037.t11 (cl @p_1222 @p_1193) :rule implies_neg2)
(step t1037.t12 (cl @p_1222 @p_1222) :rule resolution :premises (t1037.t10 t1037.t11))
(step t1037.t13 (cl @p_1222) :rule contraction :premises (t1037.t12))
(step t1037.t14 (cl @p_1179 @p_1172) :rule implies :premises (t1037.t13))
(step t1037.t15 (cl @p_1172) :rule resolution :premises (t1037.t14 t1037.a4))
(step t1037.t16 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1037.t17 (cl @p_801) :rule trans :premises (t1037.t16 t755))
(step t1037.t18 (cl (! (=> @p_1166 @p_1187) :named @p_1220) @p_1166) :rule implies_neg1)
(anchor :step t1037.t19)
(assume t1037.t19.a0 @p_1166)
(step t1037.t19.t0 (cl @p_1187) :rule symm :premises (t1037.t19.a0))
(step t1037.t19 (cl @p_1167 @p_1187) :rule subproof :discharge (t1037.t19.a0))
(step t1037.t20 (cl @p_1220 @p_1187) :rule resolution :premises (t1037.t18 t1037.t19))
(step t1037.t21 (cl @p_1220 (! (not @p_1187) :named @p_1194)) :rule implies_neg2)
(step t1037.t22 (cl @p_1220 @p_1220) :rule resolution :premises (t1037.t20 t1037.t21))
(step t1037.t23 (cl @p_1220) :rule contraction :premises (t1037.t22))
(step t1037.t24 (cl @p_1167 @p_1187) :rule implies :premises (t1037.t23))
(step t1037.t25 (cl @p_1187) :rule resolution :premises (t1037.t24 t1037.a3))
(step t1037.t26 (cl @p_1230) :rule and_intro :premises (t1037.t7 t1037.a2 t758 t1037.t15 t1037.t17 t1037.t25))
(step t1037 (cl @p_671 @p_792 @p_673 @p_1167 @p_1179 @p_974 @p_1230) :rule subproof :discharge (t1037.a0 t1037.a1 t1037.a2 t1037.a3 t1037.a4 t1037.a5))
(step t1038 (cl (! (not @p_1228) :named @p_1229) @p_670) :rule and_pos :args (0))
(step t1039 (cl @p_1229 @p_786) :rule and_pos :args (1))
(step t1040 (cl @p_1229 @p_113) :rule and_pos :args (2))
(step t1041 (cl @p_1229 @p_1166) :rule and_pos :args (3))
(step t1042 (cl @p_1229 @p_1168) :rule and_pos :args (4))
(step t1043 (cl @p_1229 @p_58) :rule and_pos :args (5))
(step t1044 (cl @p_1230 @p_1229 @p_1229 @p_1229 @p_1229 @p_1229 @p_1229) :rule resolution :premises (t1037 t1038 t1039 t1040 t1041 t1042 t1043))
(step t1045 (cl @p_1229 @p_1229 @p_1229 @p_1229 @p_1229 @p_1229 @p_1230) :rule reordering :premises (t1044))
(step t1046 (cl @p_1229 @p_1230) :rule contraction :premises (t1045))
(step t1047 (cl @p_1240 @p_1230) :rule resolution :premises (t1036 t1046))
(step t1048 (cl @p_1240 (! (not @p_1230) :named @p_1231)) :rule implies_neg2)
(step t1049 (cl @p_1240 @p_1240) :rule resolution :premises (t1047 t1048))
(step t1050 (cl @p_1240) :rule contraction :premises (t1049))
(step t1051 (cl @p_1229 @p_1230) :rule implies :premises (t1050))
(step t1052 (cl (! (=> @p_1230 false) :named @p_1232) @p_1230) :rule implies_neg1)
(anchor :step t1053)
(assume t1053.a0 @p_923)
(assume t1053.a1 @p_113)
(assume t1053.a2 @p_670)
(assume t1053.a3 @p_1172)
(assume t1053.a4 @p_801)
(assume t1053.a5 @p_1187)
(step t1053.t0 (cl @p_1166) :rule symm :premises (t1053.a5))
(step t1053.t1 (cl (! (=> @p_1166 false) :named @p_1195) @p_1166) :rule implies_neg1)
(anchor :step t1053.t2)
(assume t1053.t2.a0 @p_1166)
(step t1053.t2.t0 (cl (not (! (= (! (< (! (+ @p_7 @p_988 @p_11 (! (* -1 (! (+ @p_6 @p_690 @p_689) :named @p_691)) :named @p_692) @p_111 @p_689) :named @p_1199) (! (+ 1 @p_297 @p_850 @p_297 1 @p_298) :named @p_1233)) :named @p_1234) false) :named @p_1235)) (not @p_1234) false) :rule equiv_pos2)
(step t1053.t2.t1 (cl (= @p_1234 (! (not (! (>= @p_1199 @p_1233) :named @p_1236)) :named @p_1237))) :rule rare_rewrite :args ("arith-elim-lt" @p_1199 @p_1233))
(step t1053.t2.t2 (cl (= @p_1199 (! (+ @p_722 @p_668 @p_1007 @p_690 @p_46 @p_7 @p_617) :named @p_1216))) :rule poly_simp)
(step t1053.t2.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t1053.t2.t4 (cl (= @p_668 @p_668)) :rule refl)
(step t1053.t2.t5 (cl (= @p_1007 0)) :rule poly_simp)
(step t1053.t2.t6 (cl (= @p_690 @p_690)) :rule refl)
(step t1053.t2.t7 (cl @p_168) :rule refl)
(step t1053.t2.t8 (cl @p_167) :rule refl)
(step t1053.t2.t9 (cl (= @p_617 0)) :rule poly_simp)
(step t1053.t2.t10 (cl (= @p_1216 (! (+ 0 @p_668 0 @p_690 @p_46 @p_7 0) :named @p_1217))) :rule cong :premises (t1053.t2.t3 t1053.t2.t4 t1053.t2.t5 t1053.t2.t6 t1053.t2.t7 t1053.t2.t8 t1053.t2.t9))
(step t1053.t2.t11 (cl (= @p_1217 0)) :rule poly_simp)
(step t1053.t2.t12 (cl (= @p_1216 0)) :rule trans :premises (t1053.t2.t10 t1053.t2.t11))
(step t1053.t2.t13 (cl (= @p_1199 0)) :rule trans :premises (t1053.t2.t2 t1053.t2.t12))
(step t1053.t2.t14 (cl (= @p_297 0)) :rule evaluate)
(step t1053.t2.t15 (cl (= @p_850 -2)) :rule evaluate)
(step t1053.t2.t16 (cl (= 1 1)) :rule refl)
(step t1053.t2.t17 (cl (= @p_298 -1)) :rule evaluate)
(step t1053.t2.t18 (cl (= @p_1233 (! (+ 1 0 -2 0 1 -1) :named @p_1239))) :rule cong :premises (t1053.t2.t14 t1053.t2.t15 t1053.t2.t14 t1053.t2.t16 t1053.t2.t17))
(step t1053.t2.t19 (cl (= @p_1239 -1)) :rule evaluate)
(step t1053.t2.t20 (cl (= @p_1233 -1)) :rule trans :premises (t1053.t2.t18 t1053.t2.t19))
(step t1053.t2.t21 (cl (= @p_1236 (! (>= 0 -1) :named @p_1238))) :rule cong :premises (t1053.t2.t13 t1053.t2.t20))
(step t1053.t2.t22 (cl (= @p_1238 true)) :rule evaluate)
(step t1053.t2.t23 (cl (= @p_1236 true)) :rule trans :premises (t1053.t2.t21 t1053.t2.t22))
(step t1053.t2.t24 (cl (= @p_1237 @p_365)) :rule cong :premises (t1053.t2.t23))
(step t1053.t2.t25 (cl (= @p_365 false)) :rule evaluate)
(step t1053.t2.t26 (cl (= @p_1237 false)) :rule trans :premises (t1053.t2.t24 t1053.t2.t25))
(step t1053.t2.t27 (cl @p_1235) :rule trans :premises (t1053.t2.t1 t1053.t2.t26))
(step t1053.t2.t28 (cl @p_1167 @p_1002 (! (not (! (= @p_11 @p_850) :named @p_1205)) :named @p_1210) (! (not (! (= @p_692 @p_297) :named @p_696)) :named @p_716) @p_715 @p_954 @p_1234) :rule la_generic :args (-1/1 -1/1 -1/1 -1/1 1/1 -1/1 1/1))
(step t1053.t2.t29 (cl (=> @p_993 @p_992)) :rule la_mult_neg)
(step t1053.t2.t30 (cl (not @p_993) @p_992) :rule implies :premises (t1053.t2.t29))
(step t1053.t2.t31 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1053.t2.t32 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1053.t2.t31))
(step t1053.t2.t33 (cl @p_310) :rule evaluate)
(step t1053.t2.t34 (cl @p_308) :rule resolution :premises (t1053.t2.t32 t1053.t2.t33))
(step t1053.t2.t35 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1053.t2.t36 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1053.t2.t37 (cl @p_803) :rule poly_simp_rel :premises (t1053.t2.t36))
(step t1053.t2.t38 (cl (= @p_793 @p_800)) :rule symm :premises (t1053.t2.t37))
(step t1053.t2.t39 (cl @p_802) :rule trans :premises (t655 t1053.t2.t38))
(step t1053.t2.t40 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1053.t2.t41 (cl @p_801) :rule trans :premises (t1053.t2.t40 t755))
(step t1053.t2.t42 (cl @p_800) :rule resolution :premises (t1053.t2.t35 t1053.t2.t39 t1053.t2.t41))
(step t1053.t2.t43 (cl @p_993) :rule and_intro :premises (t1053.t2.t34 t1053.t2.t42))
(step t1053.t2.t44 (cl @p_992) :rule resolution :premises (t1053.t2.t30 t1053.t2.t43))
(step t1053.t2.t45 (cl (=> (! (and @p_308 @p_1168) :named @p_1206) @p_1205)) :rule la_mult_neg)
(step t1053.t2.t46 (cl (! (not @p_1206) :named @p_1208) @p_1205) :rule implies :premises (t1053.t2.t45))
(step t1053.t2.t47 (cl @p_1168) :rule symm :premises (t1053.a3))
(step t1053.t2.t48 (cl @p_1206) :rule and_intro :premises (t1053.t2.t34 t1053.t2.t47))
(step t1053.t2.t49 (cl @p_1205) :rule resolution :premises (t1053.t2.t46 t1053.t2.t48))
(step t1053.t2.t50 (cl (=> (! (and @p_308 (! (= @p_691 0) :named @p_697)) :named @p_698) @p_696)) :rule la_mult_neg)
(step t1053.t2.t51 (cl (not @p_698) @p_696) :rule implies :premises (t1053.t2.t50))
(step t1053.t2.t52 (cl (not (! (= @p_670 @p_697) :named @p_699)) @p_671 @p_697) :rule equiv_pos2)
(step t1053.t2.t53 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t1053.t2.t54 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t1053.t2.t53))
(step t1053.t2.t55 (cl @p_699) :rule symm :premises (t1053.t2.t54))
(step t1053.t2.t56 (cl @p_697) :rule resolution :premises (t1053.t2.t52 t1053.t2.t55 t758))
(step t1053.t2.t57 (cl @p_698) :rule and_intro :premises (t1053.t2.t34 t1053.t2.t56))
(step t1053.t2.t58 (cl @p_696) :rule resolution :premises (t1053.t2.t51 t1053.t2.t57))
(step t1053.t2.t59 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t1053.t2.t60 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t1053.t2.t61 (cl @p_703) :rule symm :premises (t1053.t2.t60))
(step t1053.t2.t62 (cl @p_700) :rule resolution :premises (t1053.t2.t59 t1053.t2.t61 t1053.a1))
(step t1053.t2.t63 (cl (=> @p_948 @p_947)) :rule la_mult_neg)
(step t1053.t2.t64 (cl @p_950 @p_947) :rule implies :premises (t1053.t2.t63))
(step t1053.t2.t65 (cl @p_58) :rule symm :premises (t1053.a0))
(step t1053.t2.t66 (cl @p_948) :rule and_intro :premises (t1053.t2.t34 t1053.t2.t65))
(step t1053.t2.t67 (cl @p_947) :rule resolution :premises (t1053.t2.t64 t1053.t2.t66))
(step t1053.t2.t68 (cl @p_1234) :rule resolution :premises (t1053.t2.t28 t1053.t2.a0 t1053.t2.t44 t1053.t2.t49 t1053.t2.t58 t1053.t2.t62 t1053.t2.t67))
(step t1053.t2.t69 (cl false) :rule resolution :premises (t1053.t2.t0 t1053.t2.t27 t1053.t2.t68))
(step t1053.t2 (cl @p_1167 false) :rule subproof :discharge (t1053.t2.a0))
(step t1053.t3 (cl @p_1195 false) :rule resolution :premises (t1053.t1 t1053.t2))
(step t1053.t4 (cl @p_1195 @p_212) :rule implies_neg2)
(step t1053.t5 (cl @p_1195 @p_1195) :rule resolution :premises (t1053.t3 t1053.t4))
(step t1053.t6 (cl @p_1195) :rule contraction :premises (t1053.t5))
(step t1053.t7 (cl (! (= @p_1195 @p_1167) :named @p_1197)) :rule implies_simplify)
(step t1053.t8 (cl (! (not @p_1195) :named @p_1196) @p_1167) :rule equiv1 :premises (t1053.t7))
(step t1053.t9 (cl @p_1167) :rule resolution :premises (t1053.t6 t1053.t8))
(step t1053.t10 (cl) :rule resolution :premises (t1053.t0 t1053.t9))
(step t1053 (cl @p_929 @p_673 @p_671 @p_1193 @p_806 @p_1194 false) :rule subproof :discharge (t1053.a0 t1053.a1 t1053.a2 t1053.a3 t1053.a4 t1053.a5))
(step t1054 (cl @p_1231 @p_923) :rule and_pos :args (0))
(step t1055 (cl @p_1231 @p_113) :rule and_pos :args (1))
(step t1056 (cl @p_1231 @p_670) :rule and_pos :args (2))
(step t1057 (cl @p_1231 @p_1172) :rule and_pos :args (3))
(step t1058 (cl @p_1231 @p_801) :rule and_pos :args (4))
(step t1059 (cl @p_1231 @p_1187) :rule and_pos :args (5))
(step t1060 (cl false @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231) :rule resolution :premises (t1053 t1054 t1055 t1056 t1057 t1058 t1059))
(step t1061 (cl @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 false) :rule reordering :premises (t1060))
(step t1062 (cl @p_1231 false) :rule contraction :premises (t1061))
(step t1063 (cl @p_1232 false) :rule resolution :premises (t1052 t1062))
(step t1064 (cl @p_1232 @p_212) :rule implies_neg2)
(step t1065 (cl @p_1232 @p_1232) :rule resolution :premises (t1063 t1064))
(step t1066 (cl @p_1232) :rule contraction :premises (t1065))
(step t1067 (cl (= @p_1232 @p_1231)) :rule implies_simplify)
(step t1068 (cl (not @p_1232) @p_1231) :rule equiv1 :premises (t1067))
(step t1069 (cl @p_1231) :rule resolution :premises (t1066 t1068))
(step t1070 (cl @p_1229) :rule resolution :premises (t1051 t1069))
(step t1071 (cl @p_671 @p_792 @p_673 @p_1167 @p_1179 @p_974) :rule not_and :premises (t1070))
(step t1072 (cl @p_1227 @p_677) :rule or_neg :args (0))
(step t1073 (cl @p_1227 @p_1017) :rule or_neg :args (1))
(step t1074 (cl @p_1227 @p_676) :rule or_neg :args (2))
(step t1075 (cl @p_1227 (! (not @p_1167) :named @p_1184)) :rule or_neg :args (3))
(step t1076 (cl @p_1227 @p_1183) :rule or_neg :args (4))
(step t1077 (cl @p_1227 @p_1016) :rule or_neg :args (5))
(step t1078 (cl @p_1227 @p_1227 @p_1227 @p_1227 @p_1227 @p_1227) :rule resolution :premises (t1071 t1072 t1073 t1074 t1075 t1076 t1077))
(step t1079 (cl @p_1227) :rule contraction :premises (t1078))
(step t1080 (cl @p_1226) :rule resolution :premises (t1032 t1035 t1079))
(step t1081 (cl @p_671 @p_792 @p_112 @p_1167 @p_1179 @p_974) :rule or :premises (t1080))
(step t1082 (cl @p_112 @p_671 @p_792 @p_1167 @p_1179 @p_974) :rule reordering :premises (t1081))
(step t1083 (cl (not (! (= (! (or @p_671 @p_792 @p_673 @p_1167 @p_1179 @p_66) :named @p_1181) (! (or @p_671 @p_792 @p_112 @p_1167 @p_1179 @p_66) :named @p_1180)) :named @p_1225)) (not @p_1181) @p_1180) :rule equiv_pos2)
(step t1084 (cl @p_1225) :rule cong :premises (t38 t1033 t1034 t882))
(step t1085 (cl (! (=> (! (and @p_670 @p_786 @p_113 @p_1166 @p_1168 @p_63) :named @p_1185) (! (and @p_1188 @p_113 @p_670 @p_1172 @p_801 @p_1187) :named @p_1189)) :named @p_1219) @p_1185) :rule implies_neg1)
(anchor :step t1086)
(assume t1086.a0 @p_670)
(assume t1086.a1 @p_786)
(assume t1086.a2 @p_113)
(assume t1086.a3 @p_1166)
(assume t1086.a4 @p_1168)
(assume t1086.a5 @p_63)
(step t1086.t0 (cl @p_1224 @p_63) :rule implies_neg1)
(anchor :step t1086.t1)
(assume t1086.t1.a0 @p_63)
(step t1086.t1.t0 (cl @p_1188) :rule symm :premises (t1086.t1.a0))
(step t1086.t1 (cl @p_66 @p_1188) :rule subproof :discharge (t1086.t1.a0))
(step t1086.t2 (cl @p_1224 @p_1188) :rule resolution :premises (t1086.t0 t1086.t1))
(step t1086.t3 (cl @p_1224 @p_1192) :rule implies_neg2)
(step t1086.t4 (cl @p_1224 @p_1224) :rule resolution :premises (t1086.t2 t1086.t3))
(step t1086.t5 (cl @p_1224) :rule contraction :premises (t1086.t4))
(step t1086.t6 (cl @p_66 @p_1188) :rule implies :premises (t1086.t5))
(step t1086.t7 (cl @p_1188) :rule resolution :premises (t1086.t6 t1086.a5))
(step t1086.t8 (cl @p_1222 @p_1168) :rule implies_neg1)
(anchor :step t1086.t9)
(assume t1086.t9.a0 @p_1168)
(step t1086.t9.t0 (cl @p_1172) :rule symm :premises (t1086.t9.a0))
(step t1086.t9 (cl @p_1179 @p_1172) :rule subproof :discharge (t1086.t9.a0))
(step t1086.t10 (cl @p_1222 @p_1172) :rule resolution :premises (t1086.t8 t1086.t9))
(step t1086.t11 (cl @p_1222 @p_1193) :rule implies_neg2)
(step t1086.t12 (cl @p_1222 @p_1222) :rule resolution :premises (t1086.t10 t1086.t11))
(step t1086.t13 (cl @p_1222) :rule contraction :premises (t1086.t12))
(step t1086.t14 (cl @p_1179 @p_1172) :rule implies :premises (t1086.t13))
(step t1086.t15 (cl @p_1172) :rule resolution :premises (t1086.t14 t1086.a4))
(step t1086.t16 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1086.t17 (cl @p_801) :rule trans :premises (t1086.t16 t755))
(step t1086.t18 (cl @p_1220 @p_1166) :rule implies_neg1)
(anchor :step t1086.t19)
(assume t1086.t19.a0 @p_1166)
(step t1086.t19.t0 (cl @p_1187) :rule symm :premises (t1086.t19.a0))
(step t1086.t19 (cl @p_1167 @p_1187) :rule subproof :discharge (t1086.t19.a0))
(step t1086.t20 (cl @p_1220 @p_1187) :rule resolution :premises (t1086.t18 t1086.t19))
(step t1086.t21 (cl @p_1220 @p_1194) :rule implies_neg2)
(step t1086.t22 (cl @p_1220 @p_1220) :rule resolution :premises (t1086.t20 t1086.t21))
(step t1086.t23 (cl @p_1220) :rule contraction :premises (t1086.t22))
(step t1086.t24 (cl @p_1167 @p_1187) :rule implies :premises (t1086.t23))
(step t1086.t25 (cl @p_1187) :rule resolution :premises (t1086.t24 t1086.a3))
(step t1086.t26 (cl @p_1189) :rule and_intro :premises (t1086.t7 t1086.a2 t758 t1086.t15 t1086.t17 t1086.t25))
(step t1086 (cl @p_671 @p_792 @p_673 @p_1167 @p_1179 @p_66 @p_1189) :rule subproof :discharge (t1086.a0 t1086.a1 t1086.a2 t1086.a3 t1086.a4 t1086.a5))
(step t1087 (cl (! (not @p_1185) :named @p_1186) @p_670) :rule and_pos :args (0))
(step t1088 (cl @p_1186 @p_786) :rule and_pos :args (1))
(step t1089 (cl @p_1186 @p_113) :rule and_pos :args (2))
(step t1090 (cl @p_1186 @p_1166) :rule and_pos :args (3))
(step t1091 (cl @p_1186 @p_1168) :rule and_pos :args (4))
(step t1092 (cl @p_1186 @p_63) :rule and_pos :args (5))
(step t1093 (cl @p_1189 @p_1186 @p_1186 @p_1186 @p_1186 @p_1186 @p_1186) :rule resolution :premises (t1086 t1087 t1088 t1089 t1090 t1091 t1092))
(step t1094 (cl @p_1186 @p_1186 @p_1186 @p_1186 @p_1186 @p_1186 @p_1189) :rule reordering :premises (t1093))
(step t1095 (cl @p_1186 @p_1189) :rule contraction :premises (t1094))
(step t1096 (cl @p_1219 @p_1189) :rule resolution :premises (t1085 t1095))
(step t1097 (cl @p_1219 (! (not @p_1189) :named @p_1190)) :rule implies_neg2)
(step t1098 (cl @p_1219 @p_1219) :rule resolution :premises (t1096 t1097))
(step t1099 (cl @p_1219) :rule contraction :premises (t1098))
(step t1100 (cl @p_1186 @p_1189) :rule implies :premises (t1099))
(step t1101 (cl (! (=> @p_1189 false) :named @p_1191) @p_1189) :rule implies_neg1)
(anchor :step t1102)
(assume t1102.a0 @p_1188)
(assume t1102.a1 @p_113)
(assume t1102.a2 @p_670)
(assume t1102.a3 @p_1172)
(assume t1102.a4 @p_801)
(assume t1102.a5 @p_1187)
(step t1102.t0 (cl @p_1166) :rule symm :premises (t1102.a5))
(step t1102.t1 (cl @p_1195 @p_1166) :rule implies_neg1)
(anchor :step t1102.t2)
(assume t1102.t2.a0 @p_1166)
(step t1102.t2.t0 (cl (not (! (= (! (< @p_1199 (! (+ 1 @p_297 @p_850 @p_297 1 @p_297) :named @p_1198)) :named @p_1200) false) :named @p_1212)) (not @p_1200) false) :rule equiv_pos2)
(step t1102.t2.t1 (cl (= @p_1200 (! (not (! (>= @p_1199 @p_1198) :named @p_1213)) :named @p_1214))) :rule rare_rewrite :args ("arith-elim-lt" @p_1199 @p_1198))
(step t1102.t2.t2 (cl (= @p_1199 @p_1216)) :rule poly_simp)
(step t1102.t2.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t1102.t2.t4 (cl (= @p_668 @p_668)) :rule refl)
(step t1102.t2.t5 (cl (= @p_1007 0)) :rule poly_simp)
(step t1102.t2.t6 (cl (= @p_690 @p_690)) :rule refl)
(step t1102.t2.t7 (cl @p_168) :rule refl)
(step t1102.t2.t8 (cl @p_167) :rule refl)
(step t1102.t2.t9 (cl (= @p_617 0)) :rule poly_simp)
(step t1102.t2.t10 (cl (= @p_1216 @p_1217)) :rule cong :premises (t1102.t2.t3 t1102.t2.t4 t1102.t2.t5 t1102.t2.t6 t1102.t2.t7 t1102.t2.t8 t1102.t2.t9))
(step t1102.t2.t11 (cl (= @p_1217 0)) :rule poly_simp)
(step t1102.t2.t12 (cl (= @p_1216 0)) :rule trans :premises (t1102.t2.t10 t1102.t2.t11))
(step t1102.t2.t13 (cl (= @p_1199 0)) :rule trans :premises (t1102.t2.t2 t1102.t2.t12))
(step t1102.t2.t14 (cl (= @p_297 0)) :rule evaluate)
(step t1102.t2.t15 (cl (= @p_850 -2)) :rule evaluate)
(step t1102.t2.t16 (cl (= 1 1)) :rule refl)
(step t1102.t2.t17 (cl (= @p_1198 (! (+ 1 0 -2 0 1 0) :named @p_1215))) :rule cong :premises (t1102.t2.t14 t1102.t2.t15 t1102.t2.t14 t1102.t2.t16 t1102.t2.t14))
(step t1102.t2.t18 (cl (= @p_1215 0)) :rule evaluate)
(step t1102.t2.t19 (cl (= @p_1198 0)) :rule trans :premises (t1102.t2.t17 t1102.t2.t18))
(step t1102.t2.t20 (cl (= @p_1213 @p_366)) :rule cong :premises (t1102.t2.t13 t1102.t2.t19))
(step t1102.t2.t21 (cl (= @p_366 true)) :rule evaluate)
(step t1102.t2.t22 (cl (= @p_1213 true)) :rule trans :premises (t1102.t2.t20 t1102.t2.t21))
(step t1102.t2.t23 (cl (= @p_1214 @p_365)) :rule cong :premises (t1102.t2.t22))
(step t1102.t2.t24 (cl (= @p_365 false)) :rule evaluate)
(step t1102.t2.t25 (cl (= @p_1214 false)) :rule trans :premises (t1102.t2.t23 t1102.t2.t24))
(step t1102.t2.t26 (cl @p_1212) :rule trans :premises (t1102.t2.t1 t1102.t2.t25))
(step t1102.t2.t27 (cl @p_1167 @p_1002 @p_1210 @p_716 @p_715 @p_1211 @p_1200) :rule la_generic :args (-1/1 -1/1 -1/1 -1/1 1/1 -1/1 1/1))
(step t1102.t2.t28 (cl (=> @p_993 @p_992)) :rule la_mult_neg)
(step t1102.t2.t29 (cl (not @p_993) @p_992) :rule implies :premises (t1102.t2.t28))
(step t1102.t2.t30 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1102.t2.t31 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1102.t2.t30))
(step t1102.t2.t32 (cl @p_310) :rule evaluate)
(step t1102.t2.t33 (cl @p_308) :rule resolution :premises (t1102.t2.t31 t1102.t2.t32))
(step t1102.t2.t34 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1102.t2.t35 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1102.t2.t36 (cl @p_803) :rule poly_simp_rel :premises (t1102.t2.t35))
(step t1102.t2.t37 (cl (= @p_793 @p_800)) :rule symm :premises (t1102.t2.t36))
(step t1102.t2.t38 (cl @p_802) :rule trans :premises (t655 t1102.t2.t37))
(step t1102.t2.t39 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1102.t2.t40 (cl @p_801) :rule trans :premises (t1102.t2.t39 t755))
(step t1102.t2.t41 (cl @p_800) :rule resolution :premises (t1102.t2.t34 t1102.t2.t38 t1102.t2.t40))
(step t1102.t2.t42 (cl @p_993) :rule and_intro :premises (t1102.t2.t33 t1102.t2.t41))
(step t1102.t2.t43 (cl @p_992) :rule resolution :premises (t1102.t2.t29 t1102.t2.t42))
(step t1102.t2.t44 (cl (=> @p_1206 @p_1205)) :rule la_mult_neg)
(step t1102.t2.t45 (cl @p_1208 @p_1205) :rule implies :premises (t1102.t2.t44))
(step t1102.t2.t46 (cl @p_1168) :rule symm :premises (t1102.a3))
(step t1102.t2.t47 (cl @p_1206) :rule and_intro :premises (t1102.t2.t33 t1102.t2.t46))
(step t1102.t2.t48 (cl @p_1205) :rule resolution :premises (t1102.t2.t45 t1102.t2.t47))
(step t1102.t2.t49 (cl (=> @p_698 @p_696)) :rule la_mult_neg)
(step t1102.t2.t50 (cl (not @p_698) @p_696) :rule implies :premises (t1102.t2.t49))
(step t1102.t2.t51 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t1102.t2.t52 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t1102.t2.t53 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t1102.t2.t52))
(step t1102.t2.t54 (cl @p_699) :rule symm :premises (t1102.t2.t53))
(step t1102.t2.t55 (cl @p_697) :rule resolution :premises (t1102.t2.t51 t1102.t2.t54 t758))
(step t1102.t2.t56 (cl @p_698) :rule and_intro :premises (t1102.t2.t33 t1102.t2.t55))
(step t1102.t2.t57 (cl @p_696) :rule resolution :premises (t1102.t2.t50 t1102.t2.t56))
(step t1102.t2.t58 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t1102.t2.t59 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t1102.t2.t60 (cl @p_703) :rule symm :premises (t1102.t2.t59))
(step t1102.t2.t61 (cl @p_700) :rule resolution :premises (t1102.t2.t58 t1102.t2.t60 t1102.a1))
(step t1102.t2.t62 (cl (=> @p_1202 @p_1201)) :rule la_mult_neg)
(step t1102.t2.t63 (cl @p_1204 @p_1201) :rule implies :premises (t1102.t2.t62))
(step t1102.t2.t64 (cl @p_63) :rule symm :premises (t1102.a0))
(step t1102.t2.t65 (cl @p_1202) :rule and_intro :premises (t1102.t2.t33 t1102.t2.t64))
(step t1102.t2.t66 (cl @p_1201) :rule resolution :premises (t1102.t2.t63 t1102.t2.t65))
(step t1102.t2.t67 (cl @p_1200) :rule resolution :premises (t1102.t2.t27 t1102.t2.a0 t1102.t2.t43 t1102.t2.t48 t1102.t2.t57 t1102.t2.t61 t1102.t2.t66))
(step t1102.t2.t68 (cl false) :rule resolution :premises (t1102.t2.t0 t1102.t2.t26 t1102.t2.t67))
(step t1102.t2 (cl @p_1167 false) :rule subproof :discharge (t1102.t2.a0))
(step t1102.t3 (cl @p_1195 false) :rule resolution :premises (t1102.t1 t1102.t2))
(step t1102.t4 (cl @p_1195 @p_212) :rule implies_neg2)
(step t1102.t5 (cl @p_1195 @p_1195) :rule resolution :premises (t1102.t3 t1102.t4))
(step t1102.t6 (cl @p_1195) :rule contraction :premises (t1102.t5))
(step t1102.t7 (cl @p_1197) :rule implies_simplify)
(step t1102.t8 (cl @p_1196 @p_1167) :rule equiv1 :premises (t1102.t7))
(step t1102.t9 (cl @p_1167) :rule resolution :premises (t1102.t6 t1102.t8))
(step t1102.t10 (cl) :rule resolution :premises (t1102.t0 t1102.t9))
(step t1102 (cl @p_1192 @p_673 @p_671 @p_1193 @p_806 @p_1194 false) :rule subproof :discharge (t1102.a0 t1102.a1 t1102.a2 t1102.a3 t1102.a4 t1102.a5))
(step t1103 (cl @p_1190 @p_1188) :rule and_pos :args (0))
(step t1104 (cl @p_1190 @p_113) :rule and_pos :args (1))
(step t1105 (cl @p_1190 @p_670) :rule and_pos :args (2))
(step t1106 (cl @p_1190 @p_1172) :rule and_pos :args (3))
(step t1107 (cl @p_1190 @p_801) :rule and_pos :args (4))
(step t1108 (cl @p_1190 @p_1187) :rule and_pos :args (5))
(step t1109 (cl false @p_1190 @p_1190 @p_1190 @p_1190 @p_1190 @p_1190) :rule resolution :premises (t1102 t1103 t1104 t1105 t1106 t1107 t1108))
(step t1110 (cl @p_1190 @p_1190 @p_1190 @p_1190 @p_1190 @p_1190 false) :rule reordering :premises (t1109))
(step t1111 (cl @p_1190 false) :rule contraction :premises (t1110))
(step t1112 (cl @p_1191 false) :rule resolution :premises (t1101 t1111))
(step t1113 (cl @p_1191 @p_212) :rule implies_neg2)
(step t1114 (cl @p_1191 @p_1191) :rule resolution :premises (t1112 t1113))
(step t1115 (cl @p_1191) :rule contraction :premises (t1114))
(step t1116 (cl (= @p_1191 @p_1190)) :rule implies_simplify)
(step t1117 (cl (not @p_1191) @p_1190) :rule equiv1 :premises (t1116))
(step t1118 (cl @p_1190) :rule resolution :premises (t1115 t1117))
(step t1119 (cl @p_1186) :rule resolution :premises (t1100 t1118))
(step t1120 (cl @p_671 @p_792 @p_673 @p_1167 @p_1179 @p_66) :rule not_and :premises (t1119))
(step t1121 (cl @p_1181 @p_677) :rule or_neg :args (0))
(step t1122 (cl @p_1181 @p_1017) :rule or_neg :args (1))
(step t1123 (cl @p_1181 @p_676) :rule or_neg :args (2))
(step t1124 (cl @p_1181 @p_1184) :rule or_neg :args (3))
(step t1125 (cl @p_1181 @p_1183) :rule or_neg :args (4))
(step t1126 (cl @p_1181 @p_1182) :rule or_neg :args (5))
(step t1127 (cl @p_1181 @p_1181 @p_1181 @p_1181 @p_1181 @p_1181) :rule resolution :premises (t1120 t1121 t1122 t1123 t1124 t1125 t1126))
(step t1128 (cl @p_1181) :rule contraction :premises (t1127))
(step t1129 (cl @p_1180) :rule resolution :premises (t1083 t1084 t1128))
(step t1130 (cl @p_671 @p_792 @p_112 @p_1167 @p_1179 @p_66) :rule or :premises (t1129))
(step t1131 (cl @p_112 @p_671 @p_792 @p_1167 @p_1179 @p_66) :rule reordering :premises (t1130))
(step t1132 (cl @p_1178 @p_1167 @p_1168) :rule equiv_pos2)
(step t1133 (cl @p_1168 @p_1167 @p_1178) :rule reordering :premises (t1132))
(step t1134 (cl @p_1169) :rule resolution :premises (t1031 a8))
(step t1135 (cl @p_112 @p_1167) :rule resolution :premises (t872 t875 t877 t880 t1082 t755 t758 t1131 t755 t758 t1133 t1134))
(step t1136 (cl (! (and @p_670 @p_786 @p_743) :named @p_795) @p_671 @p_792 @p_794) :rule and_neg)
(step t1137 (cl (! (=> @p_795 @p_793) :named @p_797) @p_795) :rule implies_neg1)
(anchor :step t1138)
(assume t1138.a0 @p_670)
(assume t1138.a1 @p_786)
(assume t1138.a2 @p_743)
(step t1138.t0 (cl (! (not @p_803) :named @p_807) @p_808 @p_793) :rule equiv_pos2)
(step t1138.t1 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1138.t2 (cl @p_803) :rule poly_simp_rel :premises (t1138.t1))
(step t1138.t3 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1138.t4 (cl (= @p_793 @p_800)) :rule symm :premises (t1138.t2))
(step t1138.t5 (cl @p_802) :rule trans :premises (t655 t1138.t4))
(step t1138.t6 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1138.t7 (cl @p_801) :rule trans :premises (t1138.t6 t755))
(step t1138.t8 (cl @p_800) :rule resolution :premises (t1138.t3 t1138.t5 t1138.t7))
(step t1138.t9 (cl @p_793) :rule resolution :premises (t1138.t0 t1138.t2 t1138.t8))
(step t1138 (cl @p_671 @p_792 @p_794 @p_793) :rule subproof :discharge (t1138.a0 t1138.a1 t1138.a2))
(step t1139 (cl (! (not @p_795) :named @p_796) @p_670) :rule and_pos :args (0))
(step t1140 (cl @p_796 @p_786) :rule and_pos :args (1))
(step t1141 (cl @p_796 @p_743) :rule and_pos :args (2))
(step t1142 (cl @p_793 @p_796 @p_796 @p_796) :rule resolution :premises (t1138 t1139 t1140 t1141))
(step t1143 (cl @p_796 @p_796 @p_796 @p_793) :rule reordering :premises (t1142))
(step t1144 (cl @p_796 @p_793) :rule contraction :premises (t1143))
(step t1145 (cl @p_797 @p_793) :rule resolution :premises (t1137 t1144))
(step t1146 (cl @p_797 @p_798) :rule implies_neg2)
(step t1147 (cl @p_797 @p_797) :rule resolution :premises (t1145 t1146))
(step t1148 (cl @p_797) :rule contraction :premises (t1147))
(step t1149 (cl @p_796 @p_793) :rule implies :premises (t1148))
(step t1150 (cl @p_671 @p_792 @p_794 @p_793) :rule resolution :premises (t1136 t1149))
(step t1151 (cl @p_671 @p_792 @p_793 @p_794) :rule reordering :premises (t1150))
(step t1152 (cl (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) @p_670) :named @p_832) (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t1153)
(assume t1153.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t1153.t0 (cl @p_670) :rule resolution :premises (t757 t226))
(step t1153 (cl @p_190 @p_670) :rule subproof :discharge (t1153.a0))
(step t1154 (cl @p_832 @p_670) :rule resolution :premises (t1152 t1153))
(step t1155 (cl @p_832 @p_671) :rule implies_neg2)
(step t1156 (cl @p_832 @p_832) :rule resolution :premises (t1154 t1155))
(step t1157 (cl @p_832) :rule contraction :premises (t1156))
(step t1158 (cl @p_190 @p_670) :rule implies :premises (t1157))
(step t1159 (cl @p_583 @p_112 @p_732 @p_66 @p_794 @p_834) :rule resolution :premises (t33 t652 t1 t649 t688 t933 t742 t758 t940 t947 t1002 t742 t755 t758 t1009 t1011 t1031 a8 t1135 t1151 t1158 t226 t754 a4))
(step t1160 (cl (not (! (= (! (or @p_227 (! (not (! (not (! (= @p_172 1) :named @p_830)) :named @p_831)) :named @p_920) @p_532 (! (not (! (>= @p_105 1) :named @p_633)) :named @p_636) @p_833) :named @p_1137) (! (or @p_227 @p_830 @p_532 @p_636 @p_833) :named @p_1136)) :named @p_1165)) (not @p_1137) @p_1136) :rule equiv_pos2)
(step t1161 (cl (= @p_920 @p_830)) :rule rare_rewrite :args ("bool-double-not-elim" @p_830))
(step t1162 (cl (= @p_636 @p_636)) :rule refl)
(step t1163 (cl (= @p_833 @p_833)) :rule refl)
(step t1164 (cl @p_1165) :rule cong :premises (t1161 t40 t1162 t1163))
(step t1165 (cl (! (and @p_224 @p_831 @p_106 @p_633) :named @p_1139) @p_227 @p_920 @p_532 @p_636) :rule and_neg)
(step t1166 (cl (! (=> @p_1139 @p_833) :named @p_1141) @p_1139) :rule implies_neg1)
(anchor :step t1167)
(assume t1167.a0 @p_224)
(assume t1167.a1 @p_831)
(assume t1167.a2 @p_106)
(assume t1167.a3 @p_633)
(step t1167.t0 (cl (! (=> (! (and @p_633 (! (not (! (= 1 @p_105) :named @p_839)) :named @p_843)) :named @p_1142) @p_833) :named @p_1157) @p_1142) :rule implies_neg1)
(anchor :step t1167.t1)
(assume t1167.t1.a0 @p_633)
(assume t1167.t1.a1 @p_843)
(step t1167.t1.t0 (cl (not (! (> @p_105 1) :named @p_1158)) @p_833) :rule la_generic :args (1/1 1/1))
(step t1167.t1.t1 (cl (! (not (! (= @p_105 1) :named @p_855)) :named @p_860)) :rule not_symm :premises (t1167.t1.a1))
(step t1167.t1.t2 (cl (or @p_855 (! (not (<= @p_105 1)) :named @p_1159) (! (not (! (<= 1 @p_105) :named @p_1162)) :named @p_1164))) :rule la_disequality)
(step t1167.t1.t3 (cl @p_855 @p_1159 @p_1164) :rule or :premises (t1167.t1.t2))
(step t1167.t1.t4 (cl (! (= @p_633 @p_1162) :named @p_1163)) :rule comp_simplify)
(step t1167.t1.t5 (cl (not @p_1163) @p_636 @p_1162) :rule equiv_pos2)
(step t1167.t1.t6 (cl @p_1162) :rule resolution :premises (t1167.t1.t4 t1167.t1.t5 t1167.t1.a0))
(step t1167.t1.t7 (cl (! (= @p_1158 @p_1159) :named @p_1161)) :rule comp_simplify)
(step t1167.t1.t8 (cl (not @p_1161) @p_1158 (! (not @p_1159) :named @p_1160)) :rule equiv_pos1)
(step t1167.t1.t9 (cl @p_1158 @p_1160) :rule resolution :premises (t1167.t1.t7 t1167.t1.t8))
(step t1167.t1.t10 (cl @p_1158) :rule resolution :premises (t1167.t1.t1 t1167.t1.t3 t1167.t1.t6 t1167.t1.t9))
(step t1167.t1.t11 (cl @p_833) :rule resolution :premises (t1167.t1.t0 t1167.t1.t10))
(step t1167.t1 (cl @p_636 (! (not @p_843) :named @p_1146) @p_833) :rule subproof :discharge (t1167.t1.a0 t1167.t1.a1))
(step t1167.t2 (cl (! (not @p_1142) :named @p_1156) @p_633) :rule and_pos :args (0))
(step t1167.t3 (cl @p_1156 @p_843) :rule and_pos :args (1))
(step t1167.t4 (cl @p_833 @p_1156 @p_1156) :rule resolution :premises (t1167.t1 t1167.t2 t1167.t3))
(step t1167.t5 (cl @p_1156 @p_1156 @p_833) :rule reordering :premises (t1167.t4))
(step t1167.t6 (cl @p_1156 @p_833) :rule contraction :premises (t1167.t5))
(step t1167.t7 (cl @p_1157 @p_833) :rule resolution :premises (t1167.t0 t1167.t6))
(step t1167.t8 (cl @p_1157 @p_834) :rule implies_neg2)
(step t1167.t9 (cl @p_1157 @p_1157) :rule resolution :premises (t1167.t7 t1167.t8))
(step t1167.t10 (cl @p_1157) :rule contraction :premises (t1167.t9))
(step t1167.t11 (cl @p_1156 @p_833) :rule implies :premises (t1167.t10))
(step t1167.t12 (cl (! (=> (! (and @p_224 @p_106 @p_831) :named @p_1143) @p_843) :named @p_1145) @p_1143) :rule implies_neg1)
(anchor :step t1167.t13)
(assume t1167.t13.a0 @p_224)
(assume t1167.t13.a1 @p_106)
(assume t1167.t13.a2 @p_831)
(step t1167.t13.t0 (cl (! (= (! (= @p_839 false) :named @p_1147) @p_843) :named @p_1155)) :rule equiv_simplify)
(step t1167.t13.t1 (cl (not @p_1147) @p_843) :rule equiv1 :premises (t1167.t13.t0))
(step t1167.t13.t2 (cl (not (! (= (! (= @p_855 false) :named @p_1148) @p_1147) :named @p_1150)) (not @p_1148) @p_1147) :rule equiv_pos2)
(step t1167.t13.t3 (cl (= @p_1148 @p_860)) :rule rare_rewrite :args ("bool-eq-false" @p_855))
(step t1167.t13.t4 (cl (= (* -1 (- @p_105 1)) (* -1 (! (- @p_104 (! (+ 1 @p_544) :named @p_1151)) :named @p_1154)))) :rule poly_simp)
(step t1167.t13.t5 (cl (= @p_855 (! (= @p_104 @p_1151) :named @p_1152))) :rule poly_simp_rel :premises (t1167.t13.t4))
(step t1167.t13.t6 (cl (= @p_860 (! (not @p_1152) :named @p_1153))) :rule cong :premises (t1167.t13.t5))
(step t1167.t13.t7 (cl (= @p_1148 @p_1153)) :rule trans :premises (t1167.t13.t3 t1167.t13.t6))
(step t1167.t13.t8 (cl @p_1155) :rule rare_rewrite :args ("bool-eq-false" @p_839))
(step t1167.t13.t9 (cl (= (* -1 (- 1 @p_105)) (* 1 @p_1154))) :rule poly_simp)
(step t1167.t13.t10 (cl (= @p_839 @p_1152)) :rule poly_simp_rel :premises (t1167.t13.t9))
(step t1167.t13.t11 (cl (= @p_843 @p_1153)) :rule cong :premises (t1167.t13.t10))
(step t1167.t13.t12 (cl (= @p_1147 @p_1153)) :rule trans :premises (t1167.t13.t8 t1167.t13.t11))
(step t1167.t13.t13 (cl (= @p_1153 @p_1147)) :rule symm :premises (t1167.t13.t12))
(step t1167.t13.t14 (cl @p_1150) :rule trans :premises (t1167.t13.t7 t1167.t13.t13))
(step t1167.t13.t15 (cl (= @p_105 k$)) :rule symm :premises (t742))
(step t1167.t13.t16 (cl (= @p_105 @p_172)) :rule trans :premises (t1167.t13.t15 t261))
(step t1167.t13.t17 (cl (= 1 1)) :rule refl)
(step t1167.t13.t18 (cl (= @p_855 @p_830)) :rule cong :premises (t1167.t13.t16 t1167.t13.t17))
(step t1167.t13.t19 (cl (= (! (= @p_830 false) :named @p_1149) @p_831)) :rule equiv_simplify)
(step t1167.t13.t20 (cl @p_1149 @p_920) :rule equiv2 :premises (t1167.t13.t19))
(step t1167.t13.t21 (cl (! (not @p_920) :named @p_1138) @p_830) :rule not_not)
(step t1167.t13.t22 (cl @p_1149 @p_830) :rule resolution :premises (t1167.t13.t20 t1167.t13.t21))
(step t1167.t13.t23 (cl @p_1149) :rule resolution :premises (t1167.t13.t22 t1167.t13.a2))
(step t1167.t13.t24 (cl @p_1148) :rule trans :premises (t1167.t13.t18 t1167.t13.t23))
(step t1167.t13.t25 (cl @p_1147) :rule resolution :premises (t1167.t13.t2 t1167.t13.t14 t1167.t13.t24))
(step t1167.t13.t26 (cl @p_843) :rule resolution :premises (t1167.t13.t1 t1167.t13.t25))
(step t1167.t13 (cl @p_227 @p_532 @p_920 @p_843) :rule subproof :discharge (t1167.t13.a0 t1167.t13.a1 t1167.t13.a2))
(step t1167.t14 (cl (! (not @p_1143) :named @p_1144) @p_224) :rule and_pos :args (0))
(step t1167.t15 (cl @p_1144 @p_106) :rule and_pos :args (1))
(step t1167.t16 (cl @p_1144 @p_831) :rule and_pos :args (2))
(step t1167.t17 (cl @p_843 @p_1144 @p_1144 @p_1144) :rule resolution :premises (t1167.t13 t1167.t14 t1167.t15 t1167.t16))
(step t1167.t18 (cl @p_1144 @p_1144 @p_1144 @p_843) :rule reordering :premises (t1167.t17))
(step t1167.t19 (cl @p_1144 @p_843) :rule contraction :premises (t1167.t18))
(step t1167.t20 (cl @p_1145 @p_843) :rule resolution :premises (t1167.t12 t1167.t19))
(step t1167.t21 (cl @p_1145 @p_1146) :rule implies_neg2)
(step t1167.t22 (cl @p_1145 @p_1145) :rule resolution :premises (t1167.t20 t1167.t21))
(step t1167.t23 (cl @p_1145) :rule contraction :premises (t1167.t22))
(step t1167.t24 (cl @p_1144 @p_843) :rule implies :premises (t1167.t23))
(step t1167.t25 (cl @p_1143) :rule and_intro :premises (t261 t742 t1167.a1))
(step t1167.t26 (cl @p_843) :rule resolution :premises (t1167.t24 t1167.t25))
(step t1167.t27 (cl @p_1142) :rule and_intro :premises (t1167.a3 t1167.t26))
(step t1167.t28 (cl @p_833) :rule resolution :premises (t1167.t11 t1167.t27))
(step t1167 (cl @p_227 @p_920 @p_532 @p_636 @p_833) :rule subproof :discharge (t1167.a0 t1167.a1 t1167.a2 t1167.a3))
(step t1168 (cl (! (not @p_1139) :named @p_1140) @p_224) :rule and_pos :args (0))
(step t1169 (cl @p_1140 @p_831) :rule and_pos :args (1))
(step t1170 (cl @p_1140 @p_106) :rule and_pos :args (2))
(step t1171 (cl @p_1140 @p_633) :rule and_pos :args (3))
(step t1172 (cl @p_833 @p_1140 @p_1140 @p_1140 @p_1140) :rule resolution :premises (t1167 t1168 t1169 t1170 t1171))
(step t1173 (cl @p_1140 @p_1140 @p_1140 @p_1140 @p_833) :rule reordering :premises (t1172))
(step t1174 (cl @p_1140 @p_833) :rule contraction :premises (t1173))
(step t1175 (cl @p_1141 @p_833) :rule resolution :premises (t1166 t1174))
(step t1176 (cl @p_1141 @p_834) :rule implies_neg2)
(step t1177 (cl @p_1141 @p_1141) :rule resolution :premises (t1175 t1176))
(step t1178 (cl @p_1141) :rule contraction :premises (t1177))
(step t1179 (cl @p_1140 @p_833) :rule implies :premises (t1178))
(step t1180 (cl @p_227 @p_920 @p_532 @p_636 @p_833) :rule resolution :premises (t1165 t1179))
(step t1181 (cl @p_1137 @p_232) :rule or_neg :args (0))
(step t1182 (cl @p_1137 @p_1138) :rule or_neg :args (1))
(step t1183 (cl @p_1137 @p_538) :rule or_neg :args (2))
(step t1184 (cl @p_1137 (not @p_636)) :rule or_neg :args (3))
(step t1185 (cl @p_1137 @p_834) :rule or_neg :args (4))
(step t1186 (cl @p_1137 @p_1137 @p_1137 @p_1137 @p_1137) :rule resolution :premises (t1180 t1181 t1182 t1183 t1184 t1185))
(step t1187 (cl @p_1137) :rule contraction :premises (t1186))
(step t1188 (cl @p_1136) :rule resolution :premises (t1160 t1164 t1187))
(step t1189 (cl @p_227 @p_830 @p_532 @p_636 @p_833) :rule or :premises (t1188))
(step t1190 (cl (not (! (= (! (or @p_671 @p_792 @p_794 (! (not (! (not (! (= @p_668 0) :named @p_759)) :named @p_760)) :named @p_767) @p_16 @p_1052) :named @p_1053) (! (or @p_671 @p_792 @p_794 @p_759 @p_16 @p_1049) :named @p_1050)) :named @p_1096)) (not @p_1053) @p_1050) :rule equiv_pos2)
(step t1191 (cl (= @p_767 @p_759)) :rule rare_rewrite :args ("bool-double-not-elim" @p_759))
(step t1192 (cl (= @p_16 @p_16)) :rule refl)
(step t1193 (cl @p_1096) :rule cong :premises (t1191 t1192 t690))
(step t1194 (cl (! (=> (! (and @p_670 @p_786 @p_743 @p_760 @p_15 @p_1051) :named @p_1056) (! (and (! (not (= 0 @p_8)) :named @p_1058) @p_1051 @p_15) :named @p_1059)) :named @p_1075) @p_1056) :rule implies_neg1)
(anchor :step t1195)
(assume t1195.a0 @p_670)
(assume t1195.a1 @p_786)
(assume t1195.a2 @p_743)
(assume t1195.a3 @p_760)
(assume t1195.a4 @p_15)
(assume t1195.a5 @p_1051)
(step t1195.t0 (cl (! (=> (! (and @p_760 (! (= @p_668 @p_1076) :named @p_1078) @p_1077) :named @p_1079) @p_1058) :named @p_1092) @p_1079) :rule implies_neg1)
(anchor :step t1195.t1)
(assume t1195.t1.a0 @p_760)
(assume t1195.t1.a1 @p_1078)
(assume t1195.t1.a2 @p_1077)
(step t1195.t1.t0 (cl (= (! (= (! (= @p_8 0) :named @p_1072) false) :named @p_1093) (! (not @p_1072) :named @p_1073))) :rule equiv_simplify)
(step t1195.t1.t1 (cl (not @p_1093) @p_1073) :rule equiv1 :premises (t1195.t1.t0))
(step t1195.t1.t2 (cl @p_807 @p_808 @p_793) :rule equiv_pos2)
(step t1195.t1.t3 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1195.t1.t4 (cl @p_803) :rule poly_simp_rel :premises (t1195.t1.t3))
(step t1195.t1.t5 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1195.t1.t6 (cl (= @p_793 @p_800)) :rule symm :premises (t1195.t1.t4))
(step t1195.t1.t7 (cl @p_802) :rule trans :premises (t655 t1195.t1.t6))
(step t1195.t1.t8 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1195.t1.t9 (cl @p_801) :rule trans :premises (t1195.t1.t8 t755))
(step t1195.t1.t10 (cl @p_800) :rule resolution :premises (t1195.t1.t5 t1195.t1.t7 t1195.t1.t9))
(step t1195.t1.t11 (cl @p_793) :rule resolution :premises (t1195.t1.t2 t1195.t1.t4 t1195.t1.t10))
(step t1195.t1.t12 (cl (! (= @p_8 @p_668) :named @p_1095)) :rule symm :premises (t1195.t1.t11))
(step t1195.t1.t13 (cl (= @p_1072 @p_759)) :rule cong :premises (t1195.t1.t12 t604))
(step t1195.t1.t14 (cl (= (! (= @p_759 false) :named @p_1094) @p_760)) :rule equiv_simplify)
(step t1195.t1.t15 (cl @p_1094 @p_767) :rule equiv2 :premises (t1195.t1.t14))
(step t1195.t1.t16 (cl (! (not @p_767) :named @p_1055) @p_759) :rule not_not)
(step t1195.t1.t17 (cl @p_1094 @p_759) :rule resolution :premises (t1195.t1.t15 t1195.t1.t16))
(step t1195.t1.t18 (cl @p_1094) :rule resolution :premises (t1195.t1.t17 t1195.t1.a0))
(step t1195.t1.t19 (cl @p_1093) :rule trans :premises (t1195.t1.t13 t1195.t1.t18))
(step t1195.t1.t20 (cl @p_1073) :rule resolution :premises (t1195.t1.t1 t1195.t1.t19))
(step t1195.t1.t21 (cl @p_1058) :rule not_symm :premises (t1195.t1.t20))
(step t1195.t1 (cl @p_767 (! (not @p_1078) :named @p_1087) @p_1083 @p_1058) :rule subproof :discharge (t1195.t1.a0 t1195.t1.a1 t1195.t1.a2))
(step t1195.t2 (cl (! (not @p_1079) :named @p_1091) @p_760) :rule and_pos :args (0))
(step t1195.t3 (cl @p_1091 @p_1078) :rule and_pos :args (1))
(step t1195.t4 (cl @p_1091 @p_1077) :rule and_pos :args (2))
(step t1195.t5 (cl @p_1058 @p_1091 @p_1091 @p_1091) :rule resolution :premises (t1195.t1 t1195.t2 t1195.t3 t1195.t4))
(step t1195.t6 (cl @p_1091 @p_1091 @p_1091 @p_1058) :rule reordering :premises (t1195.t5))
(step t1195.t7 (cl @p_1091 @p_1058) :rule contraction :premises (t1195.t6))
(step t1195.t8 (cl @p_1092 @p_1058) :rule resolution :premises (t1195.t0 t1195.t7))
(step t1195.t9 (cl @p_1092 (! (not @p_1058) :named @p_1062)) :rule implies_neg2)
(step t1195.t10 (cl @p_1092 @p_1092) :rule resolution :premises (t1195.t8 t1195.t9))
(step t1195.t11 (cl @p_1092) :rule contraction :premises (t1195.t10))
(step t1195.t12 (cl @p_1091 @p_1058) :rule implies :premises (t1195.t11))
(step t1195.t13 (cl (! (=> (! (and @p_1077 @p_801) :named @p_1084) @p_1078) :named @p_1086) @p_1084) :rule implies_neg1)
(anchor :step t1195.t14)
(assume t1195.t14.a0 @p_1077)
(assume t1195.t14.a1 @p_801)
(step t1195.t14.t0 (cl @p_807 @p_808 @p_793) :rule equiv_pos2)
(step t1195.t14.t1 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1195.t14.t2 (cl @p_803) :rule poly_simp_rel :premises (t1195.t14.t1))
(step t1195.t14.t3 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1195.t14.t4 (cl (= @p_793 @p_800)) :rule symm :premises (t1195.t14.t2))
(step t1195.t14.t5 (cl @p_802) :rule trans :premises (t655 t1195.t14.t4))
(step t1195.t14.t6 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1195.t14.t7 (cl @p_801) :rule trans :premises (t1195.t14.t6 t755))
(step t1195.t14.t8 (cl @p_800) :rule resolution :premises (t1195.t14.t3 t1195.t14.t5 t1195.t14.t7))
(step t1195.t14.t9 (cl @p_793) :rule resolution :premises (t1195.t14.t0 t1195.t14.t2 t1195.t14.t8))
(step t1195.t14.t10 (cl @p_1078) :rule trans :premises (t1195.t14.t9 t1195.t14.a0))
(step t1195.t14 (cl @p_1083 @p_806 @p_1078) :rule subproof :discharge (t1195.t14.a0 t1195.t14.a1))
(step t1195.t15 (cl (! (not @p_1084) :named @p_1085) @p_1077) :rule and_pos :args (0))
(step t1195.t16 (cl @p_1085 @p_801) :rule and_pos :args (1))
(step t1195.t17 (cl @p_1078 @p_1085 @p_1085) :rule resolution :premises (t1195.t14 t1195.t15 t1195.t16))
(step t1195.t18 (cl @p_1085 @p_1085 @p_1078) :rule reordering :premises (t1195.t17))
(step t1195.t19 (cl @p_1085 @p_1078) :rule contraction :premises (t1195.t18))
(step t1195.t20 (cl @p_1086 @p_1078) :rule resolution :premises (t1195.t13 t1195.t19))
(step t1195.t21 (cl @p_1086 @p_1087) :rule implies_neg2)
(step t1195.t22 (cl @p_1086 @p_1086) :rule resolution :premises (t1195.t20 t1195.t21))
(step t1195.t23 (cl @p_1086) :rule contraction :premises (t1195.t22))
(step t1195.t24 (cl @p_1085 @p_1078) :rule implies :premises (t1195.t23))
(step t1195.t25 (cl @p_1082 @p_743) :rule implies_neg1)
(anchor :step t1195.t26)
(assume t1195.t26.a0 @p_743)
(step t1195.t26.t0 (cl @p_746) :rule symm :premises (t1195.t26.a0))
(step t1195.t26.t1 (cl @p_1077) :rule cong :premises (t1195.t26.t0))
(step t1195.t26 (cl @p_794 @p_1077) :rule subproof :discharge (t1195.t26.a0))
(step t1195.t27 (cl @p_1082 @p_1077) :rule resolution :premises (t1195.t25 t1195.t26))
(step t1195.t28 (cl @p_1082 @p_1083) :rule implies_neg2)
(step t1195.t29 (cl @p_1082 @p_1082) :rule resolution :premises (t1195.t27 t1195.t28))
(step t1195.t30 (cl @p_1082) :rule contraction :premises (t1195.t29))
(step t1195.t31 (cl @p_794 @p_1077) :rule implies :premises (t1195.t30))
(step t1195.t32 (cl @p_1077) :rule resolution :premises (t1195.t31 t1195.a2))
(step t1195.t33 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1195.t34 (cl @p_801) :rule trans :premises (t1195.t33 t755))
(step t1195.t35 (cl @p_1084) :rule and_intro :premises (t1195.t32 t1195.t34))
(step t1195.t36 (cl @p_1078) :rule resolution :premises (t1195.t24 t1195.t35))
(step t1195.t37 (cl @p_1079) :rule and_intro :premises (t1195.a3 t1195.t36 t1195.t32))
(step t1195.t38 (cl @p_1058) :rule resolution :premises (t1195.t12 t1195.t37))
(step t1195.t39 (cl @p_1059) :rule and_intro :premises (t1195.t38 t1195.a5 t1195.a4))
(step t1195 (cl @p_671 @p_792 @p_794 @p_767 @p_16 @p_1052 @p_1059) :rule subproof :discharge (t1195.a0 t1195.a1 t1195.a2 t1195.a3 t1195.a4 t1195.a5))
(step t1196 (cl (! (not @p_1056) :named @p_1057) @p_670) :rule and_pos :args (0))
(step t1197 (cl @p_1057 @p_786) :rule and_pos :args (1))
(step t1198 (cl @p_1057 @p_743) :rule and_pos :args (2))
(step t1199 (cl @p_1057 @p_760) :rule and_pos :args (3))
(step t1200 (cl @p_1057 @p_15) :rule and_pos :args (4))
(step t1201 (cl @p_1057 @p_1051) :rule and_pos :args (5))
(step t1202 (cl @p_1059 @p_1057 @p_1057 @p_1057 @p_1057 @p_1057 @p_1057) :rule resolution :premises (t1195 t1196 t1197 t1198 t1199 t1200 t1201))
(step t1203 (cl @p_1057 @p_1057 @p_1057 @p_1057 @p_1057 @p_1057 @p_1059) :rule reordering :premises (t1202))
(step t1204 (cl @p_1057 @p_1059) :rule contraction :premises (t1203))
(step t1205 (cl @p_1075 @p_1059) :rule resolution :premises (t1194 t1204))
(step t1206 (cl @p_1075 (! (not @p_1059) :named @p_1060)) :rule implies_neg2)
(step t1207 (cl @p_1075 @p_1075) :rule resolution :premises (t1205 t1206))
(step t1208 (cl @p_1075) :rule contraction :premises (t1207))
(step t1209 (cl @p_1057 @p_1059) :rule implies :premises (t1208))
(step t1210 (cl (! (=> @p_1059 false) :named @p_1061) @p_1059) :rule implies_neg1)
(anchor :step t1211)
(assume t1211.a0 @p_1058)
(assume t1211.a1 @p_1051)
(assume t1211.a2 @p_15)
(step t1211.t0 (cl (not @p_1035) @p_1037 @p_16) :rule equiv_pos2)
(step t1211.t1 (cl @p_1035) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0))
(step t1211.t2 (cl (or @p_1072 (! (not (! (<= @p_8 0) :named @p_1065)) :named @p_1074) (! (not (<= 0 @p_8)) :named @p_1063))) :rule la_disequality)
(step t1211.t3 (cl @p_1072 @p_1074 @p_1063) :rule or :premises (t1211.t2))
(step t1211.t4 (cl @p_1073) :rule not_symm :premises (t1211.a0))
(step t1211.t5 (cl @p_1071 @p_1065) :rule la_generic :args (1/1 1/1))
(step t1211.t6 (cl @p_1070 @p_1052 @p_1066) :rule equiv_pos2)
(step t1211.t7 (cl (= @p_1066 @p_1051)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 1))
(step t1211.t8 (cl @p_1069) :rule symm :premises (t1211.t7))
(step t1211.t9 (cl @p_1066) :rule resolution :premises (t1211.t6 t1211.t8 t1211.a1))
(step t1211.t10 (cl @p_1065) :rule resolution :premises (t1211.t5 t1211.t9))
(step t1211.t11 (cl (not (! (= @p_1031 @p_1063) :named @p_1064)) @p_1031 (not @p_1063)) :rule equiv_pos1)
(step t1211.t12 (cl @p_1064) :rule comp_simplify)
(step t1211.t13 (cl @p_1031) :rule resolution :premises (t1211.t3 t1211.t4 t1211.t10 t1211.t11 t1211.t12))
(step t1211.t14 (cl @p_16) :rule resolution :premises (t1211.t0 t1211.t1 t1211.t13))
(step t1211.t15 (cl) :rule resolution :premises (t1211.a2 t1211.t14))
(step t1211 (cl @p_1062 @p_1052 @p_16 false) :rule subproof :discharge (t1211.a0 t1211.a1 t1211.a2))
(step t1212 (cl @p_1060 @p_1058) :rule and_pos :args (0))
(step t1213 (cl @p_1060 @p_1051) :rule and_pos :args (1))
(step t1214 (cl @p_1060 @p_15) :rule and_pos :args (2))
(step t1215 (cl false @p_1060 @p_1060 @p_1060) :rule resolution :premises (t1211 t1212 t1213 t1214))
(step t1216 (cl @p_1060 @p_1060 @p_1060 false) :rule reordering :premises (t1215))
(step t1217 (cl @p_1060 false) :rule contraction :premises (t1216))
(step t1218 (cl @p_1061 false) :rule resolution :premises (t1210 t1217))
(step t1219 (cl @p_1061 @p_212) :rule implies_neg2)
(step t1220 (cl @p_1061 @p_1061) :rule resolution :premises (t1218 t1219))
(step t1221 (cl @p_1061) :rule contraction :premises (t1220))
(step t1222 (cl (= @p_1061 @p_1060)) :rule implies_simplify)
(step t1223 (cl (not @p_1061) @p_1060) :rule equiv1 :premises (t1222))
(step t1224 (cl @p_1060) :rule resolution :premises (t1221 t1223))
(step t1225 (cl @p_1057) :rule resolution :premises (t1209 t1224))
(step t1226 (cl @p_671 @p_792 @p_794 @p_767 @p_16 @p_1052) :rule not_and :premises (t1225))
(step t1227 (cl @p_1053 @p_677) :rule or_neg :args (0))
(step t1228 (cl @p_1053 @p_1017) :rule or_neg :args (1))
(step t1229 (cl @p_1053 (not @p_794)) :rule or_neg :args (2))
(step t1230 (cl @p_1053 @p_1055) :rule or_neg :args (3))
(step t1231 (cl @p_1053 @p_1013) :rule or_neg :args (4))
(step t1232 (cl @p_1053 @p_1054) :rule or_neg :args (5))
(step t1233 (cl @p_1053 @p_1053 @p_1053 @p_1053 @p_1053 @p_1053) :rule resolution :premises (t1226 t1227 t1228 t1229 t1230 t1231 t1232))
(step t1234 (cl @p_1053) :rule contraction :premises (t1233))
(step t1235 (cl @p_1050) :rule resolution :premises (t1190 t1193 t1234))
(step t1236 (cl @p_671 @p_792 @p_794 @p_759 @p_16 @p_1049) :rule or :premises (t1235))
(step t1237 (cl @p_583 @p_566 @p_671 @p_792 @p_974 @p_15 @p_532) :rule or :premises (t858))
(step t1238 (cl (! (and @p_224 @p_524 @p_830 (! (= @p_6 @p_57) :named @p_899)) :named @p_971) @p_227 @p_583 @p_831 (! (not @p_899) :named @p_911)) :rule and_neg)
(step t1239 (cl (! (=> @p_971 @p_58) :named @p_973) @p_971) :rule implies_neg1)
(anchor :step t1240)
(assume t1240.a0 @p_224)
(assume t1240.a1 @p_524)
(assume t1240.a2 @p_830)
(assume t1240.a3 @p_899)
(step t1240.t0 (cl (! (=> (! (and @p_830 @p_224 @p_524 @p_899) :named @p_975) @p_58) :named @p_977) @p_975) :rule implies_neg1)
(anchor :step t1240.t1)
(assume t1240.t1.a0 @p_830)
(assume t1240.t1.a1 @p_224)
(assume t1240.t1.a2 @p_524)
(assume t1240.t1.a3 @p_899)
(step t1240.t1.t0 (cl (= @p_57 @p_6)) :rule symm :premises (t1240.t1.a3))
(step t1240.t1.t1 (cl @p_527) :rule symm :premises (t1240.t1.a2))
(step t1240.t1.t2 (cl @p_58) :rule trans :premises (t1240.t1.t0 t1240.t1.t1 t261 t1240.t1.a0))
(step t1240.t1 (cl @p_831 @p_227 @p_583 @p_911 @p_58) :rule subproof :discharge (t1240.t1.a0 t1240.t1.a1 t1240.t1.a2 t1240.t1.a3))
(step t1240.t2 (cl (! (not @p_975) :named @p_976) @p_830) :rule and_pos :args (0))
(step t1240.t3 (cl @p_976 @p_224) :rule and_pos :args (1))
(step t1240.t4 (cl @p_976 @p_524) :rule and_pos :args (2))
(step t1240.t5 (cl @p_976 @p_899) :rule and_pos :args (3))
(step t1240.t6 (cl @p_58 @p_976 @p_976 @p_976 @p_976) :rule resolution :premises (t1240.t1 t1240.t2 t1240.t3 t1240.t4 t1240.t5))
(step t1240.t7 (cl @p_976 @p_976 @p_976 @p_976 @p_58) :rule reordering :premises (t1240.t6))
(step t1240.t8 (cl @p_976 @p_58) :rule contraction :premises (t1240.t7))
(step t1240.t9 (cl @p_977 @p_58) :rule resolution :premises (t1240.t0 t1240.t8))
(step t1240.t10 (cl @p_977 @p_974) :rule implies_neg2)
(step t1240.t11 (cl @p_977 @p_977) :rule resolution :premises (t1240.t9 t1240.t10))
(step t1240.t12 (cl @p_977) :rule contraction :premises (t1240.t11))
(step t1240.t13 (cl @p_976 @p_58) :rule implies :premises (t1240.t12))
(step t1240.t14 (cl @p_975) :rule and_intro :premises (t1240.a2 t261 t1240.a1 t1240.a3))
(step t1240.t15 (cl @p_58) :rule resolution :premises (t1240.t13 t1240.t14))
(step t1240 (cl @p_227 @p_583 @p_831 @p_911 @p_58) :rule subproof :discharge (t1240.a0 t1240.a1 t1240.a2 t1240.a3))
(step t1241 (cl (! (not @p_971) :named @p_972) @p_224) :rule and_pos :args (0))
(step t1242 (cl @p_972 @p_524) :rule and_pos :args (1))
(step t1243 (cl @p_972 @p_830) :rule and_pos :args (2))
(step t1244 (cl @p_972 @p_899) :rule and_pos :args (3))
(step t1245 (cl @p_58 @p_972 @p_972 @p_972 @p_972) :rule resolution :premises (t1240 t1241 t1242 t1243 t1244))
(step t1246 (cl @p_972 @p_972 @p_972 @p_972 @p_58) :rule reordering :premises (t1245))
(step t1247 (cl @p_972 @p_58) :rule contraction :premises (t1246))
(step t1248 (cl @p_973 @p_58) :rule resolution :premises (t1239 t1247))
(step t1249 (cl @p_973 @p_974) :rule implies_neg2)
(step t1250 (cl @p_973 @p_973) :rule resolution :premises (t1248 t1249))
(step t1251 (cl @p_973) :rule contraction :premises (t1250))
(step t1252 (cl @p_972 @p_58) :rule implies :premises (t1251))
(step t1253 (cl @p_227 @p_583 @p_831 @p_911 @p_58) :rule resolution :premises (t1238 t1252))
(step t1254 (cl @p_583 @p_227 @p_58 @p_831 @p_911) :rule reordering :premises (t1253))
(step t1255 (cl (not (! (= (! (or @p_227 @p_583 @p_671 @p_831 @p_911 @p_532 (! (not (! (>= @p_7 1) :named @p_809)) :named @p_812) @p_916) :named @p_917) (! (or @p_227 @p_583 @p_671 @p_831 @p_911 @p_532 @p_812 @p_913) :named @p_914)) :named @p_970)) (not @p_917) @p_914) :rule equiv_pos2)
(step t1256 (cl @p_970) :rule cong :premises (t761))
(step t1257 (cl (! (=> (! (and @p_224 @p_524 @p_670 @p_830 @p_899 @p_106 @p_809 @p_915) :named @p_921) (! (and @p_915 @p_924 @p_923 @p_809 @p_839) :named @p_925)) :named @p_962) @p_921) :rule implies_neg1)
(anchor :step t1258)
(assume t1258.a0 @p_224)
(assume t1258.a1 @p_524)
(assume t1258.a2 @p_670)
(assume t1258.a3 @p_830)
(assume t1258.a4 @p_899)
(assume t1258.a5 @p_106)
(assume t1258.a6 @p_809)
(assume t1258.a7 @p_915)
(step t1258.t0 (cl @p_969 @p_967) :rule implies_neg1)
(anchor :step t1258.t1)
(assume t1258.t1.a0 @p_106)
(assume t1258.t1.a1 @p_524)
(assume t1258.t1.a2 @p_670)
(step t1258.t1.t0 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1258.t1.t1 (cl @p_527) :rule symm :premises (t1258.t1.a1))
(step t1258.t1.t2 (cl @p_924) :rule trans :premises (t1258.t1.t0 t1258.t1.t1 t742))
(step t1258.t1 (cl @p_532 @p_583 @p_671 @p_924) :rule subproof :discharge (t1258.t1.a0 t1258.t1.a1 t1258.t1.a2))
(step t1258.t2 (cl @p_968 @p_106) :rule and_pos :args (0))
(step t1258.t3 (cl @p_968 @p_524) :rule and_pos :args (1))
(step t1258.t4 (cl @p_968 @p_670) :rule and_pos :args (2))
(step t1258.t5 (cl @p_924 @p_968 @p_968 @p_968) :rule resolution :premises (t1258.t1 t1258.t2 t1258.t3 t1258.t4))
(step t1258.t6 (cl @p_968 @p_968 @p_968 @p_924) :rule reordering :premises (t1258.t5))
(step t1258.t7 (cl @p_968 @p_924) :rule contraction :premises (t1258.t6))
(step t1258.t8 (cl @p_969 @p_924) :rule resolution :premises (t1258.t0 t1258.t7))
(step t1258.t9 (cl @p_969 @p_928) :rule implies_neg2)
(step t1258.t10 (cl @p_969 @p_969) :rule resolution :premises (t1258.t8 t1258.t9))
(step t1258.t11 (cl @p_969) :rule contraction :premises (t1258.t10))
(step t1258.t12 (cl @p_968 @p_924) :rule implies :premises (t1258.t11))
(step t1258.t13 (cl @p_967) :rule and_intro :premises (t742 t1258.a1 t758))
(step t1258.t14 (cl @p_924) :rule resolution :premises (t1258.t12 t1258.t13))
(step t1258.t15 (cl (! (=> (! (and @p_899 @p_524 @p_224 @p_830) :named @p_963) @p_923) :named @p_966) @p_963) :rule implies_neg1)
(anchor :step t1258.t16)
(assume t1258.t16.a0 @p_899)
(assume t1258.t16.a1 @p_524)
(assume t1258.t16.a2 @p_224)
(assume t1258.t16.a3 @p_830)
(step t1258.t16.t0 (cl (! (= 1 @p_172) :named @p_844)) :rule symm :premises (t1258.t16.a3))
(step t1258.t16.t1 (cl (= @p_172 k$)) :rule symm :premises (t261))
(step t1258.t16.t2 (cl @p_923) :rule trans :premises (t1258.t16.t0 t1258.t16.t1 t1258.t16.a1 t1258.t16.a0))
(step t1258.t16 (cl @p_911 @p_583 @p_227 @p_831 @p_923) :rule subproof :discharge (t1258.t16.a0 t1258.t16.a1 t1258.t16.a2 t1258.t16.a3))
(step t1258.t17 (cl (! (not @p_963) :named @p_965) @p_899) :rule and_pos :args (0))
(step t1258.t18 (cl @p_965 @p_524) :rule and_pos :args (1))
(step t1258.t19 (cl @p_965 @p_224) :rule and_pos :args (2))
(step t1258.t20 (cl @p_965 @p_830) :rule and_pos :args (3))
(step t1258.t21 (cl @p_923 @p_965 @p_965 @p_965 @p_965) :rule resolution :premises (t1258.t16 t1258.t17 t1258.t18 t1258.t19 t1258.t20))
(step t1258.t22 (cl @p_965 @p_965 @p_965 @p_965 @p_923) :rule reordering :premises (t1258.t21))
(step t1258.t23 (cl @p_965 @p_923) :rule contraction :premises (t1258.t22))
(step t1258.t24 (cl @p_966 @p_923) :rule resolution :premises (t1258.t15 t1258.t23))
(step t1258.t25 (cl @p_966 @p_929) :rule implies_neg2)
(step t1258.t26 (cl @p_966 @p_966) :rule resolution :premises (t1258.t24 t1258.t25))
(step t1258.t27 (cl @p_966) :rule contraction :premises (t1258.t26))
(step t1258.t28 (cl @p_965 @p_923) :rule implies :premises (t1258.t27))
(step t1258.t29 (cl @p_963) :rule and_intro :premises (t1258.a4 t1258.a1 t261 t1258.a3))
(step t1258.t30 (cl @p_923) :rule resolution :premises (t1258.t28 t1258.t29))
(step t1258.t31 (cl (! (=> (! (and @p_106 @p_224 @p_830) :named @p_840) @p_839) :named @p_842) @p_840) :rule implies_neg1)
(anchor :step t1258.t32)
(assume t1258.t32.a0 @p_106)
(assume t1258.t32.a1 @p_224)
(assume t1258.t32.a2 @p_830)
(step t1258.t32.t0 (cl @p_844) :rule symm :premises (t1258.t32.a2))
(step t1258.t32.t1 (cl (= @p_172 k$)) :rule symm :premises (t261))
(step t1258.t32.t2 (cl @p_839) :rule trans :premises (t1258.t32.t0 t1258.t32.t1 t742))
(step t1258.t32 (cl @p_532 @p_227 @p_831 @p_839) :rule subproof :discharge (t1258.t32.a0 t1258.t32.a1 t1258.t32.a2))
(step t1258.t33 (cl (! (not @p_840) :named @p_841) @p_106) :rule and_pos :args (0))
(step t1258.t34 (cl @p_841 @p_224) :rule and_pos :args (1))
(step t1258.t35 (cl @p_841 @p_830) :rule and_pos :args (2))
(step t1258.t36 (cl @p_839 @p_841 @p_841 @p_841) :rule resolution :premises (t1258.t32 t1258.t33 t1258.t34 t1258.t35))
(step t1258.t37 (cl @p_841 @p_841 @p_841 @p_839) :rule reordering :premises (t1258.t36))
(step t1258.t38 (cl @p_841 @p_839) :rule contraction :premises (t1258.t37))
(step t1258.t39 (cl @p_842 @p_839) :rule resolution :premises (t1258.t31 t1258.t38))
(step t1258.t40 (cl @p_842 @p_843) :rule implies_neg2)
(step t1258.t41 (cl @p_842 @p_842) :rule resolution :premises (t1258.t39 t1258.t40))
(step t1258.t42 (cl @p_842) :rule contraction :premises (t1258.t41))
(step t1258.t43 (cl @p_841 @p_839) :rule implies :premises (t1258.t42))
(step t1258.t44 (cl @p_840) :rule and_intro :premises (t742 t261 t1258.a3))
(step t1258.t45 (cl @p_839) :rule resolution :premises (t1258.t43 t1258.t44))
(step t1258.t46 (cl @p_925) :rule and_intro :premises (t1258.a7 t1258.t14 t1258.t30 t1258.a6 t1258.t45))
(step t1258 (cl @p_227 @p_583 @p_671 @p_831 @p_911 @p_532 @p_812 @p_916 @p_925) :rule subproof :discharge (t1258.a0 t1258.a1 t1258.a2 t1258.a3 t1258.a4 t1258.a5 t1258.a6 t1258.a7))
(step t1259 (cl (! (not @p_921) :named @p_922) @p_224) :rule and_pos :args (0))
(step t1260 (cl @p_922 @p_524) :rule and_pos :args (1))
(step t1261 (cl @p_922 @p_670) :rule and_pos :args (2))
(step t1262 (cl @p_922 @p_830) :rule and_pos :args (3))
(step t1263 (cl @p_922 @p_899) :rule and_pos :args (4))
(step t1264 (cl @p_922 @p_106) :rule and_pos :args (5))
(step t1265 (cl @p_922 @p_809) :rule and_pos :args (6))
(step t1266 (cl @p_922 @p_915) :rule and_pos :args (7))
(step t1267 (cl @p_925 @p_922 @p_922 @p_922 @p_922 @p_922 @p_922 @p_922 @p_922) :rule resolution :premises (t1258 t1259 t1260 t1261 t1262 t1263 t1264 t1265 t1266))
(step t1268 (cl @p_922 @p_922 @p_922 @p_922 @p_922 @p_922 @p_922 @p_922 @p_925) :rule reordering :premises (t1267))
(step t1269 (cl @p_922 @p_925) :rule contraction :premises (t1268))
(step t1270 (cl @p_962 @p_925) :rule resolution :premises (t1257 t1269))
(step t1271 (cl @p_962 (! (not @p_925) :named @p_926)) :rule implies_neg2)
(step t1272 (cl @p_962 @p_962) :rule resolution :premises (t1270 t1271))
(step t1273 (cl @p_962) :rule contraction :premises (t1272))
(step t1274 (cl @p_922 @p_925) :rule implies :premises (t1273))
(step t1275 (cl (! (=> @p_925 false) :named @p_927) @p_925) :rule implies_neg1)
(anchor :step t1276)
(assume t1276.a0 @p_915)
(assume t1276.a1 @p_924)
(assume t1276.a2 @p_923)
(assume t1276.a3 @p_809)
(assume t1276.a4 @p_839)
(step t1276.t0 (cl @p_855) :rule symm :premises (t1276.a4))
(step t1276.t1 (cl (! (=> @p_855 false) :named @p_930) @p_855) :rule implies_neg1)
(anchor :step t1276.t2)
(assume t1276.t2.a0 @p_855)
(step t1276.t2.t0 (cl (not (! (= (! (< (! (+ @p_105 @p_46 @p_689 @p_932 @p_912) :named @p_933) (! (+ 1 @p_298 @p_298 0 1) :named @p_931)) :named @p_934) false) :named @p_957)) (not @p_934) false) :rule equiv_pos2)
(step t1276.t2.t1 (cl (= @p_934 (! (not (! (>= @p_933 @p_931) :named @p_958)) :named @p_959))) :rule rare_rewrite :args ("arith-elim-lt" @p_933 @p_931))
(step t1276.t2.t2 (cl (= @p_933 (! (+ @p_545 @p_544 @p_103 @p_104 @p_689 @p_690 @p_57 @p_668 @p_46 @p_7) :named @p_961))) :rule poly_simp)
(step t1276.t2.t3 (cl (= @p_961 0)) :rule poly_simp)
(step t1276.t2.t4 (cl (= @p_933 0)) :rule trans :premises (t1276.t2.t2 t1276.t2.t3))
(step t1276.t2.t5 (cl (= @p_298 -1)) :rule evaluate)
(step t1276.t2.t6 (cl (= 1 1)) :rule refl)
(step t1276.t2.t7 (cl (= @p_931 (! (+ 1 -1 -1 0 1) :named @p_960))) :rule cong :premises (t1276.t2.t5 t1276.t2.t5 t604 t1276.t2.t6))
(step t1276.t2.t8 (cl (= @p_960 0)) :rule evaluate)
(step t1276.t2.t9 (cl (= @p_931 0)) :rule trans :premises (t1276.t2.t7 t1276.t2.t8))
(step t1276.t2.t10 (cl (= @p_958 @p_366)) :rule cong :premises (t1276.t2.t4 t1276.t2.t9))
(step t1276.t2.t11 (cl (= @p_366 true)) :rule evaluate)
(step t1276.t2.t12 (cl (= @p_958 true)) :rule trans :premises (t1276.t2.t10 t1276.t2.t11))
(step t1276.t2.t13 (cl (= @p_959 @p_365)) :rule cong :premises (t1276.t2.t12))
(step t1276.t2.t14 (cl (= @p_365 false)) :rule evaluate)
(step t1276.t2.t15 (cl (= @p_959 false)) :rule trans :premises (t1276.t2.t13 t1276.t2.t14))
(step t1276.t2.t16 (cl @p_957) :rule trans :premises (t1276.t2.t1 t1276.t2.t15))
(step t1276.t2.t17 (cl @p_860 (not (! (<= @p_46 @p_298) :named @p_951)) @p_954 @p_955 @p_956 @p_934) :rule la_generic :args (-1/1 1/1 -1/1 -1/1 1/1 1/1))
(step t1276.t2.t18 (cl (=> (! (and @p_308 @p_809) :named @p_952) @p_951)) :rule la_mult_neg)
(step t1276.t2.t19 (cl (not @p_952) @p_951) :rule implies :premises (t1276.t2.t18))
(step t1276.t2.t20 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1276.t2.t21 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1276.t2.t20))
(step t1276.t2.t22 (cl @p_310) :rule evaluate)
(step t1276.t2.t23 (cl @p_308) :rule resolution :premises (t1276.t2.t21 t1276.t2.t22))
(step t1276.t2.t24 (cl @p_952) :rule and_intro :premises (t1276.t2.t23 t1276.a3))
(step t1276.t2.t25 (cl @p_951) :rule resolution :premises (t1276.t2.t19 t1276.t2.t24))
(step t1276.t2.t26 (cl (=> @p_948 @p_947)) :rule la_mult_neg)
(step t1276.t2.t27 (cl @p_950 @p_947) :rule implies :premises (t1276.t2.t26))
(step t1276.t2.t28 (cl @p_58) :rule symm :premises (t1276.a2))
(step t1276.t2.t29 (cl @p_948) :rule and_intro :premises (t1276.t2.t23 t1276.t2.t28))
(step t1276.t2.t30 (cl @p_947) :rule resolution :premises (t1276.t2.t27 t1276.t2.t29))
(step t1276.t2.t31 (cl @p_946 @p_928 @p_940) :rule equiv_pos2)
(step t1276.t2.t32 (cl (= (* 1 (- @p_669 @p_105)) @p_945)) :rule poly_simp)
(step t1276.t2.t33 (cl (= @p_924 @p_944)) :rule poly_simp_rel :premises (t1276.t2.t32))
(step t1276.t2.t34 (cl (= (* 1 (- @p_932 0)) @p_945)) :rule poly_simp)
(step t1276.t2.t35 (cl (= @p_940 @p_944)) :rule poly_simp_rel :premises (t1276.t2.t34))
(step t1276.t2.t36 (cl (= @p_944 @p_940)) :rule symm :premises (t1276.t2.t35))
(step t1276.t2.t37 (cl @p_942) :rule trans :premises (t1276.t2.t33 t1276.t2.t36))
(step t1276.t2.t38 (cl @p_940) :rule resolution :premises (t1276.t2.t31 t1276.t2.t37 t1276.a1))
(step t1276.t2.t39 (cl @p_939 @p_916 @p_935) :rule equiv_pos2)
(step t1276.t2.t40 (cl (= @p_935 @p_915)) :rule rare_rewrite :args ("arith-elim-lt" @p_912 1))
(step t1276.t2.t41 (cl @p_938) :rule symm :premises (t1276.t2.t40))
(step t1276.t2.t42 (cl @p_935) :rule resolution :premises (t1276.t2.t39 t1276.t2.t41 t1276.a0))
(step t1276.t2.t43 (cl @p_934) :rule resolution :premises (t1276.t2.t17 t1276.t2.a0 t1276.t2.t25 t1276.t2.t30 t1276.t2.t38 t1276.t2.t42))
(step t1276.t2.t44 (cl false) :rule resolution :premises (t1276.t2.t0 t1276.t2.t16 t1276.t2.t43))
(step t1276.t2 (cl @p_860 false) :rule subproof :discharge (t1276.t2.a0))
(step t1276.t3 (cl @p_930 false) :rule resolution :premises (t1276.t1 t1276.t2))
(step t1276.t4 (cl @p_930 @p_212) :rule implies_neg2)
(step t1276.t5 (cl @p_930 @p_930) :rule resolution :premises (t1276.t3 t1276.t4))
(step t1276.t6 (cl @p_930) :rule contraction :premises (t1276.t5))
(step t1276.t7 (cl (= @p_930 @p_860)) :rule implies_simplify)
(step t1276.t8 (cl (not @p_930) @p_860) :rule equiv1 :premises (t1276.t7))
(step t1276.t9 (cl @p_860) :rule resolution :premises (t1276.t6 t1276.t8))
(step t1276.t10 (cl) :rule resolution :premises (t1276.t0 t1276.t9))
(step t1276 (cl @p_916 @p_928 @p_929 @p_812 @p_843 false) :rule subproof :discharge (t1276.a0 t1276.a1 t1276.a2 t1276.a3 t1276.a4))
(step t1277 (cl @p_926 @p_915) :rule and_pos :args (0))
(step t1278 (cl @p_926 @p_924) :rule and_pos :args (1))
(step t1279 (cl @p_926 @p_923) :rule and_pos :args (2))
(step t1280 (cl @p_926 @p_809) :rule and_pos :args (3))
(step t1281 (cl @p_926 @p_839) :rule and_pos :args (4))
(step t1282 (cl false @p_926 @p_926 @p_926 @p_926 @p_926) :rule resolution :premises (t1276 t1277 t1278 t1279 t1280 t1281))
(step t1283 (cl @p_926 @p_926 @p_926 @p_926 @p_926 false) :rule reordering :premises (t1282))
(step t1284 (cl @p_926 false) :rule contraction :premises (t1283))
(step t1285 (cl @p_927 false) :rule resolution :premises (t1275 t1284))
(step t1286 (cl @p_927 @p_212) :rule implies_neg2)
(step t1287 (cl @p_927 @p_927) :rule resolution :premises (t1285 t1286))
(step t1288 (cl @p_927) :rule contraction :premises (t1287))
(step t1289 (cl (= @p_927 @p_926)) :rule implies_simplify)
(step t1290 (cl (not @p_927) @p_926) :rule equiv1 :premises (t1289))
(step t1291 (cl @p_926) :rule resolution :premises (t1288 t1290))
(step t1292 (cl @p_922) :rule resolution :premises (t1274 t1291))
(step t1293 (cl @p_227 @p_583 @p_671 @p_831 @p_911 @p_532 @p_812 @p_916) :rule not_and :premises (t1292))
(step t1294 (cl @p_917 @p_232) :rule or_neg :args (0))
(step t1295 (cl @p_917 @p_589) :rule or_neg :args (1))
(step t1296 (cl @p_917 @p_677) :rule or_neg :args (2))
(step t1297 (cl @p_917 @p_920) :rule or_neg :args (3))
(step t1298 (cl @p_917 (! (not @p_911) :named @p_919)) :rule or_neg :args (4))
(step t1299 (cl @p_917 @p_538) :rule or_neg :args (5))
(step t1300 (cl @p_917 (not @p_812)) :rule or_neg :args (6))
(step t1301 (cl @p_917 @p_918) :rule or_neg :args (7))
(step t1302 (cl @p_917 @p_917 @p_917 @p_917 @p_917 @p_917 @p_917 @p_917) :rule resolution :premises (t1293 t1294 t1295 t1296 t1297 t1298 t1299 t1300 t1301))
(step t1303 (cl @p_917) :rule contraction :premises (t1302))
(step t1304 (cl @p_914) :rule resolution :premises (t1255 t1256 t1303))
(step t1305 (cl @p_227 @p_583 @p_671 @p_831 @p_911 @p_532 @p_812 @p_913) :rule or :premises (t1304))
(step t1306 (cl @p_583 @p_227 @p_671 @p_831 @p_911 @p_532 @p_812 @p_913) :rule reordering :premises (t1305))
(step t1307 (cl (! (not (! (or (! (not (! (>= @p_6 0) :named @p_515)) :named @p_585) (! (>= @p_6 2) :named @p_870) @p_899) :named @p_900)) :named @p_910) @p_585 @p_870 @p_899) :rule or_pos)
(step t1308 (cl @p_585 @p_899 @p_870 @p_910) :rule reordering :premises (t1307))
(step t1309 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) (! (or @p_585 (! (>= (! (+ @p_6 @p_850) :named @p_902) 0) :named @p_903) @p_899) :named @p_904)) :named @p_905) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))) @p_900) :named @p_901)) :named @p_906)) (not @p_905) @p_901) :rule equiv_pos2)
(step t1310 (cl (= @p_850 -2)) :rule evaluate)
(step t1311 (cl (= @p_902 (! (+ @p_6 -2) :named @p_909))) :rule cong :premises (t1310))
(step t1312 (cl (= @p_909 (! (+ -2 @p_6) :named @p_907))) :rule poly_simp)
(step t1313 (cl (= @p_902 @p_907)) :rule trans :premises (t1311 t1312))
(step t1314 (cl (= @p_903 (! (>= @p_907 0) :named @p_908))) :rule cong :premises (t1313 t604))
(step t1315 (cl (= (* -2 (- @p_907 0)) (* -2 (- @p_6 2)))) :rule poly_simp)
(step t1316 (cl (= @p_908 @p_870)) :rule poly_simp_rel :premises (t1315))
(step t1317 (cl (= @p_903 @p_870)) :rule trans :premises (t1314 t1316))
(step t1318 (cl (= @p_899 @p_899)) :rule refl)
(step t1319 (cl (= @p_904 @p_900)) :rule cong :premises (t1317 t1318))
(step t1320 (cl @p_906) :rule cong :premises (t1319))
(step t1321 (cl @p_905 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t1322)
(assume t1322.a0 (forall ((?v0 Int) (?v1 Int)) (or (not (>= ?v0 0)) (>= (+ ?v0 (* -1 ?v1)) 0) (= ?v0 (modulo$ ?v0 ?v1)))))
(step t1322.t0 (cl (or @p_44 @p_904)) :rule forall_inst :args (@p_6 2))
(step t1322.t1 (cl @p_44 @p_904) :rule or :premises (t1322.t0))
(step t1322.t2 (cl @p_904) :rule resolution :premises (t1322.t1 t627))
(step t1322 (cl @p_44 @p_904) :rule subproof :discharge (t1322.a0))
(step t1323 (cl @p_905 @p_904) :rule resolution :premises (t1321 t1322))
(step t1324 (cl @p_905 (not @p_904)) :rule implies_neg2)
(step t1325 (cl @p_905 @p_905) :rule resolution :premises (t1323 t1324))
(step t1326 (cl @p_905) :rule contraction :premises (t1325))
(step t1327 (cl @p_901) :rule resolution :premises (t1309 t1320 t1326))
(step t1328 (cl @p_44 @p_900) :rule implies :premises (t1327))
(step t1329 (cl @p_900) :rule resolution :premises (t1328 t627))
(step t1330 (cl (not (! (= (! (or @p_583 (! (not @p_870) :named @p_871) @p_532 @p_838) :named @p_873) (! (or @p_583 @p_871 @p_532 @p_833) :named @p_872)) :named @p_898)) (not @p_873) @p_872) :rule equiv_pos2)
(step t1331 (cl (= @p_838 @p_833)) :rule rare_rewrite :args ("bool-double-not-elim" @p_833))
(step t1332 (cl @p_898) :rule cong :premises (t1331))
(step t1333 (cl (! (=> (! (and @p_524 @p_870 @p_106 @p_834) :named @p_875) (! (and @p_870 @p_592 @p_834) :named @p_877)) :named @p_897) @p_875) :rule implies_neg1)
(anchor :step t1334)
(assume t1334.a0 @p_524)
(assume t1334.a1 @p_870)
(assume t1334.a2 @p_106)
(assume t1334.a3 @p_834)
(step t1334.t0 (cl @p_631 @p_628) :rule implies_neg1)
(anchor :step t1334.t1)
(assume t1334.t1.a0 @p_106)
(assume t1334.t1.a1 @p_524)
(step t1334.t1.t0 (cl @p_527) :rule symm :premises (t1334.t1.a1))
(step t1334.t1.t1 (cl @p_592) :rule trans :premises (t1334.t1.t0 t742))
(step t1334.t1 (cl @p_532 @p_583 @p_592) :rule subproof :discharge (t1334.t1.a0 t1334.t1.a1))
(step t1334.t2 (cl @p_630 @p_106) :rule and_pos :args (0))
(step t1334.t3 (cl @p_630 @p_524) :rule and_pos :args (1))
(step t1334.t4 (cl @p_592 @p_630 @p_630) :rule resolution :premises (t1334.t1 t1334.t2 t1334.t3))
(step t1334.t5 (cl @p_630 @p_630 @p_592) :rule reordering :premises (t1334.t4))
(step t1334.t6 (cl @p_630 @p_592) :rule contraction :premises (t1334.t5))
(step t1334.t7 (cl @p_631 @p_592) :rule resolution :premises (t1334.t0 t1334.t6))
(step t1334.t8 (cl @p_631 @p_596) :rule implies_neg2)
(step t1334.t9 (cl @p_631 @p_631) :rule resolution :premises (t1334.t7 t1334.t8))
(step t1334.t10 (cl @p_631) :rule contraction :premises (t1334.t9))
(step t1334.t11 (cl @p_630 @p_592) :rule implies :premises (t1334.t10))
(step t1334.t12 (cl @p_628) :rule and_intro :premises (t742 t1334.a0))
(step t1334.t13 (cl @p_592) :rule resolution :premises (t1334.t11 t1334.t12))
(step t1334.t14 (cl @p_877) :rule and_intro :premises (t1334.a1 t1334.t13 t1334.a3))
(step t1334 (cl @p_583 @p_871 @p_532 @p_838 @p_877) :rule subproof :discharge (t1334.a0 t1334.a1 t1334.a2 t1334.a3))
(step t1335 (cl (! (not @p_875) :named @p_876) @p_524) :rule and_pos :args (0))
(step t1336 (cl @p_876 @p_870) :rule and_pos :args (1))
(step t1337 (cl @p_876 @p_106) :rule and_pos :args (2))
(step t1338 (cl @p_876 @p_834) :rule and_pos :args (3))
(step t1339 (cl @p_877 @p_876 @p_876 @p_876 @p_876) :rule resolution :premises (t1334 t1335 t1336 t1337 t1338))
(step t1340 (cl @p_876 @p_876 @p_876 @p_876 @p_877) :rule reordering :premises (t1339))
(step t1341 (cl @p_876 @p_877) :rule contraction :premises (t1340))
(step t1342 (cl @p_897 @p_877) :rule resolution :premises (t1333 t1341))
(step t1343 (cl @p_897 (! (not @p_877) :named @p_878)) :rule implies_neg2)
(step t1344 (cl @p_897 @p_897) :rule resolution :premises (t1342 t1343))
(step t1345 (cl @p_897) :rule contraction :premises (t1344))
(step t1346 (cl @p_876 @p_877) :rule implies :premises (t1345))
(step t1347 (cl (! (=> @p_877 false) :named @p_879) @p_877) :rule implies_neg1)
(anchor :step t1348)
(assume t1348.a0 @p_870)
(assume t1348.a1 @p_592)
(assume t1348.a2 @p_834)
(step t1348.t0 (cl @p_867 @p_838 @p_846) :rule equiv_pos2)
(step t1348.t1 (cl @p_866) :rule rare_rewrite :args ("arith-elim-lt" @p_105 2))
(step t1348.t2 (cl @p_865) :rule symm :premises (t1348.t1))
(step t1348.t3 (cl @p_846) :rule resolution :premises (t1348.t0 t1348.t2 t1348.a2))
(step t1348.t4 (cl (not (! (= @p_833 @p_869) :named @p_896)) @p_834 @p_869) :rule equiv_pos2)
(step t1348.t5 (cl (= @p_869 @p_838)) :rule cong :premises (t1348.t1))
(step t1348.t6 (cl (! (= @p_869 @p_833) :named @p_895)) :rule trans :premises (t1348.t5 t1331))
(step t1348.t7 (cl @p_896) :rule symm :premises (t1348.t6))
(step t1348.t8 (cl (not @p_895) (not @p_869) @p_833) :rule equiv_pos2)
(step t1348.t9 (cl (! (=> @p_846 false) :named @p_880) @p_846) :rule implies_neg1)
(anchor :step t1348.t10)
(assume t1348.t10.a0 @p_846)
(step t1348.t10.t0 (cl (not (! (= (! (< (! (+ @p_105 @p_601 @p_120) :named @p_882) (! (+ 2 0 @p_850) :named @p_881)) :named @p_883) false) :named @p_890)) (not @p_883) false) :rule equiv_pos2)
(step t1348.t10.t1 (cl (= @p_883 (! (not (! (>= @p_882 @p_881) :named @p_891)) :named @p_892))) :rule rare_rewrite :args ("arith-elim-lt" @p_882 @p_881))
(step t1348.t10.t2 (cl (= @p_882 (! (+ @p_545 @p_544 @p_103 @p_104 @p_120 @p_6) :named @p_894))) :rule poly_simp)
(step t1348.t10.t3 (cl (= @p_894 0)) :rule poly_simp)
(step t1348.t10.t4 (cl (= @p_882 0)) :rule trans :premises (t1348.t10.t2 t1348.t10.t3))
(step t1348.t10.t5 (cl (= @p_881 (! (+ 2 0 -2) :named @p_893))) :rule cong :premises (t1310))
(step t1348.t10.t6 (cl (= @p_893 0)) :rule evaluate)
(step t1348.t10.t7 (cl (= @p_881 0)) :rule trans :premises (t1348.t10.t5 t1348.t10.t6))
(step t1348.t10.t8 (cl (= @p_891 @p_366)) :rule cong :premises (t1348.t10.t4 t1348.t10.t7))
(step t1348.t10.t9 (cl (= @p_366 true)) :rule evaluate)
(step t1348.t10.t10 (cl (= @p_891 true)) :rule trans :premises (t1348.t10.t8 t1348.t10.t9))
(step t1348.t10.t11 (cl (= @p_892 @p_365)) :rule cong :premises (t1348.t10.t10))
(step t1348.t10.t12 (cl (= @p_365 false)) :rule evaluate)
(step t1348.t10.t13 (cl (= @p_892 false)) :rule trans :premises (t1348.t10.t11 t1348.t10.t12))
(step t1348.t10.t14 (cl @p_890) :rule trans :premises (t1348.t10.t1 t1348.t10.t13))
(step t1348.t10.t15 (cl @p_869 @p_888 (! (not (! (<= @p_120 @p_850) :named @p_884)) :named @p_889) @p_883) :rule la_generic :args (1/1 -1/1 1/1 1/1))
(step t1348.t10.t16 (cl @p_610 @p_596 @p_606) :rule equiv_pos2)
(step t1348.t10.t17 (cl (= (* 1 (- @p_601 0)) (* 1 (- @p_6 @p_105)))) :rule poly_simp)
(step t1348.t10.t18 (cl (= @p_606 @p_592)) :rule poly_simp_rel :premises (t1348.t10.t17))
(step t1348.t10.t19 (cl @p_609) :rule symm :premises (t1348.t10.t18))
(step t1348.t10.t20 (cl @p_606) :rule resolution :premises (t1348.t10.t16 t1348.t10.t19 t1348.a1))
(step t1348.t10.t21 (cl (=> (! (and @p_308 @p_870) :named @p_885) @p_884)) :rule la_mult_neg)
(step t1348.t10.t22 (cl (! (not @p_885) :named @p_887) @p_884) :rule implies :premises (t1348.t10.t21))
(step t1348.t10.t23 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1348.t10.t24 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1348.t10.t23))
(step t1348.t10.t25 (cl @p_310) :rule evaluate)
(step t1348.t10.t26 (cl @p_308) :rule resolution :premises (t1348.t10.t24 t1348.t10.t25))
(step t1348.t10.t27 (cl @p_885) :rule and_intro :premises (t1348.t10.t26 t1348.a0))
(step t1348.t10.t28 (cl @p_884) :rule resolution :premises (t1348.t10.t22 t1348.t10.t27))
(step t1348.t10.t29 (cl @p_883) :rule resolution :premises (t1348.t10.t15 t1348.t10.a0 t1348.t10.t20 t1348.t10.t28))
(step t1348.t10.t30 (cl false) :rule resolution :premises (t1348.t10.t0 t1348.t10.t14 t1348.t10.t29))
(step t1348.t10 (cl @p_869 false) :rule subproof :discharge (t1348.t10.a0))
(step t1348.t11 (cl @p_880 false) :rule resolution :premises (t1348.t9 t1348.t10))
(step t1348.t12 (cl @p_880 @p_212) :rule implies_neg2)
(step t1348.t13 (cl @p_880 @p_880) :rule resolution :premises (t1348.t11 t1348.t12))
(step t1348.t14 (cl @p_880) :rule contraction :premises (t1348.t13))
(step t1348.t15 (cl (= @p_880 @p_869)) :rule implies_simplify)
(step t1348.t16 (cl (not @p_880) @p_869) :rule equiv1 :premises (t1348.t15))
(step t1348.t17 (cl @p_869) :rule resolution :premises (t1348.t14 t1348.t16))
(step t1348.t18 (cl @p_833) :rule resolution :premises (t1348.t8 t1348.t6 t1348.t17))
(step t1348.t19 (cl @p_869) :rule resolution :premises (t1348.t4 t1348.t7 t1348.t18))
(step t1348.t20 (cl) :rule resolution :premises (t1348.t3 t1348.t19))
(step t1348 (cl @p_871 @p_596 @p_838 false) :rule subproof :discharge (t1348.a0 t1348.a1 t1348.a2))
(step t1349 (cl @p_878 @p_870) :rule and_pos :args (0))
(step t1350 (cl @p_878 @p_592) :rule and_pos :args (1))
(step t1351 (cl @p_878 @p_834) :rule and_pos :args (2))
(step t1352 (cl false @p_878 @p_878 @p_878) :rule resolution :premises (t1348 t1349 t1350 t1351))
(step t1353 (cl @p_878 @p_878 @p_878 false) :rule reordering :premises (t1352))
(step t1354 (cl @p_878 false) :rule contraction :premises (t1353))
(step t1355 (cl @p_879 false) :rule resolution :premises (t1347 t1354))
(step t1356 (cl @p_879 @p_212) :rule implies_neg2)
(step t1357 (cl @p_879 @p_879) :rule resolution :premises (t1355 t1356))
(step t1358 (cl @p_879) :rule contraction :premises (t1357))
(step t1359 (cl (= @p_879 @p_878)) :rule implies_simplify)
(step t1360 (cl (not @p_879) @p_878) :rule equiv1 :premises (t1359))
(step t1361 (cl @p_878) :rule resolution :premises (t1358 t1360))
(step t1362 (cl @p_876) :rule resolution :premises (t1346 t1361))
(step t1363 (cl @p_583 @p_871 @p_532 @p_838) :rule not_and :premises (t1362))
(step t1364 (cl @p_873 @p_589) :rule or_neg :args (0))
(step t1365 (cl @p_873 (! (not @p_871) :named @p_874)) :rule or_neg :args (1))
(step t1366 (cl @p_873 @p_538) :rule or_neg :args (2))
(step t1367 (cl @p_873 (not @p_838)) :rule or_neg :args (3))
(step t1368 (cl @p_873 @p_873 @p_873 @p_873) :rule resolution :premises (t1363 t1364 t1365 t1366 t1367))
(step t1369 (cl @p_873) :rule contraction :premises (t1368))
(step t1370 (cl @p_872) :rule resolution :premises (t1330 t1332 t1369))
(step t1371 (cl @p_583 @p_871 @p_532 @p_833) :rule or :premises (t1370))
(step t1372 (cl (! (and @p_224 @p_830 @p_106) :named @p_835) @p_227 @p_831 @p_532) :rule and_neg)
(step t1373 (cl (! (=> @p_835 @p_834) :named @p_837) @p_835) :rule implies_neg1)
(anchor :step t1374)
(assume t1374.a0 @p_224)
(assume t1374.a1 @p_830)
(assume t1374.a2 @p_106)
(step t1374.t0 (cl (! (=> @p_839 @p_834) :named @p_845) @p_839) :rule implies_neg1)
(anchor :step t1374.t1)
(assume t1374.t1.a0 @p_839)
(step t1374.t1.t0 (cl @p_868 @p_869 @p_834) :rule equiv_pos2)
(step t1374.t1.t1 (cl @p_866) :rule rare_rewrite :args ("arith-elim-lt" @p_105 2))
(step t1374.t1.t2 (cl @p_867 @p_838 @p_846) :rule equiv_pos2)
(step t1374.t1.t3 (cl @p_865) :rule symm :premises (t1374.t1.t1))
(step t1374.t1.t4 (cl @p_847 @p_833) :rule implies_neg1)
(anchor :step t1374.t1.t5)
(assume t1374.t1.t5.a0 @p_833)
(step t1374.t1.t5.t0 (cl (not (! (= (! (<= (! (+ @p_852 @p_105) :named @p_853) (! (+ @p_850 1) :named @p_851)) :named @p_854) false) :named @p_861)) (not @p_854) false) :rule equiv_pos2)
(step t1374.t1.t5.t1 (cl (= @p_853 (! (+ @p_618 @p_619) :named @p_863))) :rule poly_simp)
(step t1374.t1.t5.t2 (cl (= @p_618 0)) :rule poly_simp)
(step t1374.t1.t5.t3 (cl (= @p_619 0)) :rule poly_simp)
(step t1374.t1.t5.t4 (cl (= @p_863 (! (+ 0 0) :named @p_864))) :rule cong :premises (t1374.t1.t5.t2 t1374.t1.t5.t3))
(step t1374.t1.t5.t5 (cl (= @p_864 0)) :rule evaluate)
(step t1374.t1.t5.t6 (cl (= @p_863 0)) :rule trans :premises (t1374.t1.t5.t4 t1374.t1.t5.t5))
(step t1374.t1.t5.t7 (cl (= @p_853 0)) :rule trans :premises (t1374.t1.t5.t1 t1374.t1.t5.t6))
(step t1374.t1.t5.t8 (cl (= 1 1)) :rule refl)
(step t1374.t1.t5.t9 (cl (= @p_851 (! (+ -2 1) :named @p_862))) :rule cong :premises (t1310 t1374.t1.t5.t8))
(step t1374.t1.t5.t10 (cl (= @p_862 -1)) :rule evaluate)
(step t1374.t1.t5.t11 (cl (= @p_851 -1)) :rule trans :premises (t1374.t1.t5.t9 t1374.t1.t5.t10))
(step t1374.t1.t5.t12 (cl (= @p_854 @p_323)) :rule cong :premises (t1374.t1.t5.t7 t1374.t1.t5.t11))
(step t1374.t1.t5.t13 (cl (= @p_323 false)) :rule evaluate)
(step t1374.t1.t5.t14 (cl @p_861) :rule trans :premises (t1374.t1.t5.t12 t1374.t1.t5.t13))
(step t1374.t1.t5.t15 (cl @p_859 @p_860 @p_854) :rule la_generic :args (1/1 -1/1 1/1))
(step t1374.t1.t5.t16 (cl (=> @p_857 @p_856)) :rule la_mult_neg)
(step t1374.t1.t5.t17 (cl @p_858 @p_856) :rule implies :premises (t1374.t1.t5.t16))
(step t1374.t1.t5.t18 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1374.t1.t5.t19 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1374.t1.t5.t18))
(step t1374.t1.t5.t20 (cl @p_310) :rule evaluate)
(step t1374.t1.t5.t21 (cl @p_308) :rule resolution :premises (t1374.t1.t5.t19 t1374.t1.t5.t20))
(step t1374.t1.t5.t22 (cl @p_857) :rule and_intro :premises (t1374.t1.t5.t21 t1374.t1.t5.a0))
(step t1374.t1.t5.t23 (cl @p_856) :rule resolution :premises (t1374.t1.t5.t17 t1374.t1.t5.t22))
(step t1374.t1.t5.t24 (cl @p_855) :rule symm :premises (t1374.t1.a0))
(step t1374.t1.t5.t25 (cl @p_854) :rule resolution :premises (t1374.t1.t5.t15 t1374.t1.t5.t23 t1374.t1.t5.t24))
(step t1374.t1.t5.t26 (cl false) :rule resolution :premises (t1374.t1.t5.t0 t1374.t1.t5.t14 t1374.t1.t5.t25))
(step t1374.t1.t5 (cl @p_834 false) :rule subproof :discharge (t1374.t1.t5.a0))
(step t1374.t1.t6 (cl @p_847 false) :rule resolution :premises (t1374.t1.t4 t1374.t1.t5))
(step t1374.t1.t7 (cl @p_847 @p_212) :rule implies_neg2)
(step t1374.t1.t8 (cl @p_847 @p_847) :rule resolution :premises (t1374.t1.t6 t1374.t1.t7))
(step t1374.t1.t9 (cl @p_847) :rule contraction :premises (t1374.t1.t8))
(step t1374.t1.t10 (cl @p_849) :rule implies_simplify)
(step t1374.t1.t11 (cl @p_848 @p_834) :rule equiv1 :premises (t1374.t1.t10))
(step t1374.t1.t12 (cl @p_834) :rule resolution :premises (t1374.t1.t9 t1374.t1.t11))
(step t1374.t1.t13 (cl @p_846) :rule resolution :premises (t1374.t1.t2 t1374.t1.t3 t1374.t1.t12))
(step t1374.t1.t14 (cl @p_834) :rule resolution :premises (t1374.t1.t0 t1374.t1.t1 t1374.t1.t13))
(step t1374.t1 (cl @p_843 @p_834) :rule subproof :discharge (t1374.t1.a0))
(step t1374.t2 (cl @p_845 @p_834) :rule resolution :premises (t1374.t0 t1374.t1))
(step t1374.t3 (cl @p_845 @p_838) :rule implies_neg2)
(step t1374.t4 (cl @p_845 @p_845) :rule resolution :premises (t1374.t2 t1374.t3))
(step t1374.t5 (cl @p_845) :rule contraction :premises (t1374.t4))
(step t1374.t6 (cl @p_843 @p_834) :rule implies :premises (t1374.t5))
(step t1374.t7 (cl @p_842 @p_840) :rule implies_neg1)
(anchor :step t1374.t8)
(assume t1374.t8.a0 @p_106)
(assume t1374.t8.a1 @p_224)
(assume t1374.t8.a2 @p_830)
(step t1374.t8.t0 (cl @p_844) :rule symm :premises (t1374.t8.a2))
(step t1374.t8.t1 (cl (= @p_172 k$)) :rule symm :premises (t261))
(step t1374.t8.t2 (cl @p_839) :rule trans :premises (t1374.t8.t0 t1374.t8.t1 t742))
(step t1374.t8 (cl @p_532 @p_227 @p_831 @p_839) :rule subproof :discharge (t1374.t8.a0 t1374.t8.a1 t1374.t8.a2))
(step t1374.t9 (cl @p_841 @p_106) :rule and_pos :args (0))
(step t1374.t10 (cl @p_841 @p_224) :rule and_pos :args (1))
(step t1374.t11 (cl @p_841 @p_830) :rule and_pos :args (2))
(step t1374.t12 (cl @p_839 @p_841 @p_841 @p_841) :rule resolution :premises (t1374.t8 t1374.t9 t1374.t10 t1374.t11))
(step t1374.t13 (cl @p_841 @p_841 @p_841 @p_839) :rule reordering :premises (t1374.t12))
(step t1374.t14 (cl @p_841 @p_839) :rule contraction :premises (t1374.t13))
(step t1374.t15 (cl @p_842 @p_839) :rule resolution :premises (t1374.t7 t1374.t14))
(step t1374.t16 (cl @p_842 @p_843) :rule implies_neg2)
(step t1374.t17 (cl @p_842 @p_842) :rule resolution :premises (t1374.t15 t1374.t16))
(step t1374.t18 (cl @p_842) :rule contraction :premises (t1374.t17))
(step t1374.t19 (cl @p_841 @p_839) :rule implies :premises (t1374.t18))
(step t1374.t20 (cl @p_840) :rule and_intro :premises (t742 t261 t1374.a1))
(step t1374.t21 (cl @p_839) :rule resolution :premises (t1374.t19 t1374.t20))
(step t1374.t22 (cl @p_834) :rule resolution :premises (t1374.t6 t1374.t21))
(step t1374 (cl @p_227 @p_831 @p_532 @p_834) :rule subproof :discharge (t1374.a0 t1374.a1 t1374.a2))
(step t1375 (cl (! (not @p_835) :named @p_836) @p_224) :rule and_pos :args (0))
(step t1376 (cl @p_836 @p_830) :rule and_pos :args (1))
(step t1377 (cl @p_836 @p_106) :rule and_pos :args (2))
(step t1378 (cl @p_834 @p_836 @p_836 @p_836) :rule resolution :premises (t1374 t1375 t1376 t1377))
(step t1379 (cl @p_836 @p_836 @p_836 @p_834) :rule reordering :premises (t1378))
(step t1380 (cl @p_836 @p_834) :rule contraction :premises (t1379))
(step t1381 (cl @p_837 @p_834) :rule resolution :premises (t1373 t1380))
(step t1382 (cl @p_837 @p_838) :rule implies_neg2)
(step t1383 (cl @p_837 @p_837) :rule resolution :premises (t1381 t1382))
(step t1384 (cl @p_837) :rule contraction :premises (t1383))
(step t1385 (cl @p_836 @p_834) :rule implies :premises (t1384))
(step t1386 (cl @p_227 @p_831 @p_532 @p_834) :rule resolution :premises (t1372 t1385))
(step t1387 (cl @p_583 @p_566 @p_585 @p_831 @p_794 @p_759 @p_812) :rule resolution :premises (t33 t652 t1 t649 t1236 t755 t758 t1237 t742 t755 t758 t688 t1254 t261 t1306 t742 t758 t261 t1308 t1329 t1371 t742 t1386 t742 t261 t1151 t1158 t226 t754 a4))
(step t1388 (cl (not (! (= (! (or @p_117 @p_675 @p_809) :named @p_811) (! (or @p_117 @p_101 @p_809) :named @p_810)) :named @p_829)) (not @p_811) @p_810) :rule equiv_pos2)
(step t1389 (cl (= @p_675 @p_101)) :rule rare_rewrite :args ("bool-double-not-elim" @p_101))
(step t1390 (cl (= @p_809 @p_809)) :rule refl)
(step t1391 (cl @p_829) :rule cong :premises (t1389 t1390))
(step t1392 (cl (! (and @p_116 @p_102) :named @p_813) @p_117 @p_675) :rule and_neg)
(step t1393 (cl (! (=> @p_813 @p_809) :named @p_815) @p_813) :rule implies_neg1)
(anchor :step t1394)
(assume t1394.a0 @p_116)
(assume t1394.a1 @p_102)
(step t1394.t0 (cl (! (=> (! (and @p_116 @p_686) :named @p_816) @p_809) :named @p_821) @p_816) :rule implies_neg1)
(anchor :step t1394.t1)
(assume t1394.t1.a0 @p_116)
(assume t1394.t1.a1 @p_686)
(step t1394.t1.t0 (cl (not (! (> @p_7 0) :named @p_822)) @p_809) :rule la_generic :args (1/1 1/1))
(step t1394.t1.t1 (cl @p_102) :rule not_symm :premises (t1394.t1.a1))
(step t1394.t1.t2 (cl (or @p_101 (! (not (<= @p_7 0)) :named @p_823) (! (not (! (<= 0 @p_7) :named @p_826)) :named @p_828))) :rule la_disequality)
(step t1394.t1.t3 (cl @p_101 @p_823 @p_828) :rule or :premises (t1394.t1.t2))
(step t1394.t1.t4 (cl (! (= @p_116 @p_826) :named @p_827)) :rule comp_simplify)
(step t1394.t1.t5 (cl (not @p_827) @p_117 @p_826) :rule equiv_pos2)
(step t1394.t1.t6 (cl @p_826) :rule resolution :premises (t1394.t1.t4 t1394.t1.t5 t1394.t1.a0))
(step t1394.t1.t7 (cl (! (= @p_822 @p_823) :named @p_825)) :rule comp_simplify)
(step t1394.t1.t8 (cl (not @p_825) @p_822 (! (not @p_823) :named @p_824)) :rule equiv_pos1)
(step t1394.t1.t9 (cl @p_822 @p_824) :rule resolution :premises (t1394.t1.t7 t1394.t1.t8))
(step t1394.t1.t10 (cl @p_822) :rule resolution :premises (t1394.t1.t1 t1394.t1.t3 t1394.t1.t6 t1394.t1.t9))
(step t1394.t1.t11 (cl @p_809) :rule resolution :premises (t1394.t1.t0 t1394.t1.t10))
(step t1394.t1 (cl @p_117 (! (not @p_686) :named @p_818) @p_809) :rule subproof :discharge (t1394.t1.a0 t1394.t1.a1))
(step t1394.t2 (cl (! (not @p_816) :named @p_820) @p_116) :rule and_pos :args (0))
(step t1394.t3 (cl @p_820 @p_686) :rule and_pos :args (1))
(step t1394.t4 (cl @p_809 @p_820 @p_820) :rule resolution :premises (t1394.t1 t1394.t2 t1394.t3))
(step t1394.t5 (cl @p_820 @p_820 @p_809) :rule reordering :premises (t1394.t4))
(step t1394.t6 (cl @p_820 @p_809) :rule contraction :premises (t1394.t5))
(step t1394.t7 (cl @p_821 @p_809) :rule resolution :premises (t1394.t0 t1394.t6))
(step t1394.t8 (cl @p_821 @p_812) :rule implies_neg2)
(step t1394.t9 (cl @p_821 @p_821) :rule resolution :premises (t1394.t7 t1394.t8))
(step t1394.t10 (cl @p_821) :rule contraction :premises (t1394.t9))
(step t1394.t11 (cl @p_820 @p_809) :rule implies :premises (t1394.t10))
(step t1394.t12 (cl (! (=> @p_102 @p_686) :named @p_817) @p_102) :rule implies_neg1)
(anchor :step t1394.t13)
(assume t1394.t13.a0 @p_102)
(step t1394.t13.t0 (cl @p_686) :rule not_symm :premises (t1394.t13.a0))
(step t1394.t13 (cl @p_675 @p_686) :rule subproof :discharge (t1394.t13.a0))
(step t1394.t14 (cl @p_817 @p_686) :rule resolution :premises (t1394.t12 t1394.t13))
(step t1394.t15 (cl @p_817 @p_818) :rule implies_neg2)
(step t1394.t16 (cl @p_817 @p_817) :rule resolution :premises (t1394.t14 t1394.t15))
(step t1394.t17 (cl @p_817) :rule contraction :premises (t1394.t16))
(step t1394.t18 (cl @p_675 @p_686) :rule implies :premises (t1394.t17))
(step t1394.t19 (cl @p_686) :rule resolution :premises (t1394.t18 t1394.a1))
(step t1394.t20 (cl @p_816) :rule and_intro :premises (t1394.a0 t1394.t19))
(step t1394.t21 (cl @p_809) :rule resolution :premises (t1394.t11 t1394.t20))
(step t1394 (cl @p_117 @p_675 @p_809) :rule subproof :discharge (t1394.a0 t1394.a1))
(step t1395 (cl (! (not @p_813) :named @p_814) @p_116) :rule and_pos :args (0))
(step t1396 (cl @p_814 @p_102) :rule and_pos :args (1))
(step t1397 (cl @p_809 @p_814 @p_814) :rule resolution :premises (t1394 t1395 t1396))
(step t1398 (cl @p_814 @p_814 @p_809) :rule reordering :premises (t1397))
(step t1399 (cl @p_814 @p_809) :rule contraction :premises (t1398))
(step t1400 (cl @p_815 @p_809) :rule resolution :premises (t1393 t1399))
(step t1401 (cl @p_815 @p_812) :rule implies_neg2)
(step t1402 (cl @p_815 @p_815) :rule resolution :premises (t1400 t1401))
(step t1403 (cl @p_815) :rule contraction :premises (t1402))
(step t1404 (cl @p_814 @p_809) :rule implies :premises (t1403))
(step t1405 (cl @p_117 @p_675 @p_809) :rule resolution :premises (t1392 t1404))
(step t1406 (cl @p_811 (not @p_117)) :rule or_neg :args (0))
(step t1407 (cl @p_811 (! (not @p_675) :named @p_768)) :rule or_neg :args (1))
(step t1408 (cl @p_811 @p_812) :rule or_neg :args (2))
(step t1409 (cl @p_811 @p_811 @p_811) :rule resolution :premises (t1405 t1406 t1407 t1408))
(step t1410 (cl @p_811) :rule contraction :premises (t1409))
(step t1411 (cl @p_810) :rule resolution :premises (t1388 t1391 t1410))
(step t1412 (cl @p_117 @p_101 @p_809) :rule or :premises (t1411))
(step t1413 (cl (not (! (= (! (or (! (not (! (= @p_7 (! (divide$ @p_668 2) :named @p_751)) :named @p_752)) :named @p_758) @p_675 @p_760 (! (not (! (= (! (times$ 2 0) :named @p_69) 0) :named @p_90)) :named @p_761) (! (not (! (= (! (divide$ @p_69 2) :named @p_70) 0) :named @p_71)) :named @p_762)) :named @p_764) (! (or @p_758 @p_101 @p_760 @p_761 @p_762) :named @p_763)) :named @p_784)) (not @p_764) @p_763) :rule equiv_pos2)
(step t1414 (cl (= @p_760 @p_760)) :rule refl)
(step t1415 (cl (= @p_761 @p_761)) :rule refl)
(step t1416 (cl (= @p_762 @p_762)) :rule refl)
(step t1417 (cl @p_784) :rule cong :premises (t1389 t1414 t1415 t1416))
(step t1418 (cl (! (=> (! (and @p_752 @p_102 @p_759 @p_90 @p_71) :named @p_769) (! (and @p_680 @p_102) :named @p_771)) :named @p_777) @p_769) :rule implies_neg1)
(anchor :step t1419)
(assume t1419.a0 @p_752)
(assume t1419.a1 @p_102)
(assume t1419.a2 @p_759)
(assume t1419.a3 @p_90)
(assume t1419.a4 @p_71)
(step t1419.t0 (cl (! (=> (! (and @p_71 @p_90 @p_759 @p_752) :named @p_778) @p_680) :named @p_781) @p_778) :rule implies_neg1)
(anchor :step t1419.t1)
(assume t1419.t1.a0 @p_71)
(assume t1419.t1.a1 @p_90)
(assume t1419.t1.a2 @p_759)
(assume t1419.t1.a3 @p_752)
(step t1419.t1.t0 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (! (or @p_85 (! (= 0 @p_70) :named @p_84)) :named @p_86)) :named @p_87) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) @p_71) :named @p_83)) :named @p_88)) (not @p_87) @p_83) :rule equiv_pos2)
(step t1419.t1.t1 (cl (= (* 1 (- 0 @p_70)) (* -1 (- @p_70 0)))) :rule poly_simp)
(step t1419.t1.t2 (cl (= @p_84 @p_71)) :rule poly_simp_rel :premises (t1419.t1.t1))
(step t1419.t1.t3 (cl (= @p_86 (! (or false @p_71) :named @p_89))) :rule cong :premises (t1015 t1419.t1.t2))
(step t1419.t1.t4 (cl (= @p_89 @p_71)) :rule aci_simp)
(step t1419.t1.t5 (cl (= @p_86 @p_71)) :rule trans :premises (t1419.t1.t3 t1419.t1.t4))
(step t1419.t1.t6 (cl @p_88) :rule cong :premises (t1419.t1.t5))
(step t1419.t1.t7 (cl @p_87 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1419.t1.t8)
(assume t1419.t1.t8.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1419.t1.t8.t0 (cl (or @p_82 @p_86)) :rule forall_inst :args (2 0))
(step t1419.t1.t8.t1 (cl @p_82 @p_86) :rule or :premises (t1419.t1.t8.t0))
(step t1419.t1.t8.t2 (cl @p_86) :rule resolution :premises (t1419.t1.t8.t1 t186))
(step t1419.t1.t8 (cl @p_82 @p_86) :rule subproof :discharge (t1419.t1.t8.a0))
(step t1419.t1.t9 (cl @p_87 @p_86) :rule resolution :premises (t1419.t1.t7 t1419.t1.t8))
(step t1419.t1.t10 (cl @p_87 (not @p_86)) :rule implies_neg2)
(step t1419.t1.t11 (cl @p_87 @p_87) :rule resolution :premises (t1419.t1.t9 t1419.t1.t10))
(step t1419.t1.t12 (cl @p_87) :rule contraction :premises (t1419.t1.t11))
(step t1419.t1.t13 (cl @p_83) :rule resolution :premises (t1419.t1.t0 t1419.t1.t6 t1419.t1.t12))
(step t1419.t1.t14 (cl @p_82 @p_71) :rule implies :premises (t1419.t1.t13))
(step t1419.t1.t15 (cl @p_71) :rule resolution :premises (t1419.t1.t14 t186))
(step t1419.t1.t16 (cl @p_84) :rule symm :premises (t1419.t1.t15))
(step t1419.t1.t17 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) (! (= (! (= 0 @p_69) :named @p_95) (! (or @p_56 (! (= 2 1) :named @p_93)) :named @p_94)) :named @p_96)) :named @p_97) (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) @p_90) :named @p_92)) :named @p_98)) (not @p_97) @p_92) :rule equiv_pos2)
(step t1419.t1.t18 (cl (= (* 1 (- 0 @p_69)) (* -1 (- @p_69 0)))) :rule poly_simp)
(step t1419.t1.t19 (cl (= @p_95 @p_90)) :rule poly_simp_rel :premises (t1419.t1.t18))
(step t1419.t1.t20 (cl (= @p_93 false)) :rule evaluate)
(step t1419.t1.t21 (cl (= @p_94 (! (or true false) :named @p_100))) :rule cong :premises (t192 t1419.t1.t20))
(step t1419.t1.t22 (cl (= @p_100 true)) :rule evaluate)
(step t1419.t1.t23 (cl (= @p_94 true)) :rule trans :premises (t1419.t1.t21 t1419.t1.t22))
(step t1419.t1.t24 (cl (= @p_96 (! (= @p_90 true) :named @p_99))) :rule cong :premises (t1419.t1.t19 t1419.t1.t23))
(step t1419.t1.t25 (cl (= @p_99 @p_90)) :rule rare_rewrite :args ("bool-eq-true" @p_90))
(step t1419.t1.t26 (cl (= @p_96 @p_90)) :rule trans :premises (t1419.t1.t24 t1419.t1.t25))
(step t1419.t1.t27 (cl @p_98) :rule cong :premises (t1419.t1.t26))
(step t1419.t1.t28 (cl @p_97 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t1419.t1.t29)
(assume t1419.t1.t29.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t1419.t1.t29.t0 (cl (or @p_91 @p_96)) :rule forall_inst :args (0 2))
(step t1419.t1.t29.t1 (cl @p_91 @p_96) :rule or :premises (t1419.t1.t29.t0))
(step t1419.t1.t29.t2 (cl @p_96) :rule resolution :premises (t1419.t1.t29.t1 t1419.t1.t29.a0))
(step t1419.t1.t29 (cl @p_91 @p_96) :rule subproof :discharge (t1419.t1.t29.a0))
(step t1419.t1.t30 (cl @p_97 @p_96) :rule resolution :premises (t1419.t1.t28 t1419.t1.t29))
(step t1419.t1.t31 (cl @p_97 (not @p_96)) :rule implies_neg2)
(step t1419.t1.t32 (cl @p_97 @p_97) :rule resolution :premises (t1419.t1.t30 t1419.t1.t31))
(step t1419.t1.t33 (cl @p_97) :rule contraction :premises (t1419.t1.t32))
(step t1419.t1.t34 (cl @p_92) :rule resolution :premises (t1419.t1.t17 t1419.t1.t27 t1419.t1.t33))
(step t1419.t1.t35 (cl @p_91 @p_90) :rule implies :premises (t1419.t1.t34))
(step t1419.t1.t36 (cl @p_90) :rule resolution :premises (t1419.t1.t35 a8))
(step t1419.t1.t37 (cl (= @p_70 (! (divide$ 0 2) :named @p_782))) :rule cong :premises (t1419.t1.t36 t358))
(step t1419.t1.t38 (cl (! (= 0 @p_668) :named @p_783)) :rule symm :premises (t1419.t1.a2))
(step t1419.t1.t39 (cl (= @p_782 @p_751)) :rule cong :premises (t1419.t1.t38 t358))
(step t1419.t1.t40 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (! (or @p_85 @p_752) :named @p_754)) :named @p_755) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) @p_752) :named @p_753)) :named @p_756)) (not @p_755) @p_753) :rule equiv_pos2)
(step t1419.t1.t41 (cl (= @p_752 @p_752)) :rule refl)
(step t1419.t1.t42 (cl (= @p_754 (! (or false @p_752) :named @p_757))) :rule cong :premises (t1015 t1419.t1.t41))
(step t1419.t1.t43 (cl (= @p_757 @p_752)) :rule aci_simp)
(step t1419.t1.t44 (cl (= @p_754 @p_752)) :rule trans :premises (t1419.t1.t42 t1419.t1.t43))
(step t1419.t1.t45 (cl @p_756) :rule cong :premises (t1419.t1.t44))
(step t1419.t1.t46 (cl @p_755 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1419.t1.t47)
(assume t1419.t1.t47.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1419.t1.t47.t0 (cl (or @p_82 @p_754)) :rule forall_inst :args (2 @p_7))
(step t1419.t1.t47.t1 (cl @p_82 @p_754) :rule or :premises (t1419.t1.t47.t0))
(step t1419.t1.t47.t2 (cl @p_754) :rule resolution :premises (t1419.t1.t47.t1 t186))
(step t1419.t1.t47 (cl @p_82 @p_754) :rule subproof :discharge (t1419.t1.t47.a0))
(step t1419.t1.t48 (cl @p_755 @p_754) :rule resolution :premises (t1419.t1.t46 t1419.t1.t47))
(step t1419.t1.t49 (cl @p_755 (not @p_754)) :rule implies_neg2)
(step t1419.t1.t50 (cl @p_755 @p_755) :rule resolution :premises (t1419.t1.t48 t1419.t1.t49))
(step t1419.t1.t51 (cl @p_755) :rule contraction :premises (t1419.t1.t50))
(step t1419.t1.t52 (cl @p_753) :rule resolution :premises (t1419.t1.t40 t1419.t1.t45 t1419.t1.t51))
(step t1419.t1.t53 (cl @p_82 @p_752) :rule implies :premises (t1419.t1.t52))
(step t1419.t1.t54 (cl @p_752) :rule resolution :premises (t1419.t1.t53 t186))
(step t1419.t1.t55 (cl (= @p_751 @p_7)) :rule symm :premises (t1419.t1.t54))
(step t1419.t1.t56 (cl @p_680) :rule trans :premises (t1419.t1.t16 t1419.t1.t37 t1419.t1.t39 t1419.t1.t55))
(step t1419.t1 (cl @p_762 @p_761 @p_760 @p_758 @p_680) :rule subproof :discharge (t1419.t1.a0 t1419.t1.a1 t1419.t1.a2 t1419.t1.a3))
(step t1419.t2 (cl (! (not @p_778) :named @p_780) @p_71) :rule and_pos :args (0))
(step t1419.t3 (cl @p_780 @p_90) :rule and_pos :args (1))
(step t1419.t4 (cl @p_780 @p_759) :rule and_pos :args (2))
(step t1419.t5 (cl @p_780 @p_752) :rule and_pos :args (3))
(step t1419.t6 (cl @p_680 @p_780 @p_780 @p_780 @p_780) :rule resolution :premises (t1419.t1 t1419.t2 t1419.t3 t1419.t4 t1419.t5))
(step t1419.t7 (cl @p_780 @p_780 @p_780 @p_780 @p_680) :rule reordering :premises (t1419.t6))
(step t1419.t8 (cl @p_780 @p_680) :rule contraction :premises (t1419.t7))
(step t1419.t9 (cl @p_781 @p_680) :rule resolution :premises (t1419.t0 t1419.t8))
(step t1419.t10 (cl @p_781 @p_686) :rule implies_neg2)
(step t1419.t11 (cl @p_781 @p_781) :rule resolution :premises (t1419.t9 t1419.t10))
(step t1419.t12 (cl @p_781) :rule contraction :premises (t1419.t11))
(step t1419.t13 (cl @p_780 @p_680) :rule implies :premises (t1419.t12))
(step t1419.t14 (cl (not @p_88) (not @p_87) @p_83) :rule equiv_pos2)
(step t1419.t15 (cl (= (* 1 (- 0 @p_70)) (* -1 (- @p_70 0)))) :rule poly_simp)
(step t1419.t16 (cl (= @p_84 @p_71)) :rule poly_simp_rel :premises (t1419.t15))
(step t1419.t17 (cl (= @p_86 @p_89)) :rule cong :premises (t1015 t1419.t16))
(step t1419.t18 (cl (= @p_89 @p_71)) :rule aci_simp)
(step t1419.t19 (cl (= @p_86 @p_71)) :rule trans :premises (t1419.t17 t1419.t18))
(step t1419.t20 (cl @p_88) :rule cong :premises (t1419.t19))
(step t1419.t21 (cl @p_87 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1419.t22)
(assume t1419.t22.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1419.t22.t0 (cl (or @p_82 @p_86)) :rule forall_inst :args (2 0))
(step t1419.t22.t1 (cl @p_82 @p_86) :rule or :premises (t1419.t22.t0))
(step t1419.t22.t2 (cl @p_86) :rule resolution :premises (t1419.t22.t1 t186))
(step t1419.t22 (cl @p_82 @p_86) :rule subproof :discharge (t1419.t22.a0))
(step t1419.t23 (cl @p_87 @p_86) :rule resolution :premises (t1419.t21 t1419.t22))
(step t1419.t24 (cl @p_87 (not @p_86)) :rule implies_neg2)
(step t1419.t25 (cl @p_87 @p_87) :rule resolution :premises (t1419.t23 t1419.t24))
(step t1419.t26 (cl @p_87) :rule contraction :premises (t1419.t25))
(step t1419.t27 (cl @p_83) :rule resolution :premises (t1419.t14 t1419.t20 t1419.t26))
(step t1419.t28 (cl @p_82 @p_71) :rule implies :premises (t1419.t27))
(step t1419.t29 (cl @p_71) :rule resolution :premises (t1419.t28 t186))
(step t1419.t30 (cl (not @p_98) (not @p_97) @p_92) :rule equiv_pos2)
(step t1419.t31 (cl (= (* 1 (- 0 @p_69)) (* -1 (- @p_69 0)))) :rule poly_simp)
(step t1419.t32 (cl (= @p_95 @p_90)) :rule poly_simp_rel :premises (t1419.t31))
(step t1419.t33 (cl (= @p_93 false)) :rule evaluate)
(step t1419.t34 (cl (= @p_94 @p_100)) :rule cong :premises (t192 t1419.t33))
(step t1419.t35 (cl (= @p_100 true)) :rule evaluate)
(step t1419.t36 (cl (= @p_94 true)) :rule trans :premises (t1419.t34 t1419.t35))
(step t1419.t37 (cl (= @p_96 @p_99)) :rule cong :premises (t1419.t32 t1419.t36))
(step t1419.t38 (cl (= @p_99 @p_90)) :rule rare_rewrite :args ("bool-eq-true" @p_90))
(step t1419.t39 (cl (= @p_96 @p_90)) :rule trans :premises (t1419.t37 t1419.t38))
(step t1419.t40 (cl @p_98) :rule cong :premises (t1419.t39))
(step t1419.t41 (cl @p_97 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t1419.t42)
(assume t1419.t42.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t1419.t42.t0 (cl (or @p_91 @p_96)) :rule forall_inst :args (0 2))
(step t1419.t42.t1 (cl @p_91 @p_96) :rule or :premises (t1419.t42.t0))
(step t1419.t42.t2 (cl @p_96) :rule resolution :premises (t1419.t42.t1 t1419.t42.a0))
(step t1419.t42 (cl @p_91 @p_96) :rule subproof :discharge (t1419.t42.a0))
(step t1419.t43 (cl @p_97 @p_96) :rule resolution :premises (t1419.t41 t1419.t42))
(step t1419.t44 (cl @p_97 (not @p_96)) :rule implies_neg2)
(step t1419.t45 (cl @p_97 @p_97) :rule resolution :premises (t1419.t43 t1419.t44))
(step t1419.t46 (cl @p_97) :rule contraction :premises (t1419.t45))
(step t1419.t47 (cl @p_92) :rule resolution :premises (t1419.t30 t1419.t40 t1419.t46))
(step t1419.t48 (cl @p_91 @p_90) :rule implies :premises (t1419.t47))
(step t1419.t49 (cl @p_90) :rule resolution :premises (t1419.t48 a8))
(step t1419.t50 (cl (not @p_756) (not @p_755) @p_753) :rule equiv_pos2)
(step t1419.t51 (cl (= @p_752 @p_752)) :rule refl)
(step t1419.t52 (cl (= @p_754 @p_757)) :rule cong :premises (t1015 t1419.t51))
(step t1419.t53 (cl (= @p_757 @p_752)) :rule aci_simp)
(step t1419.t54 (cl (= @p_754 @p_752)) :rule trans :premises (t1419.t52 t1419.t53))
(step t1419.t55 (cl @p_756) :rule cong :premises (t1419.t54))
(step t1419.t56 (cl @p_755 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1419.t57)
(assume t1419.t57.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1419.t57.t0 (cl (or @p_82 @p_754)) :rule forall_inst :args (2 @p_7))
(step t1419.t57.t1 (cl @p_82 @p_754) :rule or :premises (t1419.t57.t0))
(step t1419.t57.t2 (cl @p_754) :rule resolution :premises (t1419.t57.t1 t186))
(step t1419.t57 (cl @p_82 @p_754) :rule subproof :discharge (t1419.t57.a0))
(step t1419.t58 (cl @p_755 @p_754) :rule resolution :premises (t1419.t56 t1419.t57))
(step t1419.t59 (cl @p_755 (not @p_754)) :rule implies_neg2)
(step t1419.t60 (cl @p_755 @p_755) :rule resolution :premises (t1419.t58 t1419.t59))
(step t1419.t61 (cl @p_755) :rule contraction :premises (t1419.t60))
(step t1419.t62 (cl @p_753) :rule resolution :premises (t1419.t50 t1419.t55 t1419.t61))
(step t1419.t63 (cl @p_82 @p_752) :rule implies :premises (t1419.t62))
(step t1419.t64 (cl @p_752) :rule resolution :premises (t1419.t63 t186))
(step t1419.t65 (cl @p_778) :rule and_intro :premises (t1419.t29 t1419.t49 t1419.a2 t1419.t64))
(step t1419.t66 (cl @p_680) :rule resolution :premises (t1419.t13 t1419.t65))
(step t1419.t67 (cl @p_771) :rule and_intro :premises (t1419.t66 t1419.a1))
(step t1419 (cl @p_758 @p_675 @p_760 @p_761 @p_762 @p_771) :rule subproof :discharge (t1419.a0 t1419.a1 t1419.a2 t1419.a3 t1419.a4))
(step t1420 (cl (! (not @p_769) :named @p_770) @p_752) :rule and_pos :args (0))
(step t1421 (cl @p_770 @p_102) :rule and_pos :args (1))
(step t1422 (cl @p_770 @p_759) :rule and_pos :args (2))
(step t1423 (cl @p_770 @p_90) :rule and_pos :args (3))
(step t1424 (cl @p_770 @p_71) :rule and_pos :args (4))
(step t1425 (cl @p_771 @p_770 @p_770 @p_770 @p_770 @p_770) :rule resolution :premises (t1419 t1420 t1421 t1422 t1423 t1424))
(step t1426 (cl @p_770 @p_770 @p_770 @p_770 @p_770 @p_771) :rule reordering :premises (t1425))
(step t1427 (cl @p_770 @p_771) :rule contraction :premises (t1426))
(step t1428 (cl @p_777 @p_771) :rule resolution :premises (t1418 t1427))
(step t1429 (cl @p_777 (! (not @p_771) :named @p_772)) :rule implies_neg2)
(step t1430 (cl @p_777 @p_777) :rule resolution :premises (t1428 t1429))
(step t1431 (cl @p_777) :rule contraction :premises (t1430))
(step t1432 (cl @p_770 @p_771) :rule implies :premises (t1431))
(step t1433 (cl (! (=> @p_771 false) :named @p_773) @p_771) :rule implies_neg1)
(anchor :step t1434)
(assume t1434.a0 @p_680)
(assume t1434.a1 @p_102)
(step t1434.t0 (cl @p_503 @p_504 false) :rule equiv_pos2)
(step t1434.t1 (cl @p_502) :rule evaluate)
(step t1434.t2 (cl (= (! (= @p_101 false) :named @p_775) @p_102)) :rule equiv_simplify)
(step t1434.t3 (cl @p_775 @p_675) :rule equiv2 :premises (t1434.t2))
(step t1434.t4 (cl @p_768 @p_101) :rule not_not)
(step t1434.t5 (cl @p_775 @p_101) :rule resolution :premises (t1434.t3 t1434.t4))
(step t1434.t6 (cl @p_775) :rule resolution :premises (t1434.t5 t1434.a1))
(step t1434.t7 (cl (= false @p_101)) :rule symm :premises (t1434.t6))
(step t1434.t8 (cl (= (! (= @p_101 true) :named @p_774) @p_101)) :rule equiv_simplify)
(step t1434.t9 (cl @p_774 @p_102) :rule equiv2 :premises (t1434.t8))
(step t1434.t10 (cl @p_101) :rule symm :premises (t1434.a0))
(step t1434.t11 (cl @p_774) :rule resolution :premises (t1434.t9 t1434.t10))
(step t1434.t12 (cl @p_499) :rule trans :premises (t1434.t7 t1434.t11))
(step t1434.t13 (cl false) :rule resolution :premises (t1434.t0 t1434.t1 t1434.t12))
(step t1434 (cl @p_686 @p_675 false) :rule subproof :discharge (t1434.a0 t1434.a1))
(step t1435 (cl @p_772 @p_680) :rule and_pos :args (0))
(step t1436 (cl @p_772 @p_102) :rule and_pos :args (1))
(step t1437 (cl false @p_772 @p_772) :rule resolution :premises (t1434 t1435 t1436))
(step t1438 (cl @p_772 @p_772 false) :rule reordering :premises (t1437))
(step t1439 (cl @p_772 false) :rule contraction :premises (t1438))
(step t1440 (cl @p_773 false) :rule resolution :premises (t1433 t1439))
(step t1441 (cl @p_773 @p_212) :rule implies_neg2)
(step t1442 (cl @p_773 @p_773) :rule resolution :premises (t1440 t1441))
(step t1443 (cl @p_773) :rule contraction :premises (t1442))
(step t1444 (cl (= @p_773 @p_772)) :rule implies_simplify)
(step t1445 (cl (not @p_773) @p_772) :rule equiv1 :premises (t1444))
(step t1446 (cl @p_772) :rule resolution :premises (t1443 t1445))
(step t1447 (cl @p_770) :rule resolution :premises (t1432 t1446))
(step t1448 (cl @p_758 @p_675 @p_760 @p_761 @p_762) :rule not_and :premises (t1447))
(step t1449 (cl @p_764 (not @p_758)) :rule or_neg :args (0))
(step t1450 (cl @p_764 @p_768) :rule or_neg :args (1))
(step t1451 (cl @p_764 @p_767) :rule or_neg :args (2))
(step t1452 (cl @p_764 (! (not @p_761) :named @p_766)) :rule or_neg :args (3))
(step t1453 (cl @p_764 (! (not @p_762) :named @p_765)) :rule or_neg :args (4))
(step t1454 (cl @p_764 @p_764 @p_764 @p_764 @p_764) :rule resolution :premises (t1448 t1449 t1450 t1451 t1452 t1453))
(step t1455 (cl @p_764) :rule contraction :premises (t1454))
(step t1456 (cl @p_763) :rule resolution :premises (t1413 t1417 t1455))
(step t1457 (cl @p_758 @p_101 @p_760 @p_761 @p_762) :rule or :premises (t1456))
(step t1458 (cl @p_101 @p_758 @p_760 @p_761 @p_762) :rule reordering :premises (t1457))
(step t1459 (cl (not @p_88) (not @p_87) @p_83) :rule equiv_pos2)
(step t1460 (cl (= (* 1 (- 0 @p_70)) (* -1 (- @p_70 0)))) :rule poly_simp)
(step t1461 (cl (= @p_84 @p_71)) :rule poly_simp_rel :premises (t1460))
(step t1462 (cl (= @p_86 @p_89)) :rule cong :premises (t1015 t1461))
(step t1463 (cl (= @p_89 @p_71)) :rule aci_simp)
(step t1464 (cl (= @p_86 @p_71)) :rule trans :premises (t1462 t1463))
(step t1465 (cl @p_88) :rule cong :premises (t1464))
(step t1466 (cl @p_87 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1467)
(assume t1467.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1467.t0 (cl (or @p_82 @p_86)) :rule forall_inst :args (2 0))
(step t1467.t1 (cl @p_82 @p_86) :rule or :premises (t1467.t0))
(step t1467.t2 (cl @p_86) :rule resolution :premises (t1467.t1 t186))
(step t1467 (cl @p_82 @p_86) :rule subproof :discharge (t1467.a0))
(step t1468 (cl @p_87 @p_86) :rule resolution :premises (t1466 t1467))
(step t1469 (cl @p_87 (not @p_86)) :rule implies_neg2)
(step t1470 (cl @p_87 @p_87) :rule resolution :premises (t1468 t1469))
(step t1471 (cl @p_87) :rule contraction :premises (t1470))
(step t1472 (cl @p_83) :rule resolution :premises (t1459 t1465 t1471))
(step t1473 (cl @p_82 @p_71) :rule implies :premises (t1472))
(step t1474 (cl @p_71) :rule resolution :premises (t1473 t186))
(step t1475 (cl (not @p_98) (not @p_97) @p_92) :rule equiv_pos2)
(step t1476 (cl (= (* 1 (- 0 @p_69)) (* -1 (- @p_69 0)))) :rule poly_simp)
(step t1477 (cl (= @p_95 @p_90)) :rule poly_simp_rel :premises (t1476))
(step t1478 (cl (= @p_93 false)) :rule evaluate)
(step t1479 (cl (= @p_94 @p_100)) :rule cong :premises (t192 t1478))
(step t1480 (cl (= @p_100 true)) :rule evaluate)
(step t1481 (cl (= @p_94 true)) :rule trans :premises (t1479 t1480))
(step t1482 (cl (= @p_96 @p_99)) :rule cong :premises (t1477 t1481))
(step t1483 (cl (= @p_99 @p_90)) :rule rare_rewrite :args ("bool-eq-true" @p_90))
(step t1484 (cl (= @p_96 @p_90)) :rule trans :premises (t1482 t1483))
(step t1485 (cl @p_98) :rule cong :premises (t1484))
(step t1486 (cl @p_97 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t1487)
(assume t1487.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t1487.t0 (cl (or @p_91 @p_96)) :rule forall_inst :args (0 2))
(step t1487.t1 (cl @p_91 @p_96) :rule or :premises (t1487.t0))
(step t1487.t2 (cl @p_96) :rule resolution :premises (t1487.t1 t1487.a0))
(step t1487 (cl @p_91 @p_96) :rule subproof :discharge (t1487.a0))
(step t1488 (cl @p_97 @p_96) :rule resolution :premises (t1486 t1487))
(step t1489 (cl @p_97 (not @p_96)) :rule implies_neg2)
(step t1490 (cl @p_97 @p_97) :rule resolution :premises (t1488 t1489))
(step t1491 (cl @p_97) :rule contraction :premises (t1490))
(step t1492 (cl @p_92) :rule resolution :premises (t1475 t1485 t1491))
(step t1493 (cl @p_91 @p_90) :rule implies :premises (t1492))
(step t1494 (cl @p_90) :rule resolution :premises (t1493 a8))
(step t1495 (cl (not @p_756) (not @p_755) @p_753) :rule equiv_pos2)
(step t1496 (cl (= @p_752 @p_752)) :rule refl)
(step t1497 (cl (= @p_754 @p_757)) :rule cong :premises (t1015 t1496))
(step t1498 (cl (= @p_757 @p_752)) :rule aci_simp)
(step t1499 (cl (= @p_754 @p_752)) :rule trans :premises (t1497 t1498))
(step t1500 (cl @p_756) :rule cong :premises (t1499))
(step t1501 (cl @p_755 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1502)
(assume t1502.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1502.t0 (cl (or @p_82 @p_754)) :rule forall_inst :args (2 @p_7))
(step t1502.t1 (cl @p_82 @p_754) :rule or :premises (t1502.t0))
(step t1502.t2 (cl @p_754) :rule resolution :premises (t1502.t1 t186))
(step t1502 (cl @p_82 @p_754) :rule subproof :discharge (t1502.a0))
(step t1503 (cl @p_755 @p_754) :rule resolution :premises (t1501 t1502))
(step t1504 (cl @p_755 (not @p_754)) :rule implies_neg2)
(step t1505 (cl @p_755 @p_755) :rule resolution :premises (t1503 t1504))
(step t1506 (cl @p_755) :rule contraction :premises (t1505))
(step t1507 (cl @p_753) :rule resolution :premises (t1495 t1500 t1506))
(step t1508 (cl @p_82 @p_752) :rule implies :premises (t1507))
(step t1509 (cl @p_752) :rule resolution :premises (t1508 t186))
(step t1510 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) (! (or @p_101 @p_746) :named @p_747)) :named @p_748) (! (=> (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))) @p_744) :named @p_745)) :named @p_749)) (not @p_748) @p_745) :rule equiv_pos2)
(step t1511 (cl (= (* -2 (- 2 @p_742)) (* 2 (- @p_742 2)))) :rule poly_simp)
(step t1512 (cl (= @p_746 @p_743)) :rule poly_simp_rel :premises (t1511))
(step t1513 (cl (= @p_747 @p_744)) :rule cong :premises (t1512))
(step t1514 (cl @p_749) :rule cong :premises (t1513))
(step t1515 (cl @p_748 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1516)
(assume t1516.a0 (forall ((?v0 Int) (?v1 Int)) (or (= ?v0 0) (= ?v1 (divide$ (times$ ?v0 ?v1) ?v0)))))
(step t1516.t0 (cl (or @p_82 @p_747)) :rule forall_inst :args (@p_7 2))
(step t1516.t1 (cl @p_82 @p_747) :rule or :premises (t1516.t0))
(step t1516.t2 (cl @p_747) :rule resolution :premises (t1516.t1 t186))
(step t1516 (cl @p_82 @p_747) :rule subproof :discharge (t1516.a0))
(step t1517 (cl @p_748 @p_747) :rule resolution :premises (t1515 t1516))
(step t1518 (cl @p_748 (not @p_747)) :rule implies_neg2)
(step t1519 (cl @p_748 @p_748) :rule resolution :premises (t1517 t1518))
(step t1520 (cl @p_748) :rule contraction :premises (t1519))
(step t1521 (cl @p_745) :rule resolution :premises (t1510 t1514 t1520))
(step t1522 (cl @p_82 @p_744) :rule implies :premises (t1521))
(step t1523 (cl @p_744) :rule resolution :premises (t1522 t186))
(step t1524 (cl (! (not (! (= @p_732 @p_101) :named @p_733)) :named @p_741) @p_740 @p_101) :rule equiv_pos2)
(step t1525 (cl @p_101 @p_740 @p_741) :rule reordering :premises (t1524))
(step t1526 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) (! (= @p_732 (! (or @p_101 @p_93) :named @p_735)) :named @p_736)) :named @p_737) (! (=> (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))) @p_733) :named @p_734)) :named @p_738)) (not @p_737) @p_734) :rule equiv_pos2)
(step t1527 (cl (= @p_735 (! (or @p_101 false) :named @p_739))) :rule cong :premises (t1478))
(step t1528 (cl (= @p_739 @p_101)) :rule aci_simp)
(step t1529 (cl (= @p_735 @p_101)) :rule trans :premises (t1527 t1528))
(step t1530 (cl (= @p_736 @p_733)) :rule cong :premises (t1529))
(step t1531 (cl @p_738) :rule cong :premises (t1530))
(step t1532 (cl @p_737 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1))))) :rule implies_neg1)
(anchor :step t1533)
(assume t1533.a0 (forall ((?v0 Int) (?v1 Int)) (= (= ?v0 (times$ ?v1 ?v0)) (or (= ?v0 0) (= ?v1 1)))))
(step t1533.t0 (cl (or @p_91 @p_736)) :rule forall_inst :args (@p_7 2))
(step t1533.t1 (cl @p_91 @p_736) :rule or :premises (t1533.t0))
(step t1533.t2 (cl @p_736) :rule resolution :premises (t1533.t1 t1533.a0))
(step t1533 (cl @p_91 @p_736) :rule subproof :discharge (t1533.a0))
(step t1534 (cl @p_737 @p_736) :rule resolution :premises (t1532 t1533))
(step t1535 (cl @p_737 (not @p_736)) :rule implies_neg2)
(step t1536 (cl @p_737 @p_737) :rule resolution :premises (t1534 t1535))
(step t1537 (cl @p_737) :rule contraction :premises (t1536))
(step t1538 (cl @p_734) :rule resolution :premises (t1526 t1531 t1537))
(step t1539 (cl @p_91 @p_733) :rule implies :premises (t1538))
(step t1540 (cl @p_733) :rule resolution :premises (t1539 a8))
(step t1541 (cl (not (! (= (! (or @p_583 @p_566 @p_671 @p_673 @p_102) :named @p_674) (! (or @p_583 @p_566 @p_671 @p_112 @p_102) :named @p_672)) :named @p_731)) (not @p_674) @p_672) :rule equiv_pos2)
(step t1542 (cl @p_731) :rule cong :premises (t38 t39))
(step t1543 (cl (! (=> (! (and @p_524 @p_564 @p_670 @p_113 @p_101) :named @p_678) (! (and @p_670 @p_113 @p_564 (! (= k$ @p_669) :named @p_681) @p_680) :named @p_682)) :named @p_726) @p_678) :rule implies_neg1)
(anchor :step t1544)
(assume t1544.a0 @p_524)
(assume t1544.a1 @p_564)
(assume t1544.a2 @p_670)
(assume t1544.a3 @p_113)
(assume t1544.a4 @p_101)
(step t1544.t0 (cl (! (=> (! (and @p_670 @p_524) :named @p_728) @p_681) :named @p_730) @p_728) :rule implies_neg1)
(anchor :step t1544.t1)
(assume t1544.t1.a0 @p_670)
(assume t1544.t1.a1 @p_524)
(step t1544.t1.t0 (cl @p_681) :rule trans :premises (t1544.t1.a1 t758))
(step t1544.t1 (cl @p_671 @p_583 @p_681) :rule subproof :discharge (t1544.t1.a0 t1544.t1.a1))
(step t1544.t2 (cl (! (not @p_728) :named @p_729) @p_670) :rule and_pos :args (0))
(step t1544.t3 (cl @p_729 @p_524) :rule and_pos :args (1))
(step t1544.t4 (cl @p_681 @p_729 @p_729) :rule resolution :premises (t1544.t1 t1544.t2 t1544.t3))
(step t1544.t5 (cl @p_729 @p_729 @p_681) :rule reordering :premises (t1544.t4))
(step t1544.t6 (cl @p_729 @p_681) :rule contraction :premises (t1544.t5))
(step t1544.t7 (cl @p_730 @p_681) :rule resolution :premises (t1544.t0 t1544.t6))
(step t1544.t8 (cl @p_730 (! (not @p_681) :named @p_685)) :rule implies_neg2)
(step t1544.t9 (cl @p_730 @p_730) :rule resolution :premises (t1544.t7 t1544.t8))
(step t1544.t10 (cl @p_730) :rule contraction :premises (t1544.t9))
(step t1544.t11 (cl @p_729 @p_681) :rule implies :premises (t1544.t10))
(step t1544.t12 (cl @p_728) :rule and_intro :premises (t758 t1544.a0))
(step t1544.t13 (cl @p_681) :rule resolution :premises (t1544.t11 t1544.t12))
(step t1544.t14 (cl @p_727 @p_101) :rule implies_neg1)
(anchor :step t1544.t15)
(assume t1544.t15.a0 @p_101)
(step t1544.t15.t0 (cl @p_680) :rule symm :premises (t1544.t15.a0))
(step t1544.t15 (cl @p_102 @p_680) :rule subproof :discharge (t1544.t15.a0))
(step t1544.t16 (cl @p_727 @p_680) :rule resolution :premises (t1544.t14 t1544.t15))
(step t1544.t17 (cl @p_727 @p_686) :rule implies_neg2)
(step t1544.t18 (cl @p_727 @p_727) :rule resolution :premises (t1544.t16 t1544.t17))
(step t1544.t19 (cl @p_727) :rule contraction :premises (t1544.t18))
(step t1544.t20 (cl @p_102 @p_680) :rule implies :premises (t1544.t19))
(step t1544.t21 (cl @p_680) :rule resolution :premises (t1544.t20 t1544.a4))
(step t1544.t22 (cl @p_682) :rule and_intro :premises (t758 t1544.a3 t1544.a1 t1544.t13 t1544.t21))
(step t1544 (cl @p_583 @p_566 @p_671 @p_673 @p_102 @p_682) :rule subproof :discharge (t1544.a0 t1544.a1 t1544.a2 t1544.a3 t1544.a4))
(step t1545 (cl (! (not @p_678) :named @p_679) @p_524) :rule and_pos :args (0))
(step t1546 (cl @p_679 @p_564) :rule and_pos :args (1))
(step t1547 (cl @p_679 @p_670) :rule and_pos :args (2))
(step t1548 (cl @p_679 @p_113) :rule and_pos :args (3))
(step t1549 (cl @p_679 @p_101) :rule and_pos :args (4))
(step t1550 (cl @p_682 @p_679 @p_679 @p_679 @p_679 @p_679) :rule resolution :premises (t1544 t1545 t1546 t1547 t1548 t1549))
(step t1551 (cl @p_679 @p_679 @p_679 @p_679 @p_679 @p_682) :rule reordering :premises (t1550))
(step t1552 (cl @p_679 @p_682) :rule contraction :premises (t1551))
(step t1553 (cl @p_726 @p_682) :rule resolution :premises (t1543 t1552))
(step t1554 (cl @p_726 (! (not @p_682) :named @p_683)) :rule implies_neg2)
(step t1555 (cl @p_726 @p_726) :rule resolution :premises (t1553 t1554))
(step t1556 (cl @p_726) :rule contraction :premises (t1555))
(step t1557 (cl @p_679 @p_682) :rule implies :premises (t1556))
(step t1558 (cl (! (=> @p_682 false) :named @p_684) @p_682) :rule implies_neg1)
(anchor :step t1559)
(assume t1559.a0 @p_670)
(assume t1559.a1 @p_113)
(assume t1559.a2 @p_564)
(assume t1559.a3 @p_681)
(assume t1559.a4 @p_680)
(step t1559.t0 (cl @p_101) :rule symm :premises (t1559.a4))
(step t1559.t1 (cl (! (=> @p_101 false) :named @p_687) @p_101) :rule implies_neg1)
(anchor :step t1559.t2)
(assume t1559.t2.a0 @p_101)
(step t1559.t2.t0 (cl (not (! (= (! (< (! (+ @p_7 (! (+ k$ @p_690 @p_689) :named @p_693) @p_4 @p_111 @p_692) :named @p_694) (! (+ 0 0 @p_298 1 @p_297) :named @p_688)) :named @p_695) false) :named @p_717)) (not @p_695) false) :rule equiv_pos2)
(step t1559.t2.t1 (cl (= @p_695 (! (not (! (>= @p_694 @p_688) :named @p_718)) :named @p_719))) :rule rare_rewrite :args ("arith-elim-lt" @p_694 @p_688))
(step t1559.t2.t2 (cl (= @p_694 (! (+ @p_722 @p_721 @p_46 @p_7 @p_617 @p_4 k$) :named @p_723))) :rule poly_simp)
(step t1559.t2.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t1559.t2.t4 (cl (= @p_721 0)) :rule poly_simp)
(step t1559.t2.t5 (cl @p_168) :rule refl)
(step t1559.t2.t6 (cl @p_167) :rule refl)
(step t1559.t2.t7 (cl (= @p_617 0)) :rule poly_simp)
(step t1559.t2.t8 (cl (= @p_4 @p_4)) :rule refl)
(step t1559.t2.t9 (cl (= k$ k$)) :rule refl)
(step t1559.t2.t10 (cl (= @p_723 (! (+ 0 0 @p_46 @p_7 0 @p_4 k$) :named @p_724))) :rule cong :premises (t1559.t2.t3 t1559.t2.t4 t1559.t2.t5 t1559.t2.t6 t1559.t2.t7 t1559.t2.t8 t1559.t2.t9))
(step t1559.t2.t11 (cl (= @p_724 0)) :rule poly_simp)
(step t1559.t2.t12 (cl (= @p_723 0)) :rule trans :premises (t1559.t2.t10 t1559.t2.t11))
(step t1559.t2.t13 (cl (= @p_694 0)) :rule trans :premises (t1559.t2.t2 t1559.t2.t12))
(step t1559.t2.t14 (cl (= @p_298 -1)) :rule evaluate)
(step t1559.t2.t15 (cl (= 1 1)) :rule refl)
(step t1559.t2.t16 (cl (= @p_297 0)) :rule evaluate)
(step t1559.t2.t17 (cl (= @p_688 (! (+ 0 0 -1 1 0) :named @p_720))) :rule cong :premises (t1559.t2.t14 t1559.t2.t15 t1559.t2.t16))
(step t1559.t2.t18 (cl (= @p_720 0)) :rule evaluate)
(step t1559.t2.t19 (cl (= @p_688 0)) :rule trans :premises (t1559.t2.t17 t1559.t2.t18))
(step t1559.t2.t20 (cl (= @p_718 @p_366)) :rule cong :premises (t1559.t2.t13 t1559.t2.t19))
(step t1559.t2.t21 (cl (= @p_366 true)) :rule evaluate)
(step t1559.t2.t22 (cl (= @p_718 true)) :rule trans :premises (t1559.t2.t20 t1559.t2.t21))
(step t1559.t2.t23 (cl (= @p_719 @p_365)) :rule cong :premises (t1559.t2.t22))
(step t1559.t2.t24 (cl (= @p_365 false)) :rule evaluate)
(step t1559.t2.t25 (cl (= @p_719 false)) :rule trans :premises (t1559.t2.t23 t1559.t2.t24))
(step t1559.t2.t26 (cl @p_717) :rule trans :premises (t1559.t2.t1 t1559.t2.t25))
(step t1559.t2.t27 (cl @p_102 (not (! (= @p_693 0) :named @p_708)) @p_714 @p_715 @p_716 @p_695) :rule la_generic :args (-1/1 -1/1 1/1 1/1 -1/1 1/1))
(step t1559.t2.t28 (cl (not (! (= @p_681 @p_708) :named @p_712)) @p_685 @p_708) :rule equiv_pos2)
(step t1559.t2.t29 (cl (= (* 1 (- @p_693 0)) (* 1 (- k$ @p_669)))) :rule poly_simp)
(step t1559.t2.t30 (cl (= @p_708 @p_681)) :rule poly_simp_rel :premises (t1559.t2.t29))
(step t1559.t2.t31 (cl @p_712) :rule symm :premises (t1559.t2.t30))
(step t1559.t2.t32 (cl @p_708) :rule resolution :premises (t1559.t2.t28 t1559.t2.t31 t1559.a3))
(step t1559.t2.t33 (cl (=> @p_706 @p_705)) :rule la_mult_neg)
(step t1559.t2.t34 (cl @p_707 @p_705) :rule implies :premises (t1559.t2.t33))
(step t1559.t2.t35 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1559.t2.t36 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1559.t2.t35))
(step t1559.t2.t37 (cl @p_310) :rule evaluate)
(step t1559.t2.t38 (cl @p_308) :rule resolution :premises (t1559.t2.t36 t1559.t2.t37))
(step t1559.t2.t39 (cl @p_706) :rule and_intro :premises (t1559.t2.t38 t1559.a2))
(step t1559.t2.t40 (cl @p_705) :rule resolution :premises (t1559.t2.t34 t1559.t2.t39))
(step t1559.t2.t41 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t1559.t2.t42 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t1559.t2.t43 (cl @p_703) :rule symm :premises (t1559.t2.t42))
(step t1559.t2.t44 (cl @p_700) :rule resolution :premises (t1559.t2.t41 t1559.t2.t43 t1559.a1))
(step t1559.t2.t45 (cl (=> @p_698 @p_696)) :rule la_mult_neg)
(step t1559.t2.t46 (cl (not @p_698) @p_696) :rule implies :premises (t1559.t2.t45))
(step t1559.t2.t47 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t1559.t2.t48 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t1559.t2.t49 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t1559.t2.t48))
(step t1559.t2.t50 (cl @p_699) :rule symm :premises (t1559.t2.t49))
(step t1559.t2.t51 (cl @p_697) :rule resolution :premises (t1559.t2.t47 t1559.t2.t50 t758))
(step t1559.t2.t52 (cl @p_698) :rule and_intro :premises (t1559.t2.t38 t1559.t2.t51))
(step t1559.t2.t53 (cl @p_696) :rule resolution :premises (t1559.t2.t46 t1559.t2.t52))
(step t1559.t2.t54 (cl @p_695) :rule resolution :premises (t1559.t2.t27 t1559.t2.a0 t1559.t2.t32 t1559.t2.t40 t1559.t2.t44 t1559.t2.t53))
(step t1559.t2.t55 (cl false) :rule resolution :premises (t1559.t2.t0 t1559.t2.t26 t1559.t2.t54))
(step t1559.t2 (cl @p_102 false) :rule subproof :discharge (t1559.t2.a0))
(step t1559.t3 (cl @p_687 false) :rule resolution :premises (t1559.t1 t1559.t2))
(step t1559.t4 (cl @p_687 @p_212) :rule implies_neg2)
(step t1559.t5 (cl @p_687 @p_687) :rule resolution :premises (t1559.t3 t1559.t4))
(step t1559.t6 (cl @p_687) :rule contraction :premises (t1559.t5))
(step t1559.t7 (cl (= @p_687 @p_102)) :rule implies_simplify)
(step t1559.t8 (cl (not @p_687) @p_102) :rule equiv1 :premises (t1559.t7))
(step t1559.t9 (cl @p_102) :rule resolution :premises (t1559.t6 t1559.t8))
(step t1559.t10 (cl) :rule resolution :premises (t1559.t0 t1559.t9))
(step t1559 (cl @p_671 @p_673 @p_566 @p_685 @p_686 false) :rule subproof :discharge (t1559.a0 t1559.a1 t1559.a2 t1559.a3 t1559.a4))
(step t1560 (cl @p_683 @p_670) :rule and_pos :args (0))
(step t1561 (cl @p_683 @p_113) :rule and_pos :args (1))
(step t1562 (cl @p_683 @p_564) :rule and_pos :args (2))
(step t1563 (cl @p_683 @p_681) :rule and_pos :args (3))
(step t1564 (cl @p_683 @p_680) :rule and_pos :args (4))
(step t1565 (cl false @p_683 @p_683 @p_683 @p_683 @p_683) :rule resolution :premises (t1559 t1560 t1561 t1562 t1563 t1564))
(step t1566 (cl @p_683 @p_683 @p_683 @p_683 @p_683 false) :rule reordering :premises (t1565))
(step t1567 (cl @p_683 false) :rule contraction :premises (t1566))
(step t1568 (cl @p_684 false) :rule resolution :premises (t1558 t1567))
(step t1569 (cl @p_684 @p_212) :rule implies_neg2)
(step t1570 (cl @p_684 @p_684) :rule resolution :premises (t1568 t1569))
(step t1571 (cl @p_684) :rule contraction :premises (t1570))
(step t1572 (cl (= @p_684 @p_683)) :rule implies_simplify)
(step t1573 (cl (not @p_684) @p_683) :rule equiv1 :premises (t1572))
(step t1574 (cl @p_683) :rule resolution :premises (t1571 t1573))
(step t1575 (cl @p_679) :rule resolution :premises (t1557 t1574))
(step t1576 (cl @p_583 @p_566 @p_671 @p_673 @p_102) :rule not_and :premises (t1575))
(step t1577 (cl @p_674 @p_589) :rule or_neg :args (0))
(step t1578 (cl @p_674 @p_567) :rule or_neg :args (1))
(step t1579 (cl @p_674 @p_677) :rule or_neg :args (2))
(step t1580 (cl @p_674 @p_676) :rule or_neg :args (3))
(step t1581 (cl @p_674 @p_675) :rule or_neg :args (4))
(step t1582 (cl @p_674 @p_674 @p_674 @p_674 @p_674) :rule resolution :premises (t1576 t1577 t1578 t1579 t1580 t1581))
(step t1583 (cl @p_674) :rule contraction :premises (t1582))
(step t1584 (cl @p_672) :rule resolution :premises (t1541 t1542 t1583))
(step t1585 (cl @p_583 @p_566 @p_671 @p_112 @p_102) :rule or :premises (t1584))
(step t1586 (cl @p_583 @p_566 @p_112 @p_671 @p_102) :rule reordering :premises (t1585))
(step t1587 (cl (! (not (! (= @p_116 @p_515) :named @p_516)) :named @p_666) @p_116 @p_585) :rule equiv_pos1)
(step t1588 (cl @p_116 @p_585 @p_666) :rule reordering :premises (t1587))
(step t1589 (cl (! (=> (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0))) @p_516) :named @p_667) (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :rule implies_neg1)
(anchor :step t1590)
(assume t1590.a0 (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0))))
(step t1590.t0 (cl (or (! (not (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :named @p_521) @p_516)) :rule forall_inst :args (@p_6))
(step t1590.t1 (cl @p_521 @p_516) :rule or :premises (t1590.t0))
(step t1590.t2 (cl (not (! (= (forall ((?v0 Int)) (= (<= 0 (divide$ ?v0 2)) (<= 0 ?v0))) (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :named @p_517)) (not (forall ((?v0 Int)) (= (<= 0 (divide$ ?v0 2)) (<= 0 ?v0)))) (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :rule equiv_pos2)
(anchor :step t1590.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1590.t3.t0 (cl (= (! (<= 0 (! (divide$ ?v0 2) :named @p_518)) :named @p_520) (! (>= @p_518 0) :named @p_519))) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_518))
(step t1590.t3.t1 (cl (= @p_40 @p_26)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t1590.t3.t2 (cl (= (= @p_520 @p_40) (= @p_519 @p_26))) :rule cong :premises (t1590.t3.t0 t1590.t3.t1))
(step t1590.t3 (cl @p_517) :rule bind)
(step t1590.t4 (cl (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :rule resolution :premises (t1590.t2 t1590.t3 a6))
(step t1590.t5 (cl @p_516) :rule resolution :premises (t1590.t1 t1590.t4))
(step t1590 (cl @p_521 @p_516) :rule subproof :discharge (t1590.a0))
(step t1591 (cl @p_667 @p_516) :rule resolution :premises (t1589 t1590))
(step t1592 (cl @p_667 @p_666) :rule implies_neg2)
(step t1593 (cl @p_667 @p_667) :rule resolution :premises (t1591 t1592))
(step t1594 (cl @p_667) :rule contraction :premises (t1593))
(step t1595 (cl @p_521 @p_516) :rule implies :premises (t1594))
(step t1596 (cl (not @p_517) (not (forall ((?v0 Int)) (= (<= 0 (divide$ ?v0 2)) (<= 0 ?v0)))) (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :rule equiv_pos2)
(anchor :step t1597 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1597.t0 (cl (= @p_520 @p_519)) :rule rare_rewrite :args ("arith-elim-leq" 0 @p_518))
(step t1597.t1 (cl (= @p_40 @p_26)) :rule rare_rewrite :args ("arith-elim-leq" 0 ?v0))
(step t1597.t2 (cl (= (= @p_520 @p_40) (= @p_519 @p_26))) :rule cong :premises (t1597.t0 t1597.t1))
(step t1597 (cl @p_517) :rule bind)
(step t1598 (cl (forall ((?v0 Int)) (= (>= (divide$ ?v0 2) 0) (>= ?v0 0)))) :rule resolution :premises (t1596 t1597 a6))
(step t1599 (cl @p_583 @p_566 @p_112 @p_585 @p_636) :rule resolution :premises (t1 t649 t33 t652 t688 t739 t742 t755 t758 t808 t742 t758 t859 t742 t755 t758 t872 t875 t877 t880 t1159 t1189 t742 t261 t1387 t1412 t1151 t755 t758 t1458 t1474 t1494 t1509 t35 t1523 t1525 t1540 t1586 t758 t1588 t1595 t1598))
(step t1600 (cl (or @p_521 @p_516)) :rule forall_inst :args (@p_6))
(step t1601 (cl @p_521 @p_516) :rule or :premises (t1600))
(step t1602 (cl @p_516) :rule resolution :premises (t1601 t1598))
(step t1603 (cl (not (! (= (! (or @p_444 @p_532 (! (not (! (>= @p_105 0) :named @p_533)) :named @p_535) @p_633) :named @p_635) (! (or @p_433 @p_532 @p_535 @p_633) :named @p_634)) :named @p_665)) (not @p_635) @p_634) :rule equiv_pos2)
(step t1604 (cl (= @p_535 @p_535)) :rule refl)
(step t1605 (cl (= @p_633 @p_633)) :rule refl)
(step t1606 (cl @p_665) :rule cong :premises (t231 t40 t1604 t1605))
(step t1607 (cl (! (and @p_434 @p_106 @p_533) :named @p_637) @p_444 @p_532 @p_535) :rule and_neg)
(step t1608 (cl (! (=> @p_637 @p_633) :named @p_639) @p_637) :rule implies_neg1)
(anchor :step t1609)
(assume t1609.a0 @p_434)
(assume t1609.a1 @p_106)
(assume t1609.a2 @p_533)
(step t1609.t0 (cl (! (=> (! (and (! (not (! (= 0 @p_105) :named @p_640)) :named @p_641) @p_533) :named @p_642) @p_633) :named @p_657) @p_642) :rule implies_neg1)
(anchor :step t1609.t1)
(assume t1609.t1.a0 @p_641)
(assume t1609.t1.a1 @p_533)
(step t1609.t1.t0 (cl (not (! (> @p_105 0) :named @p_658)) @p_633) :rule la_generic :args (1/1 1/1))
(step t1609.t1.t1 (cl (! (not (! (= @p_105 0) :named @p_648)) :named @p_655)) :rule not_symm :premises (t1609.t1.a0))
(step t1609.t1.t2 (cl (or @p_648 (! (not (<= @p_105 0)) :named @p_659) (! (not (! (<= 0 @p_105) :named @p_662)) :named @p_664))) :rule la_disequality)
(step t1609.t1.t3 (cl @p_648 @p_659 @p_664) :rule or :premises (t1609.t1.t2))
(step t1609.t1.t4 (cl (! (= @p_533 @p_662) :named @p_663)) :rule comp_simplify)
(step t1609.t1.t5 (cl (not @p_663) @p_535 @p_662) :rule equiv_pos2)
(step t1609.t1.t6 (cl @p_662) :rule resolution :premises (t1609.t1.t4 t1609.t1.t5 t1609.t1.a1))
(step t1609.t1.t7 (cl (! (= @p_658 @p_659) :named @p_661)) :rule comp_simplify)
(step t1609.t1.t8 (cl (not @p_661) @p_658 (! (not @p_659) :named @p_660)) :rule equiv_pos1)
(step t1609.t1.t9 (cl @p_658 @p_660) :rule resolution :premises (t1609.t1.t7 t1609.t1.t8))
(step t1609.t1.t10 (cl @p_658) :rule resolution :premises (t1609.t1.t1 t1609.t1.t3 t1609.t1.t6 t1609.t1.t9))
(step t1609.t1.t11 (cl @p_633) :rule resolution :premises (t1609.t1.t0 t1609.t1.t10))
(step t1609.t1 (cl (! (not @p_641) :named @p_646) @p_535 @p_633) :rule subproof :discharge (t1609.t1.a0 t1609.t1.a1))
(step t1609.t2 (cl (! (not @p_642) :named @p_656) @p_641) :rule and_pos :args (0))
(step t1609.t3 (cl @p_656 @p_533) :rule and_pos :args (1))
(step t1609.t4 (cl @p_633 @p_656 @p_656) :rule resolution :premises (t1609.t1 t1609.t2 t1609.t3))
(step t1609.t5 (cl @p_656 @p_656 @p_633) :rule reordering :premises (t1609.t4))
(step t1609.t6 (cl @p_656 @p_633) :rule contraction :premises (t1609.t5))
(step t1609.t7 (cl @p_657 @p_633) :rule resolution :premises (t1609.t0 t1609.t6))
(step t1609.t8 (cl @p_657 @p_636) :rule implies_neg2)
(step t1609.t9 (cl @p_657 @p_657) :rule resolution :premises (t1609.t7 t1609.t8))
(step t1609.t10 (cl @p_657) :rule contraction :premises (t1609.t9))
(step t1609.t11 (cl @p_656 @p_633) :rule implies :premises (t1609.t10))
(step t1609.t12 (cl (! (=> (! (and @p_106 @p_434) :named @p_643) @p_641) :named @p_645) @p_643) :rule implies_neg1)
(anchor :step t1609.t13)
(assume t1609.t13.a0 @p_106)
(assume t1609.t13.a1 @p_434)
(step t1609.t13.t0 (cl (! (= (! (= @p_640 false) :named @p_647) @p_641) :named @p_654)) :rule equiv_simplify)
(step t1609.t13.t1 (cl (not @p_647) @p_641) :rule equiv1 :premises (t1609.t13.t0))
(step t1609.t13.t2 (cl (not (! (= (! (= @p_648 false) :named @p_649) @p_647) :named @p_650)) (not @p_649) @p_647) :rule equiv_pos2)
(step t1609.t13.t3 (cl (= @p_649 @p_655)) :rule rare_rewrite :args ("bool-eq-false" @p_648))
(step t1609.t13.t4 (cl (= (* 1 (- @p_105 0)) (* 1 (! (- @p_104 @p_544) :named @p_653)))) :rule poly_simp)
(step t1609.t13.t5 (cl (= @p_648 (! (= @p_104 @p_544) :named @p_651))) :rule poly_simp_rel :premises (t1609.t13.t4))
(step t1609.t13.t6 (cl (= @p_655 (! (not @p_651) :named @p_652))) :rule cong :premises (t1609.t13.t5))
(step t1609.t13.t7 (cl (= @p_649 @p_652)) :rule trans :premises (t1609.t13.t3 t1609.t13.t6))
(step t1609.t13.t8 (cl @p_654) :rule rare_rewrite :args ("bool-eq-false" @p_640))
(step t1609.t13.t9 (cl (= (* 1 (- 0 @p_105)) (* -1 @p_653))) :rule poly_simp)
(step t1609.t13.t10 (cl (= @p_640 @p_651)) :rule poly_simp_rel :premises (t1609.t13.t9))
(step t1609.t13.t11 (cl (= @p_641 @p_652)) :rule cong :premises (t1609.t13.t10))
(step t1609.t13.t12 (cl (= @p_647 @p_652)) :rule trans :premises (t1609.t13.t8 t1609.t13.t11))
(step t1609.t13.t13 (cl (= @p_652 @p_647)) :rule symm :premises (t1609.t13.t12))
(step t1609.t13.t14 (cl @p_650) :rule trans :premises (t1609.t13.t7 t1609.t13.t13))
(step t1609.t13.t15 (cl (= @p_105 k$)) :rule symm :premises (t742))
(step t1609.t13.t16 (cl (= @p_648 @p_433)) :rule cong :premises (t1609.t13.t15 t604))
(step t1609.t13.t17 (cl @p_453) :rule equiv_simplify)
(step t1609.t13.t18 (cl @p_452 @p_444) :rule equiv2 :premises (t1609.t13.t17))
(step t1609.t13.t19 (cl @p_447 @p_433) :rule not_not)
(step t1609.t13.t20 (cl @p_452 @p_433) :rule resolution :premises (t1609.t13.t18 t1609.t13.t19))
(step t1609.t13.t21 (cl @p_452) :rule resolution :premises (t1609.t13.t20 t1609.t13.a1))
(step t1609.t13.t22 (cl @p_649) :rule trans :premises (t1609.t13.t16 t1609.t13.t21))
(step t1609.t13.t23 (cl @p_647) :rule resolution :premises (t1609.t13.t2 t1609.t13.t14 t1609.t13.t22))
(step t1609.t13.t24 (cl @p_641) :rule resolution :premises (t1609.t13.t1 t1609.t13.t23))
(step t1609.t13 (cl @p_532 @p_444 @p_641) :rule subproof :discharge (t1609.t13.a0 t1609.t13.a1))
(step t1609.t14 (cl (! (not @p_643) :named @p_644) @p_106) :rule and_pos :args (0))
(step t1609.t15 (cl @p_644 @p_434) :rule and_pos :args (1))
(step t1609.t16 (cl @p_641 @p_644 @p_644) :rule resolution :premises (t1609.t13 t1609.t14 t1609.t15))
(step t1609.t17 (cl @p_644 @p_644 @p_641) :rule reordering :premises (t1609.t16))
(step t1609.t18 (cl @p_644 @p_641) :rule contraction :premises (t1609.t17))
(step t1609.t19 (cl @p_645 @p_641) :rule resolution :premises (t1609.t12 t1609.t18))
(step t1609.t20 (cl @p_645 @p_646) :rule implies_neg2)
(step t1609.t21 (cl @p_645 @p_645) :rule resolution :premises (t1609.t19 t1609.t20))
(step t1609.t22 (cl @p_645) :rule contraction :premises (t1609.t21))
(step t1609.t23 (cl @p_644 @p_641) :rule implies :premises (t1609.t22))
(step t1609.t24 (cl @p_643) :rule and_intro :premises (t742 t1609.a0))
(step t1609.t25 (cl @p_641) :rule resolution :premises (t1609.t23 t1609.t24))
(step t1609.t26 (cl @p_642) :rule and_intro :premises (t1609.t25 t1609.a2))
(step t1609.t27 (cl @p_633) :rule resolution :premises (t1609.t11 t1609.t26))
(step t1609 (cl @p_444 @p_532 @p_535 @p_633) :rule subproof :discharge (t1609.a0 t1609.a1 t1609.a2))
(step t1610 (cl (! (not @p_637) :named @p_638) @p_434) :rule and_pos :args (0))
(step t1611 (cl @p_638 @p_106) :rule and_pos :args (1))
(step t1612 (cl @p_638 @p_533) :rule and_pos :args (2))
(step t1613 (cl @p_633 @p_638 @p_638 @p_638) :rule resolution :premises (t1609 t1610 t1611 t1612))
(step t1614 (cl @p_638 @p_638 @p_638 @p_633) :rule reordering :premises (t1613))
(step t1615 (cl @p_638 @p_633) :rule contraction :premises (t1614))
(step t1616 (cl @p_639 @p_633) :rule resolution :premises (t1608 t1615))
(step t1617 (cl @p_639 @p_636) :rule implies_neg2)
(step t1618 (cl @p_639 @p_639) :rule resolution :premises (t1616 t1617))
(step t1619 (cl @p_639) :rule contraction :premises (t1618))
(step t1620 (cl @p_638 @p_633) :rule implies :premises (t1619))
(step t1621 (cl @p_444 @p_532 @p_535 @p_633) :rule resolution :premises (t1607 t1620))
(step t1622 (cl @p_635 @p_447) :rule or_neg :args (0))
(step t1623 (cl @p_635 @p_538) :rule or_neg :args (1))
(step t1624 (cl @p_635 (! (not @p_535) :named @p_536)) :rule or_neg :args (2))
(step t1625 (cl @p_635 @p_636) :rule or_neg :args (3))
(step t1626 (cl @p_635 @p_635 @p_635 @p_635) :rule resolution :premises (t1621 t1622 t1623 t1624 t1625))
(step t1627 (cl @p_635) :rule contraction :premises (t1626))
(step t1628 (cl @p_634) :rule resolution :premises (t1603 t1606 t1627))
(step t1629 (cl @p_433 @p_532 @p_535 @p_633) :rule or :premises (t1628))
(step t1630 (cl @p_433 @p_532 @p_633 @p_535) :rule reordering :premises (t1629))
(step t1631 (cl (not (! (= (! (or @p_523 @p_583 (! (not @p_585) :named @p_586) @p_532) :named @p_587) (! (or @p_523 @p_583 @p_515 @p_532) :named @p_584)) :named @p_632)) (not @p_587) @p_584) :rule equiv_pos2)
(step t1632 (cl (= @p_586 @p_515)) :rule rare_rewrite :args ("bool-double-not-elim" @p_515))
(step t1633 (cl @p_632) :rule cong :premises (t1632 t40))
(step t1634 (cl (! (=> (! (and @p_5 @p_524 @p_585 @p_106) :named @p_590) (! (and @p_106 @p_592 @p_5 @p_585) :named @p_593)) :named @p_627) @p_590) :rule implies_neg1)
(anchor :step t1635)
(assume t1635.a0 @p_5)
(assume t1635.a1 @p_524)
(assume t1635.a2 @p_585)
(assume t1635.a3 @p_106)
(step t1635.t0 (cl @p_631 @p_628) :rule implies_neg1)
(anchor :step t1635.t1)
(assume t1635.t1.a0 @p_106)
(assume t1635.t1.a1 @p_524)
(step t1635.t1.t0 (cl @p_527) :rule symm :premises (t1635.t1.a1))
(step t1635.t1.t1 (cl @p_592) :rule trans :premises (t1635.t1.t0 t742))
(step t1635.t1 (cl @p_532 @p_583 @p_592) :rule subproof :discharge (t1635.t1.a0 t1635.t1.a1))
(step t1635.t2 (cl @p_630 @p_106) :rule and_pos :args (0))
(step t1635.t3 (cl @p_630 @p_524) :rule and_pos :args (1))
(step t1635.t4 (cl @p_592 @p_630 @p_630) :rule resolution :premises (t1635.t1 t1635.t2 t1635.t3))
(step t1635.t5 (cl @p_630 @p_630 @p_592) :rule reordering :premises (t1635.t4))
(step t1635.t6 (cl @p_630 @p_592) :rule contraction :premises (t1635.t5))
(step t1635.t7 (cl @p_631 @p_592) :rule resolution :premises (t1635.t0 t1635.t6))
(step t1635.t8 (cl @p_631 @p_596) :rule implies_neg2)
(step t1635.t9 (cl @p_631 @p_631) :rule resolution :premises (t1635.t7 t1635.t8))
(step t1635.t10 (cl @p_631) :rule contraction :premises (t1635.t9))
(step t1635.t11 (cl @p_630 @p_592) :rule implies :premises (t1635.t10))
(step t1635.t12 (cl @p_628) :rule and_intro :premises (t742 t1635.a1))
(step t1635.t13 (cl @p_592) :rule resolution :premises (t1635.t11 t1635.t12))
(step t1635.t14 (cl @p_593) :rule and_intro :premises (t742 t1635.t13 t1635.a0 t1635.a2))
(step t1635 (cl @p_523 @p_583 @p_586 @p_532 @p_593) :rule subproof :discharge (t1635.a0 t1635.a1 t1635.a2 t1635.a3))
(step t1636 (cl (! (not @p_590) :named @p_591) @p_5) :rule and_pos :args (0))
(step t1637 (cl @p_591 @p_524) :rule and_pos :args (1))
(step t1638 (cl @p_591 @p_585) :rule and_pos :args (2))
(step t1639 (cl @p_591 @p_106) :rule and_pos :args (3))
(step t1640 (cl @p_593 @p_591 @p_591 @p_591 @p_591) :rule resolution :premises (t1635 t1636 t1637 t1638 t1639))
(step t1641 (cl @p_591 @p_591 @p_591 @p_591 @p_593) :rule reordering :premises (t1640))
(step t1642 (cl @p_591 @p_593) :rule contraction :premises (t1641))
(step t1643 (cl @p_627 @p_593) :rule resolution :premises (t1634 t1642))
(step t1644 (cl @p_627 (! (not @p_593) :named @p_594)) :rule implies_neg2)
(step t1645 (cl @p_627 @p_627) :rule resolution :premises (t1643 t1644))
(step t1646 (cl @p_627) :rule contraction :premises (t1645))
(step t1647 (cl @p_591 @p_593) :rule implies :premises (t1646))
(step t1648 (cl (! (=> @p_593 false) :named @p_595) @p_593) :rule implies_neg1)
(anchor :step t1649)
(assume t1649.a0 @p_106)
(assume t1649.a1 @p_592)
(assume t1649.a2 @p_5)
(assume t1649.a3 @p_585)
(step t1649.t0 (cl (! (not (! (= @p_585 (! (< @p_6 0) :named @p_597)) :named @p_625)) :named @p_626) @p_586 @p_597) :rule equiv_pos2)
(step t1649.t1 (cl (= @p_597 @p_585)) :rule rare_rewrite :args ("arith-elim-lt" @p_6 0))
(step t1649.t2 (cl @p_625) :rule symm :premises (t1649.t1))
(step t1649.t3 (cl @p_597) :rule resolution :premises (t1649.t0 t1649.t2 t1649.a3))
(step t1649.t4 (cl (not (! (= @p_515 (! (not @p_597) :named @p_598)) :named @p_623)) @p_585 @p_598) :rule equiv_pos2)
(step t1649.t5 (cl (= @p_598 @p_586)) :rule cong :premises (t1649.t1))
(step t1649.t6 (cl (! (= @p_598 @p_515) :named @p_622)) :rule trans :premises (t1649.t5 t1632))
(step t1649.t7 (cl @p_623) :rule symm :premises (t1649.t6))
(step t1649.t8 (cl (not @p_622) (not @p_598) @p_515) :rule equiv_pos2)
(step t1649.t9 (cl (! (=> @p_597 false) :named @p_599) @p_597) :rule implies_neg1)
(anchor :step t1649.t10)
(assume t1649.t10.a0 @p_597)
(step t1649.t10.t0 (cl (not (! (= (! (< (! (+ @p_6 @p_4 @p_602 @p_546) :named @p_603) (! (+ 0 @p_297 @p_297 0) :named @p_600)) :named @p_604) false) :named @p_613)) (not @p_604) false) :rule equiv_pos2)
(step t1649.t10.t1 (cl (= @p_604 (! (not (! (>= @p_603 @p_600) :named @p_614)) :named @p_615))) :rule rare_rewrite :args ("arith-elim-lt" @p_603 @p_600))
(step t1649.t10.t2 (cl (= @p_603 (! (+ @p_619 @p_618 @p_617 @p_4 k$) :named @p_620))) :rule poly_simp)
(step t1649.t10.t3 (cl (= @p_619 0)) :rule poly_simp)
(step t1649.t10.t4 (cl (= @p_618 0)) :rule poly_simp)
(step t1649.t10.t5 (cl (= @p_617 0)) :rule poly_simp)
(step t1649.t10.t6 (cl (= @p_4 @p_4)) :rule refl)
(step t1649.t10.t7 (cl (= k$ k$)) :rule refl)
(step t1649.t10.t8 (cl (= @p_620 (! (+ 0 0 0 @p_4 k$) :named @p_621))) :rule cong :premises (t1649.t10.t3 t1649.t10.t4 t1649.t10.t5 t1649.t10.t6 t1649.t10.t7))
(step t1649.t10.t9 (cl (= @p_621 0)) :rule poly_simp)
(step t1649.t10.t10 (cl (= @p_620 0)) :rule trans :premises (t1649.t10.t8 t1649.t10.t9))
(step t1649.t10.t11 (cl (= @p_603 0)) :rule trans :premises (t1649.t10.t2 t1649.t10.t10))
(step t1649.t10.t12 (cl (= @p_297 0)) :rule evaluate)
(step t1649.t10.t13 (cl (= @p_600 (! (+ 0 0 0 0) :named @p_616))) :rule cong :premises (t1649.t10.t12 t1649.t10.t12 t604))
(step t1649.t10.t14 (cl (= @p_616 0)) :rule evaluate)
(step t1649.t10.t15 (cl (= @p_600 0)) :rule trans :premises (t1649.t10.t13 t1649.t10.t14))
(step t1649.t10.t16 (cl (= @p_614 @p_366)) :rule cong :premises (t1649.t10.t11 t1649.t10.t15))
(step t1649.t10.t17 (cl (= @p_366 true)) :rule evaluate)
(step t1649.t10.t18 (cl (= @p_614 true)) :rule trans :premises (t1649.t10.t16 t1649.t10.t17))
(step t1649.t10.t19 (cl (= @p_615 @p_365)) :rule cong :premises (t1649.t10.t18))
(step t1649.t10.t20 (cl (= @p_365 false)) :rule evaluate)
(step t1649.t10.t21 (cl (= @p_615 false)) :rule trans :premises (t1649.t10.t19 t1649.t10.t20))
(step t1649.t10.t22 (cl @p_613) :rule trans :premises (t1649.t10.t1 t1649.t10.t21))
(step t1649.t10.t23 (cl @p_598 (! (not (! (<= @p_4 @p_297) :named @p_551)) :named @p_556) @p_612 @p_557 @p_604) :rule la_generic :args (1/1 1/1 -1/1 -1/1 1/1))
(step t1649.t10.t24 (cl (=> (! (and @p_308 @p_5) :named @p_552) @p_551)) :rule la_mult_neg)
(step t1649.t10.t25 (cl (! (not @p_552) :named @p_553) @p_551) :rule implies :premises (t1649.t10.t24))
(step t1649.t10.t26 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1649.t10.t27 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1649.t10.t26))
(step t1649.t10.t28 (cl @p_310) :rule evaluate)
(step t1649.t10.t29 (cl @p_308) :rule resolution :premises (t1649.t10.t27 t1649.t10.t28))
(step t1649.t10.t30 (cl @p_552) :rule and_intro :premises (t1649.t10.t29 t1649.a2))
(step t1649.t10.t31 (cl @p_551) :rule resolution :premises (t1649.t10.t25 t1649.t10.t30))
(step t1649.t10.t32 (cl (=> @p_607 @p_605)) :rule la_mult_neg)
(step t1649.t10.t33 (cl @p_611 @p_605) :rule implies :premises (t1649.t10.t32))
(step t1649.t10.t34 (cl @p_610 @p_596 @p_606) :rule equiv_pos2)
(step t1649.t10.t35 (cl (= (* 1 (- @p_601 0)) (* 1 (- @p_6 @p_105)))) :rule poly_simp)
(step t1649.t10.t36 (cl (= @p_606 @p_592)) :rule poly_simp_rel :premises (t1649.t10.t35))
(step t1649.t10.t37 (cl @p_609) :rule symm :premises (t1649.t10.t36))
(step t1649.t10.t38 (cl @p_606) :rule resolution :premises (t1649.t10.t34 t1649.t10.t37 t1649.a1))
(step t1649.t10.t39 (cl @p_607) :rule and_intro :premises (t1649.t10.t29 t1649.t10.t38))
(step t1649.t10.t40 (cl @p_605) :rule resolution :premises (t1649.t10.t33 t1649.t10.t39))
(step t1649.t10.t41 (cl (not @p_550) @p_532 @p_549) :rule equiv_pos2)
(step t1649.t10.t42 (cl (= (* 1 (- @p_546 0)) (* 1 (- k$ @p_105)))) :rule poly_simp)
(step t1649.t10.t43 (cl (= @p_549 @p_106)) :rule poly_simp_rel :premises (t1649.t10.t42))
(step t1649.t10.t44 (cl @p_550) :rule symm :premises (t1649.t10.t43))
(step t1649.t10.t45 (cl @p_549) :rule resolution :premises (t1649.t10.t41 t1649.t10.t44 t742))
(step t1649.t10.t46 (cl @p_604) :rule resolution :premises (t1649.t10.t23 t1649.t10.a0 t1649.t10.t31 t1649.t10.t40 t1649.t10.t45))
(step t1649.t10.t47 (cl false) :rule resolution :premises (t1649.t10.t0 t1649.t10.t22 t1649.t10.t46))
(step t1649.t10 (cl @p_598 false) :rule subproof :discharge (t1649.t10.a0))
(step t1649.t11 (cl @p_599 false) :rule resolution :premises (t1649.t9 t1649.t10))
(step t1649.t12 (cl @p_599 @p_212) :rule implies_neg2)
(step t1649.t13 (cl @p_599 @p_599) :rule resolution :premises (t1649.t11 t1649.t12))
(step t1649.t14 (cl @p_599) :rule contraction :premises (t1649.t13))
(step t1649.t15 (cl (= @p_599 @p_598)) :rule implies_simplify)
(step t1649.t16 (cl (not @p_599) @p_598) :rule equiv1 :premises (t1649.t15))
(step t1649.t17 (cl @p_598) :rule resolution :premises (t1649.t14 t1649.t16))
(step t1649.t18 (cl @p_515) :rule resolution :premises (t1649.t8 t1649.t6 t1649.t17))
(step t1649.t19 (cl @p_598) :rule resolution :premises (t1649.t4 t1649.t7 t1649.t18))
(step t1649.t20 (cl) :rule resolution :premises (t1649.t3 t1649.t19))
(step t1649 (cl @p_532 @p_596 @p_523 @p_586 false) :rule subproof :discharge (t1649.a0 t1649.a1 t1649.a2 t1649.a3))
(step t1650 (cl @p_594 @p_106) :rule and_pos :args (0))
(step t1651 (cl @p_594 @p_592) :rule and_pos :args (1))
(step t1652 (cl @p_594 @p_5) :rule and_pos :args (2))
(step t1653 (cl @p_594 @p_585) :rule and_pos :args (3))
(step t1654 (cl false @p_594 @p_594 @p_594 @p_594) :rule resolution :premises (t1649 t1650 t1651 t1652 t1653))
(step t1655 (cl @p_594 @p_594 @p_594 @p_594 false) :rule reordering :premises (t1654))
(step t1656 (cl @p_594 false) :rule contraction :premises (t1655))
(step t1657 (cl @p_595 false) :rule resolution :premises (t1648 t1656))
(step t1658 (cl @p_595 @p_212) :rule implies_neg2)
(step t1659 (cl @p_595 @p_595) :rule resolution :premises (t1657 t1658))
(step t1660 (cl @p_595) :rule contraction :premises (t1659))
(step t1661 (cl (= @p_595 @p_594)) :rule implies_simplify)
(step t1662 (cl (not @p_595) @p_594) :rule equiv1 :premises (t1661))
(step t1663 (cl @p_594) :rule resolution :premises (t1660 t1662))
(step t1664 (cl @p_591) :rule resolution :premises (t1647 t1663))
(step t1665 (cl @p_523 @p_583 @p_586 @p_532) :rule not_and :premises (t1664))
(step t1666 (cl @p_587 @p_539) :rule or_neg :args (0))
(step t1667 (cl @p_587 @p_589) :rule or_neg :args (1))
(step t1668 (cl @p_587 (! (not @p_586) :named @p_588)) :rule or_neg :args (2))
(step t1669 (cl @p_587 @p_538) :rule or_neg :args (3))
(step t1670 (cl @p_587 @p_587 @p_587 @p_587) :rule resolution :premises (t1665 t1666 t1667 t1668 t1669))
(step t1671 (cl @p_587) :rule contraction :premises (t1670))
(step t1672 (cl @p_584) :rule resolution :premises (t1631 t1633 t1671))
(step t1673 (cl @p_523 @p_583 @p_515 @p_532) :rule or :premises (t1672))
(step t1674 (cl (not (! (= (! (or @p_523 @p_567 @p_433) :named @p_568) (! (or @p_523 @p_564 @p_433) :named @p_565)) :named @p_582)) (not @p_568) @p_565) :rule equiv_pos2)
(step t1675 (cl (= @p_567 @p_564)) :rule rare_rewrite :args ("bool-double-not-elim" @p_564))
(step t1676 (cl (= @p_433 @p_433)) :rule refl)
(step t1677 (cl @p_582) :rule cong :premises (t1675 t1676))
(step t1678 (cl (! (and @p_5 @p_566) :named @p_569) @p_523 @p_567) :rule and_neg)
(step t1679 (cl (! (=> @p_569 @p_433) :named @p_571) @p_569) :rule implies_neg1)
(anchor :step t1680)
(assume t1680.a0 @p_5)
(assume t1680.a1 @p_566)
(step t1680.t0 (cl @p_571 @p_569) :rule implies_neg1)
(anchor :step t1680.t1)
(assume t1680.t1.a0 @p_5)
(assume t1680.t1.a1 @p_566)
(step t1680.t1.t0 (cl @p_581 (! (<= k$ 0) :named @p_574)) :rule la_generic :args (1/1 1/1))
(step t1680.t1.t1 (cl @p_580 @p_567 @p_577) :rule equiv_pos2)
(step t1680.t1.t2 (cl @p_579) :rule rare_rewrite :args ("arith-elim-lt" k$ 1))
(step t1680.t1.t3 (cl @p_578) :rule symm :premises (t1680.t1.t2))
(step t1680.t1.t4 (cl @p_577) :rule resolution :premises (t1680.t1.t1 t1680.t1.t3 t1680.t1.a1))
(step t1680.t1.t5 (cl @p_574) :rule resolution :premises (t1680.t1.t0 t1680.t1.t4))
(step t1680.t1.t6 (cl (or @p_433 (! (not @p_574) :named @p_575) (! (not (! (<= 0 k$) :named @p_572)) :named @p_576))) :rule la_disequality)
(step t1680.t1.t7 (cl @p_433 @p_575 @p_576) :rule or :premises (t1680.t1.t6))
(step t1680.t1.t8 (cl (! (= @p_5 @p_572) :named @p_573)) :rule comp_simplify)
(step t1680.t1.t9 (cl (not @p_573) @p_523 @p_572) :rule equiv_pos2)
(step t1680.t1.t10 (cl @p_572) :rule resolution :premises (t1680.t1.t8 t1680.t1.t9 t1680.t1.a0))
(step t1680.t1.t11 (cl @p_433) :rule resolution :premises (t1680.t1.t5 t1680.t1.t7 t1680.t1.t10))
(step t1680.t1 (cl @p_523 @p_567 @p_433) :rule subproof :discharge (t1680.t1.a0 t1680.t1.a1))
(step t1680.t2 (cl (! (not @p_569) :named @p_570) @p_5) :rule and_pos :args (0))
(step t1680.t3 (cl @p_570 @p_566) :rule and_pos :args (1))
(step t1680.t4 (cl @p_433 @p_570 @p_570) :rule resolution :premises (t1680.t1 t1680.t2 t1680.t3))
(step t1680.t5 (cl @p_570 @p_570 @p_433) :rule reordering :premises (t1680.t4))
(step t1680.t6 (cl @p_570 @p_433) :rule contraction :premises (t1680.t5))
(step t1680.t7 (cl @p_571 @p_433) :rule resolution :premises (t1680.t0 t1680.t6))
(step t1680.t8 (cl @p_571 @p_434) :rule implies_neg2)
(step t1680.t9 (cl @p_571 @p_571) :rule resolution :premises (t1680.t7 t1680.t8))
(step t1680.t10 (cl @p_571) :rule contraction :premises (t1680.t9))
(step t1680.t11 (cl @p_570 @p_433) :rule implies :premises (t1680.t10))
(step t1680.t12 (cl @p_569) :rule and_intro :premises (t1680.a0 t1680.a1))
(step t1680.t13 (cl @p_433) :rule resolution :premises (t1680.t11 t1680.t12))
(step t1680 (cl @p_523 @p_567 @p_433) :rule subproof :discharge (t1680.a0 t1680.a1))
(step t1681 (cl @p_570 @p_5) :rule and_pos :args (0))
(step t1682 (cl @p_570 @p_566) :rule and_pos :args (1))
(step t1683 (cl @p_433 @p_570 @p_570) :rule resolution :premises (t1680 t1681 t1682))
(step t1684 (cl @p_570 @p_570 @p_433) :rule reordering :premises (t1683))
(step t1685 (cl @p_570 @p_433) :rule contraction :premises (t1684))
(step t1686 (cl @p_571 @p_433) :rule resolution :premises (t1679 t1685))
(step t1687 (cl @p_571 @p_434) :rule implies_neg2)
(step t1688 (cl @p_571 @p_571) :rule resolution :premises (t1686 t1687))
(step t1689 (cl @p_571) :rule contraction :premises (t1688))
(step t1690 (cl @p_570 @p_433) :rule implies :premises (t1689))
(step t1691 (cl @p_523 @p_567 @p_433) :rule resolution :premises (t1678 t1690))
(step t1692 (cl @p_568 @p_539) :rule or_neg :args (0))
(step t1693 (cl @p_568 (not @p_567)) :rule or_neg :args (1))
(step t1694 (cl @p_568 @p_434) :rule or_neg :args (2))
(step t1695 (cl @p_568 @p_568 @p_568) :rule resolution :premises (t1691 t1692 t1693 t1694))
(step t1696 (cl @p_568) :rule contraction :premises (t1695))
(step t1697 (cl @p_565) :rule resolution :premises (t1674 t1677 t1696))
(step t1698 (cl @p_523 @p_564 @p_433) :rule or :premises (t1697))
(step t1699 (cl @p_433 @p_523 @p_564) :rule reordering :premises (t1698))
(step t1700 (cl (not (! (= (! (or @p_523 @p_532 @p_536) :named @p_537) (! (or @p_523 @p_532 @p_533) :named @p_534)) :named @p_563)) (not @p_537) @p_534) :rule equiv_pos2)
(step t1701 (cl (= @p_536 @p_533)) :rule rare_rewrite :args ("bool-double-not-elim" @p_533))
(step t1702 (cl @p_563) :rule cong :premises (t1701))
(step t1703 (cl (! (=> (! (and @p_5 @p_106 @p_535) :named @p_540) false) :named @p_542) @p_540) :rule implies_neg1)
(anchor :step t1704)
(assume t1704.a0 @p_5)
(assume t1704.a1 @p_106)
(assume t1704.a2 @p_535)
(step t1704.t0 (cl (not (! (= (! (< (! (+ @p_105 @p_4 @p_546) :named @p_547) (! (+ 0 @p_297 0) :named @p_543)) :named @p_548) false) :named @p_558)) (not @p_548) false) :rule equiv_pos2)
(step t1704.t1 (cl (= @p_548 (! (not (! (>= @p_547 @p_543) :named @p_559)) :named @p_560))) :rule rare_rewrite :args ("arith-elim-lt" @p_547 @p_543))
(step t1704.t2 (cl (= @p_547 (! (+ @p_545 @p_544 @p_103 @p_104 @p_4 k$) :named @p_562))) :rule poly_simp)
(step t1704.t3 (cl (= @p_562 0)) :rule poly_simp)
(step t1704.t4 (cl (= @p_547 0)) :rule trans :premises (t1704.t2 t1704.t3))
(step t1704.t5 (cl (= @p_297 0)) :rule evaluate)
(step t1704.t6 (cl (= @p_543 (! (+ 0 0 0) :named @p_561))) :rule cong :premises (t1704.t5 t604))
(step t1704.t7 (cl (= @p_561 0)) :rule evaluate)
(step t1704.t8 (cl (= @p_543 0)) :rule trans :premises (t1704.t6 t1704.t7))
(step t1704.t9 (cl (= @p_559 @p_366)) :rule cong :premises (t1704.t4 t1704.t8))
(step t1704.t10 (cl (= @p_366 true)) :rule evaluate)
(step t1704.t11 (cl (= @p_559 true)) :rule trans :premises (t1704.t9 t1704.t10))
(step t1704.t12 (cl (= @p_560 @p_365)) :rule cong :premises (t1704.t11))
(step t1704.t13 (cl (= @p_365 false)) :rule evaluate)
(step t1704.t14 (cl (= @p_560 false)) :rule trans :premises (t1704.t12 t1704.t13))
(step t1704.t15 (cl @p_558) :rule trans :premises (t1704.t1 t1704.t14))
(step t1704.t16 (cl (not (! (< @p_105 0) :named @p_554)) @p_556 @p_557 @p_548) :rule la_generic :args (1/1 1/1 -1/1 1/1))
(step t1704.t17 (cl (not (! (= @p_535 @p_554) :named @p_555)) @p_536 @p_554) :rule equiv_pos2)
(step t1704.t18 (cl (= @p_554 @p_535)) :rule rare_rewrite :args ("arith-elim-lt" @p_105 0))
(step t1704.t19 (cl @p_555) :rule symm :premises (t1704.t18))
(step t1704.t20 (cl @p_554) :rule resolution :premises (t1704.t17 t1704.t19 t1704.a2))
(step t1704.t21 (cl (=> @p_552 @p_551)) :rule la_mult_neg)
(step t1704.t22 (cl @p_553 @p_551) :rule implies :premises (t1704.t21))
(step t1704.t23 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1704.t24 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1704.t23))
(step t1704.t25 (cl @p_310) :rule evaluate)
(step t1704.t26 (cl @p_308) :rule resolution :premises (t1704.t24 t1704.t25))
(step t1704.t27 (cl @p_552) :rule and_intro :premises (t1704.t26 t1704.a0))
(step t1704.t28 (cl @p_551) :rule resolution :premises (t1704.t22 t1704.t27))
(step t1704.t29 (cl (not @p_550) @p_532 @p_549) :rule equiv_pos2)
(step t1704.t30 (cl (= (* 1 (- @p_546 0)) (* 1 (- k$ @p_105)))) :rule poly_simp)
(step t1704.t31 (cl (= @p_549 @p_106)) :rule poly_simp_rel :premises (t1704.t30))
(step t1704.t32 (cl @p_550) :rule symm :premises (t1704.t31))
(step t1704.t33 (cl @p_549) :rule resolution :premises (t1704.t29 t1704.t32 t742))
(step t1704.t34 (cl @p_548) :rule resolution :premises (t1704.t16 t1704.t20 t1704.t28 t1704.t33))
(step t1704.t35 (cl false) :rule resolution :premises (t1704.t0 t1704.t15 t1704.t34))
(step t1704 (cl @p_523 @p_532 @p_536 false) :rule subproof :discharge (t1704.a0 t1704.a1 t1704.a2))
(step t1705 (cl (! (not @p_540) :named @p_541) @p_5) :rule and_pos :args (0))
(step t1706 (cl @p_541 @p_106) :rule and_pos :args (1))
(step t1707 (cl @p_541 @p_535) :rule and_pos :args (2))
(step t1708 (cl false @p_541 @p_541 @p_541) :rule resolution :premises (t1704 t1705 t1706 t1707))
(step t1709 (cl @p_541 @p_541 @p_541 false) :rule reordering :premises (t1708))
(step t1710 (cl @p_541 false) :rule contraction :premises (t1709))
(step t1711 (cl @p_542 false) :rule resolution :premises (t1703 t1710))
(step t1712 (cl @p_542 @p_212) :rule implies_neg2)
(step t1713 (cl @p_542 @p_542) :rule resolution :premises (t1711 t1712))
(step t1714 (cl @p_542) :rule contraction :premises (t1713))
(step t1715 (cl (= @p_542 @p_541)) :rule implies_simplify)
(step t1716 (cl (not @p_542) @p_541) :rule equiv1 :premises (t1715))
(step t1717 (cl @p_541) :rule resolution :premises (t1714 t1716))
(step t1718 (cl @p_523 @p_532 @p_536) :rule not_and :premises (t1717))
(step t1719 (cl @p_537 @p_539) :rule or_neg :args (0))
(step t1720 (cl @p_537 @p_538) :rule or_neg :args (1))
(step t1721 (cl @p_537 (not @p_536)) :rule or_neg :args (2))
(step t1722 (cl @p_537 @p_537 @p_537) :rule resolution :premises (t1718 t1719 t1720 t1721))
(step t1723 (cl @p_537) :rule contraction :premises (t1722))
(step t1724 (cl @p_534) :rule resolution :premises (t1700 t1702 t1723))
(step t1725 (cl @p_523 @p_532 @p_533) :rule or :premises (t1724))
(step t1726 (cl (not (! (= (! (ite @p_5 @p_527 (! (= @p_6 @p_4) :named @p_526)) :named @p_528) (! (ite @p_5 @p_524 @p_522) :named @p_525)) :named @p_531)) (! (not @p_528) :named @p_530) @p_525) :rule equiv_pos2)
(step t1727 (cl (= (* 1 (- @p_6 k$)) (* -1 (- k$ @p_6)))) :rule poly_simp)
(step t1728 (cl (= @p_527 @p_524)) :rule poly_simp_rel :premises (t1727))
(step t1729 (cl (= (* 1 (- @p_6 @p_4)) (* 1 (- k$ @p_120)))) :rule poly_simp)
(step t1730 (cl (= @p_526 @p_522)) :rule poly_simp_rel :premises (t1729))
(step t1731 (cl @p_531) :rule cong :premises (t1728 t1730))
(step t1732 (cl (not (! (= @p_528 @p_528) :named @p_529)) @p_530 @p_528) :rule equiv_pos2)
(step t1733 (cl (= k$ k$)) :rule refl)
(step t1734 (cl (= @p_527 @p_527)) :rule cong :premises (t357 t1733))
(step t1735 (cl (= @p_4 @p_4)) :rule refl)
(step t1736 (cl (= @p_526 @p_526)) :rule cong :premises (t357 t1735))
(step t1737 (cl @p_529) :rule cong :premises (t1734 t1736))
(step t1738 (cl (= @p_528 true)) :rule rare_rewrite :args ("ite-eq" @p_5 k$ @p_4))
(step t1739 (cl @p_528 @p_365) :rule equiv2 :premises (t1738))
(step t1740 (cl true) :rule true)
(step t1741 (cl @p_528) :rule resolution :premises (t1739 t1740))
(step t1742 (cl @p_528) :rule resolution :premises (t1732 t1737 t1741))
(step t1743 (cl @p_525) :rule resolution :premises (t1726 t1731 t1742))
(step t1744 (cl @p_523 @p_524) :rule ite2 :premises (t1743))
(step t1745 (cl @p_524 @p_523) :rule reordering :premises (t1744))
(step t1746 (cl @p_523) :rule resolution :premises (t87 t601 t628 t1599 t1588 t1602 t1630 t742 t168 t1673 t742 t1699 t168 t1725 t742 t1745))
(step t1747 (cl @p_5 @p_522) :rule ite1 :premises (t1743))
(step t1748 (cl @p_522) :rule resolution :premises (t1747 t1746))
(step t1749 (cl (not (! (= (! (or @p_1440 @p_539 @p_586 @p_532) :named @p_1442) (! (or @p_1440 @p_5 @p_515 @p_532) :named @p_1441)) :named @p_1491)) (not @p_1442) @p_1441) :rule equiv_pos2)
(step t1750 (cl @p_1491) :rule cong :premises (t37 t1632 t40))
(step t1751 (cl (! (=> (! (and @p_522 @p_523 @p_585 @p_106) :named @p_1445) (! (and @p_106 @p_585 @p_1447 @p_523) :named @p_1448)) :named @p_1486) @p_1445) :rule implies_neg1)
(anchor :step t1752)
(assume t1752.a0 @p_522)
(assume t1752.a1 @p_523)
(assume t1752.a2 @p_585)
(assume t1752.a3 @p_106)
(step t1752.t0 (cl @p_1490 @p_1487) :rule implies_neg1)
(anchor :step t1752.t1)
(assume t1752.t1.a0 @p_106)
(assume t1752.t1.a1 @p_522)
(step t1752.t1.t0 (cl (= @p_120 k$)) :rule symm :premises (t1752.t1.a1))
(step t1752.t1.t1 (cl @p_1447) :rule trans :premises (t1752.t1.t0 t742))
(step t1752.t1 (cl @p_532 @p_1440 @p_1447) :rule subproof :discharge (t1752.t1.a0 t1752.t1.a1))
(step t1752.t2 (cl @p_1489 @p_106) :rule and_pos :args (0))
(step t1752.t3 (cl @p_1489 @p_522) :rule and_pos :args (1))
(step t1752.t4 (cl @p_1447 @p_1489 @p_1489) :rule resolution :premises (t1752.t1 t1752.t2 t1752.t3))
(step t1752.t5 (cl @p_1489 @p_1489 @p_1447) :rule reordering :premises (t1752.t4))
(step t1752.t6 (cl @p_1489 @p_1447) :rule contraction :premises (t1752.t5))
(step t1752.t7 (cl @p_1490 @p_1447) :rule resolution :premises (t1752.t0 t1752.t6))
(step t1752.t8 (cl @p_1490 @p_1451) :rule implies_neg2)
(step t1752.t9 (cl @p_1490 @p_1490) :rule resolution :premises (t1752.t7 t1752.t8))
(step t1752.t10 (cl @p_1490) :rule contraction :premises (t1752.t9))
(step t1752.t11 (cl @p_1489 @p_1447) :rule implies :premises (t1752.t10))
(step t1752.t12 (cl @p_1487) :rule and_intro :premises (t742 t1752.a0))
(step t1752.t13 (cl @p_1447) :rule resolution :premises (t1752.t11 t1752.t12))
(step t1752.t14 (cl @p_1448) :rule and_intro :premises (t742 t1752.a2 t1752.t13 t1752.a1))
(step t1752 (cl @p_1440 @p_539 @p_586 @p_532 @p_1448) :rule subproof :discharge (t1752.a0 t1752.a1 t1752.a2 t1752.a3))
(step t1753 (cl (! (not @p_1445) :named @p_1446) @p_522) :rule and_pos :args (0))
(step t1754 (cl @p_1446 @p_523) :rule and_pos :args (1))
(step t1755 (cl @p_1446 @p_585) :rule and_pos :args (2))
(step t1756 (cl @p_1446 @p_106) :rule and_pos :args (3))
(step t1757 (cl @p_1448 @p_1446 @p_1446 @p_1446 @p_1446) :rule resolution :premises (t1752 t1753 t1754 t1755 t1756))
(step t1758 (cl @p_1446 @p_1446 @p_1446 @p_1446 @p_1448) :rule reordering :premises (t1757))
(step t1759 (cl @p_1446 @p_1448) :rule contraction :premises (t1758))
(step t1760 (cl @p_1486 @p_1448) :rule resolution :premises (t1751 t1759))
(step t1761 (cl @p_1486 (! (not @p_1448) :named @p_1449)) :rule implies_neg2)
(step t1762 (cl @p_1486 @p_1486) :rule resolution :premises (t1760 t1761))
(step t1763 (cl @p_1486) :rule contraction :premises (t1762))
(step t1764 (cl @p_1446 @p_1448) :rule implies :premises (t1763))
(step t1765 (cl (! (=> @p_1448 false) :named @p_1450) @p_1448) :rule implies_neg1)
(anchor :step t1766)
(assume t1766.a0 @p_106)
(assume t1766.a1 @p_585)
(assume t1766.a2 @p_1447)
(assume t1766.a3 @p_523)
(step t1766.t0 (cl @p_1485 @p_539 @p_1452) :rule equiv_pos2)
(step t1766.t1 (cl (= @p_1452 @p_523)) :rule rare_rewrite :args ("arith-elim-lt" k$ 0))
(step t1766.t2 (cl @p_1484) :rule symm :premises (t1766.t1))
(step t1766.t3 (cl @p_1452) :rule resolution :premises (t1766.t0 t1766.t2 t1766.a3))
(step t1766.t4 (cl (not (! (= @p_5 @p_1453) :named @p_1483)) @p_523 @p_1453) :rule equiv_pos2)
(step t1766.t5 (cl (= @p_1453 @p_539)) :rule cong :premises (t1766.t1))
(step t1766.t6 (cl (! (= @p_1453 @p_5) :named @p_1482)) :rule trans :premises (t1766.t5 t37))
(step t1766.t7 (cl @p_1483) :rule symm :premises (t1766.t6))
(step t1766.t8 (cl (not @p_1482) (not @p_1453) @p_5) :rule equiv_pos2)
(step t1766.t9 (cl (! (=> @p_1452 false) :named @p_1454) @p_1452) :rule implies_neg1)
(anchor :step t1766.t10)
(assume t1766.t10.a0 @p_1452)
(step t1766.t10.t0 (cl (not (! (= (! (< (! (+ k$ @p_1458 @p_6 @p_1456) :named @p_1459) (! (+ 0 @p_297 0 @p_297) :named @p_1455)) :named @p_1460) false) :named @p_1476)) (not @p_1460) false) :rule equiv_pos2)
(step t1766.t10.t1 (cl (= @p_1460 (! (not (! (>= @p_1459 @p_1455) :named @p_1477)) :named @p_1478))) :rule rare_rewrite :args ("arith-elim-lt" @p_1459 @p_1455))
(step t1766.t10.t2 (cl (= @p_1458 (! (+ @p_120 @p_545 @p_544) :named @p_1480))) :rule poly_simp)
(step t1766.t10.t3 (cl @p_162) :rule refl)
(step t1766.t10.t4 (cl (= @p_1456 (! (+ @p_4 @p_104 @p_103) :named @p_1479))) :rule poly_simp)
(step t1766.t10.t5 (cl (= @p_1459 (! (+ k$ @p_1480 @p_6 @p_1479) :named @p_1481))) :rule cong :premises (t1766.t10.t2 t1766.t10.t3 t1766.t10.t4))
(step t1766.t10.t6 (cl (= @p_1481 0)) :rule poly_simp)
(step t1766.t10.t7 (cl (= @p_1459 0)) :rule trans :premises (t1766.t10.t5 t1766.t10.t6))
(step t1766.t10.t8 (cl (= @p_297 0)) :rule evaluate)
(step t1766.t10.t9 (cl (= @p_1455 @p_616)) :rule cong :premises (t1766.t10.t8 t604 t1766.t10.t8))
(step t1766.t10.t10 (cl (= @p_616 0)) :rule evaluate)
(step t1766.t10.t11 (cl (= @p_1455 0)) :rule trans :premises (t1766.t10.t9 t1766.t10.t10))
(step t1766.t10.t12 (cl (= @p_1477 @p_366)) :rule cong :premises (t1766.t10.t7 t1766.t10.t11))
(step t1766.t10.t13 (cl (= @p_366 true)) :rule evaluate)
(step t1766.t10.t14 (cl (= @p_1477 true)) :rule trans :premises (t1766.t10.t12 t1766.t10.t13))
(step t1766.t10.t15 (cl (= @p_1478 @p_365)) :rule cong :premises (t1766.t10.t14))
(step t1766.t10.t16 (cl (= @p_365 false)) :rule evaluate)
(step t1766.t10.t17 (cl (= @p_1478 false)) :rule trans :premises (t1766.t10.t15 t1766.t10.t16))
(step t1766.t10.t18 (cl @p_1476) :rule trans :premises (t1766.t10.t1 t1766.t10.t17))
(step t1766.t10.t19 (cl @p_1453 @p_1474 @p_598 @p_1475 @p_1460) :rule la_generic :args (1/1 -1/1 1/1 -1/1 1/1))
(step t1766.t10.t20 (cl (=> @p_1465 @p_1463)) :rule la_mult_neg)
(step t1766.t10.t21 (cl @p_1473 @p_1463) :rule implies :premises (t1766.t10.t20))
(step t1766.t10.t22 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1766.t10.t23 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1766.t10.t22))
(step t1766.t10.t24 (cl @p_310) :rule evaluate)
(step t1766.t10.t25 (cl @p_308) :rule resolution :premises (t1766.t10.t23 t1766.t10.t24))
(step t1766.t10.t26 (cl @p_1472 @p_1451 @p_1464) :rule equiv_pos2)
(step t1766.t10.t27 (cl (= (* 1 (- @p_120 @p_105)) (* -1 @p_1471))) :rule poly_simp)
(step t1766.t10.t28 (cl (= @p_1447 @p_1470)) :rule poly_simp_rel :premises (t1766.t10.t27))
(step t1766.t10.t29 (cl (= (* 1 (- @p_1457 0)) (* 1 @p_1471))) :rule poly_simp)
(step t1766.t10.t30 (cl (= @p_1464 @p_1470)) :rule poly_simp_rel :premises (t1766.t10.t29))
(step t1766.t10.t31 (cl (= @p_1470 @p_1464)) :rule symm :premises (t1766.t10.t30))
(step t1766.t10.t32 (cl @p_1468) :rule trans :premises (t1766.t10.t28 t1766.t10.t31))
(step t1766.t10.t33 (cl @p_1464) :rule resolution :premises (t1766.t10.t26 t1766.t10.t32 t1766.a2))
(step t1766.t10.t34 (cl @p_1465) :rule and_intro :premises (t1766.t10.t25 t1766.t10.t33))
(step t1766.t10.t35 (cl @p_1463) :rule resolution :premises (t1766.t10.t21 t1766.t10.t34))
(step t1766.t10.t36 (cl @p_626 @p_586 @p_597) :rule equiv_pos2)
(step t1766.t10.t37 (cl (= @p_597 @p_585)) :rule rare_rewrite :args ("arith-elim-lt" @p_6 0))
(step t1766.t10.t38 (cl @p_625) :rule symm :premises (t1766.t10.t37))
(step t1766.t10.t39 (cl @p_597) :rule resolution :premises (t1766.t10.t36 t1766.t10.t38 t1766.a1))
(step t1766.t10.t40 (cl (=> @p_1462 @p_1461)) :rule la_mult_neg)
(step t1766.t10.t41 (cl (not @p_1462) @p_1461) :rule implies :premises (t1766.t10.t40))
(step t1766.t10.t42 (cl (not @p_550) @p_532 @p_549) :rule equiv_pos2)
(step t1766.t10.t43 (cl (= (* 1 (- @p_546 0)) (* 1 (- k$ @p_105)))) :rule poly_simp)
(step t1766.t10.t44 (cl (= @p_549 @p_106)) :rule poly_simp_rel :premises (t1766.t10.t43))
(step t1766.t10.t45 (cl @p_550) :rule symm :premises (t1766.t10.t44))
(step t1766.t10.t46 (cl @p_549) :rule resolution :premises (t1766.t10.t42 t1766.t10.t45 t742))
(step t1766.t10.t47 (cl @p_1462) :rule and_intro :premises (t1766.t10.t25 t1766.t10.t46))
(step t1766.t10.t48 (cl @p_1461) :rule resolution :premises (t1766.t10.t41 t1766.t10.t47))
(step t1766.t10.t49 (cl @p_1460) :rule resolution :premises (t1766.t10.t19 t1766.t10.a0 t1766.t10.t35 t1766.t10.t39 t1766.t10.t48))
(step t1766.t10.t50 (cl false) :rule resolution :premises (t1766.t10.t0 t1766.t10.t18 t1766.t10.t49))
(step t1766.t10 (cl @p_1453 false) :rule subproof :discharge (t1766.t10.a0))
(step t1766.t11 (cl @p_1454 false) :rule resolution :premises (t1766.t9 t1766.t10))
(step t1766.t12 (cl @p_1454 @p_212) :rule implies_neg2)
(step t1766.t13 (cl @p_1454 @p_1454) :rule resolution :premises (t1766.t11 t1766.t12))
(step t1766.t14 (cl @p_1454) :rule contraction :premises (t1766.t13))
(step t1766.t15 (cl (= @p_1454 @p_1453)) :rule implies_simplify)
(step t1766.t16 (cl (not @p_1454) @p_1453) :rule equiv1 :premises (t1766.t15))
(step t1766.t17 (cl @p_1453) :rule resolution :premises (t1766.t14 t1766.t16))
(step t1766.t18 (cl @p_5) :rule resolution :premises (t1766.t8 t1766.t6 t1766.t17))
(step t1766.t19 (cl @p_1453) :rule resolution :premises (t1766.t4 t1766.t7 t1766.t18))
(step t1766.t20 (cl) :rule resolution :premises (t1766.t3 t1766.t19))
(step t1766 (cl @p_532 @p_586 @p_1451 @p_539 false) :rule subproof :discharge (t1766.a0 t1766.a1 t1766.a2 t1766.a3))
(step t1767 (cl @p_1449 @p_106) :rule and_pos :args (0))
(step t1768 (cl @p_1449 @p_585) :rule and_pos :args (1))
(step t1769 (cl @p_1449 @p_1447) :rule and_pos :args (2))
(step t1770 (cl @p_1449 @p_523) :rule and_pos :args (3))
(step t1771 (cl false @p_1449 @p_1449 @p_1449 @p_1449) :rule resolution :premises (t1766 t1767 t1768 t1769 t1770))
(step t1772 (cl @p_1449 @p_1449 @p_1449 @p_1449 false) :rule reordering :premises (t1771))
(step t1773 (cl @p_1449 false) :rule contraction :premises (t1772))
(step t1774 (cl @p_1450 false) :rule resolution :premises (t1765 t1773))
(step t1775 (cl @p_1450 @p_212) :rule implies_neg2)
(step t1776 (cl @p_1450 @p_1450) :rule resolution :premises (t1774 t1775))
(step t1777 (cl @p_1450) :rule contraction :premises (t1776))
(step t1778 (cl (= @p_1450 @p_1449)) :rule implies_simplify)
(step t1779 (cl (not @p_1450) @p_1449) :rule equiv1 :premises (t1778))
(step t1780 (cl @p_1449) :rule resolution :premises (t1777 t1779))
(step t1781 (cl @p_1446) :rule resolution :premises (t1764 t1780))
(step t1782 (cl @p_1440 @p_539 @p_586 @p_532) :rule not_and :premises (t1781))
(step t1783 (cl @p_1442 @p_1444) :rule or_neg :args (0))
(step t1784 (cl @p_1442 @p_1443) :rule or_neg :args (1))
(step t1785 (cl @p_1442 @p_588) :rule or_neg :args (2))
(step t1786 (cl @p_1442 @p_538) :rule or_neg :args (3))
(step t1787 (cl @p_1442 @p_1442 @p_1442 @p_1442) :rule resolution :premises (t1782 t1783 t1784 t1785 t1786))
(step t1788 (cl @p_1442) :rule contraction :premises (t1787))
(step t1789 (cl @p_1441) :rule resolution :premises (t1749 t1750 t1788))
(step t1790 (cl @p_1440 @p_5 @p_515 @p_532) :rule or :premises (t1789))
(step t1791 (cl @p_5 @p_1440 @p_515 @p_532) :rule reordering :premises (t1790))
(step t1792 (cl @p_515) :rule resolution :premises (t1791 t1746 t1748 t742))
(step t1793 (cl @p_116) :rule resolution :premises (t1588 t1792 t1602))
(step t1794 (cl @p_113) :rule resolution :premises (t87 t1793 t601 t628))
(step t1795 (cl @p_102) :rule resolution :premises (t85 t1746 t1748 t1794 t742))
(step t1796 (cl @p_743) :rule resolution :premises (t35 t1795 t1523))
(step t1797 (cl (not (! (= (! (or @p_806 @p_671 @p_929 @p_871 @p_1049) :named @p_1715) (! (or @p_798 @p_671 @p_974 @p_871 @p_1049) :named @p_1714)) :named @p_1728)) (not @p_1715) @p_1714) :rule equiv_pos2)
(step t1798 (cl (= @p_671 @p_671)) :rule refl)
(step t1799 (cl (= (* -1 (- 1 @p_57)) (* 1 (- @p_57 1)))) :rule poly_simp)
(step t1800 (cl (= @p_923 @p_58)) :rule poly_simp_rel :premises (t1799))
(step t1801 (cl (= @p_929 @p_974)) :rule cong :premises (t1800))
(step t1802 (cl (= @p_871 @p_871)) :rule refl)
(step t1803 (cl (= @p_1049 @p_1049)) :rule refl)
(step t1804 (cl @p_1728) :rule cong :premises (t656 t1798 t1801 t1802 t1803))
(step t1805 (cl (not (! (= (! (or @p_806 @p_671 @p_929 @p_871 @p_1052) :named @p_1716) @p_1715) :named @p_1727)) (not @p_1716) @p_1715) :rule equiv_pos2)
(step t1806 (cl (= @p_1716 @p_1714)) :rule cong :premises (t656 t1798 t1801 t1802 t690))
(step t1807 (cl (= @p_1714 @p_1715)) :rule symm :premises (t1804))
(step t1808 (cl @p_1727) :rule trans :premises (t1806 t1807))
(step t1809 (cl (! (=> (! (and @p_801 @p_670 @p_923 @p_870 @p_1051) :named @p_1717) false) :named @p_1719) @p_1717) :rule implies_neg1)
(anchor :step t1810)
(assume t1810.a0 @p_801)
(assume t1810.a1 @p_670)
(assume t1810.a2 @p_923)
(assume t1810.a3 @p_870)
(assume t1810.a4 @p_1051)
(step t1810.t0 (cl (not (! (= (! (< (! (+ @p_8 @p_799 @p_691 @p_57 @p_120) :named @p_1721) (! (+ 1 0 0 1 @p_850) :named @p_1720)) :named @p_1722) false) :named @p_1723)) (not @p_1722) false) :rule equiv_pos2)
(step t1810.t1 (cl (= @p_1722 (! (not (! (>= @p_1721 @p_1720) :named @p_1724)) :named @p_1725))) :rule rare_rewrite :args ("arith-elim-lt" @p_1721 @p_1720))
(step t1810.t2 (cl (= @p_1721 (! (+ @p_689 @p_690 @p_11 @p_8 @p_57 @p_668 @p_120 @p_6) :named @p_1554))) :rule poly_simp)
(step t1810.t3 (cl (= @p_1554 0)) :rule poly_simp)
(step t1810.t4 (cl (= @p_1721 0)) :rule trans :premises (t1810.t2 t1810.t3))
(step t1810.t5 (cl (= @p_1720 (! (+ 1 0 0 1 -2) :named @p_1726))) :rule cong :premises (t1310))
(step t1810.t6 (cl (= @p_1726 0)) :rule evaluate)
(step t1810.t7 (cl (= @p_1720 0)) :rule trans :premises (t1810.t5 t1810.t6))
(step t1810.t8 (cl (= @p_1724 @p_366)) :rule cong :premises (t1810.t4 t1810.t7))
(step t1810.t9 (cl (= @p_366 true)) :rule evaluate)
(step t1810.t10 (cl (= @p_1724 true)) :rule trans :premises (t1810.t8 t1810.t9))
(step t1810.t11 (cl (= @p_1725 @p_365)) :rule cong :premises (t1810.t10))
(step t1810.t12 (cl (= @p_365 false)) :rule evaluate)
(step t1810.t13 (cl (= @p_1725 false)) :rule trans :premises (t1810.t11 t1810.t12))
(step t1810.t14 (cl @p_1723) :rule trans :premises (t1810.t1 t1810.t13))
(step t1810.t15 (cl @p_1071 @p_808 (! (not @p_697) :named @p_1549) @p_974 @p_889 @p_1722) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 1/1 1/1))
(step t1810.t16 (cl @p_1070 @p_1052 @p_1066) :rule equiv_pos2)
(step t1810.t17 (cl (= @p_1066 @p_1051)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 1))
(step t1810.t18 (cl @p_1069) :rule symm :premises (t1810.t17))
(step t1810.t19 (cl @p_1066) :rule resolution :premises (t1810.t16 t1810.t18 t1810.a4))
(step t1810.t20 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1810.t21 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1810.t22 (cl @p_803) :rule poly_simp_rel :premises (t1810.t21))
(step t1810.t23 (cl (= @p_793 @p_800)) :rule symm :premises (t1810.t22))
(step t1810.t24 (cl @p_802) :rule trans :premises (t655 t1810.t23))
(step t1810.t25 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1810.t26 (cl @p_801) :rule trans :premises (t1810.t25 t755))
(step t1810.t27 (cl @p_800) :rule resolution :premises (t1810.t20 t1810.t24 t1810.t26))
(step t1810.t28 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t1810.t29 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t1810.t30 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t1810.t29))
(step t1810.t31 (cl @p_699) :rule symm :premises (t1810.t30))
(step t1810.t32 (cl @p_697) :rule resolution :premises (t1810.t28 t1810.t31 t758))
(step t1810.t33 (cl @p_58) :rule symm :premises (t1810.a2))
(step t1810.t34 (cl (=> @p_885 @p_884)) :rule la_mult_neg)
(step t1810.t35 (cl @p_887 @p_884) :rule implies :premises (t1810.t34))
(step t1810.t36 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1810.t37 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1810.t36))
(step t1810.t38 (cl @p_310) :rule evaluate)
(step t1810.t39 (cl @p_308) :rule resolution :premises (t1810.t37 t1810.t38))
(step t1810.t40 (cl @p_885) :rule and_intro :premises (t1810.t39 t1810.a3))
(step t1810.t41 (cl @p_884) :rule resolution :premises (t1810.t35 t1810.t40))
(step t1810.t42 (cl @p_1722) :rule resolution :premises (t1810.t15 t1810.t19 t1810.t27 t1810.t32 t1810.t33 t1810.t41))
(step t1810.t43 (cl false) :rule resolution :premises (t1810.t0 t1810.t14 t1810.t42))
(step t1810 (cl @p_806 @p_671 @p_929 @p_871 @p_1052 false) :rule subproof :discharge (t1810.a0 t1810.a1 t1810.a2 t1810.a3 t1810.a4))
(step t1811 (cl (! (not @p_1717) :named @p_1718) @p_801) :rule and_pos :args (0))
(step t1812 (cl @p_1718 @p_670) :rule and_pos :args (1))
(step t1813 (cl @p_1718 @p_923) :rule and_pos :args (2))
(step t1814 (cl @p_1718 @p_870) :rule and_pos :args (3))
(step t1815 (cl @p_1718 @p_1051) :rule and_pos :args (4))
(step t1816 (cl false @p_1718 @p_1718 @p_1718 @p_1718 @p_1718) :rule resolution :premises (t1810 t1811 t1812 t1813 t1814 t1815))
(step t1817 (cl @p_1718 @p_1718 @p_1718 @p_1718 @p_1718 false) :rule reordering :premises (t1816))
(step t1818 (cl @p_1718 false) :rule contraction :premises (t1817))
(step t1819 (cl @p_1719 false) :rule resolution :premises (t1809 t1818))
(step t1820 (cl @p_1719 @p_212) :rule implies_neg2)
(step t1821 (cl @p_1719 @p_1719) :rule resolution :premises (t1819 t1820))
(step t1822 (cl @p_1719) :rule contraction :premises (t1821))
(step t1823 (cl (= @p_1719 @p_1718)) :rule implies_simplify)
(step t1824 (cl (not @p_1719) @p_1718) :rule equiv1 :premises (t1823))
(step t1825 (cl @p_1718) :rule resolution :premises (t1822 t1824))
(step t1826 (cl @p_806 @p_671 @p_929 @p_871 @p_1052) :rule not_and :premises (t1825))
(step t1827 (cl @p_1716 @p_983) :rule or_neg :args (0))
(step t1828 (cl @p_1716 @p_677) :rule or_neg :args (1))
(step t1829 (cl @p_1716 (! (not @p_929) :named @p_1599)) :rule or_neg :args (2))
(step t1830 (cl @p_1716 @p_874) :rule or_neg :args (3))
(step t1831 (cl @p_1716 @p_1054) :rule or_neg :args (4))
(step t1832 (cl @p_1716 @p_1716 @p_1716 @p_1716 @p_1716) :rule resolution :premises (t1826 t1827 t1828 t1829 t1830 t1831))
(step t1833 (cl @p_1716) :rule contraction :premises (t1832))
(step t1834 (cl @p_1715) :rule resolution :premises (t1805 t1808 t1833))
(step t1835 (cl @p_1714) :rule resolution :premises (t1797 t1804 t1834))
(step t1836 (cl @p_798 @p_671 @p_974 @p_871 @p_1049) :rule or :premises (t1835))
(step t1837 (cl @p_671 @p_798 @p_871 @p_974 @p_1049) :rule reordering :premises (t1836))
(step t1838 (cl @p_807 @p_808 @p_793) :rule equiv_pos2)
(step t1839 (cl (= (* 1 (- @p_799 0)) @p_804)) :rule poly_simp)
(step t1840 (cl @p_803) :rule poly_simp_rel :premises (t1839))
(step t1841 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t1842 (cl (= @p_793 @p_800)) :rule symm :premises (t1840))
(step t1843 (cl @p_802) :rule trans :premises (t655 t1842))
(step t1844 (cl (= @p_669 @p_6)) :rule symm :premises (t758))
(step t1845 (cl @p_801) :rule trans :premises (t1844 t755))
(step t1846 (cl @p_800) :rule resolution :premises (t1841 t1843 t1845))
(step t1847 (cl @p_793) :rule resolution :premises (t1838 t1840 t1846))
(step t1848 (cl (not (! (= (! (or @p_974 (! (not (! (not (! (= @p_6 1) :named @p_1612)) :named @p_1613)) :named @p_1670) @p_911) :named @p_1703) (! (or @p_974 @p_1612 @p_911) :named @p_1702)) :named @p_1713)) (not @p_1703) @p_1702) :rule equiv_pos2)
(step t1849 (cl (= @p_1670 @p_1612)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1612))
(step t1850 (cl (= @p_911 @p_911)) :rule refl)
(step t1851 (cl @p_1713) :rule cong :premises (t1849 t1850))
(step t1852 (cl (! (and @p_58 @p_1613) :named @p_1705) @p_974 @p_1670) :rule and_neg)
(step t1853 (cl (! (=> @p_1705 @p_911) :named @p_1707) @p_1705) :rule implies_neg1)
(anchor :step t1854)
(assume t1854.a0 @p_58)
(assume t1854.a1 @p_1613)
(step t1854.t0 (cl (! (=> (! (and @p_1613 @p_58) :named @p_1708) @p_911) :named @p_1711) @p_1708) :rule implies_neg1)
(anchor :step t1854.t1)
(assume t1854.t1.a0 @p_1613)
(assume t1854.t1.a1 @p_58)
(step t1854.t1.t0 (cl (! (= (! (= @p_899 false) :named @p_1533) @p_911) :named @p_1536)) :rule equiv_simplify)
(step t1854.t1.t1 (cl (! (not @p_1533) :named @p_1535) @p_911) :rule equiv1 :premises (t1854.t1.t0))
(step t1854.t1.t2 (cl (= @p_899 @p_1612)) :rule cong :premises (t1854.t1.a1))
(step t1854.t1.t3 (cl (= (! (= @p_1612 false) :named @p_1712) @p_1613)) :rule equiv_simplify)
(step t1854.t1.t4 (cl @p_1712 @p_1670) :rule equiv2 :premises (t1854.t1.t3))
(step t1854.t1.t5 (cl (! (not @p_1670) :named @p_1704) @p_1612) :rule not_not)
(step t1854.t1.t6 (cl @p_1712 @p_1612) :rule resolution :premises (t1854.t1.t4 t1854.t1.t5))
(step t1854.t1.t7 (cl @p_1712) :rule resolution :premises (t1854.t1.t6 t1854.t1.a0))
(step t1854.t1.t8 (cl @p_1533) :rule trans :premises (t1854.t1.t2 t1854.t1.t7))
(step t1854.t1.t9 (cl @p_911) :rule resolution :premises (t1854.t1.t1 t1854.t1.t8))
(step t1854.t1 (cl @p_1670 @p_974 @p_911) :rule subproof :discharge (t1854.t1.a0 t1854.t1.a1))
(step t1854.t2 (cl (! (not @p_1708) :named @p_1710) @p_1613) :rule and_pos :args (0))
(step t1854.t3 (cl @p_1710 @p_58) :rule and_pos :args (1))
(step t1854.t4 (cl @p_911 @p_1710 @p_1710) :rule resolution :premises (t1854.t1 t1854.t2 t1854.t3))
(step t1854.t5 (cl @p_1710 @p_1710 @p_911) :rule reordering :premises (t1854.t4))
(step t1854.t6 (cl @p_1710 @p_911) :rule contraction :premises (t1854.t5))
(step t1854.t7 (cl @p_1711 @p_911) :rule resolution :premises (t1854.t0 t1854.t6))
(step t1854.t8 (cl @p_1711 @p_919) :rule implies_neg2)
(step t1854.t9 (cl @p_1711 @p_1711) :rule resolution :premises (t1854.t7 t1854.t8))
(step t1854.t10 (cl @p_1711) :rule contraction :premises (t1854.t9))
(step t1854.t11 (cl @p_1710 @p_911) :rule implies :premises (t1854.t10))
(step t1854.t12 (cl @p_1708) :rule and_intro :premises (t1854.a1 t1854.a0))
(step t1854.t13 (cl @p_911) :rule resolution :premises (t1854.t11 t1854.t12))
(step t1854 (cl @p_974 @p_1670 @p_911) :rule subproof :discharge (t1854.a0 t1854.a1))
(step t1855 (cl (! (not @p_1705) :named @p_1706) @p_58) :rule and_pos :args (0))
(step t1856 (cl @p_1706 @p_1613) :rule and_pos :args (1))
(step t1857 (cl @p_911 @p_1706 @p_1706) :rule resolution :premises (t1854 t1855 t1856))
(step t1858 (cl @p_1706 @p_1706 @p_911) :rule reordering :premises (t1857))
(step t1859 (cl @p_1706 @p_911) :rule contraction :premises (t1858))
(step t1860 (cl @p_1707 @p_911) :rule resolution :premises (t1853 t1859))
(step t1861 (cl @p_1707 @p_919) :rule implies_neg2)
(step t1862 (cl @p_1707 @p_1707) :rule resolution :premises (t1860 t1861))
(step t1863 (cl @p_1707) :rule contraction :premises (t1862))
(step t1864 (cl @p_1706 @p_911) :rule implies :premises (t1863))
(step t1865 (cl @p_974 @p_1670 @p_911) :rule resolution :premises (t1852 t1864))
(step t1866 (cl @p_1703 @p_1016) :rule or_neg :args (0))
(step t1867 (cl @p_1703 @p_1704) :rule or_neg :args (1))
(step t1868 (cl @p_1703 @p_919) :rule or_neg :args (2))
(step t1869 (cl @p_1703 @p_1703 @p_1703) :rule resolution :premises (t1865 t1866 t1867 t1868))
(step t1870 (cl @p_1703) :rule contraction :premises (t1869))
(step t1871 (cl @p_1702) :rule resolution :premises (t1848 t1851 t1870))
(step t1872 (cl @p_974 @p_1612 @p_911) :rule or :premises (t1871))
(step t1873 (cl @p_1612 @p_911 @p_974) :rule reordering :premises (t1872))
(step t1874 (cl (not (! (= (! (or @p_671 @p_792 @p_798 @p_1613 @p_911 @p_767 (! (not (! (= (! (modulo$ 1 2) :named @p_1658) (! (+ 1 (* -1 (! (times$ 2 (! (divide$ 1 2) :named @p_1655)) :named @p_1656))) :named @p_1657)) :named @p_1659)) :named @p_1667)) :named @p_1669) (! (or @p_671 @p_792 @p_798 @p_1613 @p_911 @p_759 @p_1667) :named @p_1668)) :named @p_1701)) (not @p_1669) @p_1668) :rule equiv_pos2)
(step t1875 (cl (= @p_1667 @p_1667)) :rule refl)
(step t1876 (cl @p_1701) :rule cong :premises (t1191 t1875))
(step t1877 (cl (! (=> (! (and @p_670 @p_786 @p_793 @p_1612 @p_899 @p_760 @p_1659) :named @p_1671) (! (and @p_801 (! (= @p_8 @p_1656) :named @p_1675) (! (= 1 @p_1657) :named @p_1674) (! (not @p_783) :named @p_1673)) :named @p_1676)) :named @p_1688) @p_1671) :rule implies_neg1)
(anchor :step t1878)
(assume t1878.a0 @p_670)
(assume t1878.a1 @p_786)
(assume t1878.a2 @p_793)
(assume t1878.a3 @p_1612)
(assume t1878.a4 @p_899)
(assume t1878.a5 @p_760)
(assume t1878.a6 @p_1659)
(step t1878.t0 (cl (! (=> (! (and @p_1612 @p_793) :named @p_1698) @p_1675) :named @p_1700) @p_1698) :rule implies_neg1)
(anchor :step t1878.t1)
(assume t1878.t1.a0 @p_1612)
(assume t1878.t1.a1 @p_793)
(step t1878.t1.t0 (cl @p_1095) :rule symm :premises (t1847))
(step t1878.t1.t1 (cl (= @p_7 @p_1655)) :rule cong :premises (t1878.t1.a0 t358))
(step t1878.t1.t2 (cl (= @p_668 @p_1656)) :rule cong :premises (t1878.t1.t1))
(step t1878.t1.t3 (cl @p_1675) :rule trans :premises (t1878.t1.t0 t1878.t1.t2))
(step t1878.t1 (cl @p_1613 @p_798 @p_1675) :rule subproof :discharge (t1878.t1.a0 t1878.t1.a1))
(step t1878.t2 (cl (! (not @p_1698) :named @p_1699) @p_1612) :rule and_pos :args (0))
(step t1878.t3 (cl @p_1699 @p_793) :rule and_pos :args (1))
(step t1878.t4 (cl @p_1675 @p_1699 @p_1699) :rule resolution :premises (t1878.t1 t1878.t2 t1878.t3))
(step t1878.t5 (cl @p_1699 @p_1699 @p_1675) :rule reordering :premises (t1878.t4))
(step t1878.t6 (cl @p_1699 @p_1675) :rule contraction :premises (t1878.t5))
(step t1878.t7 (cl @p_1700 @p_1675) :rule resolution :premises (t1878.t0 t1878.t6))
(step t1878.t8 (cl @p_1700 (! (not @p_1675) :named @p_1679)) :rule implies_neg2)
(step t1878.t9 (cl @p_1700 @p_1700) :rule resolution :premises (t1878.t7 t1878.t8))
(step t1878.t10 (cl @p_1700) :rule contraction :premises (t1878.t9))
(step t1878.t11 (cl @p_1699 @p_1675) :rule implies :premises (t1878.t10))
(step t1878.t12 (cl @p_1698) :rule and_intro :premises (t1878.a3 t1847))
(step t1878.t13 (cl @p_1675) :rule resolution :premises (t1878.t11 t1878.t12))
(step t1878.t14 (cl (! (=> (! (and (! (= @p_57 @p_1657) :named @p_1690) @p_899 @p_1612) :named @p_1691) @p_1674) :named @p_1697) @p_1691) :rule implies_neg1)
(anchor :step t1878.t15)
(assume t1878.t15.a0 @p_1690)
(assume t1878.t15.a1 @p_899)
(assume t1878.t15.a2 @p_1612)
(step t1878.t15.t0 (cl (! (= 1 @p_6) :named @p_1624)) :rule symm :premises (t1878.t15.a2))
(step t1878.t15.t1 (cl @p_1674) :rule trans :premises (t1878.t15.t0 t1878.t15.a1 t1878.t15.a0))
(step t1878.t15 (cl (! (not @p_1690) :named @p_1695) @p_911 @p_1613 @p_1674) :rule subproof :discharge (t1878.t15.a0 t1878.t15.a1 t1878.t15.a2))
(step t1878.t16 (cl (! (not @p_1691) :named @p_1696) @p_1690) :rule and_pos :args (0))
(step t1878.t17 (cl @p_1696 @p_899) :rule and_pos :args (1))
(step t1878.t18 (cl @p_1696 @p_1612) :rule and_pos :args (2))
(step t1878.t19 (cl @p_1674 @p_1696 @p_1696 @p_1696) :rule resolution :premises (t1878.t15 t1878.t16 t1878.t17 t1878.t18))
(step t1878.t20 (cl @p_1696 @p_1696 @p_1696 @p_1674) :rule reordering :premises (t1878.t19))
(step t1878.t21 (cl @p_1696 @p_1674) :rule contraction :premises (t1878.t20))
(step t1878.t22 (cl @p_1697 @p_1674) :rule resolution :premises (t1878.t14 t1878.t21))
(step t1878.t23 (cl @p_1697 (! (not @p_1674) :named @p_1680)) :rule implies_neg2)
(step t1878.t24 (cl @p_1697 @p_1697) :rule resolution :premises (t1878.t22 t1878.t23))
(step t1878.t25 (cl @p_1697) :rule contraction :premises (t1878.t24))
(step t1878.t26 (cl @p_1696 @p_1674) :rule implies :premises (t1878.t25))
(step t1878.t27 (cl (! (=> (! (and @p_1659 @p_1612) :named @p_1692) @p_1690) :named @p_1694) @p_1692) :rule implies_neg1)
(anchor :step t1878.t28)
(assume t1878.t28.a0 @p_1659)
(assume t1878.t28.a1 @p_1612)
(step t1878.t28.t0 (cl (= @p_57 @p_1658)) :rule cong :premises (t1878.t28.a1 t358))
(step t1878.t28.t1 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) (! (= 1 (! (+ @p_1656 @p_1658) :named @p_1661)) :named @p_1662)) :named @p_1663) (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))) @p_1659) :named @p_1660)) :named @p_1664)) (not @p_1663) @p_1660) :rule equiv_pos2)
(step t1878.t28.t2 (cl (= @p_1661 (! (+ @p_1658 @p_1656) :named @p_1665))) :rule poly_simp)
(step t1878.t28.t3 (cl (= @p_1662 (! (= 1 @p_1665) :named @p_1666))) :rule cong :premises (t1878.t28.t2))
(step t1878.t28.t4 (cl (= (* -1 (- 1 @p_1665)) (* 1 (- @p_1658 @p_1657)))) :rule poly_simp)
(step t1878.t28.t5 (cl (= @p_1666 @p_1659)) :rule poly_simp_rel :premises (t1878.t28.t4))
(step t1878.t28.t6 (cl (= @p_1662 @p_1659)) :rule trans :premises (t1878.t28.t3 t1878.t28.t5))
(step t1878.t28.t7 (cl @p_1664) :rule cong :premises (t1878.t28.t6))
(step t1878.t28.t8 (cl @p_1663 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t1878.t28.t9)
(assume t1878.t28.t9.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t1878.t28.t9.t0 (cl (or @p_190 @p_1662)) :rule forall_inst :args (2 1))
(step t1878.t28.t9.t1 (cl @p_190 @p_1662) :rule or :premises (t1878.t28.t9.t0))
(step t1878.t28.t9.t2 (cl @p_1662) :rule resolution :premises (t1878.t28.t9.t1 t226))
(step t1878.t28.t9 (cl @p_190 @p_1662) :rule subproof :discharge (t1878.t28.t9.a0))
(step t1878.t28.t10 (cl @p_1663 @p_1662) :rule resolution :premises (t1878.t28.t8 t1878.t28.t9))
(step t1878.t28.t11 (cl @p_1663 (not @p_1662)) :rule implies_neg2)
(step t1878.t28.t12 (cl @p_1663 @p_1663) :rule resolution :premises (t1878.t28.t10 t1878.t28.t11))
(step t1878.t28.t13 (cl @p_1663) :rule contraction :premises (t1878.t28.t12))
(step t1878.t28.t14 (cl @p_1660) :rule resolution :premises (t1878.t28.t1 t1878.t28.t7 t1878.t28.t13))
(step t1878.t28.t15 (cl @p_190 @p_1659) :rule implies :premises (t1878.t28.t14))
(step t1878.t28.t16 (cl @p_1659) :rule resolution :premises (t1878.t28.t15 t226))
(step t1878.t28.t17 (cl @p_1690) :rule trans :premises (t1878.t28.t0 t1878.t28.t16))
(step t1878.t28 (cl @p_1667 @p_1613 @p_1690) :rule subproof :discharge (t1878.t28.a0 t1878.t28.a1))
(step t1878.t29 (cl (! (not @p_1692) :named @p_1693) @p_1659) :rule and_pos :args (0))
(step t1878.t30 (cl @p_1693 @p_1612) :rule and_pos :args (1))
(step t1878.t31 (cl @p_1690 @p_1693 @p_1693) :rule resolution :premises (t1878.t28 t1878.t29 t1878.t30))
(step t1878.t32 (cl @p_1693 @p_1693 @p_1690) :rule reordering :premises (t1878.t31))
(step t1878.t33 (cl @p_1693 @p_1690) :rule contraction :premises (t1878.t32))
(step t1878.t34 (cl @p_1694 @p_1690) :rule resolution :premises (t1878.t27 t1878.t33))
(step t1878.t35 (cl @p_1694 @p_1695) :rule implies_neg2)
(step t1878.t36 (cl @p_1694 @p_1694) :rule resolution :premises (t1878.t34 t1878.t35))
(step t1878.t37 (cl @p_1694) :rule contraction :premises (t1878.t36))
(step t1878.t38 (cl @p_1693 @p_1690) :rule implies :premises (t1878.t37))
(step t1878.t39 (cl (not @p_1664) (not @p_1663) @p_1660) :rule equiv_pos2)
(step t1878.t40 (cl (= @p_1661 @p_1665)) :rule poly_simp)
(step t1878.t41 (cl (= @p_1662 @p_1666)) :rule cong :premises (t1878.t40))
(step t1878.t42 (cl (= (* -1 (- 1 @p_1665)) (* 1 (- @p_1658 @p_1657)))) :rule poly_simp)
(step t1878.t43 (cl (= @p_1666 @p_1659)) :rule poly_simp_rel :premises (t1878.t42))
(step t1878.t44 (cl (= @p_1662 @p_1659)) :rule trans :premises (t1878.t41 t1878.t43))
(step t1878.t45 (cl @p_1664) :rule cong :premises (t1878.t44))
(step t1878.t46 (cl @p_1663 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t1878.t47)
(assume t1878.t47.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t1878.t47.t0 (cl (or @p_190 @p_1662)) :rule forall_inst :args (2 1))
(step t1878.t47.t1 (cl @p_190 @p_1662) :rule or :premises (t1878.t47.t0))
(step t1878.t47.t2 (cl @p_1662) :rule resolution :premises (t1878.t47.t1 t226))
(step t1878.t47 (cl @p_190 @p_1662) :rule subproof :discharge (t1878.t47.a0))
(step t1878.t48 (cl @p_1663 @p_1662) :rule resolution :premises (t1878.t46 t1878.t47))
(step t1878.t49 (cl @p_1663 (not @p_1662)) :rule implies_neg2)
(step t1878.t50 (cl @p_1663 @p_1663) :rule resolution :premises (t1878.t48 t1878.t49))
(step t1878.t51 (cl @p_1663) :rule contraction :premises (t1878.t50))
(step t1878.t52 (cl @p_1660) :rule resolution :premises (t1878.t39 t1878.t45 t1878.t51))
(step t1878.t53 (cl @p_190 @p_1659) :rule implies :premises (t1878.t52))
(step t1878.t54 (cl @p_1659) :rule resolution :premises (t1878.t53 t226))
(step t1878.t55 (cl @p_1692) :rule and_intro :premises (t1878.t54 t1878.a3))
(step t1878.t56 (cl @p_1690) :rule resolution :premises (t1878.t38 t1878.t55))
(step t1878.t57 (cl @p_1691) :rule and_intro :premises (t1878.t56 t1878.a4 t1878.a3))
(step t1878.t58 (cl @p_1674) :rule resolution :premises (t1878.t26 t1878.t57))
(step t1878.t59 (cl (! (=> @p_760 @p_1673) :named @p_1689) @p_760) :rule implies_neg1)
(anchor :step t1878.t60)
(assume t1878.t60.a0 @p_760)
(step t1878.t60.t0 (cl @p_1673) :rule not_symm :premises (t1878.t60.a0))
(step t1878.t60 (cl @p_767 @p_1673) :rule subproof :discharge (t1878.t60.a0))
(step t1878.t61 (cl @p_1689 @p_1673) :rule resolution :premises (t1878.t59 t1878.t60))
(step t1878.t62 (cl @p_1689 (! (not @p_1673) :named @p_1681)) :rule implies_neg2)
(step t1878.t63 (cl @p_1689 @p_1689) :rule resolution :premises (t1878.t61 t1878.t62))
(step t1878.t64 (cl @p_1689) :rule contraction :premises (t1878.t63))
(step t1878.t65 (cl @p_767 @p_1673) :rule implies :premises (t1878.t64))
(step t1878.t66 (cl @p_1673) :rule resolution :premises (t1878.t65 t1878.a5))
(step t1878.t67 (cl @p_1676) :rule and_intro :premises (t1845 t1878.t13 t1878.t58 t1878.t66))
(step t1878 (cl @p_671 @p_792 @p_798 @p_1613 @p_911 @p_767 @p_1667 @p_1676) :rule subproof :discharge (t1878.a0 t1878.a1 t1878.a2 t1878.a3 t1878.a4 t1878.a5 t1878.a6))
(step t1879 (cl (! (not @p_1671) :named @p_1672) @p_670) :rule and_pos :args (0))
(step t1880 (cl @p_1672 @p_786) :rule and_pos :args (1))
(step t1881 (cl @p_1672 @p_793) :rule and_pos :args (2))
(step t1882 (cl @p_1672 @p_1612) :rule and_pos :args (3))
(step t1883 (cl @p_1672 @p_899) :rule and_pos :args (4))
(step t1884 (cl @p_1672 @p_760) :rule and_pos :args (5))
(step t1885 (cl @p_1672 @p_1659) :rule and_pos :args (6))
(step t1886 (cl @p_1676 @p_1672 @p_1672 @p_1672 @p_1672 @p_1672 @p_1672 @p_1672) :rule resolution :premises (t1878 t1879 t1880 t1881 t1882 t1883 t1884 t1885))
(step t1887 (cl @p_1672 @p_1672 @p_1672 @p_1672 @p_1672 @p_1672 @p_1672 @p_1676) :rule reordering :premises (t1886))
(step t1888 (cl @p_1672 @p_1676) :rule contraction :premises (t1887))
(step t1889 (cl @p_1688 @p_1676) :rule resolution :premises (t1877 t1888))
(step t1890 (cl @p_1688 (! (not @p_1676) :named @p_1677)) :rule implies_neg2)
(step t1891 (cl @p_1688 @p_1688) :rule resolution :premises (t1889 t1890))
(step t1892 (cl @p_1688) :rule contraction :premises (t1891))
(step t1893 (cl @p_1672 @p_1676) :rule implies :premises (t1892))
(step t1894 (cl (! (=> @p_1676 false) :named @p_1678) @p_1676) :rule implies_neg1)
(anchor :step t1895)
(assume t1895.a0 @p_801)
(assume t1895.a1 @p_1675)
(assume t1895.a2 @p_1674)
(assume t1895.a3 @p_1673)
(step t1895.t0 (cl (! (=> (! (and @p_801 @p_1675 @p_1674) :named @p_1682) @p_783) :named @p_1685) @p_1682) :rule implies_neg1)
(anchor :step t1895.t1)
(assume t1895.t1.a0 @p_801)
(assume t1895.t1.a1 @p_1675)
(assume t1895.t1.a2 @p_1674)
(step t1895.t1.t0 (cl (not (! (= @p_1674 (! (= @p_1656 0) :named @p_1686)) :named @p_1687)) @p_1680 @p_1686) :rule equiv_pos2)
(step t1895.t1.t1 (cl (= (* 1 (- 1 @p_1657)) (* 1 (- @p_1656 0)))) :rule poly_simp)
(step t1895.t1.t2 (cl @p_1687) :rule poly_simp_rel :premises (t1895.t1.t1))
(step t1895.t1.t3 (cl @p_1686) :rule resolution :premises (t1895.t1.t0 t1895.t1.t2 t1895.t1.a2))
(step t1895.t1.t4 (cl (= 0 @p_1656)) :rule symm :premises (t1895.t1.t3))
(step t1895.t1.t5 (cl (= @p_1656 @p_8)) :rule symm :premises (t1895.t1.a1))
(step t1895.t1.t6 (cl @p_1095) :rule symm :premises (t1847))
(step t1895.t1.t7 (cl @p_783) :rule trans :premises (t1895.t1.t4 t1895.t1.t5 t1895.t1.t6))
(step t1895.t1 (cl @p_806 @p_1679 @p_1680 @p_783) :rule subproof :discharge (t1895.t1.a0 t1895.t1.a1 t1895.t1.a2))
(step t1895.t2 (cl (! (not @p_1682) :named @p_1684) @p_801) :rule and_pos :args (0))
(step t1895.t3 (cl @p_1684 @p_1675) :rule and_pos :args (1))
(step t1895.t4 (cl @p_1684 @p_1674) :rule and_pos :args (2))
(step t1895.t5 (cl @p_783 @p_1684 @p_1684 @p_1684) :rule resolution :premises (t1895.t1 t1895.t2 t1895.t3 t1895.t4))
(step t1895.t6 (cl @p_1684 @p_1684 @p_1684 @p_783) :rule reordering :premises (t1895.t5))
(step t1895.t7 (cl @p_1684 @p_783) :rule contraction :premises (t1895.t6))
(step t1895.t8 (cl @p_1685 @p_783) :rule resolution :premises (t1895.t0 t1895.t7))
(step t1895.t9 (cl @p_1685 @p_1673) :rule implies_neg2)
(step t1895.t10 (cl @p_1685 @p_1685) :rule resolution :premises (t1895.t8 t1895.t9))
(step t1895.t11 (cl @p_1685) :rule contraction :premises (t1895.t10))
(step t1895.t12 (cl @p_1684 @p_783) :rule implies :premises (t1895.t11))
(step t1895.t13 (cl @p_1682) :rule and_intro :premises (t1845 t1895.a1 t1895.a2))
(step t1895.t14 (cl @p_783) :rule resolution :premises (t1895.t12 t1895.t13))
(step t1895.t15 (cl) :rule resolution :premises (t1895.t14 t1895.a3))
(step t1895 (cl @p_806 @p_1679 @p_1680 @p_1681 false) :rule subproof :discharge (t1895.a0 t1895.a1 t1895.a2 t1895.a3))
(step t1896 (cl @p_1677 @p_801) :rule and_pos :args (0))
(step t1897 (cl @p_1677 @p_1675) :rule and_pos :args (1))
(step t1898 (cl @p_1677 @p_1674) :rule and_pos :args (2))
(step t1899 (cl @p_1677 @p_1673) :rule and_pos :args (3))
(step t1900 (cl false @p_1677 @p_1677 @p_1677 @p_1677) :rule resolution :premises (t1895 t1896 t1897 t1898 t1899))
(step t1901 (cl @p_1677 @p_1677 @p_1677 @p_1677 false) :rule reordering :premises (t1900))
(step t1902 (cl @p_1677 false) :rule contraction :premises (t1901))
(step t1903 (cl @p_1678 false) :rule resolution :premises (t1894 t1902))
(step t1904 (cl @p_1678 @p_212) :rule implies_neg2)
(step t1905 (cl @p_1678 @p_1678) :rule resolution :premises (t1903 t1904))
(step t1906 (cl @p_1678) :rule contraction :premises (t1905))
(step t1907 (cl (= @p_1678 @p_1677)) :rule implies_simplify)
(step t1908 (cl (not @p_1678) @p_1677) :rule equiv1 :premises (t1907))
(step t1909 (cl @p_1677) :rule resolution :premises (t1906 t1908))
(step t1910 (cl @p_1672) :rule resolution :premises (t1893 t1909))
(step t1911 (cl @p_671 @p_792 @p_798 @p_1613 @p_911 @p_767 @p_1667) :rule not_and :premises (t1910))
(step t1912 (cl @p_1669 @p_677) :rule or_neg :args (0))
(step t1913 (cl @p_1669 @p_1017) :rule or_neg :args (1))
(step t1914 (cl @p_1669 (not @p_798)) :rule or_neg :args (2))
(step t1915 (cl @p_1669 @p_1670) :rule or_neg :args (3))
(step t1916 (cl @p_1669 @p_919) :rule or_neg :args (4))
(step t1917 (cl @p_1669 @p_1055) :rule or_neg :args (5))
(step t1918 (cl @p_1669 (not @p_1667)) :rule or_neg :args (6))
(step t1919 (cl @p_1669 @p_1669 @p_1669 @p_1669 @p_1669 @p_1669 @p_1669) :rule resolution :premises (t1911 t1912 t1913 t1914 t1915 t1916 t1917 t1918))
(step t1920 (cl @p_1669) :rule contraction :premises (t1919))
(step t1921 (cl @p_1668) :rule resolution :premises (t1874 t1876 t1920))
(step t1922 (cl @p_671 @p_792 @p_798 @p_1613 @p_911 @p_759 @p_1667) :rule or :premises (t1921))
(step t1923 (cl @p_760) :rule resolution :premises (t1458 t1795 t1509 t1494 t1474))
(step t1924 (cl (not @p_1664) (not @p_1663) @p_1660) :rule equiv_pos2)
(step t1925 (cl (= @p_1661 @p_1665)) :rule poly_simp)
(step t1926 (cl (= @p_1662 @p_1666)) :rule cong :premises (t1925))
(step t1927 (cl (= (* -1 (- 1 @p_1665)) (* 1 (- @p_1658 @p_1657)))) :rule poly_simp)
(step t1928 (cl (= @p_1666 @p_1659)) :rule poly_simp_rel :premises (t1927))
(step t1929 (cl (= @p_1662 @p_1659)) :rule trans :premises (t1926 t1928))
(step t1930 (cl @p_1664) :rule cong :premises (t1929))
(step t1931 (cl @p_1663 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0))))) :rule implies_neg1)
(anchor :step t1932)
(assume t1932.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v1 (+ (times$ ?v0 (divide$ ?v1 ?v0)) (modulo$ ?v1 ?v0)))))
(step t1932.t0 (cl (or @p_190 @p_1662)) :rule forall_inst :args (2 1))
(step t1932.t1 (cl @p_190 @p_1662) :rule or :premises (t1932.t0))
(step t1932.t2 (cl @p_1662) :rule resolution :premises (t1932.t1 t226))
(step t1932 (cl @p_190 @p_1662) :rule subproof :discharge (t1932.a0))
(step t1933 (cl @p_1663 @p_1662) :rule resolution :premises (t1931 t1932))
(step t1934 (cl @p_1663 (not @p_1662)) :rule implies_neg2)
(step t1935 (cl @p_1663 @p_1663) :rule resolution :premises (t1933 t1934))
(step t1936 (cl @p_1663) :rule contraction :premises (t1935))
(step t1937 (cl @p_1660) :rule resolution :premises (t1924 t1930 t1936))
(step t1938 (cl @p_190 @p_1659) :rule implies :premises (t1937))
(step t1939 (cl @p_1659) :rule resolution :premises (t1938 t226))
(step t1940 (cl (not (! (= (! (or @p_871 @p_671 (! (not (! (not (! (>= @p_669 2) :named @p_1614)) :named @p_1615)) :named @p_1619)) :named @p_1642) (! (or @p_871 @p_671 @p_1614) :named @p_1641)) :named @p_1654)) (not @p_1642) @p_1641) :rule equiv_pos2)
(step t1941 (cl (= @p_1619 @p_1614)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1614))
(step t1942 (cl @p_1654) :rule cong :premises (t1941))
(step t1943 (cl (! (=> (! (and @p_870 @p_670 @p_1615) :named @p_1643) false) :named @p_1645) @p_1643) :rule implies_neg1)
(anchor :step t1944)
(assume t1944.a0 @p_870)
(assume t1944.a1 @p_670)
(assume t1944.a2 @p_1615)
(step t1944.t0 (cl (not (! (= (! (< (! (+ @p_669 @p_120 @p_691) :named @p_1647) (! (+ 2 @p_850 0) :named @p_1646)) :named @p_1648) false) :named @p_1649)) (not @p_1648) false) :rule equiv_pos2)
(step t1944.t1 (cl (= @p_1648 (! (not (! (>= @p_1647 @p_1646) :named @p_1650)) :named @p_1651))) :rule rare_rewrite :args ("arith-elim-lt" @p_1647 @p_1646))
(step t1944.t2 (cl (= @p_1647 (! (+ @p_689 @p_690 @p_57 @p_668 @p_120 @p_6) :named @p_1653))) :rule poly_simp)
(step t1944.t3 (cl (= @p_1653 0)) :rule poly_simp)
(step t1944.t4 (cl (= @p_1647 0)) :rule trans :premises (t1944.t2 t1944.t3))
(step t1944.t5 (cl (= @p_1646 (! (+ 2 -2 0) :named @p_1652))) :rule cong :premises (t1310 t604))
(step t1944.t6 (cl (= @p_1652 0)) :rule evaluate)
(step t1944.t7 (cl (= @p_1646 0)) :rule trans :premises (t1944.t5 t1944.t6))
(step t1944.t8 (cl (= @p_1650 @p_366)) :rule cong :premises (t1944.t4 t1944.t7))
(step t1944.t9 (cl (= @p_366 true)) :rule evaluate)
(step t1944.t10 (cl (= @p_1650 true)) :rule trans :premises (t1944.t8 t1944.t9))
(step t1944.t11 (cl (= @p_1651 @p_365)) :rule cong :premises (t1944.t10))
(step t1944.t12 (cl (= @p_365 false)) :rule evaluate)
(step t1944.t13 (cl (= @p_1651 false)) :rule trans :premises (t1944.t11 t1944.t12))
(step t1944.t14 (cl @p_1649) :rule trans :premises (t1944.t1 t1944.t13))
(step t1944.t15 (cl (! (not (! (< @p_669 2) :named @p_1626)) :named @p_1640) @p_889 @p_1549 @p_1648) :rule la_generic :args (1/1 1/1 -1/1 1/1))
(step t1944.t16 (cl (! (not (! (= @p_1615 @p_1626) :named @p_1637)) :named @p_1639) @p_1619 @p_1626) :rule equiv_pos2)
(step t1944.t17 (cl (! (= @p_1626 @p_1615) :named @p_1638)) :rule rare_rewrite :args ("arith-elim-lt" @p_669 2))
(step t1944.t18 (cl @p_1637) :rule symm :premises (t1944.t17))
(step t1944.t19 (cl @p_1626) :rule resolution :premises (t1944.t16 t1944.t18 t1944.a2))
(step t1944.t20 (cl (=> @p_885 @p_884)) :rule la_mult_neg)
(step t1944.t21 (cl @p_887 @p_884) :rule implies :premises (t1944.t20))
(step t1944.t22 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1944.t23 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1944.t22))
(step t1944.t24 (cl @p_310) :rule evaluate)
(step t1944.t25 (cl @p_308) :rule resolution :premises (t1944.t23 t1944.t24))
(step t1944.t26 (cl @p_885) :rule and_intro :premises (t1944.t25 t1944.a0))
(step t1944.t27 (cl @p_884) :rule resolution :premises (t1944.t21 t1944.t26))
(step t1944.t28 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t1944.t29 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t1944.t30 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t1944.t29))
(step t1944.t31 (cl @p_699) :rule symm :premises (t1944.t30))
(step t1944.t32 (cl @p_697) :rule resolution :premises (t1944.t28 t1944.t31 t758))
(step t1944.t33 (cl @p_1648) :rule resolution :premises (t1944.t15 t1944.t19 t1944.t27 t1944.t32))
(step t1944.t34 (cl false) :rule resolution :premises (t1944.t0 t1944.t14 t1944.t33))
(step t1944 (cl @p_871 @p_671 @p_1619 false) :rule subproof :discharge (t1944.a0 t1944.a1 t1944.a2))
(step t1945 (cl (! (not @p_1643) :named @p_1644) @p_870) :rule and_pos :args (0))
(step t1946 (cl @p_1644 @p_670) :rule and_pos :args (1))
(step t1947 (cl @p_1644 @p_1615) :rule and_pos :args (2))
(step t1948 (cl false @p_1644 @p_1644 @p_1644) :rule resolution :premises (t1944 t1945 t1946 t1947))
(step t1949 (cl @p_1644 @p_1644 @p_1644 false) :rule reordering :premises (t1948))
(step t1950 (cl @p_1644 false) :rule contraction :premises (t1949))
(step t1951 (cl @p_1645 false) :rule resolution :premises (t1943 t1950))
(step t1952 (cl @p_1645 @p_212) :rule implies_neg2)
(step t1953 (cl @p_1645 @p_1645) :rule resolution :premises (t1951 t1952))
(step t1954 (cl @p_1645) :rule contraction :premises (t1953))
(step t1955 (cl (= @p_1645 @p_1644)) :rule implies_simplify)
(step t1956 (cl (not @p_1645) @p_1644) :rule equiv1 :premises (t1955))
(step t1957 (cl @p_1644) :rule resolution :premises (t1954 t1956))
(step t1958 (cl @p_871 @p_671 @p_1619) :rule not_and :premises (t1957))
(step t1959 (cl @p_1642 @p_874) :rule or_neg :args (0))
(step t1960 (cl @p_1642 @p_677) :rule or_neg :args (1))
(step t1961 (cl @p_1642 (not @p_1619)) :rule or_neg :args (2))
(step t1962 (cl @p_1642 @p_1642 @p_1642) :rule resolution :premises (t1958 t1959 t1960 t1961))
(step t1963 (cl @p_1642) :rule contraction :premises (t1962))
(step t1964 (cl @p_1641) :rule resolution :premises (t1940 t1942 t1963))
(step t1965 (cl @p_871 @p_671 @p_1614) :rule or :premises (t1964))
(step t1966 (cl @p_671 @p_871 @p_1614) :rule reordering :premises (t1965))
(step t1967 (cl (! (and @p_670 @p_1612) :named @p_1616) @p_671 @p_1613) :rule and_neg)
(step t1968 (cl (! (=> @p_1616 @p_1615) :named @p_1618) @p_1616) :rule implies_neg1)
(anchor :step t1969)
(assume t1969.a0 @p_670)
(assume t1969.a1 @p_1612)
(step t1969.t0 (cl (! (=> (! (= 1 @p_669) :named @p_1620) @p_1615) :named @p_1625) @p_1620) :rule implies_neg1)
(anchor :step t1969.t1)
(assume t1969.t1.a0 @p_1620)
(step t1969.t1.t0 (cl (not @p_1638) @p_1640 @p_1615) :rule equiv_pos2)
(step t1969.t1.t1 (cl @p_1638) :rule rare_rewrite :args ("arith-elim-lt" @p_669 2))
(step t1969.t1.t2 (cl @p_1639 @p_1619 @p_1626) :rule equiv_pos2)
(step t1969.t1.t3 (cl @p_1637) :rule symm :premises (t1969.t1.t1))
(step t1969.t1.t4 (cl (! (=> @p_1614 false) :named @p_1627) @p_1614) :rule implies_neg1)
(anchor :step t1969.t1.t5)
(assume t1969.t1.t5.a0 @p_1614)
(step t1969.t1.t5.t0 (cl (not (! (= (! (<= (! (+ (! (* -1 @p_669) :named @p_1628) @p_669) :named @p_1629) @p_851) :named @p_1630) false) :named @p_1635)) (not @p_1630) false) :rule equiv_pos2)
(step t1969.t1.t5.t1 (cl (= @p_1629 (! (+ @p_722 @p_721) :named @p_1636))) :rule poly_simp)
(step t1969.t1.t5.t2 (cl (= @p_722 0)) :rule poly_simp)
(step t1969.t1.t5.t3 (cl (= @p_721 0)) :rule poly_simp)
(step t1969.t1.t5.t4 (cl (= @p_1636 @p_864)) :rule cong :premises (t1969.t1.t5.t2 t1969.t1.t5.t3))
(step t1969.t1.t5.t5 (cl (= @p_864 0)) :rule evaluate)
(step t1969.t1.t5.t6 (cl (= @p_1636 0)) :rule trans :premises (t1969.t1.t5.t4 t1969.t1.t5.t5))
(step t1969.t1.t5.t7 (cl (= @p_1629 0)) :rule trans :premises (t1969.t1.t5.t1 t1969.t1.t5.t6))
(step t1969.t1.t5.t8 (cl (= 1 1)) :rule refl)
(step t1969.t1.t5.t9 (cl (= @p_851 @p_862)) :rule cong :premises (t1310 t1969.t1.t5.t8))
(step t1969.t1.t5.t10 (cl (= @p_862 -1)) :rule evaluate)
(step t1969.t1.t5.t11 (cl (= @p_851 -1)) :rule trans :premises (t1969.t1.t5.t9 t1969.t1.t5.t10))
(step t1969.t1.t5.t12 (cl (= @p_1630 @p_323)) :rule cong :premises (t1969.t1.t5.t7 t1969.t1.t5.t11))
(step t1969.t1.t5.t13 (cl (= @p_323 false)) :rule evaluate)
(step t1969.t1.t5.t14 (cl @p_1635) :rule trans :premises (t1969.t1.t5.t12 t1969.t1.t5.t13))
(step t1969.t1.t5.t15 (cl (not (! (<= @p_1628 @p_850) :named @p_1632)) (not (! (= @p_669 1) :named @p_1631)) @p_1630) :rule la_generic :args (1/1 -1/1 1/1))
(step t1969.t1.t5.t16 (cl (=> (! (and @p_308 @p_1614) :named @p_1633) @p_1632)) :rule la_mult_neg)
(step t1969.t1.t5.t17 (cl (not @p_1633) @p_1632) :rule implies :premises (t1969.t1.t5.t16))
(step t1969.t1.t5.t18 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t1969.t1.t5.t19 (cl (not @p_310) @p_308) :rule equiv1 :premises (t1969.t1.t5.t18))
(step t1969.t1.t5.t20 (cl @p_310) :rule evaluate)
(step t1969.t1.t5.t21 (cl @p_308) :rule resolution :premises (t1969.t1.t5.t19 t1969.t1.t5.t20))
(step t1969.t1.t5.t22 (cl @p_1633) :rule and_intro :premises (t1969.t1.t5.t21 t1969.t1.t5.a0))
(step t1969.t1.t5.t23 (cl @p_1632) :rule resolution :premises (t1969.t1.t5.t17 t1969.t1.t5.t22))
(step t1969.t1.t5.t24 (cl @p_1631) :rule symm :premises (t1969.t1.a0))
(step t1969.t1.t5.t25 (cl @p_1630) :rule resolution :premises (t1969.t1.t5.t15 t1969.t1.t5.t23 t1969.t1.t5.t24))
(step t1969.t1.t5.t26 (cl false) :rule resolution :premises (t1969.t1.t5.t0 t1969.t1.t5.t14 t1969.t1.t5.t25))
(step t1969.t1.t5 (cl @p_1615 false) :rule subproof :discharge (t1969.t1.t5.a0))
(step t1969.t1.t6 (cl @p_1627 false) :rule resolution :premises (t1969.t1.t4 t1969.t1.t5))
(step t1969.t1.t7 (cl @p_1627 @p_212) :rule implies_neg2)
(step t1969.t1.t8 (cl @p_1627 @p_1627) :rule resolution :premises (t1969.t1.t6 t1969.t1.t7))
(step t1969.t1.t9 (cl @p_1627) :rule contraction :premises (t1969.t1.t8))
(step t1969.t1.t10 (cl (= @p_1627 @p_1615)) :rule implies_simplify)
(step t1969.t1.t11 (cl (not @p_1627) @p_1615) :rule equiv1 :premises (t1969.t1.t10))
(step t1969.t1.t12 (cl @p_1615) :rule resolution :premises (t1969.t1.t9 t1969.t1.t11))
(step t1969.t1.t13 (cl @p_1626) :rule resolution :premises (t1969.t1.t2 t1969.t1.t3 t1969.t1.t12))
(step t1969.t1.t14 (cl @p_1615) :rule resolution :premises (t1969.t1.t0 t1969.t1.t1 t1969.t1.t13))
(step t1969.t1 (cl (! (not @p_1620) :named @p_1623) @p_1615) :rule subproof :discharge (t1969.t1.a0))
(step t1969.t2 (cl @p_1625 @p_1615) :rule resolution :premises (t1969.t0 t1969.t1))
(step t1969.t3 (cl @p_1625 @p_1619) :rule implies_neg2)
(step t1969.t4 (cl @p_1625 @p_1625) :rule resolution :premises (t1969.t2 t1969.t3))
(step t1969.t5 (cl @p_1625) :rule contraction :premises (t1969.t4))
(step t1969.t6 (cl @p_1623 @p_1615) :rule implies :premises (t1969.t5))
(step t1969.t7 (cl (! (=> @p_1616 @p_1620) :named @p_1622) @p_1616) :rule implies_neg1)
(anchor :step t1969.t8)
(assume t1969.t8.a0 @p_670)
(assume t1969.t8.a1 @p_1612)
(step t1969.t8.t0 (cl @p_1624) :rule symm :premises (t1969.t8.a1))
(step t1969.t8.t1 (cl @p_1620) :rule trans :premises (t1969.t8.t0 t758))
(step t1969.t8 (cl @p_671 @p_1613 @p_1620) :rule subproof :discharge (t1969.t8.a0 t1969.t8.a1))
(step t1969.t9 (cl (! (not @p_1616) :named @p_1617) @p_670) :rule and_pos :args (0))
(step t1969.t10 (cl @p_1617 @p_1612) :rule and_pos :args (1))
(step t1969.t11 (cl @p_1620 @p_1617 @p_1617) :rule resolution :premises (t1969.t8 t1969.t9 t1969.t10))
(step t1969.t12 (cl @p_1617 @p_1617 @p_1620) :rule reordering :premises (t1969.t11))
(step t1969.t13 (cl @p_1617 @p_1620) :rule contraction :premises (t1969.t12))
(step t1969.t14 (cl @p_1622 @p_1620) :rule resolution :premises (t1969.t7 t1969.t13))
(step t1969.t15 (cl @p_1622 @p_1623) :rule implies_neg2)
(step t1969.t16 (cl @p_1622 @p_1622) :rule resolution :premises (t1969.t14 t1969.t15))
(step t1969.t17 (cl @p_1622) :rule contraction :premises (t1969.t16))
(step t1969.t18 (cl @p_1617 @p_1620) :rule implies :premises (t1969.t17))
(step t1969.t19 (cl @p_1616) :rule and_intro :premises (t758 t1969.a1))
(step t1969.t20 (cl @p_1620) :rule resolution :premises (t1969.t18 t1969.t19))
(step t1969.t21 (cl @p_1615) :rule resolution :premises (t1969.t6 t1969.t20))
(step t1969 (cl @p_671 @p_1613 @p_1615) :rule subproof :discharge (t1969.a0 t1969.a1))
(step t1970 (cl @p_1617 @p_670) :rule and_pos :args (0))
(step t1971 (cl @p_1617 @p_1612) :rule and_pos :args (1))
(step t1972 (cl @p_1615 @p_1617 @p_1617) :rule resolution :premises (t1969 t1970 t1971))
(step t1973 (cl @p_1617 @p_1617 @p_1615) :rule reordering :premises (t1972))
(step t1974 (cl @p_1617 @p_1615) :rule contraction :premises (t1973))
(step t1975 (cl @p_1618 @p_1615) :rule resolution :premises (t1968 t1974))
(step t1976 (cl @p_1618 @p_1619) :rule implies_neg2)
(step t1977 (cl @p_1618 @p_1618) :rule resolution :premises (t1975 t1976))
(step t1978 (cl @p_1618) :rule contraction :premises (t1977))
(step t1979 (cl @p_1617 @p_1615) :rule implies :premises (t1978))
(step t1980 (cl @p_671 @p_1613 @p_1615) :rule resolution :premises (t1967 t1979))
(step t1981 (cl @p_1613) :rule resolution :premises (t1922 t1847 t1923 t1939 t755 t758 t1308 t1329 t1792 t1966 t758 t1980 t758))
(step t1982 (cl (not (! (= (! (or @p_671 @p_673 @p_66 @p_1353 @p_916) :named @p_1576) (! (or @p_671 @p_112 @p_66 @p_732 @p_913) :named @p_1575)) :named @p_1595)) (not @p_1576) @p_1575) :rule equiv_pos2)
(step t1983 (cl @p_1595) :rule cong :premises (t38 t882 t883 t761))
(step t1984 (cl (! (=> (! (and @p_670 @p_113 @p_63 @p_740 @p_915) :named @p_1577) (! (and @p_740 @p_915 @p_1188 @p_670 @p_113) :named @p_1579)) :named @p_1594) @p_1577) :rule implies_neg1)
(anchor :step t1985)
(assume t1985.a0 @p_670)
(assume t1985.a1 @p_113)
(assume t1985.a2 @p_63)
(assume t1985.a3 @p_740)
(assume t1985.a4 @p_915)
(step t1985.t0 (cl @p_1224 @p_63) :rule implies_neg1)
(anchor :step t1985.t1)
(assume t1985.t1.a0 @p_63)
(step t1985.t1.t0 (cl @p_1188) :rule symm :premises (t1985.t1.a0))
(step t1985.t1 (cl @p_66 @p_1188) :rule subproof :discharge (t1985.t1.a0))
(step t1985.t2 (cl @p_1224 @p_1188) :rule resolution :premises (t1985.t0 t1985.t1))
(step t1985.t3 (cl @p_1224 @p_1192) :rule implies_neg2)
(step t1985.t4 (cl @p_1224 @p_1224) :rule resolution :premises (t1985.t2 t1985.t3))
(step t1985.t5 (cl @p_1224) :rule contraction :premises (t1985.t4))
(step t1985.t6 (cl @p_66 @p_1188) :rule implies :premises (t1985.t5))
(step t1985.t7 (cl @p_1188) :rule resolution :premises (t1985.t6 t1985.a2))
(step t1985.t8 (cl @p_1579) :rule and_intro :premises (t1985.a3 t1985.a4 t1985.t7 t758 t1985.a1))
(step t1985 (cl @p_671 @p_673 @p_66 @p_1353 @p_916 @p_1579) :rule subproof :discharge (t1985.a0 t1985.a1 t1985.a2 t1985.a3 t1985.a4))
(step t1986 (cl (! (not @p_1577) :named @p_1578) @p_670) :rule and_pos :args (0))
(step t1987 (cl @p_1578 @p_113) :rule and_pos :args (1))
(step t1988 (cl @p_1578 @p_63) :rule and_pos :args (2))
(step t1989 (cl @p_1578 @p_740) :rule and_pos :args (3))
(step t1990 (cl @p_1578 @p_915) :rule and_pos :args (4))
(step t1991 (cl @p_1579 @p_1578 @p_1578 @p_1578 @p_1578 @p_1578) :rule resolution :premises (t1985 t1986 t1987 t1988 t1989 t1990))
(step t1992 (cl @p_1578 @p_1578 @p_1578 @p_1578 @p_1578 @p_1579) :rule reordering :premises (t1991))
(step t1993 (cl @p_1578 @p_1579) :rule contraction :premises (t1992))
(step t1994 (cl @p_1594 @p_1579) :rule resolution :premises (t1984 t1993))
(step t1995 (cl @p_1594 (! (not @p_1579) :named @p_1580)) :rule implies_neg2)
(step t1996 (cl @p_1594 @p_1594) :rule resolution :premises (t1994 t1995))
(step t1997 (cl @p_1594) :rule contraction :premises (t1996))
(step t1998 (cl @p_1578 @p_1579) :rule implies :premises (t1997))
(step t1999 (cl (! (=> @p_1579 false) :named @p_1581) @p_1579) :rule implies_neg1)
(anchor :step t2000)
(assume t2000.a0 @p_740)
(assume t2000.a1 @p_915)
(assume t2000.a2 @p_1188)
(assume t2000.a3 @p_670)
(assume t2000.a4 @p_113)
(step t2000.t0 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t2000.t1 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t2000.t2 (cl @p_703) :rule symm :premises (t2000.t1))
(step t2000.t3 (cl @p_700) :rule resolution :premises (t2000.t0 t2000.t2 t2000.a4))
(step t2000.t4 (cl (not (! (= @p_112 @p_715) :named @p_1593)) @p_113 @p_715) :rule equiv_pos2)
(step t2000.t5 (cl (= @p_715 @p_673)) :rule cong :premises (t2000.t1))
(step t2000.t6 (cl (! (= @p_715 @p_112) :named @p_1592)) :rule trans :premises (t2000.t5 t38))
(step t2000.t7 (cl @p_1593) :rule symm :premises (t2000.t6))
(step t2000.t8 (cl (not @p_1592) (not @p_715) @p_112) :rule equiv_pos2)
(step t2000.t9 (cl (! (=> @p_700 false) :named @p_1582) @p_700) :rule implies_neg1)
(anchor :step t2000.t10)
(assume t2000.t10.a0 @p_700)
(step t2000.t10.t0 (cl (not (! (= (! (< (! (+ @p_111 @p_692 @p_689 @p_912) :named @p_1584) (! (+ 1 @p_297 @p_297 -1) :named @p_1583)) :named @p_1585) false) :named @p_1586)) (not @p_1585) false) :rule equiv_pos2)
(step t2000.t10.t1 (cl (= @p_1585 (! (not (! (>= @p_1584 @p_1583) :named @p_1587)) :named @p_1588))) :rule rare_rewrite :args ("arith-elim-lt" @p_1584 @p_1583))
(step t2000.t10.t2 (cl (= @p_1584 (! (+ @p_722 @p_721 @p_46 @p_7 @p_617) :named @p_1590))) :rule poly_simp)
(step t2000.t10.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t2000.t10.t4 (cl (= @p_721 0)) :rule poly_simp)
(step t2000.t10.t5 (cl @p_168) :rule refl)
(step t2000.t10.t6 (cl @p_167) :rule refl)
(step t2000.t10.t7 (cl (= @p_617 0)) :rule poly_simp)
(step t2000.t10.t8 (cl (= @p_1590 (! (+ 0 0 @p_46 @p_7 0) :named @p_1591))) :rule cong :premises (t2000.t10.t3 t2000.t10.t4 t2000.t10.t5 t2000.t10.t6 t2000.t10.t7))
(step t2000.t10.t9 (cl (= @p_1591 0)) :rule poly_simp)
(step t2000.t10.t10 (cl (= @p_1590 0)) :rule trans :premises (t2000.t10.t8 t2000.t10.t9))
(step t2000.t10.t11 (cl (= @p_1584 0)) :rule trans :premises (t2000.t10.t2 t2000.t10.t10))
(step t2000.t10.t12 (cl (= @p_297 0)) :rule evaluate)
(step t2000.t10.t13 (cl (= -1 -1)) :rule refl)
(step t2000.t10.t14 (cl (= @p_1583 (! (+ 1 0 0 -1) :named @p_1589))) :rule cong :premises (t2000.t10.t12 t2000.t10.t12 t2000.t10.t13))
(step t2000.t10.t15 (cl (= @p_1589 0)) :rule evaluate)
(step t2000.t10.t16 (cl (= @p_1583 0)) :rule trans :premises (t2000.t10.t14 t2000.t10.t15))
(step t2000.t10.t17 (cl (= @p_1587 @p_366)) :rule cong :premises (t2000.t10.t11 t2000.t10.t16))
(step t2000.t10.t18 (cl (= @p_366 true)) :rule evaluate)
(step t2000.t10.t19 (cl (= @p_1587 true)) :rule trans :premises (t2000.t10.t17 t2000.t10.t18))
(step t2000.t10.t20 (cl (= @p_1588 @p_365)) :rule cong :premises (t2000.t10.t19))
(step t2000.t10.t21 (cl (= @p_365 false)) :rule evaluate)
(step t2000.t10.t22 (cl (= @p_1588 false)) :rule trans :premises (t2000.t10.t20 t2000.t10.t21))
(step t2000.t10.t23 (cl @p_1586) :rule trans :premises (t2000.t10.t1 t2000.t10.t22))
(step t2000.t10.t24 (cl @p_715 @p_716 @p_1211 @p_1380 @p_1585) :rule la_generic :args (1/1 -1/1 -1/1 1/1 1/1))
(step t2000.t10.t25 (cl (=> @p_698 @p_696)) :rule la_mult_neg)
(step t2000.t10.t26 (cl (not @p_698) @p_696) :rule implies :premises (t2000.t10.t25))
(step t2000.t10.t27 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2000.t10.t28 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2000.t10.t27))
(step t2000.t10.t29 (cl @p_310) :rule evaluate)
(step t2000.t10.t30 (cl @p_308) :rule resolution :premises (t2000.t10.t28 t2000.t10.t29))
(step t2000.t10.t31 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t2000.t10.t32 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t2000.t10.t33 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t2000.t10.t32))
(step t2000.t10.t34 (cl @p_699) :rule symm :premises (t2000.t10.t33))
(step t2000.t10.t35 (cl @p_697) :rule resolution :premises (t2000.t10.t31 t2000.t10.t34 t758))
(step t2000.t10.t36 (cl @p_698) :rule and_intro :premises (t2000.t10.t30 t2000.t10.t35))
(step t2000.t10.t37 (cl @p_696) :rule resolution :premises (t2000.t10.t26 t2000.t10.t36))
(step t2000.t10.t38 (cl (=> @p_1202 @p_1201)) :rule la_mult_neg)
(step t2000.t10.t39 (cl @p_1204 @p_1201) :rule implies :premises (t2000.t10.t38))
(step t2000.t10.t40 (cl @p_63) :rule symm :premises (t2000.a2))
(step t2000.t10.t41 (cl @p_1202) :rule and_intro :premises (t2000.t10.t30 t2000.t10.t40))
(step t2000.t10.t42 (cl @p_1201) :rule resolution :premises (t2000.t10.t39 t2000.t10.t41))
(step t2000.t10.t43 (cl @p_1379 @p_1365) :rule la_generic :args (1/1 1/1))
(step t2000.t10.t44 (cl @p_1378) :rule la_disequality)
(step t2000.t10.t45 (cl @p_1372 @p_1377 @p_1367) :rule or :premises (t2000.t10.t44))
(step t2000.t10.t46 (cl @p_1376 @p_1353 @p_1373) :rule equiv_pos2)
(step t2000.t10.t47 (cl (= (* 1 (- @p_912 0)) (* 1 (- @p_7 @p_668)))) :rule poly_simp)
(step t2000.t10.t48 (cl (= @p_1372 @p_732)) :rule poly_simp_rel :premises (t2000.t10.t47))
(step t2000.t10.t49 (cl (= @p_1373 @p_740)) :rule cong :premises (t2000.t10.t48))
(step t2000.t10.t50 (cl @p_1375) :rule symm :premises (t2000.t10.t49))
(step t2000.t10.t51 (cl @p_1373) :rule resolution :premises (t2000.t10.t46 t2000.t10.t50 t2000.a0))
(step t2000.t10.t52 (cl @p_956 @p_1371) :rule la_generic :args (1/1 1/1))
(step t2000.t10.t53 (cl @p_939 @p_916 @p_935) :rule equiv_pos2)
(step t2000.t10.t54 (cl (= @p_935 @p_915)) :rule rare_rewrite :args ("arith-elim-lt" @p_912 1))
(step t2000.t10.t55 (cl @p_938) :rule symm :premises (t2000.t10.t54))
(step t2000.t10.t56 (cl @p_935) :rule resolution :premises (t2000.t10.t53 t2000.t10.t55 t2000.a1))
(step t2000.t10.t57 (cl @p_1371) :rule resolution :premises (t2000.t10.t52 t2000.t10.t56))
(step t2000.t10.t58 (cl @p_1369 @p_1366 @p_1370) :rule equiv_pos1)
(step t2000.t10.t59 (cl @p_1368) :rule comp_simplify)
(step t2000.t10.t60 (cl @p_1366) :rule resolution :premises (t2000.t10.t45 t2000.t10.t51 t2000.t10.t57 t2000.t10.t58 t2000.t10.t59))
(step t2000.t10.t61 (cl @p_1365) :rule resolution :premises (t2000.t10.t43 t2000.t10.t60))
(step t2000.t10.t62 (cl @p_1585) :rule resolution :premises (t2000.t10.t24 t2000.t10.a0 t2000.t10.t37 t2000.t10.t42 t2000.t10.t61))
(step t2000.t10.t63 (cl false) :rule resolution :premises (t2000.t10.t0 t2000.t10.t23 t2000.t10.t62))
(step t2000.t10 (cl @p_715 false) :rule subproof :discharge (t2000.t10.a0))
(step t2000.t11 (cl @p_1582 false) :rule resolution :premises (t2000.t9 t2000.t10))
(step t2000.t12 (cl @p_1582 @p_212) :rule implies_neg2)
(step t2000.t13 (cl @p_1582 @p_1582) :rule resolution :premises (t2000.t11 t2000.t12))
(step t2000.t14 (cl @p_1582) :rule contraction :premises (t2000.t13))
(step t2000.t15 (cl (= @p_1582 @p_715)) :rule implies_simplify)
(step t2000.t16 (cl (not @p_1582) @p_715) :rule equiv1 :premises (t2000.t15))
(step t2000.t17 (cl @p_715) :rule resolution :premises (t2000.t14 t2000.t16))
(step t2000.t18 (cl @p_112) :rule resolution :premises (t2000.t8 t2000.t6 t2000.t17))
(step t2000.t19 (cl @p_715) :rule resolution :premises (t2000.t4 t2000.t7 t2000.t18))
(step t2000.t20 (cl) :rule resolution :premises (t2000.t3 t2000.t19))
(step t2000 (cl @p_1353 @p_916 @p_1192 @p_671 @p_673 false) :rule subproof :discharge (t2000.a0 t2000.a1 t2000.a2 t2000.a3 t2000.a4))
(step t2001 (cl @p_1580 @p_740) :rule and_pos :args (0))
(step t2002 (cl @p_1580 @p_915) :rule and_pos :args (1))
(step t2003 (cl @p_1580 @p_1188) :rule and_pos :args (2))
(step t2004 (cl @p_1580 @p_670) :rule and_pos :args (3))
(step t2005 (cl @p_1580 @p_113) :rule and_pos :args (4))
(step t2006 (cl false @p_1580 @p_1580 @p_1580 @p_1580 @p_1580) :rule resolution :premises (t2000 t2001 t2002 t2003 t2004 t2005))
(step t2007 (cl @p_1580 @p_1580 @p_1580 @p_1580 @p_1580 false) :rule reordering :premises (t2006))
(step t2008 (cl @p_1580 false) :rule contraction :premises (t2007))
(step t2009 (cl @p_1581 false) :rule resolution :premises (t1999 t2008))
(step t2010 (cl @p_1581 @p_212) :rule implies_neg2)
(step t2011 (cl @p_1581 @p_1581) :rule resolution :premises (t2009 t2010))
(step t2012 (cl @p_1581) :rule contraction :premises (t2011))
(step t2013 (cl (= @p_1581 @p_1580)) :rule implies_simplify)
(step t2014 (cl (not @p_1581) @p_1580) :rule equiv1 :premises (t2013))
(step t2015 (cl @p_1580) :rule resolution :premises (t2012 t2014))
(step t2016 (cl @p_1578) :rule resolution :premises (t1998 t2015))
(step t2017 (cl @p_671 @p_673 @p_66 @p_1353 @p_916) :rule not_and :premises (t2016))
(step t2018 (cl @p_1576 @p_677) :rule or_neg :args (0))
(step t2019 (cl @p_1576 @p_676) :rule or_neg :args (1))
(step t2020 (cl @p_1576 @p_1182) :rule or_neg :args (2))
(step t2021 (cl @p_1576 @p_1355) :rule or_neg :args (3))
(step t2022 (cl @p_1576 @p_918) :rule or_neg :args (4))
(step t2023 (cl @p_1576 @p_1576 @p_1576 @p_1576 @p_1576) :rule resolution :premises (t2017 t2018 t2019 t2020 t2021 t2022))
(step t2024 (cl @p_1576) :rule contraction :premises (t2023))
(step t2025 (cl @p_1575) :rule resolution :premises (t1982 t1983 t2024))
(step t2026 (cl @p_671 @p_112 @p_66 @p_732 @p_913) :rule or :premises (t2025))
(step t2027 (cl @p_112 @p_671 @p_732 @p_66 @p_913) :rule reordering :premises (t2026))
(step t2028 (cl (! (=> @p_1293 @p_15) :named @p_1568) @p_1293) :rule implies_neg1)
(anchor :step t2029)
(assume t2029.a0 @p_1293)
(step t2029.t0 (cl @p_1568 @p_1293) :rule implies_neg1)
(anchor :step t2029.t1)
(assume t2029.t1.a0 @p_1293)
(step t2029.t1.t0 (cl @p_1350 @p_1351 @p_15) :rule equiv_pos2)
(step t2029.t1.t1 (cl @p_1035) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0))
(step t2029.t1.t2 (cl (= @p_1037 @p_1013)) :rule cong :premises (t2029.t1.t1))
(step t2029.t1.t3 (cl @p_1349) :rule trans :premises (t2029.t1.t2 t810))
(step t2029.t1.t4 (cl @p_1338 @p_1031) :rule implies_neg1)
(anchor :step t2029.t1.t5)
(assume t2029.t1.t5.a0 @p_1031)
(step t2029.t1.t5.t0 (cl (not (! (= (! (< @p_1322 (! (+ 0 @p_850) :named @p_1569)) :named @p_1570) false) :named @p_1571)) (not @p_1570) false) :rule equiv_pos2)
(step t2029.t1.t5.t1 (cl (= @p_1570 (! (not (! (>= @p_1322 @p_1569) :named @p_1572)) :named @p_1573))) :rule rare_rewrite :args ("arith-elim-lt" @p_1322 @p_1569))
(step t2029.t1.t5.t2 (cl (= @p_1322 0)) :rule poly_simp)
(step t2029.t1.t5.t3 (cl (= @p_1569 (! (+ 0 -2) :named @p_1574))) :rule cong :premises (t1310))
(step t2029.t1.t5.t4 (cl (= @p_1574 -2)) :rule evaluate)
(step t2029.t1.t5.t5 (cl (= @p_1569 -2)) :rule trans :premises (t2029.t1.t5.t3 t2029.t1.t5.t4))
(step t2029.t1.t5.t6 (cl (= @p_1572 @p_1332)) :rule cong :premises (t2029.t1.t5.t2 t2029.t1.t5.t5))
(step t2029.t1.t5.t7 (cl (= @p_1332 true)) :rule evaluate)
(step t2029.t1.t5.t8 (cl (= @p_1572 true)) :rule trans :premises (t2029.t1.t5.t6 t2029.t1.t5.t7))
(step t2029.t1.t5.t9 (cl (= @p_1573 @p_365)) :rule cong :premises (t2029.t1.t5.t8))
(step t2029.t1.t5.t10 (cl (= @p_365 false)) :rule evaluate)
(step t2029.t1.t5.t11 (cl (= @p_1573 false)) :rule trans :premises (t2029.t1.t5.t9 t2029.t1.t5.t10))
(step t2029.t1.t5.t12 (cl @p_1571) :rule trans :premises (t2029.t1.t5.t1 t2029.t1.t5.t11))
(step t2029.t1.t5.t13 (cl @p_1037 (! (not (! (<= @p_11 @p_850) :named @p_1560)) :named @p_1563) @p_1570) :rule la_generic :args (1/1 1/1 1/1))
(step t2029.t1.t5.t14 (cl (=> (! (and @p_308 @p_1293) :named @p_1561) @p_1560)) :rule la_mult_neg)
(step t2029.t1.t5.t15 (cl (! (not @p_1561) :named @p_1562) @p_1560) :rule implies :premises (t2029.t1.t5.t14))
(step t2029.t1.t5.t16 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2029.t1.t5.t17 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2029.t1.t5.t16))
(step t2029.t1.t5.t18 (cl @p_310) :rule evaluate)
(step t2029.t1.t5.t19 (cl @p_308) :rule resolution :premises (t2029.t1.t5.t17 t2029.t1.t5.t18))
(step t2029.t1.t5.t20 (cl @p_1561) :rule and_intro :premises (t2029.t1.t5.t19 t2029.t1.a0))
(step t2029.t1.t5.t21 (cl @p_1560) :rule resolution :premises (t2029.t1.t5.t15 t2029.t1.t5.t20))
(step t2029.t1.t5.t22 (cl @p_1570) :rule resolution :premises (t2029.t1.t5.t13 t2029.t1.t5.a0 t2029.t1.t5.t21))
(step t2029.t1.t5.t23 (cl false) :rule resolution :premises (t2029.t1.t5.t0 t2029.t1.t5.t12 t2029.t1.t5.t22))
(step t2029.t1.t5 (cl @p_1037 false) :rule subproof :discharge (t2029.t1.t5.a0))
(step t2029.t1.t6 (cl @p_1338 false) :rule resolution :premises (t2029.t1.t4 t2029.t1.t5))
(step t2029.t1.t7 (cl @p_1338 @p_212) :rule implies_neg2)
(step t2029.t1.t8 (cl @p_1338 @p_1338) :rule resolution :premises (t2029.t1.t6 t2029.t1.t7))
(step t2029.t1.t9 (cl @p_1338) :rule contraction :premises (t2029.t1.t8))
(step t2029.t1.t10 (cl @p_1340) :rule implies_simplify)
(step t2029.t1.t11 (cl @p_1339 @p_1037) :rule equiv1 :premises (t2029.t1.t10))
(step t2029.t1.t12 (cl @p_1037) :rule resolution :premises (t2029.t1.t9 t2029.t1.t11))
(step t2029.t1.t13 (cl @p_15) :rule resolution :premises (t2029.t1.t0 t2029.t1.t3 t2029.t1.t12))
(step t2029.t1 (cl @p_1294 @p_15) :rule subproof :discharge (t2029.t1.a0))
(step t2029.t2 (cl @p_1568 @p_15) :rule resolution :premises (t2029.t0 t2029.t1))
(step t2029.t3 (cl @p_1568 @p_16) :rule implies_neg2)
(step t2029.t4 (cl @p_1568 @p_1568) :rule resolution :premises (t2029.t2 t2029.t3))
(step t2029.t5 (cl @p_1568) :rule contraction :premises (t2029.t4))
(step t2029.t6 (cl @p_1294 @p_15) :rule implies :premises (t2029.t5))
(step t2029.t7 (cl @p_15) :rule resolution :premises (t2029.t6 t2029.a0))
(step t2029 (cl @p_1294 @p_15) :rule subproof :discharge (t2029.a0))
(step t2030 (cl @p_1568 @p_15) :rule resolution :premises (t2028 t2029))
(step t2031 (cl @p_1568 @p_16) :rule implies_neg2)
(step t2032 (cl @p_1568 @p_1568) :rule resolution :premises (t2030 t2031))
(step t2033 (cl @p_1568) :rule contraction :premises (t2032))
(step t2034 (cl @p_1294 @p_15) :rule implies :premises (t2033))
(step t2035 (cl (! (=> @p_1293 @p_1049) :named @p_1557) @p_1293) :rule implies_neg1)
(anchor :step t2036)
(assume t2036.a0 @p_1293)
(step t2036.t0 (cl @p_1557 @p_1293) :rule implies_neg1)
(anchor :step t2036.t1)
(assume t2036.t1.a0 @p_1293)
(step t2036.t1.t0 (cl @p_1335 @p_1336 @p_1049) :rule equiv_pos2)
(step t2036.t1.t1 (cl (= @p_1066 @p_1051)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 1))
(step t2036.t1.t2 (cl (= @p_1071 @p_1052)) :rule cong :premises (t2036.t1.t1))
(step t2036.t1.t3 (cl @p_1334) :rule trans :premises (t2036.t1.t2 t690))
(step t2036.t1.t4 (cl @p_1317 @p_1066) :rule implies_neg1)
(anchor :step t2036.t1.t5)
(assume t2036.t1.t5.a0 @p_1066)
(step t2036.t1.t5.t0 (cl (not (! (= (! (< @p_1322 (! (+ 1 @p_850) :named @p_1558)) :named @p_1559) false) :named @p_1564)) (not @p_1559) false) :rule equiv_pos2)
(step t2036.t1.t5.t1 (cl (= @p_1559 (! (not (! (>= @p_1322 @p_1558) :named @p_1565)) :named @p_1566))) :rule rare_rewrite :args ("arith-elim-lt" @p_1322 @p_1558))
(step t2036.t1.t5.t2 (cl (= @p_1322 0)) :rule poly_simp)
(step t2036.t1.t5.t3 (cl (= @p_1558 (! (+ 1 -2) :named @p_1567))) :rule cong :premises (t1310))
(step t2036.t1.t5.t4 (cl (= @p_1567 -1)) :rule evaluate)
(step t2036.t1.t5.t5 (cl (= @p_1558 -1)) :rule trans :premises (t2036.t1.t5.t3 t2036.t1.t5.t4))
(step t2036.t1.t5.t6 (cl (= @p_1565 @p_1238)) :rule cong :premises (t2036.t1.t5.t2 t2036.t1.t5.t5))
(step t2036.t1.t5.t7 (cl (= @p_1238 true)) :rule evaluate)
(step t2036.t1.t5.t8 (cl (= @p_1565 true)) :rule trans :premises (t2036.t1.t5.t6 t2036.t1.t5.t7))
(step t2036.t1.t5.t9 (cl (= @p_1566 @p_365)) :rule cong :premises (t2036.t1.t5.t8))
(step t2036.t1.t5.t10 (cl (= @p_365 false)) :rule evaluate)
(step t2036.t1.t5.t11 (cl (= @p_1566 false)) :rule trans :premises (t2036.t1.t5.t9 t2036.t1.t5.t10))
(step t2036.t1.t5.t12 (cl @p_1564) :rule trans :premises (t2036.t1.t5.t1 t2036.t1.t5.t11))
(step t2036.t1.t5.t13 (cl @p_1071 @p_1563 @p_1559) :rule la_generic :args (1/1 1/1 1/1))
(step t2036.t1.t5.t14 (cl (=> @p_1561 @p_1560)) :rule la_mult_neg)
(step t2036.t1.t5.t15 (cl @p_1562 @p_1560) :rule implies :premises (t2036.t1.t5.t14))
(step t2036.t1.t5.t16 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2036.t1.t5.t17 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2036.t1.t5.t16))
(step t2036.t1.t5.t18 (cl @p_310) :rule evaluate)
(step t2036.t1.t5.t19 (cl @p_308) :rule resolution :premises (t2036.t1.t5.t17 t2036.t1.t5.t18))
(step t2036.t1.t5.t20 (cl @p_1561) :rule and_intro :premises (t2036.t1.t5.t19 t2036.t1.a0))
(step t2036.t1.t5.t21 (cl @p_1560) :rule resolution :premises (t2036.t1.t5.t15 t2036.t1.t5.t20))
(step t2036.t1.t5.t22 (cl @p_1559) :rule resolution :premises (t2036.t1.t5.t13 t2036.t1.t5.a0 t2036.t1.t5.t21))
(step t2036.t1.t5.t23 (cl false) :rule resolution :premises (t2036.t1.t5.t0 t2036.t1.t5.t12 t2036.t1.t5.t22))
(step t2036.t1.t5 (cl @p_1071 false) :rule subproof :discharge (t2036.t1.t5.a0))
(step t2036.t1.t6 (cl @p_1317 false) :rule resolution :premises (t2036.t1.t4 t2036.t1.t5))
(step t2036.t1.t7 (cl @p_1317 @p_212) :rule implies_neg2)
(step t2036.t1.t8 (cl @p_1317 @p_1317) :rule resolution :premises (t2036.t1.t6 t2036.t1.t7))
(step t2036.t1.t9 (cl @p_1317) :rule contraction :premises (t2036.t1.t8))
(step t2036.t1.t10 (cl @p_1319) :rule implies_simplify)
(step t2036.t1.t11 (cl @p_1318 @p_1071) :rule equiv1 :premises (t2036.t1.t10))
(step t2036.t1.t12 (cl @p_1071) :rule resolution :premises (t2036.t1.t9 t2036.t1.t11))
(step t2036.t1.t13 (cl @p_1049) :rule resolution :premises (t2036.t1.t0 t2036.t1.t3 t2036.t1.t12))
(step t2036.t1 (cl @p_1294 @p_1049) :rule subproof :discharge (t2036.t1.a0))
(step t2036.t2 (cl @p_1557 @p_1049) :rule resolution :premises (t2036.t0 t2036.t1))
(step t2036.t3 (cl @p_1557 @p_1051) :rule implies_neg2)
(step t2036.t4 (cl @p_1557 @p_1557) :rule resolution :premises (t2036.t2 t2036.t3))
(step t2036.t5 (cl @p_1557) :rule contraction :premises (t2036.t4))
(step t2036.t6 (cl @p_1294 @p_1049) :rule implies :premises (t2036.t5))
(step t2036.t7 (cl @p_1049) :rule resolution :premises (t2036.t6 t2036.a0))
(step t2036 (cl @p_1294 @p_1049) :rule subproof :discharge (t2036.a0))
(step t2037 (cl @p_1557 @p_1049) :rule resolution :premises (t2035 t2036))
(step t2038 (cl @p_1557 @p_1051) :rule implies_neg2)
(step t2039 (cl @p_1557 @p_1557) :rule resolution :premises (t2037 t2038))
(step t2040 (cl @p_1557) :rule contraction :premises (t2039))
(step t2041 (cl @p_1294 @p_1049) :rule implies :premises (t2040))
(step t2042 (cl (not (! (= (! (or @p_871 @p_1192 @p_806 @p_671 @p_1293) :named @p_1539) (! (or @p_871 @p_66 @p_798 @p_671 @p_1293) :named @p_1538)) :named @p_1556)) (not @p_1539) @p_1538) :rule equiv_pos2)
(step t2043 (cl (= (* 1 (- 0 @p_57)) (* -1 (- @p_57 0)))) :rule poly_simp)
(step t2044 (cl (= @p_1188 @p_63)) :rule poly_simp_rel :premises (t2043))
(step t2045 (cl (= @p_1192 @p_66)) :rule cong :premises (t2044))
(step t2046 (cl (= @p_1293 @p_1293)) :rule refl)
(step t2047 (cl @p_1556) :rule cong :premises (t2045 t656 t1798 t2046))
(step t2048 (cl (not (! (= (! (or @p_871 @p_1192 @p_806 @p_671 @p_1295) :named @p_1540) @p_1539) :named @p_1555)) (not @p_1540) @p_1539) :rule equiv_pos2)
(step t2049 (cl (= @p_1295 @p_1293)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1293))
(step t2050 (cl (= @p_1540 @p_1538)) :rule cong :premises (t2045 t656 t1798 t2049))
(step t2051 (cl (= @p_1538 @p_1539)) :rule symm :premises (t2047))
(step t2052 (cl @p_1555) :rule trans :premises (t2050 t2051))
(step t2053 (cl (! (=> (! (and @p_870 @p_1188 @p_801 @p_670 @p_1294) :named @p_1541) false) :named @p_1543) @p_1541) :rule implies_neg1)
(anchor :step t2054)
(assume t2054.a0 @p_870)
(assume t2054.a1 @p_1188)
(assume t2054.a2 @p_801)
(assume t2054.a3 @p_670)
(assume t2054.a4 @p_1294)
(step t2054.t0 (cl (not (! (= (! (< (! (+ @p_8 @p_120 @p_57 @p_799 @p_691) :named @p_1545) (! (+ 2 @p_850 0 0 0) :named @p_1544)) :named @p_1546) false) :named @p_1550)) (not @p_1546) false) :rule equiv_pos2)
(step t2054.t1 (cl (= @p_1546 (! (not (! (>= @p_1545 @p_1544) :named @p_1551)) :named @p_1552))) :rule rare_rewrite :args ("arith-elim-lt" @p_1545 @p_1544))
(step t2054.t2 (cl (= @p_1545 @p_1554)) :rule poly_simp)
(step t2054.t3 (cl (= @p_1554 0)) :rule poly_simp)
(step t2054.t4 (cl (= @p_1545 0)) :rule trans :premises (t2054.t2 t2054.t3))
(step t2054.t5 (cl (= @p_1544 (! (+ 2 -2 0 0 0) :named @p_1553))) :rule cong :premises (t1310 t604 t604 t604))
(step t2054.t6 (cl (= @p_1553 0)) :rule evaluate)
(step t2054.t7 (cl (= @p_1544 0)) :rule trans :premises (t2054.t5 t2054.t6))
(step t2054.t8 (cl (= @p_1551 @p_366)) :rule cong :premises (t2054.t4 t2054.t7))
(step t2054.t9 (cl (= @p_366 true)) :rule evaluate)
(step t2054.t10 (cl (= @p_1551 true)) :rule trans :premises (t2054.t8 t2054.t9))
(step t2054.t11 (cl (= @p_1552 @p_365)) :rule cong :premises (t2054.t10))
(step t2054.t12 (cl (= @p_365 false)) :rule evaluate)
(step t2054.t13 (cl (= @p_1552 false)) :rule trans :premises (t2054.t11 t2054.t12))
(step t2054.t14 (cl @p_1550) :rule trans :premises (t2054.t1 t2054.t13))
(step t2054.t15 (cl @p_1311 @p_889 @p_66 @p_808 @p_1549 @p_1546) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 1/1))
(step t2054.t16 (cl (not (! (= @p_1294 @p_1302) :named @p_1548)) @p_1295 @p_1302) :rule equiv_pos2)
(step t2054.t17 (cl (= @p_1302 @p_1294)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 2))
(step t2054.t18 (cl @p_1548) :rule symm :premises (t2054.t17))
(step t2054.t19 (cl @p_1302) :rule resolution :premises (t2054.t16 t2054.t18 t2054.a4))
(step t2054.t20 (cl (=> @p_885 @p_884)) :rule la_mult_neg)
(step t2054.t21 (cl @p_887 @p_884) :rule implies :premises (t2054.t20))
(step t2054.t22 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2054.t23 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2054.t22))
(step t2054.t24 (cl @p_310) :rule evaluate)
(step t2054.t25 (cl @p_308) :rule resolution :premises (t2054.t23 t2054.t24))
(step t2054.t26 (cl @p_885) :rule and_intro :premises (t2054.t25 t2054.a0))
(step t2054.t27 (cl @p_884) :rule resolution :premises (t2054.t21 t2054.t26))
(step t2054.t28 (cl @p_63) :rule symm :premises (t2054.a1))
(step t2054.t29 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t2054.t30 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t2054.t31 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t2054.t30))
(step t2054.t32 (cl @p_699) :rule symm :premises (t2054.t31))
(step t2054.t33 (cl @p_697) :rule resolution :premises (t2054.t29 t2054.t32 t758))
(step t2054.t34 (cl @p_1546) :rule resolution :premises (t2054.t15 t2054.t19 t2054.t27 t2054.t28 t1846 t2054.t33))
(step t2054.t35 (cl false) :rule resolution :premises (t2054.t0 t2054.t14 t2054.t34))
(step t2054 (cl @p_871 @p_1192 @p_806 @p_671 @p_1295 false) :rule subproof :discharge (t2054.a0 t2054.a1 t2054.a2 t2054.a3 t2054.a4))
(step t2055 (cl (! (not @p_1541) :named @p_1542) @p_870) :rule and_pos :args (0))
(step t2056 (cl @p_1542 @p_1188) :rule and_pos :args (1))
(step t2057 (cl @p_1542 @p_801) :rule and_pos :args (2))
(step t2058 (cl @p_1542 @p_670) :rule and_pos :args (3))
(step t2059 (cl @p_1542 @p_1294) :rule and_pos :args (4))
(step t2060 (cl false @p_1542 @p_1542 @p_1542 @p_1542 @p_1542) :rule resolution :premises (t2054 t2055 t2056 t2057 t2058 t2059))
(step t2061 (cl @p_1542 @p_1542 @p_1542 @p_1542 @p_1542 false) :rule reordering :premises (t2060))
(step t2062 (cl @p_1542 false) :rule contraction :premises (t2061))
(step t2063 (cl @p_1543 false) :rule resolution :premises (t2053 t2062))
(step t2064 (cl @p_1543 @p_212) :rule implies_neg2)
(step t2065 (cl @p_1543 @p_1543) :rule resolution :premises (t2063 t2064))
(step t2066 (cl @p_1543) :rule contraction :premises (t2065))
(step t2067 (cl (= @p_1543 @p_1542)) :rule implies_simplify)
(step t2068 (cl (not @p_1543) @p_1542) :rule equiv1 :premises (t2067))
(step t2069 (cl @p_1542) :rule resolution :premises (t2066 t2068))
(step t2070 (cl @p_871 @p_1192 @p_806 @p_671 @p_1295) :rule not_and :premises (t2069))
(step t2071 (cl @p_1540 @p_874) :rule or_neg :args (0))
(step t2072 (cl @p_1540 (not @p_1192)) :rule or_neg :args (1))
(step t2073 (cl @p_1540 @p_983) :rule or_neg :args (2))
(step t2074 (cl @p_1540 @p_677) :rule or_neg :args (3))
(step t2075 (cl @p_1540 (not @p_1295)) :rule or_neg :args (4))
(step t2076 (cl @p_1540 @p_1540 @p_1540 @p_1540 @p_1540) :rule resolution :premises (t2070 t2071 t2072 t2073 t2074 t2075))
(step t2077 (cl @p_1540) :rule contraction :premises (t2076))
(step t2078 (cl @p_1539) :rule resolution :premises (t2048 t2052 t2077))
(step t2079 (cl @p_1538) :rule resolution :premises (t2042 t2047 t2078))
(step t2080 (cl @p_871 @p_66 @p_798 @p_671 @p_1293) :rule or :premises (t2079))
(step t2081 (cl @p_671 @p_798 @p_66 @p_871 @p_1293) :rule reordering :premises (t2080))
(step t2082 (cl (not (! (= (! (or @p_66 (! (not (! (not (! (= @p_6 0) :named @p_67)) :named @p_68)) :named @p_1513) @p_911) :named @p_1524) (! (or @p_66 @p_67 @p_911) :named @p_1523)) :named @p_1537)) (not @p_1524) @p_1523) :rule equiv_pos2)
(step t2083 (cl (= @p_1513 @p_67)) :rule rare_rewrite :args ("bool-double-not-elim" @p_67))
(step t2084 (cl @p_1537) :rule cong :premises (t2083 t1850))
(step t2085 (cl (! (and @p_63 @p_68) :named @p_1526) @p_66 @p_1513) :rule and_neg)
(step t2086 (cl (! (=> @p_1526 @p_911) :named @p_1528) @p_1526) :rule implies_neg1)
(anchor :step t2087)
(assume t2087.a0 @p_63)
(assume t2087.a1 @p_68)
(step t2087.t0 (cl (! (=> (! (and @p_68 @p_63) :named @p_1529) @p_911) :named @p_1532) @p_1529) :rule implies_neg1)
(anchor :step t2087.t1)
(assume t2087.t1.a0 @p_68)
(assume t2087.t1.a1 @p_63)
(step t2087.t1.t0 (cl @p_1536) :rule equiv_simplify)
(step t2087.t1.t1 (cl @p_1535 @p_911) :rule equiv1 :premises (t2087.t1.t0))
(step t2087.t1.t2 (cl (= @p_899 @p_67)) :rule cong :premises (t2087.t1.a1))
(step t2087.t1.t3 (cl (= (! (= @p_67 false) :named @p_1534) @p_68)) :rule equiv_simplify)
(step t2087.t1.t4 (cl @p_1534 @p_1513) :rule equiv2 :premises (t2087.t1.t3))
(step t2087.t1.t5 (cl (! (not @p_1513) :named @p_1525) @p_67) :rule not_not)
(step t2087.t1.t6 (cl @p_1534 @p_67) :rule resolution :premises (t2087.t1.t4 t2087.t1.t5))
(step t2087.t1.t7 (cl @p_1534) :rule resolution :premises (t2087.t1.t6 t2087.t1.a0))
(step t2087.t1.t8 (cl @p_1533) :rule trans :premises (t2087.t1.t2 t2087.t1.t7))
(step t2087.t1.t9 (cl @p_911) :rule resolution :premises (t2087.t1.t1 t2087.t1.t8))
(step t2087.t1 (cl @p_1513 @p_66 @p_911) :rule subproof :discharge (t2087.t1.a0 t2087.t1.a1))
(step t2087.t2 (cl (! (not @p_1529) :named @p_1531) @p_68) :rule and_pos :args (0))
(step t2087.t3 (cl @p_1531 @p_63) :rule and_pos :args (1))
(step t2087.t4 (cl @p_911 @p_1531 @p_1531) :rule resolution :premises (t2087.t1 t2087.t2 t2087.t3))
(step t2087.t5 (cl @p_1531 @p_1531 @p_911) :rule reordering :premises (t2087.t4))
(step t2087.t6 (cl @p_1531 @p_911) :rule contraction :premises (t2087.t5))
(step t2087.t7 (cl @p_1532 @p_911) :rule resolution :premises (t2087.t0 t2087.t6))
(step t2087.t8 (cl @p_1532 @p_919) :rule implies_neg2)
(step t2087.t9 (cl @p_1532 @p_1532) :rule resolution :premises (t2087.t7 t2087.t8))
(step t2087.t10 (cl @p_1532) :rule contraction :premises (t2087.t9))
(step t2087.t11 (cl @p_1531 @p_911) :rule implies :premises (t2087.t10))
(step t2087.t12 (cl @p_1529) :rule and_intro :premises (t2087.a1 t2087.a0))
(step t2087.t13 (cl @p_911) :rule resolution :premises (t2087.t11 t2087.t12))
(step t2087 (cl @p_66 @p_1513 @p_911) :rule subproof :discharge (t2087.a0 t2087.a1))
(step t2088 (cl (! (not @p_1526) :named @p_1527) @p_63) :rule and_pos :args (0))
(step t2089 (cl @p_1527 @p_68) :rule and_pos :args (1))
(step t2090 (cl @p_911 @p_1527 @p_1527) :rule resolution :premises (t2087 t2088 t2089))
(step t2091 (cl @p_1527 @p_1527 @p_911) :rule reordering :premises (t2090))
(step t2092 (cl @p_1527 @p_911) :rule contraction :premises (t2091))
(step t2093 (cl @p_1528 @p_911) :rule resolution :premises (t2086 t2092))
(step t2094 (cl @p_1528 @p_919) :rule implies_neg2)
(step t2095 (cl @p_1528 @p_1528) :rule resolution :premises (t2093 t2094))
(step t2096 (cl @p_1528) :rule contraction :premises (t2095))
(step t2097 (cl @p_1527 @p_911) :rule implies :premises (t2096))
(step t2098 (cl @p_66 @p_1513 @p_911) :rule resolution :premises (t2085 t2097))
(step t2099 (cl @p_1524 @p_1182) :rule or_neg :args (0))
(step t2100 (cl @p_1524 @p_1525) :rule or_neg :args (1))
(step t2101 (cl @p_1524 @p_919) :rule or_neg :args (2))
(step t2102 (cl @p_1524 @p_1524 @p_1524) :rule resolution :premises (t2098 t2099 t2100 t2101))
(step t2103 (cl @p_1524) :rule contraction :premises (t2102))
(step t2104 (cl @p_1523) :rule resolution :premises (t2082 t2084 t2103))
(step t2105 (cl @p_66 @p_67 @p_911) :rule or :premises (t2104))
(step t2106 (cl @p_67 @p_66 @p_911) :rule reordering :premises (t2105))
(step t2107 (cl (! (=> (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))) @p_106) :named @p_1522) (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t2108)
(assume t2108.a0 (forall ((?v0 Int) (?v1 Int)) (= ?v0 (+ (times$ (centered_divide$ ?v0 ?v1) ?v1) (centered_modulo$ ?v0 ?v1)))))
(step t2108.t0 (cl @p_106) :rule resolution :premises (t741 t398))
(step t2108 (cl @p_110 @p_106) :rule subproof :discharge (t2108.a0))
(step t2109 (cl @p_1522 @p_106) :rule resolution :premises (t2107 t2108))
(step t2110 (cl @p_1522 @p_532) :rule implies_neg2)
(step t2111 (cl @p_1522 @p_1522) :rule resolution :premises (t2109 t2110))
(step t2112 (cl @p_1522) :rule contraction :premises (t2111))
(step t2113 (cl @p_110 @p_106) :rule implies :premises (t2112))
(step t2114 (cl @p_112 @p_585 @p_67 @p_66) :rule resolution :premises (t2027 t758 t688 t1 t649 t33 t652 t2034 t2041 t2081 t758 t1308 t1329 t2106 t1151 t1158 t226 t754 a4 t35 t1522 t186 t1525 t1539 a8 t85 t2113 t398 t1747 t1746))
(step t2115 (cl (not (! (= (! (or @p_68 @p_675 @p_761 @p_762) :named @p_1512) (! (or @p_68 @p_101 @p_761 @p_762) :named @p_1511)) :named @p_1521)) (not @p_1512) @p_1511) :rule equiv_pos2)
(step t2116 (cl @p_1521) :rule cong :premises (t1389 t1415 t1416))
(step t2117 (cl (! (=> (! (and @p_67 @p_102 @p_90 @p_71) :named @p_1514) @p_771) :named @p_1516) @p_1514) :rule implies_neg1)
(anchor :step t2118)
(assume t2118.a0 @p_67)
(assume t2118.a1 @p_102)
(assume t2118.a2 @p_90)
(assume t2118.a3 @p_71)
(step t2118.t0 (cl (! (=> (! (and @p_67 @p_90 @p_71) :named @p_1517) @p_680) :named @p_1520) @p_1517) :rule implies_neg1)
(anchor :step t2118.t1)
(assume t2118.t1.a0 @p_67)
(assume t2118.t1.a1 @p_90)
(assume t2118.t1.a2 @p_71)
(step t2118.t1.t0 (cl @p_84) :rule symm :premises (t1474))
(step t2118.t1.t1 (cl (= @p_70 @p_782)) :rule cong :premises (t1494 t358))
(step t2118.t1.t2 (cl (= 0 @p_6)) :rule symm :premises (t2118.t1.a0))
(step t2118.t1.t3 (cl (= @p_782 @p_7)) :rule cong :premises (t2118.t1.t2 t358))
(step t2118.t1.t4 (cl @p_680) :rule trans :premises (t2118.t1.t0 t2118.t1.t1 t2118.t1.t3))
(step t2118.t1 (cl @p_68 @p_761 @p_762 @p_680) :rule subproof :discharge (t2118.t1.a0 t2118.t1.a1 t2118.t1.a2))
(step t2118.t2 (cl (! (not @p_1517) :named @p_1519) @p_67) :rule and_pos :args (0))
(step t2118.t3 (cl @p_1519 @p_90) :rule and_pos :args (1))
(step t2118.t4 (cl @p_1519 @p_71) :rule and_pos :args (2))
(step t2118.t5 (cl @p_680 @p_1519 @p_1519 @p_1519) :rule resolution :premises (t2118.t1 t2118.t2 t2118.t3 t2118.t4))
(step t2118.t6 (cl @p_1519 @p_1519 @p_1519 @p_680) :rule reordering :premises (t2118.t5))
(step t2118.t7 (cl @p_1519 @p_680) :rule contraction :premises (t2118.t6))
(step t2118.t8 (cl @p_1520 @p_680) :rule resolution :premises (t2118.t0 t2118.t7))
(step t2118.t9 (cl @p_1520 @p_686) :rule implies_neg2)
(step t2118.t10 (cl @p_1520 @p_1520) :rule resolution :premises (t2118.t8 t2118.t9))
(step t2118.t11 (cl @p_1520) :rule contraction :premises (t2118.t10))
(step t2118.t12 (cl @p_1519 @p_680) :rule implies :premises (t2118.t11))
(step t2118.t13 (cl @p_1517) :rule and_intro :premises (t2118.a0 t1494 t1474))
(step t2118.t14 (cl @p_680) :rule resolution :premises (t2118.t12 t2118.t13))
(step t2118.t15 (cl @p_771) :rule and_intro :premises (t2118.t14 t2118.a1))
(step t2118 (cl @p_68 @p_675 @p_761 @p_762 @p_771) :rule subproof :discharge (t2118.a0 t2118.a1 t2118.a2 t2118.a3))
(step t2119 (cl (! (not @p_1514) :named @p_1515) @p_67) :rule and_pos :args (0))
(step t2120 (cl @p_1515 @p_102) :rule and_pos :args (1))
(step t2121 (cl @p_1515 @p_90) :rule and_pos :args (2))
(step t2122 (cl @p_1515 @p_71) :rule and_pos :args (3))
(step t2123 (cl @p_771 @p_1515 @p_1515 @p_1515 @p_1515) :rule resolution :premises (t2118 t2119 t2120 t2121 t2122))
(step t2124 (cl @p_1515 @p_1515 @p_1515 @p_1515 @p_771) :rule reordering :premises (t2123))
(step t2125 (cl @p_1515 @p_771) :rule contraction :premises (t2124))
(step t2126 (cl @p_1516 @p_771) :rule resolution :premises (t2117 t2125))
(step t2127 (cl @p_1516 @p_772) :rule implies_neg2)
(step t2128 (cl @p_1516 @p_1516) :rule resolution :premises (t2126 t2127))
(step t2129 (cl @p_1516) :rule contraction :premises (t2128))
(step t2130 (cl @p_1515 @p_771) :rule implies :premises (t2129))
(step t2131 (cl @p_1515) :rule resolution :premises (t2130 t1446))
(step t2132 (cl @p_68 @p_675 @p_761 @p_762) :rule not_and :premises (t2131))
(step t2133 (cl @p_1512 @p_1513) :rule or_neg :args (0))
(step t2134 (cl @p_1512 @p_768) :rule or_neg :args (1))
(step t2135 (cl @p_1512 @p_766) :rule or_neg :args (2))
(step t2136 (cl @p_1512 @p_765) :rule or_neg :args (3))
(step t2137 (cl @p_1512 @p_1512 @p_1512 @p_1512) :rule resolution :premises (t2132 t2133 t2134 t2135 t2136))
(step t2138 (cl @p_1512) :rule contraction :premises (t2137))
(step t2139 (cl @p_1511) :rule resolution :premises (t2115 t2116 t2138))
(step t2140 (cl @p_68 @p_101 @p_761 @p_762) :rule or :premises (t2139))
(step t2141 (cl @p_101 @p_68 @p_761 @p_762) :rule reordering :premises (t2140))
(step t2142 (cl @p_68) :rule resolution :premises (t2141 t1795 t1494 t1474))
(step t2143 (cl @p_66) :rule resolution :premises (t2114 t1794 t1792 t2142))
(step t2144 (cl @p_60) :rule resolution :premises (t877 t2143 t880))
(step t2145 (cl @p_58) :rule resolution :premises (t872 t2144 t875))
(step t2146 (cl @p_911) :rule resolution :premises (t1873 t1981 t2145))
(step t2147 (cl @p_870) :rule resolution :premises (t1308 t1792 t2146 t1329))
(step t2148 (cl @p_1049) :rule resolution :premises (t1837 t758 t1847 t2147 t2145))
(step t2149 (cl @p_1101) :rule resolution :premises (t33 t1796 t652 t2148))
(step t2150 (cl (not (! (= (! (or @p_1065 @p_15) :named @p_1730) (! (or @p_1051 @p_15) :named @p_1729)) :named @p_1751)) (not @p_1730) @p_1729) :rule equiv_pos2)
(step t2151 (cl (= @p_1065 (! (not (! (>= @p_8 @p_1411) :named @p_1743)) :named @p_1744))) :rule rare_rewrite :args ("arith-leq-norm" @p_8 0))
(step t2152 (cl (= @p_1411 1)) :rule evaluate)
(step t2153 (cl (= @p_1743 @p_1049)) :rule cong :premises (t2152))
(step t2154 (cl (= @p_1744 @p_1051)) :rule cong :premises (t2153))
(step t2155 (cl (= @p_1065 @p_1051)) :rule trans :premises (t2151 t2154))
(step t2156 (cl (= @p_15 @p_15)) :rule refl)
(step t2157 (cl @p_1751) :rule cong :premises (t2155 t2156))
(step t2158 (cl (not (! (= (! (or (! (not @p_1074) :named @p_1731) @p_1013) :named @p_1732) @p_1730) :named @p_1750)) (not @p_1732) @p_1730) :rule equiv_pos2)
(step t2159 (cl (= @p_1731 @p_1065)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1065))
(step t2160 (cl (= @p_1731 @p_1051)) :rule trans :premises (t2159 t2155))
(step t2161 (cl (= @p_1732 @p_1729)) :rule cong :premises (t2160 t810))
(step t2162 (cl (= @p_1729 @p_1730)) :rule symm :premises (t2157))
(step t2163 (cl @p_1750) :rule trans :premises (t2161 t2162))
(step t2164 (cl (! (=> (! (and @p_1074 @p_16) :named @p_1733) false) :named @p_1735) @p_1733) :rule implies_neg1)
(anchor :step t2165)
(assume t2165.a0 @p_1074)
(assume t2165.a1 @p_16)
(step t2165.t0 (cl (not (! (= (! (< (! (+ @p_11 @p_8) :named @p_1737) (! (+ @p_297 0) :named @p_1736)) :named @p_1738) false) :named @p_1747)) (not @p_1738) false) :rule equiv_pos2)
(step t2165.t1 (cl (= @p_1738 (! (not (! (>= @p_1737 @p_1736) :named @p_1748)) :named @p_1749))) :rule rare_rewrite :args ("arith-elim-lt" @p_1737 @p_1736))
(step t2165.t2 (cl (= @p_1737 0)) :rule poly_simp)
(step t2165.t3 (cl (= @p_297 0)) :rule evaluate)
(step t2165.t4 (cl (= @p_1736 @p_864)) :rule cong :premises (t2165.t3 t604))
(step t2165.t5 (cl (= @p_864 0)) :rule evaluate)
(step t2165.t6 (cl (= @p_1736 0)) :rule trans :premises (t2165.t4 t2165.t5))
(step t2165.t7 (cl (= @p_1748 @p_366)) :rule cong :premises (t2165.t2 t2165.t6))
(step t2165.t8 (cl (= @p_366 true)) :rule evaluate)
(step t2165.t9 (cl (= @p_1748 true)) :rule trans :premises (t2165.t7 t2165.t8))
(step t2165.t10 (cl (= @p_1749 @p_365)) :rule cong :premises (t2165.t9))
(step t2165.t11 (cl (= @p_365 false)) :rule evaluate)
(step t2165.t12 (cl (= @p_1749 false)) :rule trans :premises (t2165.t10 t2165.t11))
(step t2165.t13 (cl @p_1747) :rule trans :premises (t2165.t1 t2165.t12))
(step t2165.t14 (cl (not (! (< @p_11 @p_297) :named @p_1739)) @p_1037 @p_1738) :rule la_generic :args (1/1 1/1 1/1))
(step t2165.t15 (cl (=> (! (and @p_308 (! (> @p_8 0) :named @p_1740)) :named @p_1741) @p_1739)) :rule la_mult_neg)
(step t2165.t16 (cl (not @p_1741) @p_1739) :rule implies :premises (t2165.t15))
(step t2165.t17 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2165.t18 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2165.t17))
(step t2165.t19 (cl @p_310) :rule evaluate)
(step t2165.t20 (cl @p_308) :rule resolution :premises (t2165.t18 t2165.t19))
(step t2165.t21 (cl (not (! (= @p_1074 @p_1740) :named @p_1742)) @p_1731 @p_1740) :rule equiv_pos2)
(step t2165.t22 (cl (= @p_1074 @p_1052)) :rule cong :premises (t2155))
(step t2165.t23 (cl (= @p_1074 @p_1049)) :rule trans :premises (t2165.t22 t690))
(step t2165.t24 (cl (= @p_1740 (! (not (! (>= 0 @p_8) :named @p_1745)) :named @p_1746))) :rule rare_rewrite :args ("arith-elim-gt" @p_8 0))
(step t2165.t25 (cl (= @p_1065 @p_1745)) :rule rare_rewrite :args ("arith-elim-leq" @p_8 0))
(step t2165.t26 (cl (= @p_1745 @p_1065)) :rule symm :premises (t2165.t25))
(step t2165.t27 (cl (= @p_1746 @p_1074)) :rule cong :premises (t2165.t26))
(step t2165.t28 (cl (= @p_1740 @p_1074)) :rule trans :premises (t2165.t24 t2165.t27))
(step t2165.t29 (cl (= @p_1740 @p_1049)) :rule trans :premises (t2165.t28 t2165.t23))
(step t2165.t30 (cl (= @p_1049 @p_1740)) :rule symm :premises (t2165.t29))
(step t2165.t31 (cl @p_1742) :rule trans :premises (t2165.t23 t2165.t30))
(step t2165.t32 (cl @p_1740) :rule resolution :premises (t2165.t21 t2165.t31 t2165.a0))
(step t2165.t33 (cl @p_1741) :rule and_intro :premises (t2165.t20 t2165.t32))
(step t2165.t34 (cl @p_1739) :rule resolution :premises (t2165.t16 t2165.t33))
(step t2165.t35 (cl @p_1036 @p_1013 @p_1031) :rule equiv_pos2)
(step t2165.t36 (cl @p_1035) :rule rare_rewrite :args ("arith-elim-lt" @p_8 0))
(step t2165.t37 (cl @p_1034) :rule symm :premises (t2165.t36))
(step t2165.t38 (cl @p_1031) :rule resolution :premises (t2165.t35 t2165.t37 t2165.a1))
(step t2165.t39 (cl @p_1738) :rule resolution :premises (t2165.t14 t2165.t34 t2165.t38))
(step t2165.t40 (cl false) :rule resolution :premises (t2165.t0 t2165.t13 t2165.t39))
(step t2165 (cl @p_1731 @p_1013 false) :rule subproof :discharge (t2165.a0 t2165.a1))
(step t2166 (cl (! (not @p_1733) :named @p_1734) @p_1074) :rule and_pos :args (0))
(step t2167 (cl @p_1734 @p_16) :rule and_pos :args (1))
(step t2168 (cl false @p_1734 @p_1734) :rule resolution :premises (t2165 t2166 t2167))
(step t2169 (cl @p_1734 @p_1734 false) :rule reordering :premises (t2168))
(step t2170 (cl @p_1734 false) :rule contraction :premises (t2169))
(step t2171 (cl @p_1735 false) :rule resolution :premises (t2164 t2170))
(step t2172 (cl @p_1735 @p_212) :rule implies_neg2)
(step t2173 (cl @p_1735 @p_1735) :rule resolution :premises (t2171 t2172))
(step t2174 (cl @p_1735) :rule contraction :premises (t2173))
(step t2175 (cl (= @p_1735 @p_1734)) :rule implies_simplify)
(step t2176 (cl (not @p_1735) @p_1734) :rule equiv1 :premises (t2175))
(step t2177 (cl @p_1734) :rule resolution :premises (t2174 t2176))
(step t2178 (cl @p_1731 @p_1013) :rule not_and :premises (t2177))
(step t2179 (cl @p_1732 (not @p_1731)) :rule or_neg :args (0))
(step t2180 (cl @p_1732 @p_1015) :rule or_neg :args (1))
(step t2181 (cl @p_1732 @p_1732) :rule resolution :premises (t2178 t2179 t2180))
(step t2182 (cl @p_1732) :rule contraction :premises (t2181))
(step t2183 (cl @p_1730) :rule resolution :premises (t2158 t2163 t2182))
(step t2184 (cl @p_1729) :rule resolution :premises (t2150 t2157 t2183))
(step t2185 (cl @p_1051 @p_15) :rule or :premises (t2184))
(step t2186 (cl @p_15 @p_1051) :rule reordering :premises (t2185))
(step t2187 (cl @p_15) :rule resolution :premises (t2186 t2148))
(step t2188 (cl (not (! (= (! (or @p_112 @p_929 @p_671 @p_806 @p_13) :named @p_1597) (! (or @p_112 @p_974 @p_671 @p_798 @p_13) :named @p_1596)) :named @p_1611)) (not @p_1597) @p_1596) :rule equiv_pos2)
(step t2189 (cl @p_1611) :rule cong :premises (t1801 t1798 t656 t657))
(step t2190 (cl (not (! (= (! (or @p_673 @p_929 @p_671 @p_806 @p_980) :named @p_1598) @p_1597) :named @p_1610)) (not @p_1598) @p_1597) :rule equiv_pos2)
(step t2191 (cl (= @p_1598 @p_1596)) :rule cong :premises (t38 t1801 t1798 t656 t660))
(step t2192 (cl (= @p_1596 @p_1597)) :rule symm :premises (t2189))
(step t2193 (cl @p_1610) :rule trans :premises (t2191 t2192))
(step t2194 (cl (! (=> (! (and @p_113 @p_923 @p_670 @p_801 @p_14) :named @p_1600) false) :named @p_1602) @p_1600) :rule implies_neg1)
(anchor :step t2195)
(assume t2195.a0 @p_113)
(assume t2195.a1 @p_923)
(assume t2195.a2 @p_670)
(assume t2195.a3 @p_801)
(assume t2195.a4 @p_14)
(step t2195.t0 (cl (not (! (= (! (< (! (+ @p_12 @p_111 @p_689 @p_692 @p_988) :named @p_1604) (! (+ 1 0 @p_298 @p_297 @p_297) :named @p_1603)) :named @p_1605) false) :named @p_1606)) (not @p_1605) false) :rule equiv_pos2)
(step t2195.t1 (cl (= @p_1605 (! (not (! (>= @p_1604 @p_1603) :named @p_1607)) :named @p_1608))) :rule rare_rewrite :args ("arith-elim-lt" @p_1604 @p_1603))
(step t2195.t2 (cl (= @p_1604 @p_1216)) :rule poly_simp)
(step t2195.t3 (cl (= @p_722 0)) :rule poly_simp)
(step t2195.t4 (cl (= @p_668 @p_668)) :rule refl)
(step t2195.t5 (cl (= @p_1007 0)) :rule poly_simp)
(step t2195.t6 (cl (= @p_690 @p_690)) :rule refl)
(step t2195.t7 (cl @p_168) :rule refl)
(step t2195.t8 (cl @p_167) :rule refl)
(step t2195.t9 (cl (= @p_617 0)) :rule poly_simp)
(step t2195.t10 (cl (= @p_1216 @p_1217)) :rule cong :premises (t2195.t3 t2195.t4 t2195.t5 t2195.t6 t2195.t7 t2195.t8 t2195.t9))
(step t2195.t11 (cl (= @p_1217 0)) :rule poly_simp)
(step t2195.t12 (cl (= @p_1216 0)) :rule trans :premises (t2195.t10 t2195.t11))
(step t2195.t13 (cl (= @p_1604 0)) :rule trans :premises (t2195.t2 t2195.t12))
(step t2195.t14 (cl (= @p_298 -1)) :rule evaluate)
(step t2195.t15 (cl (= @p_297 0)) :rule evaluate)
(step t2195.t16 (cl (= @p_1603 (! (+ 1 0 -1 0 0) :named @p_1609))) :rule cong :premises (t2195.t14 t2195.t15 t2195.t15))
(step t2195.t17 (cl (= @p_1609 0)) :rule evaluate)
(step t2195.t18 (cl (= @p_1603 0)) :rule trans :premises (t2195.t16 t2195.t17))
(step t2195.t19 (cl (= @p_1607 @p_366)) :rule cong :premises (t2195.t13 t2195.t18))
(step t2195.t20 (cl (= @p_366 true)) :rule evaluate)
(step t2195.t21 (cl (= @p_1607 true)) :rule trans :premises (t2195.t19 t2195.t20))
(step t2195.t22 (cl (= @p_1608 @p_365)) :rule cong :premises (t2195.t21))
(step t2195.t23 (cl (= @p_365 false)) :rule evaluate)
(step t2195.t24 (cl (= @p_1608 false)) :rule trans :premises (t2195.t22 t2195.t23))
(step t2195.t25 (cl @p_1606) :rule trans :premises (t2195.t1 t2195.t24))
(step t2195.t26 (cl @p_1001 @p_1397 @p_954 @p_716 @p_1002 @p_1605) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 1/1))
(step t2195.t27 (cl @p_1000 @p_980 @p_996) :rule equiv_pos2)
(step t2195.t28 (cl (= @p_996 @p_14)) :rule rare_rewrite :args ("arith-elim-lt" @p_12 1))
(step t2195.t29 (cl @p_999) :rule symm :premises (t2195.t28))
(step t2195.t30 (cl @p_996) :rule resolution :premises (t2195.t27 t2195.t29 t2195.a4))
(step t2195.t31 (cl @p_715 @p_1396) :rule la_generic :args (1/1 1/1))
(step t2195.t32 (cl @p_704 @p_673 @p_700) :rule equiv_pos2)
(step t2195.t33 (cl (= @p_700 @p_113)) :rule rare_rewrite :args ("arith-elim-lt" @p_111 1))
(step t2195.t34 (cl @p_703) :rule symm :premises (t2195.t33))
(step t2195.t35 (cl @p_700) :rule resolution :premises (t2195.t32 t2195.t34 t2195.a0))
(step t2195.t36 (cl @p_1396) :rule resolution :premises (t2195.t31 t2195.t35))
(step t2195.t37 (cl (=> @p_948 @p_947)) :rule la_mult_neg)
(step t2195.t38 (cl @p_950 @p_947) :rule implies :premises (t2195.t37))
(step t2195.t39 (cl (= @p_310 @p_308)) :rule equiv_simplify)
(step t2195.t40 (cl (not @p_310) @p_308) :rule equiv1 :premises (t2195.t39))
(step t2195.t41 (cl @p_310) :rule evaluate)
(step t2195.t42 (cl @p_308) :rule resolution :premises (t2195.t40 t2195.t41))
(step t2195.t43 (cl @p_58) :rule symm :premises (t2195.a1))
(step t2195.t44 (cl @p_948) :rule and_intro :premises (t2195.t42 t2195.t43))
(step t2195.t45 (cl @p_947) :rule resolution :premises (t2195.t38 t2195.t44))
(step t2195.t46 (cl (=> @p_698 @p_696)) :rule la_mult_neg)
(step t2195.t47 (cl (not @p_698) @p_696) :rule implies :premises (t2195.t46))
(step t2195.t48 (cl (not @p_699) @p_671 @p_697) :rule equiv_pos2)
(step t2195.t49 (cl (= (* 1 (- @p_691 0)) (* 1 (- @p_6 @p_669)))) :rule poly_simp)
(step t2195.t50 (cl (= @p_697 @p_670)) :rule poly_simp_rel :premises (t2195.t49))
(step t2195.t51 (cl @p_699) :rule symm :premises (t2195.t50))
(step t2195.t52 (cl @p_697) :rule resolution :premises (t2195.t48 t2195.t51 t758))
(step t2195.t53 (cl @p_698) :rule and_intro :premises (t2195.t42 t2195.t52))
(step t2195.t54 (cl @p_696) :rule resolution :premises (t2195.t47 t2195.t53))
(step t2195.t55 (cl (=> @p_993 @p_992)) :rule la_mult_neg)
(step t2195.t56 (cl (not @p_993) @p_992) :rule implies :premises (t2195.t55))
(step t2195.t57 (cl @p_993) :rule and_intro :premises (t2195.t42 t1846))
(step t2195.t58 (cl @p_992) :rule resolution :premises (t2195.t56 t2195.t57))
(step t2195.t59 (cl @p_1605) :rule resolution :premises (t2195.t26 t2195.t30 t2195.t36 t2195.t45 t2195.t54 t2195.t58))
(step t2195.t60 (cl false) :rule resolution :premises (t2195.t0 t2195.t25 t2195.t59))
(step t2195 (cl @p_673 @p_929 @p_671 @p_806 @p_980 false) :rule subproof :discharge (t2195.a0 t2195.a1 t2195.a2 t2195.a3 t2195.a4))
(step t2196 (cl (! (not @p_1600) :named @p_1601) @p_113) :rule and_pos :args (0))
(step t2197 (cl @p_1601 @p_923) :rule and_pos :args (1))
(step t2198 (cl @p_1601 @p_670) :rule and_pos :args (2))
(step t2199 (cl @p_1601 @p_801) :rule and_pos :args (3))
(step t2200 (cl @p_1601 @p_14) :rule and_pos :args (4))
(step t2201 (cl false @p_1601 @p_1601 @p_1601 @p_1601 @p_1601) :rule resolution :premises (t2195 t2196 t2197 t2198 t2199 t2200))
(step t2202 (cl @p_1601 @p_1601 @p_1601 @p_1601 @p_1601 false) :rule reordering :premises (t2201))
(step t2203 (cl @p_1601 false) :rule contraction :premises (t2202))
(step t2204 (cl @p_1602 false) :rule resolution :premises (t2194 t2203))
(step t2205 (cl @p_1602 @p_212) :rule implies_neg2)
(step t2206 (cl @p_1602 @p_1602) :rule resolution :premises (t2204 t2205))
(step t2207 (cl @p_1602) :rule contraction :premises (t2206))
(step t2208 (cl (= @p_1602 @p_1601)) :rule implies_simplify)
(step t2209 (cl (not @p_1602) @p_1601) :rule equiv1 :premises (t2208))
(step t2210 (cl @p_1601) :rule resolution :premises (t2207 t2209))
(step t2211 (cl @p_673 @p_929 @p_671 @p_806 @p_980) :rule not_and :premises (t2210))
(step t2212 (cl @p_1598 @p_676) :rule or_neg :args (0))
(step t2213 (cl @p_1598 @p_1599) :rule or_neg :args (1))
(step t2214 (cl @p_1598 @p_677) :rule or_neg :args (2))
(step t2215 (cl @p_1598 @p_983) :rule or_neg :args (3))
(step t2216 (cl @p_1598 @p_982) :rule or_neg :args (4))
(step t2217 (cl @p_1598 @p_1598 @p_1598 @p_1598 @p_1598) :rule resolution :premises (t2211 t2212 t2213 t2214 t2215 t2216))
(step t2218 (cl @p_1598) :rule contraction :premises (t2217))
(step t2219 (cl @p_1597) :rule resolution :premises (t2190 t2193 t2218))
(step t2220 (cl @p_1596) :rule resolution :premises (t2188 t2189 t2219))
(step t2221 (cl @p_112 @p_974 @p_671 @p_798 @p_13) :rule or :premises (t2220))
(step t2222 (cl @p_112 @p_671 @p_798 @p_974 @p_13) :rule reordering :premises (t2221))
(step t2223 (cl @p_807 @p_808 @p_793) :rule equiv_pos2)
(step t2224 (cl @p_805 @p_806 @p_800) :rule equiv_pos2)
(step t2225 (cl @p_800) :rule resolution :premises (t2224 t1843 t1845))
(step t2226 (cl @p_793) :rule resolution :premises (t2223 t1840 t2225))
(step t2227 (cl @p_13) :rule resolution :premises (t2222 t1794 t758 t2226 t2145))
(step t2228 (cl) :rule resolution :premises (t1 t2149 t2187 t2227 t649))
)
a78880af77f55a18cd90a04e9e7881248d3ccaeb 39 0
unsat
(
(assume a4 (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d)))))))
(assume a5 (! (not (! (pred$e 1) :named @p_1)) :named @p_2))
(step t0 (cl (! (=> (forall ((?v0 Int)) (pred$e ?v0)) @p_1) :named @p_10) (forall ((?v0 Int)) (pred$e ?v0))) :rule implies_neg1)
(anchor :step t1)
(assume t1.a0 (forall ((?v0 Int)) (pred$e ?v0)))
(step t1.t0 (cl (or (! (not (forall ((?v0 Int)) (pred$e ?v0))) :named @p_9) @p_1)) :rule forall_inst :args (1))
(step t1.t1 (cl @p_9 @p_1) :rule or :premises (t1.t0))
(step t1.t2 (cl (not (! (= (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d)))))) (forall ((?v0 Int)) (pred$e ?v0))) :named @p_3)) (not (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d))))))) (forall ((?v0 Int)) (pred$e ?v0))) :rule equiv_pos2)
(anchor :step t1.t3 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1.t3.t0 (cl (= (! (or (! (pred$d (cons$d ?v0 nil$d)) :named @p_7) (not @p_7)) :named @p_8) true)) :rule rare_rewrite :args ("bool-or-taut" rare-list @p_7 rare-list rare-list))
(step t1.t3.t1 (cl (= (and (! (pred$e ?v0) :named @p_5) @p_8) (! (and @p_5 true) :named @p_6))) :rule cong :premises (t1.t3.t0))
(step t1.t3 (cl (= (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d)))))) (forall ((?v0 Int)) (and (pred$e ?v0) true)))) :rule bind)
(anchor :step t1.t4 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t1.t4.t0 (cl (= @p_6 @p_5)) :rule aci_simp)
(step t1.t4 (cl (= (forall ((?v0 Int)) (and (pred$e ?v0) true)) (forall ((?v0 Int)) (pred$e ?v0)))) :rule bind)
(step t1.t5 (cl @p_3) :rule trans :premises (t1.t3 t1.t4))
(step t1.t6 (cl (forall ((?v0 Int)) (pred$e ?v0))) :rule resolution :premises (t1.t2 t1.t5 a4))
(step t1.t7 (cl @p_1) :rule resolution :premises (t1.t1 t1.t6))
(step t1 (cl @p_9 @p_1) :rule subproof :discharge (t1.a0))
(step t2 (cl @p_10 @p_1) :rule resolution :premises (t0 t1))
(step t3 (cl @p_10 @p_2) :rule implies_neg2)
(step t4 (cl @p_10 @p_10) :rule resolution :premises (t2 t3))
(step t5 (cl @p_10) :rule contraction :premises (t4))
(step t6 (cl @p_9 @p_1) :rule implies :premises (t5))
(step t7 (cl @p_1 @p_9) :rule reordering :premises (t6))
(step t8 (cl (not @p_3) (not (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d))))))) (forall ((?v0 Int)) (pred$e ?v0))) :rule equiv_pos2)
(anchor :step t9 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t9.t0 (cl (= @p_8 true)) :rule rare_rewrite :args ("bool-or-taut" rare-list @p_7 rare-list rare-list))
(step t9.t1 (cl (= (and @p_5 @p_8) @p_6)) :rule cong :premises (t9.t0))
(step t9 (cl (= (forall ((?v0 Int)) (and (pred$e ?v0) (or (pred$d (cons$d ?v0 nil$d)) (not (pred$d (cons$d ?v0 nil$d)))))) (forall ((?v0 Int)) (and (pred$e ?v0) true)))) :rule bind)
(anchor :step t10 :args ((?v0 Int) (:= (?v0 Int) ?v0)))
(step t10.t0 (cl (= @p_6 @p_5)) :rule aci_simp)
(step t10 (cl (= (forall ((?v0 Int)) (and (pred$e ?v0) true)) (forall ((?v0 Int)) (pred$e ?v0)))) :rule bind)
(step t11 (cl @p_3) :rule trans :premises (t9 t10))
(step t12 (cl (forall ((?v0 Int)) (pred$e ?v0))) :rule resolution :premises (t8 t11 a4))
(step t13 (cl) :rule resolution :premises (t7 a5 t12))
)
a0a1dcf06ac8195e17b92efe240610da2f7e8013 412 0
unsat
(
(assume a0 (forall ((?v0 Int)) (= (of_nat$ (g$ (some$ ?v0))) (of_nat$ (g$a (cons$ ?v0 nil$))))))
(assume a1 (forall ((?v0 Bool)) (= (of_nat$ (g$b (some$a ?v0))) (of_nat$ (g$c (cons$a ?v0 nil$a))))))
(assume a6 (forall ((?v0 Bool_list$)) (= (of_nat$ (g$c ?v0)) (of_nat$ (size$ ?v0)))))
(assume a7 (forall ((?v0 Int_list$)) (= (of_nat$ (g$a ?v0)) (of_nat$ (size$a ?v0)))))
(assume a12 (! (= (! (of_nat$ (size$ nil$a)) :named @p_1) 0) :named @p_2))
(assume a13 (! (= (! (of_nat$ (size$a nil$)) :named @p_3) 0) :named @p_4))
(assume a14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1)))))
(assume a15 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1)))))
(assume a16 (! (not (! (= (! (of_nat$ (g$ (some$ 3))) :named @p_8) (! (of_nat$ (! (g$b (! (some$a true) :named @p_5)) :named @p_6)) :named @p_7)) :named @p_9)) :named @p_10))
(step t0 (cl (not (! (= (! (or (! (not @p_2) :named @p_61) (! (not @p_4) :named @p_62) (! (not @p_10) :named @p_13) (! (not (! (= @p_8 (! (of_nat$ (g$a (! (cons$ 3 nil$) :named @p_14))) :named @p_15)) :named @p_16)) :named @p_63) (! (not (! (= @p_7 (! (of_nat$ (g$c (! (cons$a true nil$a) :named @p_19))) :named @p_20)) :named @p_21)) :named @p_64) (! (not (! (= @p_15 (! (of_nat$ (size$a @p_14)) :named @p_24)) :named @p_25)) :named @p_65) (! (not (! (= @p_20 (! (of_nat$ (size$ @p_19)) :named @p_28)) :named @p_29)) :named @p_66) (! (not (! (= @p_1 (! (+ -1 @p_28) :named @p_32)) :named @p_33)) :named @p_67) (! (not (! (= @p_3 (! (+ -1 @p_24) :named @p_47)) :named @p_48)) :named @p_68)) :named @p_70) (! (or @p_61 @p_62 @p_9 @p_63 @p_64 @p_65 @p_66 @p_67 @p_68) :named @p_69)) :named @p_95)) (not @p_70) @p_69) :rule equiv_pos2)
(step t1 (cl (= @p_13 @p_9)) :rule rare_rewrite :args ("bool-double-not-elim" @p_9))
(step t2 (cl (= @p_63 @p_63)) :rule refl)
(step t3 (cl (= @p_64 @p_64)) :rule refl)
(step t4 (cl (= @p_65 @p_65)) :rule refl)
(step t5 (cl (= @p_66 @p_66)) :rule refl)
(step t6 (cl (= @p_67 @p_67)) :rule refl)
(step t7 (cl (= @p_68 @p_68)) :rule refl)
(step t8 (cl @p_95) :rule cong :premises (t1 t2 t3 t4 t5 t6 t7))
(step t9 (cl (! (=> (! (and @p_2 @p_4 @p_10 @p_16 @p_21 @p_25 @p_29 @p_33 @p_48) :named @p_72) (! (and (! (= @p_7 @p_28) :named @p_77) (! (= 0 @p_32) :named @p_76) (! (= 0 @p_47) :named @p_75) (! (= @p_8 @p_24) :named @p_74) @p_10) :named @p_78)) :named @p_94) @p_72) :rule implies_neg1)
(anchor :step t10)
(assume t10.a0 @p_2)
(assume t10.a1 @p_4)
(assume t10.a2 @p_10)
(assume t10.a3 @p_16)
(assume t10.a4 @p_21)
(assume t10.a5 @p_25)
(assume t10.a6 @p_29)
(assume t10.a7 @p_33)
(assume t10.a8 @p_48)
(step t10.t0 (cl (! (or (! (not (forall ((?v0 Bool)) (= (of_nat$ (g$b (some$a ?v0))) (of_nat$ (g$c (cons$a ?v0 nil$a)))))) :named @p_22) @p_21) :named @p_23)) :rule forall_inst :args (true))
(step t10.t1 (cl @p_22 @p_21) :rule or :premises (t10.t0))
(step t10.t2 (cl @p_21) :rule resolution :premises (t10.t1 a1))
(step t10.t3 (cl (! (or (! (not (forall ((?v0 Bool_list$)) (= (of_nat$ (g$c ?v0)) (of_nat$ (size$ ?v0))))) :named @p_30) @p_29) :named @p_31)) :rule forall_inst :args (@p_19))
(step t10.t4 (cl @p_30 @p_29) :rule or :premises (t10.t3))
(step t10.t5 (cl @p_29) :rule resolution :premises (t10.t4 a6))
(step t10.t6 (cl @p_77) :rule trans :premises (t10.t2 t10.t5))
(step t10.t7 (cl (= 0 @p_1)) :rule symm :premises (t10.a0))
(step t10.t8 (cl (not (! (= (! (=> (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1))))) (! (= @p_28 (! (+ 1 @p_1) :named @p_43)) :named @p_44)) :named @p_45) (! (=> (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1))))) @p_33) :named @p_42)) :named @p_46)) (not @p_45) @p_42) :rule equiv_pos2)
(step t10.t9 (cl (= (* 1 (- @p_28 @p_43)) (* -1 (- @p_1 @p_32)))) :rule poly_simp)
(step t10.t10 (cl (= @p_44 @p_33)) :rule poly_simp_rel :premises (t10.t9))
(step t10.t11 (cl @p_46) :rule cong :premises (t10.t10))
(step t10.t12 (cl @p_45 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule implies_neg1)
(anchor :step t10.t13)
(assume t10.t13.a0 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1))))))
(step t10.t13.t0 (cl (or (! (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :named @p_41) @p_44)) :rule forall_inst :args (true nil$a))
(step t10.t13.t1 (cl @p_41 @p_44) :rule or :premises (t10.t13.t0))
(step t10.t13.t2 (cl (not (! (= (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1)))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :named @p_34)) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t10.t13.t3 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t10.t13.t3.t0 (cl (= (! (+ 0 1) :named @p_38) 1)) :rule evaluate)
(step t10.t13.t3.t1 (cl (= (! (+ (! (of_nat$ (size$ ?v1)) :named @p_35) @p_38) :named @p_39) (! (+ @p_35 1) :named @p_40))) :rule cong :premises (t10.t13.t3.t0))
(step t10.t13.t3.t2 (cl (= @p_40 (! (+ 1 @p_35) :named @p_36))) :rule poly_simp)
(step t10.t13.t3.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t10.t13.t3.t1 t10.t13.t3.t2))
(step t10.t13.t3.t4 (cl (= (= (! (of_nat$ (size$ (cons$a ?v0 ?v1))) :named @p_37) @p_39) (= @p_37 @p_36))) :rule cong :premises (t10.t13.t3.t3))
(step t10.t13.t3 (cl @p_34) :rule bind)
(step t10.t13.t4 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t10.t13.t2 t10.t13.t3 a14))
(step t10.t13.t5 (cl @p_44) :rule resolution :premises (t10.t13.t1 t10.t13.t4))
(step t10.t13 (cl @p_41 @p_44) :rule subproof :discharge (t10.t13.a0))
(step t10.t14 (cl @p_45 @p_44) :rule resolution :premises (t10.t12 t10.t13))
(step t10.t15 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t10.t16 (cl @p_45 @p_45) :rule resolution :premises (t10.t14 t10.t15))
(step t10.t17 (cl @p_45) :rule contraction :premises (t10.t16))
(step t10.t18 (cl @p_42) :rule resolution :premises (t10.t8 t10.t11 t10.t17))
(step t10.t19 (cl @p_41 @p_33) :rule implies :premises (t10.t18))
(step t10.t20 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t10.t21 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t10.t21.t0 (cl (= @p_38 1)) :rule evaluate)
(step t10.t21.t1 (cl (= @p_39 @p_40)) :rule cong :premises (t10.t21.t0))
(step t10.t21.t2 (cl (= @p_40 @p_36)) :rule poly_simp)
(step t10.t21.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t10.t21.t1 t10.t21.t2))
(step t10.t21.t4 (cl (= (= @p_37 @p_39) (= @p_37 @p_36))) :rule cong :premises (t10.t21.t3))
(step t10.t21 (cl @p_34) :rule bind)
(step t10.t22 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t10.t20 t10.t21 a14))
(step t10.t23 (cl @p_33) :rule resolution :premises (t10.t19 t10.t22))
(step t10.t24 (cl @p_76) :rule trans :premises (t10.t7 t10.t23))
(step t10.t25 (cl (= 0 @p_3)) :rule symm :premises (t10.a1))
(step t10.t26 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1))))) (! (= @p_24 (! (+ 1 @p_3) :named @p_57)) :named @p_58)) :named @p_59) (! (=> (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1))))) @p_48) :named @p_56)) :named @p_60)) (not @p_59) @p_56) :rule equiv_pos2)
(step t10.t27 (cl (= (* 1 (- @p_24 @p_57)) (* -1 (- @p_3 @p_47)))) :rule poly_simp)
(step t10.t28 (cl (= @p_58 @p_48)) :rule poly_simp_rel :premises (t10.t27))
(step t10.t29 (cl @p_60) :rule cong :premises (t10.t28))
(step t10.t30 (cl @p_59 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule implies_neg1)
(anchor :step t10.t31)
(assume t10.t31.a0 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1))))))
(step t10.t31.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :named @p_55) @p_58)) :rule forall_inst :args (3 nil$))
(step t10.t31.t1 (cl @p_55 @p_58) :rule or :premises (t10.t31.t0))
(step t10.t31.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1)))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :named @p_49)) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t10.t31.t3 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t10.t31.t3.t0 (cl (= @p_38 1)) :rule evaluate)
(step t10.t31.t3.t1 (cl (= (! (+ (! (of_nat$ (size$a ?v1)) :named @p_50) @p_38) :named @p_53) (! (+ @p_50 1) :named @p_54))) :rule cong :premises (t10.t31.t3.t0))
(step t10.t31.t3.t2 (cl (= @p_54 (! (+ 1 @p_50) :named @p_51))) :rule poly_simp)
(step t10.t31.t3.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t10.t31.t3.t1 t10.t31.t3.t2))
(step t10.t31.t3.t4 (cl (= (= (! (of_nat$ (size$a (cons$ ?v0 ?v1))) :named @p_52) @p_53) (= @p_52 @p_51))) :rule cong :premises (t10.t31.t3.t3))
(step t10.t31.t3 (cl @p_49) :rule bind)
(step t10.t31.t4 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t10.t31.t2 t10.t31.t3 a15))
(step t10.t31.t5 (cl @p_58) :rule resolution :premises (t10.t31.t1 t10.t31.t4))
(step t10.t31 (cl @p_55 @p_58) :rule subproof :discharge (t10.t31.a0))
(step t10.t32 (cl @p_59 @p_58) :rule resolution :premises (t10.t30 t10.t31))
(step t10.t33 (cl @p_59 (not @p_58)) :rule implies_neg2)
(step t10.t34 (cl @p_59 @p_59) :rule resolution :premises (t10.t32 t10.t33))
(step t10.t35 (cl @p_59) :rule contraction :premises (t10.t34))
(step t10.t36 (cl @p_56) :rule resolution :premises (t10.t26 t10.t29 t10.t35))
(step t10.t37 (cl @p_55 @p_48) :rule implies :premises (t10.t36))
(step t10.t38 (cl (not @p_49) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t10.t39 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t10.t39.t0 (cl (= @p_38 1)) :rule evaluate)
(step t10.t39.t1 (cl (= @p_53 @p_54)) :rule cong :premises (t10.t39.t0))
(step t10.t39.t2 (cl (= @p_54 @p_51)) :rule poly_simp)
(step t10.t39.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t10.t39.t1 t10.t39.t2))
(step t10.t39.t4 (cl (= (= @p_52 @p_53) (= @p_52 @p_51))) :rule cong :premises (t10.t39.t3))
(step t10.t39 (cl @p_49) :rule bind)
(step t10.t40 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t10.t38 t10.t39 a15))
(step t10.t41 (cl @p_48) :rule resolution :premises (t10.t37 t10.t40))
(step t10.t42 (cl @p_75) :rule trans :premises (t10.t25 t10.t41))
(step t10.t43 (cl (! (or (! (not (forall ((?v0 Int)) (= (of_nat$ (g$ (some$ ?v0))) (of_nat$ (g$a (cons$ ?v0 nil$)))))) :named @p_17) @p_16) :named @p_18)) :rule forall_inst :args (3))
(step t10.t44 (cl @p_17 @p_16) :rule or :premises (t10.t43))
(step t10.t45 (cl @p_16) :rule resolution :premises (t10.t44 a0))
(step t10.t46 (cl (! (or (! (not (forall ((?v0 Int_list$)) (= (of_nat$ (g$a ?v0)) (of_nat$ (size$a ?v0))))) :named @p_26) @p_25) :named @p_27)) :rule forall_inst :args (@p_14))
(step t10.t47 (cl @p_26 @p_25) :rule or :premises (t10.t46))
(step t10.t48 (cl @p_25) :rule resolution :premises (t10.t47 a7))
(step t10.t49 (cl @p_74) :rule trans :premises (t10.t45 t10.t48))
(step t10.t50 (cl (not (! (= @p_10 @p_10) :named @p_11)) @p_13 @p_10) :rule equiv_pos2)
(step t10.t51 (cl (! (= true true) :named @p_12)) :rule refl)
(step t10.t52 (cl @p_12) :rule symm :premises (t10.t51))
(step t10.t53 (cl (= @p_5 @p_5)) :rule cong :premises (t10.t52))
(step t10.t54 (cl (= @p_6 @p_6)) :rule cong :premises (t10.t53))
(step t10.t55 (cl (= @p_7 @p_7)) :rule cong :premises (t10.t54))
(step t10.t56 (cl (= @p_9 @p_9)) :rule cong :premises (t10.t55))
(step t10.t57 (cl @p_11) :rule cong :premises (t10.t56))
(step t10.t58 (cl @p_10) :rule resolution :premises (t10.t50 t10.t57 t10.a2))
(step t10.t59 (cl @p_78) :rule and_intro :premises (t10.t6 t10.t24 t10.t42 t10.t49 t10.t58))
(step t10 (cl @p_61 @p_62 @p_13 @p_63 @p_64 @p_65 @p_66 @p_67 @p_68 @p_78) :rule subproof :discharge (t10.a0 t10.a1 t10.a2 t10.a3 t10.a4 t10.a5 t10.a6 t10.a7 t10.a8))
(step t11 (cl (! (not @p_72) :named @p_73) @p_2) :rule and_pos :args (0))
(step t12 (cl @p_73 @p_4) :rule and_pos :args (1))
(step t13 (cl @p_73 @p_10) :rule and_pos :args (2))
(step t14 (cl @p_73 @p_16) :rule and_pos :args (3))
(step t15 (cl @p_73 @p_21) :rule and_pos :args (4))
(step t16 (cl @p_73 @p_25) :rule and_pos :args (5))
(step t17 (cl @p_73 @p_29) :rule and_pos :args (6))
(step t18 (cl @p_73 @p_33) :rule and_pos :args (7))
(step t19 (cl @p_73 @p_48) :rule and_pos :args (8))
(step t20 (cl @p_78 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73) :rule resolution :premises (t10 t11 t12 t13 t14 t15 t16 t17 t18 t19))
(step t21 (cl @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_73 @p_78) :rule reordering :premises (t20))
(step t22 (cl @p_73 @p_78) :rule contraction :premises (t21))
(step t23 (cl @p_94 @p_78) :rule resolution :premises (t9 t22))
(step t24 (cl @p_94 (! (not @p_78) :named @p_79)) :rule implies_neg2)
(step t25 (cl @p_94 @p_94) :rule resolution :premises (t23 t24))
(step t26 (cl @p_94) :rule contraction :premises (t25))
(step t27 (cl @p_73 @p_78) :rule implies :premises (t26))
(step t28 (cl (not (! (= (! (=> @p_78 (! (= false true) :named @p_80)) :named @p_81) @p_79) :named @p_90)) (not @p_81) @p_79) :rule equiv_pos2)
(step t29 (cl (= (* -1 (- 0 @p_32)) (* 1 (- @p_28 1)))) :rule poly_simp)
(step t30 (cl (! (= @p_76 (! (= @p_28 1) :named @p_85)) :named @p_86)) :rule poly_simp_rel :premises (t29))
(step t31 (cl (= (* -1 (- 0 @p_47)) (* 1 (- @p_24 1)))) :rule poly_simp)
(step t32 (cl (! (= @p_75 (! (= @p_24 1) :named @p_87)) :named @p_88)) :rule poly_simp_rel :premises (t31))
(step t33 (cl (= @p_74 @p_74)) :rule refl)
(step t34 (cl @p_11) :rule refl)
(step t35 (cl (= @p_78 (! (and @p_77 @p_85 @p_87 @p_74 @p_10) :named @p_91))) :rule cong :premises (t30 t32 t33 t34))
(step t36 (cl (= @p_80 false)) :rule evaluate)
(step t37 (cl (= @p_81 (! (=> @p_91 false) :named @p_93))) :rule cong :premises (t35 t36))
(step t38 (cl (= @p_93 (! (not @p_91) :named @p_92))) :rule rare_rewrite :args ("bool-impl-false1" @p_91))
(step t39 (cl (= @p_81 @p_92)) :rule trans :premises (t37 t38))
(step t40 (cl (= @p_79 @p_92)) :rule cong :premises (t35))
(step t41 (cl (= @p_92 @p_79)) :rule symm :premises (t40))
(step t42 (cl @p_90) :rule trans :premises (t39 t41))
(step t43 (cl @p_81 @p_78) :rule implies_neg1)
(anchor :step t44)
(assume t44.a0 @p_77)
(assume t44.a1 @p_76)
(assume t44.a2 @p_75)
(assume t44.a3 @p_74)
(assume t44.a4 @p_10)
(step t44.t0 (cl (= (! (= @p_9 false) :named @p_89) @p_10)) :rule equiv_simplify)
(step t44.t1 (cl @p_89 @p_13) :rule equiv2 :premises (t44.t0))
(step t44.t2 (cl (! (not @p_13) :named @p_71) @p_9) :rule not_not)
(step t44.t3 (cl @p_89 @p_9) :rule resolution :premises (t44.t1 t44.t2))
(step t44.t4 (cl (not @p_11) @p_13 @p_10) :rule equiv_pos2)
(step t44.t5 (cl @p_12) :rule refl)
(step t44.t6 (cl @p_12) :rule symm :premises (t44.t5))
(step t44.t7 (cl (= @p_5 @p_5)) :rule cong :premises (t44.t6))
(step t44.t8 (cl (= @p_6 @p_6)) :rule cong :premises (t44.t7))
(step t44.t9 (cl (= @p_7 @p_7)) :rule cong :premises (t44.t8))
(step t44.t10 (cl (= @p_9 @p_9)) :rule cong :premises (t44.t9))
(step t44.t11 (cl @p_11) :rule cong :premises (t44.t10))
(step t44.t12 (cl @p_10) :rule resolution :premises (t44.t4 t44.t11 t44.a4))
(step t44.t13 (cl @p_89) :rule resolution :premises (t44.t3 t44.t12))
(step t44.t14 (cl (= false @p_9)) :rule symm :premises (t44.t13))
(step t44.t15 (cl (= (! (= @p_9 true) :named @p_84) @p_9)) :rule equiv_simplify)
(step t44.t16 (cl @p_84 @p_10) :rule equiv2 :premises (t44.t15))
(step t44.t17 (cl @p_18) :rule forall_inst :args (3))
(step t44.t18 (cl @p_17 @p_16) :rule or :premises (t44.t17))
(step t44.t19 (cl @p_16) :rule resolution :premises (t44.t18 a0))
(step t44.t20 (cl @p_27) :rule forall_inst :args (@p_14))
(step t44.t21 (cl @p_26 @p_25) :rule or :premises (t44.t20))
(step t44.t22 (cl @p_25) :rule resolution :premises (t44.t21 a7))
(step t44.t23 (cl @p_74) :rule trans :premises (t44.t19 t44.t22))
(step t44.t24 (cl (not @p_88) (! (not @p_75) :named @p_83) @p_87) :rule equiv_pos2)
(step t44.t25 (cl (= 0 @p_3)) :rule symm :premises (a13))
(step t44.t26 (cl (not @p_60) (not @p_59) @p_56) :rule equiv_pos2)
(step t44.t27 (cl (= (* 1 (- @p_24 @p_57)) (* -1 (- @p_3 @p_47)))) :rule poly_simp)
(step t44.t28 (cl (= @p_58 @p_48)) :rule poly_simp_rel :premises (t44.t27))
(step t44.t29 (cl @p_60) :rule cong :premises (t44.t28))
(step t44.t30 (cl @p_59 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule implies_neg1)
(anchor :step t44.t31)
(assume t44.t31.a0 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1))))))
(step t44.t31.t0 (cl (or @p_55 @p_58)) :rule forall_inst :args (3 nil$))
(step t44.t31.t1 (cl @p_55 @p_58) :rule or :premises (t44.t31.t0))
(step t44.t31.t2 (cl (not @p_49) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t44.t31.t3 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t44.t31.t3.t0 (cl (= @p_38 1)) :rule evaluate)
(step t44.t31.t3.t1 (cl (= @p_53 @p_54)) :rule cong :premises (t44.t31.t3.t0))
(step t44.t31.t3.t2 (cl (= @p_54 @p_51)) :rule poly_simp)
(step t44.t31.t3.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t44.t31.t3.t1 t44.t31.t3.t2))
(step t44.t31.t3.t4 (cl (= (= @p_52 @p_53) (= @p_52 @p_51))) :rule cong :premises (t44.t31.t3.t3))
(step t44.t31.t3 (cl @p_49) :rule bind)
(step t44.t31.t4 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t44.t31.t2 t44.t31.t3 a15))
(step t44.t31.t5 (cl @p_58) :rule resolution :premises (t44.t31.t1 t44.t31.t4))
(step t44.t31 (cl @p_55 @p_58) :rule subproof :discharge (t44.t31.a0))
(step t44.t32 (cl @p_59 @p_58) :rule resolution :premises (t44.t30 t44.t31))
(step t44.t33 (cl @p_59 (not @p_58)) :rule implies_neg2)
(step t44.t34 (cl @p_59 @p_59) :rule resolution :premises (t44.t32 t44.t33))
(step t44.t35 (cl @p_59) :rule contraction :premises (t44.t34))
(step t44.t36 (cl @p_56) :rule resolution :premises (t44.t26 t44.t29 t44.t35))
(step t44.t37 (cl @p_55 @p_48) :rule implies :premises (t44.t36))
(step t44.t38 (cl (not @p_49) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t44.t39 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t44.t39.t0 (cl (= @p_38 1)) :rule evaluate)
(step t44.t39.t1 (cl (= @p_53 @p_54)) :rule cong :premises (t44.t39.t0))
(step t44.t39.t2 (cl (= @p_54 @p_51)) :rule poly_simp)
(step t44.t39.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t44.t39.t1 t44.t39.t2))
(step t44.t39.t4 (cl (= (= @p_52 @p_53) (= @p_52 @p_51))) :rule cong :premises (t44.t39.t3))
(step t44.t39 (cl @p_49) :rule bind)
(step t44.t40 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t44.t38 t44.t39 a15))
(step t44.t41 (cl @p_48) :rule resolution :premises (t44.t37 t44.t40))
(step t44.t42 (cl @p_75) :rule trans :premises (t44.t25 t44.t41))
(step t44.t43 (cl @p_87) :rule resolution :premises (t44.t24 t32 t44.t42))
(step t44.t44 (cl (not @p_86) (! (not @p_76) :named @p_82) @p_85) :rule equiv_pos2)
(step t44.t45 (cl (= 0 @p_1)) :rule symm :premises (a12))
(step t44.t46 (cl (not @p_46) (not @p_45) @p_42) :rule equiv_pos2)
(step t44.t47 (cl (= (* 1 (- @p_28 @p_43)) (* -1 (- @p_1 @p_32)))) :rule poly_simp)
(step t44.t48 (cl (= @p_44 @p_33)) :rule poly_simp_rel :premises (t44.t47))
(step t44.t49 (cl @p_46) :rule cong :premises (t44.t48))
(step t44.t50 (cl @p_45 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule implies_neg1)
(anchor :step t44.t51)
(assume t44.t51.a0 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1))))))
(step t44.t51.t0 (cl (or @p_41 @p_44)) :rule forall_inst :args (true nil$a))
(step t44.t51.t1 (cl @p_41 @p_44) :rule or :premises (t44.t51.t0))
(step t44.t51.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t44.t51.t3 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t44.t51.t3.t0 (cl (= @p_38 1)) :rule evaluate)
(step t44.t51.t3.t1 (cl (= @p_39 @p_40)) :rule cong :premises (t44.t51.t3.t0))
(step t44.t51.t3.t2 (cl (= @p_40 @p_36)) :rule poly_simp)
(step t44.t51.t3.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t44.t51.t3.t1 t44.t51.t3.t2))
(step t44.t51.t3.t4 (cl (= (= @p_37 @p_39) (= @p_37 @p_36))) :rule cong :premises (t44.t51.t3.t3))
(step t44.t51.t3 (cl @p_34) :rule bind)
(step t44.t51.t4 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t44.t51.t2 t44.t51.t3 a14))
(step t44.t51.t5 (cl @p_44) :rule resolution :premises (t44.t51.t1 t44.t51.t4))
(step t44.t51 (cl @p_41 @p_44) :rule subproof :discharge (t44.t51.a0))
(step t44.t52 (cl @p_45 @p_44) :rule resolution :premises (t44.t50 t44.t51))
(step t44.t53 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t44.t54 (cl @p_45 @p_45) :rule resolution :premises (t44.t52 t44.t53))
(step t44.t55 (cl @p_45) :rule contraction :premises (t44.t54))
(step t44.t56 (cl @p_42) :rule resolution :premises (t44.t46 t44.t49 t44.t55))
(step t44.t57 (cl @p_41 @p_33) :rule implies :premises (t44.t56))
(step t44.t58 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t44.t59 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t44.t59.t0 (cl (= @p_38 1)) :rule evaluate)
(step t44.t59.t1 (cl (= @p_39 @p_40)) :rule cong :premises (t44.t59.t0))
(step t44.t59.t2 (cl (= @p_40 @p_36)) :rule poly_simp)
(step t44.t59.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t44.t59.t1 t44.t59.t2))
(step t44.t59.t4 (cl (= (= @p_37 @p_39) (= @p_37 @p_36))) :rule cong :premises (t44.t59.t3))
(step t44.t59 (cl @p_34) :rule bind)
(step t44.t60 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t44.t58 t44.t59 a14))
(step t44.t61 (cl @p_33) :rule resolution :premises (t44.t57 t44.t60))
(step t44.t62 (cl @p_76) :rule trans :premises (t44.t45 t44.t61))
(step t44.t63 (cl @p_85) :rule resolution :premises (t44.t44 t30 t44.t62))
(step t44.t64 (cl (= 1 @p_28)) :rule symm :premises (t44.t63))
(step t44.t65 (cl @p_23) :rule forall_inst :args (true))
(step t44.t66 (cl @p_22 @p_21) :rule or :premises (t44.t65))
(step t44.t67 (cl @p_21) :rule resolution :premises (t44.t66 a1))
(step t44.t68 (cl @p_31) :rule forall_inst :args (@p_19))
(step t44.t69 (cl @p_30 @p_29) :rule or :premises (t44.t68))
(step t44.t70 (cl @p_29) :rule resolution :premises (t44.t69 a6))
(step t44.t71 (cl @p_77) :rule trans :premises (t44.t67 t44.t70))
(step t44.t72 (cl (= @p_28 @p_7)) :rule symm :premises (t44.t71))
(step t44.t73 (cl @p_9) :rule trans :premises (t44.t23 t44.t43 t44.t64 t44.t72))
(step t44.t74 (cl @p_84) :rule resolution :premises (t44.t16 t44.t73))
(step t44.t75 (cl @p_80) :rule trans :premises (t44.t14 t44.t74))
(step t44 (cl (not @p_77) @p_82 @p_83 (not @p_74) @p_13 @p_80) :rule subproof :discharge (t44.a0 t44.a1 t44.a2 t44.a3 t44.a4))
(step t45 (cl @p_79 @p_77) :rule and_pos :args (0))
(step t46 (cl @p_79 @p_76) :rule and_pos :args (1))
(step t47 (cl @p_79 @p_75) :rule and_pos :args (2))
(step t48 (cl @p_79 @p_74) :rule and_pos :args (3))
(step t49 (cl @p_79 @p_10) :rule and_pos :args (4))
(step t50 (cl @p_80 @p_79 @p_79 @p_79 @p_79 @p_79) :rule resolution :premises (t44 t45 t46 t47 t48 t49))
(step t51 (cl @p_79 @p_79 @p_79 @p_79 @p_79 @p_80) :rule reordering :premises (t50))
(step t52 (cl @p_79 @p_80) :rule contraction :premises (t51))
(step t53 (cl @p_81 @p_80) :rule resolution :premises (t43 t52))
(step t54 (cl @p_81 (not @p_80)) :rule implies_neg2)
(step t55 (cl @p_81 @p_81) :rule resolution :premises (t53 t54))
(step t56 (cl @p_81) :rule contraction :premises (t55))
(step t57 (cl @p_79) :rule resolution :premises (t28 t42 t56))
(step t58 (cl @p_73) :rule resolution :premises (t27 t57))
(step t59 (cl @p_61 @p_62 @p_13 @p_63 @p_64 @p_65 @p_66 @p_67 @p_68) :rule not_and :premises (t58))
(step t60 (cl @p_70 (not @p_61)) :rule or_neg :args (0))
(step t61 (cl @p_70 (not @p_62)) :rule or_neg :args (1))
(step t62 (cl @p_70 @p_71) :rule or_neg :args (2))
(step t63 (cl @p_70 (not @p_63)) :rule or_neg :args (3))
(step t64 (cl @p_70 (not @p_64)) :rule or_neg :args (4))
(step t65 (cl @p_70 (not @p_65)) :rule or_neg :args (5))
(step t66 (cl @p_70 (not @p_66)) :rule or_neg :args (6))
(step t67 (cl @p_70 (not @p_67)) :rule or_neg :args (7))
(step t68 (cl @p_70 (not @p_68)) :rule or_neg :args (8))
(step t69 (cl @p_70 @p_70 @p_70 @p_70 @p_70 @p_70 @p_70 @p_70 @p_70) :rule resolution :premises (t59 t60 t61 t62 t63 t64 t65 t66 t67 t68))
(step t70 (cl @p_70) :rule contraction :premises (t69))
(step t71 (cl @p_69) :rule resolution :premises (t0 t8 t70))
(step t72 (cl @p_61 @p_62 @p_9 @p_63 @p_64 @p_65 @p_66 @p_67 @p_68) :rule or :premises (t71))
(step t73 (cl @p_9 @p_61 @p_62 @p_63 @p_64 @p_65 @p_66 @p_67 @p_68) :rule reordering :premises (t72))
(step t74 (cl (not @p_60) (not @p_59) @p_56) :rule equiv_pos2)
(step t75 (cl (= (* 1 (- @p_24 @p_57)) (* -1 (- @p_3 @p_47)))) :rule poly_simp)
(step t76 (cl (= @p_58 @p_48)) :rule poly_simp_rel :premises (t75))
(step t77 (cl @p_60) :rule cong :premises (t76))
(step t78 (cl @p_59 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule implies_neg1)
(anchor :step t79)
(assume t79.a0 (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1))))))
(step t79.t0 (cl (or @p_55 @p_58)) :rule forall_inst :args (3 nil$))
(step t79.t1 (cl @p_55 @p_58) :rule or :premises (t79.t0))
(step t79.t2 (cl (not @p_49) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t79.t3 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t79.t3.t0 (cl (= @p_38 1)) :rule evaluate)
(step t79.t3.t1 (cl (= @p_53 @p_54)) :rule cong :premises (t79.t3.t0))
(step t79.t3.t2 (cl (= @p_54 @p_51)) :rule poly_simp)
(step t79.t3.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t79.t3.t1 t79.t3.t2))
(step t79.t3.t4 (cl (= (= @p_52 @p_53) (= @p_52 @p_51))) :rule cong :premises (t79.t3.t3))
(step t79.t3 (cl @p_49) :rule bind)
(step t79.t4 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t79.t2 t79.t3 a15))
(step t79.t5 (cl @p_58) :rule resolution :premises (t79.t1 t79.t4))
(step t79 (cl @p_55 @p_58) :rule subproof :discharge (t79.a0))
(step t80 (cl @p_59 @p_58) :rule resolution :premises (t78 t79))
(step t81 (cl @p_59 (not @p_58)) :rule implies_neg2)
(step t82 (cl @p_59 @p_59) :rule resolution :premises (t80 t81))
(step t83 (cl @p_59) :rule contraction :premises (t82))
(step t84 (cl @p_56) :rule resolution :premises (t74 t77 t83))
(step t85 (cl @p_55 @p_48) :rule implies :premises (t84))
(step t86 (cl (not @p_49) (not (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ (of_nat$ (size$a ?v1)) (+ 0 1))))) (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule equiv_pos2)
(anchor :step t87 :args ((?v0 Int) (?v1 Int_list$) (:= (?v0 Int) ?v0) (:= (?v1 Int_list$) ?v1)))
(step t87.t0 (cl (= @p_38 1)) :rule evaluate)
(step t87.t1 (cl (= @p_53 @p_54)) :rule cong :premises (t87.t0))
(step t87.t2 (cl (= @p_54 @p_51)) :rule poly_simp)
(step t87.t3 (cl (= @p_53 @p_51)) :rule trans :premises (t87.t1 t87.t2))
(step t87.t4 (cl (= (= @p_52 @p_53) (= @p_52 @p_51))) :rule cong :premises (t87.t3))
(step t87 (cl @p_49) :rule bind)
(step t88 (cl (forall ((?v0 Int) (?v1 Int_list$)) (= (of_nat$ (size$a (cons$ ?v0 ?v1))) (+ 1 (of_nat$ (size$a ?v1)))))) :rule resolution :premises (t86 t87 a15))
(step t89 (cl @p_48) :rule resolution :premises (t85 t88))
(step t90 (cl (not @p_46) (not @p_45) @p_42) :rule equiv_pos2)
(step t91 (cl (= (* 1 (- @p_28 @p_43)) (* -1 (- @p_1 @p_32)))) :rule poly_simp)
(step t92 (cl (= @p_44 @p_33)) :rule poly_simp_rel :premises (t91))
(step t93 (cl @p_46) :rule cong :premises (t92))
(step t94 (cl @p_45 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule implies_neg1)
(anchor :step t95)
(assume t95.a0 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1))))))
(step t95.t0 (cl (or @p_41 @p_44)) :rule forall_inst :args (true nil$a))
(step t95.t1 (cl @p_41 @p_44) :rule or :premises (t95.t0))
(step t95.t2 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t95.t3 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t95.t3.t0 (cl (= @p_38 1)) :rule evaluate)
(step t95.t3.t1 (cl (= @p_39 @p_40)) :rule cong :premises (t95.t3.t0))
(step t95.t3.t2 (cl (= @p_40 @p_36)) :rule poly_simp)
(step t95.t3.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t95.t3.t1 t95.t3.t2))
(step t95.t3.t4 (cl (= (= @p_37 @p_39) (= @p_37 @p_36))) :rule cong :premises (t95.t3.t3))
(step t95.t3 (cl @p_34) :rule bind)
(step t95.t4 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t95.t2 t95.t3 a14))
(step t95.t5 (cl @p_44) :rule resolution :premises (t95.t1 t95.t4))
(step t95 (cl @p_41 @p_44) :rule subproof :discharge (t95.a0))
(step t96 (cl @p_45 @p_44) :rule resolution :premises (t94 t95))
(step t97 (cl @p_45 (not @p_44)) :rule implies_neg2)
(step t98 (cl @p_45 @p_45) :rule resolution :premises (t96 t97))
(step t99 (cl @p_45) :rule contraction :premises (t98))
(step t100 (cl @p_42) :rule resolution :premises (t90 t93 t99))
(step t101 (cl @p_41 @p_33) :rule implies :premises (t100))
(step t102 (cl (not @p_34) (not (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ (of_nat$ (size$ ?v1)) (+ 0 1))))) (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule equiv_pos2)
(anchor :step t103 :args ((?v0 Bool) (?v1 Bool_list$) (:= (?v0 Bool) ?v0) (:= (?v1 Bool_list$) ?v1)))
(step t103.t0 (cl (= @p_38 1)) :rule evaluate)
(step t103.t1 (cl (= @p_39 @p_40)) :rule cong :premises (t103.t0))
(step t103.t2 (cl (= @p_40 @p_36)) :rule poly_simp)
(step t103.t3 (cl (= @p_39 @p_36)) :rule trans :premises (t103.t1 t103.t2))
(step t103.t4 (cl (= (= @p_37 @p_39) (= @p_37 @p_36))) :rule cong :premises (t103.t3))
(step t103 (cl @p_34) :rule bind)
(step t104 (cl (forall ((?v0 Bool) (?v1 Bool_list$)) (= (of_nat$ (size$ (cons$a ?v0 ?v1))) (+ 1 (of_nat$ (size$ ?v1)))))) :rule resolution :premises (t102 t103 a14))
(step t105 (cl @p_33) :rule resolution :premises (t101 t104))
(step t106 (cl @p_31) :rule forall_inst :args (@p_19))
(step t107 (cl @p_30 @p_29) :rule or :premises (t106))
(step t108 (cl @p_29) :rule resolution :premises (t107 a6))
(step t109 (cl @p_27) :rule forall_inst :args (@p_14))
(step t110 (cl @p_26 @p_25) :rule or :premises (t109))
(step t111 (cl @p_25) :rule resolution :premises (t110 a7))
(step t112 (cl @p_23) :rule forall_inst :args (true))
(step t113 (cl @p_22 @p_21) :rule or :premises (t112))
(step t114 (cl @p_21) :rule resolution :premises (t113 a1))
(step t115 (cl @p_18) :rule forall_inst :args (3))
(step t116 (cl @p_17 @p_16) :rule or :premises (t115))
(step t117 (cl @p_16) :rule resolution :premises (t116 a0))
(step t118 (cl (not @p_11) @p_13 @p_10) :rule equiv_pos2)
(step t119 (cl @p_12) :rule refl)
(step t120 (cl @p_12) :rule symm :premises (t119))
(step t121 (cl (= @p_5 @p_5)) :rule cong :premises (t120))
(step t122 (cl (= @p_6 @p_6)) :rule cong :premises (t121))
(step t123 (cl (= @p_7 @p_7)) :rule cong :premises (t122))
(step t124 (cl (= @p_9 @p_9)) :rule cong :premises (t123))
(step t125 (cl @p_11) :rule cong :premises (t124))
(step t126 (cl @p_10) :rule resolution :premises (t118 t125 a16))
(step t127 (cl) :rule resolution :premises (t73 t89 t105 t108 t111 t114 t117 a13 a12 t126))
)
8fb402e2349b6bc138b82d45e45456a7ef4cbd63 869 0
unsat
(
(define-fun @quantifiers_skolemize_14 () A$ (choice ((?v3 A$)) (not (forall ((?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))))))
(define-fun @quantifiers_skolemize_15 () A$ (choice ((?v4 A$)) (not (or (not (= x$ (fin$e @quantifiers_skolemize_14))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ @quantifiers_skolemize_14 ?v4)) (plus$f x$ x$)))))))
(assume a0 (forall ((?v0 A$)) (= (plus$ zero$ ?v0) ?v0)))
(assume a6 (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false)))
(assume a12 (forall ((?v0 A$) (?v1 A$)) (= (plus$f (fin$e ?v0) (fin$e ?v1)) (fin$e (plus$ ?v0 ?v1)))))
(assume a17 (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) pinf$e) pinf$e)))
(assume a22 (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) minf$e) minf$e)))
(assume a28 (! (not (= (! (plus$f (! (fin$e zero$) :named @p_1) x$) :named @p_2) x$)) :named @p_3))
(step t0 (cl (! (not (! (or (! (not (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$)))))) :named @p_16) (! (and (! (= x$ pinf$e) :named @p_7) (! (= pinf$e (! (plus$f x$ x$) :named @p_4)) :named @p_5) (! (not (forall ((?v3 A$)) (not (= x$ (fin$e ?v3))))) :named @p_12)) :named @p_15) @p_15 (! (and @p_7 @p_7 @p_5) :named @p_14) (! (and (! (= x$ minf$e) :named @p_6) (! (= minf$e @p_4) :named @p_10) (! (not (forall ((?v3 A$)) (not (= x$ (fin$e ?v3))))) :named @p_12)) :named @p_13) @p_13 (! (and @p_6 @p_6 @p_10) :named @p_11) (! (and @p_6 @p_7 @p_5) :named @p_9) (! (and @p_7 @p_6 @p_5) :named @p_8)) :named @p_17)) :named @p_329) @p_16 @p_15 @p_15 @p_14 @p_13 @p_13 @p_11 @p_9 @p_8) :rule or_pos)
(step t1 (cl @p_329 @p_16 @p_15 @p_14 @p_13 @p_11 @p_9 @p_8) :rule contraction :premises (t0))
(step t2 (cl @p_16 @p_15 @p_14 @p_13 @p_11 @p_9 @p_8 @p_329) :rule reordering :premises (t1))
(step t3 (cl (! (not @p_11) :named @p_328) @p_6) :rule and_pos :args (0))
(step t4 (cl @p_6 @p_328) :rule reordering :premises (t3))
(step t5 (cl (! (and @p_6 (! (= minf$e (! (plus$f @p_1 minf$e) :named @p_319)) :named @p_320)) :named @p_325) (! (not @p_6) :named @p_318) (! (not @p_320) :named @p_324)) :rule and_neg)
(step t6 (cl (! (=> @p_325 (! (= x$ @p_2) :named @p_266)) :named @p_327) @p_325) :rule implies_neg1)
(anchor :step t7)
(assume t7.a0 @p_6)
(assume t7.a1 @p_320)
(step t7.t0 (cl @p_327 @p_325) :rule implies_neg1)
(anchor :step t7.t1)
(assume t7.t1.a0 @p_6)
(assume t7.t1.a1 @p_320)
(step t7.t1.t0 (cl (or (! (not (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :named @p_323) @p_320)) :rule forall_inst :args (zero$))
(step t7.t1.t1 (cl @p_323 @p_320) :rule or :premises (t7.t1.t0))
(step t7.t1.t2 (cl (not (! (= (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) minf$e) minf$e)) (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :named @p_321)) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) minf$e) minf$e))) (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule equiv_pos2)
(anchor :step t7.t1.t3 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t7.t1.t3.t0 (cl (= (= (! (plus$f (! (fin$e ?v0) :named @p_263) minf$e) :named @p_322) minf$e) (= minf$e @p_322))) :rule rare_rewrite :args ("eq-symm" @p_322 minf$e))
(step t7.t1.t3 (cl @p_321) :rule bind)
(step t7.t1.t4 (cl (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule resolution :premises (t7.t1.t2 t7.t1.t3 a22))
(step t7.t1.t5 (cl @p_320) :rule resolution :premises (t7.t1.t1 t7.t1.t4))
(step t7.t1.t6 (cl (! (= minf$e x$) :named @p_238)) :rule symm :premises (t7.t1.a0))
(step t7.t1.t7 (cl (= @p_319 @p_2)) :rule cong :premises (t7.t1.t6))
(step t7.t1.t8 (cl @p_266) :rule trans :premises (t7.t1.a0 t7.t1.t5 t7.t1.t7))
(step t7.t1 (cl @p_318 @p_324 @p_266) :rule subproof :discharge (t7.t1.a0 t7.t1.a1))
(step t7.t2 (cl (! (not @p_325) :named @p_326) @p_6) :rule and_pos :args (0))
(step t7.t3 (cl @p_326 @p_320) :rule and_pos :args (1))
(step t7.t4 (cl @p_266 @p_326 @p_326) :rule resolution :premises (t7.t1 t7.t2 t7.t3))
(step t7.t5 (cl @p_326 @p_326 @p_266) :rule reordering :premises (t7.t4))
(step t7.t6 (cl @p_326 @p_266) :rule contraction :premises (t7.t5))
(step t7.t7 (cl @p_327 @p_266) :rule resolution :premises (t7.t0 t7.t6))
(step t7.t8 (cl @p_327 (! (not @p_266) :named @p_267)) :rule implies_neg2)
(step t7.t9 (cl @p_327 @p_327) :rule resolution :premises (t7.t7 t7.t8))
(step t7.t10 (cl @p_327) :rule contraction :premises (t7.t9))
(step t7.t11 (cl @p_326 @p_266) :rule implies :premises (t7.t10))
(step t7.t12 (cl (or @p_323 @p_320)) :rule forall_inst :args (zero$))
(step t7.t13 (cl @p_323 @p_320) :rule or :premises (t7.t12))
(step t7.t14 (cl (not @p_321) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) minf$e) minf$e))) (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule equiv_pos2)
(anchor :step t7.t15 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t7.t15.t0 (cl (= (= @p_322 minf$e) (= minf$e @p_322))) :rule rare_rewrite :args ("eq-symm" @p_322 minf$e))
(step t7.t15 (cl @p_321) :rule bind)
(step t7.t16 (cl (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule resolution :premises (t7.t14 t7.t15 a22))
(step t7.t17 (cl @p_320) :rule resolution :premises (t7.t13 t7.t16))
(step t7.t18 (cl @p_325) :rule and_intro :premises (t7.a0 t7.t17))
(step t7.t19 (cl @p_266) :rule resolution :premises (t7.t11 t7.t18))
(step t7 (cl @p_318 @p_324 @p_266) :rule subproof :discharge (t7.a0 t7.a1))
(step t8 (cl @p_326 @p_6) :rule and_pos :args (0))
(step t9 (cl @p_326 @p_320) :rule and_pos :args (1))
(step t10 (cl @p_266 @p_326 @p_326) :rule resolution :premises (t7 t8 t9))
(step t11 (cl @p_326 @p_326 @p_266) :rule reordering :premises (t10))
(step t12 (cl @p_326 @p_266) :rule contraction :premises (t11))
(step t13 (cl @p_327 @p_266) :rule resolution :premises (t6 t12))
(step t14 (cl @p_327 @p_267) :rule implies_neg2)
(step t15 (cl @p_327 @p_327) :rule resolution :premises (t13 t14))
(step t16 (cl @p_327) :rule contraction :premises (t15))
(step t17 (cl @p_326 @p_266) :rule implies :premises (t16))
(step t18 (cl @p_318 @p_324 @p_266) :rule resolution :premises (t5 t17))
(step t19 (cl @p_266 @p_318 @p_324) :rule reordering :premises (t18))
(step t20 (cl @p_267) :rule not_symm :premises (a28))
(step t21 (cl (or @p_323 @p_320)) :rule forall_inst :args (zero$))
(step t22 (cl @p_323 @p_320) :rule or :premises (t21))
(step t23 (cl (not @p_321) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) minf$e) minf$e))) (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule equiv_pos2)
(anchor :step t24 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t24.t0 (cl (= (= @p_322 minf$e) (= minf$e @p_322))) :rule rare_rewrite :args ("eq-symm" @p_322 minf$e))
(step t24 (cl @p_321) :rule bind)
(step t25 (cl (forall ((?v0 A$)) (= minf$e (plus$f (fin$e ?v0) minf$e)))) :rule resolution :premises (t23 t24 a22))
(step t26 (cl @p_320) :rule resolution :premises (t22 t25))
(step t27 (cl @p_318) :rule resolution :premises (t19 t20 t26))
(step t28 (cl @p_328) :rule resolution :premises (t4 t27))
(step t29 (cl (! (not @p_13) :named @p_317) @p_6) :rule and_pos :args (0))
(step t30 (cl @p_6 @p_317) :rule reordering :premises (t29))
(step t31 (cl @p_317) :rule resolution :premises (t30 t27))
(step t32 (cl (not (! (= (! (or (! (not @p_16) :named @p_306) (! (not (! (or (! (not (! (= x$ (! (fin$e @quantifiers_skolemize_14) :named @p_279)) :named @p_280)) :named @p_281) (! (not (= x$ (fin$e @quantifiers_skolemize_15))) :named @p_278) (! (not (! (= @p_4 (! (fin$e (plus$ @quantifiers_skolemize_14 @quantifiers_skolemize_15)) :named @p_275)) :named @p_276)) :named @p_277)) :named @p_282)) :named @p_303)) :named @p_307) (! (or (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))) @p_303) :named @p_305)) :named @p_316)) (not @p_307) @p_305) :rule equiv_pos2)
(step t33 (cl (= @p_306 (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$)))))))
(step t34 (cl (= @p_303 @p_303)) :rule refl)
(step t35 (cl @p_316) :rule cong :premises (t33 t34))
(step t36 (cl (not (! (= (! (=> @p_16 (! (not (! (or @p_281 @p_278 (! (not (! (= @p_275 @p_4) :named @p_309)) :named @p_310)) :named @p_311)) :named @p_312)) :named @p_313) (! (=> @p_16 @p_303) :named @p_308)) :named @p_315)) (not @p_313) @p_308) :rule equiv_pos2)
(step t37 (cl (= @p_309 @p_276)) :rule rare_rewrite :args ("eq-symm" @p_275 @p_4))
(step t38 (cl (= @p_310 @p_277)) :rule cong :premises (t37))
(step t39 (cl (= @p_311 @p_282)) :rule cong :premises (t38))
(step t40 (cl (= @p_312 @p_303)) :rule cong :premises (t39))
(step t41 (cl @p_315) :rule cong :premises (t40))
(step t42 (cl @p_313 @p_16) :rule implies_neg1)
(anchor :step t43)
(assume t43.a0 @p_16)
(step t43.t0 (cl (not (! (= @p_16 @p_312) :named @p_314)) @p_306 @p_312) :rule equiv_pos2)
(anchor :step t43.t1 :args ((:= (?v3 A$) @quantifiers_skolemize_14) (:= (?v4 A$) @quantifiers_skolemize_15)))
(step t43.t1.t0 (cl (= (! (or (! (not (= x$ (! (fin$e ?v3) :named @p_167))) :named @p_253) (! (not (= x$ (! (fin$e ?v4) :named @p_222))) :named @p_252) (! (not (! (= (! (fin$e (plus$ ?v3 ?v4)) :named @p_219) @p_4) :named @p_250)) :named @p_251)) :named @p_254) @p_311)) :rule refl)
(step t43.t1 (cl (= (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))) @p_311)) :rule sko_forall)
(step t43.t2 (cl @p_314) :rule cong :premises (t43.t1))
(step t43.t3 (cl @p_312) :rule resolution :premises (t43.t0 t43.t2 t43.a0))
(step t43 (cl @p_306 @p_312) :rule subproof :discharge (t43.a0))
(step t44 (cl @p_313 @p_312) :rule resolution :premises (t42 t43))
(step t45 (cl @p_313 (not @p_312)) :rule implies_neg2)
(step t46 (cl @p_313 @p_313) :rule resolution :premises (t44 t45))
(step t47 (cl @p_313) :rule contraction :premises (t46))
(step t48 (cl @p_308) :rule resolution :premises (t36 t41 t47))
(step t49 (cl @p_306 @p_303) :rule implies :premises (t48))
(step t50 (cl @p_307 (not @p_306)) :rule or_neg :args (0))
(step t51 (cl @p_307 (not @p_303)) :rule or_neg :args (1))
(step t52 (cl @p_307 @p_307) :rule resolution :premises (t49 t50 t51))
(step t53 (cl @p_307) :rule contraction :premises (t52))
(step t54 (cl @p_305) :rule resolution :premises (t32 t35 t53))
(step t55 (cl (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))) @p_303) :rule or :premises (t54))
(step t56 (cl (not (! (= (! (or @p_282 (! (not @p_281) :named @p_301)) :named @p_302) (! (or @p_282 @p_280) :named @p_300)) :named @p_304)) (not @p_302) @p_300) :rule equiv_pos2)
(step t57 (cl (= @p_301 @p_280)) :rule rare_rewrite :args ("bool-double-not-elim" @p_280))
(step t58 (cl @p_304) :rule cong :premises (t57))
(step t59 (cl @p_282 @p_301) :rule or_neg :args (0))
(step t60 (cl @p_302 @p_303) :rule or_neg :args (0))
(step t61 (cl @p_302 (not @p_301)) :rule or_neg :args (1))
(step t62 (cl @p_302 @p_302) :rule resolution :premises (t59 t60 t61))
(step t63 (cl @p_302) :rule contraction :premises (t62))
(step t64 (cl @p_300) :rule resolution :premises (t56 t58 t63))
(step t65 (cl @p_282 @p_280) :rule or :premises (t64))
(step t66 (cl @p_280 @p_282) :rule reordering :premises (t65))
(step t67 (cl (! (and @p_280 (! (= @quantifiers_skolemize_14 (! (plus$ zero$ @quantifiers_skolemize_14) :named @p_283)) :named @p_288) (! (= (! (plus$f @p_1 @p_279) :named @p_285) (! (fin$e @p_283) :named @p_284)) :named @p_286)) :named @p_294) @p_281 (! (not @p_288) :named @p_292) (! (not @p_286) :named @p_293)) :rule and_neg)
(step t68 (cl (! (=> @p_294 @p_266) :named @p_296) @p_294) :rule implies_neg1)
(anchor :step t69)
(assume t69.a0 @p_280)
(assume t69.a1 @p_288)
(assume t69.a2 @p_286)
(step t69.t0 (cl (! (=> (! (and @p_280 @p_286 @p_288) :named @p_297) @p_266) :named @p_299) @p_297) :rule implies_neg1)
(anchor :step t69.t1)
(assume t69.t1.a0 @p_280)
(assume t69.t1.a1 @p_286)
(assume t69.t1.a2 @p_288)
(step t69.t1.t0 (cl (or (! (not (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :named @p_291) @p_288)) :rule forall_inst :args (@quantifiers_skolemize_14))
(step t69.t1.t1 (cl @p_291 @p_288) :rule or :premises (t69.t1.t0))
(step t69.t1.t2 (cl (not (! (= (forall ((?v0 A$)) (= (plus$ zero$ ?v0) ?v0)) (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :named @p_289)) (not (forall ((?v0 A$)) (= (plus$ zero$ ?v0) ?v0))) (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule equiv_pos2)
(anchor :step t69.t1.t3 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t69.t1.t3.t0 (cl (= (= (! (plus$ zero$ ?v0) :named @p_290) ?v0) (= ?v0 @p_290))) :rule rare_rewrite :args ("eq-symm" @p_290 ?v0))
(step t69.t1.t3 (cl @p_289) :rule bind)
(step t69.t1.t4 (cl (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule resolution :premises (t69.t1.t2 t69.t1.t3 a0))
(step t69.t1.t5 (cl @p_288) :rule resolution :premises (t69.t1.t1 t69.t1.t4))
(step t69.t1.t6 (cl (= @p_279 @p_284)) :rule cong :premises (t69.t1.t5))
(step t69.t1.t7 (cl (or (! (not (forall ((?v0 A$) (?v1 A$)) (= (plus$f (fin$e ?v0) (fin$e ?v1)) (fin$e (plus$ ?v0 ?v1))))) :named @p_287) @p_286)) :rule forall_inst :args (zero$ @quantifiers_skolemize_14))
(step t69.t1.t8 (cl @p_287 @p_286) :rule or :premises (t69.t1.t7))
(step t69.t1.t9 (cl @p_286) :rule resolution :premises (t69.t1.t8 a12))
(step t69.t1.t10 (cl (= @p_284 @p_285)) :rule symm :premises (t69.t1.t9))
(step t69.t1.t11 (cl (= @p_279 x$)) :rule symm :premises (t69.t1.a0))
(step t69.t1.t12 (cl (= @p_285 @p_2)) :rule cong :premises (t69.t1.t11))
(step t69.t1.t13 (cl @p_266) :rule trans :premises (t69.t1.a0 t69.t1.t6 t69.t1.t10 t69.t1.t12))
(step t69.t1 (cl @p_281 @p_293 @p_292 @p_266) :rule subproof :discharge (t69.t1.a0 t69.t1.a1 t69.t1.a2))
(step t69.t2 (cl (! (not @p_297) :named @p_298) @p_280) :rule and_pos :args (0))
(step t69.t3 (cl @p_298 @p_286) :rule and_pos :args (1))
(step t69.t4 (cl @p_298 @p_288) :rule and_pos :args (2))
(step t69.t5 (cl @p_266 @p_298 @p_298 @p_298) :rule resolution :premises (t69.t1 t69.t2 t69.t3 t69.t4))
(step t69.t6 (cl @p_298 @p_298 @p_298 @p_266) :rule reordering :premises (t69.t5))
(step t69.t7 (cl @p_298 @p_266) :rule contraction :premises (t69.t6))
(step t69.t8 (cl @p_299 @p_266) :rule resolution :premises (t69.t0 t69.t7))
(step t69.t9 (cl @p_299 @p_267) :rule implies_neg2)
(step t69.t10 (cl @p_299 @p_299) :rule resolution :premises (t69.t8 t69.t9))
(step t69.t11 (cl @p_299) :rule contraction :premises (t69.t10))
(step t69.t12 (cl @p_298 @p_266) :rule implies :premises (t69.t11))
(step t69.t13 (cl (or @p_287 @p_286)) :rule forall_inst :args (zero$ @quantifiers_skolemize_14))
(step t69.t14 (cl @p_287 @p_286) :rule or :premises (t69.t13))
(step t69.t15 (cl @p_286) :rule resolution :premises (t69.t14 a12))
(step t69.t16 (cl (or @p_291 @p_288)) :rule forall_inst :args (@quantifiers_skolemize_14))
(step t69.t17 (cl @p_291 @p_288) :rule or :premises (t69.t16))
(step t69.t18 (cl (not @p_289) (not (forall ((?v0 A$)) (= (plus$ zero$ ?v0) ?v0))) (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule equiv_pos2)
(anchor :step t69.t19 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t69.t19.t0 (cl (= (= @p_290 ?v0) (= ?v0 @p_290))) :rule rare_rewrite :args ("eq-symm" @p_290 ?v0))
(step t69.t19 (cl @p_289) :rule bind)
(step t69.t20 (cl (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule resolution :premises (t69.t18 t69.t19 a0))
(step t69.t21 (cl @p_288) :rule resolution :premises (t69.t17 t69.t20))
(step t69.t22 (cl @p_297) :rule and_intro :premises (t69.a0 t69.t15 t69.t21))
(step t69.t23 (cl @p_266) :rule resolution :premises (t69.t12 t69.t22))
(step t69 (cl @p_281 @p_292 @p_293 @p_266) :rule subproof :discharge (t69.a0 t69.a1 t69.a2))
(step t70 (cl (! (not @p_294) :named @p_295) @p_280) :rule and_pos :args (0))
(step t71 (cl @p_295 @p_288) :rule and_pos :args (1))
(step t72 (cl @p_295 @p_286) :rule and_pos :args (2))
(step t73 (cl @p_266 @p_295 @p_295 @p_295) :rule resolution :premises (t69 t70 t71 t72))
(step t74 (cl @p_295 @p_295 @p_295 @p_266) :rule reordering :premises (t73))
(step t75 (cl @p_295 @p_266) :rule contraction :premises (t74))
(step t76 (cl @p_296 @p_266) :rule resolution :premises (t68 t75))
(step t77 (cl @p_296 @p_267) :rule implies_neg2)
(step t78 (cl @p_296 @p_296) :rule resolution :premises (t76 t77))
(step t79 (cl @p_296) :rule contraction :premises (t78))
(step t80 (cl @p_295 @p_266) :rule implies :premises (t79))
(step t81 (cl @p_281 @p_292 @p_293 @p_266) :rule resolution :premises (t67 t80))
(step t82 (cl @p_266 @p_281 @p_292 @p_293) :rule reordering :premises (t81))
(step t83 (cl (or @p_291 @p_288)) :rule forall_inst :args (@quantifiers_skolemize_14))
(step t84 (cl @p_291 @p_288) :rule or :premises (t83))
(step t85 (cl (not @p_289) (not (forall ((?v0 A$)) (= (plus$ zero$ ?v0) ?v0))) (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule equiv_pos2)
(anchor :step t86 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t86.t0 (cl (= (= @p_290 ?v0) (= ?v0 @p_290))) :rule rare_rewrite :args ("eq-symm" @p_290 ?v0))
(step t86 (cl @p_289) :rule bind)
(step t87 (cl (forall ((?v0 A$)) (= ?v0 (plus$ zero$ ?v0)))) :rule resolution :premises (t85 t86 a0))
(step t88 (cl @p_288) :rule resolution :premises (t84 t87))
(step t89 (cl (or @p_287 @p_286)) :rule forall_inst :args (zero$ @quantifiers_skolemize_14))
(step t90 (cl @p_287 @p_286) :rule or :premises (t89))
(step t91 (cl @p_286) :rule resolution :premises (t90 a12))
(step t92 (cl @p_281) :rule resolution :premises (t82 t20 t88 t91))
(step t93 (cl @p_282) :rule resolution :premises (t66 t92))
(step t94 (cl (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$)))))) :rule resolution :premises (t55 t93))
(step t95 (cl (! (not @p_15) :named @p_274) @p_7) :rule and_pos :args (0))
(step t96 (cl @p_7 @p_274) :rule reordering :premises (t95))
(step t97 (cl (! (and @p_7 (! (= pinf$e (! (plus$f @p_1 pinf$e) :named @p_259)) :named @p_260)) :named @p_269) (! (not @p_7) :named @p_258) (! (not @p_260) :named @p_268)) :rule and_neg)
(step t98 (cl (! (=> @p_269 @p_266) :named @p_271) @p_269) :rule implies_neg1)
(anchor :step t99)
(assume t99.a0 @p_7)
(assume t99.a1 @p_260)
(step t99.t0 (cl @p_271 @p_269) :rule implies_neg1)
(anchor :step t99.t1)
(assume t99.t1.a0 @p_7)
(assume t99.t1.a1 @p_260)
(step t99.t1.t0 (cl (or (! (not (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :named @p_265) @p_260)) :rule forall_inst :args (zero$))
(step t99.t1.t1 (cl @p_265 @p_260) :rule or :premises (t99.t1.t0))
(step t99.t1.t2 (cl (not (! (= (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) pinf$e) pinf$e)) (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :named @p_261)) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) pinf$e) pinf$e))) (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule equiv_pos2)
(anchor :step t99.t1.t3 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t99.t1.t3.t0 (cl (= (= (! (plus$f @p_263 pinf$e) :named @p_264) pinf$e) (= pinf$e @p_264))) :rule rare_rewrite :args ("eq-symm" @p_264 pinf$e))
(step t99.t1.t3 (cl @p_261) :rule bind)
(step t99.t1.t4 (cl (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule resolution :premises (t99.t1.t2 t99.t1.t3 a17))
(step t99.t1.t5 (cl @p_260) :rule resolution :premises (t99.t1.t1 t99.t1.t4))
(step t99.t1.t6 (cl (! (= pinf$e x$) :named @p_239)) :rule symm :premises (t99.t1.a0))
(step t99.t1.t7 (cl (= @p_259 @p_2)) :rule cong :premises (t99.t1.t6))
(step t99.t1.t8 (cl @p_266) :rule trans :premises (t99.t1.a0 t99.t1.t5 t99.t1.t7))
(step t99.t1 (cl @p_258 @p_268 @p_266) :rule subproof :discharge (t99.t1.a0 t99.t1.a1))
(step t99.t2 (cl (! (not @p_269) :named @p_270) @p_7) :rule and_pos :args (0))
(step t99.t3 (cl @p_270 @p_260) :rule and_pos :args (1))
(step t99.t4 (cl @p_266 @p_270 @p_270) :rule resolution :premises (t99.t1 t99.t2 t99.t3))
(step t99.t5 (cl @p_270 @p_270 @p_266) :rule reordering :premises (t99.t4))
(step t99.t6 (cl @p_270 @p_266) :rule contraction :premises (t99.t5))
(step t99.t7 (cl @p_271 @p_266) :rule resolution :premises (t99.t0 t99.t6))
(step t99.t8 (cl @p_271 @p_267) :rule implies_neg2)
(step t99.t9 (cl @p_271 @p_271) :rule resolution :premises (t99.t7 t99.t8))
(step t99.t10 (cl @p_271) :rule contraction :premises (t99.t9))
(step t99.t11 (cl @p_270 @p_266) :rule implies :premises (t99.t10))
(step t99.t12 (cl (or @p_265 @p_260)) :rule forall_inst :args (zero$))
(step t99.t13 (cl @p_265 @p_260) :rule or :premises (t99.t12))
(step t99.t14 (cl (not @p_261) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) pinf$e) pinf$e))) (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule equiv_pos2)
(anchor :step t99.t15 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t99.t15.t0 (cl (= (= @p_264 pinf$e) (= pinf$e @p_264))) :rule rare_rewrite :args ("eq-symm" @p_264 pinf$e))
(step t99.t15 (cl @p_261) :rule bind)
(step t99.t16 (cl (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule resolution :premises (t99.t14 t99.t15 a17))
(step t99.t17 (cl @p_260) :rule resolution :premises (t99.t13 t99.t16))
(step t99.t18 (cl @p_269) :rule and_intro :premises (t99.a0 t99.t17))
(step t99.t19 (cl @p_266) :rule resolution :premises (t99.t11 t99.t18))
(step t99 (cl @p_258 @p_268 @p_266) :rule subproof :discharge (t99.a0 t99.a1))
(step t100 (cl @p_270 @p_7) :rule and_pos :args (0))
(step t101 (cl @p_270 @p_260) :rule and_pos :args (1))
(step t102 (cl @p_266 @p_270 @p_270) :rule resolution :premises (t99 t100 t101))
(step t103 (cl @p_270 @p_270 @p_266) :rule reordering :premises (t102))
(step t104 (cl @p_270 @p_266) :rule contraction :premises (t103))
(step t105 (cl @p_271 @p_266) :rule resolution :premises (t98 t104))
(step t106 (cl @p_271 @p_267) :rule implies_neg2)
(step t107 (cl @p_271 @p_271) :rule resolution :premises (t105 t106))
(step t108 (cl @p_271) :rule contraction :premises (t107))
(step t109 (cl @p_270 @p_266) :rule implies :premises (t108))
(step t110 (cl @p_258 @p_268 @p_266) :rule resolution :premises (t97 t109))
(step t111 (cl @p_266 @p_258 @p_268) :rule reordering :premises (t110))
(step t112 (cl (or @p_265 @p_260)) :rule forall_inst :args (zero$))
(step t113 (cl @p_265 @p_260) :rule or :premises (t112))
(step t114 (cl (not @p_261) (not (forall ((?v0 A$)) (= (plus$f (fin$e ?v0) pinf$e) pinf$e))) (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule equiv_pos2)
(anchor :step t115 :args ((?v0 A$) (:= (?v0 A$) ?v0)))
(step t115.t0 (cl (= (= @p_264 pinf$e) (= pinf$e @p_264))) :rule rare_rewrite :args ("eq-symm" @p_264 pinf$e))
(step t115 (cl @p_261) :rule bind)
(step t116 (cl (forall ((?v0 A$)) (= pinf$e (plus$f (fin$e ?v0) pinf$e)))) :rule resolution :premises (t114 t115 a17))
(step t117 (cl @p_260) :rule resolution :premises (t113 t116))
(step t118 (cl @p_258) :rule resolution :premises (t111 t20 t117))
(step t119 (cl @p_274) :rule resolution :premises (t96 t118))
(step t120 (cl (! (not @p_14) :named @p_273) @p_7) :rule and_pos :args (0))
(step t121 (cl @p_7 @p_273) :rule reordering :premises (t120))
(step t122 (cl @p_273) :rule resolution :premises (t121 t118))
(step t123 (cl (! (not @p_9) :named @p_272) @p_7) :rule and_pos :args (1))
(step t124 (cl @p_7 @p_272) :rule reordering :premises (t123))
(step t125 (cl @p_272) :rule resolution :premises (t124 t118))
(step t126 (cl (! (not @p_8) :named @p_257) @p_7) :rule and_pos :args (0))
(step t127 (cl @p_7 @p_257) :rule reordering :premises (t126))
(step t128 (cl @p_257) :rule resolution :premises (t127 t118))
(step t129 (cl (not (! (= (! (=> (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))) (! (or (! (not (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (plus$f x$ x$) (fin$e (plus$ ?v3 ?v4))))))) :named @p_246) (! (and @p_239 @p_5 @p_12) :named @p_245) @p_245 (! (and @p_239 @p_239 @p_5) :named @p_244) (! (and @p_238 @p_10 @p_12) :named @p_243) @p_243 (! (and @p_238 @p_238 @p_10) :named @p_242) (! (and @p_238 @p_239 @p_5) :named @p_241) (! (and @p_239 @p_238 @p_5) :named @p_240)) :named @p_247)) :named @p_248) (! (=> (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))) @p_17) :named @p_237)) :named @p_249)) (not @p_248) @p_237) :rule equiv_pos2)
(anchor :step t130 :args ((?v3 A$) (?v4 A$) (:= (?v3 A$) ?v3) (:= (?v4 A$) ?v4)))
(step t130.t0 (cl (= (! (= @p_4 @p_219) :named @p_255) @p_250)) :rule rare_rewrite :args ("eq-symm" @p_4 @p_219))
(step t130.t1 (cl (= (! (not @p_255) :named @p_256) @p_251)) :rule cong :premises (t130.t0))
(step t130.t2 (cl (= (or @p_253 @p_252 @p_256) @p_254)) :rule cong :premises (t130.t1))
(step t130 (cl (= (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (plus$f x$ x$) (fin$e (plus$ ?v3 ?v4)))))) (forall ((?v3 A$) (?v4 A$)) (or (not (= x$ (fin$e ?v3))) (not (= x$ (fin$e ?v4))) (not (= (fin$e (plus$ ?v3 ?v4)) (plus$f x$ x$))))))) :rule bind)
(step t131 (cl (= @p_246 @p_16)) :rule cong :premises (t130))
(step t132 (cl (= @p_239 @p_7)) :rule rare_rewrite :args ("eq-symm" pinf$e x$))
(step t133 (cl (= @p_5 @p_5)) :rule refl)
(step t134 (cl (= @p_12 @p_12)) :rule refl)
(step t135 (cl (= @p_245 @p_15)) :rule cong :premises (t132 t133 t134))
(step t136 (cl (= @p_244 @p_14)) :rule cong :premises (t132 t132 t133))
(step t137 (cl (= @p_238 @p_6)) :rule rare_rewrite :args ("eq-symm" minf$e x$))
(step t138 (cl (= @p_10 @p_10)) :rule refl)
(step t139 (cl (= @p_243 @p_13)) :rule cong :premises (t137 t138 t134))
(step t140 (cl (= @p_242 @p_11)) :rule cong :premises (t137 t137 t138))
(step t141 (cl (= @p_241 @p_9)) :rule cong :premises (t137 t132 t133))
(step t142 (cl (= @p_240 @p_8)) :rule cong :premises (t132 t137 t133))
(step t143 (cl (= @p_247 @p_17)) :rule cong :premises (t131 t135 t135 t136 t139 t139 t140 t141 t142))
(step t144 (cl @p_249) :rule cong :premises (t143))
(step t145 (cl @p_248 (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :rule implies_neg1)
(anchor :step t146)
(assume t146.a0 (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))
(step t146.t0 (cl (or (! (not (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :named @p_236) @p_247)) :rule forall_inst :args (x$ x$))
(step t146.t1 (cl @p_236 @p_247) :rule or :premises (t146.t0))
(step t146.t2 (cl (not (! (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false)) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :named @p_18)) (not (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :rule equiv_pos2)
(anchor :step t146.t3 :args ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1) (:= (?v2 A_extended$) ?v2)))
(step t146.t3.t0 (cl (= (! (=> (! (and (! (= (! (plus$f ?v0 ?v1) :named @p_21) ?v2) :named @p_155) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (! (=> (! (and (! (= ?v0 pinf$e) :named @p_141) (! (and (! (= ?v1 pinf$e) :named @p_144) (! (= ?v2 pinf$e) :named @p_139)) :named @p_145)) :named @p_153) false) :named @p_154) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (! (=> (! (and (! (= ?v0 minf$e) :named @p_146) (! (and (! (= ?v1 minf$e) :named @p_140) (! (= ?v2 minf$e) :named @p_149)) :named @p_150)) :named @p_151) false) :named @p_152) (and (! (=> (! (and @p_146 @p_145) :named @p_147) false) :named @p_148) (! (=> (! (and @p_141 (and @p_140 @p_139)) :named @p_142) false) :named @p_143)))))))))) :named @p_156) false) :named @p_157) (! (not @p_156) :named @p_158))) :rule rare_rewrite :args ("bool-impl-false1" @p_156))
(step t146.t3.t1 (cl (= @p_156 (! (and @p_155 (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) @p_154 (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) @p_152 @p_148 @p_143) :named @p_159))) :rule aci_simp)
(step t146.t3.t2 (cl (= @p_155 (! (= ?v2 @p_21) :named @p_45))) :rule rare_rewrite :args ("eq-symm" @p_21 ?v2))
(anchor :step t146.t3.t3 :args ((?v3 A$) (?v4 A$) (:= (?v3 A$) ?v3) (:= (?v4 A$) ?v4)))
(step t146.t3.t3.t0 (cl (= (! (=> (! (and (! (= ?v0 @p_167) :named @p_168) (! (and (! (= ?v1 @p_222) :named @p_223) (! (= ?v2 @p_219) :named @p_220)) :named @p_230)) :named @p_233) false) :named @p_234) (! (not @p_233) :named @p_235))) :rule rare_rewrite :args ("bool-impl-false1" @p_233))
(step t146.t3.t3.t1 (cl (= @p_233 (! (and @p_168 @p_223 @p_220) :named @p_226))) :rule aci_simp)
(step t146.t3.t3.t2 (cl (= @p_235 (! (not @p_226) :named @p_227))) :rule cong :premises (t146.t3.t3.t1))
(step t146.t3.t3.t3 (cl (= @p_234 @p_227)) :rule trans :premises (t146.t3.t3.t0 t146.t3.t3.t2))
(step t146.t3.t3 (cl (= (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (forall ((?v3 A$) (?v4 A$)) (not (and (= ?v0 (fin$e ?v3)) (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule bind)
(anchor :step t146.t3.t4 :args ((?v3 A$) (?v4 A$) (:= (?v3 A$) ?v3) (:= (?v4 A$) ?v4)))
(step t146.t3.t4.t0 (cl (= @p_227 (! (or (! (not @p_168) :named @p_169) (! (not @p_230) :named @p_231)) :named @p_232))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_223 (rare-list @p_220)))
(step t146.t3.t4.t1 (cl (= @p_231 (! (or (! (not @p_223) :named @p_224) (! (not @p_220) :named @p_221)) :named @p_228))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_223 @p_220 rare-list))
(step t146.t3.t4.t2 (cl (= @p_232 (! (or @p_169 @p_228) :named @p_229))) :rule cong :premises (t146.t3.t4.t1))
(step t146.t3.t4.t3 (cl (= @p_227 @p_229)) :rule trans :premises (t146.t3.t4.t0 t146.t3.t4.t2))
(step t146.t3.t4.t4 (cl (= @p_229 (! (or @p_169 @p_224 @p_221) :named @p_225))) :rule aci_simp)
(step t146.t3.t4.t5 (cl (= @p_227 @p_225)) :rule trans :premises (t146.t3.t4.t3 t146.t3.t4.t4))
(step t146.t3.t4 (cl (= (forall ((?v3 A$) (?v4 A$)) (not (and (= ?v0 (fin$e ?v3)) (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule bind)
(step t146.t3.t5 (cl (= (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule trans :premises (t146.t3.t3 t146.t3.t4))
(anchor :step t146.t3.t6 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t6.t0 (cl (= (! (=> (! (and @p_168 @p_145) :named @p_214) false) :named @p_215) (! (not @p_214) :named @p_216))) :rule rare_rewrite :args ("bool-impl-false1" @p_214))
(step t146.t3.t6.t1 (cl (= @p_214 (! (and @p_168 @p_144 @p_139) :named @p_217))) :rule aci_simp)
(step t146.t3.t6.t2 (cl (= @p_144 (! (= pinf$e ?v1) :named @p_26))) :rule rare_rewrite :args ("eq-symm" ?v1 pinf$e))
(step t146.t3.t6.t3 (cl (= @p_139 (! (= pinf$e ?v2) :named @p_46))) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t146.t3.t6.t4 (cl (= @p_217 (! (and @p_168 @p_26 @p_46) :named @p_208))) :rule cong :premises (t146.t3.t6.t2 t146.t3.t6.t3))
(step t146.t3.t6.t5 (cl (= @p_214 @p_208)) :rule trans :premises (t146.t3.t6.t1 t146.t3.t6.t4))
(step t146.t3.t6.t6 (cl (= @p_216 (! (not @p_208) :named @p_209))) :rule cong :premises (t146.t3.t6.t5))
(step t146.t3.t6.t7 (cl (= @p_215 @p_209)) :rule trans :premises (t146.t3.t6.t0 t146.t3.t6.t6))
(step t146.t3.t6 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t7 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t7.t0 (cl (= @p_209 (! (or @p_169 (! (not (and @p_26 @p_46)) :named @p_212)) :named @p_213))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_26 (rare-list @p_46)))
(step t146.t3.t7.t1 (cl (= @p_212 (! (or (! (not @p_26) :named @p_74) (! (not @p_46) :named @p_71)) :named @p_210))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_26 @p_46 rare-list))
(step t146.t3.t7.t2 (cl (= @p_213 (! (or @p_169 @p_210) :named @p_211))) :rule cong :premises (t146.t3.t7.t1))
(step t146.t3.t7.t3 (cl (= @p_209 @p_211)) :rule trans :premises (t146.t3.t7.t0 t146.t3.t7.t2))
(step t146.t3.t7.t4 (cl (= @p_211 (! (or @p_169 @p_74 @p_71) :named @p_207))) :rule aci_simp)
(step t146.t3.t7.t5 (cl (= @p_209 @p_207)) :rule trans :premises (t146.t3.t7.t3 t146.t3.t7.t4))
(step t146.t3.t7 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t8 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t8.t0 (cl (= @p_207 (or @p_74 @p_71 @p_169))) :rule aci_simp)
(step t146.t3.t8 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (not (= ?v0 (fin$e ?v3))))))) :rule bind)
(step t146.t3.t9 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (not (= ?v0 (fin$e ?v3))))) (! (or @p_74 @p_71 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) :named @p_75))) :rule miniscope_split)
(step t146.t3.t10 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))) @p_75)) :rule trans :premises (t146.t3.t8 t146.t3.t9))
(step t146.t3.t11 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))) @p_75)) :rule trans :premises (t146.t3.t7 t146.t3.t10))
(step t146.t3.t12 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) @p_75)) :rule trans :premises (t146.t3.t6 t146.t3.t11))
(anchor :step t146.t3.t13 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t13.t0 (cl (= (! (=> (! (and @p_141 (and (! (= ?v1 @p_167) :named @p_181) @p_139)) :named @p_203) false) :named @p_204) (! (not @p_203) :named @p_205))) :rule rare_rewrite :args ("bool-impl-false1" @p_203))
(step t146.t3.t13.t1 (cl (= @p_203 (! (and @p_141 @p_181 @p_139) :named @p_206))) :rule aci_simp)
(step t146.t3.t13.t2 (cl (= @p_141 (! (= pinf$e ?v0) :named @p_24))) :rule rare_rewrite :args ("eq-symm" ?v0 pinf$e))
(step t146.t3.t13.t3 (cl (= @p_181 @p_181)) :rule refl)
(step t146.t3.t13.t4 (cl (= @p_139 @p_46)) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t146.t3.t13.t5 (cl (= @p_206 (! (and @p_24 @p_181 @p_46) :named @p_197))) :rule cong :premises (t146.t3.t13.t2 t146.t3.t13.t3 t146.t3.t13.t4))
(step t146.t3.t13.t6 (cl (= @p_203 @p_197)) :rule trans :premises (t146.t3.t13.t1 t146.t3.t13.t5))
(step t146.t3.t13.t7 (cl (= @p_205 (! (not @p_197) :named @p_198))) :rule cong :premises (t146.t3.t13.t6))
(step t146.t3.t13.t8 (cl (= @p_204 @p_198)) :rule trans :premises (t146.t3.t13.t0 t146.t3.t13.t7))
(step t146.t3.t13 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t14 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t14.t0 (cl (= @p_198 (! (or (! (not @p_24) :named @p_72) (! (not (and @p_181 @p_46)) :named @p_201)) :named @p_202))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_24 @p_181 (rare-list @p_46)))
(step t146.t3.t14.t1 (cl (= @p_201 (! (or (! (not @p_181) :named @p_182) @p_71) :named @p_199))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_46 rare-list))
(step t146.t3.t14.t2 (cl (= @p_202 (! (or @p_72 @p_199) :named @p_200))) :rule cong :premises (t146.t3.t14.t1))
(step t146.t3.t14.t3 (cl (= @p_198 @p_200)) :rule trans :premises (t146.t3.t14.t0 t146.t3.t14.t2))
(step t146.t3.t14.t4 (cl (= @p_200 (! (or @p_72 @p_182 @p_71) :named @p_196))) :rule aci_simp)
(step t146.t3.t14.t5 (cl (= @p_198 @p_196)) :rule trans :premises (t146.t3.t14.t3 t146.t3.t14.t4))
(step t146.t3.t14 (cl (= (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t15 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t15.t0 (cl (= @p_196 (or @p_72 @p_71 @p_182))) :rule aci_simp)
(step t146.t3.t15 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (not (= ?v1 (fin$e ?v3))))))) :rule bind)
(step t146.t3.t16 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (not (= ?v1 (fin$e ?v3))))) (! (or @p_72 @p_71 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) :named @p_73))) :rule miniscope_split)
(step t146.t3.t17 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))) @p_73)) :rule trans :premises (t146.t3.t15 t146.t3.t16))
(step t146.t3.t18 (cl (= (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))) @p_73)) :rule trans :premises (t146.t3.t14 t146.t3.t17))
(step t146.t3.t19 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) @p_73)) :rule trans :premises (t146.t3.t13 t146.t3.t18))
(step t146.t3.t20 (cl (= @p_154 (! (not @p_153) :named @p_194))) :rule rare_rewrite :args ("bool-impl-false1" @p_153))
(step t146.t3.t21 (cl (= @p_153 (! (and @p_141 @p_144 @p_139) :named @p_195))) :rule aci_simp)
(step t146.t3.t22 (cl (= @p_141 @p_24)) :rule rare_rewrite :args ("eq-symm" ?v0 pinf$e))
(step t146.t3.t23 (cl (= @p_144 @p_26)) :rule rare_rewrite :args ("eq-symm" ?v1 pinf$e))
(step t146.t3.t24 (cl (= @p_139 @p_46)) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t146.t3.t25 (cl (= @p_195 (! (and @p_24 @p_26 @p_46) :named @p_53))) :rule cong :premises (t146.t3.t22 t146.t3.t23 t146.t3.t24))
(step t146.t3.t26 (cl (= @p_153 @p_53)) :rule trans :premises (t146.t3.t21 t146.t3.t25))
(step t146.t3.t27 (cl (= @p_194 (! (not @p_53) :named @p_70))) :rule cong :premises (t146.t3.t26))
(step t146.t3.t28 (cl (= @p_154 @p_70)) :rule trans :premises (t146.t3.t20 t146.t3.t27))
(anchor :step t146.t3.t29 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t29.t0 (cl (= (! (=> (! (and @p_146 (and @p_181 @p_149)) :named @p_190) false) :named @p_191) (! (not @p_190) :named @p_192))) :rule rare_rewrite :args ("bool-impl-false1" @p_190))
(step t146.t3.t29.t1 (cl (= @p_190 (! (and @p_146 @p_181 @p_149) :named @p_193))) :rule aci_simp)
(step t146.t3.t29.t2 (cl (= @p_146 (! (= minf$e ?v0) :named @p_27))) :rule rare_rewrite :args ("eq-symm" ?v0 minf$e))
(step t146.t3.t29.t3 (cl (= @p_181 @p_181)) :rule refl)
(step t146.t3.t29.t4 (cl (= @p_149 (! (= minf$e ?v2) :named @p_49))) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t146.t3.t29.t5 (cl (= @p_193 (! (and @p_27 @p_181 @p_49) :named @p_184))) :rule cong :premises (t146.t3.t29.t2 t146.t3.t29.t3 t146.t3.t29.t4))
(step t146.t3.t29.t6 (cl (= @p_190 @p_184)) :rule trans :premises (t146.t3.t29.t1 t146.t3.t29.t5))
(step t146.t3.t29.t7 (cl (= @p_192 (! (not @p_184) :named @p_185))) :rule cong :premises (t146.t3.t29.t6))
(step t146.t3.t29.t8 (cl (= @p_191 @p_185)) :rule trans :premises (t146.t3.t29.t0 t146.t3.t29.t7))
(step t146.t3.t29 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t30 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t30.t0 (cl (= @p_185 (! (or (! (not @p_27) :named @p_68) (! (not (and @p_181 @p_49)) :named @p_188)) :named @p_189))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_27 @p_181 (rare-list @p_49)))
(step t146.t3.t30.t1 (cl (= @p_188 (! (or @p_182 (! (not @p_49) :named @p_65)) :named @p_186))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_49 rare-list))
(step t146.t3.t30.t2 (cl (= @p_189 (! (or @p_68 @p_186) :named @p_187))) :rule cong :premises (t146.t3.t30.t1))
(step t146.t3.t30.t3 (cl (= @p_185 @p_187)) :rule trans :premises (t146.t3.t30.t0 t146.t3.t30.t2))
(step t146.t3.t30.t4 (cl (= @p_187 (! (or @p_68 @p_182 @p_65) :named @p_183))) :rule aci_simp)
(step t146.t3.t30.t5 (cl (= @p_185 @p_183)) :rule trans :premises (t146.t3.t30.t3 t146.t3.t30.t4))
(step t146.t3.t30 (cl (= (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t31 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t31.t0 (cl (= @p_183 (or @p_68 @p_65 @p_182))) :rule aci_simp)
(step t146.t3.t31 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (not (= ?v1 (fin$e ?v3))))))) :rule bind)
(step t146.t3.t32 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (not (= ?v1 (fin$e ?v3))))) (! (or @p_68 @p_65 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) :named @p_69))) :rule miniscope_split)
(step t146.t3.t33 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))) @p_69)) :rule trans :premises (t146.t3.t31 t146.t3.t32))
(step t146.t3.t34 (cl (= (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))) @p_69)) :rule trans :premises (t146.t3.t30 t146.t3.t33))
(step t146.t3.t35 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) @p_69)) :rule trans :premises (t146.t3.t29 t146.t3.t34))
(anchor :step t146.t3.t36 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t36.t0 (cl (= (! (=> (! (and @p_168 @p_150) :named @p_177) false) :named @p_178) (! (not @p_177) :named @p_179))) :rule rare_rewrite :args ("bool-impl-false1" @p_177))
(step t146.t3.t36.t1 (cl (= @p_177 (! (and @p_168 @p_140 @p_149) :named @p_180))) :rule aci_simp)
(step t146.t3.t36.t2 (cl (= @p_140 (! (= minf$e ?v1) :named @p_23))) :rule rare_rewrite :args ("eq-symm" ?v1 minf$e))
(step t146.t3.t36.t3 (cl (= @p_149 @p_49)) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t146.t3.t36.t4 (cl (= @p_180 (! (and @p_168 @p_23 @p_49) :named @p_171))) :rule cong :premises (t146.t3.t36.t2 t146.t3.t36.t3))
(step t146.t3.t36.t5 (cl (= @p_177 @p_171)) :rule trans :premises (t146.t3.t36.t1 t146.t3.t36.t4))
(step t146.t3.t36.t6 (cl (= @p_179 (! (not @p_171) :named @p_172))) :rule cong :premises (t146.t3.t36.t5))
(step t146.t3.t36.t7 (cl (= @p_178 @p_172)) :rule trans :premises (t146.t3.t36.t0 t146.t3.t36.t6))
(step t146.t3.t36 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t37 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t37.t0 (cl (= @p_172 (! (or @p_169 (! (not (and @p_23 @p_49)) :named @p_175)) :named @p_176))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_23 (rare-list @p_49)))
(step t146.t3.t37.t1 (cl (= @p_175 (! (or (! (not @p_23) :named @p_66) @p_65) :named @p_173))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_23 @p_49 rare-list))
(step t146.t3.t37.t2 (cl (= @p_176 (! (or @p_169 @p_173) :named @p_174))) :rule cong :premises (t146.t3.t37.t1))
(step t146.t3.t37.t3 (cl (= @p_172 @p_174)) :rule trans :premises (t146.t3.t37.t0 t146.t3.t37.t2))
(step t146.t3.t37.t4 (cl (= @p_174 (! (or @p_169 @p_66 @p_65) :named @p_170))) :rule aci_simp)
(step t146.t3.t37.t5 (cl (= @p_172 @p_170)) :rule trans :premises (t146.t3.t37.t3 t146.t3.t37.t4))
(step t146.t3.t37 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))))) :rule bind)
(anchor :step t146.t3.t38 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t146.t3.t38.t0 (cl (= @p_170 (or @p_66 @p_65 @p_169))) :rule aci_simp)
(step t146.t3.t38 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (not (= ?v0 (fin$e ?v3))))))) :rule bind)
(step t146.t3.t39 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (not (= ?v0 (fin$e ?v3))))) (! (or @p_66 @p_65 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) :named @p_67))) :rule miniscope_split)
(step t146.t3.t40 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))) @p_67)) :rule trans :premises (t146.t3.t38 t146.t3.t39))
(step t146.t3.t41 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))) @p_67)) :rule trans :premises (t146.t3.t37 t146.t3.t40))
(step t146.t3.t42 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) @p_67)) :rule trans :premises (t146.t3.t36 t146.t3.t41))
(step t146.t3.t43 (cl (= @p_152 (! (not @p_151) :named @p_164))) :rule rare_rewrite :args ("bool-impl-false1" @p_151))
(step t146.t3.t44 (cl (= @p_151 (! (and @p_146 @p_140 @p_149) :named @p_165))) :rule aci_simp)
(step t146.t3.t45 (cl (= @p_146 @p_27)) :rule rare_rewrite :args ("eq-symm" ?v0 minf$e))
(step t146.t3.t46 (cl (= @p_140 @p_23)) :rule rare_rewrite :args ("eq-symm" ?v1 minf$e))
(step t146.t3.t47 (cl (= @p_149 @p_49)) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t146.t3.t48 (cl (= @p_165 (! (and @p_27 @p_23 @p_49) :named @p_50))) :rule cong :premises (t146.t3.t45 t146.t3.t46 t146.t3.t47))
(step t146.t3.t49 (cl (= @p_151 @p_50)) :rule trans :premises (t146.t3.t44 t146.t3.t48))
(step t146.t3.t50 (cl (= @p_164 (! (not @p_50) :named @p_64))) :rule cong :premises (t146.t3.t49))
(step t146.t3.t51 (cl (= @p_152 @p_64)) :rule trans :premises (t146.t3.t43 t146.t3.t50))
(step t146.t3.t52 (cl (= @p_148 (! (not @p_147) :named @p_162))) :rule rare_rewrite :args ("bool-impl-false1" @p_147))
(step t146.t3.t53 (cl (= @p_147 (! (and @p_146 @p_144 @p_139) :named @p_163))) :rule aci_simp)
(step t146.t3.t54 (cl (= @p_163 (! (and @p_27 @p_26 @p_46) :named @p_48))) :rule cong :premises (t146.t3.t45 t146.t3.t23 t146.t3.t24))
(step t146.t3.t55 (cl (= @p_147 @p_48)) :rule trans :premises (t146.t3.t53 t146.t3.t54))
(step t146.t3.t56 (cl (= @p_162 (! (not @p_48) :named @p_63))) :rule cong :premises (t146.t3.t55))
(step t146.t3.t57 (cl (= @p_148 @p_63)) :rule trans :premises (t146.t3.t52 t146.t3.t56))
(step t146.t3.t58 (cl (= @p_143 (! (not @p_142) :named @p_160))) :rule rare_rewrite :args ("bool-impl-false1" @p_142))
(step t146.t3.t59 (cl (= @p_142 (! (and @p_141 @p_140 @p_139) :named @p_161))) :rule aci_simp)
(step t146.t3.t60 (cl (= @p_161 (! (and @p_24 @p_23 @p_46) :named @p_47))) :rule cong :premises (t146.t3.t22 t146.t3.t46 t146.t3.t24))
(step t146.t3.t61 (cl (= @p_142 @p_47)) :rule trans :premises (t146.t3.t59 t146.t3.t60))
(step t146.t3.t62 (cl (= @p_160 (! (not @p_47) :named @p_62))) :rule cong :premises (t146.t3.t61))
(step t146.t3.t63 (cl (= @p_143 @p_62)) :rule trans :premises (t146.t3.t58 t146.t3.t62))
(step t146.t3.t64 (cl (= @p_159 (! (and @p_45 (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) @p_75 @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62) :named @p_76))) :rule cong :premises (t146.t3.t2 t146.t3.t5 t146.t3.t12 t146.t3.t19 t146.t3.t28 t146.t3.t35 t146.t3.t42 t146.t3.t51 t146.t3.t57 t146.t3.t63))
(step t146.t3.t65 (cl (= @p_156 @p_76)) :rule trans :premises (t146.t3.t1 t146.t3.t64))
(step t146.t3.t66 (cl (= @p_158 (! (not @p_76) :named @p_77))) :rule cong :premises (t146.t3.t65))
(step t146.t3.t67 (cl (= @p_157 @p_77)) :rule trans :premises (t146.t3.t0 t146.t3.t66))
(step t146.t3 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false)) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))))) :rule bind)
(anchor :step t146.t4 :args ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1) (:= (?v2 A_extended$) ?v2)))
(step t146.t4.t0 (cl (= @p_77 (! (or (! (not @p_45) :named @p_57) (! (not (and (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) @p_75 @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)) :named @p_123)) :named @p_124))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_45 (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (rare-list @p_75 @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t146.t4.t1 (cl (= @p_123 (! (or (! (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) :named @p_56) (! (not (and @p_75 @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)) :named @p_125)) :named @p_126))) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) @p_75 (rare-list @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t146.t4.t2 (cl (= @p_125 (! (or (! (not @p_75) :named @p_81) (! (not (and @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)) :named @p_127)) :named @p_128))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_75 @p_73 (rare-list @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t146.t4.t3 (cl (= @p_127 (! (or (! (not @p_73) :named @p_80) (! (not (and @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)) :named @p_129)) :named @p_130))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_73 @p_70 (rare-list @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t146.t4.t4 (cl (= @p_129 (! (or (! (not @p_70) :named @p_116) (! (not (and @p_69 @p_67 @p_64 @p_63 @p_62)) :named @p_131)) :named @p_132))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_70 @p_69 (rare-list @p_67 @p_64 @p_63 @p_62)))
(step t146.t4.t5 (cl (= @p_131 (! (or (! (not @p_69) :named @p_79) (! (not (and @p_67 @p_64 @p_63 @p_62)) :named @p_133)) :named @p_134))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_69 @p_67 (rare-list @p_64 @p_63 @p_62)))
(step t146.t4.t6 (cl (= @p_133 (! (or (! (not @p_67) :named @p_78) (! (not (and @p_64 @p_63 @p_62)) :named @p_135)) :named @p_136))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_67 @p_64 (rare-list @p_63 @p_62)))
(step t146.t4.t7 (cl (= @p_135 (! (or (! (not @p_64) :named @p_112) (! (not (and @p_63 @p_62)) :named @p_137)) :named @p_138))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_64 @p_63 (rare-list @p_62)))
(step t146.t4.t8 (cl (= @p_137 (! (or (! (not @p_63) :named @p_110) (! (not @p_62) :named @p_109)) :named @p_111))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_63 @p_62 rare-list))
(step t146.t4.t9 (cl (= @p_138 (! (or @p_112 @p_111) :named @p_113))) :rule cong :premises (t146.t4.t8))
(step t146.t4.t10 (cl (= @p_135 @p_113)) :rule trans :premises (t146.t4.t7 t146.t4.t9))
(step t146.t4.t11 (cl (= @p_136 (! (or @p_78 @p_113) :named @p_114))) :rule cong :premises (t146.t4.t10))
(step t146.t4.t12 (cl (= @p_133 @p_114)) :rule trans :premises (t146.t4.t6 t146.t4.t11))
(step t146.t4.t13 (cl (= @p_134 (! (or @p_79 @p_114) :named @p_115))) :rule cong :premises (t146.t4.t12))
(step t146.t4.t14 (cl (= @p_131 @p_115)) :rule trans :premises (t146.t4.t5 t146.t4.t13))
(step t146.t4.t15 (cl (= @p_132 (! (or @p_116 @p_115) :named @p_117))) :rule cong :premises (t146.t4.t14))
(step t146.t4.t16 (cl (= @p_129 @p_117)) :rule trans :premises (t146.t4.t4 t146.t4.t15))
(step t146.t4.t17 (cl (= @p_130 (! (or @p_80 @p_117) :named @p_118))) :rule cong :premises (t146.t4.t16))
(step t146.t4.t18 (cl (= @p_127 @p_118)) :rule trans :premises (t146.t4.t3 t146.t4.t17))
(step t146.t4.t19 (cl (= @p_128 (! (or @p_81 @p_118) :named @p_119))) :rule cong :premises (t146.t4.t18))
(step t146.t4.t20 (cl (= @p_125 @p_119)) :rule trans :premises (t146.t4.t2 t146.t4.t19))
(step t146.t4.t21 (cl (= @p_126 (! (or @p_56 @p_119) :named @p_120))) :rule cong :premises (t146.t4.t20))
(step t146.t4.t22 (cl (= @p_123 @p_120)) :rule trans :premises (t146.t4.t1 t146.t4.t21))
(step t146.t4.t23 (cl (= @p_124 (! (or @p_57 @p_120) :named @p_121))) :rule cong :premises (t146.t4.t22))
(step t146.t4.t24 (cl (= @p_77 @p_121)) :rule trans :premises (t146.t4.t0 t146.t4.t23))
(step t146.t4.t25 (cl (= @p_121 (! (or @p_57 @p_56 @p_81 @p_80 @p_116 @p_79 @p_78 @p_112 @p_110 @p_109) :named @p_122))) :rule aci_simp)
(step t146.t4.t26 (cl (= @p_116 @p_53)) :rule rare_rewrite :args ("bool-double-not-elim" @p_53))
(step t146.t4.t27 (cl (= @p_79 @p_79)) :rule refl)
(step t146.t4.t28 (cl (= @p_78 @p_78)) :rule refl)
(step t146.t4.t29 (cl (= @p_112 @p_50)) :rule rare_rewrite :args ("bool-double-not-elim" @p_50))
(step t146.t4.t30 (cl (= @p_110 @p_48)) :rule rare_rewrite :args ("bool-double-not-elim" @p_48))
(step t146.t4.t31 (cl (= @p_109 @p_47)) :rule rare_rewrite :args ("bool-double-not-elim" @p_47))
(step t146.t4.t32 (cl (= @p_122 (! (or @p_57 @p_56 @p_81 @p_80 @p_53 @p_79 @p_78 @p_50 @p_48 @p_47) :named @p_82))) :rule cong :premises (t146.t4.t26 t146.t4.t27 t146.t4.t28 t146.t4.t29 t146.t4.t30 t146.t4.t31))
(step t146.t4.t33 (cl (= @p_121 @p_82)) :rule trans :premises (t146.t4.t25 t146.t4.t32))
(step t146.t4.t34 (cl (= @p_77 @p_82)) :rule trans :premises (t146.t4.t24 t146.t4.t33))
(step t146.t4.t35 (cl (= @p_81 (! (and (! (not @p_74) :named @p_104) (! (not (or @p_71 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) :named @p_107)) :named @p_108))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_74 @p_71 (rare-list (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))))
(step t146.t4.t36 (cl (= @p_107 (! (and (! (not @p_71) :named @p_96) (! (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) :named @p_31)) :named @p_103))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_71 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))) rare-list))
(step t146.t4.t37 (cl (= @p_108 (! (and @p_104 @p_103) :named @p_105))) :rule cong :premises (t146.t4.t36))
(step t146.t4.t38 (cl (= @p_81 @p_105)) :rule trans :premises (t146.t4.t35 t146.t4.t37))
(step t146.t4.t39 (cl (= @p_105 (! (and @p_104 @p_96 @p_31) :named @p_106))) :rule aci_simp)
(step t146.t4.t40 (cl (= @p_104 @p_26)) :rule rare_rewrite :args ("bool-double-not-elim" @p_26))
(step t146.t4.t41 (cl (= @p_96 @p_46)) :rule rare_rewrite :args ("bool-double-not-elim" @p_46))
(step t146.t4.t42 (cl (= @p_31 @p_31)) :rule refl)
(step t146.t4.t43 (cl (= @p_106 (! (and @p_26 @p_46 @p_31) :named @p_55))) :rule cong :premises (t146.t4.t40 t146.t4.t41 t146.t4.t42))
(step t146.t4.t44 (cl (= @p_105 @p_55)) :rule trans :premises (t146.t4.t39 t146.t4.t43))
(step t146.t4.t45 (cl (= @p_81 @p_55)) :rule trans :premises (t146.t4.t38 t146.t4.t44))
(step t146.t4.t46 (cl (= @p_80 (! (and (! (not @p_72) :named @p_98) (! (not (or @p_71 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) :named @p_101)) :named @p_102))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_72 @p_71 (rare-list (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))))
(step t146.t4.t47 (cl (= @p_101 (! (and @p_96 (! (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) :named @p_33)) :named @p_97))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_71 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))) rare-list))
(step t146.t4.t48 (cl (= @p_102 (! (and @p_98 @p_97) :named @p_99))) :rule cong :premises (t146.t4.t47))
(step t146.t4.t49 (cl (= @p_80 @p_99)) :rule trans :premises (t146.t4.t46 t146.t4.t48))
(step t146.t4.t50 (cl (= @p_99 (! (and @p_98 @p_96 @p_33) :named @p_100))) :rule aci_simp)
(step t146.t4.t51 (cl (= @p_98 @p_24)) :rule rare_rewrite :args ("bool-double-not-elim" @p_24))
(step t146.t4.t52 (cl (= @p_33 @p_33)) :rule refl)
(step t146.t4.t53 (cl (= @p_100 (! (and @p_24 @p_46 @p_33) :named @p_54))) :rule cong :premises (t146.t4.t51 t146.t4.t41 t146.t4.t52))
(step t146.t4.t54 (cl (= @p_99 @p_54)) :rule trans :premises (t146.t4.t50 t146.t4.t53))
(step t146.t4.t55 (cl (= @p_80 @p_54)) :rule trans :premises (t146.t4.t49 t146.t4.t54))
(step t146.t4.t56 (cl (= @p_53 @p_53)) :rule refl)
(step t146.t4.t57 (cl (= @p_79 (! (and (! (not @p_68) :named @p_91) (! (not (or @p_65 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) :named @p_94)) :named @p_95))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_68 @p_65 (rare-list (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))))
(step t146.t4.t58 (cl (= @p_94 (! (and (! (not @p_65) :named @p_83) @p_33) :named @p_90))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_65 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))) rare-list))
(step t146.t4.t59 (cl (= @p_95 (! (and @p_91 @p_90) :named @p_92))) :rule cong :premises (t146.t4.t58))
(step t146.t4.t60 (cl (= @p_79 @p_92)) :rule trans :premises (t146.t4.t57 t146.t4.t59))
(step t146.t4.t61 (cl (= @p_92 (! (and @p_91 @p_83 @p_33) :named @p_93))) :rule aci_simp)
(step t146.t4.t62 (cl (= @p_91 @p_27)) :rule rare_rewrite :args ("bool-double-not-elim" @p_27))
(step t146.t4.t63 (cl (= @p_83 @p_49)) :rule rare_rewrite :args ("bool-double-not-elim" @p_49))
(step t146.t4.t64 (cl (= @p_93 (! (and @p_27 @p_49 @p_33) :named @p_52))) :rule cong :premises (t146.t4.t62 t146.t4.t63 t146.t4.t52))
(step t146.t4.t65 (cl (= @p_92 @p_52)) :rule trans :premises (t146.t4.t61 t146.t4.t64))
(step t146.t4.t66 (cl (= @p_79 @p_52)) :rule trans :premises (t146.t4.t60 t146.t4.t65))
(step t146.t4.t67 (cl (= @p_78 (! (and (! (not @p_66) :named @p_85) (! (not (or @p_65 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) :named @p_88)) :named @p_89))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_66 @p_65 (rare-list (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))))
(step t146.t4.t68 (cl (= @p_88 (! (and @p_83 @p_31) :named @p_84))) :rule rare_rewrite :args ("bool-or-de-morgan" @p_65 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))) rare-list))
(step t146.t4.t69 (cl (= @p_89 (! (and @p_85 @p_84) :named @p_86))) :rule cong :premises (t146.t4.t68))
(step t146.t4.t70 (cl (= @p_78 @p_86)) :rule trans :premises (t146.t4.t67 t146.t4.t69))
(step t146.t4.t71 (cl (= @p_86 (! (and @p_85 @p_83 @p_31) :named @p_87))) :rule aci_simp)
(step t146.t4.t72 (cl (= @p_85 @p_23)) :rule rare_rewrite :args ("bool-double-not-elim" @p_23))
(step t146.t4.t73 (cl (= @p_87 (! (and @p_23 @p_49 @p_31) :named @p_51))) :rule cong :premises (t146.t4.t72 t146.t4.t63 t146.t4.t42))
(step t146.t4.t74 (cl (= @p_86 @p_51)) :rule trans :premises (t146.t4.t71 t146.t4.t73))
(step t146.t4.t75 (cl (= @p_78 @p_51)) :rule trans :premises (t146.t4.t70 t146.t4.t74))
(step t146.t4.t76 (cl (= @p_50 @p_50)) :rule refl)
(step t146.t4.t77 (cl (= @p_48 @p_48)) :rule refl)
(step t146.t4.t78 (cl (= @p_47 @p_47)) :rule refl)
(step t146.t4.t79 (cl (= @p_82 (! (or @p_57 @p_56 @p_55 @p_54 @p_53 @p_52 @p_51 @p_50 @p_48 @p_47) :named @p_61))) :rule cong :premises (t146.t4.t45 t146.t4.t55 t146.t4.t56 t146.t4.t66 t146.t4.t75 t146.t4.t76 t146.t4.t77 t146.t4.t78))
(step t146.t4.t80 (cl (= @p_77 @p_61)) :rule trans :premises (t146.t4.t34 t146.t4.t79))
(step t146.t4 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(step t146.t5 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule qnt_join)
(step t146.t6 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))))) :rule symm :premises (t146.t5))
(anchor :step t146.t7 :args ((?v0 A_extended$) (?v1 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1)))
(anchor :step t146.t7.t0 :args ((?v2 A_extended$) (:= (?v2 A_extended$) ?v2)))
(step t146.t7.t0.t0 (cl (= @p_61 (! (or @p_57 @p_57 @p_56 @p_55 @p_54 @p_53 @p_52 @p_51 @p_50 @p_48 @p_47) :named @p_58))) :rule aci_simp)
(step t146.t7.t0 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t146.t7.t1 :args ((:= (?v2 A_extended$) @p_21)))
(step t146.t7.t1.t0 (cl (= @p_58 (! (or (! (not (! (= @p_21 @p_21) :named @p_40)) :named @p_41) @p_41 (! (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) :named @p_38) (! (and @p_26 (! (= pinf$e @p_21) :named @p_22) @p_31) :named @p_37) (! (and @p_24 @p_22 @p_33) :named @p_36) (! (and @p_24 @p_26 @p_22) :named @p_35) (! (and @p_27 (! (= minf$e @p_21) :named @p_29) @p_33) :named @p_34) (! (and @p_23 @p_29 @p_31) :named @p_32) (! (and @p_27 @p_23 @p_29) :named @p_30) (! (and @p_27 @p_26 @p_22) :named @p_28) (! (and @p_24 @p_23 @p_22) :named @p_25)) :named @p_59))) :rule refl)
(step t146.t7.t1.t1 (cl (= @p_59 (! (or @p_41 @p_38 @p_37 @p_36 @p_35 @p_34 @p_32 @p_30 @p_28 @p_25) :named @p_42))) :rule rare_rewrite :args ("or-not-refl" @p_21 (rare-list @p_41 @p_38 @p_37 @p_36 @p_35 @p_34 @p_32 @p_30 @p_28 @p_25)))
(step t146.t7.t1.t2 (cl (= @p_58 @p_42)) :rule trans :premises (t146.t7.t1.t0 t146.t7.t1.t1))
(step t146.t7.t1 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) @p_42)) :rule onepoint)
(step t146.t7.t2 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) @p_42)) :rule trans :premises (t146.t7.t0 t146.t7.t1))
(step t146.t7 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule bind)
(step t146.t8 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t146.t6 t146.t7))
(anchor :step t146.t9 :args ((?v0 A_extended$) (?v1 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1)))
(step t146.t9.t0 (cl (= @p_40 true)) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t146.t9.t1 (cl (= @p_41 (! (not true) :named @p_44))) :rule cong :premises (t146.t9.t0))
(step t146.t9.t2 (cl (= @p_44 false)) :rule evaluate)
(step t146.t9.t3 (cl (= @p_41 false)) :rule trans :premises (t146.t9.t1 t146.t9.t2))
(step t146.t9.t4 (cl (= @p_38 @p_38)) :rule refl)
(step t146.t9.t5 (cl (= @p_37 @p_37)) :rule refl)
(step t146.t9.t6 (cl (= @p_36 @p_36)) :rule refl)
(step t146.t9.t7 (cl (= @p_35 @p_35)) :rule refl)
(step t146.t9.t8 (cl (= @p_34 @p_34)) :rule refl)
(step t146.t9.t9 (cl (= @p_32 @p_32)) :rule refl)
(step t146.t9.t10 (cl (= @p_30 @p_30)) :rule refl)
(step t146.t9.t11 (cl (= @p_28 @p_28)) :rule refl)
(step t146.t9.t12 (cl (= @p_25 @p_25)) :rule refl)
(step t146.t9.t13 (cl (= @p_42 (! (or false @p_38 @p_37 @p_36 @p_35 @p_34 @p_32 @p_30 @p_28 @p_25) :named @p_43))) :rule cong :premises (t146.t9.t3 t146.t9.t4 t146.t9.t5 t146.t9.t6 t146.t9.t7 t146.t9.t8 t146.t9.t9 t146.t9.t10 t146.t9.t11 t146.t9.t12))
(step t146.t9.t14 (cl (= @p_43 (! (or @p_38 @p_37 @p_36 @p_35 @p_34 @p_32 @p_30 @p_28 @p_25) :named @p_39))) :rule aci_simp)
(step t146.t9.t15 (cl (= @p_42 @p_39)) :rule trans :premises (t146.t9.t13 t146.t9.t14))
(step t146.t9 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule bind)
(step t146.t10 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t146.t8 t146.t9))
(step t146.t11 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t146.t4 t146.t10))
(step t146.t12 (cl @p_18) :rule trans :premises (t146.t3 t146.t11))
(step t146.t13 (cl (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :rule resolution :premises (t146.t2 t146.t12 a6))
(step t146.t14 (cl @p_247) :rule resolution :premises (t146.t1 t146.t13))
(step t146 (cl @p_236 @p_247) :rule subproof :discharge (t146.a0))
(step t147 (cl @p_248 @p_247) :rule resolution :premises (t145 t146))
(step t148 (cl @p_248 (not @p_247)) :rule implies_neg2)
(step t149 (cl @p_248 @p_248) :rule resolution :premises (t147 t148))
(step t150 (cl @p_248) :rule contraction :premises (t149))
(step t151 (cl @p_237) :rule resolution :premises (t129 t144 t150))
(step t152 (cl @p_236 @p_17) :rule implies :premises (t151))
(step t153 (cl (not @p_18) (not (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :rule equiv_pos2)
(anchor :step t154 :args ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1) (:= (?v2 A_extended$) ?v2)))
(step t154.t0 (cl (= @p_157 @p_158)) :rule rare_rewrite :args ("bool-impl-false1" @p_156))
(step t154.t1 (cl (= @p_156 @p_159)) :rule aci_simp)
(step t154.t2 (cl (= @p_155 @p_45)) :rule rare_rewrite :args ("eq-symm" @p_21 ?v2))
(anchor :step t154.t3 :args ((?v3 A$) (?v4 A$) (:= (?v3 A$) ?v3) (:= (?v4 A$) ?v4)))
(step t154.t3.t0 (cl (= @p_234 @p_235)) :rule rare_rewrite :args ("bool-impl-false1" @p_233))
(step t154.t3.t1 (cl (= @p_233 @p_226)) :rule aci_simp)
(step t154.t3.t2 (cl (= @p_235 @p_227)) :rule cong :premises (t154.t3.t1))
(step t154.t3.t3 (cl (= @p_234 @p_227)) :rule trans :premises (t154.t3.t0 t154.t3.t2))
(step t154.t3 (cl (= (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (forall ((?v3 A$) (?v4 A$)) (not (and (= ?v0 (fin$e ?v3)) (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule bind)
(anchor :step t154.t4 :args ((?v3 A$) (?v4 A$) (:= (?v3 A$) ?v3) (:= (?v4 A$) ?v4)))
(step t154.t4.t0 (cl (= @p_227 @p_232)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_223 (rare-list @p_220)))
(step t154.t4.t1 (cl (= @p_231 @p_228)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_223 @p_220 rare-list))
(step t154.t4.t2 (cl (= @p_232 @p_229)) :rule cong :premises (t154.t4.t1))
(step t154.t4.t3 (cl (= @p_227 @p_229)) :rule trans :premises (t154.t4.t0 t154.t4.t2))
(step t154.t4.t4 (cl (= @p_229 @p_225)) :rule aci_simp)
(step t154.t4.t5 (cl (= @p_227 @p_225)) :rule trans :premises (t154.t4.t3 t154.t4.t4))
(step t154.t4 (cl (= (forall ((?v3 A$) (?v4 A$)) (not (and (= ?v0 (fin$e ?v3)) (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule bind)
(step t154.t5 (cl (= (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))))) :rule trans :premises (t154.t3 t154.t4))
(anchor :step t154.t6 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t6.t0 (cl (= @p_215 @p_216)) :rule rare_rewrite :args ("bool-impl-false1" @p_214))
(step t154.t6.t1 (cl (= @p_214 @p_217)) :rule aci_simp)
(step t154.t6.t2 (cl (= @p_144 @p_26)) :rule rare_rewrite :args ("eq-symm" ?v1 pinf$e))
(step t154.t6.t3 (cl (= @p_139 @p_46)) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t154.t6.t4 (cl (= @p_217 @p_208)) :rule cong :premises (t154.t6.t2 t154.t6.t3))
(step t154.t6.t5 (cl (= @p_214 @p_208)) :rule trans :premises (t154.t6.t1 t154.t6.t4))
(step t154.t6.t6 (cl (= @p_216 @p_209)) :rule cong :premises (t154.t6.t5))
(step t154.t6.t7 (cl (= @p_215 @p_209)) :rule trans :premises (t154.t6.t0 t154.t6.t6))
(step t154.t6 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t154.t7 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t7.t0 (cl (= @p_209 @p_213)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_26 (rare-list @p_46)))
(step t154.t7.t1 (cl (= @p_212 @p_210)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_26 @p_46 rare-list))
(step t154.t7.t2 (cl (= @p_213 @p_211)) :rule cong :premises (t154.t7.t1))
(step t154.t7.t3 (cl (= @p_209 @p_211)) :rule trans :premises (t154.t7.t0 t154.t7.t2))
(step t154.t7.t4 (cl (= @p_211 @p_207)) :rule aci_simp)
(step t154.t7.t5 (cl (= @p_209 @p_207)) :rule trans :premises (t154.t7.t3 t154.t7.t4))
(step t154.t7 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))))) :rule bind)
(anchor :step t154.t8 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t8.t0 (cl (= @p_207 (or @p_74 @p_71 @p_169))) :rule aci_simp)
(step t154.t8 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (not (= ?v0 (fin$e ?v3))))))) :rule bind)
(step t154.t9 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (not (= ?v0 (fin$e ?v3))))) @p_75)) :rule miniscope_split)
(step t154.t10 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= pinf$e ?v1)) (not (= pinf$e ?v2)))) @p_75)) :rule trans :premises (t154.t8 t154.t9))
(step t154.t11 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= pinf$e ?v1) (= pinf$e ?v2)))) @p_75)) :rule trans :premises (t154.t7 t154.t10))
(step t154.t12 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) @p_75)) :rule trans :premises (t154.t6 t154.t11))
(anchor :step t154.t13 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t13.t0 (cl (= @p_204 @p_205)) :rule rare_rewrite :args ("bool-impl-false1" @p_203))
(step t154.t13.t1 (cl (= @p_203 @p_206)) :rule aci_simp)
(step t154.t13.t2 (cl (= @p_141 @p_24)) :rule rare_rewrite :args ("eq-symm" ?v0 pinf$e))
(step t154.t13.t3 (cl (= @p_181 @p_181)) :rule refl)
(step t154.t13.t4 (cl (= @p_139 @p_46)) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t154.t13.t5 (cl (= @p_206 @p_197)) :rule cong :premises (t154.t13.t2 t154.t13.t3 t154.t13.t4))
(step t154.t13.t6 (cl (= @p_203 @p_197)) :rule trans :premises (t154.t13.t1 t154.t13.t5))
(step t154.t13.t7 (cl (= @p_205 @p_198)) :rule cong :premises (t154.t13.t6))
(step t154.t13.t8 (cl (= @p_204 @p_198)) :rule trans :premises (t154.t13.t0 t154.t13.t7))
(step t154.t13 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t154.t14 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t14.t0 (cl (= @p_198 @p_202)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_24 @p_181 (rare-list @p_46)))
(step t154.t14.t1 (cl (= @p_201 @p_199)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_46 rare-list))
(step t154.t14.t2 (cl (= @p_202 @p_200)) :rule cong :premises (t154.t14.t1))
(step t154.t14.t3 (cl (= @p_198 @p_200)) :rule trans :premises (t154.t14.t0 t154.t14.t2))
(step t154.t14.t4 (cl (= @p_200 @p_196)) :rule aci_simp)
(step t154.t14.t5 (cl (= @p_198 @p_196)) :rule trans :premises (t154.t14.t3 t154.t14.t4))
(step t154.t14 (cl (= (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))))) :rule bind)
(anchor :step t154.t15 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t15.t0 (cl (= @p_196 (or @p_72 @p_71 @p_182))) :rule aci_simp)
(step t154.t15 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))) (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (not (= ?v1 (fin$e ?v3))))))) :rule bind)
(step t154.t16 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (not (= ?v1 (fin$e ?v3))))) @p_73)) :rule miniscope_split)
(step t154.t17 (cl (= (forall ((?v3 A$)) (or (not (= pinf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= pinf$e ?v2)))) @p_73)) :rule trans :premises (t154.t15 t154.t16))
(step t154.t18 (cl (= (forall ((?v3 A$)) (not (and (= pinf$e ?v0) (= ?v1 (fin$e ?v3)) (= pinf$e ?v2)))) @p_73)) :rule trans :premises (t154.t14 t154.t17))
(step t154.t19 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) @p_73)) :rule trans :premises (t154.t13 t154.t18))
(step t154.t20 (cl (= @p_154 @p_194)) :rule rare_rewrite :args ("bool-impl-false1" @p_153))
(step t154.t21 (cl (= @p_153 @p_195)) :rule aci_simp)
(step t154.t22 (cl (= @p_141 @p_24)) :rule rare_rewrite :args ("eq-symm" ?v0 pinf$e))
(step t154.t23 (cl (= @p_144 @p_26)) :rule rare_rewrite :args ("eq-symm" ?v1 pinf$e))
(step t154.t24 (cl (= @p_139 @p_46)) :rule rare_rewrite :args ("eq-symm" ?v2 pinf$e))
(step t154.t25 (cl (= @p_195 @p_53)) :rule cong :premises (t154.t22 t154.t23 t154.t24))
(step t154.t26 (cl (= @p_153 @p_53)) :rule trans :premises (t154.t21 t154.t25))
(step t154.t27 (cl (= @p_194 @p_70)) :rule cong :premises (t154.t26))
(step t154.t28 (cl (= @p_154 @p_70)) :rule trans :premises (t154.t20 t154.t27))
(anchor :step t154.t29 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t29.t0 (cl (= @p_191 @p_192)) :rule rare_rewrite :args ("bool-impl-false1" @p_190))
(step t154.t29.t1 (cl (= @p_190 @p_193)) :rule aci_simp)
(step t154.t29.t2 (cl (= @p_146 @p_27)) :rule rare_rewrite :args ("eq-symm" ?v0 minf$e))
(step t154.t29.t3 (cl (= @p_181 @p_181)) :rule refl)
(step t154.t29.t4 (cl (= @p_149 @p_49)) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t154.t29.t5 (cl (= @p_193 @p_184)) :rule cong :premises (t154.t29.t2 t154.t29.t3 t154.t29.t4))
(step t154.t29.t6 (cl (= @p_190 @p_184)) :rule trans :premises (t154.t29.t1 t154.t29.t5))
(step t154.t29.t7 (cl (= @p_192 @p_185)) :rule cong :premises (t154.t29.t6))
(step t154.t29.t8 (cl (= @p_191 @p_185)) :rule trans :premises (t154.t29.t0 t154.t29.t7))
(step t154.t29 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))))) :rule bind)
(anchor :step t154.t30 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t30.t0 (cl (= @p_185 @p_189)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_27 @p_181 (rare-list @p_49)))
(step t154.t30.t1 (cl (= @p_188 @p_186)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_181 @p_49 rare-list))
(step t154.t30.t2 (cl (= @p_189 @p_187)) :rule cong :premises (t154.t30.t1))
(step t154.t30.t3 (cl (= @p_185 @p_187)) :rule trans :premises (t154.t30.t0 t154.t30.t2))
(step t154.t30.t4 (cl (= @p_187 @p_183)) :rule aci_simp)
(step t154.t30.t5 (cl (= @p_185 @p_183)) :rule trans :premises (t154.t30.t3 t154.t30.t4))
(step t154.t30 (cl (= (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))))) :rule bind)
(anchor :step t154.t31 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t31.t0 (cl (= @p_183 (or @p_68 @p_65 @p_182))) :rule aci_simp)
(step t154.t31 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (not (= ?v1 (fin$e ?v3))))))) :rule bind)
(step t154.t32 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (not (= ?v1 (fin$e ?v3))))) @p_69)) :rule miniscope_split)
(step t154.t33 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v0)) (not (= ?v1 (fin$e ?v3))) (not (= minf$e ?v2)))) @p_69)) :rule trans :premises (t154.t31 t154.t32))
(step t154.t34 (cl (= (forall ((?v3 A$)) (not (and (= minf$e ?v0) (= ?v1 (fin$e ?v3)) (= minf$e ?v2)))) @p_69)) :rule trans :premises (t154.t30 t154.t33))
(step t154.t35 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) @p_69)) :rule trans :premises (t154.t29 t154.t34))
(anchor :step t154.t36 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t36.t0 (cl (= @p_178 @p_179)) :rule rare_rewrite :args ("bool-impl-false1" @p_177))
(step t154.t36.t1 (cl (= @p_177 @p_180)) :rule aci_simp)
(step t154.t36.t2 (cl (= @p_140 @p_23)) :rule rare_rewrite :args ("eq-symm" ?v1 minf$e))
(step t154.t36.t3 (cl (= @p_149 @p_49)) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t154.t36.t4 (cl (= @p_180 @p_171)) :rule cong :premises (t154.t36.t2 t154.t36.t3))
(step t154.t36.t5 (cl (= @p_177 @p_171)) :rule trans :premises (t154.t36.t1 t154.t36.t4))
(step t154.t36.t6 (cl (= @p_179 @p_172)) :rule cong :premises (t154.t36.t5))
(step t154.t36.t7 (cl (= @p_178 @p_172)) :rule trans :premises (t154.t36.t0 t154.t36.t6))
(step t154.t36 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))))) :rule bind)
(anchor :step t154.t37 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t37.t0 (cl (= @p_172 @p_176)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_168 @p_23 (rare-list @p_49)))
(step t154.t37.t1 (cl (= @p_175 @p_173)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_23 @p_49 rare-list))
(step t154.t37.t2 (cl (= @p_176 @p_174)) :rule cong :premises (t154.t37.t1))
(step t154.t37.t3 (cl (= @p_172 @p_174)) :rule trans :premises (t154.t37.t0 t154.t37.t2))
(step t154.t37.t4 (cl (= @p_174 @p_170)) :rule aci_simp)
(step t154.t37.t5 (cl (= @p_172 @p_170)) :rule trans :premises (t154.t37.t3 t154.t37.t4))
(step t154.t37 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))))) :rule bind)
(anchor :step t154.t38 :args ((?v3 A$) (:= (?v3 A$) ?v3)))
(step t154.t38.t0 (cl (= @p_170 (or @p_66 @p_65 @p_169))) :rule aci_simp)
(step t154.t38 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))) (forall ((?v3 A$)) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (not (= ?v0 (fin$e ?v3))))))) :rule bind)
(step t154.t39 (cl (= (forall ((?v3 A$)) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (not (= ?v0 (fin$e ?v3))))) @p_67)) :rule miniscope_split)
(step t154.t40 (cl (= (forall ((?v3 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= minf$e ?v1)) (not (= minf$e ?v2)))) @p_67)) :rule trans :premises (t154.t38 t154.t39))
(step t154.t41 (cl (= (forall ((?v3 A$)) (not (and (= ?v0 (fin$e ?v3)) (= minf$e ?v1) (= minf$e ?v2)))) @p_67)) :rule trans :premises (t154.t37 t154.t40))
(step t154.t42 (cl (= (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) @p_67)) :rule trans :premises (t154.t36 t154.t41))
(step t154.t43 (cl (= @p_152 @p_164)) :rule rare_rewrite :args ("bool-impl-false1" @p_151))
(step t154.t44 (cl (= @p_151 @p_165)) :rule aci_simp)
(step t154.t45 (cl (= @p_146 @p_27)) :rule rare_rewrite :args ("eq-symm" ?v0 minf$e))
(step t154.t46 (cl (= @p_140 @p_23)) :rule rare_rewrite :args ("eq-symm" ?v1 minf$e))
(step t154.t47 (cl (= @p_149 @p_49)) :rule rare_rewrite :args ("eq-symm" ?v2 minf$e))
(step t154.t48 (cl (= @p_165 @p_50)) :rule cong :premises (t154.t45 t154.t46 t154.t47))
(step t154.t49 (cl (= @p_151 @p_50)) :rule trans :premises (t154.t44 t154.t48))
(step t154.t50 (cl (= @p_164 @p_64)) :rule cong :premises (t154.t49))
(step t154.t51 (cl (= @p_152 @p_64)) :rule trans :premises (t154.t43 t154.t50))
(step t154.t52 (cl (= @p_148 @p_162)) :rule rare_rewrite :args ("bool-impl-false1" @p_147))
(step t154.t53 (cl (= @p_147 @p_163)) :rule aci_simp)
(step t154.t54 (cl (= @p_163 @p_48)) :rule cong :premises (t154.t45 t154.t23 t154.t24))
(step t154.t55 (cl (= @p_147 @p_48)) :rule trans :premises (t154.t53 t154.t54))
(step t154.t56 (cl (= @p_162 @p_63)) :rule cong :premises (t154.t55))
(step t154.t57 (cl (= @p_148 @p_63)) :rule trans :premises (t154.t52 t154.t56))
(step t154.t58 (cl (= @p_143 @p_160)) :rule rare_rewrite :args ("bool-impl-false1" @p_142))
(step t154.t59 (cl (= @p_142 @p_161)) :rule aci_simp)
(step t154.t60 (cl (= @p_161 @p_47)) :rule cong :premises (t154.t22 t154.t46 t154.t24))
(step t154.t61 (cl (= @p_142 @p_47)) :rule trans :premises (t154.t59 t154.t60))
(step t154.t62 (cl (= @p_160 @p_62)) :rule cong :premises (t154.t61))
(step t154.t63 (cl (= @p_143 @p_62)) :rule trans :premises (t154.t58 t154.t62))
(step t154.t64 (cl (= @p_159 @p_76)) :rule cong :premises (t154.t2 t154.t5 t154.t12 t154.t19 t154.t28 t154.t35 t154.t42 t154.t51 t154.t57 t154.t63))
(step t154.t65 (cl (= @p_156 @p_76)) :rule trans :premises (t154.t1 t154.t64))
(step t154.t66 (cl (= @p_158 @p_77)) :rule cong :premises (t154.t65))
(step t154.t67 (cl (= @p_157 @p_77)) :rule trans :premises (t154.t0 t154.t66))
(step t154 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (=> (and (= (plus$f ?v0 ?v1) ?v2) (and (forall ((?v3 A$) (?v4 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 (fin$e ?v4)) (= ?v2 (fin$e (plus$ ?v3 ?v4))))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 pinf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 pinf$e))) false)) (and (=> (and (= ?v0 pinf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (and (forall ((?v3 A$)) (=> (and (= ?v0 minf$e) (and (= ?v1 (fin$e ?v3)) (= ?v2 minf$e))) false)) (and (forall ((?v3 A$)) (=> (and (= ?v0 (fin$e ?v3)) (and (= ?v1 minf$e) (= ?v2 minf$e))) false)) (and (=> (and (= ?v0 minf$e) (and (= ?v1 minf$e) (= ?v2 minf$e))) false) (and (=> (and (= ?v0 minf$e) (and (= ?v1 pinf$e) (= ?v2 pinf$e))) false) (=> (and (= ?v0 pinf$e) (and (= ?v1 minf$e) (= ?v2 pinf$e))) false)))))))))) false)) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))))) :rule bind)
(anchor :step t155 :args ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1) (:= (?v2 A_extended$) ?v2)))
(step t155.t0 (cl (= @p_77 @p_124)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_45 (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (rare-list @p_75 @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t155.t1 (cl (= @p_123 @p_126)) :rule rare_rewrite :args ("bool-and-de-morgan" (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) @p_75 (rare-list @p_73 @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t155.t2 (cl (= @p_125 @p_128)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_75 @p_73 (rare-list @p_70 @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t155.t3 (cl (= @p_127 @p_130)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_73 @p_70 (rare-list @p_69 @p_67 @p_64 @p_63 @p_62)))
(step t155.t4 (cl (= @p_129 @p_132)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_70 @p_69 (rare-list @p_67 @p_64 @p_63 @p_62)))
(step t155.t5 (cl (= @p_131 @p_134)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_69 @p_67 (rare-list @p_64 @p_63 @p_62)))
(step t155.t6 (cl (= @p_133 @p_136)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_67 @p_64 (rare-list @p_63 @p_62)))
(step t155.t7 (cl (= @p_135 @p_138)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_64 @p_63 (rare-list @p_62)))
(step t155.t8 (cl (= @p_137 @p_111)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_63 @p_62 rare-list))
(step t155.t9 (cl (= @p_138 @p_113)) :rule cong :premises (t155.t8))
(step t155.t10 (cl (= @p_135 @p_113)) :rule trans :premises (t155.t7 t155.t9))
(step t155.t11 (cl (= @p_136 @p_114)) :rule cong :premises (t155.t10))
(step t155.t12 (cl (= @p_133 @p_114)) :rule trans :premises (t155.t6 t155.t11))
(step t155.t13 (cl (= @p_134 @p_115)) :rule cong :premises (t155.t12))
(step t155.t14 (cl (= @p_131 @p_115)) :rule trans :premises (t155.t5 t155.t13))
(step t155.t15 (cl (= @p_132 @p_117)) :rule cong :premises (t155.t14))
(step t155.t16 (cl (= @p_129 @p_117)) :rule trans :premises (t155.t4 t155.t15))
(step t155.t17 (cl (= @p_130 @p_118)) :rule cong :premises (t155.t16))
(step t155.t18 (cl (= @p_127 @p_118)) :rule trans :premises (t155.t3 t155.t17))
(step t155.t19 (cl (= @p_128 @p_119)) :rule cong :premises (t155.t18))
(step t155.t20 (cl (= @p_125 @p_119)) :rule trans :premises (t155.t2 t155.t19))
(step t155.t21 (cl (= @p_126 @p_120)) :rule cong :premises (t155.t20))
(step t155.t22 (cl (= @p_123 @p_120)) :rule trans :premises (t155.t1 t155.t21))
(step t155.t23 (cl (= @p_124 @p_121)) :rule cong :premises (t155.t22))
(step t155.t24 (cl (= @p_77 @p_121)) :rule trans :premises (t155.t0 t155.t23))
(step t155.t25 (cl (= @p_121 @p_122)) :rule aci_simp)
(step t155.t26 (cl (= @p_116 @p_53)) :rule rare_rewrite :args ("bool-double-not-elim" @p_53))
(step t155.t27 (cl (= @p_79 @p_79)) :rule refl)
(step t155.t28 (cl (= @p_78 @p_78)) :rule refl)
(step t155.t29 (cl (= @p_112 @p_50)) :rule rare_rewrite :args ("bool-double-not-elim" @p_50))
(step t155.t30 (cl (= @p_110 @p_48)) :rule rare_rewrite :args ("bool-double-not-elim" @p_48))
(step t155.t31 (cl (= @p_109 @p_47)) :rule rare_rewrite :args ("bool-double-not-elim" @p_47))
(step t155.t32 (cl (= @p_122 @p_82)) :rule cong :premises (t155.t26 t155.t27 t155.t28 t155.t29 t155.t30 t155.t31))
(step t155.t33 (cl (= @p_121 @p_82)) :rule trans :premises (t155.t25 t155.t32))
(step t155.t34 (cl (= @p_77 @p_82)) :rule trans :premises (t155.t24 t155.t33))
(step t155.t35 (cl (= @p_81 @p_108)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_74 @p_71 (rare-list (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))))
(step t155.t36 (cl (= @p_107 @p_103)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_71 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))) rare-list))
(step t155.t37 (cl (= @p_108 @p_105)) :rule cong :premises (t155.t36))
(step t155.t38 (cl (= @p_81 @p_105)) :rule trans :premises (t155.t35 t155.t37))
(step t155.t39 (cl (= @p_105 @p_106)) :rule aci_simp)
(step t155.t40 (cl (= @p_104 @p_26)) :rule rare_rewrite :args ("bool-double-not-elim" @p_26))
(step t155.t41 (cl (= @p_96 @p_46)) :rule rare_rewrite :args ("bool-double-not-elim" @p_46))
(step t155.t42 (cl (= @p_31 @p_31)) :rule refl)
(step t155.t43 (cl (= @p_106 @p_55)) :rule cong :premises (t155.t40 t155.t41 t155.t42))
(step t155.t44 (cl (= @p_105 @p_55)) :rule trans :premises (t155.t39 t155.t43))
(step t155.t45 (cl (= @p_81 @p_55)) :rule trans :premises (t155.t38 t155.t44))
(step t155.t46 (cl (= @p_80 @p_102)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_72 @p_71 (rare-list (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))))
(step t155.t47 (cl (= @p_101 @p_97)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_71 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))) rare-list))
(step t155.t48 (cl (= @p_102 @p_99)) :rule cong :premises (t155.t47))
(step t155.t49 (cl (= @p_80 @p_99)) :rule trans :premises (t155.t46 t155.t48))
(step t155.t50 (cl (= @p_99 @p_100)) :rule aci_simp)
(step t155.t51 (cl (= @p_98 @p_24)) :rule rare_rewrite :args ("bool-double-not-elim" @p_24))
(step t155.t52 (cl (= @p_33 @p_33)) :rule refl)
(step t155.t53 (cl (= @p_100 @p_54)) :rule cong :premises (t155.t51 t155.t41 t155.t52))
(step t155.t54 (cl (= @p_99 @p_54)) :rule trans :premises (t155.t50 t155.t53))
(step t155.t55 (cl (= @p_80 @p_54)) :rule trans :premises (t155.t49 t155.t54))
(step t155.t56 (cl (= @p_53 @p_53)) :rule refl)
(step t155.t57 (cl (= @p_79 @p_95)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_68 @p_65 (rare-list (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))))
(step t155.t58 (cl (= @p_94 @p_90)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_65 (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))) rare-list))
(step t155.t59 (cl (= @p_95 @p_92)) :rule cong :premises (t155.t58))
(step t155.t60 (cl (= @p_79 @p_92)) :rule trans :premises (t155.t57 t155.t59))
(step t155.t61 (cl (= @p_92 @p_93)) :rule aci_simp)
(step t155.t62 (cl (= @p_91 @p_27)) :rule rare_rewrite :args ("bool-double-not-elim" @p_27))
(step t155.t63 (cl (= @p_83 @p_49)) :rule rare_rewrite :args ("bool-double-not-elim" @p_49))
(step t155.t64 (cl (= @p_93 @p_52)) :rule cong :premises (t155.t62 t155.t63 t155.t52))
(step t155.t65 (cl (= @p_92 @p_52)) :rule trans :premises (t155.t61 t155.t64))
(step t155.t66 (cl (= @p_79 @p_52)) :rule trans :premises (t155.t60 t155.t65))
(step t155.t67 (cl (= @p_78 @p_89)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_66 @p_65 (rare-list (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))))
(step t155.t68 (cl (= @p_88 @p_84)) :rule rare_rewrite :args ("bool-or-de-morgan" @p_65 (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))) rare-list))
(step t155.t69 (cl (= @p_89 @p_86)) :rule cong :premises (t155.t68))
(step t155.t70 (cl (= @p_78 @p_86)) :rule trans :premises (t155.t67 t155.t69))
(step t155.t71 (cl (= @p_86 @p_87)) :rule aci_simp)
(step t155.t72 (cl (= @p_85 @p_23)) :rule rare_rewrite :args ("bool-double-not-elim" @p_23))
(step t155.t73 (cl (= @p_87 @p_51)) :rule cong :premises (t155.t72 t155.t63 t155.t42))
(step t155.t74 (cl (= @p_86 @p_51)) :rule trans :premises (t155.t71 t155.t73))
(step t155.t75 (cl (= @p_78 @p_51)) :rule trans :premises (t155.t70 t155.t74))
(step t155.t76 (cl (= @p_50 @p_50)) :rule refl)
(step t155.t77 (cl (= @p_48 @p_48)) :rule refl)
(step t155.t78 (cl (= @p_47 @p_47)) :rule refl)
(step t155.t79 (cl (= @p_82 @p_61)) :rule cong :premises (t155.t45 t155.t55 t155.t56 t155.t66 t155.t75 t155.t76 t155.t77 t155.t78))
(step t155.t80 (cl (= @p_77 @p_61)) :rule trans :premises (t155.t34 t155.t79))
(step t155 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(step t156 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))) (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule qnt_join)
(step t157 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))))) :rule symm :premises (t156))
(anchor :step t158 :args ((?v0 A_extended$) (?v1 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1)))
(anchor :step t158.t0 :args ((?v2 A_extended$) (:= (?v2 A_extended$) ?v2)))
(step t158.t0.t0 (cl (= @p_61 @p_58)) :rule aci_simp)
(step t158.t0 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) :rule bind)
(anchor :step t158.t1 :args ((:= (?v2 A_extended$) @p_21)))
(step t158.t1.t0 (cl (= @p_58 @p_59)) :rule refl)
(step t158.t1.t1 (cl (= @p_59 @p_42)) :rule rare_rewrite :args ("or-not-refl" @p_21 (rare-list @p_41 @p_38 @p_37 @p_36 @p_35 @p_34 @p_32 @p_30 @p_28 @p_25)))
(step t158.t1.t2 (cl (= @p_58 @p_42)) :rule trans :premises (t158.t1.t0 t158.t1.t1))
(step t158.t1 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) @p_42)) :rule onepoint)
(step t158.t2 (cl (= (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) @p_42)) :rule trans :premises (t158.t0 t158.t1))
(step t158 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (forall ((?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule bind)
(step t159 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t157 t158))
(anchor :step t160 :args ((?v0 A_extended$) (?v1 A_extended$) (:= (?v0 A_extended$) ?v0) (:= (?v1 A_extended$) ?v1)))
(step t160.t0 (cl (= @p_40 true)) :rule rare_rewrite :args ("eq-refl" @p_21))
(step t160.t1 (cl (= @p_41 @p_44)) :rule cong :premises (t160.t0))
(step t160.t2 (cl (= @p_44 false)) :rule evaluate)
(step t160.t3 (cl (= @p_41 false)) :rule trans :premises (t160.t1 t160.t2))
(step t160.t4 (cl (= @p_38 @p_38)) :rule refl)
(step t160.t5 (cl (= @p_37 @p_37)) :rule refl)
(step t160.t6 (cl (= @p_36 @p_36)) :rule refl)
(step t160.t7 (cl (= @p_35 @p_35)) :rule refl)
(step t160.t8 (cl (= @p_34 @p_34)) :rule refl)
(step t160.t9 (cl (= @p_32 @p_32)) :rule refl)
(step t160.t10 (cl (= @p_30 @p_30)) :rule refl)
(step t160.t11 (cl (= @p_28 @p_28)) :rule refl)
(step t160.t12 (cl (= @p_25 @p_25)) :rule refl)
(step t160.t13 (cl (= @p_42 @p_43)) :rule cong :premises (t160.t3 t160.t4 t160.t5 t160.t6 t160.t7 t160.t8 t160.t9 t160.t10 t160.t11 t160.t12))
(step t160.t14 (cl (= @p_43 @p_39)) :rule aci_simp)
(step t160.t15 (cl (= @p_42 @p_39)) :rule trans :premises (t160.t13 t160.t14))
(step t160 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (= (plus$f ?v0 ?v1) (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule bind)
(step t161 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (or (not (= ?v2 (plus$f ?v0 ?v1))) (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= minf$e ?v0) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e ?v2) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2)) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2)) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t159 t160))
(step t162 (cl (= (forall ((?v0 A_extended$) (?v1 A_extended$) (?v2 A_extended$)) (not (and (= ?v2 (plus$f ?v0 ?v1)) (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= ?v2 (fin$e (plus$ ?v3 ?v4)))))) (or (not (= pinf$e ?v1)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (or (not (= pinf$e ?v0)) (not (= pinf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (not (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (or (not (= minf$e ?v0)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3))))) (or (not (= minf$e ?v1)) (not (= minf$e ?v2)) (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3))))) (not (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e ?v2))) (not (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e ?v2))) (not (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e ?v2)))))) (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))))))) :rule trans :premises (t155 t161))
(step t163 (cl @p_18) :rule trans :premises (t154 t162))
(step t164 (cl (forall ((?v0 A_extended$) (?v1 A_extended$)) (or (not (forall ((?v3 A$) (?v4 A$)) (or (not (= ?v0 (fin$e ?v3))) (not (= ?v1 (fin$e ?v4))) (not (= (plus$f ?v0 ?v1) (fin$e (plus$ ?v3 ?v4))))))) (and (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= pinf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v1 (fin$e ?v3)))))) (and (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1)) (not (forall ((?v3 A$)) (not (= ?v0 (fin$e ?v3)))))) (and (= minf$e ?v0) (= minf$e ?v1) (= minf$e (plus$f ?v0 ?v1))) (and (= minf$e ?v0) (= pinf$e ?v1) (= pinf$e (plus$f ?v0 ?v1))) (and (= pinf$e ?v0) (= minf$e ?v1) (= pinf$e (plus$f ?v0 ?v1)))))) :rule resolution :premises (t153 t163 a6))
(step t165 (cl @p_17) :rule resolution :premises (t152 t164))
(step t166 (cl) :rule resolution :premises (t2 t28 t31 t94 t119 t122 t125 t128 t165))
)
1fb3376be507a018d20b7f09e8eb2649611f41b0 583 0
unsat
(
(define-fun @quantifiers_skolemize_3 () A$ (choice ((?v1 A$)) (not (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1))))))
(assume a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(assume a1 (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(assume a2 (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(assume a4 (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v0 ?v1) (member$ ?v0 ?v2)))))
(assume a8 (forall ((?v0 A_b_fun$) (?v1 A_b_fun_bool_fun$)) (= (member$b ?v0 (collect$b ?v1)) (fun_app$ ?v1 ?v0))))
(assume a9 (! (member$b f0$ (collect$b uu$)) :named @p_1))
(assume a10 (! (member$b f$ (collect$b uua$)) :named @p_2))
(assume a12 (! (not (! (member$b f$ (collect$b uub$)) :named @p_3)) :named @p_4))
(step t0 (cl (! (or (! (= a$ @quantifiers_skolemize_3) :named @p_6) (! (member$ @quantifiers_skolemize_3 a$a) :named @p_5)) :named @p_7) (! (not @p_6) :named @p_111)) :rule or_neg :args (0))
(step t1 (cl (! (not (! (or @p_6 (! (= (! (fun_app$a f$ @quantifiers_skolemize_3) :named @p_23) (! (fun_app$a f0$ @quantifiers_skolemize_3) :named @p_22)) :named @p_24)) :named @p_128)) :named @p_134) @p_6 @p_24) :rule or_pos)
(step t2 (cl @p_24 @p_6 @p_134) :rule reordering :premises (t1))
(step t3 (cl (! (ite (! (member$ @quantifiers_skolemize_3 (! (insert$ a$ a$a) :named @p_9)) :named @p_10) (! (member$a @p_23 (! (b$ @quantifiers_skolemize_3) :named @p_25)) :named @p_26) @p_24) :named @p_27) @p_10 (! (not @p_24) :named @p_158)) :rule ite_neg1)
(step t4 (cl @p_10 @p_27 @p_158) :rule reordering :premises (t3))
(step t5 (cl (not (! (= (! (or @p_158 (! (not (! (not @p_26) :named @p_61)) :named @p_113) (! (not (! (member$a @p_22 @p_25) :named @p_135)) :named @p_159)) :named @p_161) (! (or @p_158 @p_26 @p_159) :named @p_160)) :named @p_170)) (not @p_161) @p_160) :rule equiv_pos2)
(step t6 (cl (= @p_113 @p_26)) :rule rare_rewrite :args ("bool-double-not-elim" @p_26))
(step t7 (cl (= @p_159 @p_159)) :rule refl)
(step t8 (cl @p_170) :rule cong :premises (t6 t7))
(step t9 (cl (! (and @p_24 @p_61) :named @p_163) @p_158 @p_113) :rule and_neg)
(step t10 (cl (! (=> @p_163 @p_159) :named @p_165) @p_163) :rule implies_neg1)
(anchor :step t11)
(assume t11.a0 @p_24)
(assume t11.a1 @p_61)
(step t11.t0 (cl (! (=> (! (and @p_61 @p_24) :named @p_166) @p_159) :named @p_168) @p_166) :rule implies_neg1)
(anchor :step t11.t1)
(assume t11.t1.a0 @p_61)
(assume t11.t1.a1 @p_24)
(step t11.t1.t0 (cl (= (! (= @p_135 false) :named @p_169) @p_159)) :rule equiv_simplify)
(step t11.t1.t1 (cl (not @p_169) @p_159) :rule equiv1 :premises (t11.t1.t0))
(step t11.t1.t2 (cl (! (= @p_22 @p_23) :named @p_54)) :rule symm :premises (t11.t1.a1))
(step t11.t1.t3 (cl (= @p_25 @p_25)) :rule refl)
(step t11.t1.t4 (cl (= @p_135 @p_26)) :rule cong :premises (t11.t1.t2 t11.t1.t3))
(step t11.t1.t5 (cl (! (= (! (= @p_26 false) :named @p_123) @p_61) :named @p_124)) :rule equiv_simplify)
(step t11.t1.t6 (cl @p_123 @p_113) :rule equiv2 :premises (t11.t1.t5))
(step t11.t1.t7 (cl (! (not @p_113) :named @p_115) @p_26) :rule not_not)
(step t11.t1.t8 (cl @p_123 @p_26) :rule resolution :premises (t11.t1.t6 t11.t1.t7))
(step t11.t1.t9 (cl @p_123) :rule resolution :premises (t11.t1.t8 t11.t1.a0))
(step t11.t1.t10 (cl @p_169) :rule trans :premises (t11.t1.t4 t11.t1.t9))
(step t11.t1.t11 (cl @p_159) :rule resolution :premises (t11.t1.t1 t11.t1.t10))
(step t11.t1 (cl @p_113 @p_158 @p_159) :rule subproof :discharge (t11.t1.a0 t11.t1.a1))
(step t11.t2 (cl (! (not @p_166) :named @p_167) @p_61) :rule and_pos :args (0))
(step t11.t3 (cl @p_167 @p_24) :rule and_pos :args (1))
(step t11.t4 (cl @p_159 @p_167 @p_167) :rule resolution :premises (t11.t1 t11.t2 t11.t3))
(step t11.t5 (cl @p_167 @p_167 @p_159) :rule reordering :premises (t11.t4))
(step t11.t6 (cl @p_167 @p_159) :rule contraction :premises (t11.t5))
(step t11.t7 (cl @p_168 @p_159) :rule resolution :premises (t11.t0 t11.t6))
(step t11.t8 (cl @p_168 (! (not @p_159) :named @p_162)) :rule implies_neg2)
(step t11.t9 (cl @p_168 @p_168) :rule resolution :premises (t11.t7 t11.t8))
(step t11.t10 (cl @p_168) :rule contraction :premises (t11.t9))
(step t11.t11 (cl @p_167 @p_159) :rule implies :premises (t11.t10))
(step t11.t12 (cl @p_166) :rule and_intro :premises (t11.a1 t11.a0))
(step t11.t13 (cl @p_159) :rule resolution :premises (t11.t11 t11.t12))
(step t11 (cl @p_158 @p_113 @p_159) :rule subproof :discharge (t11.a0 t11.a1))
(step t12 (cl (! (not @p_163) :named @p_164) @p_24) :rule and_pos :args (0))
(step t13 (cl @p_164 @p_61) :rule and_pos :args (1))
(step t14 (cl @p_159 @p_164 @p_164) :rule resolution :premises (t11 t12 t13))
(step t15 (cl @p_164 @p_164 @p_159) :rule reordering :premises (t14))
(step t16 (cl @p_164 @p_159) :rule contraction :premises (t15))
(step t17 (cl @p_165 @p_159) :rule resolution :premises (t10 t16))
(step t18 (cl @p_165 @p_162) :rule implies_neg2)
(step t19 (cl @p_165 @p_165) :rule resolution :premises (t17 t18))
(step t20 (cl @p_165) :rule contraction :premises (t19))
(step t21 (cl @p_164 @p_159) :rule implies :premises (t20))
(step t22 (cl @p_158 @p_113 @p_159) :rule resolution :premises (t9 t21))
(step t23 (cl @p_161 (not @p_158)) :rule or_neg :args (0))
(step t24 (cl @p_161 @p_115) :rule or_neg :args (1))
(step t25 (cl @p_161 @p_162) :rule or_neg :args (2))
(step t26 (cl @p_161 @p_161 @p_161) :rule resolution :premises (t22 t23 t24 t25))
(step t27 (cl @p_161) :rule contraction :premises (t26))
(step t28 (cl @p_160) :rule resolution :premises (t5 t8 t27))
(step t29 (cl @p_158 @p_26 @p_159) :rule or :premises (t28))
(step t30 (cl @p_26 @p_158 @p_159) :rule reordering :premises (t29))
(step t31 (cl (! (not (! (or (! (not @p_5) :named @p_136) @p_135) :named @p_137)) :named @p_157) @p_136 @p_135) :rule or_pos)
(step t32 (cl @p_136 @p_135 @p_157) :rule reordering :premises (t31))
(step t33 (cl (or (! (not (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1))))) :named @p_156) @p_137)) :rule forall_inst :args (@quantifiers_skolemize_3))
(step t34 (cl @p_156 @p_137) :rule or :premises (t33))
(step t35 (cl (! (not (! (= (! (fun_app$ uu$ f0$) :named @p_138) (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1))))) :named @p_139)) :named @p_155) (! (not @p_138) :named @p_154) (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1))))) :rule equiv_pos2)
(step t36 (cl @p_154 (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1)))) @p_155) :rule reordering :premises (t35))
(step t37 (cl (! (not (! (= @p_1 @p_138) :named @p_151)) :named @p_153) (! (not @p_1) :named @p_152) @p_138) :rule equiv_pos2)
(step t38 (cl @p_152 @p_138 @p_153) :rule reordering :premises (t37))
(step t39 (cl (or (! (not (forall ((?v0 A_b_fun$) (?v1 A_b_fun_bool_fun$)) (= (member$b ?v0 (collect$b ?v1)) (fun_app$ ?v1 ?v0)))) :named @p_47) @p_151)) :rule forall_inst :args (f0$ uu$))
(step t40 (cl @p_47 @p_151) :rule or :premises (t39))
(step t41 (cl @p_151) :rule resolution :premises (t40 a8))
(step t42 (cl @p_138) :rule resolution :premises (t38 a9 t41))
(step t43 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))) (! (= @p_138 (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a f0$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f0$ ?v1))))) :named @p_142)) :named @p_143) (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))) @p_139) :named @p_141)) :named @p_144)) (not @p_143) @p_141) :rule equiv_pos2)
(anchor :step t44 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t44.t0 (cl (= (! (= (! (fun_app$a f0$ ?v1) :named @p_38) @p_38) :named @p_148) true)) :rule rare_rewrite :args ("eq-refl" @p_38))
(step t44.t1 (cl (= (! (ite (! (member$ ?v1 a$a) :named @p_146) (! (member$a @p_38 (! (b$ ?v1) :named @p_40)) :named @p_145) @p_148) :named @p_149) (! (ite @p_146 @p_145 true) :named @p_150))) :rule cong :premises (t44.t0))
(step t44.t2 (cl (= @p_150 (! (or (not @p_146) @p_145) :named @p_147))) :rule rare_rewrite :args ("ite-else-true" @p_146 @p_145))
(step t44.t3 (cl (= @p_149 @p_147)) :rule trans :premises (t44.t1 t44.t2))
(step t44 (cl (= (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a f0$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1)))))) :rule bind)
(step t45 (cl (= @p_142 @p_139)) :rule cong :premises (t44))
(step t46 (cl @p_144) :rule cong :premises (t45))
(step t47 (cl @p_143 (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule implies_neg1)
(anchor :step t48)
(assume t48.a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(step t48.t0 (cl (or (! (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uu$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 a$a) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :named @p_140) @p_142)) :rule forall_inst :args (f0$))
(step t48.t1 (cl @p_140 @p_142) :rule or :premises (t48.t0))
(step t48.t2 (cl @p_142) :rule resolution :premises (t48.t1 t48.a0))
(step t48 (cl @p_140 @p_142) :rule subproof :discharge (t48.a0))
(step t49 (cl @p_143 @p_142) :rule resolution :premises (t47 t48))
(step t50 (cl @p_143 (not @p_142)) :rule implies_neg2)
(step t51 (cl @p_143 @p_143) :rule resolution :premises (t49 t50))
(step t52 (cl @p_143) :rule contraction :premises (t51))
(step t53 (cl @p_141) :rule resolution :premises (t43 t46 t52))
(step t54 (cl @p_140 @p_139) :rule implies :premises (t53))
(step t55 (cl @p_139) :rule resolution :premises (t54 a1))
(step t56 (cl (forall ((?v1 A$)) (or (not (member$ ?v1 a$a)) (member$a (fun_app$a f0$ ?v1) (b$ ?v1))))) :rule resolution :premises (t36 t42 t55))
(step t57 (cl @p_137) :rule resolution :premises (t34 t56))
(step t58 (cl (not (! (= (! (=> (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))) (! (or @p_6 @p_54) :named @p_131)) :named @p_132) (! (=> (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))) @p_128) :named @p_130)) :named @p_133)) (not @p_132) @p_130) :rule equiv_pos2)
(step t59 (cl (= @p_54 @p_24)) :rule rare_rewrite :args ("eq-symm" @p_22 @p_23))
(step t60 (cl (= @p_131 @p_128)) :rule cong :premises (t59))
(step t61 (cl @p_133) :rule cong :premises (t60))
(step t62 (cl @p_132 (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :rule implies_neg1)
(anchor :step t63)
(assume t63.a0 (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))))
(step t63.t0 (cl (or (! (not (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :named @p_129) @p_131)) :rule forall_inst :args (@quantifiers_skolemize_3))
(step t63.t1 (cl @p_129 @p_131) :rule or :premises (t63.t0))
(step t63.t2 (cl (! (not (! (and (! (member$a (! (fun_app$a f$ a$) :named @p_64) (! (b$ a$) :named @p_63)) :named @p_65) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :named @p_66)) :named @p_109) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :rule and_pos :args (1))
(step t63.t3 (cl (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))) @p_109) :rule reordering :premises (t63.t2))
(step t63.t4 (cl (! (not (! (= (! (fun_app$ uua$ f$) :named @p_67) @p_66) :named @p_68)) :named @p_108) (! (not @p_67) :named @p_107) @p_66) :rule equiv_pos2)
(step t63.t5 (cl @p_107 @p_66 @p_108) :rule reordering :premises (t63.t4))
(step t63.t6 (cl (! (not (! (= @p_2 @p_67) :named @p_104)) :named @p_106) (! (not @p_2) :named @p_105) @p_67) :rule equiv_pos2)
(step t63.t7 (cl @p_105 @p_67 @p_106) :rule reordering :premises (t63.t6))
(step t63.t8 (cl (or @p_47 @p_104)) :rule forall_inst :args (f$ uua$))
(step t63.t9 (cl @p_47 @p_104) :rule or :premises (t63.t8))
(step t63.t10 (cl @p_104) :rule resolution :premises (t63.t9 a8))
(step t63.t11 (cl @p_67) :rule resolution :premises (t63.t7 a10 t63.t10))
(step t63.t12 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))))) (! (= @p_67 (! (and @p_65 (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f$ BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))) :named @p_97)) :named @p_98)) :named @p_99) (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))))) @p_68) :named @p_96)) :named @p_100)) (not @p_99) @p_96) :rule equiv_pos2)
(anchor :step t63.t13 :args ((BOUND_VARIABLE_7521 A$) (:= (BOUND_VARIABLE_7521 A$) BOUND_VARIABLE_7521)))
(step t63.t13.t0 (cl (= (! (= (! (fun_app$a f$ BOUND_VARIABLE_7521) :named @p_101) (! (fun_app$a f0$ BOUND_VARIABLE_7521) :named @p_89)) :named @p_103) (! (= @p_89 @p_101) :named @p_102))) :rule rare_rewrite :args ("eq-symm" @p_101 @p_89))
(step t63.t13.t1 (cl (= (or (! (= a$ BOUND_VARIABLE_7521) :named @p_90) @p_103) (or @p_90 @p_102))) :rule cong :premises (t63.t13.t0))
(step t63.t13 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f$ BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t63.t14 (cl (= @p_97 @p_66)) :rule cong :premises (t63.t13))
(step t63.t15 (cl (= @p_98 @p_68)) :rule cong :premises (t63.t14))
(step t63.t16 (cl @p_100) :rule cong :premises (t63.t15))
(step t63.t17 (cl @p_99 (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule implies_neg1)
(anchor :step t63.t18)
(assume t63.t18.a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))))))
(step t63.t18.t0 (cl (or (! (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :named @p_95) @p_98)) :rule forall_inst :args (f$))
(step t63.t18.t1 (cl @p_95 @p_98) :rule or :premises (t63.t18.t0))
(step t63.t18.t2 (cl (not (! (= (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))) (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :named @p_69)) (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule equiv_pos2)
(anchor :step t63.t18.t3 :args ((?v0 A_b_fun$) (:= (?v0 A_b_fun$) ?v0)))
(anchor :step t63.t18.t3.t0 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t63.t18.t3.t0.t0 (cl (= (ite (! (= a$ ?v1) :named @p_92) (! (member$a (fun_app$a ?v0 a$) @p_63) :named @p_70) (! (= (fun_app$a ?v0 ?v1) @p_38) :named @p_91)) (and (! (or (not @p_92) @p_70) :named @p_94) (! (or @p_92 @p_91) :named @p_93)))) :rule rare_rewrite :args ("ite-expand" @p_92 @p_70 @p_91))
(step t63.t18.t3.t0 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule bind)
(step t63.t18.t3.t1 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) (! (and (forall ((?v1 A$)) (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((?v1 A$)) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) :named @p_88))) :rule miniscope_distribute)
(anchor :step t63.t18.t3.t2 :args ((BOUND_VARIABLE_7514 A$) (:= (?v1 A$) BOUND_VARIABLE_7514)))
(step t63.t18.t3.t2.t0 (cl (= @p_94 (! (or (! (not (! (= a$ BOUND_VARIABLE_7514) :named @p_80)) :named @p_81) @p_70) :named @p_87))) :rule refl)
(step t63.t18.t3.t2 (cl (= (forall ((?v1 A$)) (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))))) :rule bind)
(anchor :step t63.t18.t3.t3 :args ((BOUND_VARIABLE_7521 A$) (:= (?v1 A$) BOUND_VARIABLE_7521)))
(step t63.t18.t3.t3.t0 (cl (= @p_93 (or @p_90 (= (fun_app$a ?v0 BOUND_VARIABLE_7521) @p_89)))) :rule refl)
(step t63.t18.t3.t3 (cl (= (forall ((?v1 A$)) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t63.t18.t3.t4 (cl (= @p_88 (! (and (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))) :named @p_73))) :rule cong :premises (t63.t18.t3.t2 t63.t18.t3.t3))
(step t63.t18.t3.t5 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_73)) :rule trans :premises (t63.t18.t3.t1 t63.t18.t3.t4))
(anchor :step t63.t18.t3.t6 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t63.t18.t3.t6.t0 (cl (= @p_87 (or @p_70 @p_81))) :rule aci_simp)
(step t63.t18.t3.t6 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(step t63.t18.t3.t7 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))) (! (or @p_70 (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514)))) :named @p_74))) :rule miniscope_split)
(step t63.t18.t3.t8 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_74)) :rule trans :premises (t63.t18.t3.t6 t63.t18.t3.t7))
(anchor :step t63.t18.t3.t9 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t63.t18.t3.t9.t0 (cl (= @p_81 (! (or @p_81 @p_81) :named @p_86))) :rule aci_simp)
(step t63.t18.t3.t9.t1 (cl (= @p_80 (! (= BOUND_VARIABLE_7514 a$) :named @p_79))) :rule rare_rewrite :args ("eq-symm" a$ BOUND_VARIABLE_7514))
(step t63.t18.t3.t9.t2 (cl (= @p_81 (! (not @p_79) :named @p_82))) :rule cong :premises (t63.t18.t3.t9.t1))
(step t63.t18.t3.t9.t3 (cl (= @p_81 @p_81)) :rule refl)
(step t63.t18.t3.t9.t4 (cl (= @p_86 (! (or @p_82 @p_81) :named @p_83))) :rule cong :premises (t63.t18.t3.t9.t2 t63.t18.t3.t9.t3))
(step t63.t18.t3.t9.t5 (cl (= @p_81 @p_83)) :rule trans :premises (t63.t18.t3.t9.t0 t63.t18.t3.t9.t4))
(step t63.t18.t3.t9 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(anchor :step t63.t18.t3.t10 :args ((:= (BOUND_VARIABLE_7514 A$) a$)))
(step t63.t18.t3.t10.t0 (cl (= @p_83 (! (or (! (not (! (= a$ a$) :named @p_76)) :named @p_77) @p_77) :named @p_84))) :rule refl)
(step t63.t18.t3.t10.t1 (cl (= @p_84 @p_77)) :rule rare_rewrite :args ("or-not-refl" a$ (rare-list @p_77)))
(step t63.t18.t3.t10.t2 (cl (= @p_83 @p_77)) :rule trans :premises (t63.t18.t3.t10.t0 t63.t18.t3.t10.t1))
(step t63.t18.t3.t10 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_77)) :rule onepoint)
(step t63.t18.t3.t11 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) @p_77)) :rule trans :premises (t63.t18.t3.t9 t63.t18.t3.t10))
(step t63.t18.t3.t12 (cl (= @p_76 true)) :rule rare_rewrite :args ("eq-refl" a$))
(step t63.t18.t3.t13 (cl (= @p_77 (! (not true) :named @p_78))) :rule cong :premises (t63.t18.t3.t12))
(step t63.t18.t3.t14 (cl (= @p_78 false)) :rule evaluate)
(step t63.t18.t3.t15 (cl (= @p_77 false)) :rule trans :premises (t63.t18.t3.t13 t63.t18.t3.t14))
(step t63.t18.t3.t16 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) false)) :rule trans :premises (t63.t18.t3.t11 t63.t18.t3.t15))
(step t63.t18.t3.t17 (cl (= @p_74 (! (or @p_70 false) :named @p_75))) :rule cong :premises (t63.t18.t3.t16))
(step t63.t18.t3.t18 (cl (= @p_75 @p_70)) :rule aci_simp)
(step t63.t18.t3.t19 (cl (= @p_74 @p_70)) :rule trans :premises (t63.t18.t3.t17 t63.t18.t3.t18))
(step t63.t18.t3.t20 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_70)) :rule trans :premises (t63.t18.t3.t8 t63.t18.t3.t19))
(step t63.t18.t3.t21 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule refl)
(step t63.t18.t3.t22 (cl (= @p_73 (! (and @p_70 (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))) :named @p_71))) :rule cong :premises (t63.t18.t3.t20 t63.t18.t3.t21))
(step t63.t18.t3.t23 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_71)) :rule trans :premises (t63.t18.t3.t5 t63.t18.t3.t22))
(step t63.t18.t3.t24 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) @p_71)) :rule trans :premises (t63.t18.t3.t0 t63.t18.t3.t23))
(step t63.t18.t3.t25 (cl (= (= (! (fun_app$ uua$ ?v0) :named @p_72) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) (= @p_72 @p_71))) :rule cong :premises (t63.t18.t3.t24))
(step t63.t18.t3 (cl @p_69) :rule bind)
(step t63.t18.t4 (cl (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule resolution :premises (t63.t18.t2 t63.t18.t3 a2))
(step t63.t18.t5 (cl @p_98) :rule resolution :premises (t63.t18.t1 t63.t18.t4))
(step t63.t18 (cl @p_95 @p_98) :rule subproof :discharge (t63.t18.a0))
(step t63.t19 (cl @p_99 @p_98) :rule resolution :premises (t63.t17 t63.t18))
(step t63.t20 (cl @p_99 (not @p_98)) :rule implies_neg2)
(step t63.t21 (cl @p_99 @p_99) :rule resolution :premises (t63.t19 t63.t20))
(step t63.t22 (cl @p_99) :rule contraction :premises (t63.t21))
(step t63.t23 (cl @p_96) :rule resolution :premises (t63.t12 t63.t16 t63.t22))
(step t63.t24 (cl @p_95 @p_68) :rule implies :premises (t63.t23))
(step t63.t25 (cl (not @p_69) (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule equiv_pos2)
(anchor :step t63.t26 :args ((?v0 A_b_fun$) (:= (?v0 A_b_fun$) ?v0)))
(anchor :step t63.t26.t0 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t63.t26.t0.t0 (cl (= (ite @p_92 @p_70 @p_91) (and @p_94 @p_93))) :rule rare_rewrite :args ("ite-expand" @p_92 @p_70 @p_91))
(step t63.t26.t0 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule bind)
(step t63.t26.t1 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_88)) :rule miniscope_distribute)
(anchor :step t63.t26.t2 :args ((BOUND_VARIABLE_7514 A$) (:= (?v1 A$) BOUND_VARIABLE_7514)))
(step t63.t26.t2.t0 (cl (= @p_94 @p_87)) :rule refl)
(step t63.t26.t2 (cl (= (forall ((?v1 A$)) (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))))) :rule bind)
(anchor :step t63.t26.t3 :args ((BOUND_VARIABLE_7521 A$) (:= (?v1 A$) BOUND_VARIABLE_7521)))
(step t63.t26.t3.t0 (cl (= @p_93 (or @p_90 (= (fun_app$a ?v0 BOUND_VARIABLE_7521) @p_89)))) :rule refl)
(step t63.t26.t3 (cl (= (forall ((?v1 A$)) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t63.t26.t4 (cl (= @p_88 @p_73)) :rule cong :premises (t63.t26.t2 t63.t26.t3))
(step t63.t26.t5 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_73)) :rule trans :premises (t63.t26.t1 t63.t26.t4))
(anchor :step t63.t26.t6 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t63.t26.t6.t0 (cl (= @p_87 (or @p_70 @p_81))) :rule aci_simp)
(step t63.t26.t6 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(step t63.t26.t7 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_74)) :rule miniscope_split)
(step t63.t26.t8 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_74)) :rule trans :premises (t63.t26.t6 t63.t26.t7))
(anchor :step t63.t26.t9 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t63.t26.t9.t0 (cl (= @p_81 @p_86)) :rule aci_simp)
(step t63.t26.t9.t1 (cl (= @p_80 @p_79)) :rule rare_rewrite :args ("eq-symm" a$ BOUND_VARIABLE_7514))
(step t63.t26.t9.t2 (cl (= @p_81 @p_82)) :rule cong :premises (t63.t26.t9.t1))
(step t63.t26.t9.t3 (cl (= @p_81 @p_81)) :rule refl)
(step t63.t26.t9.t4 (cl (= @p_86 @p_83)) :rule cong :premises (t63.t26.t9.t2 t63.t26.t9.t3))
(step t63.t26.t9.t5 (cl (= @p_81 @p_83)) :rule trans :premises (t63.t26.t9.t0 t63.t26.t9.t4))
(step t63.t26.t9 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(anchor :step t63.t26.t10 :args ((:= (BOUND_VARIABLE_7514 A$) a$)))
(step t63.t26.t10.t0 (cl (= @p_83 @p_84)) :rule refl)
(step t63.t26.t10.t1 (cl (= @p_84 @p_77)) :rule rare_rewrite :args ("or-not-refl" a$ (rare-list @p_77)))
(step t63.t26.t10.t2 (cl (= @p_83 @p_77)) :rule trans :premises (t63.t26.t10.t0 t63.t26.t10.t1))
(step t63.t26.t10 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_77)) :rule onepoint)
(step t63.t26.t11 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) @p_77)) :rule trans :premises (t63.t26.t9 t63.t26.t10))
(step t63.t26.t12 (cl (= @p_76 true)) :rule rare_rewrite :args ("eq-refl" a$))
(step t63.t26.t13 (cl (= @p_77 @p_78)) :rule cong :premises (t63.t26.t12))
(step t63.t26.t14 (cl (= @p_78 false)) :rule evaluate)
(step t63.t26.t15 (cl (= @p_77 false)) :rule trans :premises (t63.t26.t13 t63.t26.t14))
(step t63.t26.t16 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) false)) :rule trans :premises (t63.t26.t11 t63.t26.t15))
(step t63.t26.t17 (cl (= @p_74 @p_75)) :rule cong :premises (t63.t26.t16))
(step t63.t26.t18 (cl (= @p_75 @p_70)) :rule aci_simp)
(step t63.t26.t19 (cl (= @p_74 @p_70)) :rule trans :premises (t63.t26.t17 t63.t26.t18))
(step t63.t26.t20 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_70)) :rule trans :premises (t63.t26.t8 t63.t26.t19))
(step t63.t26.t21 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule refl)
(step t63.t26.t22 (cl (= @p_73 @p_71)) :rule cong :premises (t63.t26.t20 t63.t26.t21))
(step t63.t26.t23 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_71)) :rule trans :premises (t63.t26.t5 t63.t26.t22))
(step t63.t26.t24 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) @p_71)) :rule trans :premises (t63.t26.t0 t63.t26.t23))
(step t63.t26.t25 (cl (= (= @p_72 (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) (= @p_72 @p_71))) :rule cong :premises (t63.t26.t24))
(step t63.t26 (cl @p_69) :rule bind)
(step t63.t27 (cl (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule resolution :premises (t63.t25 t63.t26 a2))
(step t63.t28 (cl @p_68) :rule resolution :premises (t63.t24 t63.t27))
(step t63.t29 (cl @p_66) :rule resolution :premises (t63.t5 t63.t11 t63.t28))
(step t63.t30 (cl (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :rule resolution :premises (t63.t3 t63.t29))
(step t63.t31 (cl @p_131) :rule resolution :premises (t63.t1 t63.t30))
(step t63 (cl @p_129 @p_131) :rule subproof :discharge (t63.a0))
(step t64 (cl @p_132 @p_131) :rule resolution :premises (t62 t63))
(step t65 (cl @p_132 (not @p_131)) :rule implies_neg2)
(step t66 (cl @p_132 @p_132) :rule resolution :premises (t64 t65))
(step t67 (cl @p_132) :rule contraction :premises (t66))
(step t68 (cl @p_130) :rule resolution :premises (t58 t61 t67))
(step t69 (cl @p_129 @p_128) :rule implies :premises (t68))
(step t70 (cl @p_109 (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :rule and_pos :args (1))
(step t71 (cl (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))) @p_109) :rule reordering :premises (t70))
(step t72 (cl @p_108 @p_107 @p_66) :rule equiv_pos2)
(step t73 (cl @p_107 @p_66 @p_108) :rule reordering :premises (t72))
(step t74 (cl @p_106 @p_105 @p_67) :rule equiv_pos2)
(step t75 (cl @p_105 @p_67 @p_106) :rule reordering :premises (t74))
(step t76 (cl (or @p_47 @p_104)) :rule forall_inst :args (f$ uua$))
(step t77 (cl @p_47 @p_104) :rule or :premises (t76))
(step t78 (cl @p_104) :rule resolution :premises (t77 a8))
(step t79 (cl @p_67) :rule resolution :premises (t75 a10 t78))
(step t80 (cl (not @p_100) (not @p_99) @p_96) :rule equiv_pos2)
(anchor :step t81 :args ((BOUND_VARIABLE_7521 A$) (:= (BOUND_VARIABLE_7521 A$) BOUND_VARIABLE_7521)))
(step t81.t0 (cl (= @p_103 @p_102)) :rule rare_rewrite :args ("eq-symm" @p_101 @p_89))
(step t81.t1 (cl (= (or @p_90 @p_103) (or @p_90 @p_102))) :rule cong :premises (t81.t0))
(step t81 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f$ BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t82 (cl (= @p_97 @p_66)) :rule cong :premises (t81))
(step t83 (cl (= @p_98 @p_68)) :rule cong :premises (t82))
(step t84 (cl @p_100) :rule cong :premises (t83))
(step t85 (cl @p_99 (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule implies_neg1)
(anchor :step t86)
(assume t86.a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521))))))))
(step t86.t0 (cl (or @p_95 @p_98)) :rule forall_inst :args (f$))
(step t86.t1 (cl @p_95 @p_98) :rule or :premises (t86.t0))
(step t86.t2 (cl (not @p_69) (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule equiv_pos2)
(anchor :step t86.t3 :args ((?v0 A_b_fun$) (:= (?v0 A_b_fun$) ?v0)))
(anchor :step t86.t3.t0 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t86.t3.t0.t0 (cl (= (ite @p_92 @p_70 @p_91) (and @p_94 @p_93))) :rule rare_rewrite :args ("ite-expand" @p_92 @p_70 @p_91))
(step t86.t3.t0 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule bind)
(step t86.t3.t1 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_88)) :rule miniscope_distribute)
(anchor :step t86.t3.t2 :args ((BOUND_VARIABLE_7514 A$) (:= (?v1 A$) BOUND_VARIABLE_7514)))
(step t86.t3.t2.t0 (cl (= @p_94 @p_87)) :rule refl)
(step t86.t3.t2 (cl (= (forall ((?v1 A$)) (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))))) :rule bind)
(anchor :step t86.t3.t3 :args ((BOUND_VARIABLE_7521 A$) (:= (?v1 A$) BOUND_VARIABLE_7521)))
(step t86.t3.t3.t0 (cl (= @p_93 (or @p_90 (= (fun_app$a ?v0 BOUND_VARIABLE_7521) @p_89)))) :rule refl)
(step t86.t3.t3 (cl (= (forall ((?v1 A$)) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t86.t3.t4 (cl (= @p_88 @p_73)) :rule cong :premises (t86.t3.t2 t86.t3.t3))
(step t86.t3.t5 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_73)) :rule trans :premises (t86.t3.t1 t86.t3.t4))
(anchor :step t86.t3.t6 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t86.t3.t6.t0 (cl (= @p_87 (or @p_70 @p_81))) :rule aci_simp)
(step t86.t3.t6 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(step t86.t3.t7 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_74)) :rule miniscope_split)
(step t86.t3.t8 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_74)) :rule trans :premises (t86.t3.t6 t86.t3.t7))
(anchor :step t86.t3.t9 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t86.t3.t9.t0 (cl (= @p_81 @p_86)) :rule aci_simp)
(step t86.t3.t9.t1 (cl (= @p_80 @p_79)) :rule rare_rewrite :args ("eq-symm" a$ BOUND_VARIABLE_7514))
(step t86.t3.t9.t2 (cl (= @p_81 @p_82)) :rule cong :premises (t86.t3.t9.t1))
(step t86.t3.t9.t3 (cl (= @p_81 @p_81)) :rule refl)
(step t86.t3.t9.t4 (cl (= @p_86 @p_83)) :rule cong :premises (t86.t3.t9.t2 t86.t3.t9.t3))
(step t86.t3.t9.t5 (cl (= @p_81 @p_83)) :rule trans :premises (t86.t3.t9.t0 t86.t3.t9.t4))
(step t86.t3.t9 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(anchor :step t86.t3.t10 :args ((:= (BOUND_VARIABLE_7514 A$) a$)))
(step t86.t3.t10.t0 (cl (= @p_83 @p_84)) :rule refl)
(step t86.t3.t10.t1 (cl (= @p_84 @p_77)) :rule rare_rewrite :args ("or-not-refl" a$ (rare-list @p_77)))
(step t86.t3.t10.t2 (cl (= @p_83 @p_77)) :rule trans :premises (t86.t3.t10.t0 t86.t3.t10.t1))
(step t86.t3.t10 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_77)) :rule onepoint)
(step t86.t3.t11 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) @p_77)) :rule trans :premises (t86.t3.t9 t86.t3.t10))
(step t86.t3.t12 (cl (= @p_76 true)) :rule rare_rewrite :args ("eq-refl" a$))
(step t86.t3.t13 (cl (= @p_77 @p_78)) :rule cong :premises (t86.t3.t12))
(step t86.t3.t14 (cl (= @p_78 false)) :rule evaluate)
(step t86.t3.t15 (cl (= @p_77 false)) :rule trans :premises (t86.t3.t13 t86.t3.t14))
(step t86.t3.t16 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) false)) :rule trans :premises (t86.t3.t11 t86.t3.t15))
(step t86.t3.t17 (cl (= @p_74 @p_75)) :rule cong :premises (t86.t3.t16))
(step t86.t3.t18 (cl (= @p_75 @p_70)) :rule aci_simp)
(step t86.t3.t19 (cl (= @p_74 @p_70)) :rule trans :premises (t86.t3.t17 t86.t3.t18))
(step t86.t3.t20 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_70)) :rule trans :premises (t86.t3.t8 t86.t3.t19))
(step t86.t3.t21 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule refl)
(step t86.t3.t22 (cl (= @p_73 @p_71)) :rule cong :premises (t86.t3.t20 t86.t3.t21))
(step t86.t3.t23 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_71)) :rule trans :premises (t86.t3.t5 t86.t3.t22))
(step t86.t3.t24 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) @p_71)) :rule trans :premises (t86.t3.t0 t86.t3.t23))
(step t86.t3.t25 (cl (= (= @p_72 (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) (= @p_72 @p_71))) :rule cong :premises (t86.t3.t24))
(step t86.t3 (cl @p_69) :rule bind)
(step t86.t4 (cl (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule resolution :premises (t86.t2 t86.t3 a2))
(step t86.t5 (cl @p_98) :rule resolution :premises (t86.t1 t86.t4))
(step t86 (cl @p_95 @p_98) :rule subproof :discharge (t86.a0))
(step t87 (cl @p_99 @p_98) :rule resolution :premises (t85 t86))
(step t88 (cl @p_99 (not @p_98)) :rule implies_neg2)
(step t89 (cl @p_99 @p_99) :rule resolution :premises (t87 t88))
(step t90 (cl @p_99) :rule contraction :premises (t89))
(step t91 (cl @p_96) :rule resolution :premises (t80 t84 t90))
(step t92 (cl @p_95 @p_68) :rule implies :premises (t91))
(step t93 (cl (not @p_69) (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule equiv_pos2)
(anchor :step t94 :args ((?v0 A_b_fun$) (:= (?v0 A_b_fun$) ?v0)))
(anchor :step t94.t0 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t94.t0.t0 (cl (= (ite @p_92 @p_70 @p_91) (and @p_94 @p_93))) :rule rare_rewrite :args ("ite-expand" @p_92 @p_70 @p_91))
(step t94.t0 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule bind)
(step t94.t1 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_88)) :rule miniscope_distribute)
(anchor :step t94.t2 :args ((BOUND_VARIABLE_7514 A$) (:= (?v1 A$) BOUND_VARIABLE_7514)))
(step t94.t2.t0 (cl (= @p_94 @p_87)) :rule refl)
(step t94.t2 (cl (= (forall ((?v1 A$)) (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))))) :rule bind)
(anchor :step t94.t3 :args ((BOUND_VARIABLE_7521 A$) (:= (?v1 A$) BOUND_VARIABLE_7521)))
(step t94.t3.t0 (cl (= @p_93 (or @p_90 (= (fun_app$a ?v0 BOUND_VARIABLE_7521) @p_89)))) :rule refl)
(step t94.t3 (cl (= (forall ((?v1 A$)) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule bind)
(step t94.t4 (cl (= @p_88 @p_73)) :rule cong :premises (t94.t2 t94.t3))
(step t94.t5 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_73)) :rule trans :premises (t94.t1 t94.t4))
(anchor :step t94.t6 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t94.t6.t0 (cl (= @p_87 (or @p_70 @p_81))) :rule aci_simp)
(step t94.t6 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(step t94.t7 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (member$a (fun_app$a ?v0 a$) (b$ a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_74)) :rule miniscope_split)
(step t94.t8 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_74)) :rule trans :premises (t94.t6 t94.t7))
(anchor :step t94.t9 :args ((BOUND_VARIABLE_7514 A$) (:= (BOUND_VARIABLE_7514 A$) BOUND_VARIABLE_7514)))
(step t94.t9.t0 (cl (= @p_81 @p_86)) :rule aci_simp)
(step t94.t9.t1 (cl (= @p_80 @p_79)) :rule rare_rewrite :args ("eq-symm" a$ BOUND_VARIABLE_7514))
(step t94.t9.t2 (cl (= @p_81 @p_82)) :rule cong :premises (t94.t9.t1))
(step t94.t9.t3 (cl (= @p_81 @p_81)) :rule refl)
(step t94.t9.t4 (cl (= @p_86 @p_83)) :rule cong :premises (t94.t9.t2 t94.t9.t3))
(step t94.t9.t5 (cl (= @p_81 @p_83)) :rule trans :premises (t94.t9.t0 t94.t9.t4))
(step t94.t9 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))))) :rule bind)
(anchor :step t94.t10 :args ((:= (BOUND_VARIABLE_7514 A$) a$)))
(step t94.t10.t0 (cl (= @p_83 @p_84)) :rule refl)
(step t94.t10.t1 (cl (= @p_84 @p_77)) :rule rare_rewrite :args ("or-not-refl" a$ (rare-list @p_77)))
(step t94.t10.t2 (cl (= @p_83 @p_77)) :rule trans :premises (t94.t10.t0 t94.t10.t1))
(step t94.t10 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= BOUND_VARIABLE_7514 a$)) (not (= a$ BOUND_VARIABLE_7514)))) @p_77)) :rule onepoint)
(step t94.t11 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) @p_77)) :rule trans :premises (t94.t9 t94.t10))
(step t94.t12 (cl (= @p_76 true)) :rule rare_rewrite :args ("eq-refl" a$))
(step t94.t13 (cl (= @p_77 @p_78)) :rule cong :premises (t94.t12))
(step t94.t14 (cl (= @p_78 false)) :rule evaluate)
(step t94.t15 (cl (= @p_77 false)) :rule trans :premises (t94.t13 t94.t14))
(step t94.t16 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (not (= a$ BOUND_VARIABLE_7514))) false)) :rule trans :premises (t94.t11 t94.t15))
(step t94.t17 (cl (= @p_74 @p_75)) :rule cong :premises (t94.t16))
(step t94.t18 (cl (= @p_75 @p_70)) :rule aci_simp)
(step t94.t19 (cl (= @p_74 @p_70)) :rule trans :premises (t94.t17 t94.t18))
(step t94.t20 (cl (= (forall ((BOUND_VARIABLE_7514 A$)) (or (not (= a$ BOUND_VARIABLE_7514)) (member$a (fun_app$a ?v0 a$) (b$ a$)))) @p_70)) :rule trans :premises (t94.t8 t94.t19))
(step t94.t21 (cl (= (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))) :rule refl)
(step t94.t22 (cl (= @p_73 @p_71)) :rule cong :premises (t94.t20 t94.t21))
(step t94.t23 (cl (= (forall ((?v1 A$)) (and (or (not (= a$ ?v1)) (member$a (fun_app$a ?v0 a$) (b$ a$))) (or (= a$ ?v1) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) @p_71)) :rule trans :premises (t94.t5 t94.t22))
(step t94.t24 (cl (= (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))) @p_71)) :rule trans :premises (t94.t0 t94.t23))
(step t94.t25 (cl (= (= @p_72 (forall ((?v1 A$)) (ite (= a$ ?v1) (member$a (fun_app$a ?v0 a$) (b$ a$)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))) (= @p_72 @p_71))) :rule cong :premises (t94.t24))
(step t94 (cl @p_69) :rule bind)
(step t95 (cl (forall ((?v0 A_b_fun$)) (= (fun_app$ uua$ ?v0) (and (member$a (fun_app$a ?v0 a$) (b$ a$)) (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a ?v0 BOUND_VARIABLE_7521) (fun_app$a f0$ BOUND_VARIABLE_7521)))))))) :rule resolution :premises (t93 t94 a2))
(step t96 (cl @p_68) :rule resolution :premises (t92 t95))
(step t97 (cl @p_66) :rule resolution :premises (t73 t79 t96))
(step t98 (cl (forall ((BOUND_VARIABLE_7521 A$)) (or (= a$ BOUND_VARIABLE_7521) (= (fun_app$a f0$ BOUND_VARIABLE_7521) (fun_app$a f$ BOUND_VARIABLE_7521))))) :rule resolution :premises (t71 t97))
(step t99 (cl @p_128) :rule resolution :premises (t69 t98))
(step t100 (cl (! (not @p_7) :named @p_8) @p_6 @p_5) :rule or_pos)
(step t101 (cl @p_6 @p_5 @p_8) :rule reordering :premises (t100))
(step t102 (cl (not (! (= (! (or (! (not @p_65) :named @p_110) @p_113 @p_111) :named @p_114) (! (or @p_110 @p_26 @p_111) :named @p_112)) :named @p_127)) (not @p_114) @p_112) :rule equiv_pos2)
(step t103 (cl (= @p_111 @p_111)) :rule refl)
(step t104 (cl @p_127) :rule cong :premises (t6 t103))
(step t105 (cl (! (=> (! (and @p_65 @p_61 @p_6) :named @p_116) (! (and @p_65 @p_6 @p_61) :named @p_118)) :named @p_126) @p_116) :rule implies_neg1)
(anchor :step t106)
(assume t106.a0 @p_65)
(assume t106.a1 @p_61)
(assume t106.a2 @p_6)
(step t106.t0 (cl @p_109 @p_65) :rule and_pos :args (0))
(step t106.t1 (cl @p_65 @p_109) :rule reordering :premises (t106.t0))
(step t106.t2 (cl @p_65) :rule resolution :premises (t106.t1 t97))
(step t106.t3 (cl @p_118) :rule and_intro :premises (t106.t2 t106.a2 t106.a1))
(step t106 (cl @p_110 @p_113 @p_111 @p_118) :rule subproof :discharge (t106.a0 t106.a1 t106.a2))
(step t107 (cl (! (not @p_116) :named @p_117) @p_65) :rule and_pos :args (0))
(step t108 (cl @p_117 @p_61) :rule and_pos :args (1))
(step t109 (cl @p_117 @p_6) :rule and_pos :args (2))
(step t110 (cl @p_118 @p_117 @p_117 @p_117) :rule resolution :premises (t106 t107 t108 t109))
(step t111 (cl @p_117 @p_117 @p_117 @p_118) :rule reordering :premises (t110))
(step t112 (cl @p_117 @p_118) :rule contraction :premises (t111))
(step t113 (cl @p_126 @p_118) :rule resolution :premises (t105 t112))
(step t114 (cl @p_126 (! (not @p_118) :named @p_119)) :rule implies_neg2)
(step t115 (cl @p_126 @p_126) :rule resolution :premises (t113 t114))
(step t116 (cl @p_126) :rule contraction :premises (t115))
(step t117 (cl @p_117 @p_118) :rule implies :premises (t116))
(step t118 (cl (! (=> @p_118 false) :named @p_120) @p_118) :rule implies_neg1)
(anchor :step t119)
(assume t119.a0 @p_65)
(assume t119.a1 @p_6)
(assume t119.a2 @p_61)
(step t119.t0 (cl (not (! (= (! (= false true) :named @p_121) false) :named @p_125)) (not @p_121) false) :rule equiv_pos2)
(step t119.t1 (cl @p_125) :rule evaluate)
(step t119.t2 (cl @p_124) :rule equiv_simplify)
(step t119.t3 (cl @p_123 @p_113) :rule equiv2 :premises (t119.t2))
(step t119.t4 (cl @p_115 @p_26) :rule not_not)
(step t119.t5 (cl @p_123 @p_26) :rule resolution :premises (t119.t3 t119.t4))
(step t119.t6 (cl @p_123) :rule resolution :premises (t119.t5 t119.a2))
(step t119.t7 (cl (= false @p_26)) :rule symm :premises (t119.t6))
(step t119.t8 (cl (= @quantifiers_skolemize_3 a$)) :rule symm :premises (t119.a1))
(step t119.t9 (cl (= @p_23 @p_64)) :rule cong :premises (t119.t8))
(step t119.t10 (cl (= @p_25 @p_63)) :rule cong :premises (t119.t8))
(step t119.t11 (cl (= @p_26 @p_65)) :rule cong :premises (t119.t9 t119.t10))
(step t119.t12 (cl (= (! (= @p_65 true) :named @p_122) @p_65)) :rule equiv_simplify)
(step t119.t13 (cl @p_122 @p_110) :rule equiv2 :premises (t119.t12))
(step t119.t14 (cl @p_109 @p_65) :rule and_pos :args (0))
(step t119.t15 (cl @p_65 @p_109) :rule reordering :premises (t119.t14))
(step t119.t16 (cl @p_65) :rule resolution :premises (t119.t15 t97))
(step t119.t17 (cl @p_122) :rule resolution :premises (t119.t13 t119.t16))
(step t119.t18 (cl @p_121) :rule trans :premises (t119.t7 t119.t11 t119.t17))
(step t119.t19 (cl false) :rule resolution :premises (t119.t0 t119.t1 t119.t18))
(step t119 (cl @p_110 @p_111 @p_113 false) :rule subproof :discharge (t119.a0 t119.a1 t119.a2))
(step t120 (cl @p_119 @p_65) :rule and_pos :args (0))
(step t121 (cl @p_119 @p_6) :rule and_pos :args (1))
(step t122 (cl @p_119 @p_61) :rule and_pos :args (2))
(step t123 (cl false @p_119 @p_119 @p_119) :rule resolution :premises (t119 t120 t121 t122))
(step t124 (cl @p_119 @p_119 @p_119 false) :rule reordering :premises (t123))
(step t125 (cl @p_119 false) :rule contraction :premises (t124))
(step t126 (cl @p_120 false) :rule resolution :premises (t118 t125))
(step t127 (cl @p_120 (not false)) :rule implies_neg2)
(step t128 (cl @p_120 @p_120) :rule resolution :premises (t126 t127))
(step t129 (cl @p_120) :rule contraction :premises (t128))
(step t130 (cl (= @p_120 @p_119)) :rule implies_simplify)
(step t131 (cl (not @p_120) @p_119) :rule equiv1 :premises (t130))
(step t132 (cl @p_119) :rule resolution :premises (t129 t131))
(step t133 (cl @p_117) :rule resolution :premises (t117 t132))
(step t134 (cl @p_110 @p_113 @p_111) :rule not_and :premises (t133))
(step t135 (cl @p_114 (not @p_110)) :rule or_neg :args (0))
(step t136 (cl @p_114 @p_115) :rule or_neg :args (1))
(step t137 (cl @p_114 (not @p_111)) :rule or_neg :args (2))
(step t138 (cl @p_114 @p_114 @p_114) :rule resolution :premises (t134 t135 t136 t137))
(step t139 (cl @p_114) :rule contraction :premises (t138))
(step t140 (cl @p_112) :rule resolution :premises (t102 t104 t139))
(step t141 (cl @p_110 @p_26 @p_111) :rule or :premises (t140))
(step t142 (cl @p_109 @p_65) :rule and_pos :args (0))
(step t143 (cl @p_65 @p_109) :rule reordering :premises (t142))
(step t144 (cl @p_65) :rule resolution :premises (t143 t97))
(step t145 (cl (! (not (! (= @p_10 @p_7) :named @p_11)) :named @p_62) (! (not @p_10) :named @p_21) @p_7) :rule equiv_pos2)
(step t146 (cl @p_21 @p_7 @p_62) :rule reordering :premises (t145))
(step t147 (cl (or (! (not (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v1 ?v0) (member$ ?v0 ?v2))))) :named @p_20) @p_11)) :rule forall_inst :args (@quantifiers_skolemize_3 a$ a$a))
(step t148 (cl @p_20 @p_11) :rule or :premises (t147))
(step t149 (cl (not (! (= (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v0 ?v1) (member$ ?v0 ?v2)))) (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v1 ?v0) (member$ ?v0 ?v2))))) :named @p_12)) (not (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v0 ?v1) (member$ ?v0 ?v2))))) (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v1 ?v0) (member$ ?v0 ?v2))))) :rule equiv_pos2)
(anchor :step t150 :args ((?v0 A$) (?v1 A$) (?v2 A_set$) (:= (?v0 A$) ?v0) (:= (?v1 A$) ?v1) (:= (?v2 A_set$) ?v2)))
(step t150.t0 (cl (= (! (= ?v0 ?v1) :named @p_18) (! (= ?v1 ?v0) :named @p_15))) :rule rare_rewrite :args ("eq-symm" ?v0 ?v1))
(step t150.t1 (cl (= (! (member$ ?v0 ?v2) :named @p_14) @p_14)) :rule refl)
(step t150.t2 (cl (= (! (or @p_18 @p_14) :named @p_19) (! (or @p_15 @p_14) :named @p_16))) :rule cong :premises (t150.t0 t150.t1))
(step t150.t3 (cl (= (= (! (member$ ?v0 (insert$ ?v1 ?v2)) :named @p_17) @p_19) (= @p_17 @p_16))) :rule cong :premises (t150.t2))
(step t150 (cl @p_12) :rule bind)
(step t151 (cl (forall ((?v0 A$) (?v1 A$) (?v2 A_set$)) (= (member$ ?v0 (insert$ ?v1 ?v2)) (or (= ?v1 ?v0) (member$ ?v0 ?v2))))) :rule resolution :premises (t149 t150 a4))
(step t152 (cl @p_11) :rule resolution :premises (t148 t151))
(step t153 (cl @p_27 @p_21 @p_61) :rule ite_neg2)
(step t154 (cl (not (! (= (! (or (! (not (! (not (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1))))) :named @p_29)) :named @p_51) (! (not @p_27) :named @p_28)) :named @p_52) (! (or (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))) @p_28) :named @p_50)) :named @p_60)) (not @p_52) @p_50) :rule equiv_pos2)
(step t155 (cl (= @p_51 (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1))))))
(step t156 (cl (= @p_28 @p_28)) :rule refl)
(step t157 (cl @p_60) :rule cong :premises (t155 t156))
(step t158 (cl (not (! (= (! (=> @p_29 (! (not (! (ite @p_10 @p_26 @p_54) :named @p_55)) :named @p_56)) :named @p_57) (! (=> @p_29 @p_28) :named @p_53)) :named @p_59)) (not @p_57) @p_53) :rule equiv_pos2)
(step t159 (cl (= @p_55 @p_27)) :rule cong :premises (t59))
(step t160 (cl (= @p_56 @p_28)) :rule cong :premises (t159))
(step t161 (cl @p_59) :rule cong :premises (t160))
(step t162 (cl @p_57 @p_29) :rule implies_neg1)
(anchor :step t163)
(assume t163.a0 @p_29)
(step t163.t0 (cl (not (! (= @p_29 @p_56) :named @p_58)) @p_51 @p_56) :rule equiv_pos2)
(anchor :step t163.t1 :args ((:= (?v1 A$) @quantifiers_skolemize_3)))
(step t163.t1.t0 (cl (= (! (ite (! (member$ ?v1 @p_9) :named @p_42) (! (member$a (! (fun_app$a f$ ?v1) :named @p_37) @p_40) :named @p_41) (! (= @p_38 @p_37) :named @p_39)) :named @p_43) @p_55)) :rule refl)
(step t163.t1 (cl (= (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))) @p_55)) :rule sko_forall)
(step t163.t2 (cl @p_58) :rule cong :premises (t163.t1))
(step t163.t3 (cl (! (not (! (= (! (fun_app$ uub$ f$) :named @p_30) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1))))) :named @p_31)) :named @p_49) @p_30 @p_29) :rule equiv_pos1)
(step t163.t4 (cl @p_30 @p_29 @p_49) :rule reordering :premises (t163.t3))
(step t163.t5 (cl (! (not (! (= @p_3 @p_30) :named @p_46)) :named @p_48) @p_3 (! (not @p_30) :named @p_45)) :rule equiv_pos1)
(step t163.t6 (cl @p_3 @p_45 @p_48) :rule reordering :premises (t163.t5))
(step t163.t7 (cl (or @p_47 @p_46)) :rule forall_inst :args (f$ uub$))
(step t163.t8 (cl @p_47 @p_46) :rule or :premises (t163.t7))
(step t163.t9 (cl @p_46) :rule resolution :premises (t163.t8 a8))
(step t163.t10 (cl @p_45) :rule resolution :premises (t163.t6 a12 t163.t9))
(step t163.t11 (cl (not (! (= (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))) (! (= @p_30 (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f$ ?v1) (fun_app$a f0$ ?v1))))) :named @p_34)) :named @p_35) (! (=> (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))) @p_31) :named @p_33)) :named @p_36)) (not @p_35) @p_33) :rule equiv_pos2)
(anchor :step t163.t12 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t163.t12.t0 (cl (= (! (= @p_37 @p_38) :named @p_44) @p_39)) :rule rare_rewrite :args ("eq-symm" @p_37 @p_38))
(step t163.t12.t1 (cl (= (ite @p_42 @p_41 @p_44) @p_43)) :rule cong :premises (t163.t12.t0))
(step t163.t12 (cl (= (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f$ ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))))) :rule bind)
(step t163.t13 (cl (= @p_34 @p_31)) :rule cong :premises (t163.t12))
(step t163.t14 (cl @p_36) :rule cong :premises (t163.t13))
(step t163.t15 (cl @p_35 (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule implies_neg1)
(anchor :step t163.t16)
(assume t163.t16.a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(step t163.t16.t0 (cl (or (! (not (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :named @p_32) @p_34)) :rule forall_inst :args (f$))
(step t163.t16.t1 (cl @p_32 @p_34) :rule or :premises (t163.t16.t0))
(step t163.t16.t2 (cl @p_34) :rule resolution :premises (t163.t16.t1 t163.t16.a0))
(step t163.t16 (cl @p_32 @p_34) :rule subproof :discharge (t163.t16.a0))
(step t163.t17 (cl @p_35 @p_34) :rule resolution :premises (t163.t15 t163.t16))
(step t163.t18 (cl @p_35 (not @p_34)) :rule implies_neg2)
(step t163.t19 (cl @p_35 @p_35) :rule resolution :premises (t163.t17 t163.t18))
(step t163.t20 (cl @p_35) :rule contraction :premises (t163.t19))
(step t163.t21 (cl @p_33) :rule resolution :premises (t163.t11 t163.t14 t163.t20))
(step t163.t22 (cl @p_32 @p_31) :rule implies :premises (t163.t21))
(step t163.t23 (cl @p_31) :rule resolution :premises (t163.t22 a0))
(step t163.t24 (cl @p_29) :rule resolution :premises (t163.t4 t163.t10 t163.t23))
(step t163.t25 (cl @p_56) :rule resolution :premises (t163.t0 t163.t2 t163.t24))
(step t163 (cl @p_51 @p_56) :rule subproof :discharge (t163.a0))
(step t164 (cl @p_57 @p_56) :rule resolution :premises (t162 t163))
(step t165 (cl @p_57 (not @p_56)) :rule implies_neg2)
(step t166 (cl @p_57 @p_57) :rule resolution :premises (t164 t165))
(step t167 (cl @p_57) :rule contraction :premises (t166))
(step t168 (cl @p_53) :rule resolution :premises (t158 t161 t167))
(step t169 (cl @p_51 @p_28) :rule implies :premises (t168))
(step t170 (cl @p_52 (not @p_51)) :rule or_neg :args (0))
(step t171 (cl @p_52 (not @p_28)) :rule or_neg :args (1))
(step t172 (cl @p_52 @p_52) :rule resolution :premises (t169 t170 t171))
(step t173 (cl @p_52) :rule contraction :premises (t172))
(step t174 (cl @p_50) :rule resolution :premises (t154 t157 t173))
(step t175 (cl (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))) @p_28) :rule or :premises (t174))
(step t176 (cl @p_49 @p_30 @p_29) :rule equiv_pos1)
(step t177 (cl @p_30 @p_29 @p_49) :rule reordering :premises (t176))
(step t178 (cl @p_48 @p_3 @p_45) :rule equiv_pos1)
(step t179 (cl @p_3 @p_45 @p_48) :rule reordering :premises (t178))
(step t180 (cl (or @p_47 @p_46)) :rule forall_inst :args (f$ uub$))
(step t181 (cl @p_47 @p_46) :rule or :premises (t180))
(step t182 (cl @p_46) :rule resolution :premises (t181 a8))
(step t183 (cl @p_45) :rule resolution :premises (t179 a12 t182))
(step t184 (cl (not @p_36) (not @p_35) @p_33) :rule equiv_pos2)
(anchor :step t185 :args ((?v1 A$) (:= (?v1 A$) ?v1)))
(step t185.t0 (cl (= @p_44 @p_39)) :rule rare_rewrite :args ("eq-symm" @p_37 @p_38))
(step t185.t1 (cl (= (ite @p_42 @p_41 @p_44) @p_43)) :rule cong :premises (t185.t0))
(step t185 (cl (= (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f$ ?v1) (fun_app$a f0$ ?v1)))) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a f$ ?v1) (b$ ?v1)) (= (fun_app$a f0$ ?v1) (fun_app$a f$ ?v1)))))) :rule bind)
(step t186 (cl (= @p_34 @p_31)) :rule cong :premises (t185))
(step t187 (cl @p_36) :rule cong :premises (t186))
(step t188 (cl @p_35 (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1))))))) :rule implies_neg1)
(anchor :step t189)
(assume t189.a0 (forall ((?v0 A_b_fun$)) (= (fun_app$ uub$ ?v0) (forall ((?v1 A$)) (ite (member$ ?v1 (insert$ a$ a$a)) (member$a (fun_app$a ?v0 ?v1) (b$ ?v1)) (= (fun_app$a ?v0 ?v1) (fun_app$a f0$ ?v1)))))))
(step t189.t0 (cl (or @p_32 @p_34)) :rule forall_inst :args (f$))
(step t189.t1 (cl @p_32 @p_34) :rule or :premises (t189.t0))
(step t189.t2 (cl @p_34) :rule resolution :premises (t189.t1 t189.a0))
(step t189 (cl @p_32 @p_34) :rule subproof :discharge (t189.a0))
(step t190 (cl @p_35 @p_34) :rule resolution :premises (t188 t189))
(step t191 (cl @p_35 (not @p_34)) :rule implies_neg2)
(step t192 (cl @p_35 @p_35) :rule resolution :premises (t190 t191))
(step t193 (cl @p_35) :rule contraction :premises (t192))
(step t194 (cl @p_33) :rule resolution :premises (t184 t187 t193))
(step t195 (cl @p_32 @p_31) :rule implies :premises (t194))
(step t196 (cl @p_31) :rule resolution :premises (t195 a0))
(step t197 (cl @p_29) :rule resolution :premises (t177 t183 t196))
(step t198 (cl @p_28) :rule resolution :premises (t175 t197))
(step t199 (cl @p_21) :rule resolution :premises (t30 t32 t57 t2 t99 t101 t141 t144 t146 t152 t153 t198))
(step t200 (cl @p_158) :rule resolution :premises (t4 t199 t198))
(step t201 (cl @p_6) :rule resolution :premises (t2 t200 t99))
(step t202 (cl @p_62 @p_10 @p_8) :rule equiv_pos1)
(step t203 (cl @p_10 @p_8 @p_62) :rule reordering :premises (t202))
(step t204 (cl @p_8) :rule resolution :premises (t203 t199 t152))
(step t205 (cl) :rule resolution :premises (t0 t201 t204))
)
ce639f4933182b09989c70268cb8300c8652de70 1264 0
unsat
(
(define-fun @quantifiers_skolemize_3 () I_set$ (choice ((?v0 I_set$)) (not (forall ((?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))))
(define-fun @quantifiers_skolemize_4 () Nat_a_fun$ (choice ((?v1 Nat_a_fun$)) (not (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ @quantifiers_skolemize_3 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))))
(define-fun @quantifiers_skolemize_5 () Nat$ (choice ((BOUND_VARIABLE_7817 Nat$)) (not (forall ((BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ @quantifiers_skolemize_3 @quantifiers_skolemize_4) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)))))))))
(define-fun @quantifiers_skolemize_6 () A$ (choice ((BOUND_VARIABLE_7819 A$)) (not (forall ((BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ @quantifiers_skolemize_3 @quantifiers_skolemize_4) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) @quantifiers_skolemize_5))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) @quantifiers_skolemize_5) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5)) (= BOUND_VARIABLE_7819 (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)))))))))
(define-fun @quantifiers_skolemize_7 () Nat$ (choice ((BOUND_VARIABLE_7833 Nat$)) (not (forall ((BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ @quantifiers_skolemize_3 @quantifiers_skolemize_4) a$)) (and (or (not (= (some$ @quantifiers_skolemize_6) (fun_app$d (fun_app$e (lb$ dir$) s$) @quantifiers_skolemize_5))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) @quantifiers_skolemize_5) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) @quantifiers_skolemize_6) (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5)) (= @quantifiers_skolemize_6 (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h @quantifiers_skolemize_4 BOUND_VARIABLE_7833)))))))))
(define-fun @quantifiers_skolemize_8 () A$ (choice ((BOUND_VARIABLE_7835 A$)) (not (or (not (i_satisfies_atom_set$ (pair$ @quantifiers_skolemize_3 @quantifiers_skolemize_4) a$)) (and (or (not (= (some$ @quantifiers_skolemize_6) (fun_app$d (fun_app$e (lb$ dir$) s$) @quantifiers_skolemize_5))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) @quantifiers_skolemize_5) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) @quantifiers_skolemize_6) (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5)) (= @quantifiers_skolemize_6 (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) @quantifiers_skolemize_7))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) @quantifiers_skolemize_7) @quantifiers_skolemize_3)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_7)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_7))))))))
(assume a1 (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0))))
(assume a2 (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v0)))
(assume a6 (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v3)))
(assume a7 (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v4)))
(assume a8 (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v5)))
(assume a9 (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v6)))
(assume a12 (! (= negative$ (! (direction$ uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$) :named @p_1)) :named @p_2))
(assume a13 (! (= positive$ (! (direction$ less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$) :named @p_3)) :named @p_4))
(assume a18 (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))))
(assume a20 (forall ((?v0 I_set_nat_a_fun_prod$)) (=> (i_satisfies_atom_set$ ?v0 a$) (i_satisfies_atom_set$ ?v0 ats$))))
(assume a21 (! (not (! (=> (! (or (! (= dir$ positive$) :named @p_6) (! (= dir$ negative$) :named @p_5)) :named @p_7) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))))))) :named @p_8)) :named @p_9))
(step t0 (cl (! (not (! (= (! (fun_app$b (fun_app$c less$ (! (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5) :named @p_10)) @quantifiers_skolemize_6) :named @p_13) (! (fun_app$b (! (fun_app$c uu$ @quantifiers_skolemize_6) :named @p_11) (! (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_5) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_460) (! (not @p_13) :named @p_459) @p_12) :rule equiv_pos2)
(step t1 (cl @p_459 @p_12 @p_460) :rule reordering :premises (t0))
(step t2 (cl (! (not (! (or (! (not (! (= (! (some$ @quantifiers_skolemize_6) :named @p_51) (! (fun_app$d (! (fun_app$e b_u$ s$) :named @p_91) @quantifiers_skolemize_5) :named @p_350)) :named @p_351)) :named @p_352) (! (not (! (member$ (! (fun_app$f (! (fun_app$g i_u$ s$) :named @p_107) @quantifiers_skolemize_5) :named @p_347) @quantifiers_skolemize_3) :named @p_348)) :named @p_349) @p_13 (! (= @quantifiers_skolemize_6 @p_10) :named @p_42)) :named @p_353)) :named @p_458) @p_352 @p_349 @p_13 @p_42) :rule or_pos)
(step t3 (cl @p_42 @p_352 @p_349 @p_13 @p_458) :rule reordering :premises (t2))
(step t4 (cl (! (or (! (not (! (= @p_51 (! (fun_app$d (! (fun_app$e (! (lb$ dir$) :named @p_48) s$) :named @p_49) @quantifiers_skolemize_5) :named @p_50)) :named @p_52)) :named @p_53) (! (not (! (member$ (! (fun_app$f (! (fun_app$g (! (li$ dir$) :named @p_43) s$) :named @p_44) @quantifiers_skolemize_5) :named @p_45) @quantifiers_skolemize_3) :named @p_46)) :named @p_47) (! (fun_app$b (! (fun_app$c (! (lt$ dir$) :named @p_38) @quantifiers_skolemize_6) :named @p_39) @p_10) :named @p_40) @p_42) :named @p_54) (! (not @p_42) :named @p_303)) :rule or_neg :args (3))
(step t5 (cl (! (and @p_54 (! (or (! (not (! (= (! (some$ @quantifiers_skolemize_8) :named @p_68) (! (fun_app$d (! (fun_app$e (! (ub$ dir$) :named @p_65) s$) :named @p_66) @quantifiers_skolemize_7) :named @p_67)) :named @p_69)) :named @p_70) (! (not (! (member$ (! (fun_app$f (! (fun_app$g (! (ui$ dir$) :named @p_60) s$) :named @p_61) @quantifiers_skolemize_7) :named @p_62) @quantifiers_skolemize_3) :named @p_63)) :named @p_64) (! (fun_app$b (! (fun_app$c @p_38 (! (fun_app$h @quantifiers_skolemize_4 @quantifiers_skolemize_7) :named @p_56)) :named @p_58) @quantifiers_skolemize_8) :named @p_59) (! (= @quantifiers_skolemize_8 @p_56) :named @p_57)) :named @p_71)) :named @p_229) (! (not @p_54) :named @p_55) (! (not @p_71) :named @p_75)) :rule and_neg)
(step t6 (cl (! (or (! (not (! (i_satisfies_atom_set$ (! (pair$ @quantifiers_skolemize_3 @quantifiers_skolemize_4) :named @p_159) a$) :named @p_222)) :named @p_223) @p_229) :named @p_230) (! (not @p_229) :named @p_294)) :rule or_neg :args (1))
(step t7 (cl (not (! (= (! (not (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))))) :named @p_232) (! (not @p_230) :named @p_231)) :named @p_285)) (not @p_232) @p_231) :rule equiv_pos2)
(anchor :step t8 :args ((:= (?v0 I_set$) @quantifiers_skolemize_3) (:= (?v1 Nat_a_fun$) @quantifiers_skolemize_4) (:= (BOUND_VARIABLE_7817 Nat$) @quantifiers_skolemize_5) (:= (BOUND_VARIABLE_7819 A$) @quantifiers_skolemize_6) (:= (BOUND_VARIABLE_7833 Nat$) @quantifiers_skolemize_7) (:= (BOUND_VARIABLE_7835 A$) @quantifiers_skolemize_8)))
(step t8.t0 (cl (= (or (! (not (! (i_satisfies_atom_set$ (! (pair$ ?v0 ?v1) :named @p_167) a$) :named @p_240)) :named @p_241) (and (! (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d @p_49 BOUND_VARIABLE_7817))) (not (member$ (fun_app$f @p_44 BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c @p_38 BOUND_VARIABLE_7819) (! (fun_app$h ?v1 BOUND_VARIABLE_7817) :named @p_261)) (= BOUND_VARIABLE_7819 @p_261)) :named @p_262) (! (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d @p_66 BOUND_VARIABLE_7833))) (not (member$ (fun_app$f @p_61 BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c @p_38 (! (fun_app$h ?v1 BOUND_VARIABLE_7833) :named @p_252)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 @p_252)) :named @p_253))) @p_230)) :rule refl)
(step t8 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) @p_230)) :rule sko_forall)
(step t9 (cl @p_285) :rule cong :premises (t8))
(step t10 (cl (not (! (= @p_9 (! (not (! (=> (! (or (! (= dir$ @p_3) :named @p_83) (! (= dir$ @p_1) :named @p_82)) :named @p_233) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))))) :named @p_234)) :named @p_235)) :named @p_236)) (not @p_9) @p_235) :rule equiv_pos2)
(anchor :step t11 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(anchor :step t11.t0 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t11.t0.t0 (cl (= (! (= (! (fun_app$d @p_49 ?v2) :named @p_257) (! (some$ ?v3) :named @p_179)) :named @p_283) (! (= @p_179 @p_257) :named @p_258))) :rule rare_rewrite :args ("eq-symm" @p_257 @p_179))
(step t11.t0.t1 (cl (= (! (member$ (fun_app$f @p_44 ?v2) ?v0) :named @p_255) @p_255)) :rule refl)
(step t11.t0.t2 (cl (= (! (and @p_283 @p_255) :named @p_284) (! (and @p_258 @p_255) :named @p_276))) :rule cong :premises (t11.t0.t0 t11.t0.t1))
(step t11.t0.t3 (cl (! (= (! (or (! (fun_app$b (fun_app$c @p_38 ?v3) (! (fun_app$h ?v1 ?v2) :named @p_173)) :named @p_254) (! (= ?v3 @p_173) :named @p_174)) :named @p_275) @p_275) :named @p_282)) :rule refl)
(step t11.t0.t4 (cl (= (=> @p_284 @p_275) (! (=> @p_276 @p_275) :named @p_277))) :rule cong :premises (t11.t0.t2 t11.t0.t3))
(step t11.t0 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))))) :rule bind)
(anchor :step t11.t1 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t11.t1.t0 (cl (= @p_277 (! (or (! (not @p_276) :named @p_278) @p_275) :named @p_279))) :rule rare_rewrite :args ("bool-impl-elim" @p_276 @p_275))
(step t11.t1.t1 (cl (= @p_278 (! (or (! (not @p_258) :named @p_259) (! (not @p_255) :named @p_256)) :named @p_280))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_258 @p_255 rare-list))
(step t11.t1.t2 (cl @p_282) :rule refl)
(step t11.t1.t3 (cl (= @p_279 (! (or @p_280 @p_275) :named @p_281))) :rule cong :premises (t11.t1.t1 t11.t1.t2))
(step t11.t1.t4 (cl (= @p_281 (! (or @p_259 @p_256 @p_254 @p_174) :named @p_260))) :rule aci_simp)
(step t11.t1.t5 (cl (= @p_279 @p_260)) :rule trans :premises (t11.t1.t3 t11.t1.t4))
(step t11.t1.t6 (cl (= @p_277 @p_260)) :rule trans :premises (t11.t1.t0 t11.t1.t5))
(step t11.t1 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t11.t2 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t11.t0 t11.t1))
(anchor :step t11.t3 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t11.t3.t0 (cl (= (! (= (! (fun_app$d @p_66 ?v2) :named @p_248) @p_179) :named @p_273) (! (= @p_179 @p_248) :named @p_249))) :rule rare_rewrite :args ("eq-symm" @p_248 @p_179))
(step t11.t3.t1 (cl (= (! (member$ (fun_app$f @p_61 ?v2) ?v0) :named @p_246) @p_246)) :rule refl)
(step t11.t3.t2 (cl (= (! (and @p_273 @p_246) :named @p_274) (! (and @p_249 @p_246) :named @p_266))) :rule cong :premises (t11.t3.t0 t11.t3.t1))
(step t11.t3.t3 (cl (= (! (= @p_173 ?v3) :named @p_202) @p_174)) :rule rare_rewrite :args ("eq-symm" @p_173 ?v3))
(step t11.t3.t4 (cl (= (! (or (! (fun_app$b (fun_app$c @p_38 @p_173) ?v3) :named @p_245) @p_202) :named @p_272) (! (or @p_245 @p_174) :named @p_265))) :rule cong :premises (t11.t3.t3))
(step t11.t3.t5 (cl (= (=> @p_274 @p_272) (! (=> @p_266 @p_265) :named @p_267))) :rule cong :premises (t11.t3.t2 t11.t3.t4))
(step t11.t3 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) :rule bind)
(anchor :step t11.t4 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t11.t4.t0 (cl (= @p_267 (! (or (! (not @p_266) :named @p_268) @p_265) :named @p_269))) :rule rare_rewrite :args ("bool-impl-elim" @p_266 @p_265))
(step t11.t4.t1 (cl (= @p_268 (! (or (! (not @p_249) :named @p_250) (! (not @p_246) :named @p_247)) :named @p_270))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_249 @p_246 rare-list))
(step t11.t4.t2 (cl (= @p_265 @p_265)) :rule refl)
(step t11.t4.t3 (cl (= @p_269 (! (or @p_270 @p_265) :named @p_271))) :rule cong :premises (t11.t4.t1 t11.t4.t2))
(step t11.t4.t4 (cl (= @p_271 (! (or @p_250 @p_247 @p_245 @p_174) :named @p_251))) :rule aci_simp)
(step t11.t4.t5 (cl (= @p_269 @p_251)) :rule trans :premises (t11.t4.t3 t11.t4.t4))
(step t11.t4.t6 (cl (= @p_267 @p_251)) :rule trans :premises (t11.t4.t0 t11.t4.t5))
(step t11.t4 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t11.t5 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t11.t3 t11.t4))
(step t11.t6 (cl (= (! (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))) :named @p_264) (! (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))) :named @p_239))) :rule cong :premises (t11.t2 t11.t5))
(step t11.t7 (cl (= (=> @p_240 @p_264) (! (=> @p_240 @p_239) :named @p_263))) :rule cong :premises (t11.t6))
(step t11 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t12 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t12.t0 (cl (= @p_263 (! (or @p_241 @p_239) :named @p_242))) :rule rare_rewrite :args ("bool-impl-elim" @p_240 @p_239))
(step t12 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t13 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t13.t0 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) (! (or @p_241 (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) :named @p_243))) :rule miniscope_split)
(step t13.t1 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))) (! (and (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817)))) (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))) :named @p_244))) :rule miniscope_distribute)
(step t13.t2 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817)))) (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$)) (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817)))))) :rule qnt_rm_unused)
(anchor :step t13.t3 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7817 Nat$) ?v2) (:= (BOUND_VARIABLE_7819 A$) ?v3)))
(step t13.t3.t0 (cl (= @p_262 @p_260)) :rule refl)
(step t13.t3 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$)) (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t13.t4 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t13.t2 t13.t3))
(step t13.t5 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))) (forall ((BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) :rule qnt_rm_unused)
(anchor :step t13.t6 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7833 Nat$) ?v2) (:= (BOUND_VARIABLE_7835 A$) ?v3)))
(step t13.t6.t0 (cl (= @p_253 @p_251)) :rule refl)
(step t13.t6 (cl (= (forall ((BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t13.t7 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t13.t5 t13.t6))
(step t13.t8 (cl (= @p_244 @p_239)) :rule cong :premises (t13.t4 t13.t7))
(step t13.t9 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))) @p_239)) :rule trans :premises (t13.t1 t13.t8))
(step t13.t10 (cl (= @p_243 @p_242)) :rule cong :premises (t13.t9))
(step t13.t11 (cl (= (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) @p_242)) :rule trans :premises (t13.t0 t13.t10))
(step t13.t12 (cl (= @p_242 (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule symm :premises (t13.t11))
(step t13 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))))))) :rule bind)
(step t14 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule qnt_join)
(step t15 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule trans :premises (t13 t14))
(step t16 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule trans :premises (t12 t15))
(step t17 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (lb$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (li$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e (ub$ dir$) s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule trans :premises (t11 t16))
(step t18 (cl (= @p_8 (! (=> @p_7 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833))))))) :named @p_237))) :rule cong :premises (t17))
(step t19 (cl (= @p_9 (! (not @p_237) :named @p_238))) :rule cong :premises (t18))
(step t20 (cl (= @p_6 @p_83)) :rule cong :premises (a13))
(step t21 (cl (= @p_5 @p_82)) :rule cong :premises (a12))
(step t22 (cl (= @p_7 @p_233)) :rule cong :premises (t20 t21))
(step t23 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7817 Nat$) (BOUND_VARIABLE_7819 A$) (BOUND_VARIABLE_7833 Nat$) (BOUND_VARIABLE_7835 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) a$)) (and (or (not (= (some$ BOUND_VARIABLE_7819) (fun_app$d (fun_app$e (lb$ dir$) s$) BOUND_VARIABLE_7817))) (not (member$ (fun_app$f (fun_app$g (li$ dir$) s$) BOUND_VARIABLE_7817) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) BOUND_VARIABLE_7819) (fun_app$h ?v1 BOUND_VARIABLE_7817)) (= BOUND_VARIABLE_7819 (fun_app$h ?v1 BOUND_VARIABLE_7817))) (or (not (= (some$ BOUND_VARIABLE_7835) (fun_app$d (fun_app$e (ub$ dir$) s$) BOUND_VARIABLE_7833))) (not (member$ (fun_app$f (fun_app$g (ui$ dir$) s$) BOUND_VARIABLE_7833) ?v0)) (fun_app$b (fun_app$c (lt$ dir$) (fun_app$h ?v1 BOUND_VARIABLE_7833)) BOUND_VARIABLE_7835) (= BOUND_VARIABLE_7835 (fun_app$h ?v1 BOUND_VARIABLE_7833)))))))) :rule refl)
(step t24 (cl (= @p_237 @p_234)) :rule cong :premises (t22 t23))
(step t25 (cl (= @p_238 @p_235)) :rule cong :premises (t24))
(step t26 (cl @p_236) :rule trans :premises (t19 t25))
(step t27 (cl @p_235) :rule resolution :premises (t10 t26 a21))
(step t28 (cl @p_232) :rule not_implies2 :premises (t27))
(step t29 (cl @p_231) :rule resolution :premises (t7 t9 t28))
(step t30 (cl @p_294) :rule resolution :premises (t6 t29))
(step t31 (cl (! (not (! (= (! (fun_app$b (! (fun_app$c uu$ @p_56) :named @p_392) @quantifiers_skolemize_8) :named @p_393) (! (fun_app$b (fun_app$c less$ @quantifiers_skolemize_8) @p_56) :named @p_410)) :named @p_425)) :named @p_427) @p_393 (! (not @p_410) :named @p_426)) :rule equiv_pos1)
(step t32 (cl @p_393 @p_426 @p_427) :rule reordering :premises (t31))
(step t33 (cl (or (! (not (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0)))) :named @p_15) @p_425)) :rule forall_inst :args (@p_56 @quantifiers_skolemize_8))
(step t34 (cl @p_15 @p_425) :rule or :premises (t33))
(step t35 (cl @p_425) :rule resolution :premises (t34 a1))
(step t36 (cl (! (not (! (or (! (not (! (= @p_68 (! (fun_app$d (! (fun_app$e b_l$ s$) :named @p_153) @quantifiers_skolemize_7) :named @p_368)) :named @p_369)) :named @p_373) (! (not (! (member$ (! (fun_app$f (! (fun_app$g i_l$ s$) :named @p_149) @quantifiers_skolemize_7) :named @p_380) @quantifiers_skolemize_3) :named @p_381)) :named @p_385) @p_410 @p_57) :named @p_411)) :named @p_424) @p_373 @p_385 @p_410 @p_57) :rule or_pos)
(step t37 (cl @p_57 @p_410 @p_385 @p_373 @p_424) :rule reordering :premises (t36))
(step t38 (cl (! (not (! (and @p_411 @p_353) :named @p_412)) :named @p_423) @p_411) :rule and_pos :args (0))
(step t39 (cl @p_411 @p_423) :rule reordering :premises (t38))
(step t40 (cl (! (not (! (or (! (not (! (i_satisfies_atom_set$ @p_159 ats$) :named @p_160)) :named @p_161) @p_412) :named @p_413)) :named @p_422) @p_161 @p_412) :rule or_pos)
(step t41 (cl @p_161 @p_412 @p_422) :rule reordering :premises (t40))
(step t42 (cl (! (not (! (or @p_223 @p_160) :named @p_224)) :named @p_290) @p_223 @p_160) :rule or_pos)
(step t43 (cl @p_223 @p_160 @p_290) :rule reordering :premises (t42))
(step t44 (cl (not (! (= (! (or @p_230 (! (not @p_223) :named @p_287)) :named @p_288) (! (or @p_230 @p_222) :named @p_286)) :named @p_289)) (not @p_288) @p_286) :rule equiv_pos2)
(step t45 (cl (= @p_287 @p_222)) :rule rare_rewrite :args ("bool-double-not-elim" @p_222))
(step t46 (cl @p_289) :rule cong :premises (t45))
(step t47 (cl @p_230 @p_287) :rule or_neg :args (0))
(step t48 (cl @p_288 @p_231) :rule or_neg :args (0))
(step t49 (cl @p_288 (not @p_287)) :rule or_neg :args (1))
(step t50 (cl @p_288 @p_288) :rule resolution :premises (t47 t48 t49))
(step t51 (cl @p_288) :rule contraction :premises (t50))
(step t52 (cl @p_286) :rule resolution :premises (t44 t46 t51))
(step t53 (cl @p_230 @p_222) :rule or :premises (t52))
(step t54 (cl @p_222 @p_230) :rule reordering :premises (t53))
(step t55 (cl @p_222) :rule resolution :premises (t54 t29))
(step t56 (cl (or (! (not (forall ((?v0 I_set_nat_a_fun_prod$)) (or (not (i_satisfies_atom_set$ ?v0 a$)) (i_satisfies_atom_set$ ?v0 ats$)))) :named @p_228) @p_224)) :rule forall_inst :args (@p_159))
(step t57 (cl @p_228 @p_224) :rule or :premises (t56))
(step t58 (cl (not (! (= (forall ((?v0 I_set_nat_a_fun_prod$)) (=> (i_satisfies_atom_set$ ?v0 a$) (i_satisfies_atom_set$ ?v0 ats$))) (forall ((?v0 I_set_nat_a_fun_prod$)) (or (not (i_satisfies_atom_set$ ?v0 a$)) (i_satisfies_atom_set$ ?v0 ats$)))) :named @p_225)) (not (forall ((?v0 I_set_nat_a_fun_prod$)) (=> (i_satisfies_atom_set$ ?v0 a$) (i_satisfies_atom_set$ ?v0 ats$)))) (forall ((?v0 I_set_nat_a_fun_prod$)) (or (not (i_satisfies_atom_set$ ?v0 a$)) (i_satisfies_atom_set$ ?v0 ats$)))) :rule equiv_pos2)
(anchor :step t59 :args ((?v0 I_set_nat_a_fun_prod$) (:= (?v0 I_set_nat_a_fun_prod$) ?v0)))
(step t59.t0 (cl (= (=> (! (i_satisfies_atom_set$ ?v0 a$) :named @p_227) (! (i_satisfies_atom_set$ ?v0 ats$) :named @p_226)) (or (not @p_227) @p_226))) :rule rare_rewrite :args ("bool-impl-elim" @p_227 @p_226))
(step t59 (cl @p_225) :rule bind)
(step t60 (cl (forall ((?v0 I_set_nat_a_fun_prod$)) (or (not (i_satisfies_atom_set$ ?v0 a$)) (i_satisfies_atom_set$ ?v0 ats$)))) :rule resolution :premises (t58 t59 a20))
(step t61 (cl @p_224) :rule resolution :premises (t57 t60))
(step t62 (cl @p_160) :rule resolution :premises (t43 t55 t61))
(step t63 (cl (not (! (= (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) (! (or @p_161 (! (and (! (or (! (not (! (= @p_368 @p_68) :named @p_415)) :named @p_416) @p_385 @p_410 @p_57) :named @p_417) @p_353) :named @p_418)) :named @p_419)) :named @p_420) (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_413) :named @p_414)) :named @p_421)) (not @p_420) @p_414) :rule equiv_pos2)
(step t64 (cl (= @p_415 @p_369)) :rule rare_rewrite :args ("eq-symm" @p_368 @p_68))
(step t65 (cl (= @p_416 @p_373)) :rule cong :premises (t64))
(step t66 (cl (= @p_385 @p_385)) :rule refl)
(step t67 (cl (= @p_410 @p_410)) :rule refl)
(step t68 (cl (= @p_57 @p_57)) :rule refl)
(step t69 (cl (= @p_417 @p_411)) :rule cong :premises (t65 t66 t67 t68))
(step t70 (cl (= @p_353 @p_353)) :rule refl)
(step t71 (cl (= @p_418 @p_412)) :rule cong :premises (t69 t70))
(step t72 (cl (= @p_419 @p_413)) :rule cong :premises (t71))
(step t73 (cl @p_421) :rule cong :premises (t72))
(step t74 (cl @p_420 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule implies_neg1)
(anchor :step t75)
(assume t75.a0 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))
(step t75.t0 (cl (or (! (not (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :named @p_213) @p_419)) :rule forall_inst :args (@quantifiers_skolemize_3 @quantifiers_skolemize_4 @quantifiers_skolemize_7 @quantifiers_skolemize_8 @quantifiers_skolemize_5 @quantifiers_skolemize_6))
(step t75.t1 (cl @p_213 @p_419) :rule or :premises (t75.t0))
(step t75.t2 (cl (not (! (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :named @p_163)) (not (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule equiv_pos2)
(anchor :step t75.t3 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(anchor :step t75.t3.t0 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t75.t3.t0.t0 (cl (= (! (=> (! (and (! (= (fun_app$d @p_153 ?v2) @p_179) :named @p_187) (! (member$ (fun_app$f @p_149 ?v2) ?v0) :named @p_185)) :named @p_207) (! (or (! (fun_app$b (fun_app$c less$ ?v3) @p_173) :named @p_184) @p_174) :named @p_206)) :named @p_208) (! (or (! (not @p_207) :named @p_209) (! (or (! (fun_app$b (fun_app$c less$ ?v3) @p_173) :named @p_184) @p_174) :named @p_206)) :named @p_210))) :rule rare_rewrite :args ("bool-impl-elim" @p_207 @p_206))
(step t75.t3.t0.t1 (cl (= @p_209 (! (or (! (not @p_187) :named @p_188) (! (not @p_185) :named @p_186)) :named @p_211))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_187 @p_185 rare-list))
(step t75.t3.t0.t2 (cl (= @p_206 @p_206)) :rule refl)
(step t75.t3.t0.t3 (cl (= @p_210 (! (or @p_211 @p_206) :named @p_212))) :rule cong :premises (t75.t3.t0.t1 t75.t3.t0.t2))
(step t75.t3.t0.t4 (cl (= @p_212 (! (or @p_188 @p_186 @p_184 @p_174) :named @p_189))) :rule aci_simp)
(step t75.t3.t0.t5 (cl (= @p_210 @p_189)) :rule trans :premises (t75.t3.t0.t3 t75.t3.t0.t4))
(step t75.t3.t0.t6 (cl (= @p_208 @p_189)) :rule trans :premises (t75.t3.t0.t0 t75.t3.t0.t5))
(step t75.t3.t0 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(anchor :step t75.t3.t1 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t75.t3.t1.t0 (cl (= (! (= (! (fun_app$d @p_91 ?v2) :named @p_178) @p_179) :named @p_204) (! (= @p_179 @p_178) :named @p_180))) :rule rare_rewrite :args ("eq-symm" @p_178 @p_179))
(step t75.t3.t1.t1 (cl (= (! (member$ (fun_app$f @p_107 ?v2) ?v0) :named @p_176) @p_176)) :rule refl)
(step t75.t3.t1.t2 (cl (= (! (and @p_204 @p_176) :named @p_205) (! (and @p_180 @p_176) :named @p_196))) :rule cong :premises (t75.t3.t1.t0 t75.t3.t1.t1))
(step t75.t3.t1.t3 (cl (= @p_202 @p_174)) :rule rare_rewrite :args ("eq-symm" @p_173 ?v3))
(step t75.t3.t1.t4 (cl (= (! (or (! (fun_app$b (fun_app$c less$ @p_173) ?v3) :named @p_175) @p_202) :named @p_203) (! (or @p_175 @p_174) :named @p_195))) :rule cong :premises (t75.t3.t1.t3))
(step t75.t3.t1.t5 (cl (= (=> @p_205 @p_203) (! (=> @p_196 @p_195) :named @p_197))) :rule cong :premises (t75.t3.t1.t2 t75.t3.t1.t4))
(step t75.t3.t1 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) :rule bind)
(anchor :step t75.t3.t2 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t75.t3.t2.t0 (cl (= @p_197 (! (or (! (not @p_196) :named @p_198) @p_195) :named @p_199))) :rule rare_rewrite :args ("bool-impl-elim" @p_196 @p_195))
(step t75.t3.t2.t1 (cl (= @p_198 (! (or (! (not @p_180) :named @p_181) (! (not @p_176) :named @p_177)) :named @p_200))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_180 @p_176 rare-list))
(step t75.t3.t2.t2 (cl (= @p_195 @p_195)) :rule refl)
(step t75.t3.t2.t3 (cl (= @p_199 (! (or @p_200 @p_195) :named @p_201))) :rule cong :premises (t75.t3.t2.t1 t75.t3.t2.t2))
(step t75.t3.t2.t4 (cl (= @p_201 (! (or @p_181 @p_177 @p_175 @p_174) :named @p_182))) :rule aci_simp)
(step t75.t3.t2.t5 (cl (= @p_199 @p_182)) :rule trans :premises (t75.t3.t2.t3 t75.t3.t2.t4))
(step t75.t3.t2.t6 (cl (= @p_197 @p_182)) :rule trans :premises (t75.t3.t2.t0 t75.t3.t2.t5))
(step t75.t3.t2 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t75.t3.t3 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t75.t3.t1 t75.t3.t2))
(step t75.t3.t4 (cl (= (! (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))) :named @p_192) (! (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))) :named @p_166))) :rule cong :premises (t75.t3.t0 t75.t3.t3))
(step t75.t3.t5 (cl (= (=> (! (i_satisfies_atom_set$ @p_167 ats$) :named @p_168) @p_192) (! (=> @p_168 @p_166) :named @p_191))) :rule cong :premises (t75.t3.t4))
(step t75.t3 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t75.t4 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t75.t4.t0 (cl (= @p_191 (! (or (! (not @p_168) :named @p_169) @p_166) :named @p_170))) :rule rare_rewrite :args ("bool-impl-elim" @p_168 @p_166))
(step t75.t4 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t75.t5 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t75.t5.t0 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) (! (or @p_169 (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) :named @p_171))) :rule miniscope_split)
(step t75.t5.t1 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))) (! (and (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))) :named @p_172))) :rule miniscope_distribute)
(step t75.t5.t2 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))))) :rule qnt_rm_unused)
(anchor :step t75.t5.t3 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7707 Nat$) ?v2) (:= (BOUND_VARIABLE_7709 A$) ?v3)))
(step t75.t5.t3.t0 (cl (= (or (not (= (fun_app$d @p_153 BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f @p_149 BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (! (fun_app$h ?v1 BOUND_VARIABLE_7707) :named @p_190)) (= BOUND_VARIABLE_7709 @p_190)) @p_189)) :rule refl)
(step t75.t5.t3 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t75.t5.t4 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t75.t5.t2 t75.t5.t3))
(step t75.t5.t5 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) :rule qnt_rm_unused)
(anchor :step t75.t5.t6 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7723 Nat$) ?v2) (:= (BOUND_VARIABLE_7725 A$) ?v3)))
(step t75.t5.t6.t0 (cl (= (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d @p_91 BOUND_VARIABLE_7723))) (not (member$ (fun_app$f @p_107 BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (! (fun_app$h ?v1 BOUND_VARIABLE_7723) :named @p_183)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 @p_183)) @p_182)) :rule refl)
(step t75.t5.t6 (cl (= (forall ((BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t75.t5.t7 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t75.t5.t5 t75.t5.t6))
(step t75.t5.t8 (cl (= @p_172 @p_166)) :rule cong :premises (t75.t5.t4 t75.t5.t7))
(step t75.t5.t9 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))) @p_166)) :rule trans :premises (t75.t5.t1 t75.t5.t8))
(step t75.t5.t10 (cl (= @p_171 @p_170)) :rule cong :premises (t75.t5.t9))
(step t75.t5.t11 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_170)) :rule trans :premises (t75.t5.t0 t75.t5.t10))
(step t75.t5.t12 (cl (= @p_170 (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule symm :premises (t75.t5.t11))
(step t75.t5 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))))) :rule bind)
(step t75.t6 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule qnt_join)
(step t75.t7 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule trans :premises (t75.t5 t75.t6))
(step t75.t8 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule trans :premises (t75.t4 t75.t7))
(step t75.t9 (cl @p_163) :rule trans :premises (t75.t3 t75.t8))
(step t75.t10 (cl (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule resolution :premises (t75.t2 t75.t9 a18))
(step t75.t11 (cl @p_419) :rule resolution :premises (t75.t1 t75.t10))
(step t75 (cl @p_213 @p_419) :rule subproof :discharge (t75.a0))
(step t76 (cl @p_420 @p_419) :rule resolution :premises (t74 t75))
(step t77 (cl @p_420 (not @p_419)) :rule implies_neg2)
(step t78 (cl @p_420 @p_420) :rule resolution :premises (t76 t77))
(step t79 (cl @p_420) :rule contraction :premises (t78))
(step t80 (cl @p_414) :rule resolution :premises (t63 t73 t79))
(step t81 (cl @p_213 @p_413) :rule implies :premises (t80))
(step t82 (cl (not @p_163) (not (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule equiv_pos2)
(anchor :step t83 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(anchor :step t83.t0 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t83.t0.t0 (cl (= @p_208 @p_210)) :rule rare_rewrite :args ("bool-impl-elim" @p_207 @p_206))
(step t83.t0.t1 (cl (= @p_209 @p_211)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_187 @p_185 rare-list))
(step t83.t0.t2 (cl (= @p_206 @p_206)) :rule refl)
(step t83.t0.t3 (cl (= @p_210 @p_212)) :rule cong :premises (t83.t0.t1 t83.t0.t2))
(step t83.t0.t4 (cl (= @p_212 @p_189)) :rule aci_simp)
(step t83.t0.t5 (cl (= @p_210 @p_189)) :rule trans :premises (t83.t0.t3 t83.t0.t4))
(step t83.t0.t6 (cl (= @p_208 @p_189)) :rule trans :premises (t83.t0.t0 t83.t0.t5))
(step t83.t0 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(anchor :step t83.t1 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t83.t1.t0 (cl (= @p_204 @p_180)) :rule rare_rewrite :args ("eq-symm" @p_178 @p_179))
(step t83.t1.t1 (cl (= @p_176 @p_176)) :rule refl)
(step t83.t1.t2 (cl (= @p_205 @p_196)) :rule cong :premises (t83.t1.t0 t83.t1.t1))
(step t83.t1.t3 (cl (= @p_202 @p_174)) :rule rare_rewrite :args ("eq-symm" @p_173 ?v3))
(step t83.t1.t4 (cl (= @p_203 @p_195)) :rule cong :premises (t83.t1.t3))
(step t83.t1.t5 (cl (= (=> @p_205 @p_203) @p_197)) :rule cong :premises (t83.t1.t2 t83.t1.t4))
(step t83.t1 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) :rule bind)
(anchor :step t83.t2 :args ((?v2 Nat$) (?v3 A$) (:= (?v2 Nat$) ?v2) (:= (?v3 A$) ?v3)))
(step t83.t2.t0 (cl (= @p_197 @p_199)) :rule rare_rewrite :args ("bool-impl-elim" @p_196 @p_195))
(step t83.t2.t1 (cl (= @p_198 @p_200)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_180 @p_176 rare-list))
(step t83.t2.t2 (cl (= @p_195 @p_195)) :rule refl)
(step t83.t2.t3 (cl (= @p_199 @p_201)) :rule cong :premises (t83.t2.t1 t83.t2.t2))
(step t83.t2.t4 (cl (= @p_201 @p_182)) :rule aci_simp)
(step t83.t2.t5 (cl (= @p_199 @p_182)) :rule trans :premises (t83.t2.t3 t83.t2.t4))
(step t83.t2.t6 (cl (= @p_197 @p_182)) :rule trans :premises (t83.t2.t0 t83.t2.t5))
(step t83.t2 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t83.t3 (cl (= (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t83.t1 t83.t2))
(step t83.t4 (cl (= @p_192 @p_166)) :rule cong :premises (t83.t0 t83.t3))
(step t83.t5 (cl (= (=> @p_168 @p_192) @p_191)) :rule cong :premises (t83.t4))
(step t83 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2))))) (forall ((?v2 Nat$) (?v3 A$)) (=> (and (= (fun_app$d (fun_app$e b_u$ s$) ?v2) (some$ ?v3)) (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (or (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= (fun_app$h ?v1 ?v2) ?v3))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t84 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t84.t0 (cl (= @p_191 @p_170)) :rule rare_rewrite :args ("bool-impl-elim" @p_168 @p_166))
(step t84 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))))) :rule bind)
(anchor :step t85 :args ((?v0 I_set$) (?v1 Nat_a_fun$) (:= (?v0 I_set$) ?v0) (:= (?v1 Nat_a_fun$) ?v1)))
(step t85.t0 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_171)) :rule miniscope_split)
(step t85.t1 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))) @p_172)) :rule miniscope_distribute)
(step t85.t2 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))))) :rule qnt_rm_unused)
(anchor :step t85.t3 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7707 Nat$) ?v2) (:= (BOUND_VARIABLE_7709 A$) ?v3)))
(step t85.t3.t0 (cl (= (or (not (= (fun_app$d @p_153 BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f @p_149 BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) @p_190) (= BOUND_VARIABLE_7709 @p_190)) @p_189)) :rule refl)
(step t85.t3 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t85.t4 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t85.t2 t85.t3))
(step t85.t5 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) :rule qnt_rm_unused)
(anchor :step t85.t6 :args ((?v2 Nat$) (?v3 A$) (:= (BOUND_VARIABLE_7723 Nat$) ?v2) (:= (BOUND_VARIABLE_7725 A$) ?v3)))
(step t85.t6.t0 (cl (= (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d @p_91 BOUND_VARIABLE_7723))) (not (member$ (fun_app$f @p_107 BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ @p_183) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 @p_183)) @p_182)) :rule refl)
(step t85.t6 (cl (= (forall ((BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule bind)
(step t85.t7 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2)))))) :rule trans :premises (t85.t5 t85.t6))
(step t85.t8 (cl (= @p_172 @p_166)) :rule cong :premises (t85.t4 t85.t7))
(step t85.t9 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))) @p_166)) :rule trans :premises (t85.t1 t85.t8))
(step t85.t10 (cl (= @p_171 @p_170)) :rule cong :premises (t85.t9))
(step t85.t11 (cl (= (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_170)) :rule trans :premises (t85.t0 t85.t10))
(step t85.t12 (cl (= @p_170 (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule symm :premises (t85.t11))
(step t85 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))))) :rule bind)
(step t86 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (forall ((BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule qnt_join)
(step t87 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule trans :premises (t85 t86))
(step t88 (cl (= (forall ((?v0 I_set$) (?v1 Nat_a_fun$)) (=> (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$) (and (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (fun_app$d (fun_app$e b_l$ s$) ?v2) (some$ ?v3))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ ?v3) (fun_app$h ?v1 ?v2)) (= ?v3 (fun_app$h ?v1 ?v2)))) (forall ((?v2 Nat$) (?v3 A$)) (or (not (= (some$ ?v3) (fun_app$d (fun_app$e b_u$ s$) ?v2))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) ?v2) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 ?v2)) ?v3) (= ?v3 (fun_app$h ?v1 ?v2))))))) (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))) :rule trans :premises (t84 t87))
(step t89 (cl @p_163) :rule trans :premises (t83 t88))
(step t90 (cl (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule resolution :premises (t82 t89 a18))
(step t91 (cl @p_413) :rule resolution :premises (t81 t90))
(step t92 (cl @p_412) :rule resolution :premises (t41 t62 t91))
(step t93 (cl @p_411) :rule resolution :premises (t39 t92))
(step t94 (cl (not (! (= (! (or (! (not @p_82) :named @p_366) (! (not (! (not @p_59) :named @p_81)) :named @p_128) (! (not (! (= uu$ (! (lt$ @p_1) :named @p_21)) :named @p_22)) :named @p_391) (! (not @p_393) :named @p_394)) :named @p_396) (! (or @p_366 @p_59 @p_391 @p_394) :named @p_395)) :named @p_409)) (not @p_396) @p_395) :rule equiv_pos2)
(step t95 (cl (= @p_128 @p_59)) :rule rare_rewrite :args ("bool-double-not-elim" @p_59))
(step t96 (cl (= @p_391 @p_391)) :rule refl)
(step t97 (cl (= @p_394 @p_394)) :rule refl)
(step t98 (cl @p_409) :rule cong :premises (t95 t96 t97))
(step t99 (cl (! (and @p_82 @p_81 @p_22) :named @p_400) @p_366 @p_128 @p_391) :rule and_neg)
(step t100 (cl (! (=> @p_400 @p_394) :named @p_402) @p_400) :rule implies_neg1)
(anchor :step t101)
(assume t101.a0 @p_82)
(assume t101.a1 @p_81)
(assume t101.a2 @p_22)
(step t101.t0 (cl (! (=> (! (and @p_81 @p_82 @p_22) :named @p_403) @p_394) :named @p_405) @p_403) :rule implies_neg1)
(anchor :step t101.t1)
(assume t101.t1.a0 @p_81)
(assume t101.t1.a1 @p_82)
(assume t101.t1.a2 @p_22)
(step t101.t1.t0 (cl (= (! (= @p_393 false) :named @p_406) @p_394)) :rule equiv_simplify)
(step t101.t1.t1 (cl (not @p_406) @p_394) :rule equiv1 :premises (t101.t1.t0))
(step t101.t1.t2 (cl (or (! (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_37) @p_22)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t101.t1.t3 (cl @p_37 @p_22) :rule or :premises (t101.t1.t2))
(step t101.t1.t4 (cl (not (! (= (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v0)) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_23)) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v0))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t101.t1.t5 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t101.t1.t5.t0 (cl (= (= (! (lt$ (! (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10) :named @p_35)) :named @p_36) ?v0) (= ?v0 @p_36))) :rule rare_rewrite :args ("eq-symm" @p_36 ?v0))
(step t101.t1.t5 (cl @p_23) :rule bind)
(step t101.t1.t6 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t101.t1.t4 t101.t1.t5 a2))
(step t101.t1.t7 (cl @p_22) :rule resolution :premises (t101.t1.t3 t101.t1.t6))
(step t101.t1.t8 (cl (! (= @p_1 dir$) :named @p_390)) :rule symm :premises (t101.t1.a1))
(step t101.t1.t9 (cl (! (= @p_21 @p_38) :named @p_408)) :rule cong :premises (t101.t1.t8))
(step t101.t1.t10 (cl (! (= uu$ @p_38) :named @p_407)) :rule trans :premises (t101.t1.t7 t101.t1.t9))
(step t101.t1.t11 (cl (= @p_56 @p_56)) :rule refl)
(step t101.t1.t12 (cl (= @p_392 @p_58)) :rule cong :premises (t101.t1.t10 t101.t1.t11))
(step t101.t1.t13 (cl (= @quantifiers_skolemize_8 @quantifiers_skolemize_8)) :rule refl)
(step t101.t1.t14 (cl (= @p_393 @p_59)) :rule cong :premises (t101.t1.t12 t101.t1.t13))
(step t101.t1.t15 (cl (! (= (! (= @p_59 false) :named @p_141) @p_81) :named @p_142)) :rule equiv_simplify)
(step t101.t1.t16 (cl @p_141 @p_128) :rule equiv2 :premises (t101.t1.t15))
(step t101.t1.t17 (cl (! (not @p_128) :named @p_132) @p_59) :rule not_not)
(step t101.t1.t18 (cl @p_141 @p_59) :rule resolution :premises (t101.t1.t16 t101.t1.t17))
(step t101.t1.t19 (cl @p_141) :rule resolution :premises (t101.t1.t18 t101.t1.a0))
(step t101.t1.t20 (cl @p_406) :rule trans :premises (t101.t1.t14 t101.t1.t19))
(step t101.t1.t21 (cl @p_394) :rule resolution :premises (t101.t1.t1 t101.t1.t20))
(step t101.t1 (cl @p_128 @p_366 @p_391 @p_394) :rule subproof :discharge (t101.t1.a0 t101.t1.a1 t101.t1.a2))
(step t101.t2 (cl (! (not @p_403) :named @p_404) @p_81) :rule and_pos :args (0))
(step t101.t3 (cl @p_404 @p_82) :rule and_pos :args (1))
(step t101.t4 (cl @p_404 @p_22) :rule and_pos :args (2))
(step t101.t5 (cl @p_394 @p_404 @p_404 @p_404) :rule resolution :premises (t101.t1 t101.t2 t101.t3 t101.t4))
(step t101.t6 (cl @p_404 @p_404 @p_404 @p_394) :rule reordering :premises (t101.t5))
(step t101.t7 (cl @p_404 @p_394) :rule contraction :premises (t101.t6))
(step t101.t8 (cl @p_405 @p_394) :rule resolution :premises (t101.t0 t101.t7))
(step t101.t9 (cl @p_405 (! (not @p_394) :named @p_397)) :rule implies_neg2)
(step t101.t10 (cl @p_405 @p_405) :rule resolution :premises (t101.t8 t101.t9))
(step t101.t11 (cl @p_405) :rule contraction :premises (t101.t10))
(step t101.t12 (cl @p_404 @p_394) :rule implies :premises (t101.t11))
(step t101.t13 (cl (or @p_37 @p_22)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t101.t14 (cl @p_37 @p_22) :rule or :premises (t101.t13))
(step t101.t15 (cl (not @p_23) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v0))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t101.t16 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t101.t16.t0 (cl (= (= @p_36 ?v0) (= ?v0 @p_36))) :rule rare_rewrite :args ("eq-symm" @p_36 ?v0))
(step t101.t16 (cl @p_23) :rule bind)
(step t101.t17 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t101.t15 t101.t16 a2))
(step t101.t18 (cl @p_22) :rule resolution :premises (t101.t14 t101.t17))
(step t101.t19 (cl @p_403) :rule and_intro :premises (t101.a1 t101.a0 t101.t18))
(step t101.t20 (cl @p_394) :rule resolution :premises (t101.t12 t101.t19))
(step t101 (cl @p_366 @p_128 @p_391 @p_394) :rule subproof :discharge (t101.a0 t101.a1 t101.a2))
(step t102 (cl (! (not @p_400) :named @p_401) @p_82) :rule and_pos :args (0))
(step t103 (cl @p_401 @p_81) :rule and_pos :args (1))
(step t104 (cl @p_401 @p_22) :rule and_pos :args (2))
(step t105 (cl @p_394 @p_401 @p_401 @p_401) :rule resolution :premises (t101 t102 t103 t104))
(step t106 (cl @p_401 @p_401 @p_401 @p_394) :rule reordering :premises (t105))
(step t107 (cl @p_401 @p_394) :rule contraction :premises (t106))
(step t108 (cl @p_402 @p_394) :rule resolution :premises (t100 t107))
(step t109 (cl @p_402 @p_397) :rule implies_neg2)
(step t110 (cl @p_402 @p_402) :rule resolution :premises (t108 t109))
(step t111 (cl @p_402) :rule contraction :premises (t110))
(step t112 (cl @p_401 @p_394) :rule implies :premises (t111))
(step t113 (cl @p_366 @p_128 @p_391 @p_394) :rule resolution :premises (t99 t112))
(step t114 (cl @p_396 (! (not @p_366) :named @p_399)) :rule or_neg :args (0))
(step t115 (cl @p_396 @p_132) :rule or_neg :args (1))
(step t116 (cl @p_396 (! (not @p_391) :named @p_398)) :rule or_neg :args (2))
(step t117 (cl @p_396 @p_397) :rule or_neg :args (3))
(step t118 (cl @p_396 @p_396 @p_396 @p_396) :rule resolution :premises (t113 t114 t115 t116 t117))
(step t119 (cl @p_396) :rule contraction :premises (t118))
(step t120 (cl @p_395) :rule resolution :premises (t94 t98 t119))
(step t121 (cl @p_366 @p_59 @p_391 @p_394) :rule or :premises (t120))
(step t122 (cl (or @p_37 @p_22)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t123 (cl @p_37 @p_22) :rule or :premises (t122))
(step t124 (cl (not @p_23) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v0))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t125 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t125.t0 (cl (= (= @p_36 ?v0) (= ?v0 @p_36))) :rule rare_rewrite :args ("eq-symm" @p_36 ?v0))
(step t125 (cl @p_23) :rule bind)
(step t126 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v0 (lt$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t124 t125 a2))
(step t127 (cl @p_22) :rule resolution :premises (t123 t126))
(step t128 (cl @p_233) :rule not_implies1 :premises (t27))
(step t129 (cl @p_83 @p_82) :rule or :premises (t128))
(step t130 (cl @p_82 @p_83) :rule reordering :premises (t129))
(step t131 (cl (! (not (! (or (! (not (! (= @p_51 (! (fun_app$d @p_153 @quantifiers_skolemize_5) :named @p_154)) :named @p_155)) :named @p_156) (! (not (! (member$ (! (fun_app$f @p_149 @quantifiers_skolemize_5) :named @p_150) @quantifiers_skolemize_3) :named @p_151)) :named @p_152) (! (fun_app$b (! (fun_app$c less$ @quantifiers_skolemize_6) :named @p_147) @p_10) :named @p_148) @p_42) :named @p_157)) :named @p_363) @p_156 @p_152 @p_148 @p_42) :rule or_pos)
(step t132 (cl @p_42 @p_152 @p_148 @p_156 @p_363) :rule reordering :premises (t131))
(step t133 (cl (! (not (! (and @p_157 @p_353) :named @p_354)) :named @p_362) @p_157) :rule and_pos :args (0))
(step t134 (cl @p_157 @p_362) :rule reordering :premises (t133))
(step t135 (cl (! (not (! (or @p_161 @p_354) :named @p_355)) :named @p_361) @p_161 @p_354) :rule or_pos)
(step t136 (cl @p_161 @p_354 @p_361) :rule reordering :premises (t135))
(step t137 (cl (not (! (= (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) (! (or @p_161 (! (and (! (or (! (not (! (= @p_154 @p_51) :named @p_215)) :named @p_216) @p_152 @p_148 @p_42) :named @p_217) @p_353) :named @p_357)) :named @p_358)) :named @p_359) (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_355) :named @p_356)) :named @p_360)) (not @p_359) @p_356) :rule equiv_pos2)
(step t138 (cl (= @p_215 @p_155)) :rule rare_rewrite :args ("eq-symm" @p_154 @p_51))
(step t139 (cl (= @p_216 @p_156)) :rule cong :premises (t138))
(step t140 (cl (= @p_152 @p_152)) :rule refl)
(step t141 (cl (= @p_148 @p_148)) :rule refl)
(step t142 (cl (= @p_42 @p_42)) :rule refl)
(step t143 (cl (= @p_217 @p_157)) :rule cong :premises (t139 t140 t141 t142))
(step t144 (cl (= @p_357 @p_354)) :rule cong :premises (t143 t70))
(step t145 (cl (= @p_358 @p_355)) :rule cong :premises (t144))
(step t146 (cl @p_360) :rule cong :premises (t145))
(step t147 (cl @p_359 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule implies_neg1)
(anchor :step t148)
(assume t148.a0 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))
(step t148.t0 (cl (or @p_213 @p_358)) :rule forall_inst :args (@quantifiers_skolemize_3 @quantifiers_skolemize_4 @quantifiers_skolemize_5 @quantifiers_skolemize_6 @quantifiers_skolemize_5 @quantifiers_skolemize_6))
(step t148.t1 (cl @p_213 @p_358) :rule or :premises (t148.t0))
(step t148.t2 (cl @p_358) :rule resolution :premises (t148.t1 t90))
(step t148 (cl @p_213 @p_358) :rule subproof :discharge (t148.a0))
(step t149 (cl @p_359 @p_358) :rule resolution :premises (t147 t148))
(step t150 (cl @p_359 (not @p_358)) :rule implies_neg2)
(step t151 (cl @p_359 @p_359) :rule resolution :premises (t149 t150))
(step t152 (cl @p_359) :rule contraction :premises (t151))
(step t153 (cl @p_356) :rule resolution :premises (t137 t146 t152))
(step t154 (cl @p_213 @p_355) :rule implies :premises (t153))
(step t155 (cl @p_355) :rule resolution :premises (t154 t90))
(step t156 (cl @p_354) :rule resolution :premises (t136 t62 t155))
(step t157 (cl @p_157) :rule resolution :premises (t134 t156))
(step t158 (cl (not (! (= (! (or (! (not @p_83) :named @p_84) (! (not (! (not @p_40) :named @p_41)) :named @p_333) (! (not (! (= less$ (! (lt$ @p_3) :named @p_121)) :named @p_122)) :named @p_123) (! (not @p_148) :named @p_331)) :named @p_334) (! (or @p_84 @p_40 @p_123 @p_331) :named @p_332)) :named @p_346)) (not @p_334) @p_332) :rule equiv_pos2)
(step t159 (cl (= @p_333 @p_40)) :rule rare_rewrite :args ("bool-double-not-elim" @p_40))
(step t160 (cl (= @p_123 @p_123)) :rule refl)
(step t161 (cl (= @p_331 @p_331)) :rule refl)
(step t162 (cl @p_346) :rule cong :premises (t159 t160 t161))
(step t163 (cl (! (and @p_83 @p_41 @p_122) :named @p_337) @p_84 @p_333 @p_123) :rule and_neg)
(step t164 (cl (! (=> @p_337 @p_331) :named @p_339) @p_337) :rule implies_neg1)
(anchor :step t165)
(assume t165.a0 @p_83)
(assume t165.a1 @p_41)
(assume t165.a2 @p_122)
(step t165.t0 (cl (! (=> (! (and @p_41 @p_83 @p_122) :named @p_340) @p_331) :named @p_342) @p_340) :rule implies_neg1)
(anchor :step t165.t1)
(assume t165.t1.a0 @p_41)
(assume t165.t1.a1 @p_83)
(assume t165.t1.a2 @p_122)
(step t165.t1.t0 (cl (= (! (= @p_148 false) :named @p_343) @p_331)) :rule equiv_simplify)
(step t165.t1.t1 (cl (not @p_343) @p_331) :rule equiv1 :premises (t165.t1.t0))
(step t165.t1.t2 (cl (or @p_37 @p_122)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t165.t1.t3 (cl @p_37 @p_122) :rule or :premises (t165.t1.t2))
(step t165.t1.t4 (cl @p_122) :rule resolution :premises (t165.t1.t3 t126))
(step t165.t1.t5 (cl (! (= @p_3 dir$) :named @p_120)) :rule symm :premises (t165.t1.a1))
(step t165.t1.t6 (cl (! (= @p_121 @p_38) :named @p_144)) :rule cong :premises (t165.t1.t5))
(step t165.t1.t7 (cl (! (= less$ @p_38) :named @p_143)) :rule trans :premises (t165.t1.t4 t165.t1.t6))
(step t165.t1.t8 (cl (= @quantifiers_skolemize_6 @quantifiers_skolemize_6)) :rule refl)
(step t165.t1.t9 (cl (= @p_147 @p_39)) :rule cong :premises (t165.t1.t7 t165.t1.t8))
(step t165.t1.t10 (cl (= @p_10 @p_10)) :rule refl)
(step t165.t1.t11 (cl (= @p_148 @p_40)) :rule cong :premises (t165.t1.t9 t165.t1.t10))
(step t165.t1.t12 (cl (! (= (! (= @p_40 false) :named @p_344) @p_41) :named @p_345)) :rule equiv_simplify)
(step t165.t1.t13 (cl @p_344 @p_333) :rule equiv2 :premises (t165.t1.t12))
(step t165.t1.t14 (cl (! (not @p_333) :named @p_336) @p_40) :rule not_not)
(step t165.t1.t15 (cl @p_344 @p_40) :rule resolution :premises (t165.t1.t13 t165.t1.t14))
(step t165.t1.t16 (cl @p_344) :rule resolution :premises (t165.t1.t15 t165.t1.a0))
(step t165.t1.t17 (cl @p_343) :rule trans :premises (t165.t1.t11 t165.t1.t16))
(step t165.t1.t18 (cl @p_331) :rule resolution :premises (t165.t1.t1 t165.t1.t17))
(step t165.t1 (cl @p_333 @p_84 @p_123 @p_331) :rule subproof :discharge (t165.t1.a0 t165.t1.a1 t165.t1.a2))
(step t165.t2 (cl (! (not @p_340) :named @p_341) @p_41) :rule and_pos :args (0))
(step t165.t3 (cl @p_341 @p_83) :rule and_pos :args (1))
(step t165.t4 (cl @p_341 @p_122) :rule and_pos :args (2))
(step t165.t5 (cl @p_331 @p_341 @p_341 @p_341) :rule resolution :premises (t165.t1 t165.t2 t165.t3 t165.t4))
(step t165.t6 (cl @p_341 @p_341 @p_341 @p_331) :rule reordering :premises (t165.t5))
(step t165.t7 (cl @p_341 @p_331) :rule contraction :premises (t165.t6))
(step t165.t8 (cl @p_342 @p_331) :rule resolution :premises (t165.t0 t165.t7))
(step t165.t9 (cl @p_342 (! (not @p_331) :named @p_335)) :rule implies_neg2)
(step t165.t10 (cl @p_342 @p_342) :rule resolution :premises (t165.t8 t165.t9))
(step t165.t11 (cl @p_342) :rule contraction :premises (t165.t10))
(step t165.t12 (cl @p_341 @p_331) :rule implies :premises (t165.t11))
(step t165.t13 (cl (or @p_37 @p_122)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t165.t14 (cl @p_37 @p_122) :rule or :premises (t165.t13))
(step t165.t15 (cl @p_122) :rule resolution :premises (t165.t14 t126))
(step t165.t16 (cl @p_340) :rule and_intro :premises (t165.a1 t165.a0 t165.t15))
(step t165.t17 (cl @p_331) :rule resolution :premises (t165.t12 t165.t16))
(step t165 (cl @p_84 @p_333 @p_123 @p_331) :rule subproof :discharge (t165.a0 t165.a1 t165.a2))
(step t166 (cl (! (not @p_337) :named @p_338) @p_83) :rule and_pos :args (0))
(step t167 (cl @p_338 @p_41) :rule and_pos :args (1))
(step t168 (cl @p_338 @p_122) :rule and_pos :args (2))
(step t169 (cl @p_331 @p_338 @p_338 @p_338) :rule resolution :premises (t165 t166 t167 t168))
(step t170 (cl @p_338 @p_338 @p_338 @p_331) :rule reordering :premises (t169))
(step t171 (cl @p_338 @p_331) :rule contraction :premises (t170))
(step t172 (cl @p_339 @p_331) :rule resolution :premises (t164 t171))
(step t173 (cl @p_339 @p_335) :rule implies_neg2)
(step t174 (cl @p_339 @p_339) :rule resolution :premises (t172 t173))
(step t175 (cl @p_339) :rule contraction :premises (t174))
(step t176 (cl @p_338 @p_331) :rule implies :premises (t175))
(step t177 (cl @p_84 @p_333 @p_123 @p_331) :rule resolution :premises (t163 t176))
(step t178 (cl @p_334 (! (not @p_84) :named @p_133)) :rule or_neg :args (0))
(step t179 (cl @p_334 @p_336) :rule or_neg :args (1))
(step t180 (cl @p_334 (! (not @p_123) :named @p_131)) :rule or_neg :args (2))
(step t181 (cl @p_334 @p_335) :rule or_neg :args (3))
(step t182 (cl @p_334 @p_334 @p_334 @p_334) :rule resolution :premises (t177 t178 t179 t180 t181))
(step t183 (cl @p_334) :rule contraction :premises (t182))
(step t184 (cl @p_332) :rule resolution :premises (t158 t162 t183))
(step t185 (cl @p_84 @p_40 @p_123 @p_331) :rule or :premises (t184))
(step t186 (cl (or @p_37 @p_122)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t187 (cl @p_37 @p_122) :rule or :premises (t186))
(step t188 (cl @p_122) :rule resolution :premises (t187 t126))
(step t189 (cl (! (and @p_83 @p_46 (! (= i_l$ (! (li$ @p_3) :named @p_316)) :named @p_317)) :named @p_322) @p_84 @p_47 (! (not @p_317) :named @p_321)) :rule and_neg)
(step t190 (cl (! (=> @p_322 @p_151) :named @p_324) @p_322) :rule implies_neg1)
(anchor :step t191)
(assume t191.a0 @p_83)
(assume t191.a1 @p_46)
(assume t191.a2 @p_317)
(step t191.t0 (cl (! (=> (! (and @p_46 @p_83 @p_317) :named @p_325) @p_151) :named @p_327) @p_325) :rule implies_neg1)
(anchor :step t191.t1)
(assume t191.t1.a0 @p_46)
(assume t191.t1.a1 @p_83)
(assume t191.t1.a2 @p_317)
(step t191.t1.t0 (cl (= (! (= @p_151 true) :named @p_328) @p_151)) :rule equiv_simplify)
(step t191.t1.t1 (cl (not @p_328) @p_151) :rule equiv1 :premises (t191.t1.t0))
(step t191.t1.t2 (cl (or (! (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_320) @p_317)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t191.t1.t3 (cl @p_320 @p_317) :rule or :premises (t191.t1.t2))
(step t191.t1.t4 (cl (not (! (= (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v5)) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_318)) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v5))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t191.t1.t5 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t191.t1.t5.t0 (cl (= (= (! (li$ @p_35) :named @p_319) ?v5) (= ?v5 @p_319))) :rule rare_rewrite :args ("eq-symm" @p_319 ?v5))
(step t191.t1.t5 (cl @p_318) :rule bind)
(step t191.t1.t6 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t191.t1.t4 t191.t1.t5 a8))
(step t191.t1.t7 (cl @p_317) :rule resolution :premises (t191.t1.t3 t191.t1.t6))
(step t191.t1.t8 (cl @p_120) :rule symm :premises (t191.t1.a1))
(step t191.t1.t9 (cl (= @p_316 @p_43)) :rule cong :premises (t191.t1.t8))
(step t191.t1.t10 (cl (= i_l$ @p_43)) :rule trans :premises (t191.t1.t7 t191.t1.t9))
(step t191.t1.t11 (cl (= s$ s$)) :rule refl)
(step t191.t1.t12 (cl (= @p_149 @p_44)) :rule cong :premises (t191.t1.t10 t191.t1.t11))
(step t191.t1.t13 (cl (= @quantifiers_skolemize_5 @quantifiers_skolemize_5)) :rule refl)
(step t191.t1.t14 (cl (= @p_150 @p_45)) :rule cong :premises (t191.t1.t12 t191.t1.t13))
(step t191.t1.t15 (cl (= @quantifiers_skolemize_3 @quantifiers_skolemize_3)) :rule refl)
(step t191.t1.t16 (cl (= @p_151 @p_46)) :rule cong :premises (t191.t1.t14 t191.t1.t15))
(step t191.t1.t17 (cl (! (= (! (= @p_46 true) :named @p_329) @p_46) :named @p_330)) :rule equiv_simplify)
(step t191.t1.t18 (cl @p_329 @p_47) :rule equiv2 :premises (t191.t1.t17))
(step t191.t1.t19 (cl @p_329) :rule resolution :premises (t191.t1.t18 t191.t1.a0))
(step t191.t1.t20 (cl @p_328) :rule trans :premises (t191.t1.t16 t191.t1.t19))
(step t191.t1.t21 (cl @p_151) :rule resolution :premises (t191.t1.t1 t191.t1.t20))
(step t191.t1 (cl @p_47 @p_84 @p_321 @p_151) :rule subproof :discharge (t191.t1.a0 t191.t1.a1 t191.t1.a2))
(step t191.t2 (cl (! (not @p_325) :named @p_326) @p_46) :rule and_pos :args (0))
(step t191.t3 (cl @p_326 @p_83) :rule and_pos :args (1))
(step t191.t4 (cl @p_326 @p_317) :rule and_pos :args (2))
(step t191.t5 (cl @p_151 @p_326 @p_326 @p_326) :rule resolution :premises (t191.t1 t191.t2 t191.t3 t191.t4))
(step t191.t6 (cl @p_326 @p_326 @p_326 @p_151) :rule reordering :premises (t191.t5))
(step t191.t7 (cl @p_326 @p_151) :rule contraction :premises (t191.t6))
(step t191.t8 (cl @p_327 @p_151) :rule resolution :premises (t191.t0 t191.t7))
(step t191.t9 (cl @p_327 @p_152) :rule implies_neg2)
(step t191.t10 (cl @p_327 @p_327) :rule resolution :premises (t191.t8 t191.t9))
(step t191.t11 (cl @p_327) :rule contraction :premises (t191.t10))
(step t191.t12 (cl @p_326 @p_151) :rule implies :premises (t191.t11))
(step t191.t13 (cl (or @p_320 @p_317)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t191.t14 (cl @p_320 @p_317) :rule or :premises (t191.t13))
(step t191.t15 (cl (not @p_318) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v5))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t191.t16 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t191.t16.t0 (cl (= (= @p_319 ?v5) (= ?v5 @p_319))) :rule rare_rewrite :args ("eq-symm" @p_319 ?v5))
(step t191.t16 (cl @p_318) :rule bind)
(step t191.t17 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t191.t15 t191.t16 a8))
(step t191.t18 (cl @p_317) :rule resolution :premises (t191.t14 t191.t17))
(step t191.t19 (cl @p_325) :rule and_intro :premises (t191.a1 t191.a0 t191.t18))
(step t191.t20 (cl @p_151) :rule resolution :premises (t191.t12 t191.t19))
(step t191 (cl @p_84 @p_47 @p_321 @p_151) :rule subproof :discharge (t191.a0 t191.a1 t191.a2))
(step t192 (cl (! (not @p_322) :named @p_323) @p_83) :rule and_pos :args (0))
(step t193 (cl @p_323 @p_46) :rule and_pos :args (1))
(step t194 (cl @p_323 @p_317) :rule and_pos :args (2))
(step t195 (cl @p_151 @p_323 @p_323 @p_323) :rule resolution :premises (t191 t192 t193 t194))
(step t196 (cl @p_323 @p_323 @p_323 @p_151) :rule reordering :premises (t195))
(step t197 (cl @p_323 @p_151) :rule contraction :premises (t196))
(step t198 (cl @p_324 @p_151) :rule resolution :premises (t190 t197))
(step t199 (cl @p_324 @p_152) :rule implies_neg2)
(step t200 (cl @p_324 @p_324) :rule resolution :premises (t198 t199))
(step t201 (cl @p_324) :rule contraction :premises (t200))
(step t202 (cl @p_323 @p_151) :rule implies :premises (t201))
(step t203 (cl @p_84 @p_47 @p_321 @p_151) :rule resolution :premises (t189 t202))
(step t204 (cl (or @p_320 @p_317)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t205 (cl @p_320 @p_317) :rule or :premises (t204))
(step t206 (cl (not @p_318) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v5))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t207 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t207.t0 (cl (= (= @p_319 ?v5) (= ?v5 @p_319))) :rule rare_rewrite :args ("eq-symm" @p_319 ?v5))
(step t207 (cl @p_318) :rule bind)
(step t208 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v5 (li$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t206 t207 a8))
(step t209 (cl @p_317) :rule resolution :premises (t205 t208))
(step t210 (cl (! (and @p_83 @p_52 (! (= b_l$ (! (lb$ @p_3) :named @p_304)) :named @p_305)) :named @p_310) @p_84 @p_53 (! (not @p_305) :named @p_309)) :rule and_neg)
(step t211 (cl (! (=> @p_310 @p_155) :named @p_312) @p_310) :rule implies_neg1)
(anchor :step t212)
(assume t212.a0 @p_83)
(assume t212.a1 @p_52)
(assume t212.a2 @p_305)
(step t212.t0 (cl (! (=> (! (and @p_305 @p_83 @p_52) :named @p_313) @p_155) :named @p_315) @p_313) :rule implies_neg1)
(anchor :step t212.t1)
(assume t212.t1.a0 @p_305)
(assume t212.t1.a1 @p_83)
(assume t212.t1.a2 @p_52)
(step t212.t1.t0 (cl (= @p_48 @p_304)) :rule cong :premises (t212.t1.a1))
(step t212.t1.t1 (cl (or (! (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_308) @p_305)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t212.t1.t2 (cl @p_308 @p_305) :rule or :premises (t212.t1.t1))
(step t212.t1.t3 (cl (not (! (= (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v3)) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_306)) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v3))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t212.t1.t4 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t212.t1.t4.t0 (cl (= (= (! (lb$ @p_35) :named @p_307) ?v3) (= ?v3 @p_307))) :rule rare_rewrite :args ("eq-symm" @p_307 ?v3))
(step t212.t1.t4 (cl @p_306) :rule bind)
(step t212.t1.t5 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t212.t1.t3 t212.t1.t4 a6))
(step t212.t1.t6 (cl @p_305) :rule resolution :premises (t212.t1.t2 t212.t1.t5))
(step t212.t1.t7 (cl (= @p_304 b_l$)) :rule symm :premises (t212.t1.t6))
(step t212.t1.t8 (cl (= @p_48 b_l$)) :rule trans :premises (t212.t1.t0 t212.t1.t7))
(step t212.t1.t9 (cl (= s$ s$)) :rule refl)
(step t212.t1.t10 (cl (= @p_49 @p_153)) :rule cong :premises (t212.t1.t8 t212.t1.t9))
(step t212.t1.t11 (cl (= @quantifiers_skolemize_5 @quantifiers_skolemize_5)) :rule refl)
(step t212.t1.t12 (cl (= @p_50 @p_154)) :rule cong :premises (t212.t1.t10 t212.t1.t11))
(step t212.t1.t13 (cl @p_155) :rule trans :premises (t212.t1.a2 t212.t1.t12))
(step t212.t1 (cl @p_309 @p_84 @p_53 @p_155) :rule subproof :discharge (t212.t1.a0 t212.t1.a1 t212.t1.a2))
(step t212.t2 (cl (! (not @p_313) :named @p_314) @p_305) :rule and_pos :args (0))
(step t212.t3 (cl @p_314 @p_83) :rule and_pos :args (1))
(step t212.t4 (cl @p_314 @p_52) :rule and_pos :args (2))
(step t212.t5 (cl @p_155 @p_314 @p_314 @p_314) :rule resolution :premises (t212.t1 t212.t2 t212.t3 t212.t4))
(step t212.t6 (cl @p_314 @p_314 @p_314 @p_155) :rule reordering :premises (t212.t5))
(step t212.t7 (cl @p_314 @p_155) :rule contraction :premises (t212.t6))
(step t212.t8 (cl @p_315 @p_155) :rule resolution :premises (t212.t0 t212.t7))
(step t212.t9 (cl @p_315 @p_156) :rule implies_neg2)
(step t212.t10 (cl @p_315 @p_315) :rule resolution :premises (t212.t8 t212.t9))
(step t212.t11 (cl @p_315) :rule contraction :premises (t212.t10))
(step t212.t12 (cl @p_314 @p_155) :rule implies :premises (t212.t11))
(step t212.t13 (cl (or @p_308 @p_305)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t212.t14 (cl @p_308 @p_305) :rule or :premises (t212.t13))
(step t212.t15 (cl (not @p_306) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v3))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t212.t16 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t212.t16.t0 (cl (= (= @p_307 ?v3) (= ?v3 @p_307))) :rule rare_rewrite :args ("eq-symm" @p_307 ?v3))
(step t212.t16 (cl @p_306) :rule bind)
(step t212.t17 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t212.t15 t212.t16 a6))
(step t212.t18 (cl @p_305) :rule resolution :premises (t212.t14 t212.t17))
(step t212.t19 (cl @p_313) :rule and_intro :premises (t212.t18 t212.a0 t212.a1))
(step t212.t20 (cl @p_155) :rule resolution :premises (t212.t12 t212.t19))
(step t212 (cl @p_84 @p_53 @p_309 @p_155) :rule subproof :discharge (t212.a0 t212.a1 t212.a2))
(step t213 (cl (! (not @p_310) :named @p_311) @p_83) :rule and_pos :args (0))
(step t214 (cl @p_311 @p_52) :rule and_pos :args (1))
(step t215 (cl @p_311 @p_305) :rule and_pos :args (2))
(step t216 (cl @p_155 @p_311 @p_311 @p_311) :rule resolution :premises (t212 t213 t214 t215))
(step t217 (cl @p_311 @p_311 @p_311 @p_155) :rule reordering :premises (t216))
(step t218 (cl @p_311 @p_155) :rule contraction :premises (t217))
(step t219 (cl @p_312 @p_155) :rule resolution :premises (t211 t218))
(step t220 (cl @p_312 @p_156) :rule implies_neg2)
(step t221 (cl @p_312 @p_312) :rule resolution :premises (t219 t220))
(step t222 (cl @p_312) :rule contraction :premises (t221))
(step t223 (cl @p_311 @p_155) :rule implies :premises (t222))
(step t224 (cl @p_84 @p_53 @p_309 @p_155) :rule resolution :premises (t210 t223))
(step t225 (cl (or @p_308 @p_305)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t226 (cl @p_308 @p_305) :rule or :premises (t225))
(step t227 (cl (not @p_306) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v3))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t228 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t228.t0 (cl (= (= @p_307 ?v3) (= ?v3 @p_307))) :rule rare_rewrite :args ("eq-symm" @p_307 ?v3))
(step t228 (cl @p_306) :rule bind)
(step t229 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v3 (lb$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t227 t228 a6))
(step t230 (cl @p_305) :rule resolution :premises (t226 t229))
(step t231 (cl @p_54 @p_41) :rule or_neg :args (2))
(step t232 (cl (not (! (= (! (or @p_54 (! (not @p_47) :named @p_300)) :named @p_301) (! (or @p_54 @p_46) :named @p_299)) :named @p_302)) (not @p_301) @p_299) :rule equiv_pos2)
(step t233 (cl (= @p_300 @p_46)) :rule rare_rewrite :args ("bool-double-not-elim" @p_46))
(step t234 (cl @p_302) :rule cong :premises (t233))
(step t235 (cl @p_54 @p_300) :rule or_neg :args (1))
(step t236 (cl @p_301 @p_55) :rule or_neg :args (0))
(step t237 (cl @p_301 (not @p_300)) :rule or_neg :args (1))
(step t238 (cl @p_301 @p_301) :rule resolution :premises (t235 t236 t237))
(step t239 (cl @p_301) :rule contraction :premises (t238))
(step t240 (cl @p_299) :rule resolution :premises (t232 t234 t239))
(step t241 (cl @p_54 @p_46) :rule or :premises (t240))
(step t242 (cl @p_46 @p_54) :rule reordering :premises (t241))
(step t243 (cl (not (! (= (! (or @p_54 (! (not @p_53) :named @p_296)) :named @p_297) (! (or @p_54 @p_52) :named @p_295)) :named @p_298)) (not @p_297) @p_295) :rule equiv_pos2)
(step t244 (cl (= @p_296 @p_52)) :rule rare_rewrite :args ("bool-double-not-elim" @p_52))
(step t245 (cl @p_298) :rule cong :premises (t244))
(step t246 (cl @p_54 @p_296) :rule or_neg :args (0))
(step t247 (cl @p_297 @p_55) :rule or_neg :args (0))
(step t248 (cl @p_297 (not @p_296)) :rule or_neg :args (1))
(step t249 (cl @p_297 @p_297) :rule resolution :premises (t246 t247 t248))
(step t250 (cl @p_297) :rule contraction :premises (t249))
(step t251 (cl @p_295) :rule resolution :premises (t243 t245 t250))
(step t252 (cl @p_54 @p_52) :rule or :premises (t251))
(step t253 (cl @p_52 @p_54) :rule reordering :premises (t252))
(step t254 (cl (! (not (! (or (! (not (! (= @p_68 (! (fun_app$d @p_91 @quantifiers_skolemize_7) :named @p_92)) :named @p_93)) :named @p_97) (! (not (! (member$ (! (fun_app$f @p_107 @quantifiers_skolemize_7) :named @p_108) @quantifiers_skolemize_3) :named @p_109)) :named @p_113) (! (fun_app$b (! (fun_app$c less$ @p_56) :named @p_124) @quantifiers_skolemize_8) :named @p_125) @p_57) :named @p_146)) :named @p_293) @p_97 @p_113 @p_125 @p_57) :rule or_pos)
(step t255 (cl @p_57 @p_97 @p_113 @p_125 @p_293) :rule reordering :premises (t254))
(step t256 (cl (! (not (! (and @p_157 @p_146) :named @p_158)) :named @p_292) @p_146) :rule and_pos :args (1))
(step t257 (cl @p_146 @p_292) :rule reordering :premises (t256))
(step t258 (cl (! (not (! (or @p_161 @p_158) :named @p_162)) :named @p_291) @p_161 @p_158) :rule or_pos)
(step t259 (cl @p_161 @p_158 @p_291) :rule reordering :premises (t258))
(step t260 (cl (not (! (= (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) (! (or @p_161 (! (and @p_217 @p_146) :named @p_218)) :named @p_219)) :named @p_220) (! (=> (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))) @p_162) :named @p_214)) :named @p_221)) (not @p_220) @p_214) :rule equiv_pos2)
(step t261 (cl (= @p_146 @p_146)) :rule refl)
(step t262 (cl (= @p_218 @p_158)) :rule cong :premises (t143 t261))
(step t263 (cl (= @p_219 @p_162)) :rule cong :premises (t262))
(step t264 (cl @p_221) :rule cong :premises (t263))
(step t265 (cl @p_220 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723))))))) :rule implies_neg1)
(anchor :step t266)
(assume t266.a0 (forall ((?v0 I_set$) (?v1 Nat_a_fun$) (BOUND_VARIABLE_7707 Nat$) (BOUND_VARIABLE_7709 A$) (BOUND_VARIABLE_7723 Nat$) (BOUND_VARIABLE_7725 A$)) (or (not (i_satisfies_atom_set$ (pair$ ?v0 ?v1) ats$)) (and (or (not (= (fun_app$d (fun_app$e b_l$ s$) BOUND_VARIABLE_7707) (some$ BOUND_VARIABLE_7709))) (not (member$ (fun_app$f (fun_app$g i_l$ s$) BOUND_VARIABLE_7707) ?v0)) (fun_app$b (fun_app$c less$ BOUND_VARIABLE_7709) (fun_app$h ?v1 BOUND_VARIABLE_7707)) (= BOUND_VARIABLE_7709 (fun_app$h ?v1 BOUND_VARIABLE_7707))) (or (not (= (some$ BOUND_VARIABLE_7725) (fun_app$d (fun_app$e b_u$ s$) BOUND_VARIABLE_7723))) (not (member$ (fun_app$f (fun_app$g i_u$ s$) BOUND_VARIABLE_7723) ?v0)) (fun_app$b (fun_app$c less$ (fun_app$h ?v1 BOUND_VARIABLE_7723)) BOUND_VARIABLE_7725) (= BOUND_VARIABLE_7725 (fun_app$h ?v1 BOUND_VARIABLE_7723)))))))
(step t266.t0 (cl (or @p_213 @p_219)) :rule forall_inst :args (@quantifiers_skolemize_3 @quantifiers_skolemize_4 @quantifiers_skolemize_5 @quantifiers_skolemize_6 @quantifiers_skolemize_7 @quantifiers_skolemize_8))
(step t266.t1 (cl @p_213 @p_219) :rule or :premises (t266.t0))
(step t266.t2 (cl @p_219) :rule resolution :premises (t266.t1 t90))
(step t266 (cl @p_213 @p_219) :rule subproof :discharge (t266.a0))
(step t267 (cl @p_220 @p_219) :rule resolution :premises (t265 t266))
(step t268 (cl @p_220 (not @p_219)) :rule implies_neg2)
(step t269 (cl @p_220 @p_220) :rule resolution :premises (t267 t268))
(step t270 (cl @p_220) :rule contraction :premises (t269))
(step t271 (cl @p_214) :rule resolution :premises (t260 t264 t270))
(step t272 (cl @p_213 @p_162) :rule implies :premises (t271))
(step t273 (cl @p_162) :rule resolution :premises (t272 t90))
(step t274 (cl @p_158) :rule resolution :premises (t259 t62 t273))
(step t275 (cl @p_146) :rule resolution :premises (t257 t274))
(step t276 (cl (not (! (= (! (or @p_84 @p_128 @p_123 (! (not @p_125) :named @p_126)) :named @p_129) (! (or @p_84 @p_59 @p_123 @p_126) :named @p_127)) :named @p_145)) (not @p_129) @p_127) :rule equiv_pos2)
(step t277 (cl (= @p_126 @p_126)) :rule refl)
(step t278 (cl @p_145) :rule cong :premises (t95 t160 t277))
(step t279 (cl (! (and @p_83 @p_81 @p_122) :named @p_134) @p_84 @p_128 @p_123) :rule and_neg)
(step t280 (cl (! (=> @p_134 @p_126) :named @p_136) @p_134) :rule implies_neg1)
(anchor :step t281)
(assume t281.a0 @p_83)
(assume t281.a1 @p_81)
(assume t281.a2 @p_122)
(step t281.t0 (cl (! (=> (! (and @p_81 @p_83 @p_122) :named @p_137) @p_126) :named @p_139) @p_137) :rule implies_neg1)
(anchor :step t281.t1)
(assume t281.t1.a0 @p_81)
(assume t281.t1.a1 @p_83)
(assume t281.t1.a2 @p_122)
(step t281.t1.t0 (cl (= (! (= @p_125 false) :named @p_140) @p_126)) :rule equiv_simplify)
(step t281.t1.t1 (cl (not @p_140) @p_126) :rule equiv1 :premises (t281.t1.t0))
(step t281.t1.t2 (cl @p_120) :rule symm :premises (t281.t1.a1))
(step t281.t1.t3 (cl @p_144) :rule cong :premises (t281.t1.t2))
(step t281.t1.t4 (cl @p_143) :rule trans :premises (t188 t281.t1.t3))
(step t281.t1.t5 (cl (= @p_56 @p_56)) :rule refl)
(step t281.t1.t6 (cl (= @p_124 @p_58)) :rule cong :premises (t281.t1.t4 t281.t1.t5))
(step t281.t1.t7 (cl (= @quantifiers_skolemize_8 @quantifiers_skolemize_8)) :rule refl)
(step t281.t1.t8 (cl (= @p_125 @p_59)) :rule cong :premises (t281.t1.t6 t281.t1.t7))
(step t281.t1.t9 (cl @p_142) :rule equiv_simplify)
(step t281.t1.t10 (cl @p_141 @p_128) :rule equiv2 :premises (t281.t1.t9))
(step t281.t1.t11 (cl @p_132 @p_59) :rule not_not)
(step t281.t1.t12 (cl @p_141 @p_59) :rule resolution :premises (t281.t1.t10 t281.t1.t11))
(step t281.t1.t13 (cl @p_141) :rule resolution :premises (t281.t1.t12 t281.t1.a0))
(step t281.t1.t14 (cl @p_140) :rule trans :premises (t281.t1.t8 t281.t1.t13))
(step t281.t1.t15 (cl @p_126) :rule resolution :premises (t281.t1.t1 t281.t1.t14))
(step t281.t1 (cl @p_128 @p_84 @p_123 @p_126) :rule subproof :discharge (t281.t1.a0 t281.t1.a1 t281.t1.a2))
(step t281.t2 (cl (! (not @p_137) :named @p_138) @p_81) :rule and_pos :args (0))
(step t281.t3 (cl @p_138 @p_83) :rule and_pos :args (1))
(step t281.t4 (cl @p_138 @p_122) :rule and_pos :args (2))
(step t281.t5 (cl @p_126 @p_138 @p_138 @p_138) :rule resolution :premises (t281.t1 t281.t2 t281.t3 t281.t4))
(step t281.t6 (cl @p_138 @p_138 @p_138 @p_126) :rule reordering :premises (t281.t5))
(step t281.t7 (cl @p_138 @p_126) :rule contraction :premises (t281.t6))
(step t281.t8 (cl @p_139 @p_126) :rule resolution :premises (t281.t0 t281.t7))
(step t281.t9 (cl @p_139 (! (not @p_126) :named @p_130)) :rule implies_neg2)
(step t281.t10 (cl @p_139 @p_139) :rule resolution :premises (t281.t8 t281.t9))
(step t281.t11 (cl @p_139) :rule contraction :premises (t281.t10))
(step t281.t12 (cl @p_138 @p_126) :rule implies :premises (t281.t11))
(step t281.t13 (cl @p_137) :rule and_intro :premises (t281.a1 t281.a0 t188))
(step t281.t14 (cl @p_126) :rule resolution :premises (t281.t12 t281.t13))
(step t281 (cl @p_84 @p_128 @p_123 @p_126) :rule subproof :discharge (t281.a0 t281.a1 t281.a2))
(step t282 (cl (! (not @p_134) :named @p_135) @p_83) :rule and_pos :args (0))
(step t283 (cl @p_135 @p_81) :rule and_pos :args (1))
(step t284 (cl @p_135 @p_122) :rule and_pos :args (2))
(step t285 (cl @p_126 @p_135 @p_135 @p_135) :rule resolution :premises (t281 t282 t283 t284))
(step t286 (cl @p_135 @p_135 @p_135 @p_126) :rule reordering :premises (t285))
(step t287 (cl @p_135 @p_126) :rule contraction :premises (t286))
(step t288 (cl @p_136 @p_126) :rule resolution :premises (t280 t287))
(step t289 (cl @p_136 @p_130) :rule implies_neg2)
(step t290 (cl @p_136 @p_136) :rule resolution :premises (t288 t289))
(step t291 (cl @p_136) :rule contraction :premises (t290))
(step t292 (cl @p_135 @p_126) :rule implies :premises (t291))
(step t293 (cl @p_84 @p_128 @p_123 @p_126) :rule resolution :premises (t279 t292))
(step t294 (cl @p_129 @p_133) :rule or_neg :args (0))
(step t295 (cl @p_129 @p_132) :rule or_neg :args (1))
(step t296 (cl @p_129 @p_131) :rule or_neg :args (2))
(step t297 (cl @p_129 @p_130) :rule or_neg :args (3))
(step t298 (cl @p_129 @p_129 @p_129 @p_129) :rule resolution :premises (t293 t294 t295 t296 t297))
(step t299 (cl @p_129) :rule contraction :premises (t298))
(step t300 (cl @p_127) :rule resolution :premises (t276 t278 t299))
(step t301 (cl @p_84 @p_59 @p_123 @p_126) :rule or :premises (t300))
(step t302 (cl (! (and @p_83 @p_63 (! (= i_u$ (! (ui$ @p_3) :named @p_101)) :named @p_102)) :named @p_110) @p_84 @p_64 (! (not @p_102) :named @p_106)) :rule and_neg)
(step t303 (cl (! (=> @p_110 @p_109) :named @p_112) @p_110) :rule implies_neg1)
(anchor :step t304)
(assume t304.a0 @p_83)
(assume t304.a1 @p_63)
(assume t304.a2 @p_102)
(step t304.t0 (cl (! (=> (! (and @p_63 @p_83 @p_102) :named @p_114) @p_109) :named @p_116) @p_114) :rule implies_neg1)
(anchor :step t304.t1)
(assume t304.t1.a0 @p_63)
(assume t304.t1.a1 @p_83)
(assume t304.t1.a2 @p_102)
(step t304.t1.t0 (cl (= (! (= @p_109 true) :named @p_117) @p_109)) :rule equiv_simplify)
(step t304.t1.t1 (cl (not @p_117) @p_109) :rule equiv1 :premises (t304.t1.t0))
(step t304.t1.t2 (cl (or (! (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_105) @p_102)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t304.t1.t3 (cl @p_105 @p_102) :rule or :premises (t304.t1.t2))
(step t304.t1.t4 (cl (not (! (= (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v6)) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_103)) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v6))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t304.t1.t5 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t304.t1.t5.t0 (cl (= (= (! (ui$ @p_35) :named @p_104) ?v6) (= ?v6 @p_104))) :rule rare_rewrite :args ("eq-symm" @p_104 ?v6))
(step t304.t1.t5 (cl @p_103) :rule bind)
(step t304.t1.t6 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t304.t1.t4 t304.t1.t5 a9))
(step t304.t1.t7 (cl @p_102) :rule resolution :premises (t304.t1.t3 t304.t1.t6))
(step t304.t1.t8 (cl @p_120) :rule symm :premises (t304.t1.a1))
(step t304.t1.t9 (cl (= @p_101 @p_60)) :rule cong :premises (t304.t1.t8))
(step t304.t1.t10 (cl (= i_u$ @p_60)) :rule trans :premises (t304.t1.t7 t304.t1.t9))
(step t304.t1.t11 (cl (= s$ s$)) :rule refl)
(step t304.t1.t12 (cl (= @p_107 @p_61)) :rule cong :premises (t304.t1.t10 t304.t1.t11))
(step t304.t1.t13 (cl (= @quantifiers_skolemize_7 @quantifiers_skolemize_7)) :rule refl)
(step t304.t1.t14 (cl (= @p_108 @p_62)) :rule cong :premises (t304.t1.t12 t304.t1.t13))
(step t304.t1.t15 (cl (= @quantifiers_skolemize_3 @quantifiers_skolemize_3)) :rule refl)
(step t304.t1.t16 (cl (= @p_109 @p_63)) :rule cong :premises (t304.t1.t14 t304.t1.t15))
(step t304.t1.t17 (cl (! (= (! (= @p_63 true) :named @p_118) @p_63) :named @p_119)) :rule equiv_simplify)
(step t304.t1.t18 (cl @p_118 @p_64) :rule equiv2 :premises (t304.t1.t17))
(step t304.t1.t19 (cl @p_118) :rule resolution :premises (t304.t1.t18 t304.t1.a0))
(step t304.t1.t20 (cl @p_117) :rule trans :premises (t304.t1.t16 t304.t1.t19))
(step t304.t1.t21 (cl @p_109) :rule resolution :premises (t304.t1.t1 t304.t1.t20))
(step t304.t1 (cl @p_64 @p_84 @p_106 @p_109) :rule subproof :discharge (t304.t1.a0 t304.t1.a1 t304.t1.a2))
(step t304.t2 (cl (! (not @p_114) :named @p_115) @p_63) :rule and_pos :args (0))
(step t304.t3 (cl @p_115 @p_83) :rule and_pos :args (1))
(step t304.t4 (cl @p_115 @p_102) :rule and_pos :args (2))
(step t304.t5 (cl @p_109 @p_115 @p_115 @p_115) :rule resolution :premises (t304.t1 t304.t2 t304.t3 t304.t4))
(step t304.t6 (cl @p_115 @p_115 @p_115 @p_109) :rule reordering :premises (t304.t5))
(step t304.t7 (cl @p_115 @p_109) :rule contraction :premises (t304.t6))
(step t304.t8 (cl @p_116 @p_109) :rule resolution :premises (t304.t0 t304.t7))
(step t304.t9 (cl @p_116 @p_113) :rule implies_neg2)
(step t304.t10 (cl @p_116 @p_116) :rule resolution :premises (t304.t8 t304.t9))
(step t304.t11 (cl @p_116) :rule contraction :premises (t304.t10))
(step t304.t12 (cl @p_115 @p_109) :rule implies :premises (t304.t11))
(step t304.t13 (cl (or @p_105 @p_102)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t304.t14 (cl @p_105 @p_102) :rule or :premises (t304.t13))
(step t304.t15 (cl (not @p_103) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v6))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t304.t16 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t304.t16.t0 (cl (= (= @p_104 ?v6) (= ?v6 @p_104))) :rule rare_rewrite :args ("eq-symm" @p_104 ?v6))
(step t304.t16 (cl @p_103) :rule bind)
(step t304.t17 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t304.t15 t304.t16 a9))
(step t304.t18 (cl @p_102) :rule resolution :premises (t304.t14 t304.t17))
(step t304.t19 (cl @p_114) :rule and_intro :premises (t304.a1 t304.a0 t304.t18))
(step t304.t20 (cl @p_109) :rule resolution :premises (t304.t12 t304.t19))
(step t304 (cl @p_84 @p_64 @p_106 @p_109) :rule subproof :discharge (t304.a0 t304.a1 t304.a2))
(step t305 (cl (! (not @p_110) :named @p_111) @p_83) :rule and_pos :args (0))
(step t306 (cl @p_111 @p_63) :rule and_pos :args (1))
(step t307 (cl @p_111 @p_102) :rule and_pos :args (2))
(step t308 (cl @p_109 @p_111 @p_111 @p_111) :rule resolution :premises (t304 t305 t306 t307))
(step t309 (cl @p_111 @p_111 @p_111 @p_109) :rule reordering :premises (t308))
(step t310 (cl @p_111 @p_109) :rule contraction :premises (t309))
(step t311 (cl @p_112 @p_109) :rule resolution :premises (t303 t310))
(step t312 (cl @p_112 @p_113) :rule implies_neg2)
(step t313 (cl @p_112 @p_112) :rule resolution :premises (t311 t312))
(step t314 (cl @p_112) :rule contraction :premises (t313))
(step t315 (cl @p_111 @p_109) :rule implies :premises (t314))
(step t316 (cl @p_84 @p_64 @p_106 @p_109) :rule resolution :premises (t302 t315))
(step t317 (cl (or @p_105 @p_102)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t318 (cl @p_105 @p_102) :rule or :premises (t317))
(step t319 (cl (not @p_103) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v6))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t320 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t320.t0 (cl (= (= @p_104 ?v6) (= ?v6 @p_104))) :rule rare_rewrite :args ("eq-symm" @p_104 ?v6))
(step t320 (cl @p_103) :rule bind)
(step t321 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v6 (ui$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t319 t320 a9))
(step t322 (cl @p_102) :rule resolution :premises (t318 t321))
(step t323 (cl (! (and @p_83 @p_69 (! (= b_u$ (! (ub$ @p_3) :named @p_85)) :named @p_86)) :named @p_94) @p_84 @p_70 (! (not @p_86) :named @p_90)) :rule and_neg)
(step t324 (cl (! (=> @p_94 @p_93) :named @p_96) @p_94) :rule implies_neg1)
(anchor :step t325)
(assume t325.a0 @p_83)
(assume t325.a1 @p_69)
(assume t325.a2 @p_86)
(step t325.t0 (cl (! (=> (! (and @p_86 @p_83 @p_69) :named @p_98) @p_93) :named @p_100) @p_98) :rule implies_neg1)
(anchor :step t325.t1)
(assume t325.t1.a0 @p_86)
(assume t325.t1.a1 @p_83)
(assume t325.t1.a2 @p_69)
(step t325.t1.t0 (cl (= @p_65 @p_85)) :rule cong :premises (t325.t1.a1))
(step t325.t1.t1 (cl (or (! (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_89) @p_86)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t325.t1.t2 (cl @p_89 @p_86) :rule or :premises (t325.t1.t1))
(step t325.t1.t3 (cl (not (! (= (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v4)) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :named @p_87)) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v4))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t325.t1.t4 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t325.t1.t4.t0 (cl (= (= (! (ub$ @p_35) :named @p_88) ?v4) (= ?v4 @p_88))) :rule rare_rewrite :args ("eq-symm" @p_88 ?v4))
(step t325.t1.t4 (cl @p_87) :rule bind)
(step t325.t1.t5 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t325.t1.t3 t325.t1.t4 a7))
(step t325.t1.t6 (cl @p_86) :rule resolution :premises (t325.t1.t2 t325.t1.t5))
(step t325.t1.t7 (cl (= @p_85 b_u$)) :rule symm :premises (t325.t1.t6))
(step t325.t1.t8 (cl (= @p_65 b_u$)) :rule trans :premises (t325.t1.t0 t325.t1.t7))
(step t325.t1.t9 (cl (= s$ s$)) :rule refl)
(step t325.t1.t10 (cl (= @p_66 @p_91)) :rule cong :premises (t325.t1.t8 t325.t1.t9))
(step t325.t1.t11 (cl (= @quantifiers_skolemize_7 @quantifiers_skolemize_7)) :rule refl)
(step t325.t1.t12 (cl (= @p_67 @p_92)) :rule cong :premises (t325.t1.t10 t325.t1.t11))
(step t325.t1.t13 (cl @p_93) :rule trans :premises (t325.t1.a2 t325.t1.t12))
(step t325.t1 (cl @p_90 @p_84 @p_70 @p_93) :rule subproof :discharge (t325.t1.a0 t325.t1.a1 t325.t1.a2))
(step t325.t2 (cl (! (not @p_98) :named @p_99) @p_86) :rule and_pos :args (0))
(step t325.t3 (cl @p_99 @p_83) :rule and_pos :args (1))
(step t325.t4 (cl @p_99 @p_69) :rule and_pos :args (2))
(step t325.t5 (cl @p_93 @p_99 @p_99 @p_99) :rule resolution :premises (t325.t1 t325.t2 t325.t3 t325.t4))
(step t325.t6 (cl @p_99 @p_99 @p_99 @p_93) :rule reordering :premises (t325.t5))
(step t325.t7 (cl @p_99 @p_93) :rule contraction :premises (t325.t6))
(step t325.t8 (cl @p_100 @p_93) :rule resolution :premises (t325.t0 t325.t7))
(step t325.t9 (cl @p_100 @p_97) :rule implies_neg2)
(step t325.t10 (cl @p_100 @p_100) :rule resolution :premises (t325.t8 t325.t9))
(step t325.t11 (cl @p_100) :rule contraction :premises (t325.t10))
(step t325.t12 (cl @p_99 @p_93) :rule implies :premises (t325.t11))
(step t325.t13 (cl (or @p_89 @p_86)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t325.t14 (cl @p_89 @p_86) :rule or :premises (t325.t13))
(step t325.t15 (cl (not @p_87) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v4))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t325.t16 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t325.t16.t0 (cl (= (= @p_88 ?v4) (= ?v4 @p_88))) :rule rare_rewrite :args ("eq-symm" @p_88 ?v4))
(step t325.t16 (cl @p_87) :rule bind)
(step t325.t17 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t325.t15 t325.t16 a7))
(step t325.t18 (cl @p_86) :rule resolution :premises (t325.t14 t325.t17))
(step t325.t19 (cl @p_98) :rule and_intro :premises (t325.t18 t325.a0 t325.a1))
(step t325.t20 (cl @p_93) :rule resolution :premises (t325.t12 t325.t19))
(step t325 (cl @p_84 @p_70 @p_90 @p_93) :rule subproof :discharge (t325.a0 t325.a1 t325.a2))
(step t326 (cl (! (not @p_94) :named @p_95) @p_83) :rule and_pos :args (0))
(step t327 (cl @p_95 @p_69) :rule and_pos :args (1))
(step t328 (cl @p_95 @p_86) :rule and_pos :args (2))
(step t329 (cl @p_93 @p_95 @p_95 @p_95) :rule resolution :premises (t325 t326 t327 t328))
(step t330 (cl @p_95 @p_95 @p_95 @p_93) :rule reordering :premises (t329))
(step t331 (cl @p_95 @p_93) :rule contraction :premises (t330))
(step t332 (cl @p_96 @p_93) :rule resolution :premises (t324 t331))
(step t333 (cl @p_96 @p_97) :rule implies_neg2)
(step t334 (cl @p_96 @p_96) :rule resolution :premises (t332 t333))
(step t335 (cl @p_96) :rule contraction :premises (t334))
(step t336 (cl @p_95 @p_93) :rule implies :premises (t335))
(step t337 (cl @p_84 @p_70 @p_90 @p_93) :rule resolution :premises (t323 t336))
(step t338 (cl (or @p_89 @p_86)) :rule forall_inst :args (less$ b_i_l$ b_i_u$ b_l$ b_u$ i_l$ i_u$ b_i_u_update$ leq$ geq$ less_eq$))
(step t339 (cl @p_89 @p_86) :rule or :premises (t338))
(step t340 (cl (not @p_87) (not (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10)) ?v4))) (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule equiv_pos2)
(anchor :step t341 :args ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$) (:= (?v0 A_a_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_nat_i_a_prod_mapping_fun$) ?v1) (:= (?v2 I_a_state_nat_i_a_prod_mapping_fun$) ?v2) (:= (?v3 I_a_state_nat_a_option_fun_fun$) ?v3) (:= (?v4 I_a_state_nat_a_option_fun_fun$) ?v4) (:= (?v5 I_a_state_nat_i_fun_fun$) ?v5) (:= (?v6 I_a_state_nat_i_fun_fun$) ?v6) (:= (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) ?v7) (:= (?v8 Nat_a_a_atom_fun_fun$) ?v8) (:= (?v9 Nat_a_a_atom_fun_fun$) ?v9) (:= (?v10 Rat_rat_bool_fun_fun$) ?v10)))
(step t341.t0 (cl (= (= @p_88 ?v4) (= ?v4 @p_88))) :rule rare_rewrite :args ("eq-symm" @p_88 ?v4))
(step t341 (cl @p_87) :rule bind)
(step t342 (cl (forall ((?v0 A_a_bool_fun_fun$) (?v1 I_a_state_nat_i_a_prod_mapping_fun$) (?v2 I_a_state_nat_i_a_prod_mapping_fun$) (?v3 I_a_state_nat_a_option_fun_fun$) (?v4 I_a_state_nat_a_option_fun_fun$) (?v5 I_a_state_nat_i_fun_fun$) (?v6 I_a_state_nat_i_fun_fun$) (?v7 Nat_i_a_prod_mapping_nat_i_a_prod_mapping_fun_i_a_state_i_a_state_fun_fun$) (?v8 Nat_a_a_atom_fun_fun$) (?v9 Nat_a_a_atom_fun_fun$) (?v10 Rat_rat_bool_fun_fun$)) (= ?v4 (ub$ (direction$ ?v0 ?v1 ?v2 ?v3 ?v4 ?v5 ?v6 ?v7 ?v8 ?v9 ?v10))))) :rule resolution :premises (t340 t341 a7))
(step t343 (cl @p_86) :rule resolution :premises (t339 t342))
(step t344 (cl @p_71 (not @p_57)) :rule or_neg :args (3))
(step t345 (cl @p_71 @p_81) :rule or_neg :args (2))
(step t346 (cl (not (! (= (! (or @p_71 (! (not @p_64) :named @p_78)) :named @p_79) (! (or @p_71 @p_63) :named @p_77)) :named @p_80)) (not @p_79) @p_77) :rule equiv_pos2)
(step t347 (cl (= @p_78 @p_63)) :rule rare_rewrite :args ("bool-double-not-elim" @p_63))
(step t348 (cl @p_80) :rule cong :premises (t347))
(step t349 (cl @p_71 @p_78) :rule or_neg :args (1))
(step t350 (cl @p_79 @p_75) :rule or_neg :args (0))
(step t351 (cl @p_79 (not @p_78)) :rule or_neg :args (1))
(step t352 (cl @p_79 @p_79) :rule resolution :premises (t349 t350 t351))
(step t353 (cl @p_79) :rule contraction :premises (t352))
(step t354 (cl @p_77) :rule resolution :premises (t346 t348 t353))
(step t355 (cl @p_71 @p_63) :rule or :premises (t354))
(step t356 (cl @p_63 @p_71) :rule reordering :premises (t355))
(step t357 (cl (not (! (= (! (or @p_71 (! (not @p_70) :named @p_73)) :named @p_74) (! (or @p_71 @p_69) :named @p_72)) :named @p_76)) (not @p_74) @p_72) :rule equiv_pos2)
(step t358 (cl (= @p_73 @p_69)) :rule rare_rewrite :args ("bool-double-not-elim" @p_69))
(step t359 (cl @p_76) :rule cong :premises (t358))
(step t360 (cl @p_71 @p_73) :rule or_neg :args (0))
(step t361 (cl @p_74 @p_75) :rule or_neg :args (0))
(step t362 (cl @p_74 (not @p_73)) :rule or_neg :args (1))
(step t363 (cl @p_74 @p_74) :rule resolution :premises (t360 t361 t362))
(step t364 (cl @p_74) :rule contraction :premises (t363))
(step t365 (cl @p_72) :rule resolution :premises (t357 t359 t364))
(step t366 (cl @p_71 @p_69) :rule or :premises (t365))
(step t367 (cl @p_69 @p_71) :rule reordering :premises (t366))
(step t368 (cl @p_84 @p_71) :rule resolution :premises (t255 t275 t301 t188 t316 t322 t337 t343 t344 t345 t356 t367))
(step t369 (cl @p_84) :rule resolution :premises (t132 t157 t185 t188 t203 t209 t224 t230 t4 t231 t242 t253 t5 t30 t368))
(step t370 (cl @p_82) :rule resolution :premises (t130 t369))
(step t371 (cl (! (and @p_82 @p_63 (! (= i_l$ (! (ui$ @p_1) :named @p_377)) :named @p_378)) :named @p_382) @p_366 @p_64 (! (not @p_378) :named @p_379)) :rule and_neg)
(step t372 (cl (! (=> @p_382 @p_381) :named @p_384) @p_382) :rule implies_neg1)
(anchor :step t373)
(assume t373.a0 @p_82)
(assume t373.a1 @p_63)
(assume t373.a2 @p_378)
(step t373.t0 (cl (! (=> (! (and @p_63 @p_82 @p_378) :named @p_386) @p_381) :named @p_388) @p_386) :rule implies_neg1)
(anchor :step t373.t1)
(assume t373.t1.a0 @p_63)
(assume t373.t1.a1 @p_82)
(assume t373.t1.a2 @p_378)
(step t373.t1.t0 (cl (= (! (= @p_381 true) :named @p_389) @p_381)) :rule equiv_simplify)
(step t373.t1.t1 (cl (not @p_389) @p_381) :rule equiv1 :premises (t373.t1.t0))
(step t373.t1.t2 (cl (or @p_105 @p_378)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t373.t1.t3 (cl @p_105 @p_378) :rule or :premises (t373.t1.t2))
(step t373.t1.t4 (cl @p_378) :rule resolution :premises (t373.t1.t3 t321))
(step t373.t1.t5 (cl @p_390) :rule symm :premises (t373.t1.a1))
(step t373.t1.t6 (cl (= @p_377 @p_60)) :rule cong :premises (t373.t1.t5))
(step t373.t1.t7 (cl (= i_l$ @p_60)) :rule trans :premises (t373.t1.t4 t373.t1.t6))
(step t373.t1.t8 (cl (= s$ s$)) :rule refl)
(step t373.t1.t9 (cl (= @p_149 @p_61)) :rule cong :premises (t373.t1.t7 t373.t1.t8))
(step t373.t1.t10 (cl (= @quantifiers_skolemize_7 @quantifiers_skolemize_7)) :rule refl)
(step t373.t1.t11 (cl (= @p_380 @p_62)) :rule cong :premises (t373.t1.t9 t373.t1.t10))
(step t373.t1.t12 (cl (= @quantifiers_skolemize_3 @quantifiers_skolemize_3)) :rule refl)
(step t373.t1.t13 (cl (= @p_381 @p_63)) :rule cong :premises (t373.t1.t11 t373.t1.t12))
(step t373.t1.t14 (cl @p_119) :rule equiv_simplify)
(step t373.t1.t15 (cl @p_118 @p_64) :rule equiv2 :premises (t373.t1.t14))
(step t373.t1.t16 (cl @p_118) :rule resolution :premises (t373.t1.t15 t373.t1.a0))
(step t373.t1.t17 (cl @p_389) :rule trans :premises (t373.t1.t13 t373.t1.t16))
(step t373.t1.t18 (cl @p_381) :rule resolution :premises (t373.t1.t1 t373.t1.t17))
(step t373.t1 (cl @p_64 @p_366 @p_379 @p_381) :rule subproof :discharge (t373.t1.a0 t373.t1.a1 t373.t1.a2))
(step t373.t2 (cl (! (not @p_386) :named @p_387) @p_63) :rule and_pos :args (0))
(step t373.t3 (cl @p_387 @p_82) :rule and_pos :args (1))
(step t373.t4 (cl @p_387 @p_378) :rule and_pos :args (2))
(step t373.t5 (cl @p_381 @p_387 @p_387 @p_387) :rule resolution :premises (t373.t1 t373.t2 t373.t3 t373.t4))
(step t373.t6 (cl @p_387 @p_387 @p_387 @p_381) :rule reordering :premises (t373.t5))
(step t373.t7 (cl @p_387 @p_381) :rule contraction :premises (t373.t6))
(step t373.t8 (cl @p_388 @p_381) :rule resolution :premises (t373.t0 t373.t7))
(step t373.t9 (cl @p_388 @p_385) :rule implies_neg2)
(step t373.t10 (cl @p_388 @p_388) :rule resolution :premises (t373.t8 t373.t9))
(step t373.t11 (cl @p_388) :rule contraction :premises (t373.t10))
(step t373.t12 (cl @p_387 @p_381) :rule implies :premises (t373.t11))
(step t373.t13 (cl (or @p_105 @p_378)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t373.t14 (cl @p_105 @p_378) :rule or :premises (t373.t13))
(step t373.t15 (cl @p_378) :rule resolution :premises (t373.t14 t321))
(step t373.t16 (cl @p_386) :rule and_intro :premises (t373.a1 t373.a0 t373.t15))
(step t373.t17 (cl @p_381) :rule resolution :premises (t373.t12 t373.t16))
(step t373 (cl @p_366 @p_64 @p_379 @p_381) :rule subproof :discharge (t373.a0 t373.a1 t373.a2))
(step t374 (cl (! (not @p_382) :named @p_383) @p_82) :rule and_pos :args (0))
(step t375 (cl @p_383 @p_63) :rule and_pos :args (1))
(step t376 (cl @p_383 @p_378) :rule and_pos :args (2))
(step t377 (cl @p_381 @p_383 @p_383 @p_383) :rule resolution :premises (t373 t374 t375 t376))
(step t378 (cl @p_383 @p_383 @p_383 @p_381) :rule reordering :premises (t377))
(step t379 (cl @p_383 @p_381) :rule contraction :premises (t378))
(step t380 (cl @p_384 @p_381) :rule resolution :premises (t372 t379))
(step t381 (cl @p_384 @p_385) :rule implies_neg2)
(step t382 (cl @p_384 @p_384) :rule resolution :premises (t380 t381))
(step t383 (cl @p_384) :rule contraction :premises (t382))
(step t384 (cl @p_383 @p_381) :rule implies :premises (t383))
(step t385 (cl @p_366 @p_64 @p_379 @p_381) :rule resolution :premises (t371 t384))
(step t386 (cl (or @p_105 @p_378)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t387 (cl @p_105 @p_378) :rule or :premises (t386))
(step t388 (cl @p_378) :rule resolution :premises (t387 t321))
(step t389 (cl (! (and @p_82 @p_69 (! (= b_l$ (! (ub$ @p_1) :named @p_364)) :named @p_365)) :named @p_370) @p_366 @p_70 (! (not @p_365) :named @p_367)) :rule and_neg)
(step t390 (cl (! (=> @p_370 @p_369) :named @p_372) @p_370) :rule implies_neg1)
(anchor :step t391)
(assume t391.a0 @p_82)
(assume t391.a1 @p_69)
(assume t391.a2 @p_365)
(step t391.t0 (cl (! (=> (! (and @p_365 @p_82 @p_69) :named @p_374) @p_369) :named @p_376) @p_374) :rule implies_neg1)
(anchor :step t391.t1)
(assume t391.t1.a0 @p_365)
(assume t391.t1.a1 @p_82)
(assume t391.t1.a2 @p_69)
(step t391.t1.t0 (cl (= @p_65 @p_364)) :rule cong :premises (t391.t1.a1))
(step t391.t1.t1 (cl (or @p_89 @p_365)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t391.t1.t2 (cl @p_89 @p_365) :rule or :premises (t391.t1.t1))
(step t391.t1.t3 (cl @p_365) :rule resolution :premises (t391.t1.t2 t342))
(step t391.t1.t4 (cl (= @p_364 b_l$)) :rule symm :premises (t391.t1.t3))
(step t391.t1.t5 (cl (= @p_65 b_l$)) :rule trans :premises (t391.t1.t0 t391.t1.t4))
(step t391.t1.t6 (cl (= s$ s$)) :rule refl)
(step t391.t1.t7 (cl (= @p_66 @p_153)) :rule cong :premises (t391.t1.t5 t391.t1.t6))
(step t391.t1.t8 (cl (= @quantifiers_skolemize_7 @quantifiers_skolemize_7)) :rule refl)
(step t391.t1.t9 (cl (= @p_67 @p_368)) :rule cong :premises (t391.t1.t7 t391.t1.t8))
(step t391.t1.t10 (cl @p_369) :rule trans :premises (t391.t1.a2 t391.t1.t9))
(step t391.t1 (cl @p_367 @p_366 @p_70 @p_369) :rule subproof :discharge (t391.t1.a0 t391.t1.a1 t391.t1.a2))
(step t391.t2 (cl (! (not @p_374) :named @p_375) @p_365) :rule and_pos :args (0))
(step t391.t3 (cl @p_375 @p_82) :rule and_pos :args (1))
(step t391.t4 (cl @p_375 @p_69) :rule and_pos :args (2))
(step t391.t5 (cl @p_369 @p_375 @p_375 @p_375) :rule resolution :premises (t391.t1 t391.t2 t391.t3 t391.t4))
(step t391.t6 (cl @p_375 @p_375 @p_375 @p_369) :rule reordering :premises (t391.t5))
(step t391.t7 (cl @p_375 @p_369) :rule contraction :premises (t391.t6))
(step t391.t8 (cl @p_376 @p_369) :rule resolution :premises (t391.t0 t391.t7))
(step t391.t9 (cl @p_376 @p_373) :rule implies_neg2)
(step t391.t10 (cl @p_376 @p_376) :rule resolution :premises (t391.t8 t391.t9))
(step t391.t11 (cl @p_376) :rule contraction :premises (t391.t10))
(step t391.t12 (cl @p_375 @p_369) :rule implies :premises (t391.t11))
(step t391.t13 (cl (or @p_89 @p_365)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t391.t14 (cl @p_89 @p_365) :rule or :premises (t391.t13))
(step t391.t15 (cl @p_365) :rule resolution :premises (t391.t14 t342))
(step t391.t16 (cl @p_374) :rule and_intro :premises (t391.t15 t391.a0 t391.a1))
(step t391.t17 (cl @p_369) :rule resolution :premises (t391.t12 t391.t16))
(step t391 (cl @p_366 @p_70 @p_367 @p_369) :rule subproof :discharge (t391.a0 t391.a1 t391.a2))
(step t392 (cl (! (not @p_370) :named @p_371) @p_82) :rule and_pos :args (0))
(step t393 (cl @p_371 @p_69) :rule and_pos :args (1))
(step t394 (cl @p_371 @p_365) :rule and_pos :args (2))
(step t395 (cl @p_369 @p_371 @p_371 @p_371) :rule resolution :premises (t391 t392 t393 t394))
(step t396 (cl @p_371 @p_371 @p_371 @p_369) :rule reordering :premises (t395))
(step t397 (cl @p_371 @p_369) :rule contraction :premises (t396))
(step t398 (cl @p_372 @p_369) :rule resolution :premises (t390 t397))
(step t399 (cl @p_372 @p_373) :rule implies_neg2)
(step t400 (cl @p_372 @p_372) :rule resolution :premises (t398 t399))
(step t401 (cl @p_372) :rule contraction :premises (t400))
(step t402 (cl @p_371 @p_369) :rule implies :premises (t401))
(step t403 (cl @p_366 @p_70 @p_367 @p_369) :rule resolution :premises (t389 t402))
(step t404 (cl (or @p_89 @p_365)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t405 (cl @p_89 @p_365) :rule or :premises (t404))
(step t406 (cl @p_365) :rule resolution :premises (t405 t342))
(step t407 (cl @p_71) :rule resolution :premises (t32 t35 t37 t93 t121 t127 t370 t385 t388 t370 t403 t406 t370 t344 t345 t356 t367))
(step t408 (cl @p_55) :rule resolution :premises (t5 t30 t407))
(step t409 (cl @p_303) :rule resolution :premises (t4 t408))
(step t410 (cl (! (and @p_82 @p_52 (! (= b_u$ (! (lb$ @p_1) :named @p_449)) :named @p_450)) :named @p_452) @p_366 @p_53 (! (not @p_450) :named @p_451)) :rule and_neg)
(step t411 (cl (! (=> @p_452 @p_351) :named @p_454) @p_452) :rule implies_neg1)
(anchor :step t412)
(assume t412.a0 @p_82)
(assume t412.a1 @p_52)
(assume t412.a2 @p_450)
(step t412.t0 (cl (! (=> (! (and @p_450 @p_82 @p_52) :named @p_455) @p_351) :named @p_457) @p_455) :rule implies_neg1)
(anchor :step t412.t1)
(assume t412.t1.a0 @p_450)
(assume t412.t1.a1 @p_82)
(assume t412.t1.a2 @p_52)
(step t412.t1.t0 (cl (= @p_48 @p_449)) :rule cong :premises (t412.t1.a1))
(step t412.t1.t1 (cl (or @p_308 @p_450)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t412.t1.t2 (cl @p_308 @p_450) :rule or :premises (t412.t1.t1))
(step t412.t1.t3 (cl @p_450) :rule resolution :premises (t412.t1.t2 t229))
(step t412.t1.t4 (cl (= @p_449 b_u$)) :rule symm :premises (t412.t1.t3))
(step t412.t1.t5 (cl (= @p_48 b_u$)) :rule trans :premises (t412.t1.t0 t412.t1.t4))
(step t412.t1.t6 (cl (= s$ s$)) :rule refl)
(step t412.t1.t7 (cl (= @p_49 @p_91)) :rule cong :premises (t412.t1.t5 t412.t1.t6))
(step t412.t1.t8 (cl (= @quantifiers_skolemize_5 @quantifiers_skolemize_5)) :rule refl)
(step t412.t1.t9 (cl (= @p_50 @p_350)) :rule cong :premises (t412.t1.t7 t412.t1.t8))
(step t412.t1.t10 (cl @p_351) :rule trans :premises (t412.t1.a2 t412.t1.t9))
(step t412.t1 (cl @p_451 @p_366 @p_53 @p_351) :rule subproof :discharge (t412.t1.a0 t412.t1.a1 t412.t1.a2))
(step t412.t2 (cl (! (not @p_455) :named @p_456) @p_450) :rule and_pos :args (0))
(step t412.t3 (cl @p_456 @p_82) :rule and_pos :args (1))
(step t412.t4 (cl @p_456 @p_52) :rule and_pos :args (2))
(step t412.t5 (cl @p_351 @p_456 @p_456 @p_456) :rule resolution :premises (t412.t1 t412.t2 t412.t3 t412.t4))
(step t412.t6 (cl @p_456 @p_456 @p_456 @p_351) :rule reordering :premises (t412.t5))
(step t412.t7 (cl @p_456 @p_351) :rule contraction :premises (t412.t6))
(step t412.t8 (cl @p_457 @p_351) :rule resolution :premises (t412.t0 t412.t7))
(step t412.t9 (cl @p_457 @p_352) :rule implies_neg2)
(step t412.t10 (cl @p_457 @p_457) :rule resolution :premises (t412.t8 t412.t9))
(step t412.t11 (cl @p_457) :rule contraction :premises (t412.t10))
(step t412.t12 (cl @p_456 @p_351) :rule implies :premises (t412.t11))
(step t412.t13 (cl (or @p_308 @p_450)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t412.t14 (cl @p_308 @p_450) :rule or :premises (t412.t13))
(step t412.t15 (cl @p_450) :rule resolution :premises (t412.t14 t229))
(step t412.t16 (cl @p_455) :rule and_intro :premises (t412.t15 t412.a0 t412.a1))
(step t412.t17 (cl @p_351) :rule resolution :premises (t412.t12 t412.t16))
(step t412 (cl @p_366 @p_53 @p_451 @p_351) :rule subproof :discharge (t412.a0 t412.a1 t412.a2))
(step t413 (cl (! (not @p_452) :named @p_453) @p_82) :rule and_pos :args (0))
(step t414 (cl @p_453 @p_52) :rule and_pos :args (1))
(step t415 (cl @p_453 @p_450) :rule and_pos :args (2))
(step t416 (cl @p_351 @p_453 @p_453 @p_453) :rule resolution :premises (t412 t413 t414 t415))
(step t417 (cl @p_453 @p_453 @p_453 @p_351) :rule reordering :premises (t416))
(step t418 (cl @p_453 @p_351) :rule contraction :premises (t417))
(step t419 (cl @p_454 @p_351) :rule resolution :premises (t411 t418))
(step t420 (cl @p_454 @p_352) :rule implies_neg2)
(step t421 (cl @p_454 @p_454) :rule resolution :premises (t419 t420))
(step t422 (cl @p_454) :rule contraction :premises (t421))
(step t423 (cl @p_453 @p_351) :rule implies :premises (t422))
(step t424 (cl @p_366 @p_53 @p_451 @p_351) :rule resolution :premises (t410 t423))
(step t425 (cl @p_366 @p_53 @p_351 @p_451) :rule reordering :premises (t424))
(step t426 (cl @p_52) :rule resolution :premises (t253 t408))
(step t427 (cl (or @p_308 @p_450)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t428 (cl @p_308 @p_450) :rule or :premises (t427))
(step t429 (cl @p_450) :rule resolution :premises (t428 t229))
(step t430 (cl @p_351) :rule resolution :premises (t425 t370 t426 t429))
(step t431 (cl (! (and @p_82 @p_46 (! (= i_u$ (! (li$ @p_1) :named @p_439)) :named @p_440)) :named @p_442) @p_366 @p_47 (! (not @p_440) :named @p_441)) :rule and_neg)
(step t432 (cl (! (=> @p_442 @p_348) :named @p_444) @p_442) :rule implies_neg1)
(anchor :step t433)
(assume t433.a0 @p_82)
(assume t433.a1 @p_46)
(assume t433.a2 @p_440)
(step t433.t0 (cl (! (=> (! (and @p_46 @p_82 @p_440) :named @p_445) @p_348) :named @p_447) @p_445) :rule implies_neg1)
(anchor :step t433.t1)
(assume t433.t1.a0 @p_46)
(assume t433.t1.a1 @p_82)
(assume t433.t1.a2 @p_440)
(step t433.t1.t0 (cl (= (! (= @p_348 true) :named @p_448) @p_348)) :rule equiv_simplify)
(step t433.t1.t1 (cl (not @p_448) @p_348) :rule equiv1 :premises (t433.t1.t0))
(step t433.t1.t2 (cl (or @p_320 @p_440)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t433.t1.t3 (cl @p_320 @p_440) :rule or :premises (t433.t1.t2))
(step t433.t1.t4 (cl @p_440) :rule resolution :premises (t433.t1.t3 t208))
(step t433.t1.t5 (cl @p_390) :rule symm :premises (t433.t1.a1))
(step t433.t1.t6 (cl (= @p_439 @p_43)) :rule cong :premises (t433.t1.t5))
(step t433.t1.t7 (cl (= i_u$ @p_43)) :rule trans :premises (t433.t1.t4 t433.t1.t6))
(step t433.t1.t8 (cl (= s$ s$)) :rule refl)
(step t433.t1.t9 (cl (= @p_107 @p_44)) :rule cong :premises (t433.t1.t7 t433.t1.t8))
(step t433.t1.t10 (cl (= @quantifiers_skolemize_5 @quantifiers_skolemize_5)) :rule refl)
(step t433.t1.t11 (cl (= @p_347 @p_45)) :rule cong :premises (t433.t1.t9 t433.t1.t10))
(step t433.t1.t12 (cl (= @quantifiers_skolemize_3 @quantifiers_skolemize_3)) :rule refl)
(step t433.t1.t13 (cl (= @p_348 @p_46)) :rule cong :premises (t433.t1.t11 t433.t1.t12))
(step t433.t1.t14 (cl @p_330) :rule equiv_simplify)
(step t433.t1.t15 (cl @p_329 @p_47) :rule equiv2 :premises (t433.t1.t14))
(step t433.t1.t16 (cl @p_329) :rule resolution :premises (t433.t1.t15 t433.t1.a0))
(step t433.t1.t17 (cl @p_448) :rule trans :premises (t433.t1.t13 t433.t1.t16))
(step t433.t1.t18 (cl @p_348) :rule resolution :premises (t433.t1.t1 t433.t1.t17))
(step t433.t1 (cl @p_47 @p_366 @p_441 @p_348) :rule subproof :discharge (t433.t1.a0 t433.t1.a1 t433.t1.a2))
(step t433.t2 (cl (! (not @p_445) :named @p_446) @p_46) :rule and_pos :args (0))
(step t433.t3 (cl @p_446 @p_82) :rule and_pos :args (1))
(step t433.t4 (cl @p_446 @p_440) :rule and_pos :args (2))
(step t433.t5 (cl @p_348 @p_446 @p_446 @p_446) :rule resolution :premises (t433.t1 t433.t2 t433.t3 t433.t4))
(step t433.t6 (cl @p_446 @p_446 @p_446 @p_348) :rule reordering :premises (t433.t5))
(step t433.t7 (cl @p_446 @p_348) :rule contraction :premises (t433.t6))
(step t433.t8 (cl @p_447 @p_348) :rule resolution :premises (t433.t0 t433.t7))
(step t433.t9 (cl @p_447 @p_349) :rule implies_neg2)
(step t433.t10 (cl @p_447 @p_447) :rule resolution :premises (t433.t8 t433.t9))
(step t433.t11 (cl @p_447) :rule contraction :premises (t433.t10))
(step t433.t12 (cl @p_446 @p_348) :rule implies :premises (t433.t11))
(step t433.t13 (cl (or @p_320 @p_440)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t433.t14 (cl @p_320 @p_440) :rule or :premises (t433.t13))
(step t433.t15 (cl @p_440) :rule resolution :premises (t433.t14 t208))
(step t433.t16 (cl @p_445) :rule and_intro :premises (t433.a1 t433.a0 t433.t15))
(step t433.t17 (cl @p_348) :rule resolution :premises (t433.t12 t433.t16))
(step t433 (cl @p_366 @p_47 @p_441 @p_348) :rule subproof :discharge (t433.a0 t433.a1 t433.a2))
(step t434 (cl (! (not @p_442) :named @p_443) @p_82) :rule and_pos :args (0))
(step t435 (cl @p_443 @p_46) :rule and_pos :args (1))
(step t436 (cl @p_443 @p_440) :rule and_pos :args (2))
(step t437 (cl @p_348 @p_443 @p_443 @p_443) :rule resolution :premises (t433 t434 t435 t436))
(step t438 (cl @p_443 @p_443 @p_443 @p_348) :rule reordering :premises (t437))
(step t439 (cl @p_443 @p_348) :rule contraction :premises (t438))
(step t440 (cl @p_444 @p_348) :rule resolution :premises (t432 t439))
(step t441 (cl @p_444 @p_349) :rule implies_neg2)
(step t442 (cl @p_444 @p_444) :rule resolution :premises (t440 t441))
(step t443 (cl @p_444) :rule contraction :premises (t442))
(step t444 (cl @p_443 @p_348) :rule implies :premises (t443))
(step t445 (cl @p_366 @p_47 @p_441 @p_348) :rule resolution :premises (t431 t444))
(step t446 (cl @p_366 @p_47 @p_348 @p_441) :rule reordering :premises (t445))
(step t447 (cl @p_46) :rule resolution :premises (t242 t408))
(step t448 (cl (or @p_320 @p_440)) :rule forall_inst :args (uu$ b_i_u$ b_i_l$ b_u$ b_l$ i_u$ i_l$ b_i_l_update$ geq$ leq$ uua$))
(step t449 (cl @p_320 @p_440) :rule or :premises (t448))
(step t450 (cl @p_440) :rule resolution :premises (t449 t208))
(step t451 (cl @p_348) :rule resolution :premises (t446 t370 t447 t450))
(step t452 (cl @p_362 @p_353) :rule and_pos :args (1))
(step t453 (cl @p_353 @p_362) :rule reordering :premises (t452))
(step t454 (cl @p_353) :rule resolution :premises (t453 t156))
(step t455 (cl @p_13) :rule resolution :premises (t3 t409 t430 t451 t454))
(step t456 (cl (not (! (= (! (or @p_366 @p_333 @p_391 (! (not @p_12) :named @p_20)) :named @p_429) (! (or @p_366 @p_40 @p_391 @p_20) :named @p_428)) :named @p_438)) (not @p_429) @p_428) :rule equiv_pos2)
(step t457 (cl (= @p_20 @p_20)) :rule refl)
(step t458 (cl @p_438) :rule cong :premises (t159 t96 t457))
(step t459 (cl (! (and @p_82 @p_41 @p_22) :named @p_431) @p_366 @p_333 @p_391) :rule and_neg)
(step t460 (cl (! (=> @p_431 @p_20) :named @p_433) @p_431) :rule implies_neg1)
(anchor :step t461)
(assume t461.a0 @p_82)
(assume t461.a1 @p_41)
(assume t461.a2 @p_22)
(step t461.t0 (cl (! (=> (! (and @p_41 @p_82 @p_22) :named @p_434) @p_20) :named @p_436) @p_434) :rule implies_neg1)
(anchor :step t461.t1)
(assume t461.t1.a0 @p_41)
(assume t461.t1.a1 @p_82)
(assume t461.t1.a2 @p_22)
(step t461.t1.t0 (cl (= (! (= @p_12 false) :named @p_437) @p_20)) :rule equiv_simplify)
(step t461.t1.t1 (cl (not @p_437) @p_20) :rule equiv1 :premises (t461.t1.t0))
(step t461.t1.t2 (cl @p_390) :rule symm :premises (t461.t1.a1))
(step t461.t1.t3 (cl @p_408) :rule cong :premises (t461.t1.t2))
(step t461.t1.t4 (cl @p_407) :rule trans :premises (t127 t461.t1.t3))
(step t461.t1.t5 (cl (= @quantifiers_skolemize_6 @quantifiers_skolemize_6)) :rule refl)
(step t461.t1.t6 (cl (= @p_11 @p_39)) :rule cong :premises (t461.t1.t4 t461.t1.t5))
(step t461.t1.t7 (cl (= @p_10 @p_10)) :rule refl)
(step t461.t1.t8 (cl (= @p_12 @p_40)) :rule cong :premises (t461.t1.t6 t461.t1.t7))
(step t461.t1.t9 (cl @p_345) :rule equiv_simplify)
(step t461.t1.t10 (cl @p_344 @p_333) :rule equiv2 :premises (t461.t1.t9))
(step t461.t1.t11 (cl @p_336 @p_40) :rule not_not)
(step t461.t1.t12 (cl @p_344 @p_40) :rule resolution :premises (t461.t1.t10 t461.t1.t11))
(step t461.t1.t13 (cl @p_344) :rule resolution :premises (t461.t1.t12 t461.t1.a0))
(step t461.t1.t14 (cl @p_437) :rule trans :premises (t461.t1.t8 t461.t1.t13))
(step t461.t1.t15 (cl @p_20) :rule resolution :premises (t461.t1.t1 t461.t1.t14))
(step t461.t1 (cl @p_333 @p_366 @p_391 @p_20) :rule subproof :discharge (t461.t1.a0 t461.t1.a1 t461.t1.a2))
(step t461.t2 (cl (! (not @p_434) :named @p_435) @p_41) :rule and_pos :args (0))
(step t461.t3 (cl @p_435 @p_82) :rule and_pos :args (1))
(step t461.t4 (cl @p_435 @p_22) :rule and_pos :args (2))
(step t461.t5 (cl @p_20 @p_435 @p_435 @p_435) :rule resolution :premises (t461.t1 t461.t2 t461.t3 t461.t4))
(step t461.t6 (cl @p_435 @p_435 @p_435 @p_20) :rule reordering :premises (t461.t5))
(step t461.t7 (cl @p_435 @p_20) :rule contraction :premises (t461.t6))
(step t461.t8 (cl @p_436 @p_20) :rule resolution :premises (t461.t0 t461.t7))
(step t461.t9 (cl @p_436 (! (not @p_20) :named @p_430)) :rule implies_neg2)
(step t461.t10 (cl @p_436 @p_436) :rule resolution :premises (t461.t8 t461.t9))
(step t461.t11 (cl @p_436) :rule contraction :premises (t461.t10))
(step t461.t12 (cl @p_435 @p_20) :rule implies :premises (t461.t11))
(step t461.t13 (cl @p_434) :rule and_intro :premises (t461.a1 t461.a0 t127))
(step t461.t14 (cl @p_20) :rule resolution :premises (t461.t12 t461.t13))
(step t461 (cl @p_366 @p_333 @p_391 @p_20) :rule subproof :discharge (t461.a0 t461.a1 t461.a2))
(step t462 (cl (! (not @p_431) :named @p_432) @p_82) :rule and_pos :args (0))
(step t463 (cl @p_432 @p_41) :rule and_pos :args (1))
(step t464 (cl @p_432 @p_22) :rule and_pos :args (2))
(step t465 (cl @p_20 @p_432 @p_432 @p_432) :rule resolution :premises (t461 t462 t463 t464))
(step t466 (cl @p_432 @p_432 @p_432 @p_20) :rule reordering :premises (t465))
(step t467 (cl @p_432 @p_20) :rule contraction :premises (t466))
(step t468 (cl @p_433 @p_20) :rule resolution :premises (t460 t467))
(step t469 (cl @p_433 @p_430) :rule implies_neg2)
(step t470 (cl @p_433 @p_433) :rule resolution :premises (t468 t469))
(step t471 (cl @p_433) :rule contraction :premises (t470))
(step t472 (cl @p_432 @p_20) :rule implies :premises (t471))
(step t473 (cl @p_366 @p_333 @p_391 @p_20) :rule resolution :premises (t459 t472))
(step t474 (cl @p_429 @p_399) :rule or_neg :args (0))
(step t475 (cl @p_429 @p_336) :rule or_neg :args (1))
(step t476 (cl @p_429 @p_398) :rule or_neg :args (2))
(step t477 (cl @p_429 @p_430) :rule or_neg :args (3))
(step t478 (cl @p_429 @p_429 @p_429 @p_429) :rule resolution :premises (t473 t474 t475 t476 t477))
(step t479 (cl @p_429) :rule contraction :premises (t478))
(step t480 (cl @p_428) :rule resolution :premises (t456 t458 t479))
(step t481 (cl @p_366 @p_40 @p_391 @p_20) :rule or :premises (t480))
(step t482 (cl @p_41) :rule resolution :premises (t231 t408))
(step t483 (cl @p_20) :rule resolution :premises (t481 t370 t482 t127))
(step t484 (cl (not (! (= (! (=> (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0))) (! (= @p_12 @p_13) :named @p_17)) :named @p_18) (! (=> (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0))) @p_14) :named @p_16)) :named @p_19)) (not @p_18) @p_16) :rule equiv_pos2)
(step t485 (cl (= @p_17 @p_14)) :rule rare_rewrite :args ("eq-symm" @p_12 @p_13))
(step t486 (cl @p_19) :rule cong :premises (t485))
(step t487 (cl @p_18 (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0)))) :rule implies_neg1)
(anchor :step t488)
(assume t488.a0 (forall ((?v0 A$) (?v1 A$)) (= (fun_app$b (fun_app$c uu$ ?v0) ?v1) (fun_app$b (fun_app$c less$ ?v1) ?v0))))
(step t488.t0 (cl (or @p_15 @p_17)) :rule forall_inst :args (@quantifiers_skolemize_6 @p_10))
(step t488.t1 (cl @p_15 @p_17) :rule or :premises (t488.t0))
(step t488.t2 (cl @p_17) :rule resolution :premises (t488.t1 t488.a0))
(step t488 (cl @p_15 @p_17) :rule subproof :discharge (t488.a0))
(step t489 (cl @p_18 @p_17) :rule resolution :premises (t487 t488))
(step t490 (cl @p_18 (not @p_17)) :rule implies_neg2)
(step t491 (cl @p_18 @p_18) :rule resolution :premises (t489 t490))
(step t492 (cl @p_18) :rule contraction :premises (t491))
(step t493 (cl @p_16) :rule resolution :premises (t484 t486 t492))
(step t494 (cl @p_15 @p_14) :rule implies :premises (t493))
(step t495 (cl @p_14) :rule resolution :premises (t494 a1))
(step t496 (cl) :rule resolution :premises (t1 t455 t483 t495))
)
7fc6d0e99d41dce4a03bb2a6ad5a63bac835c91f 8354 0
unsat
(
(assume a1 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(assume a2 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))))
(assume a4 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (times$a ?v0 ?v1) ?v2) (times$a ?v0 (times$a ?v1 ?v2)))))
(assume a6 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (times$a ?v1 ?v0))))
(assume a8 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(assume a10 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2)))))
(assume a12 (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1)))))
(assume a13 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2)))))
(assume a16 (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1)))))
(assume a17 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))))
(assume a19 (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))))
(assume a21 (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))))
(assume a22 (forall ((?v0 Real) (?v1 Real)) (= (< 0/1 (powr$ ?v0 ?v1)) (not (= ?v0 0/1)))))
(assume a23 (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1)))))
(assume a24 (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1)))))
(assume a25 (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0))))
(assume a26 (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0))))))
(assume a27 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(assume a28 (! (< x$ (! (divide$ 1/1 2/1) :named @p_1)) :named @p_2))
(assume a30 (! (<= (! (times$a @p_1 (! (powr$ 2/1 (! (of_int$ p$) :named @p_3)) :named @p_4)) :named @p_6) (! (- @p_4 1/1) :named @p_5)) :named @p_7))
(assume a31 (! (< (! (times$a x$ @p_4) :named @p_8) @p_6) :named @p_9))
(assume a32 (! (not (! (< (! (round_up$ p$ x$) :named @p_10) 1/1) :named @p_11)) :named @p_12))
(step t0 (cl (not (! (= (! (or (! (not (! (>= @p_10 1/1) :named @p_13)) :named @p_15) (! (not (! (= (! (divide$ 1/1 @p_4) :named @p_18) (! (powr$ 2/1 (* -1/1 @p_3)) :named @p_17)) :named @p_19)) :named @p_1192) (! (not (! (>= (! (+ (! (* -1/1 @p_10) :named @p_34) (! (powr$ 2/1 (* -1/1 @p_3)) :named @p_17) (! (round_down$ p$ x$) :named @p_33)) :named @p_35) 0/1) :named @p_36)) :named @p_1193) (! (not (! (= @p_1 1/2) :named @p_244)) :named @p_1113) (! (not (! (>= (! (+ (! (* -1/1 x$) :named @p_61) @p_1) :named @p_62) 0/1) :named @p_63)) :named @p_64) (! (not (! (= @p_33 (! (* -1/1 (! (round_up$ p$ @p_61) :named @p_208)) :named @p_209)) :named @p_210)) :named @p_1209) (! (not (! (>= (! (+ x$ @p_208) :named @p_230) 0/1) :named @p_231)) :named @p_1210) (! (not (! (not (! (>= (! (+ (! (* -1/1 @p_1) :named @p_139) @p_18) :named @p_676) 0/1) :named @p_677)) :named @p_678)) :named @p_1509)) :named @p_1512) (! (or @p_15 @p_1192 @p_1193 @p_1113 @p_64 @p_1209 @p_1210 @p_677) :named @p_1511)) :named @p_1556)) (not @p_1512) @p_1511) :rule equiv_pos2)
(step t1 (cl (= @p_1509 @p_677)) :rule rare_rewrite :args ("bool-double-not-elim" @p_677))
(step t2 (cl @p_1556) :rule cong :premises (t1))
(step t3 (cl (! (=> (! (and @p_13 @p_19 @p_36 @p_244 @p_63 @p_210 @p_231 @p_678) :named @p_1513) (! (and @p_63 (! (= 1/2 @p_1) :named @p_1264) @p_19 @p_210 @p_36 @p_231 @p_13 @p_678) :named @p_1515)) :named @p_1555) @p_1513) :rule implies_neg1)
(anchor :step t4)
(assume t4.a0 @p_13)
(assume t4.a1 @p_19)
(assume t4.a2 @p_36)
(assume t4.a3 @p_244)
(assume t4.a4 @p_63)
(assume t4.a5 @p_210)
(assume t4.a6 @p_231)
(assume t4.a7 @p_678)
(step t4.t0 (cl (! (=> @p_244 @p_1264) :named @p_1397) @p_244) :rule implies_neg1)
(anchor :step t4.t1)
(assume t4.t1.a0 @p_244)
(step t4.t1.t0 (cl @p_1264) :rule symm :premises (t4.t1.a0))
(step t4.t1 (cl @p_1113 @p_1264) :rule subproof :discharge (t4.t1.a0))
(step t4.t2 (cl @p_1397 @p_1264) :rule resolution :premises (t4.t0 t4.t1))
(step t4.t3 (cl @p_1397 (! (not @p_1264) :named @p_1268)) :rule implies_neg2)
(step t4.t4 (cl @p_1397 @p_1397) :rule resolution :premises (t4.t2 t4.t3))
(step t4.t5 (cl @p_1397) :rule contraction :premises (t4.t4))
(step t4.t6 (cl @p_1113 @p_1264) :rule implies :premises (t4.t5))
(step t4.t7 (cl @p_1264) :rule resolution :premises (t4.t6 t4.a3))
(step t4.t8 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :named @p_32) @p_19)) :rule forall_inst :args (2/1 @p_3))
(step t4.t9 (cl @p_32 @p_19) :rule or :premises (t4.t8))
(step t4.t10 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1)))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :named @p_20)) (not (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule equiv_pos2)
(anchor :step t4.t11 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t4.t11.t0 (cl (= (! (- ?v1) :named @p_28) (! (* -1/1 ?v1) :named @p_23))) :rule poly_simp)
(step t4.t11.t1 (cl (= (! (powr$ ?v0 @p_28) :named @p_29) (! (powr$ ?v0 @p_23) :named @p_24))) :rule cong :premises (t4.t11.t0))
(step t4.t11.t2 (cl (= (! (divide$ 1/1 (! (powr$ ?v0 ?v1) :named @p_25)) :named @p_26) @p_26)) :rule refl)
(step t4.t11.t3 (cl (= (! (= @p_29 @p_26) :named @p_30) (! (= @p_24 @p_26) :named @p_31))) :rule cong :premises (t4.t11.t1 t4.t11.t2))
(step t4.t11.t4 (cl (= (* 1/1 (- @p_24 @p_26)) (* -1/1 (- @p_26 @p_24)))) :rule poly_simp)
(step t4.t11.t5 (cl (= @p_31 (! (= @p_26 @p_24) :named @p_27))) :rule poly_simp_rel :premises (t4.t11.t4))
(step t4.t11.t6 (cl (= @p_30 @p_27)) :rule trans :premises (t4.t11.t3 t4.t11.t5))
(step t4.t11 (cl @p_20) :rule bind)
(step t4.t12 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule resolution :premises (t4.t10 t4.t11 a23))
(step t4.t13 (cl @p_19) :rule resolution :premises (t4.t9 t4.t12))
(step t4.t14 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))) (! (= @p_208 (! (* -1/1 (! (round_down$ p$ (! (* -1/1 @p_61) :named @p_221)) :named @p_222)) :named @p_223)) :named @p_224)) :named @p_225) (! (=> (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))) @p_210) :named @p_220)) :named @p_226)) (not @p_225) @p_220) :rule equiv_pos2)
(step t4.t15 (cl (= @p_221 x$)) :rule poly_simp)
(step t4.t16 (cl (= @p_222 @p_33)) :rule cong :premises (t4.t15))
(step t4.t17 (cl (= @p_223 (! (* -1/1 @p_33) :named @p_227))) :rule cong :premises (t4.t16))
(step t4.t18 (cl (= @p_224 (! (= @p_208 @p_227) :named @p_228))) :rule cong :premises (t4.t17))
(step t4.t19 (cl (= (* 1/1 (- @p_208 @p_227)) (! (* 1/1 (- @p_33 @p_209)) :named @p_229))) :rule poly_simp)
(step t4.t20 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t4.t19))
(step t4.t21 (cl (= @p_224 @p_210)) :rule trans :premises (t4.t18 t4.t20))
(step t4.t22 (cl @p_226) :rule cong :premises (t4.t21))
(step t4.t23 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t4.t24)
(assume t4.t24.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t4.t24.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :named @p_219) @p_224)) :rule forall_inst :args (p$ @p_61))
(step t4.t24.t1 (cl @p_219 @p_224) :rule or :premises (t4.t24.t0))
(step t4.t24.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1)))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :named @p_211)) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t4.t24.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t4.t24.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t4.t24.t3.t1 (cl (= (! (round_down$ ?v0 @p_28) :named @p_216) (! (round_down$ ?v0 @p_23) :named @p_212))) :rule cong :premises (t4.t24.t3.t0))
(step t4.t24.t3.t2 (cl (= (! (- (! (round_up$ ?v0 ?v1) :named @p_43)) :named @p_215) (! (* -1/1 @p_43) :named @p_44))) :rule poly_simp)
(step t4.t24.t3.t3 (cl (= (! (= @p_216 @p_215) :named @p_217) (! (= @p_212 @p_44) :named @p_218))) :rule cong :premises (t4.t24.t3.t1 t4.t24.t3.t2))
(step t4.t24.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 (! (* -1/1 @p_212) :named @p_213))))) :rule poly_simp)
(step t4.t24.t3.t5 (cl (= @p_218 (! (= @p_43 @p_213) :named @p_214))) :rule poly_simp_rel :premises (t4.t24.t3.t4))
(step t4.t24.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t4.t24.t3.t3 t4.t24.t3.t5))
(step t4.t24.t3 (cl @p_211) :rule bind)
(step t4.t24.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t4.t24.t2 t4.t24.t3 a24))
(step t4.t24.t5 (cl @p_224) :rule resolution :premises (t4.t24.t1 t4.t24.t4))
(step t4.t24 (cl @p_219 @p_224) :rule subproof :discharge (t4.t24.a0))
(step t4.t25 (cl @p_225 @p_224) :rule resolution :premises (t4.t23 t4.t24))
(step t4.t26 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t4.t27 (cl @p_225 @p_225) :rule resolution :premises (t4.t25 t4.t26))
(step t4.t28 (cl @p_225) :rule contraction :premises (t4.t27))
(step t4.t29 (cl @p_220) :rule resolution :premises (t4.t14 t4.t22 t4.t28))
(step t4.t30 (cl @p_219 @p_210) :rule implies :premises (t4.t29))
(step t4.t31 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t4.t32 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t4.t32.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t4.t32.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t4.t32.t0))
(step t4.t32.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t4.t32.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t4.t32.t1 t4.t32.t2))
(step t4.t32.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t4.t32.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t4.t32.t4))
(step t4.t32.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t4.t32.t3 t4.t32.t5))
(step t4.t32 (cl @p_211) :rule bind)
(step t4.t33 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t4.t31 t4.t32 a24))
(step t4.t34 (cl @p_210) :rule resolution :premises (t4.t30 t4.t33))
(step t4.t35 (cl (not (! (= (! (=> (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)) (! (>= (! (+ @p_34 @p_33 @p_17) :named @p_56) 0/1) :named @p_57)) :named @p_58) (! (=> (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)) @p_36) :named @p_55)) :named @p_59)) (not @p_58) @p_55) :rule equiv_pos2)
(step t4.t36 (cl (= @p_56 @p_35)) :rule poly_simp)
(step t4.t37 (cl (! (= 0/1 0/1) :named @p_60)) :rule refl)
(step t4.t38 (cl (= @p_57 @p_36)) :rule cong :premises (t4.t36 t4.t37))
(step t4.t39 (cl @p_59) :rule cong :premises (t4.t38))
(step t4.t40 (cl @p_58 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule implies_neg1)
(anchor :step t4.t41)
(assume t4.t41.a0 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)))
(step t4.t41.t0 (cl (or (! (not (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :named @p_54) @p_57)) :rule forall_inst :args (p$ x$))
(step t4.t41.t1 (cl @p_54 @p_57) :rule or :premises (t4.t41.t0))
(step t4.t41.t2 (cl (not (! (= (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :named @p_37)) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t4.t41.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t4.t41.t3.t0 (cl (= (! (- @p_43 (! (round_down$ ?v0 ?v1) :named @p_42)) :named @p_49) (! (+ @p_43 (* -1/1 @p_42)) :named @p_51))) :rule poly_simp)
(step t4.t41.t3.t1 (cl (= (! (- (! (of_int$ ?v0) :named @p_39)) :named @p_47) (! (* -1/1 @p_39) :named @p_40))) :rule poly_simp)
(step t4.t41.t3.t2 (cl (= (! (powr$ 2/1 @p_47) :named @p_48) (! (powr$ 2/1 @p_40) :named @p_41))) :rule cong :premises (t4.t41.t3.t1))
(step t4.t41.t3.t3 (cl (= (! (<= @p_49 @p_48) :named @p_50) (! (<= @p_51 @p_41) :named @p_52))) :rule cong :premises (t4.t41.t3.t0 t4.t41.t3.t2))
(step t4.t41.t3.t4 (cl (= @p_52 (! (>= @p_41 @p_51) :named @p_53))) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t4.t41.t3.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- (! (+ @p_44 @p_42 @p_41) :named @p_45) 0/1)))) :rule poly_simp)
(step t4.t41.t3.t6 (cl (= @p_53 (! (>= @p_45 0/1) :named @p_46))) :rule poly_simp_rel :premises (t4.t41.t3.t5))
(step t4.t41.t3.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t4.t41.t3.t4 t4.t41.t3.t6))
(step t4.t41.t3.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t4.t41.t3.t3 t4.t41.t3.t7))
(step t4.t41.t3 (cl @p_37) :rule bind)
(step t4.t41.t4 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t4.t41.t2 t4.t41.t3 a26))
(step t4.t41.t5 (cl @p_57) :rule resolution :premises (t4.t41.t1 t4.t41.t4))
(step t4.t41 (cl @p_54 @p_57) :rule subproof :discharge (t4.t41.a0))
(step t4.t42 (cl @p_58 @p_57) :rule resolution :premises (t4.t40 t4.t41))
(step t4.t43 (cl @p_58 (not @p_57)) :rule implies_neg2)
(step t4.t44 (cl @p_58 @p_58) :rule resolution :premises (t4.t42 t4.t43))
(step t4.t45 (cl @p_58) :rule contraction :premises (t4.t44))
(step t4.t46 (cl @p_55) :rule resolution :premises (t4.t35 t4.t39 t4.t45))
(step t4.t47 (cl @p_54 @p_36) :rule implies :premises (t4.t46))
(step t4.t48 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t4.t49 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t4.t49.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t4.t49.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t4.t49.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t4.t49.t1))
(step t4.t49.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t4.t49.t0 t4.t49.t2))
(step t4.t49.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t4.t49.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t4.t49.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t4.t49.t5))
(step t4.t49.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t4.t49.t4 t4.t49.t6))
(step t4.t49.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t4.t49.t3 t4.t49.t7))
(step t4.t49 (cl @p_37) :rule bind)
(step t4.t50 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t4.t48 t4.t49 a26))
(step t4.t51 (cl @p_36) :rule resolution :premises (t4.t47 t4.t50))
(step t4.t52 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)) (! (>= (! (+ @p_221 @p_208) :named @p_240) 0/1) :named @p_241)) :named @p_242) (! (=> (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)) @p_231) :named @p_239)) :named @p_243)) (not @p_242) @p_239) :rule equiv_pos2)
(step t4.t53 (cl (= @p_208 @p_208)) :rule refl)
(step t4.t54 (cl (= @p_240 @p_230)) :rule cong :premises (t4.t15 t4.t53))
(step t4.t55 (cl @p_60) :rule refl)
(step t4.t56 (cl (= @p_241 @p_231)) :rule cong :premises (t4.t54 t4.t55))
(step t4.t57 (cl @p_243) :rule cong :premises (t4.t56))
(step t4.t58 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t4.t59)
(assume t4.t59.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t4.t59.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :named @p_238) @p_241)) :rule forall_inst :args (@p_61 p$))
(step t4.t59.t1 (cl @p_238 @p_241) :rule or :premises (t4.t59.t0))
(step t4.t59.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :named @p_232)) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t4.t59.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t4.t59.t3.t0 (cl (= (! (<= ?v0 (! (round_up$ ?v1 ?v0) :named @p_233)) :named @p_236) (! (>= @p_233 ?v0) :named @p_237))) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t4.t59.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- (! (+ (! (* -1/1 ?v0) :named @p_85) @p_233) :named @p_234) 0/1)))) :rule poly_simp)
(step t4.t59.t3.t2 (cl (= @p_237 (! (>= @p_234 0/1) :named @p_235))) :rule poly_simp_rel :premises (t4.t59.t3.t1))
(step t4.t59.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t4.t59.t3.t0 t4.t59.t3.t2))
(step t4.t59.t3 (cl @p_232) :rule bind)
(step t4.t59.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t4.t59.t2 t4.t59.t3 a25))
(step t4.t59.t5 (cl @p_241) :rule resolution :premises (t4.t59.t1 t4.t59.t4))
(step t4.t59 (cl @p_238 @p_241) :rule subproof :discharge (t4.t59.a0))
(step t4.t60 (cl @p_242 @p_241) :rule resolution :premises (t4.t58 t4.t59))
(step t4.t61 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t4.t62 (cl @p_242 @p_242) :rule resolution :premises (t4.t60 t4.t61))
(step t4.t63 (cl @p_242) :rule contraction :premises (t4.t62))
(step t4.t64 (cl @p_239) :rule resolution :premises (t4.t52 t4.t57 t4.t63))
(step t4.t65 (cl @p_238 @p_231) :rule implies :premises (t4.t64))
(step t4.t66 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t4.t67 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t4.t67.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t4.t67.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t4.t67.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t4.t67.t1))
(step t4.t67.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t4.t67.t0 t4.t67.t2))
(step t4.t67 (cl @p_232) :rule bind)
(step t4.t68 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t4.t66 t4.t67 a25))
(step t4.t69 (cl @p_231) :rule resolution :premises (t4.t65 t4.t68))
(step t4.t70 (cl (not (! (= @p_12 @p_13) :named @p_14)) (not @p_12) @p_13) :rule equiv_pos2)
(step t4.t71 (cl (= @p_11 @p_15)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 1/1))
(step t4.t72 (cl (= @p_12 (! (not @p_15) :named @p_16))) :rule cong :premises (t4.t71))
(step t4.t73 (cl (= @p_16 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t4.t74 (cl @p_14) :rule trans :premises (t4.t72 t4.t73))
(step t4.t75 (cl @p_13) :rule resolution :premises (t4.t70 t4.t74 a32))
(step t4.t76 (cl @p_1515) :rule and_intro :premises (t4.a4 t4.t7 t4.t13 t4.t34 t4.t51 t4.t69 t4.t75 t4.a7))
(step t4 (cl @p_15 @p_1192 @p_1193 @p_1113 @p_64 @p_1209 @p_1210 @p_1509 @p_1515) :rule subproof :discharge (t4.a0 t4.a1 t4.a2 t4.a3 t4.a4 t4.a5 t4.a6 t4.a7))
(step t5 (cl (! (not @p_1513) :named @p_1514) @p_13) :rule and_pos :args (0))
(step t6 (cl @p_1514 @p_19) :rule and_pos :args (1))
(step t7 (cl @p_1514 @p_36) :rule and_pos :args (2))
(step t8 (cl @p_1514 @p_244) :rule and_pos :args (3))
(step t9 (cl @p_1514 @p_63) :rule and_pos :args (4))
(step t10 (cl @p_1514 @p_210) :rule and_pos :args (5))
(step t11 (cl @p_1514 @p_231) :rule and_pos :args (6))
(step t12 (cl @p_1514 @p_678) :rule and_pos :args (7))
(step t13 (cl @p_1515 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514) :rule resolution :premises (t4 t5 t6 t7 t8 t9 t10 t11 t12))
(step t14 (cl @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1514 @p_1515) :rule reordering :premises (t13))
(step t15 (cl @p_1514 @p_1515) :rule contraction :premises (t14))
(step t16 (cl @p_1555 @p_1515) :rule resolution :premises (t3 t15))
(step t17 (cl @p_1555 (! (not @p_1515) :named @p_1516)) :rule implies_neg2)
(step t18 (cl @p_1555 @p_1555) :rule resolution :premises (t16 t17))
(step t19 (cl @p_1555) :rule contraction :premises (t18))
(step t20 (cl @p_1514 @p_1515) :rule implies :premises (t19))
(step t21 (cl (! (=> @p_1515 false) :named @p_1517) @p_1515) :rule implies_neg1)
(anchor :step t22)
(assume t22.a0 @p_63)
(assume t22.a1 @p_1264)
(assume t22.a2 @p_19)
(assume t22.a3 @p_210)
(assume t22.a4 @p_36)
(assume t22.a5 @p_231)
(assume t22.a6 @p_13)
(assume t22.a7 @p_678)
(step t22.t0 (cl (not (! (= @p_678 (! (> (! (+ @p_1 (! (* -1/1 @p_18) :named @p_1518)) :named @p_1519) 0/1) :named @p_1520)) :named @p_1554)) @p_1509 @p_1520) :rule equiv_pos2)
(step t22.t1 (cl (= @p_1520 (! (not (! (>= 0/1 @p_1519) :named @p_1550)) :named @p_1552))) :rule rare_rewrite :args ("arith-elim-gt" @p_1519 0/1))
(step t22.t2 (cl (= (! (<= @p_1519 0/1) :named @p_1522) @p_1550)) :rule rare_rewrite :args ("arith-elim-leq" @p_1519 0/1))
(step t22.t3 (cl (= @p_1550 @p_1522)) :rule symm :premises (t22.t2))
(step t22.t4 (cl (= @p_1552 (! (not @p_1522) :named @p_1551))) :rule cong :premises (t22.t3))
(step t22.t5 (cl (= @p_1520 @p_1551)) :rule trans :premises (t22.t1 t22.t4))
(step t22.t6 (cl (= (* -1/1 (- 0/1 @p_1519)) (* -1/1 (- @p_676 0/1)))) :rule poly_simp)
(step t22.t7 (cl (= @p_1550 @p_677)) :rule poly_simp_rel :premises (t22.t6))
(step t22.t8 (cl (= @p_1522 @p_677)) :rule trans :premises (t22.t2 t22.t7))
(step t22.t9 (cl (= @p_1551 @p_678)) :rule cong :premises (t22.t8))
(step t22.t10 (cl (= @p_1520 @p_678)) :rule trans :premises (t22.t5 t22.t9))
(step t22.t11 (cl @p_1554) :rule symm :premises (t22.t10))
(step t22.t12 (cl @p_1520) :rule resolution :premises (t22.t0 t22.t11 t22.a7))
(step t22.t13 (cl (not (! (= @p_1522 (! (not @p_1520) :named @p_1521)) :named @p_1553)) @p_1551 @p_1521) :rule equiv_pos2)
(step t22.t14 (cl (= @p_1521 @p_1509)) :rule cong :premises (t22.t10))
(step t22.t15 (cl (= @p_1521 @p_677)) :rule trans :premises (t22.t14 t1))
(step t22.t16 (cl (= @p_677 @p_1521)) :rule symm :premises (t22.t15))
(step t22.t17 (cl @p_1553) :rule trans :premises (t22.t8 t22.t16))
(step t22.t18 (cl (not (! (= @p_1521 @p_1522) :named @p_1549)) (not @p_1521) @p_1522) :rule equiv_pos2)
(step t22.t19 (cl (= @p_677 @p_1522)) :rule symm :premises (t22.t8))
(step t22.t20 (cl @p_1549) :rule trans :premises (t22.t15 t22.t19))
(step t22.t21 (cl (! (=> @p_1520 false) :named @p_1523) @p_1520) :rule implies_neg1)
(anchor :step t22.t22)
(assume t22.t22.a0 @p_1520)
(step t22.t22.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_1519) :named @p_1528) @p_34 (! (* -1/1 @p_230) :named @p_1294) (! (+ @p_10 (! (* -1/1 @p_17) :named @p_1295) @p_227) :named @p_1296) (! (+ @p_33 @p_208) :named @p_1277) (! (* -1/1 (! (+ @p_18 @p_1295) :named @p_1526)) :named @p_1527) (! (* 2/1 @p_1) :named @p_247) (! (+ x$ @p_139) :named @p_140)) :named @p_1529) (! (+ (! (* -1/1 0/1) :named @p_175) (! (* -1/1 1/1) :named @p_737) @p_175 0/1 0/1 @p_175 (! (* 2/1 1/2) :named @p_1524) 0/1) :named @p_1525)) :named @p_1530) false) :named @p_1542)) (not @p_1530) false) :rule equiv_pos2)
(step t22.t22.t1 (cl (= @p_1530 (! (not (! (>= @p_1529 @p_1525) :named @p_1543)) :named @p_1544))) :rule rare_rewrite :args ("arith-elim-lt" @p_1529 @p_1525))
(step t22.t22.t2 (cl (= @p_1529 (! (+ @p_34 @p_247 (! (* 0/1 @p_208) :named @p_1352) @p_18 @p_227 (! (* 0/1 @p_17) :named @p_1546) @p_33 @p_1518 @p_139 @p_10 @p_139 (! (* 0/1 x$) :named @p_1351)) :named @p_1547))) :rule poly_simp)
(step t22.t22.t3 (cl (= @p_1352 0/1)) :rule poly_simp)
(step t22.t22.t4 (cl (= @p_18 @p_18)) :rule refl)
(step t22.t22.t5 (cl (= @p_227 @p_227)) :rule refl)
(step t22.t22.t6 (cl (= @p_1546 0/1)) :rule poly_simp)
(step t22.t22.t7 (cl (= @p_33 @p_33)) :rule refl)
(step t22.t22.t8 (cl (= @p_1518 @p_1518)) :rule refl)
(step t22.t22.t9 (cl (= @p_139 @p_139)) :rule refl)
(step t22.t22.t10 (cl (= @p_10 @p_10)) :rule refl)
(step t22.t22.t11 (cl (= @p_1351 0/1)) :rule poly_simp)
(step t22.t22.t12 (cl (= @p_1547 (! (+ @p_34 @p_247 0/1 @p_18 @p_227 0/1 @p_33 @p_1518 @p_139 @p_10 @p_139 0/1) :named @p_1548))) :rule cong :premises (t22.t22.t3 t22.t22.t4 t22.t22.t5 t22.t22.t6 t22.t22.t7 t22.t22.t8 t22.t22.t9 t22.t22.t10 t22.t22.t9 t22.t22.t11))
(step t22.t22.t13 (cl (= @p_1548 0/1)) :rule poly_simp)
(step t22.t22.t14 (cl (= @p_1547 0/1)) :rule trans :premises (t22.t22.t12 t22.t22.t13))
(step t22.t22.t15 (cl (= @p_1529 0/1)) :rule trans :premises (t22.t22.t2 t22.t22.t14))
(step t22.t22.t16 (cl (= @p_175 0/1)) :rule evaluate)
(step t22.t22.t17 (cl (= @p_737 -1/1)) :rule evaluate)
(step t22.t22.t18 (cl @p_60) :rule refl)
(step t22.t22.t19 (cl (= @p_1524 1/1)) :rule evaluate)
(step t22.t22.t20 (cl (= @p_1525 (! (+ 0/1 -1/1 0/1 0/1 0/1 0/1 1/1 0/1) :named @p_1545))) :rule cong :premises (t22.t22.t16 t22.t22.t17 t22.t22.t16 t22.t22.t18 t22.t22.t18 t22.t22.t16 t22.t22.t19 t22.t22.t18))
(step t22.t22.t21 (cl (= @p_1545 0/1)) :rule evaluate)
(step t22.t22.t22 (cl (= @p_1525 0/1)) :rule trans :premises (t22.t22.t20 t22.t22.t21))
(step t22.t22.t23 (cl (= @p_1543 (! (>= 0/1 0/1) :named @p_190))) :rule cong :premises (t22.t22.t15 t22.t22.t22))
(step t22.t22.t24 (cl (! (= @p_190 true) :named @p_191)) :rule evaluate)
(step t22.t22.t25 (cl (= @p_1543 true)) :rule trans :premises (t22.t22.t23 t22.t22.t24))
(step t22.t22.t26 (cl (= @p_1544 (! (not true) :named @p_189))) :rule cong :premises (t22.t22.t25))
(step t22.t22.t27 (cl (= @p_189 false)) :rule evaluate)
(step t22.t22.t28 (cl (= @p_1544 false)) :rule trans :premises (t22.t22.t26 t22.t22.t27))
(step t22.t22.t29 (cl @p_1542) :rule trans :premises (t22.t22.t1 t22.t22.t28))
(step t22.t22.t30 (cl (not (! (< @p_1528 @p_175) :named @p_1540)) (! (not (! (<= @p_34 @p_737) :named @p_1334)) :named @p_1345) (! (not (! (<= @p_1294 @p_175) :named @p_1336)) :named @p_1344) (! (not (! (<= @p_1296 0/1) :named @p_1338)) :named @p_1343) (! (not (! (= @p_1277 0/1) :named @p_1299)) :named @p_1346) (not (! (= @p_1527 @p_175) :named @p_1536)) (not (! (= @p_247 @p_1524) :named @p_1534)) (not (! (<= @p_140 0/1) :named @p_1531)) @p_1530) :rule la_generic :args (1/1 1/1 1/1 1/1 -1/1 -1/1 -1/1 1/1 1/1))
(step t22.t22.t31 (cl (=> (! (and (! (< -1/1 0/1) :named @p_183) @p_1520) :named @p_1541) @p_1540)) :rule la_mult_neg)
(step t22.t22.t32 (cl (not @p_1541) @p_1540) :rule implies :premises (t22.t22.t31))
(step t22.t22.t33 (cl (= (! (= @p_183 true) :named @p_185) @p_183)) :rule equiv_simplify)
(step t22.t22.t34 (cl (not @p_185) @p_183) :rule equiv1 :premises (t22.t22.t33))
(step t22.t22.t35 (cl @p_185) :rule evaluate)
(step t22.t22.t36 (cl @p_183) :rule resolution :premises (t22.t22.t34 t22.t22.t35))
(step t22.t22.t37 (cl @p_1541) :rule and_intro :premises (t22.t22.t36 t22.t22.a0))
(step t22.t22.t38 (cl @p_1540) :rule resolution :premises (t22.t22.t32 t22.t22.t37))
(step t22.t22.t39 (cl (=> (! (and @p_183 @p_13) :named @p_1335) @p_1334)) :rule la_mult_neg)
(step t22.t22.t40 (cl (not @p_1335) @p_1334) :rule implies :premises (t22.t22.t39))
(step t22.t22.t41 (cl (not @p_14) (not @p_12) @p_13) :rule equiv_pos2)
(step t22.t22.t42 (cl (= @p_11 @p_15)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 1/1))
(step t22.t22.t43 (cl (= @p_12 @p_16)) :rule cong :premises (t22.t22.t42))
(step t22.t22.t44 (cl (= @p_16 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t22.t22.t45 (cl @p_14) :rule trans :premises (t22.t22.t43 t22.t22.t44))
(step t22.t22.t46 (cl @p_13) :rule resolution :premises (t22.t22.t41 t22.t22.t45 a32))
(step t22.t22.t47 (cl @p_1335) :rule and_intro :premises (t22.t22.t36 t22.t22.t46))
(step t22.t22.t48 (cl @p_1334) :rule resolution :premises (t22.t22.t40 t22.t22.t47))
(step t22.t22.t49 (cl (=> (! (and @p_183 @p_231) :named @p_1337) @p_1336)) :rule la_mult_neg)
(step t22.t22.t50 (cl (not @p_1337) @p_1336) :rule implies :premises (t22.t22.t49))
(step t22.t22.t51 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t22.t22.t52 (cl (= @p_221 x$)) :rule poly_simp)
(step t22.t22.t53 (cl (= @p_208 @p_208)) :rule refl)
(step t22.t22.t54 (cl (= @p_240 @p_230)) :rule cong :premises (t22.t22.t52 t22.t22.t53))
(step t22.t22.t55 (cl @p_60) :rule refl)
(step t22.t22.t56 (cl (= @p_241 @p_231)) :rule cong :premises (t22.t22.t54 t22.t22.t55))
(step t22.t22.t57 (cl @p_243) :rule cong :premises (t22.t22.t56))
(step t22.t22.t58 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t22.t22.t59)
(assume t22.t22.t59.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t22.t22.t59.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t22.t22.t59.t1 (cl @p_238 @p_241) :rule or :premises (t22.t22.t59.t0))
(step t22.t22.t59.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t22.t22.t59.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t22.t22.t59.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t22.t22.t59.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t22.t22.t59.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t22.t22.t59.t3.t1))
(step t22.t22.t59.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t22.t22.t59.t3.t0 t22.t22.t59.t3.t2))
(step t22.t22.t59.t3 (cl @p_232) :rule bind)
(step t22.t22.t59.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t22.t22.t59.t2 t22.t22.t59.t3 a25))
(step t22.t22.t59.t5 (cl @p_241) :rule resolution :premises (t22.t22.t59.t1 t22.t22.t59.t4))
(step t22.t22.t59 (cl @p_238 @p_241) :rule subproof :discharge (t22.t22.t59.a0))
(step t22.t22.t60 (cl @p_242 @p_241) :rule resolution :premises (t22.t22.t58 t22.t22.t59))
(step t22.t22.t61 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t22.t22.t62 (cl @p_242 @p_242) :rule resolution :premises (t22.t22.t60 t22.t22.t61))
(step t22.t22.t63 (cl @p_242) :rule contraction :premises (t22.t22.t62))
(step t22.t22.t64 (cl @p_239) :rule resolution :premises (t22.t22.t51 t22.t22.t57 t22.t22.t63))
(step t22.t22.t65 (cl @p_238 @p_231) :rule implies :premises (t22.t22.t64))
(step t22.t22.t66 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t22.t22.t67 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t22.t22.t67.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t22.t22.t67.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t22.t22.t67.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t22.t22.t67.t1))
(step t22.t22.t67.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t22.t22.t67.t0 t22.t22.t67.t2))
(step t22.t22.t67 (cl @p_232) :rule bind)
(step t22.t22.t68 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t22.t22.t66 t22.t22.t67 a25))
(step t22.t22.t69 (cl @p_231) :rule resolution :premises (t22.t22.t65 t22.t22.t68))
(step t22.t22.t70 (cl @p_1337) :rule and_intro :premises (t22.t22.t36 t22.t22.t69))
(step t22.t22.t71 (cl @p_1336) :rule resolution :premises (t22.t22.t50 t22.t22.t70))
(step t22.t22.t72 (cl (not (! (= @p_36 @p_1338) :named @p_1339)) @p_1193 @p_1338) :rule equiv_pos2)
(step t22.t22.t73 (cl (= @p_1338 (! (>= 0/1 @p_1296) :named @p_1340))) :rule rare_rewrite :args ("arith-elim-leq" @p_1296 0/1))
(step t22.t22.t74 (cl (= (* -1/1 (- 0/1 @p_1296)) (* -1/1 (- @p_35 0/1)))) :rule poly_simp)
(step t22.t22.t75 (cl (= @p_1340 @p_36)) :rule poly_simp_rel :premises (t22.t22.t74))
(step t22.t22.t76 (cl (= @p_1338 @p_36)) :rule trans :premises (t22.t22.t73 t22.t22.t75))
(step t22.t22.t77 (cl @p_1339) :rule symm :premises (t22.t22.t76))
(step t22.t22.t78 (cl (not @p_59) (not @p_58) @p_55) :rule equiv_pos2)
(step t22.t22.t79 (cl (= @p_56 @p_35)) :rule poly_simp)
(step t22.t22.t80 (cl @p_60) :rule refl)
(step t22.t22.t81 (cl (= @p_57 @p_36)) :rule cong :premises (t22.t22.t79 t22.t22.t80))
(step t22.t22.t82 (cl @p_59) :rule cong :premises (t22.t22.t81))
(step t22.t22.t83 (cl @p_58 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule implies_neg1)
(anchor :step t22.t22.t84)
(assume t22.t22.t84.a0 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)))
(step t22.t22.t84.t0 (cl (or @p_54 @p_57)) :rule forall_inst :args (p$ x$))
(step t22.t22.t84.t1 (cl @p_54 @p_57) :rule or :premises (t22.t22.t84.t0))
(step t22.t22.t84.t2 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t22.t22.t84.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t22.t22.t84.t3.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t22.t22.t84.t3.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t22.t22.t84.t3.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t22.t22.t84.t3.t1))
(step t22.t22.t84.t3.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t22.t22.t84.t3.t0 t22.t22.t84.t3.t2))
(step t22.t22.t84.t3.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t22.t22.t84.t3.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t22.t22.t84.t3.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t22.t22.t84.t3.t5))
(step t22.t22.t84.t3.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t22.t22.t84.t3.t4 t22.t22.t84.t3.t6))
(step t22.t22.t84.t3.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t22.t22.t84.t3.t3 t22.t22.t84.t3.t7))
(step t22.t22.t84.t3 (cl @p_37) :rule bind)
(step t22.t22.t84.t4 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t22.t22.t84.t2 t22.t22.t84.t3 a26))
(step t22.t22.t84.t5 (cl @p_57) :rule resolution :premises (t22.t22.t84.t1 t22.t22.t84.t4))
(step t22.t22.t84 (cl @p_54 @p_57) :rule subproof :discharge (t22.t22.t84.a0))
(step t22.t22.t85 (cl @p_58 @p_57) :rule resolution :premises (t22.t22.t83 t22.t22.t84))
(step t22.t22.t86 (cl @p_58 (not @p_57)) :rule implies_neg2)
(step t22.t22.t87 (cl @p_58 @p_58) :rule resolution :premises (t22.t22.t85 t22.t22.t86))
(step t22.t22.t88 (cl @p_58) :rule contraction :premises (t22.t22.t87))
(step t22.t22.t89 (cl @p_55) :rule resolution :premises (t22.t22.t78 t22.t22.t82 t22.t22.t88))
(step t22.t22.t90 (cl @p_54 @p_36) :rule implies :premises (t22.t22.t89))
(step t22.t22.t91 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t22.t22.t92 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t22.t22.t92.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t22.t22.t92.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t22.t22.t92.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t22.t22.t92.t1))
(step t22.t22.t92.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t22.t22.t92.t0 t22.t22.t92.t2))
(step t22.t22.t92.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t22.t22.t92.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t22.t22.t92.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t22.t22.t92.t5))
(step t22.t22.t92.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t22.t22.t92.t4 t22.t22.t92.t6))
(step t22.t22.t92.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t22.t22.t92.t3 t22.t22.t92.t7))
(step t22.t22.t92 (cl @p_37) :rule bind)
(step t22.t22.t93 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t22.t22.t91 t22.t22.t92 a26))
(step t22.t22.t94 (cl @p_36) :rule resolution :premises (t22.t22.t90 t22.t22.t93))
(step t22.t22.t95 (cl @p_1338) :rule resolution :premises (t22.t22.t72 t22.t22.t77 t22.t22.t94))
(step t22.t22.t96 (cl (not (! (= @p_210 @p_1299) :named @p_1300)) @p_1209 @p_1299) :rule equiv_pos2)
(step t22.t22.t97 (cl (= (* 1/1 (- @p_1277 0/1)) @p_229)) :rule poly_simp)
(step t22.t22.t98 (cl (= @p_1299 @p_210)) :rule poly_simp_rel :premises (t22.t22.t97))
(step t22.t22.t99 (cl @p_1300) :rule symm :premises (t22.t22.t98))
(step t22.t22.t100 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t22.t22.t101 (cl (= @p_222 @p_33)) :rule cong :premises (t22.t22.t52))
(step t22.t22.t102 (cl (= @p_223 @p_227)) :rule cong :premises (t22.t22.t101))
(step t22.t22.t103 (cl (= @p_224 @p_228)) :rule cong :premises (t22.t22.t102))
(step t22.t22.t104 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t22.t22.t105 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t22.t22.t104))
(step t22.t22.t106 (cl (= @p_224 @p_210)) :rule trans :premises (t22.t22.t103 t22.t22.t105))
(step t22.t22.t107 (cl @p_226) :rule cong :premises (t22.t22.t106))
(step t22.t22.t108 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t22.t22.t109)
(assume t22.t22.t109.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t22.t22.t109.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t22.t22.t109.t1 (cl @p_219 @p_224) :rule or :premises (t22.t22.t109.t0))
(step t22.t22.t109.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t22.t22.t109.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t22.t22.t109.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t22.t22.t109.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t22.t22.t109.t3.t0))
(step t22.t22.t109.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t22.t22.t109.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t22.t22.t109.t3.t1 t22.t22.t109.t3.t2))
(step t22.t22.t109.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t22.t22.t109.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t22.t22.t109.t3.t4))
(step t22.t22.t109.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t22.t22.t109.t3.t3 t22.t22.t109.t3.t5))
(step t22.t22.t109.t3 (cl @p_211) :rule bind)
(step t22.t22.t109.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t22.t22.t109.t2 t22.t22.t109.t3 a24))
(step t22.t22.t109.t5 (cl @p_224) :rule resolution :premises (t22.t22.t109.t1 t22.t22.t109.t4))
(step t22.t22.t109 (cl @p_219 @p_224) :rule subproof :discharge (t22.t22.t109.a0))
(step t22.t22.t110 (cl @p_225 @p_224) :rule resolution :premises (t22.t22.t108 t22.t22.t109))
(step t22.t22.t111 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t22.t22.t112 (cl @p_225 @p_225) :rule resolution :premises (t22.t22.t110 t22.t22.t111))
(step t22.t22.t113 (cl @p_225) :rule contraction :premises (t22.t22.t112))
(step t22.t22.t114 (cl @p_220) :rule resolution :premises (t22.t22.t100 t22.t22.t107 t22.t22.t113))
(step t22.t22.t115 (cl @p_219 @p_210) :rule implies :premises (t22.t22.t114))
(step t22.t22.t116 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t22.t22.t117 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t22.t22.t117.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t22.t22.t117.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t22.t22.t117.t0))
(step t22.t22.t117.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t22.t22.t117.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t22.t22.t117.t1 t22.t22.t117.t2))
(step t22.t22.t117.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t22.t22.t117.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t22.t22.t117.t4))
(step t22.t22.t117.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t22.t22.t117.t3 t22.t22.t117.t5))
(step t22.t22.t117 (cl @p_211) :rule bind)
(step t22.t22.t118 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t22.t22.t116 t22.t22.t117 a24))
(step t22.t22.t119 (cl @p_210) :rule resolution :premises (t22.t22.t115 t22.t22.t118))
(step t22.t22.t120 (cl @p_1299) :rule resolution :premises (t22.t22.t96 t22.t22.t99 t22.t22.t119))
(step t22.t22.t121 (cl (=> (! (and @p_183 (! (= @p_1526 0/1) :named @p_1537)) :named @p_1538) @p_1536)) :rule la_mult_neg)
(step t22.t22.t122 (cl (not @p_1538) @p_1536) :rule implies :premises (t22.t22.t121))
(step t22.t22.t123 (cl (not (! (= @p_19 @p_1537) :named @p_1539)) @p_1192 @p_1537) :rule equiv_pos2)
(step t22.t22.t124 (cl (= (* 1/1 (- @p_1526 0/1)) (* 1/1 (- @p_18 @p_17)))) :rule poly_simp)
(step t22.t22.t125 (cl (= @p_1537 @p_19)) :rule poly_simp_rel :premises (t22.t22.t124))
(step t22.t22.t126 (cl @p_1539) :rule symm :premises (t22.t22.t125))
(step t22.t22.t127 (cl (or @p_32 @p_19)) :rule forall_inst :args (2/1 @p_3))
(step t22.t22.t128 (cl @p_32 @p_19) :rule or :premises (t22.t22.t127))
(step t22.t22.t129 (cl (not @p_20) (not (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule equiv_pos2)
(anchor :step t22.t22.t130 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t22.t22.t130.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t22.t22.t130.t1 (cl (= @p_29 @p_24)) :rule cong :premises (t22.t22.t130.t0))
(step t22.t22.t130.t2 (cl (= @p_26 @p_26)) :rule refl)
(step t22.t22.t130.t3 (cl (= @p_30 @p_31)) :rule cong :premises (t22.t22.t130.t1 t22.t22.t130.t2))
(step t22.t22.t130.t4 (cl (= (* 1/1 (- @p_24 @p_26)) (* -1/1 (- @p_26 @p_24)))) :rule poly_simp)
(step t22.t22.t130.t5 (cl (= @p_31 @p_27)) :rule poly_simp_rel :premises (t22.t22.t130.t4))
(step t22.t22.t130.t6 (cl (= @p_30 @p_27)) :rule trans :premises (t22.t22.t130.t3 t22.t22.t130.t5))
(step t22.t22.t130 (cl @p_20) :rule bind)
(step t22.t22.t131 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule resolution :premises (t22.t22.t129 t22.t22.t130 a23))
(step t22.t22.t132 (cl @p_19) :rule resolution :premises (t22.t22.t128 t22.t22.t131))
(step t22.t22.t133 (cl @p_1537) :rule resolution :premises (t22.t22.t123 t22.t22.t126 t22.t22.t132))
(step t22.t22.t134 (cl @p_1538) :rule and_intro :premises (t22.t22.t36 t22.t22.t133))
(step t22.t22.t135 (cl @p_1536) :rule resolution :premises (t22.t22.t122 t22.t22.t134))
(step t22.t22.t136 (cl (=> (! (and (! (> 2/1 0/1) :named @p_512) @p_244) :named @p_1535) @p_1534)) :rule la_mult_pos)
(step t22.t22.t137 (cl (not @p_1535) @p_1534) :rule implies :premises (t22.t22.t136))
(step t22.t22.t138 (cl (= (! (= @p_512 true) :named @p_515) @p_512)) :rule equiv_simplify)
(step t22.t22.t139 (cl (not @p_515) @p_512) :rule equiv1 :premises (t22.t22.t138))
(step t22.t22.t140 (cl @p_515) :rule evaluate)
(step t22.t22.t141 (cl @p_512) :rule resolution :premises (t22.t22.t139 t22.t22.t140))
(step t22.t22.t142 (cl @p_244) :rule symm :premises (t22.a1))
(step t22.t22.t143 (cl @p_1535) :rule and_intro :premises (t22.t22.t141 t22.t22.t142))
(step t22.t22.t144 (cl @p_1534) :rule resolution :premises (t22.t22.t137 t22.t22.t143))
(step t22.t22.t145 (cl (not (! (= @p_63 @p_1531) :named @p_1532)) @p_64 @p_1531) :rule equiv_pos2)
(step t22.t22.t146 (cl (= @p_1531 (! (>= 0/1 @p_140) :named @p_1533))) :rule rare_rewrite :args ("arith-elim-leq" @p_140 0/1))
(step t22.t22.t147 (cl (= (* -1/1 (- 0/1 @p_140)) (* -1/1 (- @p_62 0/1)))) :rule poly_simp)
(step t22.t22.t148 (cl (= @p_1533 @p_63)) :rule poly_simp_rel :premises (t22.t22.t147))
(step t22.t22.t149 (cl (= @p_1531 @p_63)) :rule trans :premises (t22.t22.t146 t22.t22.t148))
(step t22.t22.t150 (cl @p_1532) :rule symm :premises (t22.t22.t149))
(step t22.t22.t151 (cl @p_1531) :rule resolution :premises (t22.t22.t145 t22.t22.t150 t22.a0))
(step t22.t22.t152 (cl @p_1530) :rule resolution :premises (t22.t22.t30 t22.t22.t38 t22.t22.t48 t22.t22.t71 t22.t22.t95 t22.t22.t120 t22.t22.t135 t22.t22.t144 t22.t22.t151))
(step t22.t22.t153 (cl false) :rule resolution :premises (t22.t22.t0 t22.t22.t29 t22.t22.t152))
(step t22.t22 (cl @p_1521 false) :rule subproof :discharge (t22.t22.a0))
(step t22.t23 (cl @p_1523 false) :rule resolution :premises (t22.t21 t22.t22))
(step t22.t24 (cl @p_1523 (! (not false) :named @p_133)) :rule implies_neg2)
(step t22.t25 (cl @p_1523 @p_1523) :rule resolution :premises (t22.t23 t22.t24))
(step t22.t26 (cl @p_1523) :rule contraction :premises (t22.t25))
(step t22.t27 (cl (= @p_1523 @p_1521)) :rule implies_simplify)
(step t22.t28 (cl (not @p_1523) @p_1521) :rule equiv1 :premises (t22.t27))
(step t22.t29 (cl @p_1521) :rule resolution :premises (t22.t26 t22.t28))
(step t22.t30 (cl @p_1522) :rule resolution :premises (t22.t18 t22.t20 t22.t29))
(step t22.t31 (cl @p_1521) :rule resolution :premises (t22.t13 t22.t17 t22.t30))
(step t22.t32 (cl) :rule resolution :premises (t22.t12 t22.t31))
(step t22 (cl @p_64 @p_1268 @p_1192 @p_1209 @p_1193 @p_1210 @p_15 @p_1509 false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2 t22.a3 t22.a4 t22.a5 t22.a6 t22.a7))
(step t23 (cl @p_1516 @p_63) :rule and_pos :args (0))
(step t24 (cl @p_1516 @p_1264) :rule and_pos :args (1))
(step t25 (cl @p_1516 @p_19) :rule and_pos :args (2))
(step t26 (cl @p_1516 @p_210) :rule and_pos :args (3))
(step t27 (cl @p_1516 @p_36) :rule and_pos :args (4))
(step t28 (cl @p_1516 @p_231) :rule and_pos :args (5))
(step t29 (cl @p_1516 @p_13) :rule and_pos :args (6))
(step t30 (cl @p_1516 @p_678) :rule and_pos :args (7))
(step t31 (cl false @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516) :rule resolution :premises (t22 t23 t24 t25 t26 t27 t28 t29 t30))
(step t32 (cl @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 @p_1516 false) :rule reordering :premises (t31))
(step t33 (cl @p_1516 false) :rule contraction :premises (t32))
(step t34 (cl @p_1517 false) :rule resolution :premises (t21 t33))
(step t35 (cl @p_1517 @p_133) :rule implies_neg2)
(step t36 (cl @p_1517 @p_1517) :rule resolution :premises (t34 t35))
(step t37 (cl @p_1517) :rule contraction :premises (t36))
(step t38 (cl (= @p_1517 @p_1516)) :rule implies_simplify)
(step t39 (cl (not @p_1517) @p_1516) :rule equiv1 :premises (t38))
(step t40 (cl @p_1516) :rule resolution :premises (t37 t39))
(step t41 (cl @p_1514) :rule resolution :premises (t20 t40))
(step t42 (cl @p_15 @p_1192 @p_1193 @p_1113 @p_64 @p_1209 @p_1210 @p_1509) :rule not_and :premises (t41))
(step t43 (cl @p_1512 @p_16) :rule or_neg :args (0))
(step t44 (cl @p_1512 (! (not @p_1192) :named @p_1256)) :rule or_neg :args (1))
(step t45 (cl @p_1512 (! (not @p_1193) :named @p_1255)) :rule or_neg :args (2))
(step t46 (cl @p_1512 (! (not @p_1113) :named @p_1254)) :rule or_neg :args (3))
(step t47 (cl @p_1512 (! (not @p_64) :named @p_205)) :rule or_neg :args (4))
(step t48 (cl @p_1512 (! (not @p_1209) :named @p_1244)) :rule or_neg :args (5))
(step t49 (cl @p_1512 (! (not @p_1210) :named @p_1243)) :rule or_neg :args (6))
(step t50 (cl @p_1512 (not @p_1509)) :rule or_neg :args (7))
(step t51 (cl @p_1512 @p_1512 @p_1512 @p_1512 @p_1512 @p_1512 @p_1512 @p_1512) :rule resolution :premises (t42 t43 t44 t45 t46 t47 t48 t49 t50))
(step t52 (cl @p_1512) :rule contraction :premises (t51))
(step t53 (cl @p_1511) :rule resolution :premises (t0 t2 t52))
(step t54 (cl @p_15 @p_1192 @p_1193 @p_1113 @p_64 @p_1209 @p_1210 @p_677) :rule or :premises (t53))
(step t55 (cl @p_15 @p_1192 @p_1193 @p_64 @p_1113 @p_1209 @p_1210 @p_677) :rule reordering :premises (t54))
(step t56 (cl (not (! (= (! (or (! (not (! (= (! (not (! (>= (! (+ (! (* -1/1 (! (times$a (! (+ @p_139 @p_4) :named @p_679) @p_1) :named @p_681)) :named @p_682) (! (times$a @p_679 @p_18) :named @p_680)) :named @p_683) 0/1) :named @p_684)) :named @p_685) @p_678) :named @p_686)) :named @p_1506) (! (not @p_685) :named @p_1404) @p_678) :named @p_1508) (! (or @p_1506 @p_684 @p_678) :named @p_1507)) :named @p_1510)) (not @p_1508) @p_1507) :rule equiv_pos2)
(step t57 (cl (= @p_1404 @p_684)) :rule rare_rewrite :args ("bool-double-not-elim" @p_684))
(step t58 (cl (= @p_678 @p_678)) :rule refl)
(step t59 (cl @p_1510) :rule cong :premises (t57 t58))
(step t60 (cl @p_1506 @p_1404 @p_678) :rule equiv_pos2)
(step t61 (cl @p_1508 (not @p_1506)) :rule or_neg :args (0))
(step t62 (cl @p_1508 (not @p_1404)) :rule or_neg :args (1))
(step t63 (cl @p_1508 @p_1509) :rule or_neg :args (2))
(step t64 (cl @p_1508 @p_1508 @p_1508) :rule resolution :premises (t60 t61 t62 t63))
(step t65 (cl @p_1508) :rule contraction :premises (t64))
(step t66 (cl @p_1507) :rule resolution :premises (t56 t59 t65))
(step t67 (cl @p_1506 @p_684 @p_678) :rule or :premises (t66))
(step t68 (cl @p_684 @p_678 @p_1506) :rule reordering :premises (t67))
(step t69 (cl (not (! (= (! (or (! (not (! (not (! (>= @p_140 0/1) :named @p_141)) :named @p_142)) :named @p_163) @p_15 (! (not (! (= @p_6 (! (times$a @p_4 @p_1) :named @p_65)) :named @p_410)) :named @p_424) (! (not (! (= @p_1 (! (divide$ @p_6 @p_4) :named @p_1116)) :named @p_1188)) :named @p_1191) @p_1192 @p_1193 (! (not (! (= @p_4 (! (times$a @p_247 @p_4) :named @p_248)) :named @p_249)) :named @p_574) @p_1113 (! (not (! (= @p_65 (! (divide$ (! (times$a @p_4 1/1) :named @p_361) 2/1) :named @p_362)) :named @p_406)) :named @p_427) (! (not (! (= (! (divide$ @p_6 @p_1) :named @p_932) (! (times$a @p_1 (! (divide$ @p_4 @p_1) :named @p_296)) :named @p_314)) :named @p_969)) :named @p_1042) (! (not (! (= @p_1116 (! (times$a @p_1 (! (divide$ @p_4 @p_4) :named @p_1098)) :named @p_1099)) :named @p_1117)) :named @p_1199) (! (not (! (not (! (= @p_6 1/1) :named @p_1122)) :named @p_1123)) :named @p_1402) (! (not (! (= (! (times$a 1/1 @p_4) :named @p_301) @p_361) :named @p_405)) :named @p_428) (! (not (! (= @p_4 @p_361) :named @p_396)) :named @p_429) (! (not (! (= (! (times$a 1/1 2/1) :named @p_306) 2/1) :named @p_385)) :named @p_430) (! (not (! (= (! (times$a @p_4 1/1) :named @p_361) (! (times$a @p_362 2/1) :named @p_363)) :named @p_364)) :named @p_431) (! (not (! (= (! (divide$ @p_306 1/1) :named @p_309) 2/1) :named @p_344)) :named @p_432) (! (not (! (= @p_296 (! (divide$ (! (times$a @p_4 2/1) :named @p_304) 1/1) :named @p_341)) :named @p_342)) :named @p_433) (! (not (! (= @p_18 (! (times$a @p_247 @p_18) :named @p_1055)) :named @p_1103)) :named @p_1201) (! (not (! (= @p_314 (! (times$a @p_296 @p_1) :named @p_339)) :named @p_340)) :named @p_434) (! (not (! (= (! (times$a @p_65 @p_1098) :named @p_1101) (! (times$a @p_4 @p_1099) :named @p_1100)) :named @p_1102)) :named @p_1202) (! (not (! (= @p_65 (! (+ (! (* -1/1 (! (times$a @p_139 @p_1) :named @p_892)) :named @p_895) @p_681) :named @p_1088)) :named @p_1089)) :named @p_1400) (! (not (! (= (! (times$a @p_139 @p_18) :named @p_1051) (! (+ (* -1/1 (! (times$a @p_4 @p_18) :named @p_936)) @p_680) :named @p_1080)) :named @p_1081)) :named @p_1204) (! (not (! (= @p_1055 (! (* 1/2 (! (times$a (! (* 4/1 @p_1) :named @p_1066) @p_18) :named @p_1067)) :named @p_1068)) :named @p_1069)) :named @p_1205) (! (not (! (= (! (times$a @p_1 @p_18) :named @p_1053) (! (* 1/2 @p_1055) :named @p_1056)) :named @p_1057)) :named @p_1206) (! (not (! (= (! (times$a @p_1 @p_18) :named @p_1053) (! (* -1/1 @p_1051) :named @p_1052)) :named @p_1054)) :named @p_1207) (! (not (! (= @p_1 (! (divide$ @p_314 @p_296) :named @p_862)) :named @p_960)) :named @p_1208) @p_1209 @p_1210 (! (not (! (>= @p_6 1/1) :named @p_938)) :named @p_941) (! (not (! (= @p_936 (! (divide$ @p_361 @p_4) :named @p_935)) :named @p_937)) :named @p_1211) (! (not (! (= (! (times$a @p_4 @p_309) :named @p_310) (! (divide$ (! (times$a @p_4 @p_306) :named @p_307) 1/1) :named @p_308)) :named @p_311)) :named @p_437) (! (not (! (= (! (times$a @p_4 2/1) :named @p_304) (! (times$a 2/1 @p_4) :named @p_270)) :named @p_305)) :named @p_438) (! (not (! (= (! (divide$ @p_4 @p_932) :named @p_933) (! (divide$ @p_65 @p_6) :named @p_931)) :named @p_934)) :named @p_1214) (! (not (! (= (! (divide$ @p_6 @p_362) :named @p_929) (! (divide$ (! (times$a @p_6 2/1) :named @p_290) @p_361) :named @p_928)) :named @p_930)) :named @p_1215) (! (not (! (= @p_4 (! (divide$ @p_270 2/1) :named @p_921)) :named @p_922)) :named @p_1216) (! (not (! (= (! (divide$ @p_304 @p_4) :named @p_912) 2/1) :named @p_913)) :named @p_1217) (! (not (! (= (! (times$a @p_270 @p_1) :named @p_294) (! (times$a 2/1 @p_65) :named @p_293)) :named @p_295)) :named @p_441) (! (not (! (= (! (times$a @p_6 2/1) :named @p_290) (! (times$a 2/1 @p_6) :named @p_289)) :named @p_291)) :named @p_442) (! (not (! (= (! (times$a @p_1 @p_1) :named @p_890) (! (* 1/2 (! (times$a @p_247 @p_1) :named @p_900)) :named @p_901)) :named @p_902)) :named @p_1219) (! (not (! (= @p_892 (! (* -1/1 @p_890) :named @p_891)) :named @p_893)) :named @p_1220) (! (not (! (= (! (divide$ @p_306 2/1) :named @p_874) 1/1) :named @p_875)) :named @p_1221) (! (not (! (= (! (divide$ (! (times$a 1/1 2/1) :named @p_306) (! (divide$ @p_270 @p_4) :named @p_871)) :named @p_872) (! (divide$ (! (times$a @p_306 @p_4) :named @p_869) (! (times$a 2/1 @p_4) :named @p_270)) :named @p_870)) :named @p_873)) :named @p_1222) (! (not (! (= (! (divide$ @p_4 (! (divide$ @p_304 2/1) :named @p_866)) :named @p_867) (! (divide$ @p_304 @p_304) :named @p_865)) :named @p_868)) :named @p_1223) (! (not (! (= (! (times$a @p_247 @p_862) :named @p_863) (! (divide$ (! (times$a @p_247 @p_314) :named @p_860) (! (divide$ @p_4 @p_1) :named @p_296)) :named @p_861)) :named @p_864)) :named @p_1226) @p_685) :named @p_1403) (! (or @p_141 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_1122 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226 @p_685) :named @p_1401)) :named @p_1505)) (not @p_1403) @p_1401) :rule equiv_pos2)
(step t70 (cl (= @p_163 @p_141)) :rule rare_rewrite :args ("bool-double-not-elim" @p_141))
(step t71 (cl (= @p_15 @p_15)) :rule refl)
(step t72 (cl (= @p_424 @p_424)) :rule refl)
(step t73 (cl (= @p_1191 @p_1191)) :rule refl)
(step t74 (cl (= @p_1192 @p_1192)) :rule refl)
(step t75 (cl (= @p_1193 @p_1193)) :rule refl)
(step t76 (cl (= @p_574 @p_574)) :rule refl)
(step t77 (cl (= @p_1113 @p_1113)) :rule refl)
(step t78 (cl (= @p_427 @p_427)) :rule refl)
(step t79 (cl (= @p_1042 @p_1042)) :rule refl)
(step t80 (cl (= @p_1199 @p_1199)) :rule refl)
(step t81 (cl (= @p_1402 @p_1122)) :rule rare_rewrite :args ("bool-double-not-elim" @p_1122))
(step t82 (cl (= @p_428 @p_428)) :rule refl)
(step t83 (cl (= @p_429 @p_429)) :rule refl)
(step t84 (cl (= @p_430 @p_430)) :rule refl)
(step t85 (cl (= @p_431 @p_431)) :rule refl)
(step t86 (cl (= @p_432 @p_432)) :rule refl)
(step t87 (cl (= @p_433 @p_433)) :rule refl)
(step t88 (cl (= @p_1201 @p_1201)) :rule refl)
(step t89 (cl (= @p_434 @p_434)) :rule refl)
(step t90 (cl (= @p_1202 @p_1202)) :rule refl)
(step t91 (cl (= @p_1400 @p_1400)) :rule refl)
(step t92 (cl (= @p_1204 @p_1204)) :rule refl)
(step t93 (cl (= @p_1205 @p_1205)) :rule refl)
(step t94 (cl (= @p_1206 @p_1206)) :rule refl)
(step t95 (cl (= @p_1207 @p_1207)) :rule refl)
(step t96 (cl (= @p_1208 @p_1208)) :rule refl)
(step t97 (cl (= @p_1209 @p_1209)) :rule refl)
(step t98 (cl (= @p_1210 @p_1210)) :rule refl)
(step t99 (cl (= @p_941 @p_941)) :rule refl)
(step t100 (cl (= @p_1211 @p_1211)) :rule refl)
(step t101 (cl (= @p_437 @p_437)) :rule refl)
(step t102 (cl (= @p_438 @p_438)) :rule refl)
(step t103 (cl (= @p_1214 @p_1214)) :rule refl)
(step t104 (cl (= @p_1215 @p_1215)) :rule refl)
(step t105 (cl (= @p_1216 @p_1216)) :rule refl)
(step t106 (cl (= @p_1217 @p_1217)) :rule refl)
(step t107 (cl (= @p_441 @p_441)) :rule refl)
(step t108 (cl (= @p_442 @p_442)) :rule refl)
(step t109 (cl (= @p_1219 @p_1219)) :rule refl)
(step t110 (cl (= @p_1220 @p_1220)) :rule refl)
(step t111 (cl (= @p_1221 @p_1221)) :rule refl)
(step t112 (cl (= @p_1222 @p_1222)) :rule refl)
(step t113 (cl (= @p_1223 @p_1223)) :rule refl)
(step t114 (cl (= @p_1226 @p_1226)) :rule refl)
(step t115 (cl (= @p_685 @p_685)) :rule refl)
(step t116 (cl @p_1505) :rule cong :premises (t70 t71 t72 t73 t74 t75 t76 t77 t78 t79 t80 t81 t82 t83 t84 t85 t86 t87 t88 t89 t90 t91 t92 t93 t94 t95 t96 t97 t98 t99 t100 t101 t102 t103 t104 t105 t106 t107 t108 t109 t110 t111 t112 t113 t114 t115))
(step t117 (cl (! (and @p_142 @p_13 @p_410 @p_1188 @p_19 @p_36 @p_249 @p_244 @p_406 @p_969 @p_1117 @p_1123 @p_405 @p_396 @p_385 @p_364 @p_344 @p_342 @p_1103 @p_340 @p_1102 @p_1089 @p_1081 @p_1069 @p_1057 @p_1054 @p_960 @p_210 @p_231 @p_938 @p_937 @p_311 @p_305 @p_934 @p_930 @p_922 @p_913 @p_295 @p_291 @p_902 @p_893 @p_875 @p_873 @p_868 @p_864) :named @p_1405) @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_1402 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226) :rule and_neg)
(step t118 (cl (! (=> @p_1405 @p_685) :named @p_1407) @p_1405) :rule implies_neg1)
(anchor :step t119)
(assume t119.a0 @p_142)
(assume t119.a1 @p_13)
(assume t119.a2 @p_410)
(assume t119.a3 @p_1188)
(assume t119.a4 @p_19)
(assume t119.a5 @p_36)
(assume t119.a6 @p_249)
(assume t119.a7 @p_244)
(assume t119.a8 @p_406)
(assume t119.a9 @p_969)
(assume t119.a10 @p_1117)
(assume t119.a11 @p_1123)
(assume t119.a12 @p_405)
(assume t119.a13 @p_396)
(assume t119.a14 @p_385)
(assume t119.a15 @p_364)
(assume t119.a16 @p_344)
(assume t119.a17 @p_342)
(assume t119.a18 @p_1103)
(assume t119.a19 @p_340)
(assume t119.a20 @p_1102)
(assume t119.a21 @p_1089)
(assume t119.a22 @p_1081)
(assume t119.a23 @p_1069)
(assume t119.a24 @p_1057)
(assume t119.a25 @p_1054)
(assume t119.a26 @p_960)
(assume t119.a27 @p_210)
(assume t119.a28 @p_231)
(assume t119.a29 @p_938)
(assume t119.a30 @p_937)
(assume t119.a31 @p_311)
(assume t119.a32 @p_305)
(assume t119.a33 @p_934)
(assume t119.a34 @p_930)
(assume t119.a35 @p_922)
(assume t119.a36 @p_913)
(assume t119.a37 @p_295)
(assume t119.a38 @p_291)
(assume t119.a39 @p_902)
(assume t119.a40 @p_893)
(assume t119.a41 @p_875)
(assume t119.a42 @p_873)
(assume t119.a43 @p_868)
(assume t119.a44 @p_864)
(step t119.t0 (cl (! (=> (! (and (! (= 1/1 @p_936) :named @p_1411) (! (= @p_6 @p_1088) :named @p_1410) (! (not (! (>= (! (* -1/1 @p_6) :named @p_638) -1/1) :named @p_1408)) :named @p_1409) @p_210 @p_36 @p_231 @p_13 @p_1069 (! (= @p_17 @p_1068) :named @p_1260) (! (= 1/2 @p_900) :named @p_1261) @p_902 @p_893 @p_1081 (! (= @p_1052 @p_1056) :named @p_1262) @p_1264 @p_142) :named @p_1412) @p_685) :named @p_1436) @p_1412) :rule implies_neg1)
(anchor :step t119.t1)
(assume t119.t1.a0 @p_1411)
(assume t119.t1.a1 @p_1410)
(assume t119.t1.a2 @p_1409)
(assume t119.t1.a3 @p_210)
(assume t119.t1.a4 @p_36)
(assume t119.t1.a5 @p_231)
(assume t119.t1.a6 @p_13)
(assume t119.t1.a7 @p_1069)
(assume t119.t1.a8 @p_1260)
(assume t119.t1.a9 @p_1261)
(assume t119.t1.a10 @p_902)
(assume t119.t1.a11 @p_893)
(assume t119.t1.a12 @p_1081)
(assume t119.t1.a13 @p_1262)
(assume t119.t1.a14 @p_1264)
(assume t119.t1.a15 @p_142)
(step t119.t1.t0 (cl (not (! (= (! (> (! (+ @p_681 (! (* -1/1 @p_680) :named @p_1278)) :named @p_1438) 0/1) :named @p_1439) @p_685) :named @p_1502)) (not @p_1439) @p_685) :rule equiv_pos2)
(step t119.t1.t1 (cl (= @p_1439 (! (not (! (>= 0/1 @p_1438) :named @p_1503)) :named @p_1504))) :rule rare_rewrite :args ("arith-elim-gt" @p_1438 0/1))
(step t119.t1.t2 (cl (= (! (<= @p_1438 0/1) :named @p_1440) @p_1503)) :rule rare_rewrite :args ("arith-elim-leq" @p_1438 0/1))
(step t119.t1.t3 (cl (= @p_1503 @p_1440)) :rule symm :premises (t119.t1.t2))
(step t119.t1.t4 (cl (= @p_1504 (! (not @p_1440) :named @p_1441))) :rule cong :premises (t119.t1.t3))
(step t119.t1.t5 (cl (= @p_1439 @p_1441)) :rule trans :premises (t119.t1.t1 t119.t1.t4))
(step t119.t1.t6 (cl (= (* 1/1 (- 0/1 @p_1438)) (* 1/1 (- @p_683 0/1)))) :rule poly_simp)
(step t119.t1.t7 (cl (= @p_1503 @p_684)) :rule poly_simp_rel :premises (t119.t1.t6))
(step t119.t1.t8 (cl (= @p_1440 @p_684)) :rule trans :premises (t119.t1.t2 t119.t1.t7))
(step t119.t1.t9 (cl (= @p_1441 @p_685)) :rule cong :premises (t119.t1.t8))
(step t119.t1.t10 (cl @p_1502) :rule trans :premises (t119.t1.t5 t119.t1.t9))
(step t119.t1.t11 (cl (not (! (= @p_1441 @p_1439) :named @p_1501)) (not @p_1441) @p_1439) :rule equiv_pos2)
(step t119.t1.t12 (cl (= @p_685 @p_1439)) :rule symm :premises (t119.t1.t10))
(step t119.t1.t13 (cl @p_1501) :rule trans :premises (t119.t1.t9 t119.t1.t12))
(step t119.t1.t14 (cl (! (=> @p_1440 false) :named @p_1442) @p_1440) :rule implies_neg1)
(anchor :step t119.t1.t15)
(assume t119.t1.t15.a0 @p_1440)
(step t119.t1.t15.t0 (cl (not (! (= (! (< (! (+ @p_1438 (! (* 1/2 @p_140) :named @p_1457) (! (* 1/2 @p_1) :named @p_1456) (! (* 1/2 (! (+ @p_1055 (! (* 2/1 @p_1051) :named @p_1281)) :named @p_1282)) :named @p_1455) (! (* -1/1 (! (+ @p_1051 @p_936 @p_1278) :named @p_1283)) :named @p_1454) (! (* -1/1 (! (+ @p_892 @p_890) :named @p_1285)) :named @p_1453) (! (+ @p_890 (! (* -1/2 @p_900) :named @p_1287)) :named @p_1288) @p_901 (! (* 1/2 (! (+ @p_17 (! (* -1/2 @p_1067) :named @p_1290)) :named @p_1291)) :named @p_1452) (! (* -1/2 (! (+ @p_1055 @p_1290) :named @p_1292)) :named @p_1451) (! (* -1/2 @p_10) :named @p_1450) (! (* -1/2 @p_230) :named @p_1449) (! (* 1/2 @p_1296) :named @p_1448) (! (* 1/2 @p_1277) :named @p_1447) @p_638 (! (+ @p_6 @p_892 @p_682) :named @p_1446) @p_936) :named @p_1458) (! (+ 0/1 (! (* 1/2 0/1) :named @p_492) (! (* 1/2 1/2) :named @p_1444) @p_492 @p_175 @p_175 0/1 @p_1444 @p_492 (! (* -1/2 0/1) :named @p_586) (! (* -1/2 1/1) :named @p_1443) @p_586 @p_492 @p_492 @p_737 0/1 1/1) :named @p_1445)) :named @p_1459) false) :named @p_1489)) (not @p_1459) false) :rule equiv_pos2)
(step t119.t1.t15.t1 (cl (= @p_1459 (! (not (! (>= @p_1458 @p_1445) :named @p_1490)) :named @p_1491))) :rule rare_rewrite :args ("arith-elim-lt" @p_1458 @p_1445))
(step t119.t1.t15.t2 (cl (= @p_1458 (! (+ @p_1287 @p_901 @p_1450 @p_1051 (! (* 0/1 @p_680) :named @p_1358) (! (* 0/1 @p_1067) :named @p_1357) @p_682 @p_681 @p_1456 (! (* 0/1 @p_890) :named @p_1356) (! (* 0/1 @p_892) :named @p_1355) (! (* 0/1 @p_936) :named @p_1354) @p_1052 (! (* 0/1 @p_1055) :named @p_1353) @p_1352 @p_638 (! (* -1/2 @p_33) :named @p_1498) (! (* -1/2 @p_17) :named @p_1497) (! (* 1/2 @p_33) :named @p_1496) (! (* 1/2 @p_17) :named @p_1495) (! (* -1/2 @p_1) :named @p_1494) (! (* 1/2 @p_10) :named @p_1493) @p_6 @p_1351) :named @p_1499))) :rule poly_simp)
(step t119.t1.t15.t3 (cl (= @p_1358 0/1)) :rule poly_simp)
(step t119.t1.t15.t4 (cl (= @p_1357 0/1)) :rule poly_simp)
(step t119.t1.t15.t5 (cl (= @p_682 @p_682)) :rule refl)
(step t119.t1.t15.t6 (cl (= @p_681 @p_681)) :rule refl)
(step t119.t1.t15.t7 (cl (= @p_1456 @p_1456)) :rule refl)
(step t119.t1.t15.t8 (cl (= @p_1356 0/1)) :rule poly_simp)
(step t119.t1.t15.t9 (cl (= @p_1355 0/1)) :rule poly_simp)
(step t119.t1.t15.t10 (cl (= @p_1354 0/1)) :rule poly_simp)
(step t119.t1.t15.t11 (cl (= @p_1052 @p_1052)) :rule refl)
(step t119.t1.t15.t12 (cl (= @p_1353 0/1)) :rule poly_simp)
(step t119.t1.t15.t13 (cl (= @p_1352 0/1)) :rule poly_simp)
(step t119.t1.t15.t14 (cl (= @p_638 @p_638)) :rule refl)
(step t119.t1.t15.t15 (cl (= @p_1498 @p_1498)) :rule refl)
(step t119.t1.t15.t16 (cl (= @p_1497 @p_1497)) :rule refl)
(step t119.t1.t15.t17 (cl (= @p_1496 @p_1496)) :rule refl)
(step t119.t1.t15.t18 (cl (= @p_1495 @p_1495)) :rule refl)
(step t119.t1.t15.t19 (cl (= @p_1494 @p_1494)) :rule refl)
(step t119.t1.t15.t20 (cl (= @p_1493 @p_1493)) :rule refl)
(step t119.t1.t15.t21 (cl (= @p_6 @p_6)) :rule refl)
(step t119.t1.t15.t22 (cl (= @p_1351 0/1)) :rule poly_simp)
(step t119.t1.t15.t23 (cl (= @p_1499 (! (+ @p_1287 @p_901 @p_1450 @p_1051 0/1 0/1 @p_682 @p_681 @p_1456 0/1 0/1 0/1 @p_1052 0/1 0/1 @p_638 @p_1498 @p_1497 @p_1496 @p_1495 @p_1494 @p_1493 @p_6 0/1) :named @p_1500))) :rule cong :premises (t119.t1.t15.t3 t119.t1.t15.t4 t119.t1.t15.t5 t119.t1.t15.t6 t119.t1.t15.t7 t119.t1.t15.t8 t119.t1.t15.t9 t119.t1.t15.t10 t119.t1.t15.t11 t119.t1.t15.t12 t119.t1.t15.t13 t119.t1.t15.t14 t119.t1.t15.t15 t119.t1.t15.t16 t119.t1.t15.t17 t119.t1.t15.t18 t119.t1.t15.t19 t119.t1.t15.t20 t119.t1.t15.t21 t119.t1.t15.t22))
(step t119.t1.t15.t24 (cl (= @p_1500 0/1)) :rule poly_simp)
(step t119.t1.t15.t25 (cl (= @p_1499 0/1)) :rule trans :premises (t119.t1.t15.t23 t119.t1.t15.t24))
(step t119.t1.t15.t26 (cl (= @p_1458 0/1)) :rule trans :premises (t119.t1.t15.t2 t119.t1.t15.t25))
(step t119.t1.t15.t27 (cl (= @p_492 0/1)) :rule evaluate)
(step t119.t1.t15.t28 (cl (= @p_1444 1/4)) :rule evaluate)
(step t119.t1.t15.t29 (cl (= @p_175 0/1)) :rule evaluate)
(step t119.t1.t15.t30 (cl @p_60) :rule refl)
(step t119.t1.t15.t31 (cl (= @p_586 0/1)) :rule evaluate)
(step t119.t1.t15.t32 (cl (= @p_1443 -1/2)) :rule evaluate)
(step t119.t1.t15.t33 (cl (= @p_737 -1/1)) :rule evaluate)
(step t119.t1.t15.t34 (cl (! (= 1/1 1/1) :named @p_388)) :rule refl)
(step t119.t1.t15.t35 (cl (= @p_1445 (! (+ 0/1 0/1 1/4 0/1 0/1 0/1 0/1 1/4 0/1 0/1 -1/2 0/1 0/1 0/1 -1/1 0/1 1/1) :named @p_1492))) :rule cong :premises (t119.t1.t15.t27 t119.t1.t15.t28 t119.t1.t15.t27 t119.t1.t15.t29 t119.t1.t15.t29 t119.t1.t15.t30 t119.t1.t15.t28 t119.t1.t15.t27 t119.t1.t15.t31 t119.t1.t15.t32 t119.t1.t15.t31 t119.t1.t15.t27 t119.t1.t15.t27 t119.t1.t15.t33 t119.t1.t15.t30 t119.t1.t15.t34))
(step t119.t1.t15.t36 (cl (= @p_1492 0/1)) :rule evaluate)
(step t119.t1.t15.t37 (cl (= @p_1445 0/1)) :rule trans :premises (t119.t1.t15.t35 t119.t1.t15.t36))
(step t119.t1.t15.t38 (cl (= @p_1490 @p_190)) :rule cong :premises (t119.t1.t15.t26 t119.t1.t15.t37))
(step t119.t1.t15.t39 (cl @p_191) :rule evaluate)
(step t119.t1.t15.t40 (cl (= @p_1490 true)) :rule trans :premises (t119.t1.t15.t38 t119.t1.t15.t39))
(step t119.t1.t15.t41 (cl (= @p_1491 @p_189)) :rule cong :premises (t119.t1.t15.t40))
(step t119.t1.t15.t42 (cl (= @p_189 false)) :rule evaluate)
(step t119.t1.t15.t43 (cl (= @p_1491 false)) :rule trans :premises (t119.t1.t15.t41 t119.t1.t15.t42))
(step t119.t1.t15.t44 (cl @p_1489) :rule trans :premises (t119.t1.t15.t1 t119.t1.t15.t43))
(step t119.t1.t15.t45 (cl @p_1441 (not (! (< @p_1457 @p_492) :named @p_1487)) (not (! (= @p_1456 @p_1444) :named @p_1485)) (not (! (= @p_1455 @p_492) :named @p_1483)) (not (! (= @p_1454 @p_175) :named @p_1481)) (not (! (= @p_1453 @p_175) :named @p_1479)) (not (! (= @p_1288 0/1) :named @p_1323)) (not (! (= @p_901 @p_1444) :named @p_1477)) (not (! (= @p_1452 @p_492) :named @p_1475)) (not (! (= @p_1451 @p_586) :named @p_1473)) (not (! (<= @p_1450 @p_1443) :named @p_1471)) (not (! (<= @p_1449 @p_586) :named @p_1469)) (not (! (<= @p_1448 @p_492) :named @p_1467)) (not (! (= @p_1447 @p_492) :named @p_1465)) (not (! (< @p_638 @p_737) :named @p_1462)) (not (! (= @p_1446 0/1) :named @p_1460)) (not (! (= @p_936 1/1) :named @p_1384)) @p_1459) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1 1/1 1/1 -1/1 1/1 -1/1 -1/1 1/1))
(step t119.t1.t15.t46 (cl (=> (! (and (! (> 1/2 0/1) :named @p_536) (! (< @p_140 0/1) :named @p_1273)) :named @p_1488) @p_1487)) :rule la_mult_pos)
(step t119.t1.t15.t47 (cl (not @p_1488) @p_1487) :rule implies :premises (t119.t1.t15.t46))
(step t119.t1.t15.t48 (cl (= (! (= @p_536 true) :named @p_542) @p_536)) :rule equiv_simplify)
(step t119.t1.t15.t49 (cl (not @p_542) @p_536) :rule equiv1 :premises (t119.t1.t15.t48))
(step t119.t1.t15.t50 (cl @p_542) :rule evaluate)
(step t119.t1.t15.t51 (cl @p_536) :rule resolution :premises (t119.t1.t15.t49 t119.t1.t15.t50))
(step t119.t1.t15.t52 (cl (! (not (! (= @p_142 @p_1273) :named @p_1341)) :named @p_1342) @p_163 @p_1273) :rule equiv_pos2)
(step t119.t1.t15.t53 (cl (= @p_1273 @p_142)) :rule rare_rewrite :args ("arith-elim-lt" @p_140 0/1))
(step t119.t1.t15.t54 (cl @p_1341) :rule symm :premises (t119.t1.t15.t53))
(step t119.t1.t15.t55 (cl (! (not (! (= @p_2 @p_142) :named @p_155)) :named @p_159) (! (not @p_2) :named @p_160) @p_142) :rule equiv_pos2)
(step t119.t1.t15.t56 (cl (= @p_2 (! (not (! (>= x$ @p_1) :named @p_156)) :named @p_157))) :rule rare_rewrite :args ("arith-elim-lt" x$ @p_1))
(step t119.t1.t15.t57 (cl (= (* 1/1 (! (- x$ @p_1) :named @p_158)) (* 1/1 (- @p_140 0/1)))) :rule poly_simp)
(step t119.t1.t15.t58 (cl (= @p_156 @p_141)) :rule poly_simp_rel :premises (t119.t1.t15.t57))
(step t119.t1.t15.t59 (cl (= @p_157 @p_142)) :rule cong :premises (t119.t1.t15.t58))
(step t119.t1.t15.t60 (cl @p_155) :rule trans :premises (t119.t1.t15.t56 t119.t1.t15.t59))
(step t119.t1.t15.t61 (cl @p_142) :rule resolution :premises (t119.t1.t15.t55 t119.t1.t15.t60 a28))
(step t119.t1.t15.t62 (cl @p_1273) :rule resolution :premises (t119.t1.t15.t52 t119.t1.t15.t54 t119.t1.t15.t61))
(step t119.t1.t15.t63 (cl @p_1488) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t62))
(step t119.t1.t15.t64 (cl @p_1487) :rule resolution :premises (t119.t1.t15.t47 t119.t1.t15.t63))
(step t119.t1.t15.t65 (cl (=> (! (and @p_536 @p_244) :named @p_1486) @p_1485)) :rule la_mult_pos)
(step t119.t1.t15.t66 (cl (not @p_1486) @p_1485) :rule implies :premises (t119.t1.t15.t65))
(step t119.t1.t15.t67 (cl @p_244) :rule symm :premises (t119.t1.a14))
(step t119.t1.t15.t68 (cl @p_1486) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t67))
(step t119.t1.t15.t69 (cl @p_1485) :rule resolution :premises (t119.t1.t15.t66 t119.t1.t15.t68))
(step t119.t1.t15.t70 (cl (=> (! (and @p_536 (! (= @p_1282 0/1) :named @p_1308)) :named @p_1484) @p_1483)) :rule la_mult_pos)
(step t119.t1.t15.t71 (cl (not @p_1484) @p_1483) :rule implies :premises (t119.t1.t15.t70))
(step t119.t1.t15.t72 (cl (! (not (! (= @p_1262 @p_1308) :named @p_1309)) :named @p_1313) (! (not @p_1262) :named @p_1270) @p_1308) :rule equiv_pos2)
(step t119.t1.t15.t73 (cl (= (* 2/1 (- @p_1052 @p_1056)) (* -1/1 (! (- @p_1055 (! (* -2/1 @p_1051) :named @p_1310)) :named @p_1312)))) :rule poly_simp)
(step t119.t1.t15.t74 (cl (= @p_1262 (! (= @p_1055 @p_1310) :named @p_1311))) :rule poly_simp_rel :premises (t119.t1.t15.t73))
(step t119.t1.t15.t75 (cl (= (* 2/1 (- @p_1282 0/1)) (* 2/1 @p_1312))) :rule poly_simp)
(step t119.t1.t15.t76 (cl (= @p_1308 @p_1311)) :rule poly_simp_rel :premises (t119.t1.t15.t75))
(step t119.t1.t15.t77 (cl (= @p_1311 @p_1308)) :rule symm :premises (t119.t1.t15.t76))
(step t119.t1.t15.t78 (cl @p_1309) :rule trans :premises (t119.t1.t15.t74 t119.t1.t15.t77))
(step t119.t1.t15.t79 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :named @p_326) @p_1054)) :rule forall_inst :args (@p_1 @p_18))
(step t119.t1.t15.t80 (cl @p_326 @p_1054) :rule or :premises (t119.t1.t15.t79))
(step t119.t1.t15.t81 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1)))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :named @p_316)) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t82 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t1.t15.t82.t0 (cl (= (! (- ?v0) :named @p_321) @p_85)) :rule poly_simp)
(step t119.t1.t15.t82.t1 (cl (! (= ?v1 ?v1) :named @p_22)) :rule refl)
(step t119.t1.t15.t82.t2 (cl (= (! (times$a @p_321 ?v1) :named @p_322) (! (times$a @p_85 ?v1) :named @p_317))) :rule cong :premises (t119.t1.t15.t82.t0 t119.t1.t15.t82.t1))
(step t119.t1.t15.t82.t3 (cl (= (! (- (! (times$a ?v0 ?v1) :named @p_79)) :named @p_320) (! (* -1/1 @p_79) :named @p_324))) :rule poly_simp)
(step t119.t1.t15.t82.t4 (cl (= (! (= @p_322 @p_320) :named @p_323) (! (= @p_317 @p_324) :named @p_325))) :rule cong :premises (t119.t1.t15.t82.t2 t119.t1.t15.t82.t3))
(step t119.t1.t15.t82.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 (! (* -1/1 @p_317) :named @p_318))))) :rule poly_simp)
(step t119.t1.t15.t82.t6 (cl (= @p_325 (! (= @p_79 @p_318) :named @p_319))) :rule poly_simp_rel :premises (t119.t1.t15.t82.t5))
(step t119.t1.t15.t82.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t119.t1.t15.t82.t4 t119.t1.t15.t82.t6))
(step t119.t1.t15.t82 (cl @p_316) :rule bind)
(step t119.t1.t15.t83 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t119.t1.t15.t81 t119.t1.t15.t82 a16))
(step t119.t1.t15.t84 (cl @p_1054) :rule resolution :premises (t119.t1.t15.t80 t119.t1.t15.t83))
(step t119.t1.t15.t85 (cl (= @p_1052 @p_1053)) :rule symm :premises (t119.t1.t15.t84))
(step t119.t1.t15.t86 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a (! (+ @p_1 @p_1) :named @p_332) @p_18) :named @p_1060) (! (+ @p_1053 @p_1053) :named @p_1059)) :named @p_1061)) :named @p_1062) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_1057) :named @p_1058)) :named @p_1063)) (not @p_1062) @p_1058) :rule equiv_pos2)
(step t119.t1.t15.t87 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t119.t1.t15.t88 (cl (= @p_18 @p_18)) :rule refl)
(step t119.t1.t15.t89 (cl (= @p_1060 @p_1055)) :rule cong :premises (t119.t1.t15.t87 t119.t1.t15.t88))
(step t119.t1.t15.t90 (cl (= @p_1059 (! (* 2/1 @p_1053) :named @p_1064))) :rule poly_simp)
(step t119.t1.t15.t91 (cl (= @p_1061 (! (= @p_1055 @p_1064) :named @p_1065))) :rule cong :premises (t119.t1.t15.t89 t119.t1.t15.t90))
(step t119.t1.t15.t92 (cl (= (* 1/1 (- @p_1055 @p_1064)) (* -2/1 (- @p_1053 @p_1056)))) :rule poly_simp)
(step t119.t1.t15.t93 (cl (= @p_1065 @p_1057)) :rule poly_simp_rel :premises (t119.t1.t15.t92))
(step t119.t1.t15.t94 (cl (= @p_1061 @p_1057)) :rule trans :premises (t119.t1.t15.t91 t119.t1.t15.t93))
(step t119.t1.t15.t95 (cl @p_1063) :rule cong :premises (t119.t1.t15.t94))
(step t119.t1.t15.t96 (cl @p_1062 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t97)
(assume t119.t1.t15.t97.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t1.t15.t97.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :named @p_279) @p_1061)) :rule forall_inst :args (@p_1 @p_1 @p_18))
(step t119.t1.t15.t97.t1 (cl @p_279 @p_1061) :rule or :premises (t119.t1.t15.t97.t0))
(step t119.t1.t15.t97.t2 (cl @p_1061) :rule resolution :premises (t119.t1.t15.t97.t1 t119.t1.t15.t97.a0))
(step t119.t1.t15.t97 (cl @p_279 @p_1061) :rule subproof :discharge (t119.t1.t15.t97.a0))
(step t119.t1.t15.t98 (cl @p_1062 @p_1061) :rule resolution :premises (t119.t1.t15.t96 t119.t1.t15.t97))
(step t119.t1.t15.t99 (cl @p_1062 (not @p_1061)) :rule implies_neg2)
(step t119.t1.t15.t100 (cl @p_1062 @p_1062) :rule resolution :premises (t119.t1.t15.t98 t119.t1.t15.t99))
(step t119.t1.t15.t101 (cl @p_1062) :rule contraction :premises (t119.t1.t15.t100))
(step t119.t1.t15.t102 (cl @p_1058) :rule resolution :premises (t119.t1.t15.t86 t119.t1.t15.t95 t119.t1.t15.t101))
(step t119.t1.t15.t103 (cl @p_279 @p_1057) :rule implies :premises (t119.t1.t15.t102))
(step t119.t1.t15.t104 (cl @p_1057) :rule resolution :premises (t119.t1.t15.t103 a1))
(step t119.t1.t15.t105 (cl @p_1262) :rule trans :premises (t119.t1.t15.t85 t119.t1.t15.t104))
(step t119.t1.t15.t106 (cl @p_1308) :rule resolution :premises (t119.t1.t15.t72 t119.t1.t15.t78 t119.t1.t15.t105))
(step t119.t1.t15.t107 (cl @p_1484) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t106))
(step t119.t1.t15.t108 (cl @p_1483) :rule resolution :premises (t119.t1.t15.t71 t119.t1.t15.t107))
(step t119.t1.t15.t109 (cl (=> (! (and @p_183 (! (= @p_1283 0/1) :named @p_1315)) :named @p_1482) @p_1481)) :rule la_mult_neg)
(step t119.t1.t15.t110 (cl (not @p_1482) @p_1481) :rule implies :premises (t119.t1.t15.t109))
(step t119.t1.t15.t111 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t119.t1.t15.t112 (cl (not @p_185) @p_183) :rule equiv1 :premises (t119.t1.t15.t111))
(step t119.t1.t15.t113 (cl @p_185) :rule evaluate)
(step t119.t1.t15.t114 (cl @p_183) :rule resolution :premises (t119.t1.t15.t112 t119.t1.t15.t113))
(step t119.t1.t15.t115 (cl (not (! (= @p_1081 @p_1315) :named @p_1317)) @p_1204 @p_1315) :rule equiv_pos2)
(step t119.t1.t15.t116 (cl (= (* 1/1 (- @p_1283 0/1)) (* 1/1 (! (- @p_1051 @p_1080) :named @p_1087)))) :rule poly_simp)
(step t119.t1.t15.t117 (cl (= @p_1315 @p_1081)) :rule poly_simp_rel :premises (t119.t1.t15.t116))
(step t119.t1.t15.t118 (cl @p_1317) :rule symm :premises (t119.t1.t15.t117))
(step t119.t1.t15.t119 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= @p_680 (! (+ @p_1051 @p_936) :named @p_1083)) :named @p_1084)) :named @p_1085) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_1081) :named @p_1082)) :named @p_1086)) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t119.t1.t15.t120 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t119.t1.t15.t121 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t119.t1.t15.t120))
(step t119.t1.t15.t122 (cl @p_1086) :rule cong :premises (t119.t1.t15.t121))
(step t119.t1.t15.t123 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t124)
(assume t119.t1.t15.t124.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t1.t15.t124.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t119.t1.t15.t124.t1 (cl @p_279 @p_1084) :rule or :premises (t119.t1.t15.t124.t0))
(step t119.t1.t15.t124.t2 (cl @p_1084) :rule resolution :premises (t119.t1.t15.t124.t1 t119.t1.t15.t124.a0))
(step t119.t1.t15.t124 (cl @p_279 @p_1084) :rule subproof :discharge (t119.t1.t15.t124.a0))
(step t119.t1.t15.t125 (cl @p_1085 @p_1084) :rule resolution :premises (t119.t1.t15.t123 t119.t1.t15.t124))
(step t119.t1.t15.t126 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t119.t1.t15.t127 (cl @p_1085 @p_1085) :rule resolution :premises (t119.t1.t15.t125 t119.t1.t15.t126))
(step t119.t1.t15.t128 (cl @p_1085) :rule contraction :premises (t119.t1.t15.t127))
(step t119.t1.t15.t129 (cl @p_1082) :rule resolution :premises (t119.t1.t15.t119 t119.t1.t15.t122 t119.t1.t15.t128))
(step t119.t1.t15.t130 (cl @p_279 @p_1081) :rule implies :premises (t119.t1.t15.t129))
(step t119.t1.t15.t131 (cl @p_1081) :rule resolution :premises (t119.t1.t15.t130 a1))
(step t119.t1.t15.t132 (cl @p_1315) :rule resolution :premises (t119.t1.t15.t115 t119.t1.t15.t118 t119.t1.t15.t131))
(step t119.t1.t15.t133 (cl @p_1482) :rule and_intro :premises (t119.t1.t15.t114 t119.t1.t15.t132))
(step t119.t1.t15.t134 (cl @p_1481) :rule resolution :premises (t119.t1.t15.t110 t119.t1.t15.t133))
(step t119.t1.t15.t135 (cl (=> (! (and @p_183 (! (= @p_1285 0/1) :named @p_1319)) :named @p_1480) @p_1479)) :rule la_mult_neg)
(step t119.t1.t15.t136 (cl (not @p_1480) @p_1479) :rule implies :premises (t119.t1.t15.t135))
(step t119.t1.t15.t137 (cl (not (! (= @p_893 @p_1319) :named @p_1321)) @p_1220 @p_1319) :rule equiv_pos2)
(step t119.t1.t15.t138 (cl (= (* 1/1 (- @p_1285 0/1)) (! (* 1/1 (- @p_892 @p_891)) :named @p_899))) :rule poly_simp)
(step t119.t1.t15.t139 (cl (= @p_1319 @p_893)) :rule poly_simp_rel :premises (t119.t1.t15.t138))
(step t119.t1.t15.t140 (cl @p_1321) :rule symm :premises (t119.t1.t15.t139))
(step t119.t1.t15.t141 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))) (! (= @p_890 @p_895) :named @p_896)) :named @p_897) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))) @p_893) :named @p_894)) :named @p_898)) (not @p_897) @p_894) :rule equiv_pos2)
(step t119.t1.t15.t142 (cl (= (* 1/1 (- @p_890 @p_895)) @p_899)) :rule poly_simp)
(step t119.t1.t15.t143 (cl (= @p_896 @p_893)) :rule poly_simp_rel :premises (t119.t1.t15.t142))
(step t119.t1.t15.t144 (cl @p_898) :rule cong :premises (t119.t1.t15.t143))
(step t119.t1.t15.t145 (cl @p_897 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t146)
(assume t119.t1.t15.t146.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))))
(step t119.t1.t15.t146.t0 (cl (or @p_326 @p_896)) :rule forall_inst :args (@p_1 @p_1))
(step t119.t1.t15.t146.t1 (cl @p_326 @p_896) :rule or :premises (t119.t1.t15.t146.t0))
(step t119.t1.t15.t146.t2 (cl @p_896) :rule resolution :premises (t119.t1.t15.t146.t1 t119.t1.t15.t83))
(step t119.t1.t15.t146 (cl @p_326 @p_896) :rule subproof :discharge (t119.t1.t15.t146.a0))
(step t119.t1.t15.t147 (cl @p_897 @p_896) :rule resolution :premises (t119.t1.t15.t145 t119.t1.t15.t146))
(step t119.t1.t15.t148 (cl @p_897 (not @p_896)) :rule implies_neg2)
(step t119.t1.t15.t149 (cl @p_897 @p_897) :rule resolution :premises (t119.t1.t15.t147 t119.t1.t15.t148))
(step t119.t1.t15.t150 (cl @p_897) :rule contraction :premises (t119.t1.t15.t149))
(step t119.t1.t15.t151 (cl @p_894) :rule resolution :premises (t119.t1.t15.t141 t119.t1.t15.t144 t119.t1.t15.t150))
(step t119.t1.t15.t152 (cl @p_326 @p_893) :rule implies :premises (t119.t1.t15.t151))
(step t119.t1.t15.t153 (cl @p_893) :rule resolution :premises (t119.t1.t15.t152 t119.t1.t15.t83))
(step t119.t1.t15.t154 (cl @p_1319) :rule resolution :premises (t119.t1.t15.t137 t119.t1.t15.t140 t119.t1.t15.t153))
(step t119.t1.t15.t155 (cl @p_1480) :rule and_intro :premises (t119.t1.t15.t114 t119.t1.t15.t154))
(step t119.t1.t15.t156 (cl @p_1479) :rule resolution :premises (t119.t1.t15.t136 t119.t1.t15.t155))
(step t119.t1.t15.t157 (cl (not (! (= @p_902 @p_1323) :named @p_1325)) @p_1219 @p_1323) :rule equiv_pos2)
(step t119.t1.t15.t158 (cl (= (* 1/1 (- @p_1288 0/1)) (* 1/1 (! (- @p_890 @p_901) :named @p_911)))) :rule poly_simp)
(step t119.t1.t15.t159 (cl (= @p_1323 @p_902)) :rule poly_simp_rel :premises (t119.t1.t15.t158))
(step t119.t1.t15.t160 (cl @p_1325) :rule symm :premises (t119.t1.t15.t159))
(step t119.t1.t15.t161 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a @p_332 @p_1) :named @p_905) (! (+ @p_890 @p_890) :named @p_904)) :named @p_906)) :named @p_907) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_902) :named @p_903)) :named @p_908)) (not @p_907) @p_903) :rule equiv_pos2)
(step t119.t1.t15.t162 (cl (= @p_1 @p_1)) :rule refl)
(step t119.t1.t15.t163 (cl (= @p_905 @p_900)) :rule cong :premises (t119.t1.t15.t87 t119.t1.t15.t162))
(step t119.t1.t15.t164 (cl (= @p_904 (! (* 2/1 @p_890) :named @p_909))) :rule poly_simp)
(step t119.t1.t15.t165 (cl (= @p_906 (! (= @p_900 @p_909) :named @p_910))) :rule cong :premises (t119.t1.t15.t163 t119.t1.t15.t164))
(step t119.t1.t15.t166 (cl (= (* 1/1 (- @p_900 @p_909)) (* -2/1 @p_911))) :rule poly_simp)
(step t119.t1.t15.t167 (cl (= @p_910 @p_902)) :rule poly_simp_rel :premises (t119.t1.t15.t166))
(step t119.t1.t15.t168 (cl (= @p_906 @p_902)) :rule trans :premises (t119.t1.t15.t165 t119.t1.t15.t167))
(step t119.t1.t15.t169 (cl @p_908) :rule cong :premises (t119.t1.t15.t168))
(step t119.t1.t15.t170 (cl @p_907 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t171)
(assume t119.t1.t15.t171.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t1.t15.t171.t0 (cl (or @p_279 @p_906)) :rule forall_inst :args (@p_1 @p_1 @p_1))
(step t119.t1.t15.t171.t1 (cl @p_279 @p_906) :rule or :premises (t119.t1.t15.t171.t0))
(step t119.t1.t15.t171.t2 (cl @p_906) :rule resolution :premises (t119.t1.t15.t171.t1 t119.t1.t15.t171.a0))
(step t119.t1.t15.t171 (cl @p_279 @p_906) :rule subproof :discharge (t119.t1.t15.t171.a0))
(step t119.t1.t15.t172 (cl @p_907 @p_906) :rule resolution :premises (t119.t1.t15.t170 t119.t1.t15.t171))
(step t119.t1.t15.t173 (cl @p_907 (not @p_906)) :rule implies_neg2)
(step t119.t1.t15.t174 (cl @p_907 @p_907) :rule resolution :premises (t119.t1.t15.t172 t119.t1.t15.t173))
(step t119.t1.t15.t175 (cl @p_907) :rule contraction :premises (t119.t1.t15.t174))
(step t119.t1.t15.t176 (cl @p_903) :rule resolution :premises (t119.t1.t15.t161 t119.t1.t15.t169 t119.t1.t15.t175))
(step t119.t1.t15.t177 (cl @p_279 @p_902) :rule implies :premises (t119.t1.t15.t176))
(step t119.t1.t15.t178 (cl @p_902) :rule resolution :premises (t119.t1.t15.t177 a1))
(step t119.t1.t15.t179 (cl @p_1323) :rule resolution :premises (t119.t1.t15.t157 t119.t1.t15.t160 t119.t1.t15.t178))
(step t119.t1.t15.t180 (cl (=> (! (and @p_536 (! (= @p_900 1/2) :named @p_1326)) :named @p_1478) @p_1477)) :rule la_mult_pos)
(step t119.t1.t15.t181 (cl (not @p_1478) @p_1477) :rule implies :premises (t119.t1.t15.t180))
(step t119.t1.t15.t182 (cl @p_1326) :rule symm :premises (t119.t1.a9))
(step t119.t1.t15.t183 (cl @p_1478) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t182))
(step t119.t1.t15.t184 (cl @p_1477) :rule resolution :premises (t119.t1.t15.t181 t119.t1.t15.t183))
(step t119.t1.t15.t185 (cl (=> (! (and @p_536 (! (= @p_1291 0/1) :named @p_1327)) :named @p_1476) @p_1475)) :rule la_mult_pos)
(step t119.t1.t15.t186 (cl (not @p_1476) @p_1475) :rule implies :premises (t119.t1.t15.t185))
(step t119.t1.t15.t187 (cl (! (not (! (= @p_1260 @p_1327) :named @p_1328)) :named @p_1329) (! (not @p_1260) :named @p_1272) @p_1327) :rule equiv_pos2)
(step t119.t1.t15.t188 (cl (= (* 1/1 (- @p_1291 0/1)) (* 1/1 (- @p_17 @p_1068)))) :rule poly_simp)
(step t119.t1.t15.t189 (cl (= @p_1327 @p_1260)) :rule poly_simp_rel :premises (t119.t1.t15.t188))
(step t119.t1.t15.t190 (cl @p_1328) :rule symm :premises (t119.t1.t15.t189))
(step t119.t1.t15.t191 (cl @p_1327) :rule resolution :premises (t119.t1.t15.t187 t119.t1.t15.t190 t119.t1.a8))
(step t119.t1.t15.t192 (cl @p_1476) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t191))
(step t119.t1.t15.t193 (cl @p_1475) :rule resolution :premises (t119.t1.t15.t186 t119.t1.t15.t192))
(step t119.t1.t15.t194 (cl (=> (! (and (! (< -1/2 0/1) :named @p_602) (! (= @p_1292 0/1) :named @p_1331)) :named @p_1474) @p_1473)) :rule la_mult_neg)
(step t119.t1.t15.t195 (cl (not @p_1474) @p_1473) :rule implies :premises (t119.t1.t15.t194))
(step t119.t1.t15.t196 (cl (= (! (= @p_602 true) :named @p_604) @p_602)) :rule equiv_simplify)
(step t119.t1.t15.t197 (cl (not @p_604) @p_602) :rule equiv1 :premises (t119.t1.t15.t196))
(step t119.t1.t15.t198 (cl @p_604) :rule evaluate)
(step t119.t1.t15.t199 (cl @p_602) :rule resolution :premises (t119.t1.t15.t197 t119.t1.t15.t198))
(step t119.t1.t15.t200 (cl (not (! (= @p_1069 @p_1331) :named @p_1333)) @p_1205 @p_1331) :rule equiv_pos2)
(step t119.t1.t15.t201 (cl (= (* 1/1 (- @p_1292 0/1)) (* 1/1 (! (- @p_1055 @p_1068) :named @p_1079)))) :rule poly_simp)
(step t119.t1.t15.t202 (cl (= @p_1331 @p_1069)) :rule poly_simp_rel :premises (t119.t1.t15.t201))
(step t119.t1.t15.t203 (cl @p_1333) :rule symm :premises (t119.t1.t15.t202))
(step t119.t1.t15.t204 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a (! (+ @p_247 @p_247) :named @p_1072) @p_18) :named @p_1073) (! (+ @p_1055 @p_1055) :named @p_1071)) :named @p_1074)) :named @p_1075) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_1069) :named @p_1070)) :named @p_1076)) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t119.t1.t15.t205 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t119.t1.t15.t206 (cl (= @p_1073 @p_1067)) :rule cong :premises (t119.t1.t15.t205 t119.t1.t15.t88))
(step t119.t1.t15.t207 (cl (= @p_1071 (! (* 2/1 @p_1055) :named @p_1077))) :rule poly_simp)
(step t119.t1.t15.t208 (cl (= @p_1074 (! (= @p_1067 @p_1077) :named @p_1078))) :rule cong :premises (t119.t1.t15.t206 t119.t1.t15.t207))
(step t119.t1.t15.t209 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t119.t1.t15.t210 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t119.t1.t15.t209))
(step t119.t1.t15.t211 (cl (= @p_1074 @p_1069)) :rule trans :premises (t119.t1.t15.t208 t119.t1.t15.t210))
(step t119.t1.t15.t212 (cl @p_1076) :rule cong :premises (t119.t1.t15.t211))
(step t119.t1.t15.t213 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t214)
(assume t119.t1.t15.t214.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t1.t15.t214.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t119.t1.t15.t214.t1 (cl @p_279 @p_1074) :rule or :premises (t119.t1.t15.t214.t0))
(step t119.t1.t15.t214.t2 (cl @p_1074) :rule resolution :premises (t119.t1.t15.t214.t1 t119.t1.t15.t214.a0))
(step t119.t1.t15.t214 (cl @p_279 @p_1074) :rule subproof :discharge (t119.t1.t15.t214.a0))
(step t119.t1.t15.t215 (cl @p_1075 @p_1074) :rule resolution :premises (t119.t1.t15.t213 t119.t1.t15.t214))
(step t119.t1.t15.t216 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t119.t1.t15.t217 (cl @p_1075 @p_1075) :rule resolution :premises (t119.t1.t15.t215 t119.t1.t15.t216))
(step t119.t1.t15.t218 (cl @p_1075) :rule contraction :premises (t119.t1.t15.t217))
(step t119.t1.t15.t219 (cl @p_1070) :rule resolution :premises (t119.t1.t15.t204 t119.t1.t15.t212 t119.t1.t15.t218))
(step t119.t1.t15.t220 (cl @p_279 @p_1069) :rule implies :premises (t119.t1.t15.t219))
(step t119.t1.t15.t221 (cl @p_1069) :rule resolution :premises (t119.t1.t15.t220 a1))
(step t119.t1.t15.t222 (cl @p_1331) :rule resolution :premises (t119.t1.t15.t200 t119.t1.t15.t203 t119.t1.t15.t221))
(step t119.t1.t15.t223 (cl @p_1474) :rule and_intro :premises (t119.t1.t15.t199 t119.t1.t15.t222))
(step t119.t1.t15.t224 (cl @p_1473) :rule resolution :premises (t119.t1.t15.t195 t119.t1.t15.t223))
(step t119.t1.t15.t225 (cl (=> (! (and @p_602 @p_13) :named @p_1472) @p_1471)) :rule la_mult_neg)
(step t119.t1.t15.t226 (cl (not @p_1472) @p_1471) :rule implies :premises (t119.t1.t15.t225))
(step t119.t1.t15.t227 (cl (not @p_14) (not @p_12) @p_13) :rule equiv_pos2)
(step t119.t1.t15.t228 (cl (= @p_11 @p_15)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 1/1))
(step t119.t1.t15.t229 (cl (= @p_12 @p_16)) :rule cong :premises (t119.t1.t15.t228))
(step t119.t1.t15.t230 (cl (= @p_16 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t119.t1.t15.t231 (cl @p_14) :rule trans :premises (t119.t1.t15.t229 t119.t1.t15.t230))
(step t119.t1.t15.t232 (cl @p_13) :rule resolution :premises (t119.t1.t15.t227 t119.t1.t15.t231 a32))
(step t119.t1.t15.t233 (cl @p_1472) :rule and_intro :premises (t119.t1.t15.t199 t119.t1.t15.t232))
(step t119.t1.t15.t234 (cl @p_1471) :rule resolution :premises (t119.t1.t15.t226 t119.t1.t15.t233))
(step t119.t1.t15.t235 (cl (=> (! (and @p_602 @p_231) :named @p_1470) @p_1469)) :rule la_mult_neg)
(step t119.t1.t15.t236 (cl (not @p_1470) @p_1469) :rule implies :premises (t119.t1.t15.t235))
(step t119.t1.t15.t237 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t119.t1.t15.t238 (cl (= @p_221 x$)) :rule poly_simp)
(step t119.t1.t15.t239 (cl (= @p_208 @p_208)) :rule refl)
(step t119.t1.t15.t240 (cl (= @p_240 @p_230)) :rule cong :premises (t119.t1.t15.t238 t119.t1.t15.t239))
(step t119.t1.t15.t241 (cl @p_60) :rule refl)
(step t119.t1.t15.t242 (cl (= @p_241 @p_231)) :rule cong :premises (t119.t1.t15.t240 t119.t1.t15.t241))
(step t119.t1.t15.t243 (cl @p_243) :rule cong :premises (t119.t1.t15.t242))
(step t119.t1.t15.t244 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t119.t1.t15.t245)
(assume t119.t1.t15.t245.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t119.t1.t15.t245.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t119.t1.t15.t245.t1 (cl @p_238 @p_241) :rule or :premises (t119.t1.t15.t245.t0))
(step t119.t1.t15.t245.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t245.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t119.t1.t15.t245.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t119.t1.t15.t245.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t119.t1.t15.t245.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t119.t1.t15.t245.t3.t1))
(step t119.t1.t15.t245.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t119.t1.t15.t245.t3.t0 t119.t1.t15.t245.t3.t2))
(step t119.t1.t15.t245.t3 (cl @p_232) :rule bind)
(step t119.t1.t15.t245.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t119.t1.t15.t245.t2 t119.t1.t15.t245.t3 a25))
(step t119.t1.t15.t245.t5 (cl @p_241) :rule resolution :premises (t119.t1.t15.t245.t1 t119.t1.t15.t245.t4))
(step t119.t1.t15.t245 (cl @p_238 @p_241) :rule subproof :discharge (t119.t1.t15.t245.a0))
(step t119.t1.t15.t246 (cl @p_242 @p_241) :rule resolution :premises (t119.t1.t15.t244 t119.t1.t15.t245))
(step t119.t1.t15.t247 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t119.t1.t15.t248 (cl @p_242 @p_242) :rule resolution :premises (t119.t1.t15.t246 t119.t1.t15.t247))
(step t119.t1.t15.t249 (cl @p_242) :rule contraction :premises (t119.t1.t15.t248))
(step t119.t1.t15.t250 (cl @p_239) :rule resolution :premises (t119.t1.t15.t237 t119.t1.t15.t243 t119.t1.t15.t249))
(step t119.t1.t15.t251 (cl @p_238 @p_231) :rule implies :premises (t119.t1.t15.t250))
(step t119.t1.t15.t252 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t253 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t119.t1.t15.t253.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t119.t1.t15.t253.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t119.t1.t15.t253.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t119.t1.t15.t253.t1))
(step t119.t1.t15.t253.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t119.t1.t15.t253.t0 t119.t1.t15.t253.t2))
(step t119.t1.t15.t253 (cl @p_232) :rule bind)
(step t119.t1.t15.t254 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t119.t1.t15.t252 t119.t1.t15.t253 a25))
(step t119.t1.t15.t255 (cl @p_231) :rule resolution :premises (t119.t1.t15.t251 t119.t1.t15.t254))
(step t119.t1.t15.t256 (cl @p_1470) :rule and_intro :premises (t119.t1.t15.t199 t119.t1.t15.t255))
(step t119.t1.t15.t257 (cl @p_1469) :rule resolution :premises (t119.t1.t15.t236 t119.t1.t15.t256))
(step t119.t1.t15.t258 (cl (=> (! (and @p_536 @p_1338) :named @p_1468) @p_1467)) :rule la_mult_pos)
(step t119.t1.t15.t259 (cl (not @p_1468) @p_1467) :rule implies :premises (t119.t1.t15.t258))
(step t119.t1.t15.t260 (cl (not @p_1339) @p_1193 @p_1338) :rule equiv_pos2)
(step t119.t1.t15.t261 (cl (= @p_1338 @p_1340)) :rule rare_rewrite :args ("arith-elim-leq" @p_1296 0/1))
(step t119.t1.t15.t262 (cl (= (* -1/1 (- 0/1 @p_1296)) (* -1/1 (- @p_35 0/1)))) :rule poly_simp)
(step t119.t1.t15.t263 (cl (= @p_1340 @p_36)) :rule poly_simp_rel :premises (t119.t1.t15.t262))
(step t119.t1.t15.t264 (cl (= @p_1338 @p_36)) :rule trans :premises (t119.t1.t15.t261 t119.t1.t15.t263))
(step t119.t1.t15.t265 (cl @p_1339) :rule symm :premises (t119.t1.t15.t264))
(step t119.t1.t15.t266 (cl (not @p_59) (not @p_58) @p_55) :rule equiv_pos2)
(step t119.t1.t15.t267 (cl (= @p_56 @p_35)) :rule poly_simp)
(step t119.t1.t15.t268 (cl @p_60) :rule refl)
(step t119.t1.t15.t269 (cl (= @p_57 @p_36)) :rule cong :premises (t119.t1.t15.t267 t119.t1.t15.t268))
(step t119.t1.t15.t270 (cl @p_59) :rule cong :premises (t119.t1.t15.t269))
(step t119.t1.t15.t271 (cl @p_58 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule implies_neg1)
(anchor :step t119.t1.t15.t272)
(assume t119.t1.t15.t272.a0 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)))
(step t119.t1.t15.t272.t0 (cl (or @p_54 @p_57)) :rule forall_inst :args (p$ x$))
(step t119.t1.t15.t272.t1 (cl @p_54 @p_57) :rule or :premises (t119.t1.t15.t272.t0))
(step t119.t1.t15.t272.t2 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t272.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t1.t15.t272.t3.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t119.t1.t15.t272.t3.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t119.t1.t15.t272.t3.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t119.t1.t15.t272.t3.t1))
(step t119.t1.t15.t272.t3.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t119.t1.t15.t272.t3.t0 t119.t1.t15.t272.t3.t2))
(step t119.t1.t15.t272.t3.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t119.t1.t15.t272.t3.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t119.t1.t15.t272.t3.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t119.t1.t15.t272.t3.t5))
(step t119.t1.t15.t272.t3.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t119.t1.t15.t272.t3.t4 t119.t1.t15.t272.t3.t6))
(step t119.t1.t15.t272.t3.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t119.t1.t15.t272.t3.t3 t119.t1.t15.t272.t3.t7))
(step t119.t1.t15.t272.t3 (cl @p_37) :rule bind)
(step t119.t1.t15.t272.t4 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t119.t1.t15.t272.t2 t119.t1.t15.t272.t3 a26))
(step t119.t1.t15.t272.t5 (cl @p_57) :rule resolution :premises (t119.t1.t15.t272.t1 t119.t1.t15.t272.t4))
(step t119.t1.t15.t272 (cl @p_54 @p_57) :rule subproof :discharge (t119.t1.t15.t272.a0))
(step t119.t1.t15.t273 (cl @p_58 @p_57) :rule resolution :premises (t119.t1.t15.t271 t119.t1.t15.t272))
(step t119.t1.t15.t274 (cl @p_58 (not @p_57)) :rule implies_neg2)
(step t119.t1.t15.t275 (cl @p_58 @p_58) :rule resolution :premises (t119.t1.t15.t273 t119.t1.t15.t274))
(step t119.t1.t15.t276 (cl @p_58) :rule contraction :premises (t119.t1.t15.t275))
(step t119.t1.t15.t277 (cl @p_55) :rule resolution :premises (t119.t1.t15.t266 t119.t1.t15.t270 t119.t1.t15.t276))
(step t119.t1.t15.t278 (cl @p_54 @p_36) :rule implies :premises (t119.t1.t15.t277))
(step t119.t1.t15.t279 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t280 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t1.t15.t280.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t119.t1.t15.t280.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t119.t1.t15.t280.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t119.t1.t15.t280.t1))
(step t119.t1.t15.t280.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t119.t1.t15.t280.t0 t119.t1.t15.t280.t2))
(step t119.t1.t15.t280.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t119.t1.t15.t280.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t119.t1.t15.t280.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t119.t1.t15.t280.t5))
(step t119.t1.t15.t280.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t119.t1.t15.t280.t4 t119.t1.t15.t280.t6))
(step t119.t1.t15.t280.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t119.t1.t15.t280.t3 t119.t1.t15.t280.t7))
(step t119.t1.t15.t280 (cl @p_37) :rule bind)
(step t119.t1.t15.t281 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t119.t1.t15.t279 t119.t1.t15.t280 a26))
(step t119.t1.t15.t282 (cl @p_36) :rule resolution :premises (t119.t1.t15.t278 t119.t1.t15.t281))
(step t119.t1.t15.t283 (cl @p_1338) :rule resolution :premises (t119.t1.t15.t260 t119.t1.t15.t265 t119.t1.t15.t282))
(step t119.t1.t15.t284 (cl @p_1468) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t283))
(step t119.t1.t15.t285 (cl @p_1467) :rule resolution :premises (t119.t1.t15.t259 t119.t1.t15.t284))
(step t119.t1.t15.t286 (cl (=> (! (and @p_536 @p_1299) :named @p_1466) @p_1465)) :rule la_mult_pos)
(step t119.t1.t15.t287 (cl (not @p_1466) @p_1465) :rule implies :premises (t119.t1.t15.t286))
(step t119.t1.t15.t288 (cl (not @p_1300) @p_1209 @p_1299) :rule equiv_pos2)
(step t119.t1.t15.t289 (cl (= (* 1/1 (- @p_1277 0/1)) @p_229)) :rule poly_simp)
(step t119.t1.t15.t290 (cl (= @p_1299 @p_210)) :rule poly_simp_rel :premises (t119.t1.t15.t289))
(step t119.t1.t15.t291 (cl @p_1300) :rule symm :premises (t119.t1.t15.t290))
(step t119.t1.t15.t292 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t119.t1.t15.t293 (cl (= @p_222 @p_33)) :rule cong :premises (t119.t1.t15.t238))
(step t119.t1.t15.t294 (cl (= @p_223 @p_227)) :rule cong :premises (t119.t1.t15.t293))
(step t119.t1.t15.t295 (cl (= @p_224 @p_228)) :rule cong :premises (t119.t1.t15.t294))
(step t119.t1.t15.t296 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t119.t1.t15.t297 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t119.t1.t15.t296))
(step t119.t1.t15.t298 (cl (= @p_224 @p_210)) :rule trans :premises (t119.t1.t15.t295 t119.t1.t15.t297))
(step t119.t1.t15.t299 (cl @p_226) :rule cong :premises (t119.t1.t15.t298))
(step t119.t1.t15.t300 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t301)
(assume t119.t1.t15.t301.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t119.t1.t15.t301.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t119.t1.t15.t301.t1 (cl @p_219 @p_224) :rule or :premises (t119.t1.t15.t301.t0))
(step t119.t1.t15.t301.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t301.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t1.t15.t301.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t1.t15.t301.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t119.t1.t15.t301.t3.t0))
(step t119.t1.t15.t301.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t119.t1.t15.t301.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t119.t1.t15.t301.t3.t1 t119.t1.t15.t301.t3.t2))
(step t119.t1.t15.t301.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t119.t1.t15.t301.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t119.t1.t15.t301.t3.t4))
(step t119.t1.t15.t301.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t119.t1.t15.t301.t3.t3 t119.t1.t15.t301.t3.t5))
(step t119.t1.t15.t301.t3 (cl @p_211) :rule bind)
(step t119.t1.t15.t301.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t119.t1.t15.t301.t2 t119.t1.t15.t301.t3 a24))
(step t119.t1.t15.t301.t5 (cl @p_224) :rule resolution :premises (t119.t1.t15.t301.t1 t119.t1.t15.t301.t4))
(step t119.t1.t15.t301 (cl @p_219 @p_224) :rule subproof :discharge (t119.t1.t15.t301.a0))
(step t119.t1.t15.t302 (cl @p_225 @p_224) :rule resolution :premises (t119.t1.t15.t300 t119.t1.t15.t301))
(step t119.t1.t15.t303 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t119.t1.t15.t304 (cl @p_225 @p_225) :rule resolution :premises (t119.t1.t15.t302 t119.t1.t15.t303))
(step t119.t1.t15.t305 (cl @p_225) :rule contraction :premises (t119.t1.t15.t304))
(step t119.t1.t15.t306 (cl @p_220) :rule resolution :premises (t119.t1.t15.t292 t119.t1.t15.t299 t119.t1.t15.t305))
(step t119.t1.t15.t307 (cl @p_219 @p_210) :rule implies :premises (t119.t1.t15.t306))
(step t119.t1.t15.t308 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t119.t1.t15.t309 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t1.t15.t309.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t1.t15.t309.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t119.t1.t15.t309.t0))
(step t119.t1.t15.t309.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t119.t1.t15.t309.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t119.t1.t15.t309.t1 t119.t1.t15.t309.t2))
(step t119.t1.t15.t309.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t119.t1.t15.t309.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t119.t1.t15.t309.t4))
(step t119.t1.t15.t309.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t119.t1.t15.t309.t3 t119.t1.t15.t309.t5))
(step t119.t1.t15.t309 (cl @p_211) :rule bind)
(step t119.t1.t15.t310 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t119.t1.t15.t308 t119.t1.t15.t309 a24))
(step t119.t1.t15.t311 (cl @p_210) :rule resolution :premises (t119.t1.t15.t307 t119.t1.t15.t310))
(step t119.t1.t15.t312 (cl @p_1299) :rule resolution :premises (t119.t1.t15.t288 t119.t1.t15.t291 t119.t1.t15.t311))
(step t119.t1.t15.t313 (cl @p_1466) :rule and_intro :premises (t119.t1.t15.t51 t119.t1.t15.t312))
(step t119.t1.t15.t314 (cl @p_1465) :rule resolution :premises (t119.t1.t15.t287 t119.t1.t15.t313))
(step t119.t1.t15.t315 (cl (=> (! (and @p_183 (! (> @p_6 1/1) :named @p_1420)) :named @p_1463) @p_1462)) :rule la_mult_neg)
(step t119.t1.t15.t316 (cl (not @p_1463) @p_1462) :rule implies :premises (t119.t1.t15.t315))
(step t119.t1.t15.t317 (cl (not (! (= @p_1409 @p_1420) :named @p_1464)) (! (not @p_1409) :named @p_1419) @p_1420) :rule equiv_pos2)
(step t119.t1.t15.t318 (cl (= @p_1420 (! (not (! (>= 1/1 @p_6) :named @p_1429)) :named @p_1430))) :rule rare_rewrite :args ("arith-elim-gt" @p_6 1/1))
(step t119.t1.t15.t319 (cl (= (! (<= @p_6 1/1) :named @p_1421) @p_1429)) :rule rare_rewrite :args ("arith-elim-leq" @p_6 1/1))
(step t119.t1.t15.t320 (cl (= @p_1429 @p_1421)) :rule symm :premises (t119.t1.t15.t319))
(step t119.t1.t15.t321 (cl (= @p_1430 (! (not @p_1421) :named @p_1422))) :rule cong :premises (t119.t1.t15.t320))
(step t119.t1.t15.t322 (cl (! (= @p_1420 @p_1422) :named @p_1424)) :rule trans :premises (t119.t1.t15.t318 t119.t1.t15.t321))
(step t119.t1.t15.t323 (cl (= (* 1/1 (! (- 1/1 @p_6) :named @p_1133)) (* 1/1 (- @p_638 -1/1)))) :rule poly_simp)
(step t119.t1.t15.t324 (cl (= @p_1429 @p_1408)) :rule poly_simp_rel :premises (t119.t1.t15.t323))
(step t119.t1.t15.t325 (cl (= @p_1421 @p_1408)) :rule trans :premises (t119.t1.t15.t319 t119.t1.t15.t324))
(step t119.t1.t15.t326 (cl (= @p_1422 @p_1409)) :rule cong :premises (t119.t1.t15.t325))
(step t119.t1.t15.t327 (cl (! (= @p_1420 @p_1409) :named @p_1428)) :rule trans :premises (t119.t1.t15.t322 t119.t1.t15.t326))
(step t119.t1.t15.t328 (cl @p_1464) :rule symm :premises (t119.t1.t15.t327))
(step t119.t1.t15.t329 (cl @p_1420) :rule resolution :premises (t119.t1.t15.t317 t119.t1.t15.t328 t119.t1.a2))
(step t119.t1.t15.t330 (cl @p_1463) :rule and_intro :premises (t119.t1.t15.t114 t119.t1.t15.t329))
(step t119.t1.t15.t331 (cl @p_1462) :rule resolution :premises (t119.t1.t15.t316 t119.t1.t15.t330))
(step t119.t1.t15.t332 (cl (not (! (= @p_1410 @p_1460) :named @p_1461)) (! (not @p_1410) :named @p_1437) @p_1460) :rule equiv_pos2)
(step t119.t1.t15.t333 (cl (= (* 1/1 (- @p_1446 0/1)) (* 1/1 (- @p_6 @p_1088)))) :rule poly_simp)
(step t119.t1.t15.t334 (cl (= @p_1460 @p_1410)) :rule poly_simp_rel :premises (t119.t1.t15.t333))
(step t119.t1.t15.t335 (cl @p_1461) :rule symm :premises (t119.t1.t15.t334))
(step t119.t1.t15.t336 (cl (! (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (times$a ?v1 ?v0)))) :named @p_292) @p_410) :named @p_411)) :rule forall_inst :args (@p_1 @p_4))
(step t119.t1.t15.t337 (cl @p_292 @p_410) :rule or :premises (t119.t1.t15.t336))
(step t119.t1.t15.t338 (cl @p_410) :rule resolution :premises (t119.t1.t15.t337 a6))
(step t119.t1.t15.t339 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a (! (+ @p_4 @p_139) :named @p_1092) @p_1) :named @p_1093) (! (+ @p_65 @p_892) :named @p_1091)) :named @p_1094)) :named @p_1095) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_1089) :named @p_1090)) :named @p_1096)) (not @p_1095) @p_1090) :rule equiv_pos2)
(step t119.t1.t15.t340 (cl (= @p_1092 @p_679)) :rule poly_simp)
(step t119.t1.t15.t341 (cl (= @p_1093 @p_681)) :rule cong :premises (t119.t1.t15.t340 t119.t1.t15.t162))
(step t119.t1.t15.t342 (cl (= @p_1091 @p_1091)) :rule refl)
(step t119.t1.t15.t343 (cl (= @p_1094 (! (= @p_681 @p_1091) :named @p_1097))) :rule cong :premises (t119.t1.t15.t341 t119.t1.t15.t342))
(step t119.t1.t15.t344 (cl (= (* 1/1 (- @p_681 @p_1091)) (* -1/1 (- @p_65 @p_1088)))) :rule poly_simp)
(step t119.t1.t15.t345 (cl (= @p_1097 @p_1089)) :rule poly_simp_rel :premises (t119.t1.t15.t344))
(step t119.t1.t15.t346 (cl (= @p_1094 @p_1089)) :rule trans :premises (t119.t1.t15.t343 t119.t1.t15.t345))
(step t119.t1.t15.t347 (cl @p_1096) :rule cong :premises (t119.t1.t15.t346))
(step t119.t1.t15.t348 (cl @p_1095 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t1.t15.t349)
(assume t119.t1.t15.t349.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t1.t15.t349.t0 (cl (or @p_279 @p_1094)) :rule forall_inst :args (@p_4 @p_139 @p_1))
(step t119.t1.t15.t349.t1 (cl @p_279 @p_1094) :rule or :premises (t119.t1.t15.t349.t0))
(step t119.t1.t15.t349.t2 (cl @p_1094) :rule resolution :premises (t119.t1.t15.t349.t1 t119.t1.t15.t349.a0))
(step t119.t1.t15.t349 (cl @p_279 @p_1094) :rule subproof :discharge (t119.t1.t15.t349.a0))
(step t119.t1.t15.t350 (cl @p_1095 @p_1094) :rule resolution :premises (t119.t1.t15.t348 t119.t1.t15.t349))
(step t119.t1.t15.t351 (cl @p_1095 (not @p_1094)) :rule implies_neg2)
(step t119.t1.t15.t352 (cl @p_1095 @p_1095) :rule resolution :premises (t119.t1.t15.t350 t119.t1.t15.t351))
(step t119.t1.t15.t353 (cl @p_1095) :rule contraction :premises (t119.t1.t15.t352))
(step t119.t1.t15.t354 (cl @p_1090) :rule resolution :premises (t119.t1.t15.t339 t119.t1.t15.t347 t119.t1.t15.t353))
(step t119.t1.t15.t355 (cl @p_279 @p_1089) :rule implies :premises (t119.t1.t15.t354))
(step t119.t1.t15.t356 (cl @p_1089) :rule resolution :premises (t119.t1.t15.t355 a1))
(step t119.t1.t15.t357 (cl @p_1410) :rule trans :premises (t119.t1.t15.t338 t119.t1.t15.t356))
(step t119.t1.t15.t358 (cl @p_1460) :rule resolution :premises (t119.t1.t15.t332 t119.t1.t15.t335 t119.t1.t15.t357))
(step t119.t1.t15.t359 (cl @p_1384) :rule symm :premises (t119.t1.a0))
(step t119.t1.t15.t360 (cl @p_1459) :rule resolution :premises (t119.t1.t15.t45 t119.t1.t15.a0 t119.t1.t15.t64 t119.t1.t15.t69 t119.t1.t15.t108 t119.t1.t15.t134 t119.t1.t15.t156 t119.t1.t15.t179 t119.t1.t15.t184 t119.t1.t15.t193 t119.t1.t15.t224 t119.t1.t15.t234 t119.t1.t15.t257 t119.t1.t15.t285 t119.t1.t15.t314 t119.t1.t15.t331 t119.t1.t15.t358 t119.t1.t15.t359))
(step t119.t1.t15.t361 (cl false) :rule resolution :premises (t119.t1.t15.t0 t119.t1.t15.t44 t119.t1.t15.t360))
(step t119.t1.t15 (cl @p_1441 false) :rule subproof :discharge (t119.t1.t15.a0))
(step t119.t1.t16 (cl @p_1442 false) :rule resolution :premises (t119.t1.t14 t119.t1.t15))
(step t119.t1.t17 (cl @p_1442 @p_133) :rule implies_neg2)
(step t119.t1.t18 (cl @p_1442 @p_1442) :rule resolution :premises (t119.t1.t16 t119.t1.t17))
(step t119.t1.t19 (cl @p_1442) :rule contraction :premises (t119.t1.t18))
(step t119.t1.t20 (cl (= @p_1442 @p_1441)) :rule implies_simplify)
(step t119.t1.t21 (cl (not @p_1442) @p_1441) :rule equiv1 :premises (t119.t1.t20))
(step t119.t1.t22 (cl @p_1441) :rule resolution :premises (t119.t1.t19 t119.t1.t21))
(step t119.t1.t23 (cl @p_1439) :rule resolution :premises (t119.t1.t11 t119.t1.t13 t119.t1.t22))
(step t119.t1.t24 (cl @p_685) :rule resolution :premises (t119.t1.t0 t119.t1.t10 t119.t1.t23))
(step t119.t1 (cl (! (not @p_1411) :named @p_1434) @p_1437 @p_1419 @p_1209 @p_1193 @p_1210 @p_15 @p_1205 @p_1272 (! (not @p_1261) :named @p_1271) @p_1219 @p_1220 @p_1204 @p_1270 @p_1268 @p_163 @p_685) :rule subproof :discharge (t119.t1.a0 t119.t1.a1 t119.t1.a2 t119.t1.a3 t119.t1.a4 t119.t1.a5 t119.t1.a6 t119.t1.a7 t119.t1.a8 t119.t1.a9 t119.t1.a10 t119.t1.a11 t119.t1.a12 t119.t1.a13 t119.t1.a14 t119.t1.a15))
(step t119.t2 (cl (! (not @p_1412) :named @p_1435) @p_1411) :rule and_pos :args (0))
(step t119.t3 (cl @p_1435 @p_1410) :rule and_pos :args (1))
(step t119.t4 (cl @p_1435 @p_1409) :rule and_pos :args (2))
(step t119.t5 (cl @p_1435 @p_210) :rule and_pos :args (3))
(step t119.t6 (cl @p_1435 @p_36) :rule and_pos :args (4))
(step t119.t7 (cl @p_1435 @p_231) :rule and_pos :args (5))
(step t119.t8 (cl @p_1435 @p_13) :rule and_pos :args (6))
(step t119.t9 (cl @p_1435 @p_1069) :rule and_pos :args (7))
(step t119.t10 (cl @p_1435 @p_1260) :rule and_pos :args (8))
(step t119.t11 (cl @p_1435 @p_1261) :rule and_pos :args (9))
(step t119.t12 (cl @p_1435 @p_902) :rule and_pos :args (10))
(step t119.t13 (cl @p_1435 @p_893) :rule and_pos :args (11))
(step t119.t14 (cl @p_1435 @p_1081) :rule and_pos :args (12))
(step t119.t15 (cl @p_1435 @p_1262) :rule and_pos :args (13))
(step t119.t16 (cl @p_1435 @p_1264) :rule and_pos :args (14))
(step t119.t17 (cl @p_1435 @p_142) :rule and_pos :args (15))
(step t119.t18 (cl @p_685 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435) :rule resolution :premises (t119.t1 t119.t2 t119.t3 t119.t4 t119.t5 t119.t6 t119.t7 t119.t8 t119.t9 t119.t10 t119.t11 t119.t12 t119.t13 t119.t14 t119.t15 t119.t16 t119.t17))
(step t119.t19 (cl @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_1435 @p_685) :rule reordering :premises (t119.t18))
(step t119.t20 (cl @p_1435 @p_685) :rule contraction :premises (t119.t19))
(step t119.t21 (cl @p_1436 @p_685) :rule resolution :premises (t119.t0 t119.t20))
(step t119.t22 (cl @p_1436 @p_1404) :rule implies_neg2)
(step t119.t23 (cl @p_1436 @p_1436) :rule resolution :premises (t119.t21 t119.t22))
(step t119.t24 (cl @p_1436) :rule contraction :premises (t119.t23))
(step t119.t25 (cl @p_1435 @p_685) :rule implies :premises (t119.t24))
(step t119.t26 (cl (! (=> (! (and @p_937 @p_405 @p_396 @p_364 @p_406 @p_410 @p_930 @p_1188 @p_1117 @p_1102 @p_934 @p_291 @p_295 @p_305 @p_344 @p_311 @p_385 @p_342 @p_340 @p_969 @p_922 @p_868 @p_873 @p_913 @p_875) :named @p_1431) @p_1411) :named @p_1433) @p_1431) :rule implies_neg1)
(anchor :step t119.t27)
(assume t119.t27.a0 @p_937)
(assume t119.t27.a1 @p_405)
(assume t119.t27.a2 @p_396)
(assume t119.t27.a3 @p_364)
(assume t119.t27.a4 @p_406)
(assume t119.t27.a5 @p_410)
(assume t119.t27.a6 @p_930)
(assume t119.t27.a7 @p_1188)
(assume t119.t27.a8 @p_1117)
(assume t119.t27.a9 @p_1102)
(assume t119.t27.a10 @p_934)
(assume t119.t27.a11 @p_291)
(assume t119.t27.a12 @p_295)
(assume t119.t27.a13 @p_305)
(assume t119.t27.a14 @p_344)
(assume t119.t27.a15 @p_311)
(assume t119.t27.a16 @p_385)
(assume t119.t27.a17 @p_342)
(assume t119.t27.a18 @p_340)
(assume t119.t27.a19 @p_969)
(assume t119.t27.a20 @p_922)
(assume t119.t27.a21 @p_868)
(assume t119.t27.a22 @p_873)
(assume t119.t27.a23 @p_913)
(assume t119.t27.a24 @p_875)
(step t119.t27.t0 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (! (or (! (= 2/1 0/1) :named @p_126) (! (= 1/1 @p_874) :named @p_885)) :named @p_886)) :named @p_887) (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) @p_875) :named @p_884)) :named @p_888)) (not @p_887) @p_884) :rule equiv_pos2)
(step t119.t27.t1 (cl (= @p_126 false)) :rule evaluate)
(step t119.t27.t2 (cl (= (* -1/1 (- 1/1 @p_874)) (* 1/1 (- @p_874 1/1)))) :rule poly_simp)
(step t119.t27.t3 (cl (= @p_885 @p_875)) :rule poly_simp_rel :premises (t119.t27.t2))
(step t119.t27.t4 (cl (= @p_886 (! (or false @p_875) :named @p_889))) :rule cong :premises (t119.t27.t1 t119.t27.t3))
(step t119.t27.t5 (cl (= @p_889 @p_875)) :rule aci_simp)
(step t119.t27.t6 (cl (= @p_886 @p_875)) :rule trans :premises (t119.t27.t4 t119.t27.t5))
(step t119.t27.t7 (cl @p_888) :rule cong :premises (t119.t27.t6))
(step t119.t27.t8 (cl @p_887 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule implies_neg1)
(anchor :step t119.t27.t9)
(assume t119.t27.t9.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))
(step t119.t27.t9.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :named @p_883) @p_886)) :rule forall_inst :args (2/1 1/1))
(step t119.t27.t9.t1 (cl @p_883 @p_886) :rule or :premises (t119.t27.t9.t0))
(step t119.t27.t9.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :named @p_876)) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t27.t9.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t9.t3.t0 (cl (= (* 1/1 (- (! (divide$ (! (times$a ?v1 ?v0) :named @p_366) ?v0) :named @p_877) ?v1)) (* -1/1 (- ?v1 @p_877)))) :rule poly_simp)
(step t119.t27.t9.t3.t1 (cl (= (! (= @p_877 ?v1) :named @p_882) (! (= ?v1 @p_877) :named @p_878))) :rule poly_simp_rel :premises (t119.t27.t9.t3.t0))
(step t119.t27.t9.t3.t2 (cl (= (=> (! (not (! (= ?v0 0/1) :named @p_116)) :named @p_117) @p_882) (! (=> @p_117 @p_878) :named @p_880))) :rule cong :premises (t119.t27.t9.t3.t1))
(step t119.t27.t9.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(anchor :step t119.t27.t9.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t9.t4.t0 (cl (= @p_880 (! (or (! (not @p_117) :named @p_350) @p_878) :named @p_881))) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_878))
(step t119.t27.t9.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t9.t4.t2 (cl (= @p_878 @p_878)) :rule refl)
(step t119.t27.t9.t4.t3 (cl (= @p_881 (! (or @p_116 @p_878) :named @p_879))) :rule cong :premises (t119.t27.t9.t4.t1 t119.t27.t9.t4.t2))
(step t119.t27.t9.t4.t4 (cl (= @p_880 @p_879)) :rule trans :premises (t119.t27.t9.t4.t0 t119.t27.t9.t4.t3))
(step t119.t27.t9.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(step t119.t27.t9.t5 (cl @p_876) :rule trans :premises (t119.t27.t9.t3 t119.t27.t9.t4))
(step t119.t27.t9.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule resolution :premises (t119.t27.t9.t2 t119.t27.t9.t5 a21))
(step t119.t27.t9.t7 (cl @p_886) :rule resolution :premises (t119.t27.t9.t1 t119.t27.t9.t6))
(step t119.t27.t9 (cl @p_883 @p_886) :rule subproof :discharge (t119.t27.t9.a0))
(step t119.t27.t10 (cl @p_887 @p_886) :rule resolution :premises (t119.t27.t8 t119.t27.t9))
(step t119.t27.t11 (cl @p_887 (not @p_886)) :rule implies_neg2)
(step t119.t27.t12 (cl @p_887 @p_887) :rule resolution :premises (t119.t27.t10 t119.t27.t11))
(step t119.t27.t13 (cl @p_887) :rule contraction :premises (t119.t27.t12))
(step t119.t27.t14 (cl @p_884) :rule resolution :premises (t119.t27.t0 t119.t27.t7 t119.t27.t13))
(step t119.t27.t15 (cl @p_883 @p_875) :rule implies :premises (t119.t27.t14))
(step t119.t27.t16 (cl (not @p_876) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t27.t17 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t17.t0 (cl (= (* 1/1 (- @p_877 ?v1)) (* -1/1 (- ?v1 @p_877)))) :rule poly_simp)
(step t119.t27.t17.t1 (cl (= @p_882 @p_878)) :rule poly_simp_rel :premises (t119.t27.t17.t0))
(step t119.t27.t17.t2 (cl (= (=> @p_117 @p_882) @p_880)) :rule cong :premises (t119.t27.t17.t1))
(step t119.t27.t17 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(anchor :step t119.t27.t18 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t18.t0 (cl (= @p_880 @p_881)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_878))
(step t119.t27.t18.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t18.t2 (cl (= @p_878 @p_878)) :rule refl)
(step t119.t27.t18.t3 (cl (= @p_881 @p_879)) :rule cong :premises (t119.t27.t18.t1 t119.t27.t18.t2))
(step t119.t27.t18.t4 (cl (= @p_880 @p_879)) :rule trans :premises (t119.t27.t18.t0 t119.t27.t18.t3))
(step t119.t27.t18 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(step t119.t27.t19 (cl @p_876) :rule trans :premises (t119.t27.t17 t119.t27.t18))
(step t119.t27.t20 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule resolution :premises (t119.t27.t16 t119.t27.t19 a21))
(step t119.t27.t21 (cl @p_875) :rule resolution :premises (t119.t27.t15 t119.t27.t20))
(step t119.t27.t22 (cl @p_885) :rule symm :premises (t119.t27.t21))
(step t119.t27.t23 (cl (! (= 2/1 @p_912) :named @p_916)) :rule symm :premises (t119.t27.a23))
(step t119.t27.t24 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t119.t27.t25 (cl @p_292 @p_305) :rule or :premises (t119.t27.t24))
(step t119.t27.t26 (cl @p_305) :rule resolution :premises (t119.t27.t25 a6))
(step t119.t27.t27 (cl (= @p_4 @p_4)) :rule refl)
(step t119.t27.t28 (cl (= @p_912 @p_871)) :rule cong :premises (t119.t27.t26 t119.t27.t27))
(step t119.t27.t29 (cl (= 2/1 @p_871)) :rule trans :premises (t119.t27.t23 t119.t27.t28))
(step t119.t27.t30 (cl (= @p_874 @p_872)) :rule cong :premises (t119.t27.t29))
(step t119.t27.t31 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1)))) :named @p_343) @p_873)) :rule forall_inst :args (@p_306 @p_270 @p_4))
(step t119.t27.t32 (cl @p_343 @p_873) :rule or :premises (t119.t27.t31))
(step t119.t27.t33 (cl @p_873) :rule resolution :premises (t119.t27.t32 a2))
(step t119.t27.t34 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) (! (= (! (or @p_126 @p_388) :named @p_389) (! (= 2/1 @p_306) :named @p_387)) :named @p_390)) :named @p_391) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) @p_385) :named @p_386)) :named @p_392)) (not @p_391) @p_386) :rule equiv_pos2)
(step t119.t27.t35 (cl (= @p_388 true)) :rule evaluate)
(step t119.t27.t36 (cl (= @p_389 (! (or false true) :named @p_395))) :rule cong :premises (t119.t27.t1 t119.t27.t35))
(step t119.t27.t37 (cl (= @p_395 true)) :rule evaluate)
(step t119.t27.t38 (cl (= @p_389 true)) :rule trans :premises (t119.t27.t36 t119.t27.t37))
(step t119.t27.t39 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t119.t27.t40 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t119.t27.t39))
(step t119.t27.t41 (cl (= @p_390 (! (= true @p_385) :named @p_393))) :rule cong :premises (t119.t27.t38 t119.t27.t40))
(step t119.t27.t42 (cl (= @p_393 (! (= @p_385 true) :named @p_394))) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t119.t27.t43 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t119.t27.t44 (cl (= @p_393 @p_385)) :rule trans :premises (t119.t27.t42 t119.t27.t43))
(step t119.t27.t45 (cl (= @p_390 @p_385)) :rule trans :premises (t119.t27.t41 t119.t27.t44))
(step t119.t27.t46 (cl @p_392) :rule cong :premises (t119.t27.t45))
(step t119.t27.t47 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t119.t27.t48)
(assume t119.t27.t48.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t119.t27.t48.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :named @p_258) @p_390)) :rule forall_inst :args (1/1 2/1))
(step t119.t27.t48.t1 (cl @p_258 @p_390) :rule or :premises (t119.t27.t48.t0))
(step t119.t27.t48.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1)))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :named @p_251)) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t27.t48.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t48.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t119.t27.t48.t3.t1 (cl (= (! (= @p_79 ?v1) :named @p_255) (! (= ?v1 @p_79) :named @p_252))) :rule poly_simp_rel :premises (t119.t27.t48.t3.t0))
(step t119.t27.t48.t3.t2 (cl (= (! (or (= ?v1 0/1) (= ?v0 1/1)) :named @p_253) @p_253)) :rule refl)
(step t119.t27.t48.t3.t3 (cl (= (! (= @p_255 @p_253) :named @p_256) (! (= @p_252 @p_253) :named @p_257))) :rule cong :premises (t119.t27.t48.t3.t1 t119.t27.t48.t3.t2))
(step t119.t27.t48.t3.t4 (cl (= @p_257 (! (= @p_253 @p_252) :named @p_254))) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t119.t27.t48.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t119.t27.t48.t3.t3 t119.t27.t48.t3.t4))
(step t119.t27.t48.t3 (cl @p_251) :rule bind)
(step t119.t27.t48.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t119.t27.t48.t2 t119.t27.t48.t3 a12))
(step t119.t27.t48.t5 (cl @p_390) :rule resolution :premises (t119.t27.t48.t1 t119.t27.t48.t4))
(step t119.t27.t48 (cl @p_258 @p_390) :rule subproof :discharge (t119.t27.t48.a0))
(step t119.t27.t49 (cl @p_391 @p_390) :rule resolution :premises (t119.t27.t47 t119.t27.t48))
(step t119.t27.t50 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t119.t27.t51 (cl @p_391 @p_391) :rule resolution :premises (t119.t27.t49 t119.t27.t50))
(step t119.t27.t52 (cl @p_391) :rule contraction :premises (t119.t27.t51))
(step t119.t27.t53 (cl @p_386) :rule resolution :premises (t119.t27.t34 t119.t27.t46 t119.t27.t52))
(step t119.t27.t54 (cl @p_258 @p_385) :rule implies :premises (t119.t27.t53))
(step t119.t27.t55 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t27.t56 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t56.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t119.t27.t56.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t119.t27.t56.t0))
(step t119.t27.t56.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t119.t27.t56.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t119.t27.t56.t1 t119.t27.t56.t2))
(step t119.t27.t56.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t119.t27.t56.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t119.t27.t56.t3 t119.t27.t56.t4))
(step t119.t27.t56 (cl @p_251) :rule bind)
(step t119.t27.t57 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t119.t27.t55 t119.t27.t56 a12))
(step t119.t27.t58 (cl @p_385) :rule resolution :premises (t119.t27.t54 t119.t27.t57))
(step t119.t27.t59 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))) (! (= @p_396 (! (or (! (= @p_4 0/1) :named @p_245) @p_388) :named @p_399)) :named @p_400)) :named @p_401) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))) @p_396) :named @p_398)) :named @p_402)) (not @p_401) @p_398) :rule equiv_pos2)
(step t119.t27.t60 (cl (= @p_399 (! (or @p_245 true) :named @p_404))) :rule cong :premises (t119.t27.t35))
(step t119.t27.t61 (cl (= @p_404 true)) :rule or_simplify)
(step t119.t27.t62 (cl (= @p_399 true)) :rule trans :premises (t119.t27.t60 t119.t27.t61))
(step t119.t27.t63 (cl (= @p_400 (! (= @p_396 true) :named @p_403))) :rule cong :premises (t119.t27.t62))
(step t119.t27.t64 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t119.t27.t65 (cl (= @p_400 @p_396)) :rule trans :premises (t119.t27.t63 t119.t27.t64))
(step t119.t27.t66 (cl @p_402) :rule cong :premises (t119.t27.t65))
(step t119.t27.t67 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t119.t27.t68)
(assume t119.t27.t68.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t119.t27.t68.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :named @p_397) @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t119.t27.t68.t1 (cl @p_397 @p_400) :rule or :premises (t119.t27.t68.t0))
(step t119.t27.t68.t2 (cl @p_400) :rule resolution :premises (t119.t27.t68.t1 t119.t27.t68.a0))
(step t119.t27.t68 (cl @p_397 @p_400) :rule subproof :discharge (t119.t27.t68.a0))
(step t119.t27.t69 (cl @p_401 @p_400) :rule resolution :premises (t119.t27.t67 t119.t27.t68))
(step t119.t27.t70 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t119.t27.t71 (cl @p_401 @p_401) :rule resolution :premises (t119.t27.t69 t119.t27.t70))
(step t119.t27.t72 (cl @p_401) :rule contraction :premises (t119.t27.t71))
(step t119.t27.t73 (cl @p_398) :rule resolution :premises (t119.t27.t59 t119.t27.t66 t119.t27.t72))
(step t119.t27.t74 (cl @p_397 @p_396) :rule implies :premises (t119.t27.t73))
(step t119.t27.t75 (cl @p_396) :rule resolution :premises (t119.t27.t74 a8))
(step t119.t27.t76 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (! (or @p_126 (! (= (! (= @p_362 @p_362) :named @p_377) @p_364) :named @p_378)) :named @p_379)) :named @p_380) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) @p_364) :named @p_376)) :named @p_381)) (not @p_380) @p_376) :rule equiv_pos2)
(step t119.t27.t77 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t119.t27.t78 (cl (= @p_364 @p_364)) :rule refl)
(step t119.t27.t79 (cl (= @p_378 (! (= true @p_364) :named @p_383))) :rule cong :premises (t119.t27.t77 t119.t27.t78))
(step t119.t27.t80 (cl (= @p_383 (! (= @p_364 true) :named @p_384))) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t119.t27.t81 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t119.t27.t82 (cl (= @p_383 @p_364)) :rule trans :premises (t119.t27.t80 t119.t27.t81))
(step t119.t27.t83 (cl (= @p_378 @p_364)) :rule trans :premises (t119.t27.t79 t119.t27.t82))
(step t119.t27.t84 (cl (= @p_379 (! (or false @p_364) :named @p_382))) :rule cong :premises (t119.t27.t1 t119.t27.t83))
(step t119.t27.t85 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t119.t27.t86 (cl (= @p_379 @p_364)) :rule trans :premises (t119.t27.t84 t119.t27.t85))
(step t119.t27.t87 (cl @p_381) :rule cong :premises (t119.t27.t86))
(step t119.t27.t88 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t119.t27.t89)
(assume t119.t27.t89.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t119.t27.t89.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :named @p_375) @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t119.t27.t89.t1 (cl @p_375 @p_379) :rule or :premises (t119.t27.t89.t0))
(step t119.t27.t89.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :named @p_365)) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t119.t27.t89.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t27.t89.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t119.t27.t89.t3.t1 (cl (= (! (= @p_366 ?v2) :named @p_373) (! (= ?v2 @p_366) :named @p_367))) :rule poly_simp_rel :premises (t119.t27.t89.t3.t0))
(step t119.t27.t89.t3.t2 (cl (= (! (= (! (= ?v1 (divide$ ?v2 ?v0)) :named @p_368) @p_373) :named @p_374) (! (= @p_368 @p_367) :named @p_369))) :rule cong :premises (t119.t27.t89.t3.t1))
(step t119.t27.t89.t3.t3 (cl (= (=> @p_117 @p_374) (! (=> @p_117 @p_369) :named @p_371))) :rule cong :premises (t119.t27.t89.t3.t2))
(step t119.t27.t89.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t119.t27.t89.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t27.t89.t4.t0 (cl (= @p_371 (! (or @p_350 @p_369) :named @p_372))) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t119.t27.t89.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t89.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t119.t27.t89.t4.t3 (cl (= @p_372 (! (or @p_116 @p_369) :named @p_370))) :rule cong :premises (t119.t27.t89.t4.t1 t119.t27.t89.t4.t2))
(step t119.t27.t89.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t119.t27.t89.t4.t0 t119.t27.t89.t4.t3))
(step t119.t27.t89.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t119.t27.t89.t5 (cl @p_365) :rule trans :premises (t119.t27.t89.t3 t119.t27.t89.t4))
(step t119.t27.t89.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t119.t27.t89.t2 t119.t27.t89.t5 a17))
(step t119.t27.t89.t7 (cl @p_379) :rule resolution :premises (t119.t27.t89.t1 t119.t27.t89.t6))
(step t119.t27.t89 (cl @p_375 @p_379) :rule subproof :discharge (t119.t27.t89.a0))
(step t119.t27.t90 (cl @p_380 @p_379) :rule resolution :premises (t119.t27.t88 t119.t27.t89))
(step t119.t27.t91 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t119.t27.t92 (cl @p_380 @p_380) :rule resolution :premises (t119.t27.t90 t119.t27.t91))
(step t119.t27.t93 (cl @p_380) :rule contraction :premises (t119.t27.t92))
(step t119.t27.t94 (cl @p_376) :rule resolution :premises (t119.t27.t76 t119.t27.t87 t119.t27.t93))
(step t119.t27.t95 (cl @p_375 @p_364) :rule implies :premises (t119.t27.t94))
(step t119.t27.t96 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t119.t27.t97 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t27.t97.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t119.t27.t97.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t119.t27.t97.t0))
(step t119.t27.t97.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t119.t27.t97.t1))
(step t119.t27.t97.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t119.t27.t97.t2))
(step t119.t27.t97 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t119.t27.t98 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t27.t98.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t119.t27.t98.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t98.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t119.t27.t98.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t119.t27.t98.t1 t119.t27.t98.t2))
(step t119.t27.t98.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t119.t27.t98.t0 t119.t27.t98.t3))
(step t119.t27.t98 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t119.t27.t99 (cl @p_365) :rule trans :premises (t119.t27.t97 t119.t27.t98))
(step t119.t27.t100 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t119.t27.t96 t119.t27.t99 a17))
(step t119.t27.t101 (cl @p_364) :rule resolution :premises (t119.t27.t95 t119.t27.t100))
(step t119.t27.t102 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :named @p_312) @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t119.t27.t103 (cl @p_312 @p_406) :rule or :premises (t119.t27.t102))
(step t119.t27.t104 (cl @p_406) :rule resolution :premises (t119.t27.t103 a27))
(step t119.t27.t105 (cl (= @p_362 @p_65)) :rule symm :premises (t119.t27.t104))
(step t119.t27.t106 (cl @p_411) :rule forall_inst :args (@p_1 @p_4))
(step t119.t27.t107 (cl @p_292 @p_410) :rule or :premises (t119.t27.t106))
(step t119.t27.t108 (cl @p_410) :rule resolution :premises (t119.t27.t107 a6))
(step t119.t27.t109 (cl (= @p_65 @p_6)) :rule symm :premises (t119.t27.t108))
(step t119.t27.t110 (cl (= @p_362 @p_6)) :rule trans :premises (t119.t27.t105 t119.t27.t109))
(step t119.t27.t111 (cl (= 2/1 2/1)) :rule refl)
(step t119.t27.t112 (cl (= @p_363 @p_290)) :rule cong :premises (t119.t27.t110 t119.t27.t111))
(step t119.t27.t113 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t119.t27.t114 (cl @p_292 @p_291) :rule or :premises (t119.t27.t113))
(step t119.t27.t115 (cl @p_291) :rule resolution :premises (t119.t27.t114 a6))
(step t119.t27.t116 (cl (= @p_289 @p_293)) :rule cong :premises (t119.t27.t108))
(step t119.t27.t117 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (times$a ?v0 ?v1) ?v2) (times$a ?v0 (times$a ?v1 ?v2))))) :named @p_273) @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t119.t27.t118 (cl @p_273 @p_295) :rule or :premises (t119.t27.t117))
(step t119.t27.t119 (cl @p_295) :rule resolution :premises (t119.t27.t118 a4))
(step t119.t27.t120 (cl (= @p_293 @p_294)) :rule symm :premises (t119.t27.t119))
(step t119.t27.t121 (cl (= @p_270 @p_304)) :rule symm :premises (t119.t27.t26))
(step t119.t27.t122 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (! (or (! (= 1/1 0/1) :named @p_356) (! (= 2/1 @p_309) :named @p_355)) :named @p_357)) :named @p_358) (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) @p_344) :named @p_354)) :named @p_359)) (not @p_358) @p_354) :rule equiv_pos2)
(step t119.t27.t123 (cl (= @p_356 false)) :rule evaluate)
(step t119.t27.t124 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t119.t27.t125 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t119.t27.t124))
(step t119.t27.t126 (cl (= @p_357 (! (or false @p_344) :named @p_360))) :rule cong :premises (t119.t27.t123 t119.t27.t125))
(step t119.t27.t127 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t119.t27.t128 (cl (= @p_357 @p_344)) :rule trans :premises (t119.t27.t126 t119.t27.t127))
(step t119.t27.t129 (cl @p_359) :rule cong :premises (t119.t27.t128))
(step t119.t27.t130 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t119.t27.t131)
(assume t119.t27.t131.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t119.t27.t131.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :named @p_353) @p_357)) :rule forall_inst :args (1/1 2/1))
(step t119.t27.t131.t1 (cl @p_353 @p_357) :rule or :premises (t119.t27.t131.t0))
(step t119.t27.t131.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :named @p_345)) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t27.t131.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t131.t3.t0 (cl (= (* 1/1 (- (! (divide$ @p_79 ?v0) :named @p_346) ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t119.t27.t131.t3.t1 (cl (= (! (= @p_346 ?v1) :named @p_352) (! (= ?v1 @p_346) :named @p_347))) :rule poly_simp_rel :premises (t119.t27.t131.t3.t0))
(step t119.t27.t131.t3.t2 (cl (= (=> @p_117 @p_352) (! (=> @p_117 @p_347) :named @p_349))) :rule cong :premises (t119.t27.t131.t3.t1))
(step t119.t27.t131.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t119.t27.t131.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t131.t4.t0 (cl (= @p_349 (! (or @p_350 @p_347) :named @p_351))) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t119.t27.t131.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t131.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t119.t27.t131.t4.t3 (cl (= @p_351 (! (or @p_116 @p_347) :named @p_348))) :rule cong :premises (t119.t27.t131.t4.t1 t119.t27.t131.t4.t2))
(step t119.t27.t131.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t119.t27.t131.t4.t0 t119.t27.t131.t4.t3))
(step t119.t27.t131.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t119.t27.t131.t5 (cl @p_345) :rule trans :premises (t119.t27.t131.t3 t119.t27.t131.t4))
(step t119.t27.t131.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t119.t27.t131.t2 t119.t27.t131.t5 a19))
(step t119.t27.t131.t7 (cl @p_357) :rule resolution :premises (t119.t27.t131.t1 t119.t27.t131.t6))
(step t119.t27.t131 (cl @p_353 @p_357) :rule subproof :discharge (t119.t27.t131.a0))
(step t119.t27.t132 (cl @p_358 @p_357) :rule resolution :premises (t119.t27.t130 t119.t27.t131))
(step t119.t27.t133 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t119.t27.t134 (cl @p_358 @p_358) :rule resolution :premises (t119.t27.t132 t119.t27.t133))
(step t119.t27.t135 (cl @p_358) :rule contraction :premises (t119.t27.t134))
(step t119.t27.t136 (cl @p_354) :rule resolution :premises (t119.t27.t122 t119.t27.t129 t119.t27.t135))
(step t119.t27.t137 (cl @p_353 @p_344) :rule implies :premises (t119.t27.t136))
(step t119.t27.t138 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t27.t139 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t139.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t119.t27.t139.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t119.t27.t139.t0))
(step t119.t27.t139.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t119.t27.t139.t1))
(step t119.t27.t139 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t119.t27.t140 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t27.t140.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t119.t27.t140.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t27.t140.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t119.t27.t140.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t119.t27.t140.t1 t119.t27.t140.t2))
(step t119.t27.t140.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t119.t27.t140.t0 t119.t27.t140.t3))
(step t119.t27.t140 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t119.t27.t141 (cl @p_345) :rule trans :premises (t119.t27.t139 t119.t27.t140))
(step t119.t27.t142 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t119.t27.t138 t119.t27.t141 a19))
(step t119.t27.t143 (cl @p_344) :rule resolution :premises (t119.t27.t137 t119.t27.t142))
(step t119.t27.t144 (cl @p_355) :rule symm :premises (t119.t27.t143))
(step t119.t27.t145 (cl (= @p_304 @p_310)) :rule cong :premises (t119.t27.t144))
(step t119.t27.t146 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t119.t27.t147 (cl @p_312 @p_311) :rule or :premises (t119.t27.t146))
(step t119.t27.t148 (cl @p_311) :rule resolution :premises (t119.t27.t147 a27))
(step t119.t27.t149 (cl (= @p_307 @p_304)) :rule cong :premises (t119.t27.t58))
(step t119.t27.t150 (cl @p_388) :rule refl)
(step t119.t27.t151 (cl (= @p_308 @p_341)) :rule cong :premises (t119.t27.t149 t119.t27.t150))
(step t119.t27.t152 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t119.t27.t153 (cl @p_343 @p_342) :rule or :premises (t119.t27.t152))
(step t119.t27.t154 (cl @p_342) :rule resolution :premises (t119.t27.t153 a2))
(step t119.t27.t155 (cl (= @p_341 @p_296)) :rule symm :premises (t119.t27.t154))
(step t119.t27.t156 (cl (= @p_270 @p_296)) :rule trans :premises (t119.t27.t121 t119.t27.t145 t119.t27.t148 t119.t27.t151 t119.t27.t155))
(step t119.t27.t157 (cl (= @p_1 @p_1)) :rule refl)
(step t119.t27.t158 (cl (= @p_294 @p_339)) :rule cong :premises (t119.t27.t156 t119.t27.t157))
(step t119.t27.t159 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t119.t27.t160 (cl @p_292 @p_340) :rule or :premises (t119.t27.t159))
(step t119.t27.t161 (cl @p_340) :rule resolution :premises (t119.t27.t160 a6))
(step t119.t27.t162 (cl (= @p_339 @p_314)) :rule symm :premises (t119.t27.t161))
(step t119.t27.t163 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a @p_332 @p_296) :named @p_333) (! (+ @p_314 @p_314) :named @p_331)) :named @p_334)) :named @p_335) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= @p_314 (! (* 1/2 (! (times$a @p_247 @p_296) :named @p_327)) :named @p_328)) :named @p_329)) :named @p_330)) :named @p_336)) (not @p_335) @p_330) :rule equiv_pos2)
(step t119.t27.t164 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t119.t27.t165 (cl (= @p_296 @p_296)) :rule refl)
(step t119.t27.t166 (cl (= @p_333 @p_327)) :rule cong :premises (t119.t27.t164 t119.t27.t165))
(step t119.t27.t167 (cl (= @p_331 (! (* 2/1 @p_314) :named @p_337))) :rule poly_simp)
(step t119.t27.t168 (cl (= @p_334 (! (= @p_327 @p_337) :named @p_338))) :rule cong :premises (t119.t27.t166 t119.t27.t167))
(step t119.t27.t169 (cl (= (* 1/1 (- @p_327 @p_337)) (* -2/1 (- @p_314 @p_328)))) :rule poly_simp)
(step t119.t27.t170 (cl (= @p_338 @p_329)) :rule poly_simp_rel :premises (t119.t27.t169))
(step t119.t27.t171 (cl (= @p_334 @p_329)) :rule trans :premises (t119.t27.t168 t119.t27.t170))
(step t119.t27.t172 (cl @p_336) :rule cong :premises (t119.t27.t171))
(step t119.t27.t173 (cl @p_335 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t27.t174)
(assume t119.t27.t174.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t27.t174.t0 (cl (or @p_279 @p_334)) :rule forall_inst :args (@p_1 @p_1 @p_296))
(step t119.t27.t174.t1 (cl @p_279 @p_334) :rule or :premises (t119.t27.t174.t0))
(step t119.t27.t174.t2 (cl @p_334) :rule resolution :premises (t119.t27.t174.t1 t119.t27.t174.a0))
(step t119.t27.t174 (cl @p_279 @p_334) :rule subproof :discharge (t119.t27.t174.a0))
(step t119.t27.t175 (cl @p_335 @p_334) :rule resolution :premises (t119.t27.t173 t119.t27.t174))
(step t119.t27.t176 (cl @p_335 (not @p_334)) :rule implies_neg2)
(step t119.t27.t177 (cl @p_335 @p_335) :rule resolution :premises (t119.t27.t175 t119.t27.t176))
(step t119.t27.t178 (cl @p_335) :rule contraction :premises (t119.t27.t177))
(step t119.t27.t179 (cl @p_330) :rule resolution :premises (t119.t27.t163 t119.t27.t172 t119.t27.t178))
(step t119.t27.t180 (cl @p_279 @p_329) :rule implies :premises (t119.t27.t179))
(step t119.t27.t181 (cl @p_329) :rule resolution :premises (t119.t27.t180 a1))
(step t119.t27.t182 (cl (! (= @p_4 @p_328) :named @p_473)) :rule trans :premises (t119.t27.t75 t119.t27.t101 t119.t27.t112 t119.t27.t115 t119.t27.t116 t119.t27.t120 t119.t27.t158 t119.t27.t162 t119.t27.t181))
(step t119.t27.t183 (cl (= @p_328 @p_314)) :rule symm :premises (t119.t27.t181))
(step t119.t27.t184 (cl (or @p_312 (! (= @p_314 @p_932) :named @p_971))) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t119.t27.t185 (cl @p_312 @p_971) :rule or :premises (t119.t27.t184))
(step t119.t27.t186 (cl @p_971) :rule resolution :premises (t119.t27.t185 a27))
(step t119.t27.t187 (cl (! (= @p_4 @p_932) :named @p_974)) :rule trans :premises (t119.t27.t182 t119.t27.t183 t119.t27.t186))
(step t119.t27.t188 (cl (= @p_869 (! (times$a 2/1 @p_932) :named @p_1387))) :rule cong :premises (t119.t27.t58 t119.t27.t187))
(step t119.t27.t189 (cl (= @p_270 @p_1387)) :rule cong :premises (t119.t27.t187))
(step t119.t27.t190 (cl (= @p_1387 @p_270)) :rule symm :premises (t119.t27.t189))
(step t119.t27.t191 (cl (= @p_869 @p_304)) :rule trans :premises (t119.t27.t188 t119.t27.t190 t119.t27.t121))
(step t119.t27.t192 (cl (= (! (times$a @p_306 @p_314) :named @p_1385) @p_1387)) :rule cong :premises (t119.t27.t58 t119.t27.t186))
(step t119.t27.t193 (cl (= @p_1385 @p_304)) :rule trans :premises (t119.t27.t192 t119.t27.t190 t119.t27.t121))
(step t119.t27.t194 (cl (= @p_304 @p_1385)) :rule symm :premises (t119.t27.t193))
(step t119.t27.t195 (cl (= @p_869 @p_1385)) :rule trans :premises (t119.t27.t191 t119.t27.t194))
(step t119.t27.t196 (cl (= @p_870 (! (divide$ @p_1385 @p_296) :named @p_1386))) :rule cong :premises (t119.t27.t195 t119.t27.t156))
(step t119.t27.t197 (cl @p_387) :rule symm :premises (t119.t27.t58))
(step t119.t27.t198 (cl (= @p_304 @p_307)) :rule cong :premises (t119.t27.t197))
(step t119.t27.t199 (cl (= @p_341 @p_308)) :rule cong :premises (t119.t27.t198 t119.t27.t150))
(step t119.t27.t200 (cl (= @p_308 @p_310)) :rule symm :premises (t119.t27.t148))
(step t119.t27.t201 (cl (= @p_310 @p_304)) :rule cong :premises (t119.t27.t143))
(step t119.t27.t202 (cl (= @p_296 @p_304)) :rule trans :premises (t119.t27.t154 t119.t27.t199 t119.t27.t200 t119.t27.t201))
(step t119.t27.t203 (cl (= @p_1386 @p_865)) :rule cong :premises (t119.t27.t193 t119.t27.t202))
(step t119.t27.t204 (cl (or @p_343 @p_868)) :rule forall_inst :args (@p_4 @p_304 2/1))
(step t119.t27.t205 (cl @p_343 @p_868) :rule or :premises (t119.t27.t204))
(step t119.t27.t206 (cl @p_868) :rule resolution :premises (t119.t27.t205 a2))
(step t119.t27.t207 (cl (= @p_865 @p_867)) :rule symm :premises (t119.t27.t206))
(step t119.t27.t208 (cl (= @p_866 @p_921)) :rule cong :premises (t119.t27.t26 t119.t27.t111))
(step t119.t27.t209 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (! (or @p_126 @p_922) :named @p_924)) :named @p_925) (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) @p_922) :named @p_923)) :named @p_926)) (not @p_925) @p_923) :rule equiv_pos2)
(step t119.t27.t210 (cl (= @p_922 @p_922)) :rule refl)
(step t119.t27.t211 (cl (= @p_924 (! (or false @p_922) :named @p_927))) :rule cong :premises (t119.t27.t1 t119.t27.t210))
(step t119.t27.t212 (cl (= @p_927 @p_922)) :rule aci_simp)
(step t119.t27.t213 (cl (= @p_924 @p_922)) :rule trans :premises (t119.t27.t211 t119.t27.t212))
(step t119.t27.t214 (cl @p_926) :rule cong :premises (t119.t27.t213))
(step t119.t27.t215 (cl @p_925 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t119.t27.t216)
(assume t119.t27.t216.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t119.t27.t216.t0 (cl (or @p_353 @p_924)) :rule forall_inst :args (2/1 @p_4))
(step t119.t27.t216.t1 (cl @p_353 @p_924) :rule or :premises (t119.t27.t216.t0))
(step t119.t27.t216.t2 (cl @p_924) :rule resolution :premises (t119.t27.t216.t1 t119.t27.t142))
(step t119.t27.t216 (cl @p_353 @p_924) :rule subproof :discharge (t119.t27.t216.a0))
(step t119.t27.t217 (cl @p_925 @p_924) :rule resolution :premises (t119.t27.t215 t119.t27.t216))
(step t119.t27.t218 (cl @p_925 (not @p_924)) :rule implies_neg2)
(step t119.t27.t219 (cl @p_925 @p_925) :rule resolution :premises (t119.t27.t217 t119.t27.t218))
(step t119.t27.t220 (cl @p_925) :rule contraction :premises (t119.t27.t219))
(step t119.t27.t221 (cl @p_923) :rule resolution :premises (t119.t27.t209 t119.t27.t214 t119.t27.t220))
(step t119.t27.t222 (cl @p_353 @p_922) :rule implies :premises (t119.t27.t221))
(step t119.t27.t223 (cl @p_922) :rule resolution :premises (t119.t27.t222 t119.t27.t142))
(step t119.t27.t224 (cl (= @p_921 @p_4)) :rule symm :premises (t119.t27.t223))
(step t119.t27.t225 (cl (= @p_866 @p_932)) :rule trans :premises (t119.t27.t208 t119.t27.t224 t119.t27.t75 t119.t27.t101 t119.t27.t112 t119.t27.t115 t119.t27.t116 t119.t27.t120 t119.t27.t158 t119.t27.t162 t119.t27.t186))
(step t119.t27.t226 (cl (= @p_867 @p_933)) :rule cong :premises (t119.t27.t225))
(step t119.t27.t227 (cl (or @p_343 @p_934)) :rule forall_inst :args (@p_4 @p_6 @p_1))
(step t119.t27.t228 (cl @p_343 @p_934) :rule or :premises (t119.t27.t227))
(step t119.t27.t229 (cl @p_934) :rule resolution :premises (t119.t27.t228 a2))
(step t119.t27.t230 (cl (or @p_273 @p_1102)) :rule forall_inst :args (@p_4 @p_1 @p_1098))
(step t119.t27.t231 (cl @p_273 @p_1102) :rule or :premises (t119.t27.t230))
(step t119.t27.t232 (cl @p_1102) :rule resolution :premises (t119.t27.t231 a4))
(step t119.t27.t233 (cl (or @p_312 (! (= @p_1099 @p_1116) :named @p_1119))) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t119.t27.t234 (cl @p_312 @p_1119) :rule or :premises (t119.t27.t233))
(step t119.t27.t235 (cl @p_1119) :rule resolution :premises (t119.t27.t234 a27))
(step t119.t27.t236 (cl (! (= @p_1116 @p_1) :named @p_1392)) :rule symm :premises (t119.t27.a7))
(step t119.t27.t237 (cl (! (= @p_1099 @p_1) :named @p_1391)) :rule trans :premises (t119.t27.t235 t119.t27.t236))
(step t119.t27.t238 (cl (! (= @p_1100 @p_65) :named @p_1390)) :rule cong :premises (t119.t27.t237))
(step t119.t27.t239 (cl (! (= @p_1101 @p_6) :named @p_1389)) :rule trans :premises (t119.t27.t232 t119.t27.t238 t119.t27.t109))
(step t119.t27.t240 (cl (! (= @p_6 @p_1101) :named @p_1393)) :rule symm :premises (t119.t27.t239))
(step t119.t27.t241 (cl (= @p_65 @p_1101)) :rule trans :premises (t119.t27.t109 t119.t27.t240))
(step t119.t27.t242 (cl (= @p_931 (! (divide$ @p_1101 @p_65) :named @p_1388))) :rule cong :premises (t119.t27.t241 t119.t27.t108))
(step t119.t27.t243 (cl (= @p_1388 @p_929)) :rule cong :premises (t119.t27.t239 t119.t27.t104))
(step t119.t27.t244 (cl (or @p_343 @p_930)) :rule forall_inst :args (@p_6 @p_361 2/1))
(step t119.t27.t245 (cl @p_343 @p_930) :rule or :premises (t119.t27.t244))
(step t119.t27.t246 (cl @p_930) :rule resolution :premises (t119.t27.t245 a2))
(step t119.t27.t247 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t119.t27.t248 (cl @p_292 @p_405) :rule or :premises (t119.t27.t247))
(step t119.t27.t249 (cl @p_405) :rule resolution :premises (t119.t27.t248 a6))
(step t119.t27.t250 (cl (= @p_301 @p_290)) :rule trans :premises (t119.t27.t249 t119.t27.t101 t119.t27.t112))
(step t119.t27.t251 (cl (= @p_290 @p_301)) :rule symm :premises (t119.t27.t250))
(step t119.t27.t252 (cl (= @p_361 @p_4)) :rule symm :premises (t119.t27.t75))
(step t119.t27.t253 (cl (= @p_301 @p_4)) :rule trans :premises (t119.t27.t249 t119.t27.t252))
(step t119.t27.t254 (cl (= @p_290 @p_4)) :rule trans :premises (t119.t27.t251 t119.t27.t253))
(step t119.t27.t255 (cl (= @p_928 @p_1098)) :rule cong :premises (t119.t27.t254 t119.t27.t252))
(step t119.t27.t256 (cl (= @p_935 @p_1098)) :rule cong :premises (t119.t27.t252 t119.t27.t27))
(step t119.t27.t257 (cl (= @p_1098 @p_935)) :rule symm :premises (t119.t27.t256))
(step t119.t27.t258 (cl (or @p_312 @p_937)) :rule forall_inst :args (@p_4 1/1 @p_4))
(step t119.t27.t259 (cl @p_312 @p_937) :rule or :premises (t119.t27.t258))
(step t119.t27.t260 (cl @p_937) :rule resolution :premises (t119.t27.t259 a27))
(step t119.t27.t261 (cl (= @p_935 @p_936)) :rule symm :premises (t119.t27.t260))
(step t119.t27.t262 (cl @p_1411) :rule trans :premises (t119.t27.t22 t119.t27.t30 t119.t27.t33 t119.t27.t196 t119.t27.t203 t119.t27.t207 t119.t27.t226 t119.t27.t229 t119.t27.t242 t119.t27.t243 t119.t27.t246 t119.t27.t255 t119.t27.t257 t119.t27.t261))
(step t119.t27 (cl @p_1211 @p_428 @p_429 @p_431 @p_427 @p_424 @p_1215 @p_1191 @p_1199 @p_1202 @p_1214 @p_442 @p_441 @p_438 @p_432 @p_437 @p_430 @p_433 @p_434 @p_1042 @p_1216 @p_1223 @p_1222 @p_1217 @p_1221 @p_1411) :rule subproof :discharge (t119.t27.a0 t119.t27.a1 t119.t27.a2 t119.t27.a3 t119.t27.a4 t119.t27.a5 t119.t27.a6 t119.t27.a7 t119.t27.a8 t119.t27.a9 t119.t27.a10 t119.t27.a11 t119.t27.a12 t119.t27.a13 t119.t27.a14 t119.t27.a15 t119.t27.a16 t119.t27.a17 t119.t27.a18 t119.t27.a19 t119.t27.a20 t119.t27.a21 t119.t27.a22 t119.t27.a23 t119.t27.a24))
(step t119.t28 (cl (! (not @p_1431) :named @p_1432) @p_937) :rule and_pos :args (0))
(step t119.t29 (cl @p_1432 @p_405) :rule and_pos :args (1))
(step t119.t30 (cl @p_1432 @p_396) :rule and_pos :args (2))
(step t119.t31 (cl @p_1432 @p_364) :rule and_pos :args (3))
(step t119.t32 (cl @p_1432 @p_406) :rule and_pos :args (4))
(step t119.t33 (cl @p_1432 @p_410) :rule and_pos :args (5))
(step t119.t34 (cl @p_1432 @p_930) :rule and_pos :args (6))
(step t119.t35 (cl @p_1432 @p_1188) :rule and_pos :args (7))
(step t119.t36 (cl @p_1432 @p_1117) :rule and_pos :args (8))
(step t119.t37 (cl @p_1432 @p_1102) :rule and_pos :args (9))
(step t119.t38 (cl @p_1432 @p_934) :rule and_pos :args (10))
(step t119.t39 (cl @p_1432 @p_291) :rule and_pos :args (11))
(step t119.t40 (cl @p_1432 @p_295) :rule and_pos :args (12))
(step t119.t41 (cl @p_1432 @p_305) :rule and_pos :args (13))
(step t119.t42 (cl @p_1432 @p_344) :rule and_pos :args (14))
(step t119.t43 (cl @p_1432 @p_311) :rule and_pos :args (15))
(step t119.t44 (cl @p_1432 @p_385) :rule and_pos :args (16))
(step t119.t45 (cl @p_1432 @p_342) :rule and_pos :args (17))
(step t119.t46 (cl @p_1432 @p_340) :rule and_pos :args (18))
(step t119.t47 (cl @p_1432 @p_969) :rule and_pos :args (19))
(step t119.t48 (cl @p_1432 @p_922) :rule and_pos :args (20))
(step t119.t49 (cl @p_1432 @p_868) :rule and_pos :args (21))
(step t119.t50 (cl @p_1432 @p_873) :rule and_pos :args (22))
(step t119.t51 (cl @p_1432 @p_913) :rule and_pos :args (23))
(step t119.t52 (cl @p_1432 @p_875) :rule and_pos :args (24))
(step t119.t53 (cl @p_1411 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432) :rule resolution :premises (t119.t27 t119.t28 t119.t29 t119.t30 t119.t31 t119.t32 t119.t33 t119.t34 t119.t35 t119.t36 t119.t37 t119.t38 t119.t39 t119.t40 t119.t41 t119.t42 t119.t43 t119.t44 t119.t45 t119.t46 t119.t47 t119.t48 t119.t49 t119.t50 t119.t51 t119.t52))
(step t119.t54 (cl @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1432 @p_1411) :rule reordering :premises (t119.t53))
(step t119.t55 (cl @p_1432 @p_1411) :rule contraction :premises (t119.t54))
(step t119.t56 (cl @p_1433 @p_1411) :rule resolution :premises (t119.t26 t119.t55))
(step t119.t57 (cl @p_1433 @p_1434) :rule implies_neg2)
(step t119.t58 (cl @p_1433 @p_1433) :rule resolution :premises (t119.t56 t119.t57))
(step t119.t59 (cl @p_1433) :rule contraction :premises (t119.t58))
(step t119.t60 (cl @p_1432 @p_1411) :rule implies :premises (t119.t59))
(step t119.t61 (cl (or @p_312 @p_937)) :rule forall_inst :args (@p_4 1/1 @p_4))
(step t119.t62 (cl @p_312 @p_937) :rule or :premises (t119.t61))
(step t119.t63 (cl @p_937) :rule resolution :premises (t119.t62 a27))
(step t119.t64 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t119.t65 (cl @p_292 @p_405) :rule or :premises (t119.t64))
(step t119.t66 (cl @p_405) :rule resolution :premises (t119.t65 a6))
(step t119.t67 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t119.t68 (cl (= @p_388 true)) :rule evaluate)
(step t119.t69 (cl (= @p_399 @p_404)) :rule cong :premises (t119.t68))
(step t119.t70 (cl (= @p_404 true)) :rule or_simplify)
(step t119.t71 (cl (= @p_399 true)) :rule trans :premises (t119.t69 t119.t70))
(step t119.t72 (cl (= @p_400 @p_403)) :rule cong :premises (t119.t71))
(step t119.t73 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t119.t74 (cl (= @p_400 @p_396)) :rule trans :premises (t119.t72 t119.t73))
(step t119.t75 (cl @p_402) :rule cong :premises (t119.t74))
(step t119.t76 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t119.t77)
(assume t119.t77.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t119.t77.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t119.t77.t1 (cl @p_397 @p_400) :rule or :premises (t119.t77.t0))
(step t119.t77.t2 (cl @p_400) :rule resolution :premises (t119.t77.t1 t119.t77.a0))
(step t119.t77 (cl @p_397 @p_400) :rule subproof :discharge (t119.t77.a0))
(step t119.t78 (cl @p_401 @p_400) :rule resolution :premises (t119.t76 t119.t77))
(step t119.t79 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t119.t80 (cl @p_401 @p_401) :rule resolution :premises (t119.t78 t119.t79))
(step t119.t81 (cl @p_401) :rule contraction :premises (t119.t80))
(step t119.t82 (cl @p_398) :rule resolution :premises (t119.t67 t119.t75 t119.t81))
(step t119.t83 (cl @p_397 @p_396) :rule implies :premises (t119.t82))
(step t119.t84 (cl @p_396) :rule resolution :premises (t119.t83 a8))
(step t119.t85 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t119.t86 (cl (= @p_126 false)) :rule evaluate)
(step t119.t87 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t119.t88 (cl (= @p_364 @p_364)) :rule refl)
(step t119.t89 (cl (= @p_378 @p_383)) :rule cong :premises (t119.t87 t119.t88))
(step t119.t90 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t119.t91 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t119.t92 (cl (= @p_383 @p_364)) :rule trans :premises (t119.t90 t119.t91))
(step t119.t93 (cl (= @p_378 @p_364)) :rule trans :premises (t119.t89 t119.t92))
(step t119.t94 (cl (= @p_379 @p_382)) :rule cong :premises (t119.t86 t119.t93))
(step t119.t95 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t119.t96 (cl (= @p_379 @p_364)) :rule trans :premises (t119.t94 t119.t95))
(step t119.t97 (cl @p_381) :rule cong :premises (t119.t96))
(step t119.t98 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t119.t99)
(assume t119.t99.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t119.t99.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t119.t99.t1 (cl @p_375 @p_379) :rule or :premises (t119.t99.t0))
(step t119.t99.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t119.t99.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t99.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t119.t99.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t119.t99.t3.t0))
(step t119.t99.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t119.t99.t3.t1))
(step t119.t99.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t119.t99.t3.t2))
(step t119.t99.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t119.t99.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t99.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t119.t99.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t99.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t119.t99.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t119.t99.t4.t1 t119.t99.t4.t2))
(step t119.t99.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t119.t99.t4.t0 t119.t99.t4.t3))
(step t119.t99.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t119.t99.t5 (cl @p_365) :rule trans :premises (t119.t99.t3 t119.t99.t4))
(step t119.t99.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t119.t99.t2 t119.t99.t5 a17))
(step t119.t99.t7 (cl @p_379) :rule resolution :premises (t119.t99.t1 t119.t99.t6))
(step t119.t99 (cl @p_375 @p_379) :rule subproof :discharge (t119.t99.a0))
(step t119.t100 (cl @p_380 @p_379) :rule resolution :premises (t119.t98 t119.t99))
(step t119.t101 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t119.t102 (cl @p_380 @p_380) :rule resolution :premises (t119.t100 t119.t101))
(step t119.t103 (cl @p_380) :rule contraction :premises (t119.t102))
(step t119.t104 (cl @p_376) :rule resolution :premises (t119.t85 t119.t97 t119.t103))
(step t119.t105 (cl @p_375 @p_364) :rule implies :premises (t119.t104))
(step t119.t106 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t119.t107 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t107.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t119.t107.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t119.t107.t0))
(step t119.t107.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t119.t107.t1))
(step t119.t107.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t119.t107.t2))
(step t119.t107 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t119.t108 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t119.t108.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t119.t108.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t108.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t119.t108.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t119.t108.t1 t119.t108.t2))
(step t119.t108.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t119.t108.t0 t119.t108.t3))
(step t119.t108 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t119.t109 (cl @p_365) :rule trans :premises (t119.t107 t119.t108))
(step t119.t110 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t119.t106 t119.t109 a17))
(step t119.t111 (cl @p_364) :rule resolution :premises (t119.t105 t119.t110))
(step t119.t112 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t119.t113 (cl @p_312 @p_406) :rule or :premises (t119.t112))
(step t119.t114 (cl @p_406) :rule resolution :premises (t119.t113 a27))
(step t119.t115 (cl @p_411) :rule forall_inst :args (@p_1 @p_4))
(step t119.t116 (cl @p_292 @p_410) :rule or :premises (t119.t115))
(step t119.t117 (cl @p_410) :rule resolution :premises (t119.t116 a6))
(step t119.t118 (cl (or @p_343 @p_930)) :rule forall_inst :args (@p_6 @p_361 2/1))
(step t119.t119 (cl @p_343 @p_930) :rule or :premises (t119.t118))
(step t119.t120 (cl @p_930) :rule resolution :premises (t119.t119 a2))
(step t119.t121 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))) @p_1119) :named @p_1120) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))) @p_1117) :named @p_1118)) :named @p_1121)) (not @p_1120) @p_1118) :rule equiv_pos2)
(step t119.t122 (cl (= (* 1/1 (- @p_1099 @p_1116)) (* -1/1 (- @p_1116 @p_1099)))) :rule poly_simp)
(step t119.t123 (cl (= @p_1119 @p_1117)) :rule poly_simp_rel :premises (t119.t122))
(step t119.t124 (cl @p_1121) :rule cong :premises (t119.t123))
(step t119.t125 (cl @p_1120 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t119.t126)
(assume t119.t126.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t119.t126.t0 (cl (or @p_312 @p_1119)) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t119.t126.t1 (cl @p_312 @p_1119) :rule or :premises (t119.t126.t0))
(step t119.t126.t2 (cl @p_1119) :rule resolution :premises (t119.t126.t1 t119.t126.a0))
(step t119.t126 (cl @p_312 @p_1119) :rule subproof :discharge (t119.t126.a0))
(step t119.t127 (cl @p_1120 @p_1119) :rule resolution :premises (t119.t125 t119.t126))
(step t119.t128 (cl @p_1120 (not @p_1119)) :rule implies_neg2)
(step t119.t129 (cl @p_1120 @p_1120) :rule resolution :premises (t119.t127 t119.t128))
(step t119.t130 (cl @p_1120) :rule contraction :premises (t119.t129))
(step t119.t131 (cl @p_1118) :rule resolution :premises (t119.t121 t119.t124 t119.t130))
(step t119.t132 (cl @p_312 @p_1117) :rule implies :premises (t119.t131))
(step t119.t133 (cl @p_1117) :rule resolution :premises (t119.t132 a27))
(step t119.t134 (cl (or @p_273 @p_1102)) :rule forall_inst :args (@p_4 @p_1 @p_1098))
(step t119.t135 (cl @p_273 @p_1102) :rule or :premises (t119.t134))
(step t119.t136 (cl @p_1102) :rule resolution :premises (t119.t135 a4))
(step t119.t137 (cl (or @p_343 @p_934)) :rule forall_inst :args (@p_4 @p_6 @p_1))
(step t119.t138 (cl @p_343 @p_934) :rule or :premises (t119.t137))
(step t119.t139 (cl @p_934) :rule resolution :premises (t119.t138 a2))
(step t119.t140 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t119.t141 (cl @p_292 @p_291) :rule or :premises (t119.t140))
(step t119.t142 (cl @p_291) :rule resolution :premises (t119.t141 a6))
(step t119.t143 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t119.t144 (cl @p_273 @p_295) :rule or :premises (t119.t143))
(step t119.t145 (cl @p_295) :rule resolution :premises (t119.t144 a4))
(step t119.t146 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t119.t147 (cl @p_292 @p_305) :rule or :premises (t119.t146))
(step t119.t148 (cl @p_305) :rule resolution :premises (t119.t147 a6))
(step t119.t149 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t119.t150 (cl (= @p_356 false)) :rule evaluate)
(step t119.t151 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t119.t152 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t119.t151))
(step t119.t153 (cl (= @p_357 @p_360)) :rule cong :premises (t119.t150 t119.t152))
(step t119.t154 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t119.t155 (cl (= @p_357 @p_344)) :rule trans :premises (t119.t153 t119.t154))
(step t119.t156 (cl @p_359) :rule cong :premises (t119.t155))
(step t119.t157 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t119.t158)
(assume t119.t158.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t119.t158.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t119.t158.t1 (cl @p_353 @p_357) :rule or :premises (t119.t158.t0))
(step t119.t158.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t158.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t158.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t119.t158.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t119.t158.t3.t0))
(step t119.t158.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t119.t158.t3.t1))
(step t119.t158.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t119.t158.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t158.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t119.t158.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t158.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t119.t158.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t119.t158.t4.t1 t119.t158.t4.t2))
(step t119.t158.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t119.t158.t4.t0 t119.t158.t4.t3))
(step t119.t158.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t119.t158.t5 (cl @p_345) :rule trans :premises (t119.t158.t3 t119.t158.t4))
(step t119.t158.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t119.t158.t2 t119.t158.t5 a19))
(step t119.t158.t7 (cl @p_357) :rule resolution :premises (t119.t158.t1 t119.t158.t6))
(step t119.t158 (cl @p_353 @p_357) :rule subproof :discharge (t119.t158.a0))
(step t119.t159 (cl @p_358 @p_357) :rule resolution :premises (t119.t157 t119.t158))
(step t119.t160 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t119.t161 (cl @p_358 @p_358) :rule resolution :premises (t119.t159 t119.t160))
(step t119.t162 (cl @p_358) :rule contraction :premises (t119.t161))
(step t119.t163 (cl @p_354) :rule resolution :premises (t119.t149 t119.t156 t119.t162))
(step t119.t164 (cl @p_353 @p_344) :rule implies :premises (t119.t163))
(step t119.t165 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t166 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t166.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t119.t166.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t119.t166.t0))
(step t119.t166.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t119.t166.t1))
(step t119.t166 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t119.t167 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t167.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t119.t167.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t167.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t119.t167.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t119.t167.t1 t119.t167.t2))
(step t119.t167.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t119.t167.t0 t119.t167.t3))
(step t119.t167 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t119.t168 (cl @p_345) :rule trans :premises (t119.t166 t119.t167))
(step t119.t169 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t119.t165 t119.t168 a19))
(step t119.t170 (cl @p_344) :rule resolution :premises (t119.t164 t119.t169))
(step t119.t171 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t119.t172 (cl @p_312 @p_311) :rule or :premises (t119.t171))
(step t119.t173 (cl @p_311) :rule resolution :premises (t119.t172 a27))
(step t119.t174 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t119.t175 (cl (= @p_389 @p_395)) :rule cong :premises (t119.t86 t119.t68))
(step t119.t176 (cl (= @p_395 true)) :rule evaluate)
(step t119.t177 (cl (= @p_389 true)) :rule trans :premises (t119.t175 t119.t176))
(step t119.t178 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t119.t179 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t119.t178))
(step t119.t180 (cl (= @p_390 @p_393)) :rule cong :premises (t119.t177 t119.t179))
(step t119.t181 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t119.t182 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t119.t183 (cl (= @p_393 @p_385)) :rule trans :premises (t119.t181 t119.t182))
(step t119.t184 (cl (= @p_390 @p_385)) :rule trans :premises (t119.t180 t119.t183))
(step t119.t185 (cl @p_392) :rule cong :premises (t119.t184))
(step t119.t186 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t119.t187)
(assume t119.t187.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t119.t187.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t119.t187.t1 (cl @p_258 @p_390) :rule or :premises (t119.t187.t0))
(step t119.t187.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t187.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t187.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t119.t187.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t119.t187.t3.t0))
(step t119.t187.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t119.t187.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t119.t187.t3.t1 t119.t187.t3.t2))
(step t119.t187.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t119.t187.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t119.t187.t3.t3 t119.t187.t3.t4))
(step t119.t187.t3 (cl @p_251) :rule bind)
(step t119.t187.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t119.t187.t2 t119.t187.t3 a12))
(step t119.t187.t5 (cl @p_390) :rule resolution :premises (t119.t187.t1 t119.t187.t4))
(step t119.t187 (cl @p_258 @p_390) :rule subproof :discharge (t119.t187.a0))
(step t119.t188 (cl @p_391 @p_390) :rule resolution :premises (t119.t186 t119.t187))
(step t119.t189 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t119.t190 (cl @p_391 @p_391) :rule resolution :premises (t119.t188 t119.t189))
(step t119.t191 (cl @p_391) :rule contraction :premises (t119.t190))
(step t119.t192 (cl @p_386) :rule resolution :premises (t119.t174 t119.t185 t119.t191))
(step t119.t193 (cl @p_258 @p_385) :rule implies :premises (t119.t192))
(step t119.t194 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t195 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t195.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t119.t195.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t119.t195.t0))
(step t119.t195.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t119.t195.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t119.t195.t1 t119.t195.t2))
(step t119.t195.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t119.t195.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t119.t195.t3 t119.t195.t4))
(step t119.t195 (cl @p_251) :rule bind)
(step t119.t196 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t119.t194 t119.t195 a12))
(step t119.t197 (cl @p_385) :rule resolution :premises (t119.t193 t119.t196))
(step t119.t198 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t119.t199 (cl @p_343 @p_342) :rule or :premises (t119.t198))
(step t119.t200 (cl @p_342) :rule resolution :premises (t119.t199 a2))
(step t119.t201 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t119.t202 (cl @p_292 @p_340) :rule or :premises (t119.t201))
(step t119.t203 (cl @p_340) :rule resolution :premises (t119.t202 a6))
(step t119.t204 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))) @p_971) :named @p_972) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))) @p_969) :named @p_970)) :named @p_973)) (not @p_972) @p_970) :rule equiv_pos2)
(step t119.t205 (cl (= (* 1/1 (- @p_314 @p_932)) (* -1/1 (- @p_932 @p_314)))) :rule poly_simp)
(step t119.t206 (cl (= @p_971 @p_969)) :rule poly_simp_rel :premises (t119.t205))
(step t119.t207 (cl @p_973) :rule cong :premises (t119.t206))
(step t119.t208 (cl @p_972 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t119.t209)
(assume t119.t209.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t119.t209.t0 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t119.t209.t1 (cl @p_312 @p_971) :rule or :premises (t119.t209.t0))
(step t119.t209.t2 (cl @p_971) :rule resolution :premises (t119.t209.t1 t119.t209.a0))
(step t119.t209 (cl @p_312 @p_971) :rule subproof :discharge (t119.t209.a0))
(step t119.t210 (cl @p_972 @p_971) :rule resolution :premises (t119.t208 t119.t209))
(step t119.t211 (cl @p_972 (not @p_971)) :rule implies_neg2)
(step t119.t212 (cl @p_972 @p_972) :rule resolution :premises (t119.t210 t119.t211))
(step t119.t213 (cl @p_972) :rule contraction :premises (t119.t212))
(step t119.t214 (cl @p_970) :rule resolution :premises (t119.t204 t119.t207 t119.t213))
(step t119.t215 (cl @p_312 @p_969) :rule implies :premises (t119.t214))
(step t119.t216 (cl @p_969) :rule resolution :premises (t119.t215 a27))
(step t119.t217 (cl (not @p_926) (not @p_925) @p_923) :rule equiv_pos2)
(step t119.t218 (cl (= @p_922 @p_922)) :rule refl)
(step t119.t219 (cl (= @p_924 @p_927)) :rule cong :premises (t119.t86 t119.t218))
(step t119.t220 (cl (= @p_927 @p_922)) :rule aci_simp)
(step t119.t221 (cl (= @p_924 @p_922)) :rule trans :premises (t119.t219 t119.t220))
(step t119.t222 (cl @p_926) :rule cong :premises (t119.t221))
(step t119.t223 (cl @p_925 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t119.t224)
(assume t119.t224.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t119.t224.t0 (cl (or @p_353 @p_924)) :rule forall_inst :args (2/1 @p_4))
(step t119.t224.t1 (cl @p_353 @p_924) :rule or :premises (t119.t224.t0))
(step t119.t224.t2 (cl @p_924) :rule resolution :premises (t119.t224.t1 t119.t169))
(step t119.t224 (cl @p_353 @p_924) :rule subproof :discharge (t119.t224.a0))
(step t119.t225 (cl @p_925 @p_924) :rule resolution :premises (t119.t223 t119.t224))
(step t119.t226 (cl @p_925 (not @p_924)) :rule implies_neg2)
(step t119.t227 (cl @p_925 @p_925) :rule resolution :premises (t119.t225 t119.t226))
(step t119.t228 (cl @p_925) :rule contraction :premises (t119.t227))
(step t119.t229 (cl @p_923) :rule resolution :premises (t119.t217 t119.t222 t119.t228))
(step t119.t230 (cl @p_353 @p_922) :rule implies :premises (t119.t229))
(step t119.t231 (cl @p_922) :rule resolution :premises (t119.t230 t119.t169))
(step t119.t232 (cl (or @p_343 @p_868)) :rule forall_inst :args (@p_4 @p_304 2/1))
(step t119.t233 (cl @p_343 @p_868) :rule or :premises (t119.t232))
(step t119.t234 (cl @p_868) :rule resolution :premises (t119.t233 a2))
(step t119.t235 (cl (or @p_343 @p_873)) :rule forall_inst :args (@p_306 @p_270 @p_4))
(step t119.t236 (cl @p_343 @p_873) :rule or :premises (t119.t235))
(step t119.t237 (cl @p_873) :rule resolution :premises (t119.t236 a2))
(step t119.t238 (cl (not @p_888) (not @p_887) @p_884) :rule equiv_pos2)
(step t119.t239 (cl (= (* -1/1 (- 1/1 @p_874)) (* 1/1 (- @p_874 1/1)))) :rule poly_simp)
(step t119.t240 (cl (= @p_885 @p_875)) :rule poly_simp_rel :premises (t119.t239))
(step t119.t241 (cl (= @p_886 @p_889)) :rule cong :premises (t119.t86 t119.t240))
(step t119.t242 (cl (= @p_889 @p_875)) :rule aci_simp)
(step t119.t243 (cl (= @p_886 @p_875)) :rule trans :premises (t119.t241 t119.t242))
(step t119.t244 (cl @p_888) :rule cong :premises (t119.t243))
(step t119.t245 (cl @p_887 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule implies_neg1)
(anchor :step t119.t246)
(assume t119.t246.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))
(step t119.t246.t0 (cl (or @p_883 @p_886)) :rule forall_inst :args (2/1 1/1))
(step t119.t246.t1 (cl @p_883 @p_886) :rule or :premises (t119.t246.t0))
(step t119.t246.t2 (cl (not @p_876) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t246.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t246.t3.t0 (cl (= (* 1/1 (- @p_877 ?v1)) (* -1/1 (- ?v1 @p_877)))) :rule poly_simp)
(step t119.t246.t3.t1 (cl (= @p_882 @p_878)) :rule poly_simp_rel :premises (t119.t246.t3.t0))
(step t119.t246.t3.t2 (cl (= (=> @p_117 @p_882) @p_880)) :rule cong :premises (t119.t246.t3.t1))
(step t119.t246.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(anchor :step t119.t246.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t246.t4.t0 (cl (= @p_880 @p_881)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_878))
(step t119.t246.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t246.t4.t2 (cl (= @p_878 @p_878)) :rule refl)
(step t119.t246.t4.t3 (cl (= @p_881 @p_879)) :rule cong :premises (t119.t246.t4.t1 t119.t246.t4.t2))
(step t119.t246.t4.t4 (cl (= @p_880 @p_879)) :rule trans :premises (t119.t246.t4.t0 t119.t246.t4.t3))
(step t119.t246.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(step t119.t246.t5 (cl @p_876) :rule trans :premises (t119.t246.t3 t119.t246.t4))
(step t119.t246.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule resolution :premises (t119.t246.t2 t119.t246.t5 a21))
(step t119.t246.t7 (cl @p_886) :rule resolution :premises (t119.t246.t1 t119.t246.t6))
(step t119.t246 (cl @p_883 @p_886) :rule subproof :discharge (t119.t246.a0))
(step t119.t247 (cl @p_887 @p_886) :rule resolution :premises (t119.t245 t119.t246))
(step t119.t248 (cl @p_887 (not @p_886)) :rule implies_neg2)
(step t119.t249 (cl @p_887 @p_887) :rule resolution :premises (t119.t247 t119.t248))
(step t119.t250 (cl @p_887) :rule contraction :premises (t119.t249))
(step t119.t251 (cl @p_884) :rule resolution :premises (t119.t238 t119.t244 t119.t250))
(step t119.t252 (cl @p_883 @p_875) :rule implies :premises (t119.t251))
(step t119.t253 (cl (not @p_876) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule equiv_pos2)
(anchor :step t119.t254 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t254.t0 (cl (= (* 1/1 (- @p_877 ?v1)) (* -1/1 (- ?v1 @p_877)))) :rule poly_simp)
(step t119.t254.t1 (cl (= @p_882 @p_878)) :rule poly_simp_rel :premises (t119.t254.t0))
(step t119.t254.t2 (cl (= (=> @p_117 @p_882) @p_880)) :rule cong :premises (t119.t254.t1))
(step t119.t254 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(anchor :step t119.t255 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t255.t0 (cl (= @p_880 @p_881)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_878))
(step t119.t255.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t119.t255.t2 (cl (= @p_878 @p_878)) :rule refl)
(step t119.t255.t3 (cl (= @p_881 @p_879)) :rule cong :premises (t119.t255.t1 t119.t255.t2))
(step t119.t255.t4 (cl (= @p_880 @p_879)) :rule trans :premises (t119.t255.t0 t119.t255.t3))
(step t119.t255 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(step t119.t256 (cl @p_876) :rule trans :premises (t119.t254 t119.t255))
(step t119.t257 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule resolution :premises (t119.t253 t119.t256 a21))
(step t119.t258 (cl @p_875) :rule resolution :premises (t119.t252 t119.t257))
(step t119.t259 (cl @p_1431) :rule and_intro :premises (t119.t63 t119.t66 t119.t84 t119.t111 t119.t114 t119.t117 t119.t120 t119.a3 t119.t133 t119.t136 t119.t139 t119.t142 t119.t145 t119.t148 t119.t170 t119.t173 t119.t197 t119.t200 t119.t203 t119.t216 t119.t231 t119.t234 t119.t237 t119.a36 t119.t258))
(step t119.t260 (cl @p_1411) :rule resolution :premises (t119.t60 t119.t259))
(step t119.t261 (cl (not @p_1096) (not @p_1095) @p_1090) :rule equiv_pos2)
(step t119.t262 (cl (= @p_1092 @p_679)) :rule poly_simp)
(step t119.t263 (cl (= @p_1 @p_1)) :rule refl)
(step t119.t264 (cl (= @p_1093 @p_681)) :rule cong :premises (t119.t262 t119.t263))
(step t119.t265 (cl (= @p_1091 @p_1091)) :rule refl)
(step t119.t266 (cl (= @p_1094 @p_1097)) :rule cong :premises (t119.t264 t119.t265))
(step t119.t267 (cl (= (* 1/1 (- @p_681 @p_1091)) (* -1/1 (- @p_65 @p_1088)))) :rule poly_simp)
(step t119.t268 (cl (= @p_1097 @p_1089)) :rule poly_simp_rel :premises (t119.t267))
(step t119.t269 (cl (= @p_1094 @p_1089)) :rule trans :premises (t119.t266 t119.t268))
(step t119.t270 (cl @p_1096) :rule cong :premises (t119.t269))
(step t119.t271 (cl @p_1095 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t272)
(assume t119.t272.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t272.t0 (cl (or @p_279 @p_1094)) :rule forall_inst :args (@p_4 @p_139 @p_1))
(step t119.t272.t1 (cl @p_279 @p_1094) :rule or :premises (t119.t272.t0))
(step t119.t272.t2 (cl @p_1094) :rule resolution :premises (t119.t272.t1 t119.t272.a0))
(step t119.t272 (cl @p_279 @p_1094) :rule subproof :discharge (t119.t272.a0))
(step t119.t273 (cl @p_1095 @p_1094) :rule resolution :premises (t119.t271 t119.t272))
(step t119.t274 (cl @p_1095 (not @p_1094)) :rule implies_neg2)
(step t119.t275 (cl @p_1095 @p_1095) :rule resolution :premises (t119.t273 t119.t274))
(step t119.t276 (cl @p_1095) :rule contraction :premises (t119.t275))
(step t119.t277 (cl @p_1090) :rule resolution :premises (t119.t261 t119.t270 t119.t276))
(step t119.t278 (cl @p_279 @p_1089) :rule implies :premises (t119.t277))
(step t119.t279 (cl @p_1089) :rule resolution :premises (t119.t278 a1))
(step t119.t280 (cl @p_1410) :rule trans :premises (t119.t117 t119.t279))
(step t119.t281 (cl (! (=> (! (and @p_938 (! (not (! (= 1/1 @p_6) :named @p_1128)) :named @p_1413)) :named @p_1414) @p_1409) :named @p_1418) @p_1414) :rule implies_neg1)
(anchor :step t119.t282)
(assume t119.t282.a0 @p_938)
(assume t119.t282.a1 @p_1413)
(step t119.t282.t0 (cl (not @p_1428) (not @p_1420) @p_1409) :rule equiv_pos2)
(step t119.t282.t1 (cl (= @p_1420 @p_1430)) :rule rare_rewrite :args ("arith-elim-gt" @p_6 1/1))
(step t119.t282.t2 (cl (= @p_1421 @p_1429)) :rule rare_rewrite :args ("arith-elim-leq" @p_6 1/1))
(step t119.t282.t3 (cl (= @p_1429 @p_1421)) :rule symm :premises (t119.t282.t2))
(step t119.t282.t4 (cl (= @p_1430 @p_1422)) :rule cong :premises (t119.t282.t3))
(step t119.t282.t5 (cl @p_1424) :rule trans :premises (t119.t282.t1 t119.t282.t4))
(step t119.t282.t6 (cl (= (* 1/1 @p_1133) (* 1/1 (- @p_638 -1/1)))) :rule poly_simp)
(step t119.t282.t7 (cl (= @p_1429 @p_1408)) :rule poly_simp_rel :premises (t119.t282.t6))
(step t119.t282.t8 (cl (= @p_1421 @p_1408)) :rule trans :premises (t119.t282.t2 t119.t282.t7))
(step t119.t282.t9 (cl (= @p_1422 @p_1409)) :rule cong :premises (t119.t282.t8))
(step t119.t282.t10 (cl @p_1428) :rule trans :premises (t119.t282.t5 t119.t282.t9))
(step t119.t282.t11 (cl @p_1123) :rule not_symm :premises (t119.t282.a1))
(step t119.t282.t12 (cl (or @p_1122 @p_1422 (! (not (! (<= 1/1 @p_6) :named @p_1425)) :named @p_1427))) :rule la_disequality)
(step t119.t282.t13 (cl @p_1122 @p_1422 @p_1427) :rule or :premises (t119.t282.t12))
(step t119.t282.t14 (cl (! (= @p_938 @p_1425) :named @p_1426)) :rule comp_simplify)
(step t119.t282.t15 (cl (not @p_1426) @p_941 @p_1425) :rule equiv_pos2)
(step t119.t282.t16 (cl @p_1425) :rule resolution :premises (t119.t282.t14 t119.t282.t15 t119.t282.a0))
(step t119.t282.t17 (cl @p_1424) :rule comp_simplify)
(step t119.t282.t18 (cl (not @p_1424) @p_1420 (! (not @p_1422) :named @p_1423)) :rule equiv_pos1)
(step t119.t282.t19 (cl @p_1420 @p_1423) :rule resolution :premises (t119.t282.t17 t119.t282.t18))
(step t119.t282.t20 (cl @p_1420) :rule resolution :premises (t119.t282.t11 t119.t282.t13 t119.t282.t16 t119.t282.t19))
(step t119.t282.t21 (cl @p_1409) :rule resolution :premises (t119.t282.t0 t119.t282.t10 t119.t282.t20))
(step t119.t282 (cl @p_941 (! (not @p_1413) :named @p_1416) @p_1409) :rule subproof :discharge (t119.t282.a0 t119.t282.a1))
(step t119.t283 (cl (! (not @p_1414) :named @p_1417) @p_938) :rule and_pos :args (0))
(step t119.t284 (cl @p_1417 @p_1413) :rule and_pos :args (1))
(step t119.t285 (cl @p_1409 @p_1417 @p_1417) :rule resolution :premises (t119.t282 t119.t283 t119.t284))
(step t119.t286 (cl @p_1417 @p_1417 @p_1409) :rule reordering :premises (t119.t285))
(step t119.t287 (cl @p_1417 @p_1409) :rule contraction :premises (t119.t286))
(step t119.t288 (cl @p_1418 @p_1409) :rule resolution :premises (t119.t281 t119.t287))
(step t119.t289 (cl @p_1418 @p_1419) :rule implies_neg2)
(step t119.t290 (cl @p_1418 @p_1418) :rule resolution :premises (t119.t288 t119.t289))
(step t119.t291 (cl @p_1418) :rule contraction :premises (t119.t290))
(step t119.t292 (cl @p_1417 @p_1409) :rule implies :premises (t119.t291))
(step t119.t293 (cl (! (=> @p_1123 @p_1413) :named @p_1415) @p_1123) :rule implies_neg1)
(anchor :step t119.t294)
(assume t119.t294.a0 @p_1123)
(step t119.t294.t0 (cl @p_1413) :rule not_symm :premises (t119.t294.a0))
(step t119.t294 (cl @p_1402 @p_1413) :rule subproof :discharge (t119.t294.a0))
(step t119.t295 (cl @p_1415 @p_1413) :rule resolution :premises (t119.t293 t119.t294))
(step t119.t296 (cl @p_1415 @p_1416) :rule implies_neg2)
(step t119.t297 (cl @p_1415 @p_1415) :rule resolution :premises (t119.t295 t119.t296))
(step t119.t298 (cl @p_1415) :rule contraction :premises (t119.t297))
(step t119.t299 (cl @p_1402 @p_1413) :rule implies :premises (t119.t298))
(step t119.t300 (cl @p_1413) :rule resolution :premises (t119.t299 t119.a11))
(step t119.t301 (cl @p_1414) :rule and_intro :premises (t119.a29 t119.t300))
(step t119.t302 (cl @p_1409) :rule resolution :premises (t119.t292 t119.t301))
(step t119.t303 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t119.t304 (cl (= @p_221 x$)) :rule poly_simp)
(step t119.t305 (cl (= @p_222 @p_33)) :rule cong :premises (t119.t304))
(step t119.t306 (cl (= @p_223 @p_227)) :rule cong :premises (t119.t305))
(step t119.t307 (cl (= @p_224 @p_228)) :rule cong :premises (t119.t306))
(step t119.t308 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t119.t309 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t119.t308))
(step t119.t310 (cl (= @p_224 @p_210)) :rule trans :premises (t119.t307 t119.t309))
(step t119.t311 (cl @p_226) :rule cong :premises (t119.t310))
(step t119.t312 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t119.t313)
(assume t119.t313.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t119.t313.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t119.t313.t1 (cl @p_219 @p_224) :rule or :premises (t119.t313.t0))
(step t119.t313.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t119.t313.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t313.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t313.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t119.t313.t3.t0))
(step t119.t313.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t119.t313.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t119.t313.t3.t1 t119.t313.t3.t2))
(step t119.t313.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t119.t313.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t119.t313.t3.t4))
(step t119.t313.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t119.t313.t3.t3 t119.t313.t3.t5))
(step t119.t313.t3 (cl @p_211) :rule bind)
(step t119.t313.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t119.t313.t2 t119.t313.t3 a24))
(step t119.t313.t5 (cl @p_224) :rule resolution :premises (t119.t313.t1 t119.t313.t4))
(step t119.t313 (cl @p_219 @p_224) :rule subproof :discharge (t119.t313.a0))
(step t119.t314 (cl @p_225 @p_224) :rule resolution :premises (t119.t312 t119.t313))
(step t119.t315 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t119.t316 (cl @p_225 @p_225) :rule resolution :premises (t119.t314 t119.t315))
(step t119.t317 (cl @p_225) :rule contraction :premises (t119.t316))
(step t119.t318 (cl @p_220) :rule resolution :premises (t119.t303 t119.t311 t119.t317))
(step t119.t319 (cl @p_219 @p_210) :rule implies :premises (t119.t318))
(step t119.t320 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t119.t321 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t321.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t321.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t119.t321.t0))
(step t119.t321.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t119.t321.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t119.t321.t1 t119.t321.t2))
(step t119.t321.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t119.t321.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t119.t321.t4))
(step t119.t321.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t119.t321.t3 t119.t321.t5))
(step t119.t321 (cl @p_211) :rule bind)
(step t119.t322 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t119.t320 t119.t321 a24))
(step t119.t323 (cl @p_210) :rule resolution :premises (t119.t319 t119.t322))
(step t119.t324 (cl (not @p_59) (not @p_58) @p_55) :rule equiv_pos2)
(step t119.t325 (cl (= @p_56 @p_35)) :rule poly_simp)
(step t119.t326 (cl @p_60) :rule refl)
(step t119.t327 (cl (= @p_57 @p_36)) :rule cong :premises (t119.t325 t119.t326))
(step t119.t328 (cl @p_59) :rule cong :premises (t119.t327))
(step t119.t329 (cl @p_58 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule implies_neg1)
(anchor :step t119.t330)
(assume t119.t330.a0 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)))
(step t119.t330.t0 (cl (or @p_54 @p_57)) :rule forall_inst :args (p$ x$))
(step t119.t330.t1 (cl @p_54 @p_57) :rule or :premises (t119.t330.t0))
(step t119.t330.t2 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t119.t330.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t330.t3.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t119.t330.t3.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t119.t330.t3.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t119.t330.t3.t1))
(step t119.t330.t3.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t119.t330.t3.t0 t119.t330.t3.t2))
(step t119.t330.t3.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t119.t330.t3.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t119.t330.t3.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t119.t330.t3.t5))
(step t119.t330.t3.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t119.t330.t3.t4 t119.t330.t3.t6))
(step t119.t330.t3.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t119.t330.t3.t3 t119.t330.t3.t7))
(step t119.t330.t3 (cl @p_37) :rule bind)
(step t119.t330.t4 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t119.t330.t2 t119.t330.t3 a26))
(step t119.t330.t5 (cl @p_57) :rule resolution :premises (t119.t330.t1 t119.t330.t4))
(step t119.t330 (cl @p_54 @p_57) :rule subproof :discharge (t119.t330.a0))
(step t119.t331 (cl @p_58 @p_57) :rule resolution :premises (t119.t329 t119.t330))
(step t119.t332 (cl @p_58 (not @p_57)) :rule implies_neg2)
(step t119.t333 (cl @p_58 @p_58) :rule resolution :premises (t119.t331 t119.t332))
(step t119.t334 (cl @p_58) :rule contraction :premises (t119.t333))
(step t119.t335 (cl @p_55) :rule resolution :premises (t119.t324 t119.t328 t119.t334))
(step t119.t336 (cl @p_54 @p_36) :rule implies :premises (t119.t335))
(step t119.t337 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t119.t338 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t338.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t119.t338.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t119.t338.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t119.t338.t1))
(step t119.t338.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t119.t338.t0 t119.t338.t2))
(step t119.t338.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t119.t338.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t119.t338.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t119.t338.t5))
(step t119.t338.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t119.t338.t4 t119.t338.t6))
(step t119.t338.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t119.t338.t3 t119.t338.t7))
(step t119.t338 (cl @p_37) :rule bind)
(step t119.t339 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t119.t337 t119.t338 a26))
(step t119.t340 (cl @p_36) :rule resolution :premises (t119.t336 t119.t339))
(step t119.t341 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t119.t342 (cl (= @p_208 @p_208)) :rule refl)
(step t119.t343 (cl (= @p_240 @p_230)) :rule cong :premises (t119.t304 t119.t342))
(step t119.t344 (cl @p_60) :rule refl)
(step t119.t345 (cl (= @p_241 @p_231)) :rule cong :premises (t119.t343 t119.t344))
(step t119.t346 (cl @p_243) :rule cong :premises (t119.t345))
(step t119.t347 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t119.t348)
(assume t119.t348.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t119.t348.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t119.t348.t1 (cl @p_238 @p_241) :rule or :premises (t119.t348.t0))
(step t119.t348.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t119.t348.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t119.t348.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t119.t348.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t119.t348.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t119.t348.t3.t1))
(step t119.t348.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t119.t348.t3.t0 t119.t348.t3.t2))
(step t119.t348.t3 (cl @p_232) :rule bind)
(step t119.t348.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t119.t348.t2 t119.t348.t3 a25))
(step t119.t348.t5 (cl @p_241) :rule resolution :premises (t119.t348.t1 t119.t348.t4))
(step t119.t348 (cl @p_238 @p_241) :rule subproof :discharge (t119.t348.a0))
(step t119.t349 (cl @p_242 @p_241) :rule resolution :premises (t119.t347 t119.t348))
(step t119.t350 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t119.t351 (cl @p_242 @p_242) :rule resolution :premises (t119.t349 t119.t350))
(step t119.t352 (cl @p_242) :rule contraction :premises (t119.t351))
(step t119.t353 (cl @p_239) :rule resolution :premises (t119.t341 t119.t346 t119.t352))
(step t119.t354 (cl @p_238 @p_231) :rule implies :premises (t119.t353))
(step t119.t355 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t119.t356 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t119.t356.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t119.t356.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t119.t356.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t119.t356.t1))
(step t119.t356.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t119.t356.t0 t119.t356.t2))
(step t119.t356 (cl @p_232) :rule bind)
(step t119.t357 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t119.t355 t119.t356 a25))
(step t119.t358 (cl @p_231) :rule resolution :premises (t119.t354 t119.t357))
(step t119.t359 (cl (not @p_14) (not @p_12) @p_13) :rule equiv_pos2)
(step t119.t360 (cl (= @p_11 @p_15)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 1/1))
(step t119.t361 (cl (= @p_12 @p_16)) :rule cong :premises (t119.t360))
(step t119.t362 (cl (= @p_16 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t119.t363 (cl @p_14) :rule trans :premises (t119.t361 t119.t362))
(step t119.t364 (cl @p_13) :rule resolution :premises (t119.t359 t119.t363 a32))
(step t119.t365 (cl (not @p_1076) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t119.t366 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t119.t367 (cl (= @p_18 @p_18)) :rule refl)
(step t119.t368 (cl (= @p_1073 @p_1067)) :rule cong :premises (t119.t366 t119.t367))
(step t119.t369 (cl (= @p_1071 @p_1077)) :rule poly_simp)
(step t119.t370 (cl (= @p_1074 @p_1078)) :rule cong :premises (t119.t368 t119.t369))
(step t119.t371 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t119.t372 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t119.t371))
(step t119.t373 (cl (= @p_1074 @p_1069)) :rule trans :premises (t119.t370 t119.t372))
(step t119.t374 (cl @p_1076) :rule cong :premises (t119.t373))
(step t119.t375 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t376)
(assume t119.t376.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t376.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t119.t376.t1 (cl @p_279 @p_1074) :rule or :premises (t119.t376.t0))
(step t119.t376.t2 (cl @p_1074) :rule resolution :premises (t119.t376.t1 t119.t376.a0))
(step t119.t376 (cl @p_279 @p_1074) :rule subproof :discharge (t119.t376.a0))
(step t119.t377 (cl @p_1075 @p_1074) :rule resolution :premises (t119.t375 t119.t376))
(step t119.t378 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t119.t379 (cl @p_1075 @p_1075) :rule resolution :premises (t119.t377 t119.t378))
(step t119.t380 (cl @p_1075) :rule contraction :premises (t119.t379))
(step t119.t381 (cl @p_1070) :rule resolution :premises (t119.t365 t119.t374 t119.t380))
(step t119.t382 (cl @p_279 @p_1069) :rule implies :premises (t119.t381))
(step t119.t383 (cl @p_1069) :rule resolution :premises (t119.t382 a1))
(step t119.t384 (cl (! (=> (! (and @p_1069 @p_1103 @p_19) :named @p_1365) @p_1260) :named @p_1367) @p_1365) :rule implies_neg1)
(anchor :step t119.t385)
(assume t119.t385.a0 @p_1069)
(assume t119.t385.a1 @p_1103)
(assume t119.t385.a2 @p_19)
(step t119.t385.t0 (cl (or @p_32 @p_19)) :rule forall_inst :args (2/1 @p_3))
(step t119.t385.t1 (cl @p_32 @p_19) :rule or :premises (t119.t385.t0))
(step t119.t385.t2 (cl (not @p_20) (not (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t385.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t385.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t385.t3.t1 (cl (= @p_29 @p_24)) :rule cong :premises (t119.t385.t3.t0))
(step t119.t385.t3.t2 (cl (= @p_26 @p_26)) :rule refl)
(step t119.t385.t3.t3 (cl (= @p_30 @p_31)) :rule cong :premises (t119.t385.t3.t1 t119.t385.t3.t2))
(step t119.t385.t3.t4 (cl (= (* 1/1 (- @p_24 @p_26)) (* -1/1 (- @p_26 @p_24)))) :rule poly_simp)
(step t119.t385.t3.t5 (cl (= @p_31 @p_27)) :rule poly_simp_rel :premises (t119.t385.t3.t4))
(step t119.t385.t3.t6 (cl (= @p_30 @p_27)) :rule trans :premises (t119.t385.t3.t3 t119.t385.t3.t5))
(step t119.t385.t3 (cl @p_20) :rule bind)
(step t119.t385.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule resolution :premises (t119.t385.t2 t119.t385.t3 a23))
(step t119.t385.t5 (cl @p_19) :rule resolution :premises (t119.t385.t1 t119.t385.t4))
(step t119.t385.t6 (cl (= @p_17 @p_18)) :rule symm :premises (t119.t385.t5))
(step t119.t385.t7 (cl @p_1260) :rule trans :premises (t119.t385.t6 t119.t385.a1 t119.t383))
(step t119.t385 (cl @p_1205 @p_1201 @p_1192 @p_1260) :rule subproof :discharge (t119.t385.a0 t119.t385.a1 t119.t385.a2))
(step t119.t386 (cl (! (not @p_1365) :named @p_1366) @p_1069) :rule and_pos :args (0))
(step t119.t387 (cl @p_1366 @p_1103) :rule and_pos :args (1))
(step t119.t388 (cl @p_1366 @p_19) :rule and_pos :args (2))
(step t119.t389 (cl @p_1260 @p_1366 @p_1366 @p_1366) :rule resolution :premises (t119.t385 t119.t386 t119.t387 t119.t388))
(step t119.t390 (cl @p_1366 @p_1366 @p_1366 @p_1260) :rule reordering :premises (t119.t389))
(step t119.t391 (cl @p_1366 @p_1260) :rule contraction :premises (t119.t390))
(step t119.t392 (cl @p_1367 @p_1260) :rule resolution :premises (t119.t384 t119.t391))
(step t119.t393 (cl @p_1367 @p_1272) :rule implies_neg2)
(step t119.t394 (cl @p_1367 @p_1367) :rule resolution :premises (t119.t392 t119.t393))
(step t119.t395 (cl @p_1367) :rule contraction :premises (t119.t394))
(step t119.t396 (cl @p_1366 @p_1260) :rule implies :premises (t119.t395))
(step t119.t397 (cl (or @p_32 @p_19)) :rule forall_inst :args (2/1 @p_3))
(step t119.t398 (cl @p_32 @p_19) :rule or :premises (t119.t397))
(step t119.t399 (cl (not @p_20) (not (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule equiv_pos2)
(anchor :step t119.t400 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t400.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t119.t400.t1 (cl (= @p_29 @p_24)) :rule cong :premises (t119.t400.t0))
(step t119.t400.t2 (cl (= @p_26 @p_26)) :rule refl)
(step t119.t400.t3 (cl (= @p_30 @p_31)) :rule cong :premises (t119.t400.t1 t119.t400.t2))
(step t119.t400.t4 (cl (= (* 1/1 (- @p_24 @p_26)) (* -1/1 (- @p_26 @p_24)))) :rule poly_simp)
(step t119.t400.t5 (cl (= @p_31 @p_27)) :rule poly_simp_rel :premises (t119.t400.t4))
(step t119.t400.t6 (cl (= @p_30 @p_27)) :rule trans :premises (t119.t400.t3 t119.t400.t5))
(step t119.t400 (cl @p_20) :rule bind)
(step t119.t401 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule resolution :premises (t119.t399 t119.t400 a23))
(step t119.t402 (cl @p_19) :rule resolution :premises (t119.t398 t119.t401))
(step t119.t403 (cl @p_1365) :rule and_intro :premises (t119.t383 t119.a18 t119.t402))
(step t119.t404 (cl @p_1260) :rule resolution :premises (t119.t396 t119.t403))
(step t119.t405 (cl (! (=> (! (and (! (= @p_1 @p_900) :named @p_1368) @p_244) :named @p_1369) @p_1261) :named @p_1376) @p_1369) :rule implies_neg1)
(anchor :step t119.t406)
(assume t119.t406.a0 @p_1368)
(assume t119.t406.a1 @p_244)
(step t119.t406.t0 (cl @p_1264) :rule symm :premises (t119.t406.a1))
(step t119.t406.t1 (cl @p_1261) :rule trans :premises (t119.t406.t0 t119.t406.a0))
(step t119.t406 (cl (! (not @p_1368) :named @p_1373) @p_1113 @p_1261) :rule subproof :discharge (t119.t406.a0 t119.t406.a1))
(step t119.t407 (cl (! (not @p_1369) :named @p_1375) @p_1368) :rule and_pos :args (0))
(step t119.t408 (cl @p_1375 @p_244) :rule and_pos :args (1))
(step t119.t409 (cl @p_1261 @p_1375 @p_1375) :rule resolution :premises (t119.t406 t119.t407 t119.t408))
(step t119.t410 (cl @p_1375 @p_1375 @p_1261) :rule reordering :premises (t119.t409))
(step t119.t411 (cl @p_1375 @p_1261) :rule contraction :premises (t119.t410))
(step t119.t412 (cl @p_1376 @p_1261) :rule resolution :premises (t119.t405 t119.t411))
(step t119.t413 (cl @p_1376 @p_1271) :rule implies_neg2)
(step t119.t414 (cl @p_1376 @p_1376) :rule resolution :premises (t119.t412 t119.t413))
(step t119.t415 (cl @p_1376) :rule contraction :premises (t119.t414))
(step t119.t416 (cl @p_1375 @p_1261) :rule implies :premises (t119.t415))
(step t119.t417 (cl (! (=> (! (and @p_960 @p_864 @p_340 @p_342 @p_385 @p_311 @p_344 @p_305 @p_295 @p_410 @p_291 @p_406 @p_364 @p_396 @p_249) :named @p_1370) @p_1368) :named @p_1372) @p_1370) :rule implies_neg1)
(anchor :step t119.t418)
(assume t119.t418.a0 @p_960)
(assume t119.t418.a1 @p_864)
(assume t119.t418.a2 @p_340)
(assume t119.t418.a3 @p_342)
(assume t119.t418.a4 @p_385)
(assume t119.t418.a5 @p_311)
(assume t119.t418.a6 @p_344)
(assume t119.t418.a7 @p_305)
(assume t119.t418.a8 @p_295)
(assume t119.t418.a9 @p_410)
(assume t119.t418.a10 @p_291)
(assume t119.t418.a11 @p_406)
(assume t119.t418.a12 @p_364)
(assume t119.t418.a13 @p_396)
(assume t119.t418.a14 @p_249)
(step t119.t418.t0 (cl (= @p_270 @p_304)) :rule symm :premises (t119.t148))
(step t119.t418.t1 (cl @p_355) :rule symm :premises (t119.t170))
(step t119.t418.t2 (cl (= @p_304 @p_310)) :rule cong :premises (t119.t418.t1))
(step t119.t418.t3 (cl (= @p_307 @p_304)) :rule cong :premises (t119.t197))
(step t119.t418.t4 (cl @p_388) :rule refl)
(step t119.t418.t5 (cl (= @p_308 @p_341)) :rule cong :premises (t119.t418.t3 t119.t418.t4))
(step t119.t418.t6 (cl (= @p_341 @p_296)) :rule symm :premises (t119.t200))
(step t119.t418.t7 (cl (= @p_270 @p_296)) :rule trans :premises (t119.t418.t0 t119.t418.t2 t119.t173 t119.t418.t5 t119.t418.t6))
(step t119.t418.t8 (cl (= @p_294 @p_339)) :rule cong :premises (t119.t418.t7 t119.t263))
(step t119.t418.t9 (cl (= @p_339 @p_294)) :rule symm :premises (t119.t418.t8))
(step t119.t418.t10 (cl (= @p_289 @p_293)) :rule cong :premises (t119.t117))
(step t119.t418.t11 (cl (= @p_293 @p_289)) :rule symm :premises (t119.t418.t10))
(step t119.t418.t12 (cl (= @p_289 @p_290)) :rule symm :premises (t119.t142))
(step t119.t418.t13 (cl (= @p_362 @p_65)) :rule symm :premises (t119.t114))
(step t119.t418.t14 (cl (= @p_65 @p_6)) :rule symm :premises (t119.t117))
(step t119.t418.t15 (cl (= @p_362 @p_6)) :rule trans :premises (t119.t418.t13 t119.t418.t14))
(step t119.t418.t16 (cl (= 2/1 2/1)) :rule refl)
(step t119.t418.t17 (cl (= @p_363 @p_290)) :rule cong :premises (t119.t418.t15 t119.t418.t16))
(step t119.t418.t18 (cl (= @p_290 @p_363)) :rule symm :premises (t119.t418.t17))
(step t119.t418.t19 (cl (= @p_363 @p_361)) :rule symm :premises (t119.t111))
(step t119.t418.t20 (cl (= @p_361 @p_4)) :rule symm :premises (t119.t84))
(step t119.t418.t21 (cl (= @p_314 @p_248)) :rule trans :premises (t119.t203 t119.t418.t9 t119.t145 t119.t418.t11 t119.t418.t12 t119.t418.t18 t119.t418.t19 t119.t418.t20 t119.t418.a14))
(step t119.t418.t22 (cl (= @p_293 @p_294)) :rule symm :premises (t119.t145))
(step t119.t418.t23 (cl (= @p_339 @p_314)) :rule symm :premises (t119.t203))
(step t119.t418.t24 (cl (= @p_4 @p_314)) :rule trans :premises (t119.t84 t119.t111 t119.t418.t17 t119.t142 t119.t418.t10 t119.t418.t22 t119.t418.t8 t119.t418.t23))
(step t119.t418.t25 (cl (= @p_248 @p_860)) :rule cong :premises (t119.t418.t24))
(step t119.t418.t26 (cl (= @p_314 @p_860)) :rule trans :premises (t119.t418.t21 t119.t418.t25))
(step t119.t418.t27 (cl (= @p_296 @p_296)) :rule refl)
(step t119.t418.t28 (cl (= @p_862 @p_861)) :rule cong :premises (t119.t418.t26 t119.t418.t27))
(step t119.t418.t29 (cl (or @p_312 @p_864)) :rule forall_inst :args (@p_247 @p_314 @p_296))
(step t119.t418.t30 (cl @p_312 @p_864) :rule or :premises (t119.t418.t29))
(step t119.t418.t31 (cl @p_864) :rule resolution :premises (t119.t418.t30 a27))
(step t119.t418.t32 (cl (= @p_861 @p_863)) :rule symm :premises (t119.t418.t31))
(step t119.t418.t33 (cl (! (= @p_862 @p_1) :named @p_1374)) :rule symm :premises (t119.t418.a0))
(step t119.t418.t34 (cl (= @p_863 @p_900)) :rule cong :premises (t119.t418.t33))
(step t119.t418.t35 (cl @p_1368) :rule trans :premises (t119.t418.a0 t119.t418.t28 t119.t418.t32 t119.t418.t34))
(step t119.t418 (cl @p_1208 @p_1226 @p_434 @p_433 @p_430 @p_437 @p_432 @p_438 @p_441 @p_424 @p_442 @p_427 @p_431 @p_429 @p_574 @p_1368) :rule subproof :discharge (t119.t418.a0 t119.t418.a1 t119.t418.a2 t119.t418.a3 t119.t418.a4 t119.t418.a5 t119.t418.a6 t119.t418.a7 t119.t418.a8 t119.t418.a9 t119.t418.a10 t119.t418.a11 t119.t418.a12 t119.t418.a13 t119.t418.a14))
(step t119.t419 (cl (! (not @p_1370) :named @p_1371) @p_960) :rule and_pos :args (0))
(step t119.t420 (cl @p_1371 @p_864) :rule and_pos :args (1))
(step t119.t421 (cl @p_1371 @p_340) :rule and_pos :args (2))
(step t119.t422 (cl @p_1371 @p_342) :rule and_pos :args (3))
(step t119.t423 (cl @p_1371 @p_385) :rule and_pos :args (4))
(step t119.t424 (cl @p_1371 @p_311) :rule and_pos :args (5))
(step t119.t425 (cl @p_1371 @p_344) :rule and_pos :args (6))
(step t119.t426 (cl @p_1371 @p_305) :rule and_pos :args (7))
(step t119.t427 (cl @p_1371 @p_295) :rule and_pos :args (8))
(step t119.t428 (cl @p_1371 @p_410) :rule and_pos :args (9))
(step t119.t429 (cl @p_1371 @p_291) :rule and_pos :args (10))
(step t119.t430 (cl @p_1371 @p_406) :rule and_pos :args (11))
(step t119.t431 (cl @p_1371 @p_364) :rule and_pos :args (12))
(step t119.t432 (cl @p_1371 @p_396) :rule and_pos :args (13))
(step t119.t433 (cl @p_1371 @p_249) :rule and_pos :args (14))
(step t119.t434 (cl @p_1368 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371) :rule resolution :premises (t119.t418 t119.t419 t119.t420 t119.t421 t119.t422 t119.t423 t119.t424 t119.t425 t119.t426 t119.t427 t119.t428 t119.t429 t119.t430 t119.t431 t119.t432 t119.t433))
(step t119.t435 (cl @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1368) :rule reordering :premises (t119.t434))
(step t119.t436 (cl @p_1371 @p_1368) :rule contraction :premises (t119.t435))
(step t119.t437 (cl @p_1372 @p_1368) :rule resolution :premises (t119.t417 t119.t436))
(step t119.t438 (cl @p_1372 @p_1373) :rule implies_neg2)
(step t119.t439 (cl @p_1372 @p_1372) :rule resolution :premises (t119.t437 t119.t438))
(step t119.t440 (cl @p_1372) :rule contraction :premises (t119.t439))
(step t119.t441 (cl @p_1371 @p_1368) :rule implies :premises (t119.t440))
(step t119.t442 (cl (or @p_312 @p_864)) :rule forall_inst :args (@p_247 @p_314 @p_296))
(step t119.t443 (cl @p_312 @p_864) :rule or :premises (t119.t442))
(step t119.t444 (cl @p_864) :rule resolution :premises (t119.t443 a27))
(step t119.t445 (cl @p_1370) :rule and_intro :premises (t119.a26 t119.t444 t119.t203 t119.t200 t119.t197 t119.t173 t119.t170 t119.t148 t119.t145 t119.t117 t119.t142 t119.t114 t119.t111 t119.t84 t119.a6))
(step t119.t446 (cl @p_1368) :rule resolution :premises (t119.t441 t119.t445))
(step t119.t447 (cl @p_1369) :rule and_intro :premises (t119.t446 t119.a7))
(step t119.t448 (cl @p_1261) :rule resolution :premises (t119.t416 t119.t447))
(step t119.t449 (cl (not @p_908) (not @p_907) @p_903) :rule equiv_pos2)
(step t119.t450 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t119.t451 (cl (= @p_905 @p_900)) :rule cong :premises (t119.t450 t119.t263))
(step t119.t452 (cl (= @p_904 @p_909)) :rule poly_simp)
(step t119.t453 (cl (= @p_906 @p_910)) :rule cong :premises (t119.t451 t119.t452))
(step t119.t454 (cl (= (* 1/1 (- @p_900 @p_909)) (* -2/1 @p_911))) :rule poly_simp)
(step t119.t455 (cl (= @p_910 @p_902)) :rule poly_simp_rel :premises (t119.t454))
(step t119.t456 (cl (= @p_906 @p_902)) :rule trans :premises (t119.t453 t119.t455))
(step t119.t457 (cl @p_908) :rule cong :premises (t119.t456))
(step t119.t458 (cl @p_907 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t459)
(assume t119.t459.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t459.t0 (cl (or @p_279 @p_906)) :rule forall_inst :args (@p_1 @p_1 @p_1))
(step t119.t459.t1 (cl @p_279 @p_906) :rule or :premises (t119.t459.t0))
(step t119.t459.t2 (cl @p_906) :rule resolution :premises (t119.t459.t1 t119.t459.a0))
(step t119.t459 (cl @p_279 @p_906) :rule subproof :discharge (t119.t459.a0))
(step t119.t460 (cl @p_907 @p_906) :rule resolution :premises (t119.t458 t119.t459))
(step t119.t461 (cl @p_907 (not @p_906)) :rule implies_neg2)
(step t119.t462 (cl @p_907 @p_907) :rule resolution :premises (t119.t460 t119.t461))
(step t119.t463 (cl @p_907) :rule contraction :premises (t119.t462))
(step t119.t464 (cl @p_903) :rule resolution :premises (t119.t449 t119.t457 t119.t463))
(step t119.t465 (cl @p_279 @p_902) :rule implies :premises (t119.t464))
(step t119.t466 (cl @p_902) :rule resolution :premises (t119.t465 a1))
(step t119.t467 (cl (not @p_898) (not @p_897) @p_894) :rule equiv_pos2)
(step t119.t468 (cl (= (* 1/1 (- @p_890 @p_895)) @p_899)) :rule poly_simp)
(step t119.t469 (cl (= @p_896 @p_893)) :rule poly_simp_rel :premises (t119.t468))
(step t119.t470 (cl @p_898) :rule cong :premises (t119.t469))
(step t119.t471 (cl @p_897 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t119.t472)
(assume t119.t472.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))))
(step t119.t472.t0 (cl (or @p_326 @p_896)) :rule forall_inst :args (@p_1 @p_1))
(step t119.t472.t1 (cl @p_326 @p_896) :rule or :premises (t119.t472.t0))
(step t119.t472.t2 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t119.t472.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t472.t3.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t119.t472.t3.t1 (cl @p_22) :rule refl)
(step t119.t472.t3.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t119.t472.t3.t0 t119.t472.t3.t1))
(step t119.t472.t3.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t119.t472.t3.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t119.t472.t3.t2 t119.t472.t3.t3))
(step t119.t472.t3.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t119.t472.t3.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t119.t472.t3.t5))
(step t119.t472.t3.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t119.t472.t3.t4 t119.t472.t3.t6))
(step t119.t472.t3 (cl @p_316) :rule bind)
(step t119.t472.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t119.t472.t2 t119.t472.t3 a16))
(step t119.t472.t5 (cl @p_896) :rule resolution :premises (t119.t472.t1 t119.t472.t4))
(step t119.t472 (cl @p_326 @p_896) :rule subproof :discharge (t119.t472.a0))
(step t119.t473 (cl @p_897 @p_896) :rule resolution :premises (t119.t471 t119.t472))
(step t119.t474 (cl @p_897 (not @p_896)) :rule implies_neg2)
(step t119.t475 (cl @p_897 @p_897) :rule resolution :premises (t119.t473 t119.t474))
(step t119.t476 (cl @p_897) :rule contraction :premises (t119.t475))
(step t119.t477 (cl @p_894) :rule resolution :premises (t119.t467 t119.t470 t119.t476))
(step t119.t478 (cl @p_326 @p_893) :rule implies :premises (t119.t477))
(step t119.t479 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t119.t480 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t119.t480.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t119.t480.t1 (cl @p_22) :rule refl)
(step t119.t480.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t119.t480.t0 t119.t480.t1))
(step t119.t480.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t119.t480.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t119.t480.t2 t119.t480.t3))
(step t119.t480.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t119.t480.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t119.t480.t5))
(step t119.t480.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t119.t480.t4 t119.t480.t6))
(step t119.t480 (cl @p_316) :rule bind)
(step t119.t481 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t119.t479 t119.t480 a16))
(step t119.t482 (cl @p_893) :rule resolution :premises (t119.t478 t119.t481))
(step t119.t483 (cl (not @p_1086) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t119.t484 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t119.t485 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t119.t484))
(step t119.t486 (cl @p_1086) :rule cong :premises (t119.t485))
(step t119.t487 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t488)
(assume t119.t488.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t488.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t119.t488.t1 (cl @p_279 @p_1084) :rule or :premises (t119.t488.t0))
(step t119.t488.t2 (cl @p_1084) :rule resolution :premises (t119.t488.t1 t119.t488.a0))
(step t119.t488 (cl @p_279 @p_1084) :rule subproof :discharge (t119.t488.a0))
(step t119.t489 (cl @p_1085 @p_1084) :rule resolution :premises (t119.t487 t119.t488))
(step t119.t490 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t119.t491 (cl @p_1085 @p_1085) :rule resolution :premises (t119.t489 t119.t490))
(step t119.t492 (cl @p_1085) :rule contraction :premises (t119.t491))
(step t119.t493 (cl @p_1082) :rule resolution :premises (t119.t483 t119.t486 t119.t492))
(step t119.t494 (cl @p_279 @p_1081) :rule implies :premises (t119.t493))
(step t119.t495 (cl @p_1081) :rule resolution :premises (t119.t494 a1))
(step t119.t496 (cl (or @p_326 @p_1054)) :rule forall_inst :args (@p_1 @p_18))
(step t119.t497 (cl @p_326 @p_1054) :rule or :premises (t119.t496))
(step t119.t498 (cl @p_1054) :rule resolution :premises (t119.t497 t119.t481))
(step t119.t499 (cl (= @p_1052 @p_1053)) :rule symm :premises (t119.t498))
(step t119.t500 (cl (not @p_1063) (not @p_1062) @p_1058) :rule equiv_pos2)
(step t119.t501 (cl (= @p_1060 @p_1055)) :rule cong :premises (t119.t450 t119.t367))
(step t119.t502 (cl (= @p_1059 @p_1064)) :rule poly_simp)
(step t119.t503 (cl (= @p_1061 @p_1065)) :rule cong :premises (t119.t501 t119.t502))
(step t119.t504 (cl (= (* 1/1 (- @p_1055 @p_1064)) (* -2/1 (- @p_1053 @p_1056)))) :rule poly_simp)
(step t119.t505 (cl (= @p_1065 @p_1057)) :rule poly_simp_rel :premises (t119.t504))
(step t119.t506 (cl (= @p_1061 @p_1057)) :rule trans :premises (t119.t503 t119.t505))
(step t119.t507 (cl @p_1063) :rule cong :premises (t119.t506))
(step t119.t508 (cl @p_1062 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t119.t509)
(assume t119.t509.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t119.t509.t0 (cl (or @p_279 @p_1061)) :rule forall_inst :args (@p_1 @p_1 @p_18))
(step t119.t509.t1 (cl @p_279 @p_1061) :rule or :premises (t119.t509.t0))
(step t119.t509.t2 (cl @p_1061) :rule resolution :premises (t119.t509.t1 t119.t509.a0))
(step t119.t509 (cl @p_279 @p_1061) :rule subproof :discharge (t119.t509.a0))
(step t119.t510 (cl @p_1062 @p_1061) :rule resolution :premises (t119.t508 t119.t509))
(step t119.t511 (cl @p_1062 (not @p_1061)) :rule implies_neg2)
(step t119.t512 (cl @p_1062 @p_1062) :rule resolution :premises (t119.t510 t119.t511))
(step t119.t513 (cl @p_1062) :rule contraction :premises (t119.t512))
(step t119.t514 (cl @p_1058) :rule resolution :premises (t119.t500 t119.t507 t119.t513))
(step t119.t515 (cl @p_279 @p_1057) :rule implies :premises (t119.t514))
(step t119.t516 (cl @p_1057) :rule resolution :premises (t119.t515 a1))
(step t119.t517 (cl @p_1262) :rule trans :premises (t119.t499 t119.t516))
(step t119.t518 (cl @p_1397 @p_244) :rule implies_neg1)
(anchor :step t119.t519)
(assume t119.t519.a0 @p_244)
(step t119.t519.t0 (cl @p_1264) :rule symm :premises (t119.t519.a0))
(step t119.t519 (cl @p_1113 @p_1264) :rule subproof :discharge (t119.t519.a0))
(step t119.t520 (cl @p_1397 @p_1264) :rule resolution :premises (t119.t518 t119.t519))
(step t119.t521 (cl @p_1397 @p_1268) :rule implies_neg2)
(step t119.t522 (cl @p_1397 @p_1397) :rule resolution :premises (t119.t520 t119.t521))
(step t119.t523 (cl @p_1397) :rule contraction :premises (t119.t522))
(step t119.t524 (cl @p_1113 @p_1264) :rule implies :premises (t119.t523))
(step t119.t525 (cl @p_1264) :rule resolution :premises (t119.t524 t119.a7))
(step t119.t526 (cl @p_159 @p_160 @p_142) :rule equiv_pos2)
(step t119.t527 (cl (= @p_2 @p_157)) :rule rare_rewrite :args ("arith-elim-lt" x$ @p_1))
(step t119.t528 (cl (= (* 1/1 @p_158) (* 1/1 (- @p_140 0/1)))) :rule poly_simp)
(step t119.t529 (cl (= @p_156 @p_141)) :rule poly_simp_rel :premises (t119.t528))
(step t119.t530 (cl (= @p_157 @p_142)) :rule cong :premises (t119.t529))
(step t119.t531 (cl @p_155) :rule trans :premises (t119.t527 t119.t530))
(step t119.t532 (cl @p_142) :rule resolution :premises (t119.t526 t119.t531 a28))
(step t119.t533 (cl @p_1412) :rule and_intro :premises (t119.t260 t119.t280 t119.t302 t119.t323 t119.t340 t119.t358 t119.t364 t119.t383 t119.t404 t119.t448 t119.t466 t119.t482 t119.t495 t119.t517 t119.t525 t119.t532))
(step t119.t534 (cl @p_685) :rule resolution :premises (t119.t25 t119.t533))
(step t119 (cl @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_1402 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226 @p_685) :rule subproof :discharge (t119.a0 t119.a1 t119.a2 t119.a3 t119.a4 t119.a5 t119.a6 t119.a7 t119.a8 t119.a9 t119.a10 t119.a11 t119.a12 t119.a13 t119.a14 t119.a15 t119.a16 t119.a17 t119.a18 t119.a19 t119.a20 t119.a21 t119.a22 t119.a23 t119.a24 t119.a25 t119.a26 t119.a27 t119.a28 t119.a29 t119.a30 t119.a31 t119.a32 t119.a33 t119.a34 t119.a35 t119.a36 t119.a37 t119.a38 t119.a39 t119.a40 t119.a41 t119.a42 t119.a43 t119.a44))
(step t120 (cl (! (not @p_1405) :named @p_1406) @p_142) :rule and_pos :args (0))
(step t121 (cl @p_1406 @p_13) :rule and_pos :args (1))
(step t122 (cl @p_1406 @p_410) :rule and_pos :args (2))
(step t123 (cl @p_1406 @p_1188) :rule and_pos :args (3))
(step t124 (cl @p_1406 @p_19) :rule and_pos :args (4))
(step t125 (cl @p_1406 @p_36) :rule and_pos :args (5))
(step t126 (cl @p_1406 @p_249) :rule and_pos :args (6))
(step t127 (cl @p_1406 @p_244) :rule and_pos :args (7))
(step t128 (cl @p_1406 @p_406) :rule and_pos :args (8))
(step t129 (cl @p_1406 @p_969) :rule and_pos :args (9))
(step t130 (cl @p_1406 @p_1117) :rule and_pos :args (10))
(step t131 (cl @p_1406 @p_1123) :rule and_pos :args (11))
(step t132 (cl @p_1406 @p_405) :rule and_pos :args (12))
(step t133 (cl @p_1406 @p_396) :rule and_pos :args (13))
(step t134 (cl @p_1406 @p_385) :rule and_pos :args (14))
(step t135 (cl @p_1406 @p_364) :rule and_pos :args (15))
(step t136 (cl @p_1406 @p_344) :rule and_pos :args (16))
(step t137 (cl @p_1406 @p_342) :rule and_pos :args (17))
(step t138 (cl @p_1406 @p_1103) :rule and_pos :args (18))
(step t139 (cl @p_1406 @p_340) :rule and_pos :args (19))
(step t140 (cl @p_1406 @p_1102) :rule and_pos :args (20))
(step t141 (cl @p_1406 @p_1089) :rule and_pos :args (21))
(step t142 (cl @p_1406 @p_1081) :rule and_pos :args (22))
(step t143 (cl @p_1406 @p_1069) :rule and_pos :args (23))
(step t144 (cl @p_1406 @p_1057) :rule and_pos :args (24))
(step t145 (cl @p_1406 @p_1054) :rule and_pos :args (25))
(step t146 (cl @p_1406 @p_960) :rule and_pos :args (26))
(step t147 (cl @p_1406 @p_210) :rule and_pos :args (27))
(step t148 (cl @p_1406 @p_231) :rule and_pos :args (28))
(step t149 (cl @p_1406 @p_938) :rule and_pos :args (29))
(step t150 (cl @p_1406 @p_937) :rule and_pos :args (30))
(step t151 (cl @p_1406 @p_311) :rule and_pos :args (31))
(step t152 (cl @p_1406 @p_305) :rule and_pos :args (32))
(step t153 (cl @p_1406 @p_934) :rule and_pos :args (33))
(step t154 (cl @p_1406 @p_930) :rule and_pos :args (34))
(step t155 (cl @p_1406 @p_922) :rule and_pos :args (35))
(step t156 (cl @p_1406 @p_913) :rule and_pos :args (36))
(step t157 (cl @p_1406 @p_295) :rule and_pos :args (37))
(step t158 (cl @p_1406 @p_291) :rule and_pos :args (38))
(step t159 (cl @p_1406 @p_902) :rule and_pos :args (39))
(step t160 (cl @p_1406 @p_893) :rule and_pos :args (40))
(step t161 (cl @p_1406 @p_875) :rule and_pos :args (41))
(step t162 (cl @p_1406 @p_873) :rule and_pos :args (42))
(step t163 (cl @p_1406 @p_868) :rule and_pos :args (43))
(step t164 (cl @p_1406 @p_864) :rule and_pos :args (44))
(step t165 (cl @p_685 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406) :rule resolution :premises (t119 t120 t121 t122 t123 t124 t125 t126 t127 t128 t129 t130 t131 t132 t133 t134 t135 t136 t137 t138 t139 t140 t141 t142 t143 t144 t145 t146 t147 t148 t149 t150 t151 t152 t153 t154 t155 t156 t157 t158 t159 t160 t161 t162 t163 t164))
(step t166 (cl @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_1406 @p_685) :rule reordering :premises (t165))
(step t167 (cl @p_1406 @p_685) :rule contraction :premises (t166))
(step t168 (cl @p_1407 @p_685) :rule resolution :premises (t118 t167))
(step t169 (cl @p_1407 @p_1404) :rule implies_neg2)
(step t170 (cl @p_1407 @p_1407) :rule resolution :premises (t168 t169))
(step t171 (cl @p_1407) :rule contraction :premises (t170))
(step t172 (cl @p_1406 @p_685) :rule implies :premises (t171))
(step t173 (cl @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_1402 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226 @p_685) :rule resolution :premises (t117 t172))
(step t174 (cl @p_1403 (! (not @p_163) :named @p_166)) :rule or_neg :args (0))
(step t175 (cl @p_1403 @p_16) :rule or_neg :args (1))
(step t176 (cl @p_1403 (! (not @p_424) :named @p_469)) :rule or_neg :args (2))
(step t177 (cl @p_1403 (! (not @p_1191) :named @p_1257)) :rule or_neg :args (3))
(step t178 (cl @p_1403 @p_1256) :rule or_neg :args (4))
(step t179 (cl @p_1403 @p_1255) :rule or_neg :args (5))
(step t180 (cl @p_1403 (! (not @p_574) :named @p_575)) :rule or_neg :args (6))
(step t181 (cl @p_1403 @p_1254) :rule or_neg :args (7))
(step t182 (cl @p_1403 (! (not @p_427) :named @p_466)) :rule or_neg :args (8))
(step t183 (cl @p_1403 (! (not @p_1042) :named @p_1253)) :rule or_neg :args (9))
(step t184 (cl @p_1403 (! (not @p_1199) :named @p_1252)) :rule or_neg :args (10))
(step t185 (cl @p_1403 (not @p_1402)) :rule or_neg :args (11))
(step t186 (cl @p_1403 (! (not @p_428) :named @p_465)) :rule or_neg :args (12))
(step t187 (cl @p_1403 (! (not @p_429) :named @p_464)) :rule or_neg :args (13))
(step t188 (cl @p_1403 (! (not @p_430) :named @p_463)) :rule or_neg :args (14))
(step t189 (cl @p_1403 (! (not @p_431) :named @p_462)) :rule or_neg :args (15))
(step t190 (cl @p_1403 (! (not @p_432) :named @p_461)) :rule or_neg :args (16))
(step t191 (cl @p_1403 (! (not @p_433) :named @p_460)) :rule or_neg :args (17))
(step t192 (cl @p_1403 (! (not @p_1201) :named @p_1251)) :rule or_neg :args (18))
(step t193 (cl @p_1403 (! (not @p_434) :named @p_459)) :rule or_neg :args (19))
(step t194 (cl @p_1403 (! (not @p_1202) :named @p_1250)) :rule or_neg :args (20))
(step t195 (cl @p_1403 (not @p_1400)) :rule or_neg :args (21))
(step t196 (cl @p_1403 (! (not @p_1204) :named @p_1249)) :rule or_neg :args (22))
(step t197 (cl @p_1403 (! (not @p_1205) :named @p_1248)) :rule or_neg :args (23))
(step t198 (cl @p_1403 (! (not @p_1206) :named @p_1247)) :rule or_neg :args (24))
(step t199 (cl @p_1403 (! (not @p_1207) :named @p_1246)) :rule or_neg :args (25))
(step t200 (cl @p_1403 (! (not @p_1208) :named @p_1245)) :rule or_neg :args (26))
(step t201 (cl @p_1403 @p_1244) :rule or_neg :args (27))
(step t202 (cl @p_1403 @p_1243) :rule or_neg :args (28))
(step t203 (cl @p_1403 (! (not @p_941) :named @p_942)) :rule or_neg :args (29))
(step t204 (cl @p_1403 (! (not @p_1211) :named @p_1242)) :rule or_neg :args (30))
(step t205 (cl @p_1403 (! (not @p_437) :named @p_456)) :rule or_neg :args (31))
(step t206 (cl @p_1403 (! (not @p_438) :named @p_455)) :rule or_neg :args (32))
(step t207 (cl @p_1403 (! (not @p_1214) :named @p_1241)) :rule or_neg :args (33))
(step t208 (cl @p_1403 (! (not @p_1215) :named @p_1240)) :rule or_neg :args (34))
(step t209 (cl @p_1403 (! (not @p_1216) :named @p_1239)) :rule or_neg :args (35))
(step t210 (cl @p_1403 (! (not @p_1217) :named @p_1238)) :rule or_neg :args (36))
(step t211 (cl @p_1403 (! (not @p_441) :named @p_452)) :rule or_neg :args (37))
(step t212 (cl @p_1403 (! (not @p_442) :named @p_451)) :rule or_neg :args (38))
(step t213 (cl @p_1403 (! (not @p_1219) :named @p_1237)) :rule or_neg :args (39))
(step t214 (cl @p_1403 (! (not @p_1220) :named @p_1236)) :rule or_neg :args (40))
(step t215 (cl @p_1403 (! (not @p_1221) :named @p_1235)) :rule or_neg :args (41))
(step t216 (cl @p_1403 (! (not @p_1222) :named @p_1234)) :rule or_neg :args (42))
(step t217 (cl @p_1403 (! (not @p_1223) :named @p_1233)) :rule or_neg :args (43))
(step t218 (cl @p_1403 (! (not @p_1226) :named @p_1232)) :rule or_neg :args (44))
(step t219 (cl @p_1403 @p_1404) :rule or_neg :args (45))
(step t220 (cl @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403 @p_1403) :rule resolution :premises (t173 t174 t175 t176 t177 t178 t179 t180 t181 t182 t183 t184 t185 t186 t187 t188 t189 t190 t191 t192 t193 t194 t195 t196 t197 t198 t199 t200 t201 t202 t203 t204 t205 t206 t207 t208 t209 t210 t211 t212 t213 t214 t215 t216 t217 t218 t219))
(step t221 (cl @p_1403) :rule contraction :premises (t220))
(step t222 (cl @p_1401) :rule resolution :premises (t69 t116 t221))
(step t223 (cl @p_141 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_1122 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226 @p_685) :rule or :premises (t222))
(step t224 (cl @p_141 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_1122 @p_574 @p_1113 @p_427 @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1201 @p_434 @p_1202 @p_1400 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_941 @p_1211 @p_437 @p_438 @p_685 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1226) :rule reordering :premises (t223))
(step t225 (cl @p_159 @p_160 @p_142) :rule equiv_pos2)
(step t226 (cl (= @p_2 @p_157)) :rule rare_rewrite :args ("arith-elim-lt" x$ @p_1))
(step t227 (cl (= (* 1/1 @p_158) (* 1/1 (- @p_140 0/1)))) :rule poly_simp)
(step t228 (cl (= @p_156 @p_141)) :rule poly_simp_rel :premises (t227))
(step t229 (cl (= @p_157 @p_142)) :rule cong :premises (t228))
(step t230 (cl @p_155) :rule trans :premises (t226 t229))
(step t231 (cl @p_142) :rule resolution :premises (t225 t230 a28))
(step t232 (cl (not @p_14) (not @p_12) @p_13) :rule equiv_pos2)
(step t233 (cl (= @p_11 @p_15)) :rule rare_rewrite :args ("arith-elim-lt" @p_10 1/1))
(step t234 (cl (= @p_12 @p_16)) :rule cong :premises (t233))
(step t235 (cl (= @p_16 @p_13)) :rule rare_rewrite :args ("bool-double-not-elim" @p_13))
(step t236 (cl @p_14) :rule trans :premises (t234 t235))
(step t237 (cl @p_13) :rule resolution :premises (t232 t236 a32))
(step t238 (cl @p_411) :rule forall_inst :args (@p_1 @p_4))
(step t239 (cl @p_292 @p_410) :rule or :premises (t238))
(step t240 (cl @p_410) :rule resolution :premises (t239 a6))
(step t241 (cl (! (not (! (or @p_245 @p_1188) :named @p_1189)) :named @p_1190) @p_245 @p_1188) :rule or_pos)
(step t242 (cl @p_245 @p_1188 @p_1190) :rule reordering :premises (t241))
(step t243 (cl (! (or @p_245 (! (= x$ @p_1) :named @p_625)) :named @p_626) (! (not @p_245) :named @p_624)) :rule or_neg :args (0))
(step t244 (cl (! (not (! (= (! (= @p_6 @p_8) :named @p_628) @p_626) :named @p_629)) :named @p_674) @p_628 (! (not @p_626) :named @p_627)) :rule equiv_pos1)
(step t245 (cl @p_628 @p_627 @p_674) :rule reordering :premises (t244))
(step t246 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ @p_638 @p_8) :named @p_639) 0/1) :named @p_640)) :named @p_641)) :named @p_647) (! (not @p_628) :named @p_637)) :named @p_648) (! (or @p_640 @p_637) :named @p_646)) :named @p_673)) (not @p_648) @p_646) :rule equiv_pos2)
(step t247 (cl (= @p_647 @p_640)) :rule rare_rewrite :args ("bool-double-not-elim" @p_640))
(step t248 (cl (= @p_637 @p_637)) :rule refl)
(step t249 (cl @p_673) :rule cong :premises (t247 t248))
(step t250 (cl (! (=> @p_641 @p_637) :named @p_650) @p_641) :rule implies_neg1)
(anchor :step t251)
(assume t251.a0 @p_641)
(step t251.t0 (cl @p_650 @p_641) :rule implies_neg1)
(anchor :step t251.t1)
(assume t251.t1.a0 @p_641)
(step t251.t1.t0 (cl (! (=> @p_628 false) :named @p_651) @p_628) :rule implies_neg1)
(anchor :step t251.t1.t1)
(assume t251.t1.t1.a0 @p_628)
(step t251.t1.t1.t0 (cl (not (! (= (! (< (! (+ @p_6 (! (* -1/1 (! (+ @p_6 (* -1/1 @p_8)) :named @p_653)) :named @p_654)) :named @p_655) (! (+ @p_8 @p_175) :named @p_652)) :named @p_656) false) :named @p_665)) (not @p_656) false) :rule equiv_pos2)
(step t251.t1.t1.t1 (cl (= @p_656 (! (not (! (>= @p_655 @p_652) :named @p_666)) :named @p_667))) :rule rare_rewrite :args ("arith-elim-lt" @p_655 @p_652))
(step t251.t1.t1.t2 (cl (= @p_654 @p_639)) :rule poly_simp)
(step t251.t1.t1.t3 (cl (= @p_655 (! (+ @p_6 @p_639) :named @p_672))) :rule cong :premises (t251.t1.t1.t2))
(step t251.t1.t1.t4 (cl (= @p_672 @p_8)) :rule poly_simp)
(step t251.t1.t1.t5 (cl (= @p_655 @p_8)) :rule trans :premises (t251.t1.t1.t3 t251.t1.t1.t4))
(step t251.t1.t1.t6 (cl (= @p_175 0/1)) :rule evaluate)
(step t251.t1.t1.t7 (cl (= @p_652 (! (+ @p_8 0/1) :named @p_671))) :rule cong :premises (t251.t1.t1.t6))
(step t251.t1.t1.t8 (cl (= @p_671 @p_8)) :rule poly_simp)
(step t251.t1.t1.t9 (cl (= @p_652 @p_8)) :rule trans :premises (t251.t1.t1.t7 t251.t1.t1.t8))
(step t251.t1.t1.t10 (cl (= @p_666 (! (>= @p_8 @p_8) :named @p_668))) :rule cong :premises (t251.t1.t1.t5 t251.t1.t1.t9))
(step t251.t1.t1.t11 (cl (= @p_668 (! (>= (! (- @p_8 @p_8) :named @p_669) 0/1) :named @p_670))) :rule rare_rewrite :args ("arith-geq-norm1-real" @p_8 @p_8))
(step t251.t1.t1.t12 (cl (= @p_669 0/1)) :rule poly_simp)
(step t251.t1.t1.t13 (cl @p_60) :rule refl)
(step t251.t1.t1.t14 (cl (= @p_670 @p_190)) :rule cong :premises (t251.t1.t1.t12 t251.t1.t1.t13))
(step t251.t1.t1.t15 (cl @p_191) :rule evaluate)
(step t251.t1.t1.t16 (cl (= @p_670 true)) :rule trans :premises (t251.t1.t1.t14 t251.t1.t1.t15))
(step t251.t1.t1.t17 (cl (= @p_668 true)) :rule trans :premises (t251.t1.t1.t11 t251.t1.t1.t16))
(step t251.t1.t1.t18 (cl (= @p_666 true)) :rule trans :premises (t251.t1.t1.t10 t251.t1.t1.t17))
(step t251.t1.t1.t19 (cl (= @p_667 @p_189)) :rule cong :premises (t251.t1.t1.t18))
(step t251.t1.t1.t20 (cl (= @p_189 false)) :rule evaluate)
(step t251.t1.t1.t21 (cl (= @p_667 false)) :rule trans :premises (t251.t1.t1.t19 t251.t1.t1.t20))
(step t251.t1.t1.t22 (cl @p_665) :rule trans :premises (t251.t1.t1.t1 t251.t1.t1.t21))
(step t251.t1.t1.t23 (cl @p_637 (not (! (< @p_654 @p_175) :named @p_657)) @p_656) :rule la_generic :args (-1/1 1/1 1/1))
(step t251.t1.t1.t24 (cl (=> (! (and @p_183 (! (> @p_653 0/1) :named @p_658)) :named @p_659) @p_657)) :rule la_mult_neg)
(step t251.t1.t1.t25 (cl (not @p_659) @p_657) :rule implies :premises (t251.t1.t1.t24))
(step t251.t1.t1.t26 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t251.t1.t1.t27 (cl (not @p_185) @p_183) :rule equiv1 :premises (t251.t1.t1.t26))
(step t251.t1.t1.t28 (cl @p_185) :rule evaluate)
(step t251.t1.t1.t29 (cl @p_183) :rule resolution :premises (t251.t1.t1.t27 t251.t1.t1.t28))
(step t251.t1.t1.t30 (cl (not (! (= @p_641 @p_658) :named @p_660)) @p_647 @p_658) :rule equiv_pos2)
(step t251.t1.t1.t31 (cl (= @p_658 (! (not (! (>= 0/1 @p_653) :named @p_663)) :named @p_664))) :rule rare_rewrite :args ("arith-elim-gt" @p_653 0/1))
(step t251.t1.t1.t32 (cl (= (! (<= @p_653 0/1) :named @p_661) @p_663)) :rule rare_rewrite :args ("arith-elim-leq" @p_653 0/1))
(step t251.t1.t1.t33 (cl (= @p_663 @p_661)) :rule symm :premises (t251.t1.t1.t32))
(step t251.t1.t1.t34 (cl (= @p_664 (! (not @p_661) :named @p_662))) :rule cong :premises (t251.t1.t1.t33))
(step t251.t1.t1.t35 (cl (= @p_658 @p_662)) :rule trans :premises (t251.t1.t1.t31 t251.t1.t1.t34))
(step t251.t1.t1.t36 (cl (= (* -1/1 (- 0/1 @p_653)) (! (* -1/1 (- @p_639 0/1)) :named @p_645))) :rule poly_simp)
(step t251.t1.t1.t37 (cl (= @p_663 @p_640)) :rule poly_simp_rel :premises (t251.t1.t1.t36))
(step t251.t1.t1.t38 (cl (= @p_661 @p_640)) :rule trans :premises (t251.t1.t1.t32 t251.t1.t1.t37))
(step t251.t1.t1.t39 (cl (= @p_662 @p_641)) :rule cong :premises (t251.t1.t1.t38))
(step t251.t1.t1.t40 (cl (= @p_658 @p_641)) :rule trans :premises (t251.t1.t1.t35 t251.t1.t1.t39))
(step t251.t1.t1.t41 (cl @p_660) :rule symm :premises (t251.t1.t1.t40))
(step t251.t1.t1.t42 (cl (not (! (= @p_9 @p_641) :named @p_642)) (not @p_9) @p_641) :rule equiv_pos2)
(step t251.t1.t1.t43 (cl (= @p_9 (! (not (! (>= @p_8 @p_6) :named @p_643)) :named @p_644))) :rule rare_rewrite :args ("arith-elim-lt" @p_8 @p_6))
(step t251.t1.t1.t44 (cl (= (* -1/1 (- @p_8 @p_6)) @p_645)) :rule poly_simp)
(step t251.t1.t1.t45 (cl (= @p_643 @p_640)) :rule poly_simp_rel :premises (t251.t1.t1.t44))
(step t251.t1.t1.t46 (cl (= @p_644 @p_641)) :rule cong :premises (t251.t1.t1.t45))
(step t251.t1.t1.t47 (cl @p_642) :rule trans :premises (t251.t1.t1.t43 t251.t1.t1.t46))
(step t251.t1.t1.t48 (cl @p_641) :rule resolution :premises (t251.t1.t1.t42 t251.t1.t1.t47 a31))
(step t251.t1.t1.t49 (cl @p_658) :rule resolution :premises (t251.t1.t1.t30 t251.t1.t1.t41 t251.t1.t1.t48))
(step t251.t1.t1.t50 (cl @p_659) :rule and_intro :premises (t251.t1.t1.t29 t251.t1.t1.t49))
(step t251.t1.t1.t51 (cl @p_657) :rule resolution :premises (t251.t1.t1.t25 t251.t1.t1.t50))
(step t251.t1.t1.t52 (cl @p_656) :rule resolution :premises (t251.t1.t1.t23 t251.t1.t1.a0 t251.t1.t1.t51))
(step t251.t1.t1.t53 (cl false) :rule resolution :premises (t251.t1.t1.t0 t251.t1.t1.t22 t251.t1.t1.t52))
(step t251.t1.t1 (cl @p_637 false) :rule subproof :discharge (t251.t1.t1.a0))
(step t251.t1.t2 (cl @p_651 false) :rule resolution :premises (t251.t1.t0 t251.t1.t1))
(step t251.t1.t3 (cl @p_651 @p_133) :rule implies_neg2)
(step t251.t1.t4 (cl @p_651 @p_651) :rule resolution :premises (t251.t1.t2 t251.t1.t3))
(step t251.t1.t5 (cl @p_651) :rule contraction :premises (t251.t1.t4))
(step t251.t1.t6 (cl (= @p_651 @p_637)) :rule implies_simplify)
(step t251.t1.t7 (cl (not @p_651) @p_637) :rule equiv1 :premises (t251.t1.t6))
(step t251.t1.t8 (cl @p_637) :rule resolution :premises (t251.t1.t5 t251.t1.t7))
(step t251.t1 (cl @p_647 @p_637) :rule subproof :discharge (t251.t1.a0))
(step t251.t2 (cl @p_650 @p_637) :rule resolution :premises (t251.t0 t251.t1))
(step t251.t3 (cl @p_650 (! (not @p_637) :named @p_649)) :rule implies_neg2)
(step t251.t4 (cl @p_650 @p_650) :rule resolution :premises (t251.t2 t251.t3))
(step t251.t5 (cl @p_650) :rule contraction :premises (t251.t4))
(step t251.t6 (cl @p_647 @p_637) :rule implies :premises (t251.t5))
(step t251.t7 (cl (not @p_642) (not @p_9) @p_641) :rule equiv_pos2)
(step t251.t8 (cl (= @p_9 @p_644)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 @p_6))
(step t251.t9 (cl (= (* -1/1 (- @p_8 @p_6)) @p_645)) :rule poly_simp)
(step t251.t10 (cl (= @p_643 @p_640)) :rule poly_simp_rel :premises (t251.t9))
(step t251.t11 (cl (= @p_644 @p_641)) :rule cong :premises (t251.t10))
(step t251.t12 (cl @p_642) :rule trans :premises (t251.t8 t251.t11))
(step t251.t13 (cl @p_641) :rule resolution :premises (t251.t7 t251.t12 a31))
(step t251.t14 (cl @p_637) :rule resolution :premises (t251.t6 t251.t13))
(step t251 (cl @p_647 @p_637) :rule subproof :discharge (t251.a0))
(step t252 (cl @p_650 @p_637) :rule resolution :premises (t250 t251))
(step t253 (cl @p_650 @p_649) :rule implies_neg2)
(step t254 (cl @p_650 @p_650) :rule resolution :premises (t252 t253))
(step t255 (cl @p_650) :rule contraction :premises (t254))
(step t256 (cl @p_647 @p_637) :rule implies :premises (t255))
(step t257 (cl @p_648 (not @p_647)) :rule or_neg :args (0))
(step t258 (cl @p_648 @p_649) :rule or_neg :args (1))
(step t259 (cl @p_648 @p_648) :rule resolution :premises (t256 t257 t258))
(step t260 (cl @p_648) :rule contraction :premises (t259))
(step t261 (cl @p_646) :rule resolution :premises (t246 t249 t260))
(step t262 (cl @p_640 @p_637) :rule or :premises (t261))
(step t263 (cl (not @p_642) (not @p_9) @p_641) :rule equiv_pos2)
(step t264 (cl (= @p_9 @p_644)) :rule rare_rewrite :args ("arith-elim-lt" @p_8 @p_6))
(step t265 (cl (= (* -1/1 (- @p_8 @p_6)) @p_645)) :rule poly_simp)
(step t266 (cl (= @p_643 @p_640)) :rule poly_simp_rel :premises (t265))
(step t267 (cl (= @p_644 @p_641)) :rule cong :premises (t266))
(step t268 (cl @p_642) :rule trans :premises (t264 t267))
(step t269 (cl @p_641) :rule resolution :premises (t263 t268 a31))
(step t270 (cl @p_637) :rule resolution :premises (t262 t269))
(step t271 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2)))) (! (= @p_628 (! (or @p_245 (! (= @p_1 x$) :named @p_632)) :named @p_633)) :named @p_634)) :named @p_635) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2)))) @p_629) :named @p_631)) :named @p_636)) (not @p_635) @p_631) :rule equiv_pos2)
(step t272 (cl (= (* 1/1 (- @p_1 x$)) (* -1/1 @p_158))) :rule poly_simp)
(step t273 (cl (= @p_632 @p_625)) :rule poly_simp_rel :premises (t272))
(step t274 (cl (= @p_633 @p_626)) :rule cong :premises (t273))
(step t275 (cl (= @p_634 @p_629)) :rule cong :premises (t274))
(step t276 (cl @p_636) :rule cong :premises (t275))
(step t277 (cl @p_635 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2))))) :rule implies_neg1)
(anchor :step t278)
(assume t278.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2)))))
(step t278.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (= (times$a ?v0 ?v1) (times$a ?v2 ?v1)) (or (= ?v1 0/1) (= ?v0 ?v2))))) :named @p_630) @p_634)) :rule forall_inst :args (@p_1 @p_4 x$))
(step t278.t1 (cl @p_630 @p_634) :rule or :premises (t278.t0))
(step t278.t2 (cl @p_634) :rule resolution :premises (t278.t1 t278.a0))
(step t278 (cl @p_630 @p_634) :rule subproof :discharge (t278.a0))
(step t279 (cl @p_635 @p_634) :rule resolution :premises (t277 t278))
(step t280 (cl @p_635 (not @p_634)) :rule implies_neg2)
(step t281 (cl @p_635 @p_635) :rule resolution :premises (t279 t280))
(step t282 (cl @p_635) :rule contraction :premises (t281))
(step t283 (cl @p_631) :rule resolution :premises (t271 t276 t282))
(step t284 (cl @p_630 @p_629) :rule implies :premises (t283))
(step t285 (cl @p_629) :rule resolution :premises (t284 a10))
(step t286 (cl @p_627) :rule resolution :premises (t245 t270 t285))
(step t287 (cl @p_624) :rule resolution :premises (t243 t286))
(step t288 (cl (or @p_883 @p_1189)) :rule forall_inst :args (@p_4 @p_1))
(step t289 (cl @p_883 @p_1189) :rule or :premises (t288))
(step t290 (cl (not @p_876) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule equiv_pos2)
(anchor :step t291 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t291.t0 (cl (= (* 1/1 (- @p_877 ?v1)) (* -1/1 (- ?v1 @p_877)))) :rule poly_simp)
(step t291.t1 (cl (= @p_882 @p_878)) :rule poly_simp_rel :premises (t291.t0))
(step t291.t2 (cl (= (=> @p_117 @p_882) @p_880)) :rule cong :premises (t291.t1))
(step t291 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v1 ?v0) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(anchor :step t292 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t292.t0 (cl (= @p_880 @p_881)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_878))
(step t292.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t292.t2 (cl (= @p_878 @p_878)) :rule refl)
(step t292.t3 (cl (= @p_881 @p_879)) :rule cong :premises (t292.t1 t292.t2))
(step t292.t4 (cl (= @p_880 @p_879)) :rule trans :premises (t292.t0 t292.t3))
(step t292 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))) :rule bind)
(step t293 (cl @p_876) :rule trans :premises (t291 t292))
(step t294 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule resolution :premises (t290 t293 a21))
(step t295 (cl @p_1189) :rule resolution :premises (t289 t294))
(step t296 (cl @p_1188) :rule resolution :premises (t242 t287 t295))
(step t297 (cl (or @p_32 @p_19)) :rule forall_inst :args (2/1 @p_3))
(step t298 (cl @p_32 @p_19) :rule or :premises (t297))
(step t299 (cl (not @p_20) (not (forall ((?v0 Real) (?v1 Real)) (= (powr$ ?v0 (- ?v1)) (divide$ 1/1 (powr$ ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule equiv_pos2)
(anchor :step t300 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t300.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t300.t1 (cl (= @p_29 @p_24)) :rule cong :premises (t300.t0))
(step t300.t2 (cl (= @p_26 @p_26)) :rule refl)
(step t300.t3 (cl (= @p_30 @p_31)) :rule cong :premises (t300.t1 t300.t2))
(step t300.t4 (cl (= (* 1/1 (- @p_24 @p_26)) (* -1/1 (- @p_26 @p_24)))) :rule poly_simp)
(step t300.t5 (cl (= @p_31 @p_27)) :rule poly_simp_rel :premises (t300.t4))
(step t300.t6 (cl (= @p_30 @p_27)) :rule trans :premises (t300.t3 t300.t5))
(step t300 (cl @p_20) :rule bind)
(step t301 (cl (forall ((?v0 Real) (?v1 Real)) (= (divide$ 1/1 (powr$ ?v0 ?v1)) (powr$ ?v0 (* -1/1 ?v1))))) :rule resolution :premises (t299 t300 a23))
(step t302 (cl @p_19) :rule resolution :premises (t298 t301))
(step t303 (cl (not @p_59) (not @p_58) @p_55) :rule equiv_pos2)
(step t304 (cl (= @p_56 @p_35)) :rule poly_simp)
(step t305 (cl @p_60) :rule refl)
(step t306 (cl (= @p_57 @p_36)) :rule cong :premises (t304 t305))
(step t307 (cl @p_59) :rule cong :premises (t306))
(step t308 (cl @p_58 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule implies_neg1)
(anchor :step t309)
(assume t309.a0 (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1)))
(step t309.t0 (cl (or @p_54 @p_57)) :rule forall_inst :args (p$ x$))
(step t309.t1 (cl @p_54 @p_57) :rule or :premises (t309.t0))
(step t309.t2 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t309.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t309.t3.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t309.t3.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t309.t3.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t309.t3.t1))
(step t309.t3.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t309.t3.t0 t309.t3.t2))
(step t309.t3.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t309.t3.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t309.t3.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t309.t3.t5))
(step t309.t3.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t309.t3.t4 t309.t3.t6))
(step t309.t3.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t309.t3.t3 t309.t3.t7))
(step t309.t3 (cl @p_37) :rule bind)
(step t309.t4 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t309.t2 t309.t3 a26))
(step t309.t5 (cl @p_57) :rule resolution :premises (t309.t1 t309.t4))
(step t309 (cl @p_54 @p_57) :rule subproof :discharge (t309.a0))
(step t310 (cl @p_58 @p_57) :rule resolution :premises (t308 t309))
(step t311 (cl @p_58 (not @p_57)) :rule implies_neg2)
(step t312 (cl @p_58 @p_58) :rule resolution :premises (t310 t311))
(step t313 (cl @p_58) :rule contraction :premises (t312))
(step t314 (cl @p_55) :rule resolution :premises (t303 t307 t313))
(step t315 (cl @p_54 @p_36) :rule implies :premises (t314))
(step t316 (cl (not @p_37) (not (forall ((?v0 Int) (?v1 Real)) (<= (- (round_up$ ?v0 ?v1) (round_down$ ?v0 ?v1)) (powr$ 2/1 (- (of_int$ ?v0)))))) (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule equiv_pos2)
(anchor :step t317 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t317.t0 (cl (= @p_49 @p_51)) :rule poly_simp)
(step t317.t1 (cl (= @p_47 @p_40)) :rule poly_simp)
(step t317.t2 (cl (= @p_48 @p_41)) :rule cong :premises (t317.t1))
(step t317.t3 (cl (= @p_50 @p_52)) :rule cong :premises (t317.t0 t317.t2))
(step t317.t4 (cl (= @p_52 @p_53)) :rule rare_rewrite :args ("arith-elim-leq" @p_51 @p_41))
(step t317.t5 (cl (= (* -1/1 (- @p_41 @p_51)) (* -1/1 (- @p_45 0/1)))) :rule poly_simp)
(step t317.t6 (cl (= @p_53 @p_46)) :rule poly_simp_rel :premises (t317.t5))
(step t317.t7 (cl (= @p_52 @p_46)) :rule trans :premises (t317.t4 t317.t6))
(step t317.t8 (cl (= @p_50 @p_46)) :rule trans :premises (t317.t3 t317.t7))
(step t317 (cl @p_37) :rule bind)
(step t318 (cl (forall ((?v0 Int) (?v1 Real)) (>= (+ (* -1/1 (round_up$ ?v0 ?v1)) (round_down$ ?v0 ?v1) (powr$ 2/1 (* -1/1 (of_int$ ?v0)))) 0/1))) :rule resolution :premises (t316 t317 a26))
(step t319 (cl @p_36) :rule resolution :premises (t315 t318))
(step t320 (cl (! (not (! (= (! (= @p_1 @p_18) :named @p_1124) @p_1122) :named @p_1125)) :named @p_1399) @p_1124 @p_1123) :rule equiv_pos1)
(step t321 (cl @p_1124 @p_1123 @p_1399) :rule reordering :premises (t320))
(step t322 (cl (not (! (= (! (or @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 (! (not (! (= @p_932 (! (divide$ @p_290 1/1) :named @p_1186)) :named @p_1187)) :named @p_1194) (! (not (! (= (! (divide$ 1/1 @p_18) :named @p_1184) (! (divide$ @p_301 1/1) :named @p_1159)) :named @p_1185)) :named @p_1195) @p_574 @p_1113 (! (not @p_1124) :named @p_1135) (! (not (! (= @p_4 (! (divide$ @p_248 @p_247) :named @p_1150)) :named @p_1176)) :named @p_1196) (! (not (! (= @p_1055 (! (divide$ (! (times$a @p_247 1/1) :named @p_1157) @p_4) :named @p_1174)) :named @p_1175)) :named @p_1197) @p_427 (! (not (! (= @p_1051 (! (divide$ (times$a @p_139 1/1) @p_4) :named @p_1167)) :named @p_1173)) :named @p_1198) @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 (! (not (! (= @p_1167 (! (divide$ @p_139 (! (divide$ @p_4 1/1) :named @p_1165)) :named @p_1166)) :named @p_1168)) :named @p_1200) @p_1201 @p_434 @p_1202 (! (not (! (= (! (times$a (! (times$a @p_139 @p_247) :named @p_1144) @p_18) :named @p_1163) (! (times$a @p_139 @p_1055) :named @p_1162)) :named @p_1164)) :named @p_1203) @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_1211 @p_437 (! (not (! (= (! (divide$ @p_247 @p_1159) :named @p_1160) (! (divide$ @p_1157 @p_301) :named @p_1158)) :named @p_1161)) :named @p_1212) @p_438 (! (not (! (= (! (times$a @p_247 @p_139) :named @p_1153) @p_1144) :named @p_1156)) :named @p_1213) @p_1214 @p_1215 @p_1216 @p_1217 @p_441 (! (not (! (= (! (times$a @p_1153 @p_1) :named @p_1154) (! (times$a @p_247 @p_892) :named @p_1137)) :named @p_1155)) :named @p_1218) @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 (! (not (! (= (! (divide$ @p_139 @p_1150) :named @p_1151) (! (divide$ @p_1144 @p_248) :named @p_1149)) :named @p_1152)) :named @p_1224) (! (not (! (= (! (times$a @p_139 (! (divide$ @p_247 (! (divide$ @p_1098 @p_18) :named @p_1143)) :named @p_1146)) :named @p_1147) (! (divide$ @p_1144 @p_1143) :named @p_1145)) :named @p_1148)) :named @p_1225) @p_1226 (! (not (! (= (! (times$a @p_892 @p_247) :named @p_1136) (! (times$a @p_139 (! (times$a @p_1 @p_247) :named @p_1139)) :named @p_1141)) :named @p_1142)) :named @p_1227) (! (not (! (= @p_1139 @p_900) :named @p_1140)) :named @p_1228) (! (not (! (= @p_1137 @p_1136) :named @p_1138)) :named @p_1229)) :named @p_1231) (! (or @p_141 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_1194 @p_1195 @p_574 @p_1113 @p_1135 @p_1196 @p_1197 @p_427 @p_1198 @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1200 @p_1201 @p_434 @p_1202 @p_1203 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_1211 @p_437 @p_1212 @p_438 @p_1213 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_1218 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1224 @p_1225 @p_1226 @p_1227 @p_1228 @p_1229) :named @p_1230)) :named @p_1398)) (not @p_1231) @p_1230) :rule equiv_pos2)
(step t323 (cl (= @p_1194 @p_1194)) :rule refl)
(step t324 (cl (= @p_1195 @p_1195)) :rule refl)
(step t325 (cl (= @p_1135 @p_1135)) :rule refl)
(step t326 (cl (= @p_1196 @p_1196)) :rule refl)
(step t327 (cl (= @p_1197 @p_1197)) :rule refl)
(step t328 (cl (= @p_1198 @p_1198)) :rule refl)
(step t329 (cl (= @p_1200 @p_1200)) :rule refl)
(step t330 (cl (= @p_1203 @p_1203)) :rule refl)
(step t331 (cl (= @p_1212 @p_1212)) :rule refl)
(step t332 (cl (= @p_1213 @p_1213)) :rule refl)
(step t333 (cl (= @p_1218 @p_1218)) :rule refl)
(step t334 (cl (= @p_1224 @p_1224)) :rule refl)
(step t335 (cl (= @p_1225 @p_1225)) :rule refl)
(step t336 (cl (= @p_1227 @p_1227)) :rule refl)
(step t337 (cl (= @p_1228 @p_1228)) :rule refl)
(step t338 (cl (= @p_1229 @p_1229)) :rule refl)
(step t339 (cl @p_1398) :rule cong :premises (t70 t71 t72 t73 t74 t75 t323 t324 t76 t77 t325 t326 t327 t78 t328 t79 t80 t82 t83 t84 t85 t86 t87 t329 t88 t89 t90 t330 t92 t93 t94 t95 t96 t97 t98 t100 t101 t331 t102 t332 t103 t104 t105 t106 t107 t333 t108 t109 t110 t111 t112 t113 t334 t335 t114 t336 t337 t338))
(step t340 (cl (! (=> (! (and @p_142 @p_13 @p_410 @p_1188 @p_19 @p_36 @p_1187 @p_1185 @p_249 @p_244 @p_1124 @p_1176 @p_1175 @p_406 @p_1173 @p_969 @p_1117 @p_405 @p_396 @p_385 @p_364 @p_344 @p_342 @p_1168 @p_1103 @p_340 @p_1102 @p_1164 @p_1081 @p_1069 @p_1057 @p_1054 @p_960 @p_210 @p_231 @p_937 @p_311 @p_1161 @p_305 @p_1156 @p_934 @p_930 @p_922 @p_913 @p_295 @p_1155 @p_291 @p_902 @p_893 @p_875 @p_873 @p_868 @p_1152 @p_1148 @p_864 @p_1142 @p_1140 @p_1138) :named @p_1258) (! (and @p_210 @p_1264 (! (= @p_892 @p_1080) :named @p_1263) @p_1262 @p_1081 @p_893 @p_902 @p_1261 @p_1260 @p_1069 @p_13 @p_231 @p_36 @p_142) :named @p_1265)) :named @p_1364) @p_1258) :rule implies_neg1)
(anchor :step t341)
(assume t341.a0 @p_142)
(assume t341.a1 @p_13)
(assume t341.a2 @p_410)
(assume t341.a3 @p_1188)
(assume t341.a4 @p_19)
(assume t341.a5 @p_36)
(assume t341.a6 @p_1187)
(assume t341.a7 @p_1185)
(assume t341.a8 @p_249)
(assume t341.a9 @p_244)
(assume t341.a10 @p_1124)
(assume t341.a11 @p_1176)
(assume t341.a12 @p_1175)
(assume t341.a13 @p_406)
(assume t341.a14 @p_1173)
(assume t341.a15 @p_969)
(assume t341.a16 @p_1117)
(assume t341.a17 @p_405)
(assume t341.a18 @p_396)
(assume t341.a19 @p_385)
(assume t341.a20 @p_364)
(assume t341.a21 @p_344)
(assume t341.a22 @p_342)
(assume t341.a23 @p_1168)
(assume t341.a24 @p_1103)
(assume t341.a25 @p_340)
(assume t341.a26 @p_1102)
(assume t341.a27 @p_1164)
(assume t341.a28 @p_1081)
(assume t341.a29 @p_1069)
(assume t341.a30 @p_1057)
(assume t341.a31 @p_1054)
(assume t341.a32 @p_960)
(assume t341.a33 @p_210)
(assume t341.a34 @p_231)
(assume t341.a35 @p_937)
(assume t341.a36 @p_311)
(assume t341.a37 @p_1161)
(assume t341.a38 @p_305)
(assume t341.a39 @p_1156)
(assume t341.a40 @p_934)
(assume t341.a41 @p_930)
(assume t341.a42 @p_922)
(assume t341.a43 @p_913)
(assume t341.a44 @p_295)
(assume t341.a45 @p_1155)
(assume t341.a46 @p_291)
(assume t341.a47 @p_902)
(assume t341.a48 @p_893)
(assume t341.a49 @p_875)
(assume t341.a50 @p_873)
(assume t341.a51 @p_868)
(assume t341.a52 @p_1152)
(assume t341.a53 @p_1148)
(assume t341.a54 @p_864)
(assume t341.a55 @p_1142)
(assume t341.a56 @p_1140)
(assume t341.a57 @p_1138)
(step t341.t0 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t341.t1 (cl (= @p_221 x$)) :rule poly_simp)
(step t341.t2 (cl (= @p_222 @p_33)) :rule cong :premises (t341.t1))
(step t341.t3 (cl (= @p_223 @p_227)) :rule cong :premises (t341.t2))
(step t341.t4 (cl (= @p_224 @p_228)) :rule cong :premises (t341.t3))
(step t341.t5 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t341.t6 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t341.t5))
(step t341.t7 (cl (= @p_224 @p_210)) :rule trans :premises (t341.t4 t341.t6))
(step t341.t8 (cl @p_226) :rule cong :premises (t341.t7))
(step t341.t9 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t341.t10)
(assume t341.t10.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t341.t10.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t341.t10.t1 (cl @p_219 @p_224) :rule or :premises (t341.t10.t0))
(step t341.t10.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t341.t10.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t10.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t341.t10.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t341.t10.t3.t0))
(step t341.t10.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t341.t10.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t341.t10.t3.t1 t341.t10.t3.t2))
(step t341.t10.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t341.t10.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t341.t10.t3.t4))
(step t341.t10.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t341.t10.t3.t3 t341.t10.t3.t5))
(step t341.t10.t3 (cl @p_211) :rule bind)
(step t341.t10.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t341.t10.t2 t341.t10.t3 a24))
(step t341.t10.t5 (cl @p_224) :rule resolution :premises (t341.t10.t1 t341.t10.t4))
(step t341.t10 (cl @p_219 @p_224) :rule subproof :discharge (t341.t10.a0))
(step t341.t11 (cl @p_225 @p_224) :rule resolution :premises (t341.t9 t341.t10))
(step t341.t12 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t341.t13 (cl @p_225 @p_225) :rule resolution :premises (t341.t11 t341.t12))
(step t341.t14 (cl @p_225) :rule contraction :premises (t341.t13))
(step t341.t15 (cl @p_220) :rule resolution :premises (t341.t0 t341.t8 t341.t14))
(step t341.t16 (cl @p_219 @p_210) :rule implies :premises (t341.t15))
(step t341.t17 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t341.t18 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t18.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t341.t18.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t341.t18.t0))
(step t341.t18.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t341.t18.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t341.t18.t1 t341.t18.t2))
(step t341.t18.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t341.t18.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t341.t18.t4))
(step t341.t18.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t341.t18.t3 t341.t18.t5))
(step t341.t18 (cl @p_211) :rule bind)
(step t341.t19 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t341.t17 t341.t18 a24))
(step t341.t20 (cl @p_210) :rule resolution :premises (t341.t16 t341.t19))
(step t341.t21 (cl @p_1397 @p_244) :rule implies_neg1)
(anchor :step t341.t22)
(assume t341.t22.a0 @p_244)
(step t341.t22.t0 (cl @p_1264) :rule symm :premises (t341.t22.a0))
(step t341.t22 (cl @p_1113 @p_1264) :rule subproof :discharge (t341.t22.a0))
(step t341.t23 (cl @p_1397 @p_1264) :rule resolution :premises (t341.t21 t341.t22))
(step t341.t24 (cl @p_1397 @p_1268) :rule implies_neg2)
(step t341.t25 (cl @p_1397 @p_1397) :rule resolution :premises (t341.t23 t341.t24))
(step t341.t26 (cl @p_1397) :rule contraction :premises (t341.t25))
(step t341.t27 (cl @p_1113 @p_1264) :rule implies :premises (t341.t26))
(step t341.t28 (cl @p_1264) :rule resolution :premises (t341.t27 t341.a9))
(step t341.t29 (cl (! (=> (! (and @p_1081 (! (= @p_1051 @p_892) :named @p_1377)) :named @p_1378) @p_1263) :named @p_1396) @p_1378) :rule implies_neg1)
(anchor :step t341.t30)
(assume t341.t30.a0 @p_1081)
(assume t341.t30.a1 @p_1377)
(step t341.t30.t0 (cl (= @p_892 @p_1051)) :rule symm :premises (t341.t30.a1))
(step t341.t30.t1 (cl (not @p_1086) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t341.t30.t2 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t341.t30.t3 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t341.t30.t2))
(step t341.t30.t4 (cl @p_1086) :rule cong :premises (t341.t30.t3))
(step t341.t30.t5 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t30.t6)
(assume t341.t30.t6.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t30.t6.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t341.t30.t6.t1 (cl @p_279 @p_1084) :rule or :premises (t341.t30.t6.t0))
(step t341.t30.t6.t2 (cl @p_1084) :rule resolution :premises (t341.t30.t6.t1 t341.t30.t6.a0))
(step t341.t30.t6 (cl @p_279 @p_1084) :rule subproof :discharge (t341.t30.t6.a0))
(step t341.t30.t7 (cl @p_1085 @p_1084) :rule resolution :premises (t341.t30.t5 t341.t30.t6))
(step t341.t30.t8 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t341.t30.t9 (cl @p_1085 @p_1085) :rule resolution :premises (t341.t30.t7 t341.t30.t8))
(step t341.t30.t10 (cl @p_1085) :rule contraction :premises (t341.t30.t9))
(step t341.t30.t11 (cl @p_1082) :rule resolution :premises (t341.t30.t1 t341.t30.t4 t341.t30.t10))
(step t341.t30.t12 (cl @p_279 @p_1081) :rule implies :premises (t341.t30.t11))
(step t341.t30.t13 (cl @p_1081) :rule resolution :premises (t341.t30.t12 a1))
(step t341.t30.t14 (cl @p_1263) :rule trans :premises (t341.t30.t0 t341.t30.t13))
(step t341.t30 (cl @p_1204 (! (not @p_1377) :named @p_1382) @p_1263) :rule subproof :discharge (t341.t30.a0 t341.t30.a1))
(step t341.t31 (cl (! (not @p_1378) :named @p_1395) @p_1081) :rule and_pos :args (0))
(step t341.t32 (cl @p_1395 @p_1377) :rule and_pos :args (1))
(step t341.t33 (cl @p_1263 @p_1395 @p_1395) :rule resolution :premises (t341.t30 t341.t31 t341.t32))
(step t341.t34 (cl @p_1395 @p_1395 @p_1263) :rule reordering :premises (t341.t33))
(step t341.t35 (cl @p_1395 @p_1263) :rule contraction :premises (t341.t34))
(step t341.t36 (cl @p_1396 @p_1263) :rule resolution :premises (t341.t29 t341.t35))
(step t341.t37 (cl @p_1396 (! (not @p_1263) :named @p_1269)) :rule implies_neg2)
(step t341.t38 (cl @p_1396 @p_1396) :rule resolution :premises (t341.t36 t341.t37))
(step t341.t39 (cl @p_1396) :rule contraction :premises (t341.t38))
(step t341.t40 (cl @p_1395 @p_1263) :rule implies :premises (t341.t39))
(step t341.t41 (cl (not @p_1086) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t341.t42 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t341.t43 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t341.t42))
(step t341.t44 (cl @p_1086) :rule cong :premises (t341.t43))
(step t341.t45 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t46)
(assume t341.t46.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t46.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t341.t46.t1 (cl @p_279 @p_1084) :rule or :premises (t341.t46.t0))
(step t341.t46.t2 (cl @p_1084) :rule resolution :premises (t341.t46.t1 t341.t46.a0))
(step t341.t46 (cl @p_279 @p_1084) :rule subproof :discharge (t341.t46.a0))
(step t341.t47 (cl @p_1085 @p_1084) :rule resolution :premises (t341.t45 t341.t46))
(step t341.t48 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t341.t49 (cl @p_1085 @p_1085) :rule resolution :premises (t341.t47 t341.t48))
(step t341.t50 (cl @p_1085) :rule contraction :premises (t341.t49))
(step t341.t51 (cl @p_1082) :rule resolution :premises (t341.t41 t341.t44 t341.t50))
(step t341.t52 (cl @p_279 @p_1081) :rule implies :premises (t341.t51))
(step t341.t53 (cl @p_1081) :rule resolution :premises (t341.t52 a1))
(step t341.t54 (cl (! (=> (! (and @p_960 @p_340 @p_342 @p_385 @p_311 @p_344 @p_305 @p_295 @p_410 @p_291 @p_406 @p_364 @p_396 @p_249 @p_864 @p_1140 @p_1142 @p_1138 @p_1155 @p_1156 @p_1124 @p_1164 @p_1175 @p_405 @p_1161 @p_1185 @p_875 @p_913 @p_873 @p_969 @p_868 @p_922 @p_934 @p_1188 @p_1117 @p_1102 @p_930 @p_937 @p_1148 @p_1187 @p_1152 @p_1176 @p_1168 @p_1173) :named @p_1379) @p_1377) :named @p_1381) @p_1379) :rule implies_neg1)
(anchor :step t341.t55)
(assume t341.t55.a0 @p_960)
(assume t341.t55.a1 @p_340)
(assume t341.t55.a2 @p_342)
(assume t341.t55.a3 @p_385)
(assume t341.t55.a4 @p_311)
(assume t341.t55.a5 @p_344)
(assume t341.t55.a6 @p_305)
(assume t341.t55.a7 @p_295)
(assume t341.t55.a8 @p_410)
(assume t341.t55.a9 @p_291)
(assume t341.t55.a10 @p_406)
(assume t341.t55.a11 @p_364)
(assume t341.t55.a12 @p_396)
(assume t341.t55.a13 @p_249)
(assume t341.t55.a14 @p_864)
(assume t341.t55.a15 @p_1140)
(assume t341.t55.a16 @p_1142)
(assume t341.t55.a17 @p_1138)
(assume t341.t55.a18 @p_1155)
(assume t341.t55.a19 @p_1156)
(assume t341.t55.a20 @p_1124)
(assume t341.t55.a21 @p_1164)
(assume t341.t55.a22 @p_1175)
(assume t341.t55.a23 @p_405)
(assume t341.t55.a24 @p_1161)
(assume t341.t55.a25 @p_1185)
(assume t341.t55.a26 @p_875)
(assume t341.t55.a27 @p_913)
(assume t341.t55.a28 @p_873)
(assume t341.t55.a29 @p_969)
(assume t341.t55.a30 @p_868)
(assume t341.t55.a31 @p_922)
(assume t341.t55.a32 @p_934)
(assume t341.t55.a33 @p_1188)
(assume t341.t55.a34 @p_1117)
(assume t341.t55.a35 @p_1102)
(assume t341.t55.a36 @p_930)
(assume t341.t55.a37 @p_937)
(assume t341.t55.a38 @p_1148)
(assume t341.t55.a39 @p_1187)
(assume t341.t55.a40 @p_1152)
(assume t341.t55.a41 @p_1176)
(assume t341.t55.a42 @p_1168)
(assume t341.t55.a43 @p_1173)
(step t341.t55.t0 (cl (or @p_312 @p_1173)) :rule forall_inst :args (@p_139 1/1 @p_4))
(step t341.t55.t1 (cl @p_312 @p_1173) :rule or :premises (t341.t55.t0))
(step t341.t55.t2 (cl @p_1173) :rule resolution :premises (t341.t55.t1 a27))
(step t341.t55.t3 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))) (! (= @p_1166 @p_1167) :named @p_1170)) :named @p_1171) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))) @p_1168) :named @p_1169)) :named @p_1172)) (not @p_1171) @p_1169) :rule equiv_pos2)
(step t341.t55.t4 (cl (= (* -1/1 (- @p_1166 @p_1167)) (* 1/1 (- @p_1167 @p_1166)))) :rule poly_simp)
(step t341.t55.t5 (cl (= @p_1170 @p_1168)) :rule poly_simp_rel :premises (t341.t55.t4))
(step t341.t55.t6 (cl @p_1172) :rule cong :premises (t341.t55.t5))
(step t341.t55.t7 (cl @p_1171 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1)))) :rule implies_neg1)
(anchor :step t341.t55.t8)
(assume t341.t55.t8.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))))
(step t341.t55.t8.t0 (cl (or @p_343 @p_1170)) :rule forall_inst :args (@p_139 @p_4 1/1))
(step t341.t55.t8.t1 (cl @p_343 @p_1170) :rule or :premises (t341.t55.t8.t0))
(step t341.t55.t8.t2 (cl @p_1170) :rule resolution :premises (t341.t55.t8.t1 t341.t55.t8.a0))
(step t341.t55.t8 (cl @p_343 @p_1170) :rule subproof :discharge (t341.t55.t8.a0))
(step t341.t55.t9 (cl @p_1171 @p_1170) :rule resolution :premises (t341.t55.t7 t341.t55.t8))
(step t341.t55.t10 (cl @p_1171 (not @p_1170)) :rule implies_neg2)
(step t341.t55.t11 (cl @p_1171 @p_1171) :rule resolution :premises (t341.t55.t9 t341.t55.t10))
(step t341.t55.t12 (cl @p_1171) :rule contraction :premises (t341.t55.t11))
(step t341.t55.t13 (cl @p_1169) :rule resolution :premises (t341.t55.t3 t341.t55.t6 t341.t55.t12))
(step t341.t55.t14 (cl @p_343 @p_1168) :rule implies :premises (t341.t55.t13))
(step t341.t55.t15 (cl @p_1168) :rule resolution :premises (t341.t55.t14 a2))
(step t341.t55.t16 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t341.t55.t17 (cl (= @p_388 true)) :rule evaluate)
(step t341.t55.t18 (cl (= @p_399 @p_404)) :rule cong :premises (t341.t55.t17))
(step t341.t55.t19 (cl (= @p_404 true)) :rule or_simplify)
(step t341.t55.t20 (cl (= @p_399 true)) :rule trans :premises (t341.t55.t18 t341.t55.t19))
(step t341.t55.t21 (cl (= @p_400 @p_403)) :rule cong :premises (t341.t55.t20))
(step t341.t55.t22 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t341.t55.t23 (cl (= @p_400 @p_396)) :rule trans :premises (t341.t55.t21 t341.t55.t22))
(step t341.t55.t24 (cl @p_402) :rule cong :premises (t341.t55.t23))
(step t341.t55.t25 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t341.t55.t26)
(assume t341.t55.t26.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t341.t55.t26.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t341.t55.t26.t1 (cl @p_397 @p_400) :rule or :premises (t341.t55.t26.t0))
(step t341.t55.t26.t2 (cl @p_400) :rule resolution :premises (t341.t55.t26.t1 t341.t55.t26.a0))
(step t341.t55.t26 (cl @p_397 @p_400) :rule subproof :discharge (t341.t55.t26.a0))
(step t341.t55.t27 (cl @p_401 @p_400) :rule resolution :premises (t341.t55.t25 t341.t55.t26))
(step t341.t55.t28 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t341.t55.t29 (cl @p_401 @p_401) :rule resolution :premises (t341.t55.t27 t341.t55.t28))
(step t341.t55.t30 (cl @p_401) :rule contraction :premises (t341.t55.t29))
(step t341.t55.t31 (cl @p_398) :rule resolution :premises (t341.t55.t16 t341.t55.t24 t341.t55.t30))
(step t341.t55.t32 (cl @p_397 @p_396) :rule implies :premises (t341.t55.t31))
(step t341.t55.t33 (cl @p_396) :rule resolution :premises (t341.t55.t32 a8))
(step t341.t55.t34 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t341.t55.t35 (cl @p_292 @p_405) :rule or :premises (t341.t55.t34))
(step t341.t55.t36 (cl @p_405) :rule resolution :premises (t341.t55.t35 a6))
(step t341.t55.t37 (cl (= @p_361 @p_301)) :rule symm :premises (t341.t55.t36))
(step t341.t55.t38 (cl (= @p_4 @p_301)) :rule trans :premises (t341.t55.t33 t341.t55.t37))
(step t341.t55.t39 (cl @p_388) :rule refl)
(step t341.t55.t40 (cl (= @p_1165 @p_1159)) :rule cong :premises (t341.t55.t38 t341.t55.t39))
(step t341.t55.t41 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t341.t55.t42 (cl (= @p_126 false)) :rule evaluate)
(step t341.t55.t43 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t341.t55.t44 (cl (= @p_364 @p_364)) :rule refl)
(step t341.t55.t45 (cl (= @p_378 @p_383)) :rule cong :premises (t341.t55.t43 t341.t55.t44))
(step t341.t55.t46 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t341.t55.t47 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t341.t55.t48 (cl (= @p_383 @p_364)) :rule trans :premises (t341.t55.t46 t341.t55.t47))
(step t341.t55.t49 (cl (= @p_378 @p_364)) :rule trans :premises (t341.t55.t45 t341.t55.t48))
(step t341.t55.t50 (cl (= @p_379 @p_382)) :rule cong :premises (t341.t55.t42 t341.t55.t49))
(step t341.t55.t51 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t341.t55.t52 (cl (= @p_379 @p_364)) :rule trans :premises (t341.t55.t50 t341.t55.t51))
(step t341.t55.t53 (cl @p_381) :rule cong :premises (t341.t55.t52))
(step t341.t55.t54 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t341.t55.t55)
(assume t341.t55.t55.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t341.t55.t55.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t341.t55.t55.t1 (cl @p_375 @p_379) :rule or :premises (t341.t55.t55.t0))
(step t341.t55.t55.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t341.t55.t55.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t55.t55.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t341.t55.t55.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t341.t55.t55.t3.t0))
(step t341.t55.t55.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t341.t55.t55.t3.t1))
(step t341.t55.t55.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t341.t55.t55.t3.t2))
(step t341.t55.t55.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t341.t55.t55.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t55.t55.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t341.t55.t55.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t55.t55.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t341.t55.t55.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t341.t55.t55.t4.t1 t341.t55.t55.t4.t2))
(step t341.t55.t55.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t341.t55.t55.t4.t0 t341.t55.t55.t4.t3))
(step t341.t55.t55.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t341.t55.t55.t5 (cl @p_365) :rule trans :premises (t341.t55.t55.t3 t341.t55.t55.t4))
(step t341.t55.t55.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t341.t55.t55.t2 t341.t55.t55.t5 a17))
(step t341.t55.t55.t7 (cl @p_379) :rule resolution :premises (t341.t55.t55.t1 t341.t55.t55.t6))
(step t341.t55.t55 (cl @p_375 @p_379) :rule subproof :discharge (t341.t55.t55.a0))
(step t341.t55.t56 (cl @p_380 @p_379) :rule resolution :premises (t341.t55.t54 t341.t55.t55))
(step t341.t55.t57 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t341.t55.t58 (cl @p_380 @p_380) :rule resolution :premises (t341.t55.t56 t341.t55.t57))
(step t341.t55.t59 (cl @p_380) :rule contraction :premises (t341.t55.t58))
(step t341.t55.t60 (cl @p_376) :rule resolution :premises (t341.t55.t41 t341.t55.t53 t341.t55.t59))
(step t341.t55.t61 (cl @p_375 @p_364) :rule implies :premises (t341.t55.t60))
(step t341.t55.t62 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t341.t55.t63 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t55.t63.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t341.t55.t63.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t341.t55.t63.t0))
(step t341.t55.t63.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t341.t55.t63.t1))
(step t341.t55.t63.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t341.t55.t63.t2))
(step t341.t55.t63 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t341.t55.t64 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t55.t64.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t341.t55.t64.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t55.t64.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t341.t55.t64.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t341.t55.t64.t1 t341.t55.t64.t2))
(step t341.t55.t64.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t341.t55.t64.t0 t341.t55.t64.t3))
(step t341.t55.t64 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t341.t55.t65 (cl @p_365) :rule trans :premises (t341.t55.t63 t341.t55.t64))
(step t341.t55.t66 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t341.t55.t62 t341.t55.t65 a17))
(step t341.t55.t67 (cl @p_364) :rule resolution :premises (t341.t55.t61 t341.t55.t66))
(step t341.t55.t68 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t341.t55.t69 (cl @p_312 @p_406) :rule or :premises (t341.t55.t68))
(step t341.t55.t70 (cl @p_406) :rule resolution :premises (t341.t55.t69 a27))
(step t341.t55.t71 (cl (= @p_362 @p_65)) :rule symm :premises (t341.t55.t70))
(step t341.t55.t72 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t341.t55.t73 (cl (= @p_362 @p_6)) :rule trans :premises (t341.t55.t71 t341.t55.t72))
(step t341.t55.t74 (cl (= 2/1 2/1)) :rule refl)
(step t341.t55.t75 (cl (= @p_363 @p_290)) :rule cong :premises (t341.t55.t73 t341.t55.t74))
(step t341.t55.t76 (cl (= @p_301 @p_290)) :rule trans :premises (t341.t55.t36 t341.t55.t67 t341.t55.t75))
(step t341.t55.t77 (cl (= @p_290 @p_301)) :rule symm :premises (t341.t55.t76))
(step t341.t55.t78 (cl (= @p_1186 @p_1159)) :rule cong :premises (t341.t55.t77 t341.t55.t39))
(step t341.t55.t79 (cl (= @p_1159 @p_1186)) :rule symm :premises (t341.t55.t78))
(step t341.t55.t80 (cl (or @p_343 @p_1187)) :rule forall_inst :args (@p_6 1/1 2/1))
(step t341.t55.t81 (cl @p_343 @p_1187) :rule or :premises (t341.t55.t80))
(step t341.t55.t82 (cl @p_1187) :rule resolution :premises (t341.t55.t81 a2))
(step t341.t55.t83 (cl (= @p_1186 @p_932)) :rule symm :premises (t341.t55.t82))
(step t341.t55.t84 (cl (not @p_973) (not @p_972) @p_970) :rule equiv_pos2)
(step t341.t55.t85 (cl (= (* 1/1 (- @p_314 @p_932)) (* -1/1 (- @p_932 @p_314)))) :rule poly_simp)
(step t341.t55.t86 (cl (= @p_971 @p_969)) :rule poly_simp_rel :premises (t341.t55.t85))
(step t341.t55.t87 (cl @p_973) :rule cong :premises (t341.t55.t86))
(step t341.t55.t88 (cl @p_972 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t341.t55.t89)
(assume t341.t55.t89.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t341.t55.t89.t0 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t341.t55.t89.t1 (cl @p_312 @p_971) :rule or :premises (t341.t55.t89.t0))
(step t341.t55.t89.t2 (cl @p_971) :rule resolution :premises (t341.t55.t89.t1 t341.t55.t89.a0))
(step t341.t55.t89 (cl @p_312 @p_971) :rule subproof :discharge (t341.t55.t89.a0))
(step t341.t55.t90 (cl @p_972 @p_971) :rule resolution :premises (t341.t55.t88 t341.t55.t89))
(step t341.t55.t91 (cl @p_972 (not @p_971)) :rule implies_neg2)
(step t341.t55.t92 (cl @p_972 @p_972) :rule resolution :premises (t341.t55.t90 t341.t55.t91))
(step t341.t55.t93 (cl @p_972) :rule contraction :premises (t341.t55.t92))
(step t341.t55.t94 (cl @p_970) :rule resolution :premises (t341.t55.t84 t341.t55.t87 t341.t55.t93))
(step t341.t55.t95 (cl @p_312 @p_969) :rule implies :premises (t341.t55.t94))
(step t341.t55.t96 (cl @p_969) :rule resolution :premises (t341.t55.t95 a27))
(step t341.t55.t97 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t341.t55.t98 (cl @p_292 @p_340) :rule or :premises (t341.t55.t97))
(step t341.t55.t99 (cl @p_340) :rule resolution :premises (t341.t55.t98 a6))
(step t341.t55.t100 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t341.t55.t101 (cl @p_292 @p_305) :rule or :premises (t341.t55.t100))
(step t341.t55.t102 (cl @p_305) :rule resolution :premises (t341.t55.t101 a6))
(step t341.t55.t103 (cl (= @p_270 @p_304)) :rule symm :premises (t341.t55.t102))
(step t341.t55.t104 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t341.t55.t105 (cl (= @p_356 false)) :rule evaluate)
(step t341.t55.t106 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t341.t55.t107 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t341.t55.t106))
(step t341.t55.t108 (cl (= @p_357 @p_360)) :rule cong :premises (t341.t55.t105 t341.t55.t107))
(step t341.t55.t109 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t341.t55.t110 (cl (= @p_357 @p_344)) :rule trans :premises (t341.t55.t108 t341.t55.t109))
(step t341.t55.t111 (cl @p_359) :rule cong :premises (t341.t55.t110))
(step t341.t55.t112 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t341.t55.t113)
(assume t341.t55.t113.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t341.t55.t113.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t341.t55.t113.t1 (cl @p_353 @p_357) :rule or :premises (t341.t55.t113.t0))
(step t341.t55.t113.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t341.t55.t113.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t113.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t341.t55.t113.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t341.t55.t113.t3.t0))
(step t341.t55.t113.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t341.t55.t113.t3.t1))
(step t341.t55.t113.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t341.t55.t113.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t113.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t341.t55.t113.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t55.t113.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t341.t55.t113.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t341.t55.t113.t4.t1 t341.t55.t113.t4.t2))
(step t341.t55.t113.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t341.t55.t113.t4.t0 t341.t55.t113.t4.t3))
(step t341.t55.t113.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t341.t55.t113.t5 (cl @p_345) :rule trans :premises (t341.t55.t113.t3 t341.t55.t113.t4))
(step t341.t55.t113.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t341.t55.t113.t2 t341.t55.t113.t5 a19))
(step t341.t55.t113.t7 (cl @p_357) :rule resolution :premises (t341.t55.t113.t1 t341.t55.t113.t6))
(step t341.t55.t113 (cl @p_353 @p_357) :rule subproof :discharge (t341.t55.t113.a0))
(step t341.t55.t114 (cl @p_358 @p_357) :rule resolution :premises (t341.t55.t112 t341.t55.t113))
(step t341.t55.t115 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t341.t55.t116 (cl @p_358 @p_358) :rule resolution :premises (t341.t55.t114 t341.t55.t115))
(step t341.t55.t117 (cl @p_358) :rule contraction :premises (t341.t55.t116))
(step t341.t55.t118 (cl @p_354) :rule resolution :premises (t341.t55.t104 t341.t55.t111 t341.t55.t117))
(step t341.t55.t119 (cl @p_353 @p_344) :rule implies :premises (t341.t55.t118))
(step t341.t55.t120 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t341.t55.t121 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t121.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t341.t55.t121.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t341.t55.t121.t0))
(step t341.t55.t121.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t341.t55.t121.t1))
(step t341.t55.t121 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t341.t55.t122 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t122.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t341.t55.t122.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t55.t122.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t341.t55.t122.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t341.t55.t122.t1 t341.t55.t122.t2))
(step t341.t55.t122.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t341.t55.t122.t0 t341.t55.t122.t3))
(step t341.t55.t122 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t341.t55.t123 (cl @p_345) :rule trans :premises (t341.t55.t121 t341.t55.t122))
(step t341.t55.t124 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t341.t55.t120 t341.t55.t123 a19))
(step t341.t55.t125 (cl @p_344) :rule resolution :premises (t341.t55.t119 t341.t55.t124))
(step t341.t55.t126 (cl @p_355) :rule symm :premises (t341.t55.t125))
(step t341.t55.t127 (cl (= @p_304 @p_310)) :rule cong :premises (t341.t55.t126))
(step t341.t55.t128 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t341.t55.t129 (cl @p_312 @p_311) :rule or :premises (t341.t55.t128))
(step t341.t55.t130 (cl @p_311) :rule resolution :premises (t341.t55.t129 a27))
(step t341.t55.t131 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t341.t55.t132 (cl (= @p_389 @p_395)) :rule cong :premises (t341.t55.t42 t341.t55.t17))
(step t341.t55.t133 (cl (= @p_395 true)) :rule evaluate)
(step t341.t55.t134 (cl (= @p_389 true)) :rule trans :premises (t341.t55.t132 t341.t55.t133))
(step t341.t55.t135 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t341.t55.t136 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t341.t55.t135))
(step t341.t55.t137 (cl (= @p_390 @p_393)) :rule cong :premises (t341.t55.t134 t341.t55.t136))
(step t341.t55.t138 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t341.t55.t139 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t341.t55.t140 (cl (= @p_393 @p_385)) :rule trans :premises (t341.t55.t138 t341.t55.t139))
(step t341.t55.t141 (cl (= @p_390 @p_385)) :rule trans :premises (t341.t55.t137 t341.t55.t140))
(step t341.t55.t142 (cl @p_392) :rule cong :premises (t341.t55.t141))
(step t341.t55.t143 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t341.t55.t144)
(assume t341.t55.t144.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t341.t55.t144.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t341.t55.t144.t1 (cl @p_258 @p_390) :rule or :premises (t341.t55.t144.t0))
(step t341.t55.t144.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t341.t55.t144.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t144.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t341.t55.t144.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t341.t55.t144.t3.t0))
(step t341.t55.t144.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t341.t55.t144.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t341.t55.t144.t3.t1 t341.t55.t144.t3.t2))
(step t341.t55.t144.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t341.t55.t144.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t341.t55.t144.t3.t3 t341.t55.t144.t3.t4))
(step t341.t55.t144.t3 (cl @p_251) :rule bind)
(step t341.t55.t144.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t341.t55.t144.t2 t341.t55.t144.t3 a12))
(step t341.t55.t144.t5 (cl @p_390) :rule resolution :premises (t341.t55.t144.t1 t341.t55.t144.t4))
(step t341.t55.t144 (cl @p_258 @p_390) :rule subproof :discharge (t341.t55.t144.a0))
(step t341.t55.t145 (cl @p_391 @p_390) :rule resolution :premises (t341.t55.t143 t341.t55.t144))
(step t341.t55.t146 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t341.t55.t147 (cl @p_391 @p_391) :rule resolution :premises (t341.t55.t145 t341.t55.t146))
(step t341.t55.t148 (cl @p_391) :rule contraction :premises (t341.t55.t147))
(step t341.t55.t149 (cl @p_386) :rule resolution :premises (t341.t55.t131 t341.t55.t142 t341.t55.t148))
(step t341.t55.t150 (cl @p_258 @p_385) :rule implies :premises (t341.t55.t149))
(step t341.t55.t151 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t341.t55.t152 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t55.t152.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t341.t55.t152.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t341.t55.t152.t0))
(step t341.t55.t152.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t341.t55.t152.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t341.t55.t152.t1 t341.t55.t152.t2))
(step t341.t55.t152.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t341.t55.t152.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t341.t55.t152.t3 t341.t55.t152.t4))
(step t341.t55.t152 (cl @p_251) :rule bind)
(step t341.t55.t153 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t341.t55.t151 t341.t55.t152 a12))
(step t341.t55.t154 (cl @p_385) :rule resolution :premises (t341.t55.t150 t341.t55.t153))
(step t341.t55.t155 (cl (= @p_307 @p_304)) :rule cong :premises (t341.t55.t154))
(step t341.t55.t156 (cl (= @p_308 @p_341)) :rule cong :premises (t341.t55.t155 t341.t55.t39))
(step t341.t55.t157 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t341.t55.t158 (cl @p_343 @p_342) :rule or :premises (t341.t55.t157))
(step t341.t55.t159 (cl @p_342) :rule resolution :premises (t341.t55.t158 a2))
(step t341.t55.t160 (cl (= @p_341 @p_296)) :rule symm :premises (t341.t55.t159))
(step t341.t55.t161 (cl (= @p_270 @p_296)) :rule trans :premises (t341.t55.t103 t341.t55.t127 t341.t55.t130 t341.t55.t156 t341.t55.t160))
(step t341.t55.t162 (cl (= @p_1 @p_1)) :rule refl)
(step t341.t55.t163 (cl (= @p_294 @p_339)) :rule cong :premises (t341.t55.t161 t341.t55.t162))
(step t341.t55.t164 (cl (= @p_339 @p_294)) :rule symm :premises (t341.t55.t163))
(step t341.t55.t165 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t341.t55.t166 (cl @p_273 @p_295) :rule or :premises (t341.t55.t165))
(step t341.t55.t167 (cl @p_295) :rule resolution :premises (t341.t55.t166 a4))
(step t341.t55.t168 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t341.t55.t169 (cl (= @p_293 @p_289)) :rule symm :premises (t341.t55.t168))
(step t341.t55.t170 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t341.t55.t171 (cl @p_292 @p_291) :rule or :premises (t341.t55.t170))
(step t341.t55.t172 (cl @p_291) :rule resolution :premises (t341.t55.t171 a6))
(step t341.t55.t173 (cl (= @p_289 @p_290)) :rule symm :premises (t341.t55.t172))
(step t341.t55.t174 (cl (= @p_290 @p_363)) :rule symm :premises (t341.t55.t75))
(step t341.t55.t175 (cl (= @p_363 @p_361)) :rule symm :premises (t341.t55.t67))
(step t341.t55.t176 (cl (= @p_361 @p_4)) :rule symm :premises (t341.t55.t33))
(step t341.t55.t177 (cl (= @p_1165 @p_1150)) :rule trans :premises (t341.t55.t40 t341.t55.t79 t341.t55.t83 t341.t55.t96 t341.t55.t99 t341.t55.t164 t341.t55.t167 t341.t55.t169 t341.t55.t173 t341.t55.t174 t341.t55.t175 t341.t55.t176 t341.t55.a41))
(step t341.t55.t178 (cl (= @p_1166 @p_1151)) :rule cong :premises (t341.t55.t177))
(step t341.t55.t179 (cl (or @p_343 @p_1152)) :rule forall_inst :args (@p_139 @p_248 @p_247))
(step t341.t55.t180 (cl @p_343 @p_1152) :rule or :premises (t341.t55.t179))
(step t341.t55.t181 (cl @p_1152) :rule resolution :premises (t341.t55.t180 a2))
(step t341.t55.t182 (cl (or @p_292 @p_1156)) :rule forall_inst :args (@p_247 @p_139))
(step t341.t55.t183 (cl @p_292 @p_1156) :rule or :premises (t341.t55.t182))
(step t341.t55.t184 (cl @p_1156) :rule resolution :premises (t341.t55.t183 a6))
(step t341.t55.t185 (cl (= @p_1144 @p_1153)) :rule symm :premises (t341.t55.t184))
(step t341.t55.t186 (cl (= @p_248 @p_4)) :rule symm :premises (t341.t55.a13))
(step t341.t55.t187 (cl (= @p_1149 (! (divide$ @p_1153 @p_4) :named @p_1394))) :rule cong :premises (t341.t55.t185 t341.t55.t186))
(step t341.t55.t188 (cl (= @p_293 @p_294)) :rule symm :premises (t341.t55.t167))
(step t341.t55.t189 (cl (= @p_339 @p_314)) :rule symm :premises (t341.t55.t99))
(step t341.t55.t190 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t341.t55.t191 (cl @p_312 @p_971) :rule or :premises (t341.t55.t190))
(step t341.t55.t192 (cl @p_971) :rule resolution :premises (t341.t55.t191 a27))
(step t341.t55.t193 (cl (or @p_343 @p_1185)) :rule forall_inst :args (1/1 1/1 @p_4))
(step t341.t55.t194 (cl @p_343 @p_1185) :rule or :premises (t341.t55.t193))
(step t341.t55.t195 (cl @p_1185) :rule resolution :premises (t341.t55.t194 a2))
(step t341.t55.t196 (cl (= @p_1159 @p_1184)) :rule symm :premises (t341.t55.t195))
(step t341.t55.t197 (cl (= @p_4 @p_4)) :rule refl)
(step t341.t55.t198 (cl (= @p_935 @p_1098)) :rule cong :premises (t341.t55.t176 t341.t55.t197))
(step t341.t55.t199 (cl (= @p_1098 @p_935)) :rule symm :premises (t341.t55.t198))
(step t341.t55.t200 (cl (or @p_312 @p_937)) :rule forall_inst :args (@p_4 1/1 @p_4))
(step t341.t55.t201 (cl @p_312 @p_937) :rule or :premises (t341.t55.t200))
(step t341.t55.t202 (cl @p_937) :rule resolution :premises (t341.t55.t201 a27))
(step t341.t55.t203 (cl (= @p_935 @p_936)) :rule symm :premises (t341.t55.t202))
(step t341.t55.t204 (cl (= @p_1098 @p_936)) :rule trans :premises (t341.t55.t199 t341.t55.t203))
(step t341.t55.t205 (cl (= @p_4 @p_290)) :rule trans :premises (t341.t55.t38 t341.t55.t76))
(step t341.t55.t206 (cl (= @p_1098 @p_928)) :rule cong :premises (t341.t55.t205 t341.t55.t33))
(step t341.t55.t207 (cl (or @p_343 @p_930)) :rule forall_inst :args (@p_6 @p_361 2/1))
(step t341.t55.t208 (cl @p_343 @p_930) :rule or :premises (t341.t55.t207))
(step t341.t55.t209 (cl @p_930) :rule resolution :premises (t341.t55.t208 a2))
(step t341.t55.t210 (cl (= @p_928 @p_929)) :rule symm :premises (t341.t55.t209))
(step t341.t55.t211 (cl (or @p_273 @p_1102)) :rule forall_inst :args (@p_4 @p_1 @p_1098))
(step t341.t55.t212 (cl @p_273 @p_1102) :rule or :premises (t341.t55.t211))
(step t341.t55.t213 (cl @p_1102) :rule resolution :premises (t341.t55.t212 a4))
(step t341.t55.t214 (cl (or @p_312 @p_1119)) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t341.t55.t215 (cl @p_312 @p_1119) :rule or :premises (t341.t55.t214))
(step t341.t55.t216 (cl @p_1119) :rule resolution :premises (t341.t55.t215 a27))
(step t341.t55.t217 (cl @p_1392) :rule symm :premises (t341.t55.a33))
(step t341.t55.t218 (cl @p_1391) :rule trans :premises (t341.t55.t216 t341.t55.t217))
(step t341.t55.t219 (cl @p_1390) :rule cong :premises (t341.t55.t218))
(step t341.t55.t220 (cl @p_1389) :rule trans :premises (t341.t55.t213 t341.t55.t219 t341.t55.t72))
(step t341.t55.t221 (cl @p_1393) :rule symm :premises (t341.t55.t220))
(step t341.t55.t222 (cl (= @p_929 @p_1388)) :rule cong :premises (t341.t55.t221 t341.t55.t71))
(step t341.t55.t223 (cl (= @p_1101 @p_65)) :rule trans :premises (t341.t55.t220 t240))
(step t341.t55.t224 (cl (= @p_1388 @p_931)) :rule cong :premises (t341.t55.t223 t341.t55.t72))
(step t341.t55.t225 (cl (or @p_343 @p_934)) :rule forall_inst :args (@p_4 @p_6 @p_1))
(step t341.t55.t226 (cl @p_343 @p_934) :rule or :premises (t341.t55.t225))
(step t341.t55.t227 (cl @p_934) :rule resolution :premises (t341.t55.t226 a2))
(step t341.t55.t228 (cl (= @p_931 @p_933)) :rule symm :premises (t341.t55.t227))
(step t341.t55.t229 (cl (not @p_926) (not @p_925) @p_923) :rule equiv_pos2)
(step t341.t55.t230 (cl (= @p_922 @p_922)) :rule refl)
(step t341.t55.t231 (cl (= @p_924 @p_927)) :rule cong :premises (t341.t55.t42 t341.t55.t230))
(step t341.t55.t232 (cl (= @p_927 @p_922)) :rule aci_simp)
(step t341.t55.t233 (cl (= @p_924 @p_922)) :rule trans :premises (t341.t55.t231 t341.t55.t232))
(step t341.t55.t234 (cl @p_926) :rule cong :premises (t341.t55.t233))
(step t341.t55.t235 (cl @p_925 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t341.t55.t236)
(assume t341.t55.t236.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t341.t55.t236.t0 (cl (or @p_353 @p_924)) :rule forall_inst :args (2/1 @p_4))
(step t341.t55.t236.t1 (cl @p_353 @p_924) :rule or :premises (t341.t55.t236.t0))
(step t341.t55.t236.t2 (cl @p_924) :rule resolution :premises (t341.t55.t236.t1 t341.t55.t124))
(step t341.t55.t236 (cl @p_353 @p_924) :rule subproof :discharge (t341.t55.t236.a0))
(step t341.t55.t237 (cl @p_925 @p_924) :rule resolution :premises (t341.t55.t235 t341.t55.t236))
(step t341.t55.t238 (cl @p_925 (not @p_924)) :rule implies_neg2)
(step t341.t55.t239 (cl @p_925 @p_925) :rule resolution :premises (t341.t55.t237 t341.t55.t238))
(step t341.t55.t240 (cl @p_925) :rule contraction :premises (t341.t55.t239))
(step t341.t55.t241 (cl @p_923) :rule resolution :premises (t341.t55.t229 t341.t55.t234 t341.t55.t240))
(step t341.t55.t242 (cl @p_353 @p_922) :rule implies :premises (t341.t55.t241))
(step t341.t55.t243 (cl @p_922) :rule resolution :premises (t341.t55.t242 t341.t55.t124))
(step t341.t55.t244 (cl (= @p_921 @p_866)) :rule cong :premises (t341.t55.t103 t341.t55.t74))
(step t341.t55.t245 (cl (= @p_932 @p_866)) :rule trans :premises (t341.t55.t96 t341.t55.t99 t341.t55.t164 t341.t55.t167 t341.t55.t169 t341.t55.t173 t341.t55.t174 t341.t55.t175 t341.t55.t176 t341.t55.t243 t341.t55.t244))
(step t341.t55.t246 (cl (= @p_933 @p_867)) :rule cong :premises (t341.t55.t245))
(step t341.t55.t247 (cl (or @p_343 @p_868)) :rule forall_inst :args (@p_4 @p_304 2/1))
(step t341.t55.t248 (cl @p_343 @p_868) :rule or :premises (t341.t55.t247))
(step t341.t55.t249 (cl @p_868) :rule resolution :premises (t341.t55.t248 a2))
(step t341.t55.t250 (cl (= @p_1385 @p_1387)) :rule cong :premises (t341.t55.t154 t341.t55.t192))
(step t341.t55.t251 (cl (not @p_336) (not @p_335) @p_330) :rule equiv_pos2)
(step t341.t55.t252 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t341.t55.t253 (cl (= @p_296 @p_296)) :rule refl)
(step t341.t55.t254 (cl (= @p_333 @p_327)) :rule cong :premises (t341.t55.t252 t341.t55.t253))
(step t341.t55.t255 (cl (= @p_331 @p_337)) :rule poly_simp)
(step t341.t55.t256 (cl (= @p_334 @p_338)) :rule cong :premises (t341.t55.t254 t341.t55.t255))
(step t341.t55.t257 (cl (= (* 1/1 (- @p_327 @p_337)) (* -2/1 (- @p_314 @p_328)))) :rule poly_simp)
(step t341.t55.t258 (cl (= @p_338 @p_329)) :rule poly_simp_rel :premises (t341.t55.t257))
(step t341.t55.t259 (cl (= @p_334 @p_329)) :rule trans :premises (t341.t55.t256 t341.t55.t258))
(step t341.t55.t260 (cl @p_336) :rule cong :premises (t341.t55.t259))
(step t341.t55.t261 (cl @p_335 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t55.t262)
(assume t341.t55.t262.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t55.t262.t0 (cl (or @p_279 @p_334)) :rule forall_inst :args (@p_1 @p_1 @p_296))
(step t341.t55.t262.t1 (cl @p_279 @p_334) :rule or :premises (t341.t55.t262.t0))
(step t341.t55.t262.t2 (cl @p_334) :rule resolution :premises (t341.t55.t262.t1 t341.t55.t262.a0))
(step t341.t55.t262 (cl @p_279 @p_334) :rule subproof :discharge (t341.t55.t262.a0))
(step t341.t55.t263 (cl @p_335 @p_334) :rule resolution :premises (t341.t55.t261 t341.t55.t262))
(step t341.t55.t264 (cl @p_335 (not @p_334)) :rule implies_neg2)
(step t341.t55.t265 (cl @p_335 @p_335) :rule resolution :premises (t341.t55.t263 t341.t55.t264))
(step t341.t55.t266 (cl @p_335) :rule contraction :premises (t341.t55.t265))
(step t341.t55.t267 (cl @p_330) :rule resolution :premises (t341.t55.t251 t341.t55.t260 t341.t55.t266))
(step t341.t55.t268 (cl @p_279 @p_329) :rule implies :premises (t341.t55.t267))
(step t341.t55.t269 (cl @p_329) :rule resolution :premises (t341.t55.t268 a1))
(step t341.t55.t270 (cl @p_473) :rule trans :premises (t341.t55.t33 t341.t55.t67 t341.t55.t75 t341.t55.t172 t341.t55.t168 t341.t55.t188 t341.t55.t163 t341.t55.t189 t341.t55.t269))
(step t341.t55.t271 (cl (= @p_328 @p_314)) :rule symm :premises (t341.t55.t269))
(step t341.t55.t272 (cl @p_974) :rule trans :premises (t341.t55.t270 t341.t55.t271 t341.t55.t192))
(step t341.t55.t273 (cl (= @p_270 @p_1387)) :rule cong :premises (t341.t55.t272))
(step t341.t55.t274 (cl (= @p_1387 @p_270)) :rule symm :premises (t341.t55.t273))
(step t341.t55.t275 (cl (= @p_1385 @p_304)) :rule trans :premises (t341.t55.t250 t341.t55.t274 t341.t55.t103))
(step t341.t55.t276 (cl (= @p_304 @p_1385)) :rule symm :premises (t341.t55.t275))
(step t341.t55.t277 (cl (= @p_304 @p_296)) :rule trans :premises (t341.t55.t127 t341.t55.t130 t341.t55.t156 t341.t55.t160))
(step t341.t55.t278 (cl (= @p_865 @p_1386)) :rule cong :premises (t341.t55.t276 t341.t55.t277))
(step t341.t55.t279 (cl @p_387) :rule symm :premises (t341.t55.t154))
(step t341.t55.t280 (cl (= @p_932 @p_4)) :rule trans :premises (t341.t55.t96 t341.t55.t99 t341.t55.t164 t341.t55.t167 t341.t55.t169 t341.t55.t173 t341.t55.t174 t341.t55.t175 t341.t55.t176))
(step t341.t55.t281 (cl (= @p_1387 @p_869)) :rule cong :premises (t341.t55.t279 t341.t55.t280))
(step t341.t55.t282 (cl (= @p_304 @p_869)) :rule trans :premises (t341.t55.t102 t341.t55.t273 t341.t55.t281))
(step t341.t55.t283 (cl (= @p_1385 @p_869)) :rule trans :premises (t341.t55.t275 t341.t55.t282))
(step t341.t55.t284 (cl (= @p_304 @p_307)) :rule cong :premises (t341.t55.t279))
(step t341.t55.t285 (cl (= @p_341 @p_308)) :rule cong :premises (t341.t55.t284 t341.t55.t39))
(step t341.t55.t286 (cl (= @p_308 @p_310)) :rule symm :premises (t341.t55.t130))
(step t341.t55.t287 (cl (= @p_310 @p_304)) :rule cong :premises (t341.t55.t125))
(step t341.t55.t288 (cl (= @p_296 @p_270)) :rule trans :premises (t341.t55.t159 t341.t55.t285 t341.t55.t286 t341.t55.t287 t341.t55.t102))
(step t341.t55.t289 (cl (= @p_1386 @p_870)) :rule cong :premises (t341.t55.t283 t341.t55.t288))
(step t341.t55.t290 (cl (or @p_343 @p_873)) :rule forall_inst :args (@p_306 @p_270 @p_4))
(step t341.t55.t291 (cl @p_343 @p_873) :rule or :premises (t341.t55.t290))
(step t341.t55.t292 (cl @p_873) :rule resolution :premises (t341.t55.t291 a2))
(step t341.t55.t293 (cl (= @p_870 @p_872)) :rule symm :premises (t341.t55.t292))
(step t341.t55.t294 (cl (= @p_871 @p_912)) :rule cong :premises (t341.t55.t103 t341.t55.t197))
(step t341.t55.t295 (cl (= @p_871 2/1)) :rule trans :premises (t341.t55.t294 t341.t55.a27))
(step t341.t55.t296 (cl (= @p_872 @p_874)) :rule cong :premises (t341.t55.t295))
(step t341.t55.t297 (cl (not @p_888) (not @p_887) @p_884) :rule equiv_pos2)
(step t341.t55.t298 (cl (= (* -1/1 (- 1/1 @p_874)) (* 1/1 (- @p_874 1/1)))) :rule poly_simp)
(step t341.t55.t299 (cl (= @p_885 @p_875)) :rule poly_simp_rel :premises (t341.t55.t298))
(step t341.t55.t300 (cl (= @p_886 @p_889)) :rule cong :premises (t341.t55.t42 t341.t55.t299))
(step t341.t55.t301 (cl (= @p_889 @p_875)) :rule aci_simp)
(step t341.t55.t302 (cl (= @p_886 @p_875)) :rule trans :premises (t341.t55.t300 t341.t55.t301))
(step t341.t55.t303 (cl @p_888) :rule cong :premises (t341.t55.t302))
(step t341.t55.t304 (cl @p_887 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule implies_neg1)
(anchor :step t341.t55.t305)
(assume t341.t55.t305.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))
(step t341.t55.t305.t0 (cl (or @p_883 @p_886)) :rule forall_inst :args (2/1 1/1))
(step t341.t55.t305.t1 (cl @p_883 @p_886) :rule or :premises (t341.t55.t305.t0))
(step t341.t55.t305.t2 (cl @p_886) :rule resolution :premises (t341.t55.t305.t1 t294))
(step t341.t55.t305 (cl @p_883 @p_886) :rule subproof :discharge (t341.t55.t305.a0))
(step t341.t55.t306 (cl @p_887 @p_886) :rule resolution :premises (t341.t55.t304 t341.t55.t305))
(step t341.t55.t307 (cl @p_887 (not @p_886)) :rule implies_neg2)
(step t341.t55.t308 (cl @p_887 @p_887) :rule resolution :premises (t341.t55.t306 t341.t55.t307))
(step t341.t55.t309 (cl @p_887) :rule contraction :premises (t341.t55.t308))
(step t341.t55.t310 (cl @p_884) :rule resolution :premises (t341.t55.t297 t341.t55.t303 t341.t55.t309))
(step t341.t55.t311 (cl @p_883 @p_875) :rule implies :premises (t341.t55.t310))
(step t341.t55.t312 (cl @p_875) :rule resolution :premises (t341.t55.t311 t294))
(step t341.t55.t313 (cl @p_1384) :rule trans :premises (t341.t55.t202 t341.t55.t198 t341.t55.t206 t341.t55.t210 t341.t55.t222 t341.t55.t224 t341.t55.t228 t341.t55.t246 t341.t55.t249 t341.t55.t278 t341.t55.t289 t341.t55.t293 t341.t55.t296 t341.t55.t312))
(step t341.t55.t314 (cl (= @p_1098 1/1)) :rule trans :premises (t341.t55.t204 t341.t55.t313))
(step t341.t55.t315 (cl (= @p_18 @p_18)) :rule refl)
(step t341.t55.t316 (cl (= @p_1143 @p_1184)) :rule cong :premises (t341.t55.t314 t341.t55.t315))
(step t341.t55.t317 (cl (= @p_1184 @p_1143)) :rule symm :premises (t341.t55.t316))
(step t341.t55.t318 (cl (= @p_4 @p_1143)) :rule trans :premises (t341.t55.t33 t341.t55.t67 t341.t55.t75 t341.t55.t172 t341.t55.t168 t341.t55.t188 t341.t55.t163 t341.t55.t189 t341.t55.t192 t341.t55.t82 t341.t55.t78 t341.t55.t196 t341.t55.t317))
(step t341.t55.t319 (cl (= @p_1394 @p_1145)) :rule cong :premises (t341.t55.t184 t341.t55.t318))
(step t341.t55.t320 (cl (or @p_312 @p_1148)) :rule forall_inst :args (@p_139 @p_247 @p_1143))
(step t341.t55.t321 (cl @p_312 @p_1148) :rule or :premises (t341.t55.t320))
(step t341.t55.t322 (cl @p_1148) :rule resolution :premises (t341.t55.t321 a27))
(step t341.t55.t323 (cl (= @p_1145 @p_1147)) :rule symm :premises (t341.t55.t322))
(step t341.t55.t324 (cl (= @p_1143 @p_1159)) :rule trans :premises (t341.t55.t316 t341.t55.t195))
(step t341.t55.t325 (cl (= @p_1146 @p_1160)) :rule cong :premises (t341.t55.t324))
(step t341.t55.t326 (cl (or @p_343 @p_1161)) :rule forall_inst :args (@p_247 @p_301 1/1))
(step t341.t55.t327 (cl @p_343 @p_1161) :rule or :premises (t341.t55.t326))
(step t341.t55.t328 (cl @p_1161) :rule resolution :premises (t341.t55.t327 a2))
(step t341.t55.t329 (cl (= @p_301 @p_4)) :rule trans :premises (t341.t55.t36 t341.t55.t176))
(step t341.t55.t330 (cl (= @p_1158 @p_1174)) :rule cong :premises (t341.t55.t329))
(step t341.t55.t331 (cl (or @p_312 @p_1175)) :rule forall_inst :args (@p_247 1/1 @p_4))
(step t341.t55.t332 (cl @p_312 @p_1175) :rule or :premises (t341.t55.t331))
(step t341.t55.t333 (cl @p_1175) :rule resolution :premises (t341.t55.t332 a27))
(step t341.t55.t334 (cl (= @p_1174 @p_1055)) :rule symm :premises (t341.t55.t333))
(step t341.t55.t335 (cl (= @p_1146 @p_1055)) :rule trans :premises (t341.t55.t325 t341.t55.t328 t341.t55.t330 t341.t55.t334))
(step t341.t55.t336 (cl (= @p_1147 @p_1162)) :rule cong :premises (t341.t55.t335))
(step t341.t55.t337 (cl (or @p_273 @p_1164)) :rule forall_inst :args (@p_139 @p_247 @p_18))
(step t341.t55.t338 (cl @p_273 @p_1164) :rule or :premises (t341.t55.t337))
(step t341.t55.t339 (cl @p_1164) :rule resolution :premises (t341.t55.t338 a4))
(step t341.t55.t340 (cl (= @p_1162 @p_1163)) :rule symm :premises (t341.t55.t339))
(step t341.t55.t341 (cl (= @p_1163 (! (times$a @p_1153 @p_18) :named @p_1383))) :rule cong :premises (t341.t55.t185 t341.t55.t315))
(step t341.t55.t342 (cl (= @p_18 @p_1)) :rule symm :premises (t341.t55.a20))
(step t341.t55.t343 (cl (= @p_1383 @p_1154)) :rule cong :premises (t341.t55.t342))
(step t341.t55.t344 (cl (or @p_273 @p_1155)) :rule forall_inst :args (@p_247 @p_139 @p_1))
(step t341.t55.t345 (cl @p_273 @p_1155) :rule or :premises (t341.t55.t344))
(step t341.t55.t346 (cl @p_1155) :rule resolution :premises (t341.t55.t345 a4))
(step t341.t55.t347 (cl (or @p_292 @p_1138)) :rule forall_inst :args (@p_247 @p_892))
(step t341.t55.t348 (cl @p_292 @p_1138) :rule or :premises (t341.t55.t347))
(step t341.t55.t349 (cl @p_1138) :rule resolution :premises (t341.t55.t348 a6))
(step t341.t55.t350 (cl (or @p_273 @p_1142)) :rule forall_inst :args (@p_139 @p_1 @p_247))
(step t341.t55.t351 (cl @p_273 @p_1142) :rule or :premises (t341.t55.t350))
(step t341.t55.t352 (cl @p_1142) :rule resolution :premises (t341.t55.t351 a4))
(step t341.t55.t353 (cl (or @p_292 @p_1140)) :rule forall_inst :args (@p_1 @p_247))
(step t341.t55.t354 (cl @p_292 @p_1140) :rule or :premises (t341.t55.t353))
(step t341.t55.t355 (cl @p_1140) :rule resolution :premises (t341.t55.t354 a6))
(step t341.t55.t356 (cl (= @p_900 @p_863)) :rule cong :premises (t341.t55.a0))
(step t341.t55.t357 (cl (or @p_312 @p_864)) :rule forall_inst :args (@p_247 @p_314 @p_296))
(step t341.t55.t358 (cl @p_312 @p_864) :rule or :premises (t341.t55.t357))
(step t341.t55.t359 (cl @p_864) :rule resolution :premises (t341.t55.t358 a27))
(step t341.t55.t360 (cl (= @p_314 @p_4)) :rule trans :premises (t341.t55.t99 t341.t55.t164 t341.t55.t167 t341.t55.t169 t341.t55.t173 t341.t55.t174 t341.t55.t175 t341.t55.t176))
(step t341.t55.t361 (cl (= @p_860 @p_248)) :rule cong :premises (t341.t55.t360))
(step t341.t55.t362 (cl (= @p_248 @p_314)) :rule trans :premises (t341.t55.t186 t341.t55.t33 t341.t55.t67 t341.t55.t75 t341.t55.t172 t341.t55.t168 t341.t55.t188 t341.t55.t163 t341.t55.t189))
(step t341.t55.t363 (cl (= @p_860 @p_314)) :rule trans :premises (t341.t55.t361 t341.t55.t362))
(step t341.t55.t364 (cl (= @p_861 @p_862)) :rule cong :premises (t341.t55.t363 t341.t55.t253))
(step t341.t55.t365 (cl @p_1374) :rule symm :premises (t341.t55.a0))
(step t341.t55.t366 (cl (= @p_1139 @p_1)) :rule trans :premises (t341.t55.t355 t341.t55.t356 t341.t55.t359 t341.t55.t364 t341.t55.t365))
(step t341.t55.t367 (cl (= @p_1141 @p_892)) :rule cong :premises (t341.t55.t366))
(step t341.t55.t368 (cl @p_1377) :rule trans :premises (t341.t55.t2 t341.t55.t15 t341.t55.t178 t341.t55.t181 t341.t55.t187 t341.t55.t319 t341.t55.t323 t341.t55.t336 t341.t55.t340 t341.t55.t341 t341.t55.t343 t341.t55.t346 t341.t55.t349 t341.t55.t352 t341.t55.t367))
(step t341.t55 (cl @p_1208 @p_434 @p_433 @p_430 @p_437 @p_432 @p_438 @p_441 @p_424 @p_442 @p_427 @p_431 @p_429 @p_574 @p_1226 @p_1228 @p_1227 @p_1229 @p_1218 @p_1213 @p_1135 @p_1203 @p_1197 @p_428 @p_1212 @p_1195 @p_1221 @p_1217 @p_1222 @p_1042 @p_1223 @p_1216 @p_1214 @p_1191 @p_1199 @p_1202 @p_1215 @p_1211 @p_1225 @p_1194 @p_1224 @p_1196 @p_1200 @p_1198 @p_1377) :rule subproof :discharge (t341.t55.a0 t341.t55.a1 t341.t55.a2 t341.t55.a3 t341.t55.a4 t341.t55.a5 t341.t55.a6 t341.t55.a7 t341.t55.a8 t341.t55.a9 t341.t55.a10 t341.t55.a11 t341.t55.a12 t341.t55.a13 t341.t55.a14 t341.t55.a15 t341.t55.a16 t341.t55.a17 t341.t55.a18 t341.t55.a19 t341.t55.a20 t341.t55.a21 t341.t55.a22 t341.t55.a23 t341.t55.a24 t341.t55.a25 t341.t55.a26 t341.t55.a27 t341.t55.a28 t341.t55.a29 t341.t55.a30 t341.t55.a31 t341.t55.a32 t341.t55.a33 t341.t55.a34 t341.t55.a35 t341.t55.a36 t341.t55.a37 t341.t55.a38 t341.t55.a39 t341.t55.a40 t341.t55.a41 t341.t55.a42 t341.t55.a43))
(step t341.t56 (cl (! (not @p_1379) :named @p_1380) @p_960) :rule and_pos :args (0))
(step t341.t57 (cl @p_1380 @p_340) :rule and_pos :args (1))
(step t341.t58 (cl @p_1380 @p_342) :rule and_pos :args (2))
(step t341.t59 (cl @p_1380 @p_385) :rule and_pos :args (3))
(step t341.t60 (cl @p_1380 @p_311) :rule and_pos :args (4))
(step t341.t61 (cl @p_1380 @p_344) :rule and_pos :args (5))
(step t341.t62 (cl @p_1380 @p_305) :rule and_pos :args (6))
(step t341.t63 (cl @p_1380 @p_295) :rule and_pos :args (7))
(step t341.t64 (cl @p_1380 @p_410) :rule and_pos :args (8))
(step t341.t65 (cl @p_1380 @p_291) :rule and_pos :args (9))
(step t341.t66 (cl @p_1380 @p_406) :rule and_pos :args (10))
(step t341.t67 (cl @p_1380 @p_364) :rule and_pos :args (11))
(step t341.t68 (cl @p_1380 @p_396) :rule and_pos :args (12))
(step t341.t69 (cl @p_1380 @p_249) :rule and_pos :args (13))
(step t341.t70 (cl @p_1380 @p_864) :rule and_pos :args (14))
(step t341.t71 (cl @p_1380 @p_1140) :rule and_pos :args (15))
(step t341.t72 (cl @p_1380 @p_1142) :rule and_pos :args (16))
(step t341.t73 (cl @p_1380 @p_1138) :rule and_pos :args (17))
(step t341.t74 (cl @p_1380 @p_1155) :rule and_pos :args (18))
(step t341.t75 (cl @p_1380 @p_1156) :rule and_pos :args (19))
(step t341.t76 (cl @p_1380 @p_1124) :rule and_pos :args (20))
(step t341.t77 (cl @p_1380 @p_1164) :rule and_pos :args (21))
(step t341.t78 (cl @p_1380 @p_1175) :rule and_pos :args (22))
(step t341.t79 (cl @p_1380 @p_405) :rule and_pos :args (23))
(step t341.t80 (cl @p_1380 @p_1161) :rule and_pos :args (24))
(step t341.t81 (cl @p_1380 @p_1185) :rule and_pos :args (25))
(step t341.t82 (cl @p_1380 @p_875) :rule and_pos :args (26))
(step t341.t83 (cl @p_1380 @p_913) :rule and_pos :args (27))
(step t341.t84 (cl @p_1380 @p_873) :rule and_pos :args (28))
(step t341.t85 (cl @p_1380 @p_969) :rule and_pos :args (29))
(step t341.t86 (cl @p_1380 @p_868) :rule and_pos :args (30))
(step t341.t87 (cl @p_1380 @p_922) :rule and_pos :args (31))
(step t341.t88 (cl @p_1380 @p_934) :rule and_pos :args (32))
(step t341.t89 (cl @p_1380 @p_1188) :rule and_pos :args (33))
(step t341.t90 (cl @p_1380 @p_1117) :rule and_pos :args (34))
(step t341.t91 (cl @p_1380 @p_1102) :rule and_pos :args (35))
(step t341.t92 (cl @p_1380 @p_930) :rule and_pos :args (36))
(step t341.t93 (cl @p_1380 @p_937) :rule and_pos :args (37))
(step t341.t94 (cl @p_1380 @p_1148) :rule and_pos :args (38))
(step t341.t95 (cl @p_1380 @p_1187) :rule and_pos :args (39))
(step t341.t96 (cl @p_1380 @p_1152) :rule and_pos :args (40))
(step t341.t97 (cl @p_1380 @p_1176) :rule and_pos :args (41))
(step t341.t98 (cl @p_1380 @p_1168) :rule and_pos :args (42))
(step t341.t99 (cl @p_1380 @p_1173) :rule and_pos :args (43))
(step t341.t100 (cl @p_1377 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380) :rule resolution :premises (t341.t55 t341.t56 t341.t57 t341.t58 t341.t59 t341.t60 t341.t61 t341.t62 t341.t63 t341.t64 t341.t65 t341.t66 t341.t67 t341.t68 t341.t69 t341.t70 t341.t71 t341.t72 t341.t73 t341.t74 t341.t75 t341.t76 t341.t77 t341.t78 t341.t79 t341.t80 t341.t81 t341.t82 t341.t83 t341.t84 t341.t85 t341.t86 t341.t87 t341.t88 t341.t89 t341.t90 t341.t91 t341.t92 t341.t93 t341.t94 t341.t95 t341.t96 t341.t97 t341.t98 t341.t99))
(step t341.t101 (cl @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1380 @p_1377) :rule reordering :premises (t341.t100))
(step t341.t102 (cl @p_1380 @p_1377) :rule contraction :premises (t341.t101))
(step t341.t103 (cl @p_1381 @p_1377) :rule resolution :premises (t341.t54 t341.t102))
(step t341.t104 (cl @p_1381 @p_1382) :rule implies_neg2)
(step t341.t105 (cl @p_1381 @p_1381) :rule resolution :premises (t341.t103 t341.t104))
(step t341.t106 (cl @p_1381) :rule contraction :premises (t341.t105))
(step t341.t107 (cl @p_1380 @p_1377) :rule implies :premises (t341.t106))
(step t341.t108 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t341.t109 (cl @p_292 @p_340) :rule or :premises (t341.t108))
(step t341.t110 (cl @p_340) :rule resolution :premises (t341.t109 a6))
(step t341.t111 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t341.t112 (cl @p_343 @p_342) :rule or :premises (t341.t111))
(step t341.t113 (cl @p_342) :rule resolution :premises (t341.t112 a2))
(step t341.t114 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t341.t115 (cl (= @p_126 false)) :rule evaluate)
(step t341.t116 (cl (= @p_388 true)) :rule evaluate)
(step t341.t117 (cl (= @p_389 @p_395)) :rule cong :premises (t341.t115 t341.t116))
(step t341.t118 (cl (= @p_395 true)) :rule evaluate)
(step t341.t119 (cl (= @p_389 true)) :rule trans :premises (t341.t117 t341.t118))
(step t341.t120 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t341.t121 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t341.t120))
(step t341.t122 (cl (= @p_390 @p_393)) :rule cong :premises (t341.t119 t341.t121))
(step t341.t123 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t341.t124 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t341.t125 (cl (= @p_393 @p_385)) :rule trans :premises (t341.t123 t341.t124))
(step t341.t126 (cl (= @p_390 @p_385)) :rule trans :premises (t341.t122 t341.t125))
(step t341.t127 (cl @p_392) :rule cong :premises (t341.t126))
(step t341.t128 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t341.t129)
(assume t341.t129.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t341.t129.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t341.t129.t1 (cl @p_258 @p_390) :rule or :premises (t341.t129.t0))
(step t341.t129.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t341.t129.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t129.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t341.t129.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t341.t129.t3.t0))
(step t341.t129.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t341.t129.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t341.t129.t3.t1 t341.t129.t3.t2))
(step t341.t129.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t341.t129.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t341.t129.t3.t3 t341.t129.t3.t4))
(step t341.t129.t3 (cl @p_251) :rule bind)
(step t341.t129.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t341.t129.t2 t341.t129.t3 a12))
(step t341.t129.t5 (cl @p_390) :rule resolution :premises (t341.t129.t1 t341.t129.t4))
(step t341.t129 (cl @p_258 @p_390) :rule subproof :discharge (t341.t129.a0))
(step t341.t130 (cl @p_391 @p_390) :rule resolution :premises (t341.t128 t341.t129))
(step t341.t131 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t341.t132 (cl @p_391 @p_391) :rule resolution :premises (t341.t130 t341.t131))
(step t341.t133 (cl @p_391) :rule contraction :premises (t341.t132))
(step t341.t134 (cl @p_386) :rule resolution :premises (t341.t114 t341.t127 t341.t133))
(step t341.t135 (cl @p_258 @p_385) :rule implies :premises (t341.t134))
(step t341.t136 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t341.t137 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t137.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t341.t137.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t341.t137.t0))
(step t341.t137.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t341.t137.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t341.t137.t1 t341.t137.t2))
(step t341.t137.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t341.t137.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t341.t137.t3 t341.t137.t4))
(step t341.t137 (cl @p_251) :rule bind)
(step t341.t138 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t341.t136 t341.t137 a12))
(step t341.t139 (cl @p_385) :rule resolution :premises (t341.t135 t341.t138))
(step t341.t140 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t341.t141 (cl @p_312 @p_311) :rule or :premises (t341.t140))
(step t341.t142 (cl @p_311) :rule resolution :premises (t341.t141 a27))
(step t341.t143 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t341.t144 (cl (= @p_356 false)) :rule evaluate)
(step t341.t145 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t341.t146 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t341.t145))
(step t341.t147 (cl (= @p_357 @p_360)) :rule cong :premises (t341.t144 t341.t146))
(step t341.t148 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t341.t149 (cl (= @p_357 @p_344)) :rule trans :premises (t341.t147 t341.t148))
(step t341.t150 (cl @p_359) :rule cong :premises (t341.t149))
(step t341.t151 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t341.t152)
(assume t341.t152.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t341.t152.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t341.t152.t1 (cl @p_353 @p_357) :rule or :premises (t341.t152.t0))
(step t341.t152.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t341.t152.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t152.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t341.t152.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t341.t152.t3.t0))
(step t341.t152.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t341.t152.t3.t1))
(step t341.t152.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t341.t152.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t152.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t341.t152.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t152.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t341.t152.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t341.t152.t4.t1 t341.t152.t4.t2))
(step t341.t152.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t341.t152.t4.t0 t341.t152.t4.t3))
(step t341.t152.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t341.t152.t5 (cl @p_345) :rule trans :premises (t341.t152.t3 t341.t152.t4))
(step t341.t152.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t341.t152.t2 t341.t152.t5 a19))
(step t341.t152.t7 (cl @p_357) :rule resolution :premises (t341.t152.t1 t341.t152.t6))
(step t341.t152 (cl @p_353 @p_357) :rule subproof :discharge (t341.t152.a0))
(step t341.t153 (cl @p_358 @p_357) :rule resolution :premises (t341.t151 t341.t152))
(step t341.t154 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t341.t155 (cl @p_358 @p_358) :rule resolution :premises (t341.t153 t341.t154))
(step t341.t156 (cl @p_358) :rule contraction :premises (t341.t155))
(step t341.t157 (cl @p_354) :rule resolution :premises (t341.t143 t341.t150 t341.t156))
(step t341.t158 (cl @p_353 @p_344) :rule implies :premises (t341.t157))
(step t341.t159 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t341.t160 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t160.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t341.t160.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t341.t160.t0))
(step t341.t160.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t341.t160.t1))
(step t341.t160 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t341.t161 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t161.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t341.t161.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t161.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t341.t161.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t341.t161.t1 t341.t161.t2))
(step t341.t161.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t341.t161.t0 t341.t161.t3))
(step t341.t161 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t341.t162 (cl @p_345) :rule trans :premises (t341.t160 t341.t161))
(step t341.t163 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t341.t159 t341.t162 a19))
(step t341.t164 (cl @p_344) :rule resolution :premises (t341.t158 t341.t163))
(step t341.t165 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t341.t166 (cl @p_292 @p_305) :rule or :premises (t341.t165))
(step t341.t167 (cl @p_305) :rule resolution :premises (t341.t166 a6))
(step t341.t168 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t341.t169 (cl @p_273 @p_295) :rule or :premises (t341.t168))
(step t341.t170 (cl @p_295) :rule resolution :premises (t341.t169 a4))
(step t341.t171 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t341.t172 (cl @p_292 @p_291) :rule or :premises (t341.t171))
(step t341.t173 (cl @p_291) :rule resolution :premises (t341.t172 a6))
(step t341.t174 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t341.t175 (cl @p_312 @p_406) :rule or :premises (t341.t174))
(step t341.t176 (cl @p_406) :rule resolution :premises (t341.t175 a27))
(step t341.t177 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t341.t178 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t341.t179 (cl (= @p_364 @p_364)) :rule refl)
(step t341.t180 (cl (= @p_378 @p_383)) :rule cong :premises (t341.t178 t341.t179))
(step t341.t181 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t341.t182 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t341.t183 (cl (= @p_383 @p_364)) :rule trans :premises (t341.t181 t341.t182))
(step t341.t184 (cl (= @p_378 @p_364)) :rule trans :premises (t341.t180 t341.t183))
(step t341.t185 (cl (= @p_379 @p_382)) :rule cong :premises (t341.t115 t341.t184))
(step t341.t186 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t341.t187 (cl (= @p_379 @p_364)) :rule trans :premises (t341.t185 t341.t186))
(step t341.t188 (cl @p_381) :rule cong :premises (t341.t187))
(step t341.t189 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t341.t190)
(assume t341.t190.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t341.t190.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t341.t190.t1 (cl @p_375 @p_379) :rule or :premises (t341.t190.t0))
(step t341.t190.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t341.t190.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t190.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t341.t190.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t341.t190.t3.t0))
(step t341.t190.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t341.t190.t3.t1))
(step t341.t190.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t341.t190.t3.t2))
(step t341.t190.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t341.t190.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t190.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t341.t190.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t190.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t341.t190.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t341.t190.t4.t1 t341.t190.t4.t2))
(step t341.t190.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t341.t190.t4.t0 t341.t190.t4.t3))
(step t341.t190.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t341.t190.t5 (cl @p_365) :rule trans :premises (t341.t190.t3 t341.t190.t4))
(step t341.t190.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t341.t190.t2 t341.t190.t5 a17))
(step t341.t190.t7 (cl @p_379) :rule resolution :premises (t341.t190.t1 t341.t190.t6))
(step t341.t190 (cl @p_375 @p_379) :rule subproof :discharge (t341.t190.a0))
(step t341.t191 (cl @p_380 @p_379) :rule resolution :premises (t341.t189 t341.t190))
(step t341.t192 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t341.t193 (cl @p_380 @p_380) :rule resolution :premises (t341.t191 t341.t192))
(step t341.t194 (cl @p_380) :rule contraction :premises (t341.t193))
(step t341.t195 (cl @p_376) :rule resolution :premises (t341.t177 t341.t188 t341.t194))
(step t341.t196 (cl @p_375 @p_364) :rule implies :premises (t341.t195))
(step t341.t197 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t341.t198 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t198.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t341.t198.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t341.t198.t0))
(step t341.t198.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t341.t198.t1))
(step t341.t198.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t341.t198.t2))
(step t341.t198 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t341.t199 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t341.t199.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t341.t199.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t341.t199.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t341.t199.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t341.t199.t1 t341.t199.t2))
(step t341.t199.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t341.t199.t0 t341.t199.t3))
(step t341.t199 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t341.t200 (cl @p_365) :rule trans :premises (t341.t198 t341.t199))
(step t341.t201 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t341.t197 t341.t200 a17))
(step t341.t202 (cl @p_364) :rule resolution :premises (t341.t196 t341.t201))
(step t341.t203 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t341.t204 (cl (= @p_399 @p_404)) :rule cong :premises (t341.t116))
(step t341.t205 (cl (= @p_404 true)) :rule or_simplify)
(step t341.t206 (cl (= @p_399 true)) :rule trans :premises (t341.t204 t341.t205))
(step t341.t207 (cl (= @p_400 @p_403)) :rule cong :premises (t341.t206))
(step t341.t208 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t341.t209 (cl (= @p_400 @p_396)) :rule trans :premises (t341.t207 t341.t208))
(step t341.t210 (cl @p_402) :rule cong :premises (t341.t209))
(step t341.t211 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t341.t212)
(assume t341.t212.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t341.t212.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t341.t212.t1 (cl @p_397 @p_400) :rule or :premises (t341.t212.t0))
(step t341.t212.t2 (cl @p_400) :rule resolution :premises (t341.t212.t1 t341.t212.a0))
(step t341.t212 (cl @p_397 @p_400) :rule subproof :discharge (t341.t212.a0))
(step t341.t213 (cl @p_401 @p_400) :rule resolution :premises (t341.t211 t341.t212))
(step t341.t214 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t341.t215 (cl @p_401 @p_401) :rule resolution :premises (t341.t213 t341.t214))
(step t341.t216 (cl @p_401) :rule contraction :premises (t341.t215))
(step t341.t217 (cl @p_398) :rule resolution :premises (t341.t203 t341.t210 t341.t216))
(step t341.t218 (cl @p_397 @p_396) :rule implies :premises (t341.t217))
(step t341.t219 (cl @p_396) :rule resolution :premises (t341.t218 a8))
(step t341.t220 (cl (or @p_312 @p_864)) :rule forall_inst :args (@p_247 @p_314 @p_296))
(step t341.t221 (cl @p_312 @p_864) :rule or :premises (t341.t220))
(step t341.t222 (cl @p_864) :rule resolution :premises (t341.t221 a27))
(step t341.t223 (cl (or @p_292 @p_1140)) :rule forall_inst :args (@p_1 @p_247))
(step t341.t224 (cl @p_292 @p_1140) :rule or :premises (t341.t223))
(step t341.t225 (cl @p_1140) :rule resolution :premises (t341.t224 a6))
(step t341.t226 (cl (or @p_273 @p_1142)) :rule forall_inst :args (@p_139 @p_1 @p_247))
(step t341.t227 (cl @p_273 @p_1142) :rule or :premises (t341.t226))
(step t341.t228 (cl @p_1142) :rule resolution :premises (t341.t227 a4))
(step t341.t229 (cl (or @p_292 @p_1138)) :rule forall_inst :args (@p_247 @p_892))
(step t341.t230 (cl @p_292 @p_1138) :rule or :premises (t341.t229))
(step t341.t231 (cl @p_1138) :rule resolution :premises (t341.t230 a6))
(step t341.t232 (cl (or @p_273 @p_1155)) :rule forall_inst :args (@p_247 @p_139 @p_1))
(step t341.t233 (cl @p_273 @p_1155) :rule or :premises (t341.t232))
(step t341.t234 (cl @p_1155) :rule resolution :premises (t341.t233 a4))
(step t341.t235 (cl (or @p_292 @p_1156)) :rule forall_inst :args (@p_247 @p_139))
(step t341.t236 (cl @p_292 @p_1156) :rule or :premises (t341.t235))
(step t341.t237 (cl @p_1156) :rule resolution :premises (t341.t236 a6))
(step t341.t238 (cl (or @p_273 @p_1164)) :rule forall_inst :args (@p_139 @p_247 @p_18))
(step t341.t239 (cl @p_273 @p_1164) :rule or :premises (t341.t238))
(step t341.t240 (cl @p_1164) :rule resolution :premises (t341.t239 a4))
(step t341.t241 (cl (or @p_312 @p_1175)) :rule forall_inst :args (@p_247 1/1 @p_4))
(step t341.t242 (cl @p_312 @p_1175) :rule or :premises (t341.t241))
(step t341.t243 (cl @p_1175) :rule resolution :premises (t341.t242 a27))
(step t341.t244 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t341.t245 (cl @p_292 @p_405) :rule or :premises (t341.t244))
(step t341.t246 (cl @p_405) :rule resolution :premises (t341.t245 a6))
(step t341.t247 (cl (or @p_343 @p_1161)) :rule forall_inst :args (@p_247 @p_301 1/1))
(step t341.t248 (cl @p_343 @p_1161) :rule or :premises (t341.t247))
(step t341.t249 (cl @p_1161) :rule resolution :premises (t341.t248 a2))
(step t341.t250 (cl (or @p_343 @p_1185)) :rule forall_inst :args (1/1 1/1 @p_4))
(step t341.t251 (cl @p_343 @p_1185) :rule or :premises (t341.t250))
(step t341.t252 (cl @p_1185) :rule resolution :premises (t341.t251 a2))
(step t341.t253 (cl (not @p_888) (not @p_887) @p_884) :rule equiv_pos2)
(step t341.t254 (cl (= (* -1/1 (- 1/1 @p_874)) (* 1/1 (- @p_874 1/1)))) :rule poly_simp)
(step t341.t255 (cl (= @p_885 @p_875)) :rule poly_simp_rel :premises (t341.t254))
(step t341.t256 (cl (= @p_886 @p_889)) :rule cong :premises (t341.t115 t341.t255))
(step t341.t257 (cl (= @p_889 @p_875)) :rule aci_simp)
(step t341.t258 (cl (= @p_886 @p_875)) :rule trans :premises (t341.t256 t341.t257))
(step t341.t259 (cl @p_888) :rule cong :premises (t341.t258))
(step t341.t260 (cl @p_887 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule implies_neg1)
(anchor :step t341.t261)
(assume t341.t261.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))
(step t341.t261.t0 (cl (or @p_883 @p_886)) :rule forall_inst :args (2/1 1/1))
(step t341.t261.t1 (cl @p_883 @p_886) :rule or :premises (t341.t261.t0))
(step t341.t261.t2 (cl @p_886) :rule resolution :premises (t341.t261.t1 t294))
(step t341.t261 (cl @p_883 @p_886) :rule subproof :discharge (t341.t261.a0))
(step t341.t262 (cl @p_887 @p_886) :rule resolution :premises (t341.t260 t341.t261))
(step t341.t263 (cl @p_887 (not @p_886)) :rule implies_neg2)
(step t341.t264 (cl @p_887 @p_887) :rule resolution :premises (t341.t262 t341.t263))
(step t341.t265 (cl @p_887) :rule contraction :premises (t341.t264))
(step t341.t266 (cl @p_884) :rule resolution :premises (t341.t253 t341.t259 t341.t265))
(step t341.t267 (cl @p_883 @p_875) :rule implies :premises (t341.t266))
(step t341.t268 (cl @p_875) :rule resolution :premises (t341.t267 t294))
(step t341.t269 (cl (or @p_343 @p_873)) :rule forall_inst :args (@p_306 @p_270 @p_4))
(step t341.t270 (cl @p_343 @p_873) :rule or :premises (t341.t269))
(step t341.t271 (cl @p_873) :rule resolution :premises (t341.t270 a2))
(step t341.t272 (cl (not @p_973) (not @p_972) @p_970) :rule equiv_pos2)
(step t341.t273 (cl (= (* 1/1 (- @p_314 @p_932)) (* -1/1 (- @p_932 @p_314)))) :rule poly_simp)
(step t341.t274 (cl (= @p_971 @p_969)) :rule poly_simp_rel :premises (t341.t273))
(step t341.t275 (cl @p_973) :rule cong :premises (t341.t274))
(step t341.t276 (cl @p_972 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t341.t277)
(assume t341.t277.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t341.t277.t0 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t341.t277.t1 (cl @p_312 @p_971) :rule or :premises (t341.t277.t0))
(step t341.t277.t2 (cl @p_971) :rule resolution :premises (t341.t277.t1 t341.t277.a0))
(step t341.t277 (cl @p_312 @p_971) :rule subproof :discharge (t341.t277.a0))
(step t341.t278 (cl @p_972 @p_971) :rule resolution :premises (t341.t276 t341.t277))
(step t341.t279 (cl @p_972 (not @p_971)) :rule implies_neg2)
(step t341.t280 (cl @p_972 @p_972) :rule resolution :premises (t341.t278 t341.t279))
(step t341.t281 (cl @p_972) :rule contraction :premises (t341.t280))
(step t341.t282 (cl @p_970) :rule resolution :premises (t341.t272 t341.t275 t341.t281))
(step t341.t283 (cl @p_312 @p_969) :rule implies :premises (t341.t282))
(step t341.t284 (cl @p_969) :rule resolution :premises (t341.t283 a27))
(step t341.t285 (cl (or @p_343 @p_868)) :rule forall_inst :args (@p_4 @p_304 2/1))
(step t341.t286 (cl @p_343 @p_868) :rule or :premises (t341.t285))
(step t341.t287 (cl @p_868) :rule resolution :premises (t341.t286 a2))
(step t341.t288 (cl (not @p_926) (not @p_925) @p_923) :rule equiv_pos2)
(step t341.t289 (cl (= @p_922 @p_922)) :rule refl)
(step t341.t290 (cl (= @p_924 @p_927)) :rule cong :premises (t341.t115 t341.t289))
(step t341.t291 (cl (= @p_927 @p_922)) :rule aci_simp)
(step t341.t292 (cl (= @p_924 @p_922)) :rule trans :premises (t341.t290 t341.t291))
(step t341.t293 (cl @p_926) :rule cong :premises (t341.t292))
(step t341.t294 (cl @p_925 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t341.t295)
(assume t341.t295.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t341.t295.t0 (cl (or @p_353 @p_924)) :rule forall_inst :args (2/1 @p_4))
(step t341.t295.t1 (cl @p_353 @p_924) :rule or :premises (t341.t295.t0))
(step t341.t295.t2 (cl @p_924) :rule resolution :premises (t341.t295.t1 t341.t163))
(step t341.t295 (cl @p_353 @p_924) :rule subproof :discharge (t341.t295.a0))
(step t341.t296 (cl @p_925 @p_924) :rule resolution :premises (t341.t294 t341.t295))
(step t341.t297 (cl @p_925 (not @p_924)) :rule implies_neg2)
(step t341.t298 (cl @p_925 @p_925) :rule resolution :premises (t341.t296 t341.t297))
(step t341.t299 (cl @p_925) :rule contraction :premises (t341.t298))
(step t341.t300 (cl @p_923) :rule resolution :premises (t341.t288 t341.t293 t341.t299))
(step t341.t301 (cl @p_353 @p_922) :rule implies :premises (t341.t300))
(step t341.t302 (cl @p_922) :rule resolution :premises (t341.t301 t341.t163))
(step t341.t303 (cl (or @p_343 @p_934)) :rule forall_inst :args (@p_4 @p_6 @p_1))
(step t341.t304 (cl @p_343 @p_934) :rule or :premises (t341.t303))
(step t341.t305 (cl @p_934) :rule resolution :premises (t341.t304 a2))
(step t341.t306 (cl (not @p_1121) (not @p_1120) @p_1118) :rule equiv_pos2)
(step t341.t307 (cl (= (* 1/1 (- @p_1099 @p_1116)) (* -1/1 (- @p_1116 @p_1099)))) :rule poly_simp)
(step t341.t308 (cl (= @p_1119 @p_1117)) :rule poly_simp_rel :premises (t341.t307))
(step t341.t309 (cl @p_1121) :rule cong :premises (t341.t308))
(step t341.t310 (cl @p_1120 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t341.t311)
(assume t341.t311.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t341.t311.t0 (cl (or @p_312 @p_1119)) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t341.t311.t1 (cl @p_312 @p_1119) :rule or :premises (t341.t311.t0))
(step t341.t311.t2 (cl @p_1119) :rule resolution :premises (t341.t311.t1 t341.t311.a0))
(step t341.t311 (cl @p_312 @p_1119) :rule subproof :discharge (t341.t311.a0))
(step t341.t312 (cl @p_1120 @p_1119) :rule resolution :premises (t341.t310 t341.t311))
(step t341.t313 (cl @p_1120 (not @p_1119)) :rule implies_neg2)
(step t341.t314 (cl @p_1120 @p_1120) :rule resolution :premises (t341.t312 t341.t313))
(step t341.t315 (cl @p_1120) :rule contraction :premises (t341.t314))
(step t341.t316 (cl @p_1118) :rule resolution :premises (t341.t306 t341.t309 t341.t315))
(step t341.t317 (cl @p_312 @p_1117) :rule implies :premises (t341.t316))
(step t341.t318 (cl @p_1117) :rule resolution :premises (t341.t317 a27))
(step t341.t319 (cl (or @p_273 @p_1102)) :rule forall_inst :args (@p_4 @p_1 @p_1098))
(step t341.t320 (cl @p_273 @p_1102) :rule or :premises (t341.t319))
(step t341.t321 (cl @p_1102) :rule resolution :premises (t341.t320 a4))
(step t341.t322 (cl (or @p_343 @p_930)) :rule forall_inst :args (@p_6 @p_361 2/1))
(step t341.t323 (cl @p_343 @p_930) :rule or :premises (t341.t322))
(step t341.t324 (cl @p_930) :rule resolution :premises (t341.t323 a2))
(step t341.t325 (cl (or @p_312 @p_937)) :rule forall_inst :args (@p_4 1/1 @p_4))
(step t341.t326 (cl @p_312 @p_937) :rule or :premises (t341.t325))
(step t341.t327 (cl @p_937) :rule resolution :premises (t341.t326 a27))
(step t341.t328 (cl (or @p_312 @p_1148)) :rule forall_inst :args (@p_139 @p_247 @p_1143))
(step t341.t329 (cl @p_312 @p_1148) :rule or :premises (t341.t328))
(step t341.t330 (cl @p_1148) :rule resolution :premises (t341.t329 a27))
(step t341.t331 (cl (or @p_343 @p_1187)) :rule forall_inst :args (@p_6 1/1 2/1))
(step t341.t332 (cl @p_343 @p_1187) :rule or :premises (t341.t331))
(step t341.t333 (cl @p_1187) :rule resolution :premises (t341.t332 a2))
(step t341.t334 (cl (or @p_343 @p_1152)) :rule forall_inst :args (@p_139 @p_248 @p_247))
(step t341.t335 (cl @p_343 @p_1152) :rule or :premises (t341.t334))
(step t341.t336 (cl @p_1152) :rule resolution :premises (t341.t335 a2))
(step t341.t337 (cl (not @p_1172) (not @p_1171) @p_1169) :rule equiv_pos2)
(step t341.t338 (cl (= (* -1/1 (- @p_1166 @p_1167)) (* 1/1 (- @p_1167 @p_1166)))) :rule poly_simp)
(step t341.t339 (cl (= @p_1170 @p_1168)) :rule poly_simp_rel :premises (t341.t338))
(step t341.t340 (cl @p_1172) :rule cong :premises (t341.t339))
(step t341.t341 (cl @p_1171 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1)))) :rule implies_neg1)
(anchor :step t341.t342)
(assume t341.t342.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))))
(step t341.t342.t0 (cl (or @p_343 @p_1170)) :rule forall_inst :args (@p_139 @p_4 1/1))
(step t341.t342.t1 (cl @p_343 @p_1170) :rule or :premises (t341.t342.t0))
(step t341.t342.t2 (cl @p_1170) :rule resolution :premises (t341.t342.t1 t341.t342.a0))
(step t341.t342 (cl @p_343 @p_1170) :rule subproof :discharge (t341.t342.a0))
(step t341.t343 (cl @p_1171 @p_1170) :rule resolution :premises (t341.t341 t341.t342))
(step t341.t344 (cl @p_1171 (not @p_1170)) :rule implies_neg2)
(step t341.t345 (cl @p_1171 @p_1171) :rule resolution :premises (t341.t343 t341.t344))
(step t341.t346 (cl @p_1171) :rule contraction :premises (t341.t345))
(step t341.t347 (cl @p_1169) :rule resolution :premises (t341.t337 t341.t340 t341.t346))
(step t341.t348 (cl @p_343 @p_1168) :rule implies :premises (t341.t347))
(step t341.t349 (cl @p_1168) :rule resolution :premises (t341.t348 a2))
(step t341.t350 (cl (or @p_312 @p_1173)) :rule forall_inst :args (@p_139 1/1 @p_4))
(step t341.t351 (cl @p_312 @p_1173) :rule or :premises (t341.t350))
(step t341.t352 (cl @p_1173) :rule resolution :premises (t341.t351 a27))
(step t341.t353 (cl @p_1379) :rule and_intro :premises (t341.a32 t341.t110 t341.t113 t341.t139 t341.t142 t341.t164 t341.t167 t341.t170 t240 t341.t173 t341.t176 t341.t202 t341.t219 t341.a8 t341.t222 t341.t225 t341.t228 t341.t231 t341.t234 t341.t237 t341.a10 t341.t240 t341.t243 t341.t246 t341.t249 t341.t252 t341.t268 t341.a43 t341.t271 t341.t284 t341.t287 t341.t302 t341.t305 t341.a3 t341.t318 t341.t321 t341.t324 t341.t327 t341.t330 t341.t333 t341.t336 t341.a11 t341.t349 t341.t352))
(step t341.t354 (cl @p_1377) :rule resolution :premises (t341.t107 t341.t353))
(step t341.t355 (cl @p_1378) :rule and_intro :premises (t341.t53 t341.t354))
(step t341.t356 (cl @p_1263) :rule resolution :premises (t341.t40 t341.t355))
(step t341.t357 (cl (or @p_326 @p_1054)) :rule forall_inst :args (@p_1 @p_18))
(step t341.t358 (cl @p_326 @p_1054) :rule or :premises (t341.t357))
(step t341.t359 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t341.t360 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t341.t360.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t341.t360.t1 (cl @p_22) :rule refl)
(step t341.t360.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t341.t360.t0 t341.t360.t1))
(step t341.t360.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t341.t360.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t341.t360.t2 t341.t360.t3))
(step t341.t360.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t341.t360.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t341.t360.t5))
(step t341.t360.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t341.t360.t4 t341.t360.t6))
(step t341.t360 (cl @p_316) :rule bind)
(step t341.t361 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t341.t359 t341.t360 a16))
(step t341.t362 (cl @p_1054) :rule resolution :premises (t341.t358 t341.t361))
(step t341.t363 (cl (= @p_1052 @p_1053)) :rule symm :premises (t341.t362))
(step t341.t364 (cl (not @p_1063) (not @p_1062) @p_1058) :rule equiv_pos2)
(step t341.t365 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t341.t366 (cl (= @p_18 @p_18)) :rule refl)
(step t341.t367 (cl (= @p_1060 @p_1055)) :rule cong :premises (t341.t365 t341.t366))
(step t341.t368 (cl (= @p_1059 @p_1064)) :rule poly_simp)
(step t341.t369 (cl (= @p_1061 @p_1065)) :rule cong :premises (t341.t367 t341.t368))
(step t341.t370 (cl (= (* 1/1 (- @p_1055 @p_1064)) (* -2/1 (- @p_1053 @p_1056)))) :rule poly_simp)
(step t341.t371 (cl (= @p_1065 @p_1057)) :rule poly_simp_rel :premises (t341.t370))
(step t341.t372 (cl (= @p_1061 @p_1057)) :rule trans :premises (t341.t369 t341.t371))
(step t341.t373 (cl @p_1063) :rule cong :premises (t341.t372))
(step t341.t374 (cl @p_1062 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t375)
(assume t341.t375.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t375.t0 (cl (or @p_279 @p_1061)) :rule forall_inst :args (@p_1 @p_1 @p_18))
(step t341.t375.t1 (cl @p_279 @p_1061) :rule or :premises (t341.t375.t0))
(step t341.t375.t2 (cl @p_1061) :rule resolution :premises (t341.t375.t1 t341.t375.a0))
(step t341.t375 (cl @p_279 @p_1061) :rule subproof :discharge (t341.t375.a0))
(step t341.t376 (cl @p_1062 @p_1061) :rule resolution :premises (t341.t374 t341.t375))
(step t341.t377 (cl @p_1062 (not @p_1061)) :rule implies_neg2)
(step t341.t378 (cl @p_1062 @p_1062) :rule resolution :premises (t341.t376 t341.t377))
(step t341.t379 (cl @p_1062) :rule contraction :premises (t341.t378))
(step t341.t380 (cl @p_1058) :rule resolution :premises (t341.t364 t341.t373 t341.t379))
(step t341.t381 (cl @p_279 @p_1057) :rule implies :premises (t341.t380))
(step t341.t382 (cl @p_1057) :rule resolution :premises (t341.t381 a1))
(step t341.t383 (cl @p_1262) :rule trans :premises (t341.t363 t341.t382))
(step t341.t384 (cl (not @p_898) (not @p_897) @p_894) :rule equiv_pos2)
(step t341.t385 (cl (= (* 1/1 (- @p_890 @p_895)) @p_899)) :rule poly_simp)
(step t341.t386 (cl (= @p_896 @p_893)) :rule poly_simp_rel :premises (t341.t385))
(step t341.t387 (cl @p_898) :rule cong :premises (t341.t386))
(step t341.t388 (cl @p_897 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t341.t389)
(assume t341.t389.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))))
(step t341.t389.t0 (cl (or @p_326 @p_896)) :rule forall_inst :args (@p_1 @p_1))
(step t341.t389.t1 (cl @p_326 @p_896) :rule or :premises (t341.t389.t0))
(step t341.t389.t2 (cl @p_896) :rule resolution :premises (t341.t389.t1 t341.t361))
(step t341.t389 (cl @p_326 @p_896) :rule subproof :discharge (t341.t389.a0))
(step t341.t390 (cl @p_897 @p_896) :rule resolution :premises (t341.t388 t341.t389))
(step t341.t391 (cl @p_897 (not @p_896)) :rule implies_neg2)
(step t341.t392 (cl @p_897 @p_897) :rule resolution :premises (t341.t390 t341.t391))
(step t341.t393 (cl @p_897) :rule contraction :premises (t341.t392))
(step t341.t394 (cl @p_894) :rule resolution :premises (t341.t384 t341.t387 t341.t393))
(step t341.t395 (cl @p_326 @p_893) :rule implies :premises (t341.t394))
(step t341.t396 (cl @p_893) :rule resolution :premises (t341.t395 t341.t361))
(step t341.t397 (cl (not @p_908) (not @p_907) @p_903) :rule equiv_pos2)
(step t341.t398 (cl (= @p_1 @p_1)) :rule refl)
(step t341.t399 (cl (= @p_905 @p_900)) :rule cong :premises (t341.t365 t341.t398))
(step t341.t400 (cl (= @p_904 @p_909)) :rule poly_simp)
(step t341.t401 (cl (= @p_906 @p_910)) :rule cong :premises (t341.t399 t341.t400))
(step t341.t402 (cl (= (* 1/1 (- @p_900 @p_909)) (* -2/1 @p_911))) :rule poly_simp)
(step t341.t403 (cl (= @p_910 @p_902)) :rule poly_simp_rel :premises (t341.t402))
(step t341.t404 (cl (= @p_906 @p_902)) :rule trans :premises (t341.t401 t341.t403))
(step t341.t405 (cl @p_908) :rule cong :premises (t341.t404))
(step t341.t406 (cl @p_907 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t407)
(assume t341.t407.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t407.t0 (cl (or @p_279 @p_906)) :rule forall_inst :args (@p_1 @p_1 @p_1))
(step t341.t407.t1 (cl @p_279 @p_906) :rule or :premises (t341.t407.t0))
(step t341.t407.t2 (cl @p_906) :rule resolution :premises (t341.t407.t1 t341.t407.a0))
(step t341.t407 (cl @p_279 @p_906) :rule subproof :discharge (t341.t407.a0))
(step t341.t408 (cl @p_907 @p_906) :rule resolution :premises (t341.t406 t341.t407))
(step t341.t409 (cl @p_907 (not @p_906)) :rule implies_neg2)
(step t341.t410 (cl @p_907 @p_907) :rule resolution :premises (t341.t408 t341.t409))
(step t341.t411 (cl @p_907) :rule contraction :premises (t341.t410))
(step t341.t412 (cl @p_903) :rule resolution :premises (t341.t397 t341.t405 t341.t411))
(step t341.t413 (cl @p_279 @p_902) :rule implies :premises (t341.t412))
(step t341.t414 (cl @p_902) :rule resolution :premises (t341.t413 a1))
(step t341.t415 (cl @p_1376 @p_1369) :rule implies_neg1)
(anchor :step t341.t416)
(assume t341.t416.a0 @p_1368)
(assume t341.t416.a1 @p_244)
(step t341.t416.t0 (cl @p_1264) :rule symm :premises (t341.t416.a1))
(step t341.t416.t1 (cl @p_1261) :rule trans :premises (t341.t416.t0 t341.t416.a0))
(step t341.t416 (cl @p_1373 @p_1113 @p_1261) :rule subproof :discharge (t341.t416.a0 t341.t416.a1))
(step t341.t417 (cl @p_1375 @p_1368) :rule and_pos :args (0))
(step t341.t418 (cl @p_1375 @p_244) :rule and_pos :args (1))
(step t341.t419 (cl @p_1261 @p_1375 @p_1375) :rule resolution :premises (t341.t416 t341.t417 t341.t418))
(step t341.t420 (cl @p_1375 @p_1375 @p_1261) :rule reordering :premises (t341.t419))
(step t341.t421 (cl @p_1375 @p_1261) :rule contraction :premises (t341.t420))
(step t341.t422 (cl @p_1376 @p_1261) :rule resolution :premises (t341.t415 t341.t421))
(step t341.t423 (cl @p_1376 @p_1271) :rule implies_neg2)
(step t341.t424 (cl @p_1376 @p_1376) :rule resolution :premises (t341.t422 t341.t423))
(step t341.t425 (cl @p_1376) :rule contraction :premises (t341.t424))
(step t341.t426 (cl @p_1375 @p_1261) :rule implies :premises (t341.t425))
(step t341.t427 (cl @p_1372 @p_1370) :rule implies_neg1)
(anchor :step t341.t428)
(assume t341.t428.a0 @p_960)
(assume t341.t428.a1 @p_864)
(assume t341.t428.a2 @p_340)
(assume t341.t428.a3 @p_342)
(assume t341.t428.a4 @p_385)
(assume t341.t428.a5 @p_311)
(assume t341.t428.a6 @p_344)
(assume t341.t428.a7 @p_305)
(assume t341.t428.a8 @p_295)
(assume t341.t428.a9 @p_410)
(assume t341.t428.a10 @p_291)
(assume t341.t428.a11 @p_406)
(assume t341.t428.a12 @p_364)
(assume t341.t428.a13 @p_396)
(assume t341.t428.a14 @p_249)
(step t341.t428.t0 (cl (= @p_270 @p_304)) :rule symm :premises (t341.t167))
(step t341.t428.t1 (cl @p_355) :rule symm :premises (t341.t164))
(step t341.t428.t2 (cl (= @p_304 @p_310)) :rule cong :premises (t341.t428.t1))
(step t341.t428.t3 (cl (= @p_307 @p_304)) :rule cong :premises (t341.t139))
(step t341.t428.t4 (cl @p_388) :rule refl)
(step t341.t428.t5 (cl (= @p_308 @p_341)) :rule cong :premises (t341.t428.t3 t341.t428.t4))
(step t341.t428.t6 (cl (= @p_341 @p_296)) :rule symm :premises (t341.t113))
(step t341.t428.t7 (cl (= @p_270 @p_296)) :rule trans :premises (t341.t428.t0 t341.t428.t2 t341.t142 t341.t428.t5 t341.t428.t6))
(step t341.t428.t8 (cl (= @p_294 @p_339)) :rule cong :premises (t341.t428.t7 t341.t398))
(step t341.t428.t9 (cl (= @p_339 @p_294)) :rule symm :premises (t341.t428.t8))
(step t341.t428.t10 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t341.t428.t11 (cl (= @p_293 @p_289)) :rule symm :premises (t341.t428.t10))
(step t341.t428.t12 (cl (= @p_289 @p_290)) :rule symm :premises (t341.t173))
(step t341.t428.t13 (cl (= @p_362 @p_65)) :rule symm :premises (t341.t176))
(step t341.t428.t14 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t341.t428.t15 (cl (= @p_362 @p_6)) :rule trans :premises (t341.t428.t13 t341.t428.t14))
(step t341.t428.t16 (cl (= 2/1 2/1)) :rule refl)
(step t341.t428.t17 (cl (= @p_363 @p_290)) :rule cong :premises (t341.t428.t15 t341.t428.t16))
(step t341.t428.t18 (cl (= @p_290 @p_363)) :rule symm :premises (t341.t428.t17))
(step t341.t428.t19 (cl (= @p_363 @p_361)) :rule symm :premises (t341.t202))
(step t341.t428.t20 (cl (= @p_361 @p_4)) :rule symm :premises (t341.t219))
(step t341.t428.t21 (cl (= @p_314 @p_248)) :rule trans :premises (t341.t110 t341.t428.t9 t341.t170 t341.t428.t11 t341.t428.t12 t341.t428.t18 t341.t428.t19 t341.t428.t20 t341.t428.a14))
(step t341.t428.t22 (cl (= @p_293 @p_294)) :rule symm :premises (t341.t170))
(step t341.t428.t23 (cl (= @p_339 @p_314)) :rule symm :premises (t341.t110))
(step t341.t428.t24 (cl (= @p_4 @p_314)) :rule trans :premises (t341.t219 t341.t202 t341.t428.t17 t341.t173 t341.t428.t10 t341.t428.t22 t341.t428.t8 t341.t428.t23))
(step t341.t428.t25 (cl (= @p_248 @p_860)) :rule cong :premises (t341.t428.t24))
(step t341.t428.t26 (cl (= @p_314 @p_860)) :rule trans :premises (t341.t428.t21 t341.t428.t25))
(step t341.t428.t27 (cl (= @p_296 @p_296)) :rule refl)
(step t341.t428.t28 (cl (= @p_862 @p_861)) :rule cong :premises (t341.t428.t26 t341.t428.t27))
(step t341.t428.t29 (cl (= @p_861 @p_863)) :rule symm :premises (t341.t222))
(step t341.t428.t30 (cl @p_1374) :rule symm :premises (t341.t428.a0))
(step t341.t428.t31 (cl (= @p_863 @p_900)) :rule cong :premises (t341.t428.t30))
(step t341.t428.t32 (cl @p_1368) :rule trans :premises (t341.t428.a0 t341.t428.t28 t341.t428.t29 t341.t428.t31))
(step t341.t428 (cl @p_1208 @p_1226 @p_434 @p_433 @p_430 @p_437 @p_432 @p_438 @p_441 @p_424 @p_442 @p_427 @p_431 @p_429 @p_574 @p_1368) :rule subproof :discharge (t341.t428.a0 t341.t428.a1 t341.t428.a2 t341.t428.a3 t341.t428.a4 t341.t428.a5 t341.t428.a6 t341.t428.a7 t341.t428.a8 t341.t428.a9 t341.t428.a10 t341.t428.a11 t341.t428.a12 t341.t428.a13 t341.t428.a14))
(step t341.t429 (cl @p_1371 @p_960) :rule and_pos :args (0))
(step t341.t430 (cl @p_1371 @p_864) :rule and_pos :args (1))
(step t341.t431 (cl @p_1371 @p_340) :rule and_pos :args (2))
(step t341.t432 (cl @p_1371 @p_342) :rule and_pos :args (3))
(step t341.t433 (cl @p_1371 @p_385) :rule and_pos :args (4))
(step t341.t434 (cl @p_1371 @p_311) :rule and_pos :args (5))
(step t341.t435 (cl @p_1371 @p_344) :rule and_pos :args (6))
(step t341.t436 (cl @p_1371 @p_305) :rule and_pos :args (7))
(step t341.t437 (cl @p_1371 @p_295) :rule and_pos :args (8))
(step t341.t438 (cl @p_1371 @p_410) :rule and_pos :args (9))
(step t341.t439 (cl @p_1371 @p_291) :rule and_pos :args (10))
(step t341.t440 (cl @p_1371 @p_406) :rule and_pos :args (11))
(step t341.t441 (cl @p_1371 @p_364) :rule and_pos :args (12))
(step t341.t442 (cl @p_1371 @p_396) :rule and_pos :args (13))
(step t341.t443 (cl @p_1371 @p_249) :rule and_pos :args (14))
(step t341.t444 (cl @p_1368 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371) :rule resolution :premises (t341.t428 t341.t429 t341.t430 t341.t431 t341.t432 t341.t433 t341.t434 t341.t435 t341.t436 t341.t437 t341.t438 t341.t439 t341.t440 t341.t441 t341.t442 t341.t443))
(step t341.t445 (cl @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1371 @p_1368) :rule reordering :premises (t341.t444))
(step t341.t446 (cl @p_1371 @p_1368) :rule contraction :premises (t341.t445))
(step t341.t447 (cl @p_1372 @p_1368) :rule resolution :premises (t341.t427 t341.t446))
(step t341.t448 (cl @p_1372 @p_1373) :rule implies_neg2)
(step t341.t449 (cl @p_1372 @p_1372) :rule resolution :premises (t341.t447 t341.t448))
(step t341.t450 (cl @p_1372) :rule contraction :premises (t341.t449))
(step t341.t451 (cl @p_1371 @p_1368) :rule implies :premises (t341.t450))
(step t341.t452 (cl @p_1370) :rule and_intro :premises (t341.a32 t341.t222 t341.t110 t341.t113 t341.t139 t341.t142 t341.t164 t341.t167 t341.t170 t240 t341.t173 t341.t176 t341.t202 t341.t219 t341.a8))
(step t341.t453 (cl @p_1368) :rule resolution :premises (t341.t451 t341.t452))
(step t341.t454 (cl @p_1369) :rule and_intro :premises (t341.t453 t341.a9))
(step t341.t455 (cl @p_1261) :rule resolution :premises (t341.t426 t341.t454))
(step t341.t456 (cl @p_1367 @p_1365) :rule implies_neg1)
(anchor :step t341.t457)
(assume t341.t457.a0 @p_1069)
(assume t341.t457.a1 @p_1103)
(assume t341.t457.a2 @p_19)
(step t341.t457.t0 (cl (= @p_17 @p_18)) :rule symm :premises (t302))
(step t341.t457.t1 (cl (not @p_1076) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t341.t457.t2 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t341.t457.t3 (cl (= @p_1073 @p_1067)) :rule cong :premises (t341.t457.t2 t341.t366))
(step t341.t457.t4 (cl (= @p_1071 @p_1077)) :rule poly_simp)
(step t341.t457.t5 (cl (= @p_1074 @p_1078)) :rule cong :premises (t341.t457.t3 t341.t457.t4))
(step t341.t457.t6 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t341.t457.t7 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t341.t457.t6))
(step t341.t457.t8 (cl (= @p_1074 @p_1069)) :rule trans :premises (t341.t457.t5 t341.t457.t7))
(step t341.t457.t9 (cl @p_1076) :rule cong :premises (t341.t457.t8))
(step t341.t457.t10 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t457.t11)
(assume t341.t457.t11.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t457.t11.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t341.t457.t11.t1 (cl @p_279 @p_1074) :rule or :premises (t341.t457.t11.t0))
(step t341.t457.t11.t2 (cl @p_1074) :rule resolution :premises (t341.t457.t11.t1 t341.t457.t11.a0))
(step t341.t457.t11 (cl @p_279 @p_1074) :rule subproof :discharge (t341.t457.t11.a0))
(step t341.t457.t12 (cl @p_1075 @p_1074) :rule resolution :premises (t341.t457.t10 t341.t457.t11))
(step t341.t457.t13 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t341.t457.t14 (cl @p_1075 @p_1075) :rule resolution :premises (t341.t457.t12 t341.t457.t13))
(step t341.t457.t15 (cl @p_1075) :rule contraction :premises (t341.t457.t14))
(step t341.t457.t16 (cl @p_1070) :rule resolution :premises (t341.t457.t1 t341.t457.t9 t341.t457.t15))
(step t341.t457.t17 (cl @p_279 @p_1069) :rule implies :premises (t341.t457.t16))
(step t341.t457.t18 (cl @p_1069) :rule resolution :premises (t341.t457.t17 a1))
(step t341.t457.t19 (cl @p_1260) :rule trans :premises (t341.t457.t0 t341.t457.a1 t341.t457.t18))
(step t341.t457 (cl @p_1205 @p_1201 @p_1192 @p_1260) :rule subproof :discharge (t341.t457.a0 t341.t457.a1 t341.t457.a2))
(step t341.t458 (cl @p_1366 @p_1069) :rule and_pos :args (0))
(step t341.t459 (cl @p_1366 @p_1103) :rule and_pos :args (1))
(step t341.t460 (cl @p_1366 @p_19) :rule and_pos :args (2))
(step t341.t461 (cl @p_1260 @p_1366 @p_1366 @p_1366) :rule resolution :premises (t341.t457 t341.t458 t341.t459 t341.t460))
(step t341.t462 (cl @p_1366 @p_1366 @p_1366 @p_1260) :rule reordering :premises (t341.t461))
(step t341.t463 (cl @p_1366 @p_1260) :rule contraction :premises (t341.t462))
(step t341.t464 (cl @p_1367 @p_1260) :rule resolution :premises (t341.t456 t341.t463))
(step t341.t465 (cl @p_1367 @p_1272) :rule implies_neg2)
(step t341.t466 (cl @p_1367 @p_1367) :rule resolution :premises (t341.t464 t341.t465))
(step t341.t467 (cl @p_1367) :rule contraction :premises (t341.t466))
(step t341.t468 (cl @p_1366 @p_1260) :rule implies :premises (t341.t467))
(step t341.t469 (cl (not @p_1076) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t341.t470 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t341.t471 (cl (= @p_1073 @p_1067)) :rule cong :premises (t341.t470 t341.t366))
(step t341.t472 (cl (= @p_1071 @p_1077)) :rule poly_simp)
(step t341.t473 (cl (= @p_1074 @p_1078)) :rule cong :premises (t341.t471 t341.t472))
(step t341.t474 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t341.t475 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t341.t474))
(step t341.t476 (cl (= @p_1074 @p_1069)) :rule trans :premises (t341.t473 t341.t475))
(step t341.t477 (cl @p_1076) :rule cong :premises (t341.t476))
(step t341.t478 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t341.t479)
(assume t341.t479.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t341.t479.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t341.t479.t1 (cl @p_279 @p_1074) :rule or :premises (t341.t479.t0))
(step t341.t479.t2 (cl @p_1074) :rule resolution :premises (t341.t479.t1 t341.t479.a0))
(step t341.t479 (cl @p_279 @p_1074) :rule subproof :discharge (t341.t479.a0))
(step t341.t480 (cl @p_1075 @p_1074) :rule resolution :premises (t341.t478 t341.t479))
(step t341.t481 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t341.t482 (cl @p_1075 @p_1075) :rule resolution :premises (t341.t480 t341.t481))
(step t341.t483 (cl @p_1075) :rule contraction :premises (t341.t482))
(step t341.t484 (cl @p_1070) :rule resolution :premises (t341.t469 t341.t477 t341.t483))
(step t341.t485 (cl @p_279 @p_1069) :rule implies :premises (t341.t484))
(step t341.t486 (cl @p_1069) :rule resolution :premises (t341.t485 a1))
(step t341.t487 (cl @p_1365) :rule and_intro :premises (t341.t486 t341.a24 t302))
(step t341.t488 (cl @p_1260) :rule resolution :premises (t341.t468 t341.t487))
(step t341.t489 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t341.t490 (cl (= @p_208 @p_208)) :rule refl)
(step t341.t491 (cl (= @p_240 @p_230)) :rule cong :premises (t341.t1 t341.t490))
(step t341.t492 (cl @p_60) :rule refl)
(step t341.t493 (cl (= @p_241 @p_231)) :rule cong :premises (t341.t491 t341.t492))
(step t341.t494 (cl @p_243) :rule cong :premises (t341.t493))
(step t341.t495 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t341.t496)
(assume t341.t496.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t341.t496.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t341.t496.t1 (cl @p_238 @p_241) :rule or :premises (t341.t496.t0))
(step t341.t496.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t341.t496.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t341.t496.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t341.t496.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t341.t496.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t341.t496.t3.t1))
(step t341.t496.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t341.t496.t3.t0 t341.t496.t3.t2))
(step t341.t496.t3 (cl @p_232) :rule bind)
(step t341.t496.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t341.t496.t2 t341.t496.t3 a25))
(step t341.t496.t5 (cl @p_241) :rule resolution :premises (t341.t496.t1 t341.t496.t4))
(step t341.t496 (cl @p_238 @p_241) :rule subproof :discharge (t341.t496.a0))
(step t341.t497 (cl @p_242 @p_241) :rule resolution :premises (t341.t495 t341.t496))
(step t341.t498 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t341.t499 (cl @p_242 @p_242) :rule resolution :premises (t341.t497 t341.t498))
(step t341.t500 (cl @p_242) :rule contraction :premises (t341.t499))
(step t341.t501 (cl @p_239) :rule resolution :premises (t341.t489 t341.t494 t341.t500))
(step t341.t502 (cl @p_238 @p_231) :rule implies :premises (t341.t501))
(step t341.t503 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t341.t504 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t341.t504.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t341.t504.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t341.t504.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t341.t504.t1))
(step t341.t504.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t341.t504.t0 t341.t504.t2))
(step t341.t504 (cl @p_232) :rule bind)
(step t341.t505 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t341.t503 t341.t504 a25))
(step t341.t506 (cl @p_231) :rule resolution :premises (t341.t502 t341.t505))
(step t341.t507 (cl @p_1265) :rule and_intro :premises (t341.t20 t341.t28 t341.t356 t341.t383 t341.t53 t341.t396 t341.t414 t341.t455 t341.t488 t341.t486 t237 t341.t506 t319 t231))
(step t341 (cl @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_1194 @p_1195 @p_574 @p_1113 @p_1135 @p_1196 @p_1197 @p_427 @p_1198 @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1200 @p_1201 @p_434 @p_1202 @p_1203 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_1211 @p_437 @p_1212 @p_438 @p_1213 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_1218 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1224 @p_1225 @p_1226 @p_1227 @p_1228 @p_1229 @p_1265) :rule subproof :discharge (t341.a0 t341.a1 t341.a2 t341.a3 t341.a4 t341.a5 t341.a6 t341.a7 t341.a8 t341.a9 t341.a10 t341.a11 t341.a12 t341.a13 t341.a14 t341.a15 t341.a16 t341.a17 t341.a18 t341.a19 t341.a20 t341.a21 t341.a22 t341.a23 t341.a24 t341.a25 t341.a26 t341.a27 t341.a28 t341.a29 t341.a30 t341.a31 t341.a32 t341.a33 t341.a34 t341.a35 t341.a36 t341.a37 t341.a38 t341.a39 t341.a40 t341.a41 t341.a42 t341.a43 t341.a44 t341.a45 t341.a46 t341.a47 t341.a48 t341.a49 t341.a50 t341.a51 t341.a52 t341.a53 t341.a54 t341.a55 t341.a56 t341.a57))
(step t342 (cl (! (not @p_1258) :named @p_1259) @p_142) :rule and_pos :args (0))
(step t343 (cl @p_1259 @p_13) :rule and_pos :args (1))
(step t344 (cl @p_1259 @p_410) :rule and_pos :args (2))
(step t345 (cl @p_1259 @p_1188) :rule and_pos :args (3))
(step t346 (cl @p_1259 @p_19) :rule and_pos :args (4))
(step t347 (cl @p_1259 @p_36) :rule and_pos :args (5))
(step t348 (cl @p_1259 @p_1187) :rule and_pos :args (6))
(step t349 (cl @p_1259 @p_1185) :rule and_pos :args (7))
(step t350 (cl @p_1259 @p_249) :rule and_pos :args (8))
(step t351 (cl @p_1259 @p_244) :rule and_pos :args (9))
(step t352 (cl @p_1259 @p_1124) :rule and_pos :args (10))
(step t353 (cl @p_1259 @p_1176) :rule and_pos :args (11))
(step t354 (cl @p_1259 @p_1175) :rule and_pos :args (12))
(step t355 (cl @p_1259 @p_406) :rule and_pos :args (13))
(step t356 (cl @p_1259 @p_1173) :rule and_pos :args (14))
(step t357 (cl @p_1259 @p_969) :rule and_pos :args (15))
(step t358 (cl @p_1259 @p_1117) :rule and_pos :args (16))
(step t359 (cl @p_1259 @p_405) :rule and_pos :args (17))
(step t360 (cl @p_1259 @p_396) :rule and_pos :args (18))
(step t361 (cl @p_1259 @p_385) :rule and_pos :args (19))
(step t362 (cl @p_1259 @p_364) :rule and_pos :args (20))
(step t363 (cl @p_1259 @p_344) :rule and_pos :args (21))
(step t364 (cl @p_1259 @p_342) :rule and_pos :args (22))
(step t365 (cl @p_1259 @p_1168) :rule and_pos :args (23))
(step t366 (cl @p_1259 @p_1103) :rule and_pos :args (24))
(step t367 (cl @p_1259 @p_340) :rule and_pos :args (25))
(step t368 (cl @p_1259 @p_1102) :rule and_pos :args (26))
(step t369 (cl @p_1259 @p_1164) :rule and_pos :args (27))
(step t370 (cl @p_1259 @p_1081) :rule and_pos :args (28))
(step t371 (cl @p_1259 @p_1069) :rule and_pos :args (29))
(step t372 (cl @p_1259 @p_1057) :rule and_pos :args (30))
(step t373 (cl @p_1259 @p_1054) :rule and_pos :args (31))
(step t374 (cl @p_1259 @p_960) :rule and_pos :args (32))
(step t375 (cl @p_1259 @p_210) :rule and_pos :args (33))
(step t376 (cl @p_1259 @p_231) :rule and_pos :args (34))
(step t377 (cl @p_1259 @p_937) :rule and_pos :args (35))
(step t378 (cl @p_1259 @p_311) :rule and_pos :args (36))
(step t379 (cl @p_1259 @p_1161) :rule and_pos :args (37))
(step t380 (cl @p_1259 @p_305) :rule and_pos :args (38))
(step t381 (cl @p_1259 @p_1156) :rule and_pos :args (39))
(step t382 (cl @p_1259 @p_934) :rule and_pos :args (40))
(step t383 (cl @p_1259 @p_930) :rule and_pos :args (41))
(step t384 (cl @p_1259 @p_922) :rule and_pos :args (42))
(step t385 (cl @p_1259 @p_913) :rule and_pos :args (43))
(step t386 (cl @p_1259 @p_295) :rule and_pos :args (44))
(step t387 (cl @p_1259 @p_1155) :rule and_pos :args (45))
(step t388 (cl @p_1259 @p_291) :rule and_pos :args (46))
(step t389 (cl @p_1259 @p_902) :rule and_pos :args (47))
(step t390 (cl @p_1259 @p_893) :rule and_pos :args (48))
(step t391 (cl @p_1259 @p_875) :rule and_pos :args (49))
(step t392 (cl @p_1259 @p_873) :rule and_pos :args (50))
(step t393 (cl @p_1259 @p_868) :rule and_pos :args (51))
(step t394 (cl @p_1259 @p_1152) :rule and_pos :args (52))
(step t395 (cl @p_1259 @p_1148) :rule and_pos :args (53))
(step t396 (cl @p_1259 @p_864) :rule and_pos :args (54))
(step t397 (cl @p_1259 @p_1142) :rule and_pos :args (55))
(step t398 (cl @p_1259 @p_1140) :rule and_pos :args (56))
(step t399 (cl @p_1259 @p_1138) :rule and_pos :args (57))
(step t400 (cl @p_1265 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259) :rule resolution :premises (t341 t342 t343 t344 t345 t346 t347 t348 t349 t350 t351 t352 t353 t354 t355 t356 t357 t358 t359 t360 t361 t362 t363 t364 t365 t366 t367 t368 t369 t370 t371 t372 t373 t374 t375 t376 t377 t378 t379 t380 t381 t382 t383 t384 t385 t386 t387 t388 t389 t390 t391 t392 t393 t394 t395 t396 t397 t398 t399))
(step t401 (cl @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1259 @p_1265) :rule reordering :premises (t400))
(step t402 (cl @p_1259 @p_1265) :rule contraction :premises (t401))
(step t403 (cl @p_1364 @p_1265) :rule resolution :premises (t340 t402))
(step t404 (cl @p_1364 (! (not @p_1265) :named @p_1266)) :rule implies_neg2)
(step t405 (cl @p_1364 @p_1364) :rule resolution :premises (t403 t404))
(step t406 (cl @p_1364) :rule contraction :premises (t405))
(step t407 (cl @p_1259 @p_1265) :rule implies :premises (t406))
(step t408 (cl (! (=> @p_1265 false) :named @p_1267) @p_1265) :rule implies_neg1)
(anchor :step t409)
(assume t409.a0 @p_210)
(assume t409.a1 @p_1264)
(assume t409.a2 @p_1263)
(assume t409.a3 @p_1262)
(assume t409.a4 @p_1081)
(assume t409.a5 @p_893)
(assume t409.a6 @p_902)
(assume t409.a7 @p_1261)
(assume t409.a8 @p_1260)
(assume t409.a9 @p_1069)
(assume t409.a10 @p_13)
(assume t409.a11 @p_231)
(assume t409.a12 @p_36)
(assume t409.a13 @p_142)
(step t409.t0 (cl @p_1342 @p_163 @p_1273) :rule equiv_pos2)
(step t409.t1 (cl (= @p_1273 @p_142)) :rule rare_rewrite :args ("arith-elim-lt" @p_140 0/1))
(step t409.t2 (cl @p_1341) :rule symm :premises (t409.t1))
(step t409.t3 (cl @p_1273) :rule resolution :premises (t409.t0 t409.t2 t231))
(step t409.t4 (cl (not (! (= @p_141 (! (not @p_1273) :named @p_1274)) :named @p_1363)) @p_142 @p_1274) :rule equiv_pos2)
(step t409.t5 (cl (= @p_1274 @p_163)) :rule cong :premises (t409.t1))
(step t409.t6 (cl (! (= @p_1274 @p_141) :named @p_1362)) :rule trans :premises (t409.t5 t70))
(step t409.t7 (cl @p_1363) :rule symm :premises (t409.t6))
(step t409.t8 (cl (not @p_1362) (not @p_1274) @p_141) :rule equiv_pos2)
(step t409.t9 (cl (! (=> @p_1273 false) :named @p_1275) @p_1273) :rule implies_neg1)
(anchor :step t409.t10)
(assume t409.t10.a0 @p_1273)
(step t409.t10.t0 (cl (not (! (= (! (< (! (+ @p_140 @p_1296 @p_1294 @p_34 (! (* -1/1 @p_1292) :named @p_1293) @p_1291 @p_900 (! (* 2/1 @p_1288) :named @p_1289) (! (* -2/1 @p_1285) :named @p_1286) (! (* -2/1 @p_1283) :named @p_1284) @p_1282 (! (* 2/1 (! (+ @p_936 @p_892 @p_1278) :named @p_1279)) :named @p_1280) @p_1 @p_1277) :named @p_1297) (! (+ 0/1 0/1 @p_175 @p_737 @p_175 0/1 1/2 (! (* 2/1 0/1) :named @p_490) (! (* -2/1 0/1) :named @p_491) @p_491 0/1 @p_490 1/2 0/1) :named @p_1276)) :named @p_1298) false) :named @p_1347)) (not @p_1298) false) :rule equiv_pos2)
(step t409.t10.t1 (cl (= @p_1298 (! (not (! (>= @p_1297 @p_1276) :named @p_1348)) :named @p_1349))) :rule rare_rewrite :args ("arith-elim-lt" @p_1297 @p_1276))
(step t409.t10.t2 (cl (= @p_1297 (! (+ (! (* -1/1 @p_900) :named @p_1359) @p_900 @p_34 @p_1281 @p_1358 @p_1357 @p_1356 @p_1355 @p_1354 @p_1310 @p_1353 @p_1352 @p_227 @p_1295 @p_33 @p_17 @p_139 @p_10 @p_1 @p_1351) :named @p_1360))) :rule poly_simp)
(step t409.t10.t3 (cl (= @p_1358 0/1)) :rule poly_simp)
(step t409.t10.t4 (cl (= @p_1357 0/1)) :rule poly_simp)
(step t409.t10.t5 (cl (= @p_1356 0/1)) :rule poly_simp)
(step t409.t10.t6 (cl (= @p_1355 0/1)) :rule poly_simp)
(step t409.t10.t7 (cl (= @p_1354 0/1)) :rule poly_simp)
(step t409.t10.t8 (cl (= @p_1310 @p_1310)) :rule refl)
(step t409.t10.t9 (cl (= @p_1353 0/1)) :rule poly_simp)
(step t409.t10.t10 (cl (= @p_1352 0/1)) :rule poly_simp)
(step t409.t10.t11 (cl (= @p_227 @p_227)) :rule refl)
(step t409.t10.t12 (cl (= @p_1295 @p_1295)) :rule refl)
(step t409.t10.t13 (cl (= @p_33 @p_33)) :rule refl)
(step t409.t10.t14 (cl (= @p_17 @p_17)) :rule refl)
(step t409.t10.t15 (cl (= @p_139 @p_139)) :rule refl)
(step t409.t10.t16 (cl (= @p_10 @p_10)) :rule refl)
(step t409.t10.t17 (cl (= @p_1 @p_1)) :rule refl)
(step t409.t10.t18 (cl (= @p_1351 0/1)) :rule poly_simp)
(step t409.t10.t19 (cl (= @p_1360 (! (+ @p_1359 @p_900 @p_34 @p_1281 0/1 0/1 0/1 0/1 0/1 @p_1310 0/1 0/1 @p_227 @p_1295 @p_33 @p_17 @p_139 @p_10 @p_1 0/1) :named @p_1361))) :rule cong :premises (t409.t10.t3 t409.t10.t4 t409.t10.t5 t409.t10.t6 t409.t10.t7 t409.t10.t8 t409.t10.t9 t409.t10.t10 t409.t10.t11 t409.t10.t12 t409.t10.t13 t409.t10.t14 t409.t10.t15 t409.t10.t16 t409.t10.t17 t409.t10.t18))
(step t409.t10.t20 (cl (= @p_1361 0/1)) :rule poly_simp)
(step t409.t10.t21 (cl (= @p_1360 0/1)) :rule trans :premises (t409.t10.t19 t409.t10.t20))
(step t409.t10.t22 (cl (= @p_1297 0/1)) :rule trans :premises (t409.t10.t2 t409.t10.t21))
(step t409.t10.t23 (cl (= @p_175 0/1)) :rule evaluate)
(step t409.t10.t24 (cl (= @p_737 -1/1)) :rule evaluate)
(step t409.t10.t25 (cl @p_60) :rule refl)
(step t409.t10.t26 (cl (= 1/2 1/2)) :rule refl)
(step t409.t10.t27 (cl (= @p_490 0/1)) :rule evaluate)
(step t409.t10.t28 (cl (= @p_491 0/1)) :rule evaluate)
(step t409.t10.t29 (cl (= @p_1276 (! (+ 0/1 0/1 0/1 -1/1 0/1 0/1 1/2 0/1 0/1 0/1 0/1 0/1 1/2 0/1) :named @p_1350))) :rule cong :premises (t409.t10.t23 t409.t10.t24 t409.t10.t23 t409.t10.t25 t409.t10.t26 t409.t10.t27 t409.t10.t28 t409.t10.t28 t409.t10.t25 t409.t10.t27 t409.t10.t26 t409.t10.t25))
(step t409.t10.t30 (cl (= @p_1350 0/1)) :rule evaluate)
(step t409.t10.t31 (cl (= @p_1276 0/1)) :rule trans :premises (t409.t10.t29 t409.t10.t30))
(step t409.t10.t32 (cl (= @p_1348 @p_190)) :rule cong :premises (t409.t10.t22 t409.t10.t31))
(step t409.t10.t33 (cl @p_191) :rule evaluate)
(step t409.t10.t34 (cl (= @p_1348 true)) :rule trans :premises (t409.t10.t32 t409.t10.t33))
(step t409.t10.t35 (cl (= @p_1349 @p_189)) :rule cong :premises (t409.t10.t34))
(step t409.t10.t36 (cl (= @p_189 false)) :rule evaluate)
(step t409.t10.t37 (cl (= @p_1349 false)) :rule trans :premises (t409.t10.t35 t409.t10.t36))
(step t409.t10.t38 (cl @p_1347) :rule trans :premises (t409.t10.t1 t409.t10.t37))
(step t409.t10.t39 (cl @p_1274 @p_1343 @p_1344 @p_1345 (not (! (= @p_1293 @p_175) :named @p_1330)) (not @p_1327) (not @p_1326) (not (! (= @p_1289 @p_490) :named @p_1322)) (not (! (= @p_1286 @p_491) :named @p_1318)) (not (! (= @p_1284 @p_491) :named @p_1314)) (not @p_1308) (not (! (= @p_1280 @p_490) :named @p_1301)) @p_1113 @p_1346 @p_1298) :rule la_generic :args (1/1 1/1 1/1 1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t409.t10.t40 (cl @p_1342 @p_163 @p_1273) :rule equiv_pos2)
(step t409.t10.t41 (cl @p_159 @p_160 @p_142) :rule equiv_pos2)
(step t409.t10.t42 (cl @p_142) :rule resolution :premises (t409.t10.t41 t230 a28))
(step t409.t10.t43 (cl @p_1273) :rule resolution :premises (t409.t10.t40 t409.t2 t409.t10.t42))
(step t409.t10.t44 (cl (not @p_1339) @p_1193 @p_1338) :rule equiv_pos2)
(step t409.t10.t45 (cl (= @p_1338 @p_1340)) :rule rare_rewrite :args ("arith-elim-leq" @p_1296 0/1))
(step t409.t10.t46 (cl (= (* -1/1 (- 0/1 @p_1296)) (* -1/1 (- @p_35 0/1)))) :rule poly_simp)
(step t409.t10.t47 (cl (= @p_1340 @p_36)) :rule poly_simp_rel :premises (t409.t10.t46))
(step t409.t10.t48 (cl (= @p_1338 @p_36)) :rule trans :premises (t409.t10.t45 t409.t10.t47))
(step t409.t10.t49 (cl @p_1339) :rule symm :premises (t409.t10.t48))
(step t409.t10.t50 (cl @p_1338) :rule resolution :premises (t409.t10.t44 t409.t10.t49 t319))
(step t409.t10.t51 (cl (=> @p_1337 @p_1336)) :rule la_mult_neg)
(step t409.t10.t52 (cl (not @p_1337) @p_1336) :rule implies :premises (t409.t10.t51))
(step t409.t10.t53 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t409.t10.t54 (cl (not @p_185) @p_183) :rule equiv1 :premises (t409.t10.t53))
(step t409.t10.t55 (cl @p_185) :rule evaluate)
(step t409.t10.t56 (cl @p_183) :rule resolution :premises (t409.t10.t54 t409.t10.t55))
(step t409.t10.t57 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t409.t10.t58 (cl (= @p_221 x$)) :rule poly_simp)
(step t409.t10.t59 (cl (= @p_208 @p_208)) :rule refl)
(step t409.t10.t60 (cl (= @p_240 @p_230)) :rule cong :premises (t409.t10.t58 t409.t10.t59))
(step t409.t10.t61 (cl @p_60) :rule refl)
(step t409.t10.t62 (cl (= @p_241 @p_231)) :rule cong :premises (t409.t10.t60 t409.t10.t61))
(step t409.t10.t63 (cl @p_243) :rule cong :premises (t409.t10.t62))
(step t409.t10.t64 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t409.t10.t65)
(assume t409.t10.t65.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t409.t10.t65.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t409.t10.t65.t1 (cl @p_238 @p_241) :rule or :premises (t409.t10.t65.t0))
(step t409.t10.t65.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t409.t10.t65.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t409.t10.t65.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t409.t10.t65.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t409.t10.t65.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t409.t10.t65.t3.t1))
(step t409.t10.t65.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t409.t10.t65.t3.t0 t409.t10.t65.t3.t2))
(step t409.t10.t65.t3 (cl @p_232) :rule bind)
(step t409.t10.t65.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t409.t10.t65.t2 t409.t10.t65.t3 a25))
(step t409.t10.t65.t5 (cl @p_241) :rule resolution :premises (t409.t10.t65.t1 t409.t10.t65.t4))
(step t409.t10.t65 (cl @p_238 @p_241) :rule subproof :discharge (t409.t10.t65.a0))
(step t409.t10.t66 (cl @p_242 @p_241) :rule resolution :premises (t409.t10.t64 t409.t10.t65))
(step t409.t10.t67 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t409.t10.t68 (cl @p_242 @p_242) :rule resolution :premises (t409.t10.t66 t409.t10.t67))
(step t409.t10.t69 (cl @p_242) :rule contraction :premises (t409.t10.t68))
(step t409.t10.t70 (cl @p_239) :rule resolution :premises (t409.t10.t57 t409.t10.t63 t409.t10.t69))
(step t409.t10.t71 (cl @p_238 @p_231) :rule implies :premises (t409.t10.t70))
(step t409.t10.t72 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t409.t10.t73 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t409.t10.t73.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t409.t10.t73.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t409.t10.t73.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t409.t10.t73.t1))
(step t409.t10.t73.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t409.t10.t73.t0 t409.t10.t73.t2))
(step t409.t10.t73 (cl @p_232) :rule bind)
(step t409.t10.t74 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t409.t10.t72 t409.t10.t73 a25))
(step t409.t10.t75 (cl @p_231) :rule resolution :premises (t409.t10.t71 t409.t10.t74))
(step t409.t10.t76 (cl @p_1337) :rule and_intro :premises (t409.t10.t56 t409.t10.t75))
(step t409.t10.t77 (cl @p_1336) :rule resolution :premises (t409.t10.t52 t409.t10.t76))
(step t409.t10.t78 (cl (=> @p_1335 @p_1334)) :rule la_mult_neg)
(step t409.t10.t79 (cl (not @p_1335) @p_1334) :rule implies :premises (t409.t10.t78))
(step t409.t10.t80 (cl @p_1335) :rule and_intro :premises (t409.t10.t56 t237))
(step t409.t10.t81 (cl @p_1334) :rule resolution :premises (t409.t10.t79 t409.t10.t80))
(step t409.t10.t82 (cl (=> (! (and @p_183 @p_1331) :named @p_1332) @p_1330)) :rule la_mult_neg)
(step t409.t10.t83 (cl (not @p_1332) @p_1330) :rule implies :premises (t409.t10.t82))
(step t409.t10.t84 (cl (not @p_1333) @p_1205 @p_1331) :rule equiv_pos2)
(step t409.t10.t85 (cl (= (* 1/1 (- @p_1292 0/1)) (* 1/1 @p_1079))) :rule poly_simp)
(step t409.t10.t86 (cl (= @p_1331 @p_1069)) :rule poly_simp_rel :premises (t409.t10.t85))
(step t409.t10.t87 (cl @p_1333) :rule symm :premises (t409.t10.t86))
(step t409.t10.t88 (cl (not @p_1076) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t409.t10.t89 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t409.t10.t90 (cl (= @p_18 @p_18)) :rule refl)
(step t409.t10.t91 (cl (= @p_1073 @p_1067)) :rule cong :premises (t409.t10.t89 t409.t10.t90))
(step t409.t10.t92 (cl (= @p_1071 @p_1077)) :rule poly_simp)
(step t409.t10.t93 (cl (= @p_1074 @p_1078)) :rule cong :premises (t409.t10.t91 t409.t10.t92))
(step t409.t10.t94 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t409.t10.t95 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t409.t10.t94))
(step t409.t10.t96 (cl (= @p_1074 @p_1069)) :rule trans :premises (t409.t10.t93 t409.t10.t95))
(step t409.t10.t97 (cl @p_1076) :rule cong :premises (t409.t10.t96))
(step t409.t10.t98 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t409.t10.t99)
(assume t409.t10.t99.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t409.t10.t99.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t409.t10.t99.t1 (cl @p_279 @p_1074) :rule or :premises (t409.t10.t99.t0))
(step t409.t10.t99.t2 (cl @p_1074) :rule resolution :premises (t409.t10.t99.t1 t409.t10.t99.a0))
(step t409.t10.t99 (cl @p_279 @p_1074) :rule subproof :discharge (t409.t10.t99.a0))
(step t409.t10.t100 (cl @p_1075 @p_1074) :rule resolution :premises (t409.t10.t98 t409.t10.t99))
(step t409.t10.t101 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t409.t10.t102 (cl @p_1075 @p_1075) :rule resolution :premises (t409.t10.t100 t409.t10.t101))
(step t409.t10.t103 (cl @p_1075) :rule contraction :premises (t409.t10.t102))
(step t409.t10.t104 (cl @p_1070) :rule resolution :premises (t409.t10.t88 t409.t10.t97 t409.t10.t103))
(step t409.t10.t105 (cl @p_279 @p_1069) :rule implies :premises (t409.t10.t104))
(step t409.t10.t106 (cl @p_1069) :rule resolution :premises (t409.t10.t105 a1))
(step t409.t10.t107 (cl @p_1331) :rule resolution :premises (t409.t10.t84 t409.t10.t87 t409.t10.t106))
(step t409.t10.t108 (cl @p_1332) :rule and_intro :premises (t409.t10.t56 t409.t10.t107))
(step t409.t10.t109 (cl @p_1330) :rule resolution :premises (t409.t10.t83 t409.t10.t108))
(step t409.t10.t110 (cl @p_1329 @p_1272 @p_1327) :rule equiv_pos2)
(step t409.t10.t111 (cl (= (* 1/1 (- @p_1291 0/1)) (* 1/1 (- @p_17 @p_1068)))) :rule poly_simp)
(step t409.t10.t112 (cl (= @p_1327 @p_1260)) :rule poly_simp_rel :premises (t409.t10.t111))
(step t409.t10.t113 (cl @p_1328) :rule symm :premises (t409.t10.t112))
(step t409.t10.t114 (cl @p_1327) :rule resolution :premises (t409.t10.t110 t409.t10.t113 t409.a8))
(step t409.t10.t115 (cl @p_1326) :rule symm :premises (t409.a7))
(step t409.t10.t116 (cl (=> (! (and @p_512 @p_1323) :named @p_1324) @p_1322)) :rule la_mult_pos)
(step t409.t10.t117 (cl (not @p_1324) @p_1322) :rule implies :premises (t409.t10.t116))
(step t409.t10.t118 (cl (= @p_515 @p_512)) :rule equiv_simplify)
(step t409.t10.t119 (cl (not @p_515) @p_512) :rule equiv1 :premises (t409.t10.t118))
(step t409.t10.t120 (cl @p_515) :rule evaluate)
(step t409.t10.t121 (cl @p_512) :rule resolution :premises (t409.t10.t119 t409.t10.t120))
(step t409.t10.t122 (cl (not @p_1325) @p_1219 @p_1323) :rule equiv_pos2)
(step t409.t10.t123 (cl (= (* 1/1 (- @p_1288 0/1)) (* 1/1 @p_911))) :rule poly_simp)
(step t409.t10.t124 (cl (= @p_1323 @p_902)) :rule poly_simp_rel :premises (t409.t10.t123))
(step t409.t10.t125 (cl @p_1325) :rule symm :premises (t409.t10.t124))
(step t409.t10.t126 (cl (not @p_908) (not @p_907) @p_903) :rule equiv_pos2)
(step t409.t10.t127 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t409.t10.t128 (cl (= @p_905 @p_900)) :rule cong :premises (t409.t10.t127 t409.t10.t17))
(step t409.t10.t129 (cl (= @p_904 @p_909)) :rule poly_simp)
(step t409.t10.t130 (cl (= @p_906 @p_910)) :rule cong :premises (t409.t10.t128 t409.t10.t129))
(step t409.t10.t131 (cl (= (* 1/1 (- @p_900 @p_909)) (* -2/1 @p_911))) :rule poly_simp)
(step t409.t10.t132 (cl (= @p_910 @p_902)) :rule poly_simp_rel :premises (t409.t10.t131))
(step t409.t10.t133 (cl (= @p_906 @p_902)) :rule trans :premises (t409.t10.t130 t409.t10.t132))
(step t409.t10.t134 (cl @p_908) :rule cong :premises (t409.t10.t133))
(step t409.t10.t135 (cl @p_907 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t409.t10.t136)
(assume t409.t10.t136.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t409.t10.t136.t0 (cl (or @p_279 @p_906)) :rule forall_inst :args (@p_1 @p_1 @p_1))
(step t409.t10.t136.t1 (cl @p_279 @p_906) :rule or :premises (t409.t10.t136.t0))
(step t409.t10.t136.t2 (cl @p_906) :rule resolution :premises (t409.t10.t136.t1 t409.t10.t136.a0))
(step t409.t10.t136 (cl @p_279 @p_906) :rule subproof :discharge (t409.t10.t136.a0))
(step t409.t10.t137 (cl @p_907 @p_906) :rule resolution :premises (t409.t10.t135 t409.t10.t136))
(step t409.t10.t138 (cl @p_907 (not @p_906)) :rule implies_neg2)
(step t409.t10.t139 (cl @p_907 @p_907) :rule resolution :premises (t409.t10.t137 t409.t10.t138))
(step t409.t10.t140 (cl @p_907) :rule contraction :premises (t409.t10.t139))
(step t409.t10.t141 (cl @p_903) :rule resolution :premises (t409.t10.t126 t409.t10.t134 t409.t10.t140))
(step t409.t10.t142 (cl @p_279 @p_902) :rule implies :premises (t409.t10.t141))
(step t409.t10.t143 (cl @p_902) :rule resolution :premises (t409.t10.t142 a1))
(step t409.t10.t144 (cl @p_1323) :rule resolution :premises (t409.t10.t122 t409.t10.t125 t409.t10.t143))
(step t409.t10.t145 (cl @p_1324) :rule and_intro :premises (t409.t10.t121 t409.t10.t144))
(step t409.t10.t146 (cl @p_1322) :rule resolution :premises (t409.t10.t117 t409.t10.t145))
(step t409.t10.t147 (cl (=> (! (and (! (< -2/1 0/1) :named @p_530) @p_1319) :named @p_1320) @p_1318)) :rule la_mult_neg)
(step t409.t10.t148 (cl (not @p_1320) @p_1318) :rule implies :premises (t409.t10.t147))
(step t409.t10.t149 (cl (= (! (= @p_530 true) :named @p_533) @p_530)) :rule equiv_simplify)
(step t409.t10.t150 (cl (not @p_533) @p_530) :rule equiv1 :premises (t409.t10.t149))
(step t409.t10.t151 (cl @p_533) :rule evaluate)
(step t409.t10.t152 (cl @p_530) :rule resolution :premises (t409.t10.t150 t409.t10.t151))
(step t409.t10.t153 (cl (not @p_1321) @p_1220 @p_1319) :rule equiv_pos2)
(step t409.t10.t154 (cl (= (* 1/1 (- @p_1285 0/1)) @p_899)) :rule poly_simp)
(step t409.t10.t155 (cl (= @p_1319 @p_893)) :rule poly_simp_rel :premises (t409.t10.t154))
(step t409.t10.t156 (cl @p_1321) :rule symm :premises (t409.t10.t155))
(step t409.t10.t157 (cl (not @p_898) (not @p_897) @p_894) :rule equiv_pos2)
(step t409.t10.t158 (cl (= (* 1/1 (- @p_890 @p_895)) @p_899)) :rule poly_simp)
(step t409.t10.t159 (cl (= @p_896 @p_893)) :rule poly_simp_rel :premises (t409.t10.t158))
(step t409.t10.t160 (cl @p_898) :rule cong :premises (t409.t10.t159))
(step t409.t10.t161 (cl @p_897 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t409.t10.t162)
(assume t409.t10.t162.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))))
(step t409.t10.t162.t0 (cl (or @p_326 @p_896)) :rule forall_inst :args (@p_1 @p_1))
(step t409.t10.t162.t1 (cl @p_326 @p_896) :rule or :premises (t409.t10.t162.t0))
(step t409.t10.t162.t2 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t409.t10.t162.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t409.t10.t162.t3.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t409.t10.t162.t3.t1 (cl @p_22) :rule refl)
(step t409.t10.t162.t3.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t409.t10.t162.t3.t0 t409.t10.t162.t3.t1))
(step t409.t10.t162.t3.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t409.t10.t162.t3.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t409.t10.t162.t3.t2 t409.t10.t162.t3.t3))
(step t409.t10.t162.t3.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t409.t10.t162.t3.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t409.t10.t162.t3.t5))
(step t409.t10.t162.t3.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t409.t10.t162.t3.t4 t409.t10.t162.t3.t6))
(step t409.t10.t162.t3 (cl @p_316) :rule bind)
(step t409.t10.t162.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t409.t10.t162.t2 t409.t10.t162.t3 a16))
(step t409.t10.t162.t5 (cl @p_896) :rule resolution :premises (t409.t10.t162.t1 t409.t10.t162.t4))
(step t409.t10.t162 (cl @p_326 @p_896) :rule subproof :discharge (t409.t10.t162.a0))
(step t409.t10.t163 (cl @p_897 @p_896) :rule resolution :premises (t409.t10.t161 t409.t10.t162))
(step t409.t10.t164 (cl @p_897 (not @p_896)) :rule implies_neg2)
(step t409.t10.t165 (cl @p_897 @p_897) :rule resolution :premises (t409.t10.t163 t409.t10.t164))
(step t409.t10.t166 (cl @p_897) :rule contraction :premises (t409.t10.t165))
(step t409.t10.t167 (cl @p_894) :rule resolution :premises (t409.t10.t157 t409.t10.t160 t409.t10.t166))
(step t409.t10.t168 (cl @p_326 @p_893) :rule implies :premises (t409.t10.t167))
(step t409.t10.t169 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t409.t10.t170 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t409.t10.t170.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t409.t10.t170.t1 (cl @p_22) :rule refl)
(step t409.t10.t170.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t409.t10.t170.t0 t409.t10.t170.t1))
(step t409.t10.t170.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t409.t10.t170.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t409.t10.t170.t2 t409.t10.t170.t3))
(step t409.t10.t170.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t409.t10.t170.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t409.t10.t170.t5))
(step t409.t10.t170.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t409.t10.t170.t4 t409.t10.t170.t6))
(step t409.t10.t170 (cl @p_316) :rule bind)
(step t409.t10.t171 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t409.t10.t169 t409.t10.t170 a16))
(step t409.t10.t172 (cl @p_893) :rule resolution :premises (t409.t10.t168 t409.t10.t171))
(step t409.t10.t173 (cl @p_1319) :rule resolution :premises (t409.t10.t153 t409.t10.t156 t409.t10.t172))
(step t409.t10.t174 (cl @p_1320) :rule and_intro :premises (t409.t10.t152 t409.t10.t173))
(step t409.t10.t175 (cl @p_1318) :rule resolution :premises (t409.t10.t148 t409.t10.t174))
(step t409.t10.t176 (cl (=> (! (and @p_530 @p_1315) :named @p_1316) @p_1314)) :rule la_mult_neg)
(step t409.t10.t177 (cl (not @p_1316) @p_1314) :rule implies :premises (t409.t10.t176))
(step t409.t10.t178 (cl (not @p_1317) @p_1204 @p_1315) :rule equiv_pos2)
(step t409.t10.t179 (cl (= (* 1/1 (- @p_1283 0/1)) (* 1/1 @p_1087))) :rule poly_simp)
(step t409.t10.t180 (cl (= @p_1315 @p_1081)) :rule poly_simp_rel :premises (t409.t10.t179))
(step t409.t10.t181 (cl @p_1317) :rule symm :premises (t409.t10.t180))
(step t409.t10.t182 (cl (not @p_1086) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t409.t10.t183 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t409.t10.t184 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t409.t10.t183))
(step t409.t10.t185 (cl @p_1086) :rule cong :premises (t409.t10.t184))
(step t409.t10.t186 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t409.t10.t187)
(assume t409.t10.t187.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t409.t10.t187.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t409.t10.t187.t1 (cl @p_279 @p_1084) :rule or :premises (t409.t10.t187.t0))
(step t409.t10.t187.t2 (cl @p_1084) :rule resolution :premises (t409.t10.t187.t1 t409.t10.t187.a0))
(step t409.t10.t187 (cl @p_279 @p_1084) :rule subproof :discharge (t409.t10.t187.a0))
(step t409.t10.t188 (cl @p_1085 @p_1084) :rule resolution :premises (t409.t10.t186 t409.t10.t187))
(step t409.t10.t189 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t409.t10.t190 (cl @p_1085 @p_1085) :rule resolution :premises (t409.t10.t188 t409.t10.t189))
(step t409.t10.t191 (cl @p_1085) :rule contraction :premises (t409.t10.t190))
(step t409.t10.t192 (cl @p_1082) :rule resolution :premises (t409.t10.t182 t409.t10.t185 t409.t10.t191))
(step t409.t10.t193 (cl @p_279 @p_1081) :rule implies :premises (t409.t10.t192))
(step t409.t10.t194 (cl @p_1081) :rule resolution :premises (t409.t10.t193 a1))
(step t409.t10.t195 (cl @p_1315) :rule resolution :premises (t409.t10.t178 t409.t10.t181 t409.t10.t194))
(step t409.t10.t196 (cl @p_1316) :rule and_intro :premises (t409.t10.t152 t409.t10.t195))
(step t409.t10.t197 (cl @p_1314) :rule resolution :premises (t409.t10.t177 t409.t10.t196))
(step t409.t10.t198 (cl @p_1313 @p_1270 @p_1308) :rule equiv_pos2)
(step t409.t10.t199 (cl (= (* 2/1 (- @p_1052 @p_1056)) (* -1/1 @p_1312))) :rule poly_simp)
(step t409.t10.t200 (cl (= @p_1262 @p_1311)) :rule poly_simp_rel :premises (t409.t10.t199))
(step t409.t10.t201 (cl (= (* 2/1 (- @p_1282 0/1)) (* 2/1 @p_1312))) :rule poly_simp)
(step t409.t10.t202 (cl (= @p_1308 @p_1311)) :rule poly_simp_rel :premises (t409.t10.t201))
(step t409.t10.t203 (cl (= @p_1311 @p_1308)) :rule symm :premises (t409.t10.t202))
(step t409.t10.t204 (cl @p_1309) :rule trans :premises (t409.t10.t200 t409.t10.t203))
(step t409.t10.t205 (cl (or @p_326 @p_1054)) :rule forall_inst :args (@p_1 @p_18))
(step t409.t10.t206 (cl @p_326 @p_1054) :rule or :premises (t409.t10.t205))
(step t409.t10.t207 (cl @p_1054) :rule resolution :premises (t409.t10.t206 t409.t10.t171))
(step t409.t10.t208 (cl (= @p_1052 @p_1053)) :rule symm :premises (t409.t10.t207))
(step t409.t10.t209 (cl (not @p_1063) (not @p_1062) @p_1058) :rule equiv_pos2)
(step t409.t10.t210 (cl (= @p_1060 @p_1055)) :rule cong :premises (t409.t10.t127 t409.t10.t90))
(step t409.t10.t211 (cl (= @p_1059 @p_1064)) :rule poly_simp)
(step t409.t10.t212 (cl (= @p_1061 @p_1065)) :rule cong :premises (t409.t10.t210 t409.t10.t211))
(step t409.t10.t213 (cl (= (* 1/1 (- @p_1055 @p_1064)) (* -2/1 (- @p_1053 @p_1056)))) :rule poly_simp)
(step t409.t10.t214 (cl (= @p_1065 @p_1057)) :rule poly_simp_rel :premises (t409.t10.t213))
(step t409.t10.t215 (cl (= @p_1061 @p_1057)) :rule trans :premises (t409.t10.t212 t409.t10.t214))
(step t409.t10.t216 (cl @p_1063) :rule cong :premises (t409.t10.t215))
(step t409.t10.t217 (cl @p_1062 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t409.t10.t218)
(assume t409.t10.t218.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t409.t10.t218.t0 (cl (or @p_279 @p_1061)) :rule forall_inst :args (@p_1 @p_1 @p_18))
(step t409.t10.t218.t1 (cl @p_279 @p_1061) :rule or :premises (t409.t10.t218.t0))
(step t409.t10.t218.t2 (cl @p_1061) :rule resolution :premises (t409.t10.t218.t1 t409.t10.t218.a0))
(step t409.t10.t218 (cl @p_279 @p_1061) :rule subproof :discharge (t409.t10.t218.a0))
(step t409.t10.t219 (cl @p_1062 @p_1061) :rule resolution :premises (t409.t10.t217 t409.t10.t218))
(step t409.t10.t220 (cl @p_1062 (not @p_1061)) :rule implies_neg2)
(step t409.t10.t221 (cl @p_1062 @p_1062) :rule resolution :premises (t409.t10.t219 t409.t10.t220))
(step t409.t10.t222 (cl @p_1062) :rule contraction :premises (t409.t10.t221))
(step t409.t10.t223 (cl @p_1058) :rule resolution :premises (t409.t10.t209 t409.t10.t216 t409.t10.t222))
(step t409.t10.t224 (cl @p_279 @p_1057) :rule implies :premises (t409.t10.t223))
(step t409.t10.t225 (cl @p_1057) :rule resolution :premises (t409.t10.t224 a1))
(step t409.t10.t226 (cl @p_1262) :rule trans :premises (t409.t10.t208 t409.t10.t225))
(step t409.t10.t227 (cl @p_1308) :rule resolution :premises (t409.t10.t198 t409.t10.t204 t409.t10.t226))
(step t409.t10.t228 (cl (=> (! (and @p_512 (! (= @p_1279 0/1) :named @p_1302)) :named @p_1303) @p_1301)) :rule la_mult_pos)
(step t409.t10.t229 (cl (not @p_1303) @p_1301) :rule implies :premises (t409.t10.t228))
(step t409.t10.t230 (cl (not (! (= @p_1263 @p_1302) :named @p_1304)) @p_1269 @p_1302) :rule equiv_pos2)
(step t409.t10.t231 (cl (= (* 1/1 (- @p_892 @p_1080)) (! (* 1/1 (- @p_936 (! (+ @p_895 @p_680) :named @p_1305))) :named @p_1307))) :rule poly_simp)
(step t409.t10.t232 (cl (= @p_1263 (! (= @p_936 @p_1305) :named @p_1306))) :rule poly_simp_rel :premises (t409.t10.t231))
(step t409.t10.t233 (cl (= (* 1/1 (- @p_1279 0/1)) @p_1307)) :rule poly_simp)
(step t409.t10.t234 (cl (= @p_1302 @p_1306)) :rule poly_simp_rel :premises (t409.t10.t233))
(step t409.t10.t235 (cl (= @p_1306 @p_1302)) :rule symm :premises (t409.t10.t234))
(step t409.t10.t236 (cl @p_1304) :rule trans :premises (t409.t10.t232 t409.t10.t235))
(step t409.t10.t237 (cl @p_1302) :rule resolution :premises (t409.t10.t230 t409.t10.t236 t409.a2))
(step t409.t10.t238 (cl @p_1303) :rule and_intro :premises (t409.t10.t121 t409.t10.t237))
(step t409.t10.t239 (cl @p_1301) :rule resolution :premises (t409.t10.t229 t409.t10.t238))
(step t409.t10.t240 (cl @p_244) :rule symm :premises (t409.a1))
(step t409.t10.t241 (cl (not @p_1300) @p_1209 @p_1299) :rule equiv_pos2)
(step t409.t10.t242 (cl (= (* 1/1 (- @p_1277 0/1)) @p_229)) :rule poly_simp)
(step t409.t10.t243 (cl (= @p_1299 @p_210)) :rule poly_simp_rel :premises (t409.t10.t242))
(step t409.t10.t244 (cl @p_1300) :rule symm :premises (t409.t10.t243))
(step t409.t10.t245 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t409.t10.t246 (cl (= @p_222 @p_33)) :rule cong :premises (t409.t10.t58))
(step t409.t10.t247 (cl (= @p_223 @p_227)) :rule cong :premises (t409.t10.t246))
(step t409.t10.t248 (cl (= @p_224 @p_228)) :rule cong :premises (t409.t10.t247))
(step t409.t10.t249 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t409.t10.t250 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t409.t10.t249))
(step t409.t10.t251 (cl (= @p_224 @p_210)) :rule trans :premises (t409.t10.t248 t409.t10.t250))
(step t409.t10.t252 (cl @p_226) :rule cong :premises (t409.t10.t251))
(step t409.t10.t253 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t409.t10.t254)
(assume t409.t10.t254.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t409.t10.t254.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t409.t10.t254.t1 (cl @p_219 @p_224) :rule or :premises (t409.t10.t254.t0))
(step t409.t10.t254.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t409.t10.t254.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t409.t10.t254.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t409.t10.t254.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t409.t10.t254.t3.t0))
(step t409.t10.t254.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t409.t10.t254.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t409.t10.t254.t3.t1 t409.t10.t254.t3.t2))
(step t409.t10.t254.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t409.t10.t254.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t409.t10.t254.t3.t4))
(step t409.t10.t254.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t409.t10.t254.t3.t3 t409.t10.t254.t3.t5))
(step t409.t10.t254.t3 (cl @p_211) :rule bind)
(step t409.t10.t254.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t409.t10.t254.t2 t409.t10.t254.t3 a24))
(step t409.t10.t254.t5 (cl @p_224) :rule resolution :premises (t409.t10.t254.t1 t409.t10.t254.t4))
(step t409.t10.t254 (cl @p_219 @p_224) :rule subproof :discharge (t409.t10.t254.a0))
(step t409.t10.t255 (cl @p_225 @p_224) :rule resolution :premises (t409.t10.t253 t409.t10.t254))
(step t409.t10.t256 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t409.t10.t257 (cl @p_225 @p_225) :rule resolution :premises (t409.t10.t255 t409.t10.t256))
(step t409.t10.t258 (cl @p_225) :rule contraction :premises (t409.t10.t257))
(step t409.t10.t259 (cl @p_220) :rule resolution :premises (t409.t10.t245 t409.t10.t252 t409.t10.t258))
(step t409.t10.t260 (cl @p_219 @p_210) :rule implies :premises (t409.t10.t259))
(step t409.t10.t261 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t409.t10.t262 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t409.t10.t262.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t409.t10.t262.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t409.t10.t262.t0))
(step t409.t10.t262.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t409.t10.t262.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t409.t10.t262.t1 t409.t10.t262.t2))
(step t409.t10.t262.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t409.t10.t262.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t409.t10.t262.t4))
(step t409.t10.t262.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t409.t10.t262.t3 t409.t10.t262.t5))
(step t409.t10.t262 (cl @p_211) :rule bind)
(step t409.t10.t263 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t409.t10.t261 t409.t10.t262 a24))
(step t409.t10.t264 (cl @p_210) :rule resolution :premises (t409.t10.t260 t409.t10.t263))
(step t409.t10.t265 (cl @p_1299) :rule resolution :premises (t409.t10.t241 t409.t10.t244 t409.t10.t264))
(step t409.t10.t266 (cl @p_1298) :rule resolution :premises (t409.t10.t39 t409.t10.t43 t409.t10.t50 t409.t10.t77 t409.t10.t81 t409.t10.t109 t409.t10.t114 t409.t10.t115 t409.t10.t146 t409.t10.t175 t409.t10.t197 t409.t10.t227 t409.t10.t239 t409.t10.t240 t409.t10.t265))
(step t409.t10.t267 (cl false) :rule resolution :premises (t409.t10.t0 t409.t10.t38 t409.t10.t266))
(step t409.t10 (cl @p_1274 false) :rule subproof :discharge (t409.t10.a0))
(step t409.t11 (cl @p_1275 false) :rule resolution :premises (t409.t9 t409.t10))
(step t409.t12 (cl @p_1275 @p_133) :rule implies_neg2)
(step t409.t13 (cl @p_1275 @p_1275) :rule resolution :premises (t409.t11 t409.t12))
(step t409.t14 (cl @p_1275) :rule contraction :premises (t409.t13))
(step t409.t15 (cl (= @p_1275 @p_1274)) :rule implies_simplify)
(step t409.t16 (cl (not @p_1275) @p_1274) :rule equiv1 :premises (t409.t15))
(step t409.t17 (cl @p_1274) :rule resolution :premises (t409.t14 t409.t16))
(step t409.t18 (cl @p_141) :rule resolution :premises (t409.t8 t409.t6 t409.t17))
(step t409.t19 (cl @p_1274) :rule resolution :premises (t409.t4 t409.t7 t409.t18))
(step t409.t20 (cl) :rule resolution :premises (t409.t3 t409.t19))
(step t409 (cl @p_1209 @p_1268 @p_1269 @p_1270 @p_1204 @p_1220 @p_1219 @p_1271 @p_1272 @p_1205 @p_15 @p_1210 @p_1193 @p_163 false) :rule subproof :discharge (t409.a0 t409.a1 t409.a2 t409.a3 t409.a4 t409.a5 t409.a6 t409.a7 t409.a8 t409.a9 t409.a10 t409.a11 t409.a12 t409.a13))
(step t410 (cl @p_1266 @p_210) :rule and_pos :args (0))
(step t411 (cl @p_1266 @p_1264) :rule and_pos :args (1))
(step t412 (cl @p_1266 @p_1263) :rule and_pos :args (2))
(step t413 (cl @p_1266 @p_1262) :rule and_pos :args (3))
(step t414 (cl @p_1266 @p_1081) :rule and_pos :args (4))
(step t415 (cl @p_1266 @p_893) :rule and_pos :args (5))
(step t416 (cl @p_1266 @p_902) :rule and_pos :args (6))
(step t417 (cl @p_1266 @p_1261) :rule and_pos :args (7))
(step t418 (cl @p_1266 @p_1260) :rule and_pos :args (8))
(step t419 (cl @p_1266 @p_1069) :rule and_pos :args (9))
(step t420 (cl @p_1266 @p_13) :rule and_pos :args (10))
(step t421 (cl @p_1266 @p_231) :rule and_pos :args (11))
(step t422 (cl @p_1266 @p_36) :rule and_pos :args (12))
(step t423 (cl @p_1266 @p_142) :rule and_pos :args (13))
(step t424 (cl false @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266) :rule resolution :premises (t409 t410 t411 t412 t413 t414 t415 t416 t417 t418 t419 t420 t421 t422 t423))
(step t425 (cl @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 @p_1266 false) :rule reordering :premises (t424))
(step t426 (cl @p_1266 false) :rule contraction :premises (t425))
(step t427 (cl @p_1267 false) :rule resolution :premises (t408 t426))
(step t428 (cl @p_1267 @p_133) :rule implies_neg2)
(step t429 (cl @p_1267 @p_1267) :rule resolution :premises (t427 t428))
(step t430 (cl @p_1267) :rule contraction :premises (t429))
(step t431 (cl (= @p_1267 @p_1266)) :rule implies_simplify)
(step t432 (cl (not @p_1267) @p_1266) :rule equiv1 :premises (t431))
(step t433 (cl @p_1266) :rule resolution :premises (t430 t432))
(step t434 (cl @p_1259) :rule resolution :premises (t407 t433))
(step t435 (cl @p_163 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_1194 @p_1195 @p_574 @p_1113 @p_1135 @p_1196 @p_1197 @p_427 @p_1198 @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1200 @p_1201 @p_434 @p_1202 @p_1203 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_1211 @p_437 @p_1212 @p_438 @p_1213 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_1218 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1224 @p_1225 @p_1226 @p_1227 @p_1228 @p_1229) :rule not_and :premises (t434))
(step t436 (cl @p_1231 @p_166) :rule or_neg :args (0))
(step t437 (cl @p_1231 @p_16) :rule or_neg :args (1))
(step t438 (cl @p_1231 @p_469) :rule or_neg :args (2))
(step t439 (cl @p_1231 @p_1257) :rule or_neg :args (3))
(step t440 (cl @p_1231 @p_1256) :rule or_neg :args (4))
(step t441 (cl @p_1231 @p_1255) :rule or_neg :args (5))
(step t442 (cl @p_1231 (not @p_1194)) :rule or_neg :args (6))
(step t443 (cl @p_1231 (not @p_1195)) :rule or_neg :args (7))
(step t444 (cl @p_1231 @p_575) :rule or_neg :args (8))
(step t445 (cl @p_1231 @p_1254) :rule or_neg :args (9))
(step t446 (cl @p_1231 (not @p_1135)) :rule or_neg :args (10))
(step t447 (cl @p_1231 (not @p_1196)) :rule or_neg :args (11))
(step t448 (cl @p_1231 (not @p_1197)) :rule or_neg :args (12))
(step t449 (cl @p_1231 @p_466) :rule or_neg :args (13))
(step t450 (cl @p_1231 (not @p_1198)) :rule or_neg :args (14))
(step t451 (cl @p_1231 @p_1253) :rule or_neg :args (15))
(step t452 (cl @p_1231 @p_1252) :rule or_neg :args (16))
(step t453 (cl @p_1231 @p_465) :rule or_neg :args (17))
(step t454 (cl @p_1231 @p_464) :rule or_neg :args (18))
(step t455 (cl @p_1231 @p_463) :rule or_neg :args (19))
(step t456 (cl @p_1231 @p_462) :rule or_neg :args (20))
(step t457 (cl @p_1231 @p_461) :rule or_neg :args (21))
(step t458 (cl @p_1231 @p_460) :rule or_neg :args (22))
(step t459 (cl @p_1231 (not @p_1200)) :rule or_neg :args (23))
(step t460 (cl @p_1231 @p_1251) :rule or_neg :args (24))
(step t461 (cl @p_1231 @p_459) :rule or_neg :args (25))
(step t462 (cl @p_1231 @p_1250) :rule or_neg :args (26))
(step t463 (cl @p_1231 (not @p_1203)) :rule or_neg :args (27))
(step t464 (cl @p_1231 @p_1249) :rule or_neg :args (28))
(step t465 (cl @p_1231 @p_1248) :rule or_neg :args (29))
(step t466 (cl @p_1231 @p_1247) :rule or_neg :args (30))
(step t467 (cl @p_1231 @p_1246) :rule or_neg :args (31))
(step t468 (cl @p_1231 @p_1245) :rule or_neg :args (32))
(step t469 (cl @p_1231 @p_1244) :rule or_neg :args (33))
(step t470 (cl @p_1231 @p_1243) :rule or_neg :args (34))
(step t471 (cl @p_1231 @p_1242) :rule or_neg :args (35))
(step t472 (cl @p_1231 @p_456) :rule or_neg :args (36))
(step t473 (cl @p_1231 (not @p_1212)) :rule or_neg :args (37))
(step t474 (cl @p_1231 @p_455) :rule or_neg :args (38))
(step t475 (cl @p_1231 (not @p_1213)) :rule or_neg :args (39))
(step t476 (cl @p_1231 @p_1241) :rule or_neg :args (40))
(step t477 (cl @p_1231 @p_1240) :rule or_neg :args (41))
(step t478 (cl @p_1231 @p_1239) :rule or_neg :args (42))
(step t479 (cl @p_1231 @p_1238) :rule or_neg :args (43))
(step t480 (cl @p_1231 @p_452) :rule or_neg :args (44))
(step t481 (cl @p_1231 (not @p_1218)) :rule or_neg :args (45))
(step t482 (cl @p_1231 @p_451) :rule or_neg :args (46))
(step t483 (cl @p_1231 @p_1237) :rule or_neg :args (47))
(step t484 (cl @p_1231 @p_1236) :rule or_neg :args (48))
(step t485 (cl @p_1231 @p_1235) :rule or_neg :args (49))
(step t486 (cl @p_1231 @p_1234) :rule or_neg :args (50))
(step t487 (cl @p_1231 @p_1233) :rule or_neg :args (51))
(step t488 (cl @p_1231 (not @p_1224)) :rule or_neg :args (52))
(step t489 (cl @p_1231 (not @p_1225)) :rule or_neg :args (53))
(step t490 (cl @p_1231 @p_1232) :rule or_neg :args (54))
(step t491 (cl @p_1231 (not @p_1227)) :rule or_neg :args (55))
(step t492 (cl @p_1231 (not @p_1228)) :rule or_neg :args (56))
(step t493 (cl @p_1231 (not @p_1229)) :rule or_neg :args (57))
(step t494 (cl @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231 @p_1231) :rule resolution :premises (t435 t436 t437 t438 t439 t440 t441 t442 t443 t444 t445 t446 t447 t448 t449 t450 t451 t452 t453 t454 t455 t456 t457 t458 t459 t460 t461 t462 t463 t464 t465 t466 t467 t468 t469 t470 t471 t472 t473 t474 t475 t476 t477 t478 t479 t480 t481 t482 t483 t484 t485 t486 t487 t488 t489 t490 t491 t492 t493))
(step t495 (cl @p_1231) :rule contraction :premises (t494))
(step t496 (cl @p_1230) :rule resolution :premises (t322 t339 t495))
(step t497 (cl @p_141 @p_15 @p_424 @p_1191 @p_1192 @p_1193 @p_1194 @p_1195 @p_574 @p_1113 @p_1135 @p_1196 @p_1197 @p_427 @p_1198 @p_1042 @p_1199 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_1200 @p_1201 @p_434 @p_1202 @p_1203 @p_1204 @p_1205 @p_1206 @p_1207 @p_1208 @p_1209 @p_1210 @p_1211 @p_437 @p_1212 @p_438 @p_1213 @p_1214 @p_1215 @p_1216 @p_1217 @p_441 @p_1218 @p_442 @p_1219 @p_1220 @p_1221 @p_1222 @p_1223 @p_1224 @p_1225 @p_1226 @p_1227 @p_1228 @p_1229) :rule or :premises (t496))
(step t498 (cl (or @p_343 @p_1187)) :rule forall_inst :args (@p_6 1/1 2/1))
(step t499 (cl @p_343 @p_1187) :rule or :premises (t498))
(step t500 (cl @p_1187) :rule resolution :premises (t499 a2))
(step t501 (cl (or @p_343 @p_1185)) :rule forall_inst :args (1/1 1/1 @p_4))
(step t502 (cl @p_343 @p_1185) :rule or :premises (t501))
(step t503 (cl @p_1185) :rule resolution :premises (t502 a2))
(step t504 (cl (not (! (= (! (or (! (not (! (= @p_6 (! (* 1/2 @p_248) :named @p_412)) :named @p_413)) :named @p_423) @p_424 (! (not (! (= @p_6 (! (* -1/1 (! (times$a @p_139 @p_4) :named @p_274)) :named @p_408)) :named @p_409)) :named @p_425) (! (not (! (= @p_274 (! (times$a @p_4 @p_139) :named @p_268)) :named @p_407)) :named @p_426) @p_427 @p_575 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 (! (not @p_329) :named @p_435) (! (not (! (= @p_314 (! (* -1/1 (! (times$a @p_139 @p_296) :named @p_298)) :named @p_313)) :named @p_315)) :named @p_436) @p_437 @p_438 (! (not (! (= (! (times$a @p_301 @p_139) :named @p_302) (! (times$a 1/1 @p_268) :named @p_300)) :named @p_303)) :named @p_439) (! (not (! (= @p_298 (! (times$a @p_296 @p_139) :named @p_297)) :named @p_299)) :named @p_440) @p_441 @p_442 (! (not (! (= (! (times$a 1/1 @p_274) :named @p_277) (! (* 1/2 (! (times$a 2/1 @p_274) :named @p_275)) :named @p_276)) :named @p_278)) :named @p_443) (! (not (! (= (! (times$a @p_270 @p_139) :named @p_271) (! (times$a 2/1 @p_268) :named @p_269)) :named @p_272)) :named @p_444) (! (not (! (>= (! (+ (! (* -1/1 @p_4) :named @p_71) @p_248) :named @p_266) 0/1) :named @p_267)) :named @p_446)) :named @p_576) (! (or @p_423 @p_424 @p_425 @p_426 @p_427 @p_249 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_446) :named @p_573)) :named @p_622)) (not @p_576) @p_573) :rule equiv_pos2)
(step t505 (cl (= @p_575 @p_249)) :rule rare_rewrite :args ("bool-double-not-elim" @p_249))
(step t506 (cl (= @p_435 @p_435)) :rule refl)
(step t507 (cl (= @p_436 @p_436)) :rule refl)
(step t508 (cl (= @p_439 @p_439)) :rule refl)
(step t509 (cl (= @p_440 @p_440)) :rule refl)
(step t510 (cl (= @p_443 @p_443)) :rule refl)
(step t511 (cl (= @p_444 @p_444)) :rule refl)
(step t512 (cl (= @p_446 @p_446)) :rule refl)
(step t513 (cl @p_622) :rule cong :premises (t505 t82 t83 t84 t85 t86 t87 t89 t506 t507 t101 t102 t508 t509 t107 t108 t510 t511 t512))
(step t514 (cl (! (=> (! (and @p_413 @p_410 @p_409 @p_407 @p_406 @p_574 @p_405 @p_396 @p_385 @p_364 @p_344 @p_342 @p_340 @p_329 @p_315 @p_311 @p_305 @p_303 @p_299 @p_295 @p_291 @p_278 @p_272 @p_267) :named @p_577) (! (and @p_413 (! (= @p_298 @p_275) :named @p_476) (! (= @p_274 @p_276) :named @p_475) @p_409 (! (= @p_328 @p_313) :named @p_474) @p_473 @p_574 @p_267) :named @p_579)) :named @p_621) @p_577) :rule implies_neg1)
(anchor :step t515)
(assume t515.a0 @p_413)
(assume t515.a1 @p_410)
(assume t515.a2 @p_409)
(assume t515.a3 @p_407)
(assume t515.a4 @p_406)
(assume t515.a5 @p_574)
(assume t515.a6 @p_405)
(assume t515.a7 @p_396)
(assume t515.a8 @p_385)
(assume t515.a9 @p_364)
(assume t515.a10 @p_344)
(assume t515.a11 @p_342)
(assume t515.a12 @p_340)
(assume t515.a13 @p_329)
(assume t515.a14 @p_315)
(assume t515.a15 @p_311)
(assume t515.a16 @p_305)
(assume t515.a17 @p_303)
(assume t515.a18 @p_299)
(assume t515.a19 @p_295)
(assume t515.a20 @p_291)
(assume t515.a21 @p_278)
(assume t515.a22 @p_272)
(assume t515.a23 @p_267)
(step t515.t0 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a @p_332 @p_4) :named @p_416) (! (+ @p_6 @p_6) :named @p_415)) :named @p_417)) :named @p_418) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_413) :named @p_414)) :named @p_419)) (not @p_418) @p_414) :rule equiv_pos2)
(step t515.t1 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t515.t2 (cl (= @p_4 @p_4)) :rule refl)
(step t515.t3 (cl (= @p_416 @p_248)) :rule cong :premises (t515.t1 t515.t2))
(step t515.t4 (cl (= @p_415 (! (* 2/1 @p_6) :named @p_420))) :rule poly_simp)
(step t515.t5 (cl (= @p_417 (! (= @p_248 @p_420) :named @p_421))) :rule cong :premises (t515.t3 t515.t4))
(step t515.t6 (cl (= (* 1/1 (- @p_248 @p_420)) (* -2/1 (! (- @p_6 @p_412) :named @p_422)))) :rule poly_simp)
(step t515.t7 (cl (= @p_421 @p_413)) :rule poly_simp_rel :premises (t515.t6))
(step t515.t8 (cl (= @p_417 @p_413)) :rule trans :premises (t515.t5 t515.t7))
(step t515.t9 (cl @p_419) :rule cong :premises (t515.t8))
(step t515.t10 (cl @p_418 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t515.t11)
(assume t515.t11.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t515.t11.t0 (cl (or @p_279 @p_417)) :rule forall_inst :args (@p_1 @p_1 @p_4))
(step t515.t11.t1 (cl @p_279 @p_417) :rule or :premises (t515.t11.t0))
(step t515.t11.t2 (cl @p_417) :rule resolution :premises (t515.t11.t1 t515.t11.a0))
(step t515.t11 (cl @p_279 @p_417) :rule subproof :discharge (t515.t11.a0))
(step t515.t12 (cl @p_418 @p_417) :rule resolution :premises (t515.t10 t515.t11))
(step t515.t13 (cl @p_418 (not @p_417)) :rule implies_neg2)
(step t515.t14 (cl @p_418 @p_418) :rule resolution :premises (t515.t12 t515.t13))
(step t515.t15 (cl @p_418) :rule contraction :premises (t515.t14))
(step t515.t16 (cl @p_414) :rule resolution :premises (t515.t0 t515.t9 t515.t15))
(step t515.t17 (cl @p_279 @p_413) :rule implies :premises (t515.t16))
(step t515.t18 (cl @p_413) :rule resolution :premises (t515.t17 a1))
(step t515.t19 (cl (or @p_292 @p_299)) :rule forall_inst :args (@p_139 @p_296))
(step t515.t20 (cl @p_292 @p_299) :rule or :premises (t515.t19))
(step t515.t21 (cl @p_299) :rule resolution :premises (t515.t20 a6))
(step t515.t22 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t515.t23 (cl @p_343 @p_342) :rule or :premises (t515.t22))
(step t515.t24 (cl @p_342) :rule resolution :premises (t515.t23 a2))
(step t515.t25 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t515.t26 (cl (= @p_126 false)) :rule evaluate)
(step t515.t27 (cl (= @p_388 true)) :rule evaluate)
(step t515.t28 (cl (= @p_389 @p_395)) :rule cong :premises (t515.t26 t515.t27))
(step t515.t29 (cl (= @p_395 true)) :rule evaluate)
(step t515.t30 (cl (= @p_389 true)) :rule trans :premises (t515.t28 t515.t29))
(step t515.t31 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t515.t32 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t515.t31))
(step t515.t33 (cl (= @p_390 @p_393)) :rule cong :premises (t515.t30 t515.t32))
(step t515.t34 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t515.t35 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t515.t36 (cl (= @p_393 @p_385)) :rule trans :premises (t515.t34 t515.t35))
(step t515.t37 (cl (= @p_390 @p_385)) :rule trans :premises (t515.t33 t515.t36))
(step t515.t38 (cl @p_392) :rule cong :premises (t515.t37))
(step t515.t39 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t515.t40)
(assume t515.t40.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t515.t40.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t515.t40.t1 (cl @p_258 @p_390) :rule or :premises (t515.t40.t0))
(step t515.t40.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t515.t40.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t40.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t515.t40.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t515.t40.t3.t0))
(step t515.t40.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t515.t40.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t515.t40.t3.t1 t515.t40.t3.t2))
(step t515.t40.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t515.t40.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t515.t40.t3.t3 t515.t40.t3.t4))
(step t515.t40.t3 (cl @p_251) :rule bind)
(step t515.t40.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t515.t40.t2 t515.t40.t3 a12))
(step t515.t40.t5 (cl @p_390) :rule resolution :premises (t515.t40.t1 t515.t40.t4))
(step t515.t40 (cl @p_258 @p_390) :rule subproof :discharge (t515.t40.a0))
(step t515.t41 (cl @p_391 @p_390) :rule resolution :premises (t515.t39 t515.t40))
(step t515.t42 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t515.t43 (cl @p_391 @p_391) :rule resolution :premises (t515.t41 t515.t42))
(step t515.t44 (cl @p_391) :rule contraction :premises (t515.t43))
(step t515.t45 (cl @p_386) :rule resolution :premises (t515.t25 t515.t38 t515.t44))
(step t515.t46 (cl @p_258 @p_385) :rule implies :premises (t515.t45))
(step t515.t47 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t515.t48 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t48.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t515.t48.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t515.t48.t0))
(step t515.t48.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t515.t48.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t515.t48.t1 t515.t48.t2))
(step t515.t48.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t515.t48.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t515.t48.t3 t515.t48.t4))
(step t515.t48 (cl @p_251) :rule bind)
(step t515.t49 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t515.t47 t515.t48 a12))
(step t515.t50 (cl @p_385) :rule resolution :premises (t515.t46 t515.t49))
(step t515.t51 (cl @p_387) :rule symm :premises (t515.t50))
(step t515.t52 (cl (= @p_304 @p_307)) :rule cong :premises (t515.t51))
(step t515.t53 (cl @p_388) :rule refl)
(step t515.t54 (cl (= @p_341 @p_308)) :rule cong :premises (t515.t52 t515.t53))
(step t515.t55 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t515.t56 (cl @p_312 @p_311) :rule or :premises (t515.t55))
(step t515.t57 (cl @p_311) :rule resolution :premises (t515.t56 a27))
(step t515.t58 (cl (= @p_308 @p_310)) :rule symm :premises (t515.t57))
(step t515.t59 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t515.t60 (cl (= @p_356 false)) :rule evaluate)
(step t515.t61 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t515.t62 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t515.t61))
(step t515.t63 (cl (= @p_357 @p_360)) :rule cong :premises (t515.t60 t515.t62))
(step t515.t64 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t515.t65 (cl (= @p_357 @p_344)) :rule trans :premises (t515.t63 t515.t64))
(step t515.t66 (cl @p_359) :rule cong :premises (t515.t65))
(step t515.t67 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t515.t68)
(assume t515.t68.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t515.t68.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t515.t68.t1 (cl @p_353 @p_357) :rule or :premises (t515.t68.t0))
(step t515.t68.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t515.t68.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t68.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t515.t68.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t515.t68.t3.t0))
(step t515.t68.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t515.t68.t3.t1))
(step t515.t68.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t515.t68.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t68.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t515.t68.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t515.t68.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t515.t68.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t515.t68.t4.t1 t515.t68.t4.t2))
(step t515.t68.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t515.t68.t4.t0 t515.t68.t4.t3))
(step t515.t68.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t515.t68.t5 (cl @p_345) :rule trans :premises (t515.t68.t3 t515.t68.t4))
(step t515.t68.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t515.t68.t2 t515.t68.t5 a19))
(step t515.t68.t7 (cl @p_357) :rule resolution :premises (t515.t68.t1 t515.t68.t6))
(step t515.t68 (cl @p_353 @p_357) :rule subproof :discharge (t515.t68.a0))
(step t515.t69 (cl @p_358 @p_357) :rule resolution :premises (t515.t67 t515.t68))
(step t515.t70 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t515.t71 (cl @p_358 @p_358) :rule resolution :premises (t515.t69 t515.t70))
(step t515.t72 (cl @p_358) :rule contraction :premises (t515.t71))
(step t515.t73 (cl @p_354) :rule resolution :premises (t515.t59 t515.t66 t515.t72))
(step t515.t74 (cl @p_353 @p_344) :rule implies :premises (t515.t73))
(step t515.t75 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t515.t76 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t76.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t515.t76.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t515.t76.t0))
(step t515.t76.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t515.t76.t1))
(step t515.t76 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t515.t77 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t77.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t515.t77.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t515.t77.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t515.t77.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t515.t77.t1 t515.t77.t2))
(step t515.t77.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t515.t77.t0 t515.t77.t3))
(step t515.t77 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t515.t78 (cl @p_345) :rule trans :premises (t515.t76 t515.t77))
(step t515.t79 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t515.t75 t515.t78 a19))
(step t515.t80 (cl @p_344) :rule resolution :premises (t515.t74 t515.t79))
(step t515.t81 (cl (= @p_310 @p_304)) :rule cong :premises (t515.t80))
(step t515.t82 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t515.t83 (cl @p_292 @p_305) :rule or :premises (t515.t82))
(step t515.t84 (cl @p_305) :rule resolution :premises (t515.t83 a6))
(step t515.t85 (cl (= @p_296 @p_270)) :rule trans :premises (t515.t24 t515.t54 t515.t58 t515.t81 t515.t84))
(step t515.t86 (cl (= @p_139 @p_139)) :rule refl)
(step t515.t87 (cl (= @p_297 @p_271)) :rule cong :premises (t515.t85 t515.t86))
(step t515.t88 (cl (or @p_273 @p_272)) :rule forall_inst :args (2/1 @p_4 @p_139))
(step t515.t89 (cl @p_273 @p_272) :rule or :premises (t515.t88))
(step t515.t90 (cl @p_272) :rule resolution :premises (t515.t89 a4))
(step t515.t91 (cl (or @p_292 @p_407)) :rule forall_inst :args (@p_139 @p_4))
(step t515.t92 (cl @p_292 @p_407) :rule or :premises (t515.t91))
(step t515.t93 (cl @p_407) :rule resolution :premises (t515.t92 a6))
(step t515.t94 (cl (= @p_268 @p_274)) :rule symm :premises (t515.t93))
(step t515.t95 (cl (= @p_269 @p_275)) :rule cong :premises (t515.t94))
(step t515.t96 (cl @p_476) :rule trans :premises (t515.t21 t515.t87 t515.t90 t515.t95))
(step t515.t97 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t515.t98 (cl (= @p_399 @p_404)) :rule cong :premises (t515.t27))
(step t515.t99 (cl (= @p_404 true)) :rule or_simplify)
(step t515.t100 (cl (= @p_399 true)) :rule trans :premises (t515.t98 t515.t99))
(step t515.t101 (cl (= @p_400 @p_403)) :rule cong :premises (t515.t100))
(step t515.t102 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t515.t103 (cl (= @p_400 @p_396)) :rule trans :premises (t515.t101 t515.t102))
(step t515.t104 (cl @p_402) :rule cong :premises (t515.t103))
(step t515.t105 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t515.t106)
(assume t515.t106.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t515.t106.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t515.t106.t1 (cl @p_397 @p_400) :rule or :premises (t515.t106.t0))
(step t515.t106.t2 (cl @p_400) :rule resolution :premises (t515.t106.t1 t515.t106.a0))
(step t515.t106 (cl @p_397 @p_400) :rule subproof :discharge (t515.t106.a0))
(step t515.t107 (cl @p_401 @p_400) :rule resolution :premises (t515.t105 t515.t106))
(step t515.t108 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t515.t109 (cl @p_401 @p_401) :rule resolution :premises (t515.t107 t515.t108))
(step t515.t110 (cl @p_401) :rule contraction :premises (t515.t109))
(step t515.t111 (cl @p_398) :rule resolution :premises (t515.t97 t515.t104 t515.t110))
(step t515.t112 (cl @p_397 @p_396) :rule implies :premises (t515.t111))
(step t515.t113 (cl @p_396) :rule resolution :premises (t515.t112 a8))
(step t515.t114 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t515.t115 (cl @p_292 @p_405) :rule or :premises (t515.t114))
(step t515.t116 (cl @p_405) :rule resolution :premises (t515.t115 a6))
(step t515.t117 (cl (= @p_361 @p_301)) :rule symm :premises (t515.t116))
(step t515.t118 (cl (= @p_4 @p_301)) :rule trans :premises (t515.t113 t515.t117))
(step t515.t119 (cl (= @p_268 @p_302)) :rule cong :premises (t515.t118 t515.t86))
(step t515.t120 (cl (or @p_273 @p_303)) :rule forall_inst :args (1/1 @p_4 @p_139))
(step t515.t121 (cl @p_273 @p_303) :rule or :premises (t515.t120))
(step t515.t122 (cl @p_303) :rule resolution :premises (t515.t121 a4))
(step t515.t123 (cl (= @p_300 @p_277)) :rule cong :premises (t515.t94))
(step t515.t124 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) (! (= (! (times$a (! (+ 1/1 1/1) :named @p_282) @p_274) :named @p_283) (! (+ @p_277 @p_277) :named @p_281)) :named @p_284)) :named @p_285) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))) @p_278) :named @p_280)) :named @p_286)) (not @p_285) @p_280) :rule equiv_pos2)
(step t515.t125 (cl (= @p_282 2/1)) :rule evaluate)
(step t515.t126 (cl (= @p_274 @p_274)) :rule refl)
(step t515.t127 (cl (= @p_283 @p_275)) :rule cong :premises (t515.t125 t515.t126))
(step t515.t128 (cl (= @p_281 (! (* 2/1 @p_277) :named @p_287))) :rule poly_simp)
(step t515.t129 (cl (= @p_284 (! (= @p_275 @p_287) :named @p_288))) :rule cong :premises (t515.t127 t515.t128))
(step t515.t130 (cl (= (* -1/2 (- @p_275 @p_287)) (* 1/1 (- @p_277 @p_276)))) :rule poly_simp)
(step t515.t131 (cl (= @p_288 @p_278)) :rule poly_simp_rel :premises (t515.t130))
(step t515.t132 (cl (= @p_284 @p_278)) :rule trans :premises (t515.t129 t515.t131))
(step t515.t133 (cl @p_286) :rule cong :premises (t515.t132))
(step t515.t134 (cl @p_285 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t515.t135)
(assume t515.t135.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t515.t135.t0 (cl (or @p_279 @p_284)) :rule forall_inst :args (1/1 1/1 @p_274))
(step t515.t135.t1 (cl @p_279 @p_284) :rule or :premises (t515.t135.t0))
(step t515.t135.t2 (cl @p_284) :rule resolution :premises (t515.t135.t1 t515.t135.a0))
(step t515.t135 (cl @p_279 @p_284) :rule subproof :discharge (t515.t135.a0))
(step t515.t136 (cl @p_285 @p_284) :rule resolution :premises (t515.t134 t515.t135))
(step t515.t137 (cl @p_285 (not @p_284)) :rule implies_neg2)
(step t515.t138 (cl @p_285 @p_285) :rule resolution :premises (t515.t136 t515.t137))
(step t515.t139 (cl @p_285) :rule contraction :premises (t515.t138))
(step t515.t140 (cl @p_280) :rule resolution :premises (t515.t124 t515.t133 t515.t139))
(step t515.t141 (cl @p_279 @p_278) :rule implies :premises (t515.t140))
(step t515.t142 (cl @p_278) :rule resolution :premises (t515.t141 a1))
(step t515.t143 (cl @p_475) :rule trans :premises (t515.t93 t515.t119 t515.t122 t515.t123 t515.t142))
(step t515.t144 (cl (or @p_326 @p_409)) :rule forall_inst :args (@p_1 @p_4))
(step t515.t145 (cl @p_326 @p_409) :rule or :premises (t515.t144))
(step t515.t146 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t515.t147 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t515.t147.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t515.t147.t1 (cl @p_22) :rule refl)
(step t515.t147.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t515.t147.t0 t515.t147.t1))
(step t515.t147.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t515.t147.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t515.t147.t2 t515.t147.t3))
(step t515.t147.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t515.t147.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t515.t147.t5))
(step t515.t147.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t515.t147.t4 t515.t147.t6))
(step t515.t147 (cl @p_316) :rule bind)
(step t515.t148 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t515.t146 t515.t147 a16))
(step t515.t149 (cl @p_409) :rule resolution :premises (t515.t145 t515.t148))
(step t515.t150 (cl (not @p_336) (not @p_335) @p_330) :rule equiv_pos2)
(step t515.t151 (cl (= @p_296 @p_296)) :rule refl)
(step t515.t152 (cl (= @p_333 @p_327)) :rule cong :premises (t515.t1 t515.t151))
(step t515.t153 (cl (= @p_331 @p_337)) :rule poly_simp)
(step t515.t154 (cl (= @p_334 @p_338)) :rule cong :premises (t515.t152 t515.t153))
(step t515.t155 (cl (= (* 1/1 (- @p_327 @p_337)) (* -2/1 (- @p_314 @p_328)))) :rule poly_simp)
(step t515.t156 (cl (= @p_338 @p_329)) :rule poly_simp_rel :premises (t515.t155))
(step t515.t157 (cl (= @p_334 @p_329)) :rule trans :premises (t515.t154 t515.t156))
(step t515.t158 (cl @p_336) :rule cong :premises (t515.t157))
(step t515.t159 (cl @p_335 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t515.t160)
(assume t515.t160.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t515.t160.t0 (cl (or @p_279 @p_334)) :rule forall_inst :args (@p_1 @p_1 @p_296))
(step t515.t160.t1 (cl @p_279 @p_334) :rule or :premises (t515.t160.t0))
(step t515.t160.t2 (cl @p_334) :rule resolution :premises (t515.t160.t1 t515.t160.a0))
(step t515.t160 (cl @p_279 @p_334) :rule subproof :discharge (t515.t160.a0))
(step t515.t161 (cl @p_335 @p_334) :rule resolution :premises (t515.t159 t515.t160))
(step t515.t162 (cl @p_335 (not @p_334)) :rule implies_neg2)
(step t515.t163 (cl @p_335 @p_335) :rule resolution :premises (t515.t161 t515.t162))
(step t515.t164 (cl @p_335) :rule contraction :premises (t515.t163))
(step t515.t165 (cl @p_330) :rule resolution :premises (t515.t150 t515.t158 t515.t164))
(step t515.t166 (cl @p_279 @p_329) :rule implies :premises (t515.t165))
(step t515.t167 (cl @p_329) :rule resolution :premises (t515.t166 a1))
(step t515.t168 (cl (= @p_328 @p_314)) :rule symm :premises (t515.t167))
(step t515.t169 (cl (or @p_326 @p_315)) :rule forall_inst :args (@p_1 @p_296))
(step t515.t170 (cl @p_326 @p_315) :rule or :premises (t515.t169))
(step t515.t171 (cl @p_315) :rule resolution :premises (t515.t170 t515.t148))
(step t515.t172 (cl @p_474) :rule trans :premises (t515.t168 t515.t171))
(step t515.t173 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t515.t174 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t515.t175 (cl (= @p_364 @p_364)) :rule refl)
(step t515.t176 (cl (= @p_378 @p_383)) :rule cong :premises (t515.t174 t515.t175))
(step t515.t177 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t515.t178 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t515.t179 (cl (= @p_383 @p_364)) :rule trans :premises (t515.t177 t515.t178))
(step t515.t180 (cl (= @p_378 @p_364)) :rule trans :premises (t515.t176 t515.t179))
(step t515.t181 (cl (= @p_379 @p_382)) :rule cong :premises (t515.t26 t515.t180))
(step t515.t182 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t515.t183 (cl (= @p_379 @p_364)) :rule trans :premises (t515.t181 t515.t182))
(step t515.t184 (cl @p_381) :rule cong :premises (t515.t183))
(step t515.t185 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t515.t186)
(assume t515.t186.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t515.t186.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t515.t186.t1 (cl @p_375 @p_379) :rule or :premises (t515.t186.t0))
(step t515.t186.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t515.t186.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t515.t186.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t515.t186.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t515.t186.t3.t0))
(step t515.t186.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t515.t186.t3.t1))
(step t515.t186.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t515.t186.t3.t2))
(step t515.t186.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t515.t186.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t515.t186.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t515.t186.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t515.t186.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t515.t186.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t515.t186.t4.t1 t515.t186.t4.t2))
(step t515.t186.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t515.t186.t4.t0 t515.t186.t4.t3))
(step t515.t186.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t515.t186.t5 (cl @p_365) :rule trans :premises (t515.t186.t3 t515.t186.t4))
(step t515.t186.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t515.t186.t2 t515.t186.t5 a17))
(step t515.t186.t7 (cl @p_379) :rule resolution :premises (t515.t186.t1 t515.t186.t6))
(step t515.t186 (cl @p_375 @p_379) :rule subproof :discharge (t515.t186.a0))
(step t515.t187 (cl @p_380 @p_379) :rule resolution :premises (t515.t185 t515.t186))
(step t515.t188 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t515.t189 (cl @p_380 @p_380) :rule resolution :premises (t515.t187 t515.t188))
(step t515.t190 (cl @p_380) :rule contraction :premises (t515.t189))
(step t515.t191 (cl @p_376) :rule resolution :premises (t515.t173 t515.t184 t515.t190))
(step t515.t192 (cl @p_375 @p_364) :rule implies :premises (t515.t191))
(step t515.t193 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t515.t194 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t515.t194.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t515.t194.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t515.t194.t0))
(step t515.t194.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t515.t194.t1))
(step t515.t194.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t515.t194.t2))
(step t515.t194 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t515.t195 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t515.t195.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t515.t195.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t515.t195.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t515.t195.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t515.t195.t1 t515.t195.t2))
(step t515.t195.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t515.t195.t0 t515.t195.t3))
(step t515.t195 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t515.t196 (cl @p_365) :rule trans :premises (t515.t194 t515.t195))
(step t515.t197 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t515.t193 t515.t196 a17))
(step t515.t198 (cl @p_364) :rule resolution :premises (t515.t192 t515.t197))
(step t515.t199 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t515.t200 (cl @p_312 @p_406) :rule or :premises (t515.t199))
(step t515.t201 (cl @p_406) :rule resolution :premises (t515.t200 a27))
(step t515.t202 (cl (= @p_362 @p_65)) :rule symm :premises (t515.t201))
(step t515.t203 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t515.t204 (cl (= @p_362 @p_6)) :rule trans :premises (t515.t202 t515.t203))
(step t515.t205 (cl (= 2/1 2/1)) :rule refl)
(step t515.t206 (cl (= @p_363 @p_290)) :rule cong :premises (t515.t204 t515.t205))
(step t515.t207 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t515.t208 (cl @p_292 @p_291) :rule or :premises (t515.t207))
(step t515.t209 (cl @p_291) :rule resolution :premises (t515.t208 a6))
(step t515.t210 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t515.t211 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t515.t212 (cl @p_273 @p_295) :rule or :premises (t515.t211))
(step t515.t213 (cl @p_295) :rule resolution :premises (t515.t212 a4))
(step t515.t214 (cl (= @p_293 @p_294)) :rule symm :premises (t515.t213))
(step t515.t215 (cl (= @p_270 @p_304)) :rule symm :premises (t515.t84))
(step t515.t216 (cl @p_355) :rule symm :premises (t515.t80))
(step t515.t217 (cl (= @p_304 @p_310)) :rule cong :premises (t515.t216))
(step t515.t218 (cl (= @p_307 @p_304)) :rule cong :premises (t515.t50))
(step t515.t219 (cl (= @p_308 @p_341)) :rule cong :premises (t515.t218 t515.t53))
(step t515.t220 (cl (= @p_341 @p_296)) :rule symm :premises (t515.t24))
(step t515.t221 (cl (= @p_270 @p_296)) :rule trans :premises (t515.t215 t515.t217 t515.t57 t515.t219 t515.t220))
(step t515.t222 (cl (= @p_1 @p_1)) :rule refl)
(step t515.t223 (cl (= @p_294 @p_339)) :rule cong :premises (t515.t221 t515.t222))
(step t515.t224 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t515.t225 (cl @p_292 @p_340) :rule or :premises (t515.t224))
(step t515.t226 (cl @p_340) :rule resolution :premises (t515.t225 a6))
(step t515.t227 (cl (= @p_339 @p_314)) :rule symm :premises (t515.t226))
(step t515.t228 (cl @p_473) :rule trans :premises (t515.t113 t515.t198 t515.t206 t515.t209 t515.t210 t515.t214 t515.t223 t515.t227 t515.t167))
(step t515.t229 (cl @p_579) :rule and_intro :premises (t515.t18 t515.t96 t515.t143 t515.t149 t515.t172 t515.t228 t515.a5 t515.a23))
(step t515 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_575 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_446 @p_579) :rule subproof :discharge (t515.a0 t515.a1 t515.a2 t515.a3 t515.a4 t515.a5 t515.a6 t515.a7 t515.a8 t515.a9 t515.a10 t515.a11 t515.a12 t515.a13 t515.a14 t515.a15 t515.a16 t515.a17 t515.a18 t515.a19 t515.a20 t515.a21 t515.a22 t515.a23))
(step t516 (cl (! (not @p_577) :named @p_578) @p_413) :rule and_pos :args (0))
(step t517 (cl @p_578 @p_410) :rule and_pos :args (1))
(step t518 (cl @p_578 @p_409) :rule and_pos :args (2))
(step t519 (cl @p_578 @p_407) :rule and_pos :args (3))
(step t520 (cl @p_578 @p_406) :rule and_pos :args (4))
(step t521 (cl @p_578 @p_574) :rule and_pos :args (5))
(step t522 (cl @p_578 @p_405) :rule and_pos :args (6))
(step t523 (cl @p_578 @p_396) :rule and_pos :args (7))
(step t524 (cl @p_578 @p_385) :rule and_pos :args (8))
(step t525 (cl @p_578 @p_364) :rule and_pos :args (9))
(step t526 (cl @p_578 @p_344) :rule and_pos :args (10))
(step t527 (cl @p_578 @p_342) :rule and_pos :args (11))
(step t528 (cl @p_578 @p_340) :rule and_pos :args (12))
(step t529 (cl @p_578 @p_329) :rule and_pos :args (13))
(step t530 (cl @p_578 @p_315) :rule and_pos :args (14))
(step t531 (cl @p_578 @p_311) :rule and_pos :args (15))
(step t532 (cl @p_578 @p_305) :rule and_pos :args (16))
(step t533 (cl @p_578 @p_303) :rule and_pos :args (17))
(step t534 (cl @p_578 @p_299) :rule and_pos :args (18))
(step t535 (cl @p_578 @p_295) :rule and_pos :args (19))
(step t536 (cl @p_578 @p_291) :rule and_pos :args (20))
(step t537 (cl @p_578 @p_278) :rule and_pos :args (21))
(step t538 (cl @p_578 @p_272) :rule and_pos :args (22))
(step t539 (cl @p_578 @p_267) :rule and_pos :args (23))
(step t540 (cl @p_579 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578) :rule resolution :premises (t515 t516 t517 t518 t519 t520 t521 t522 t523 t524 t525 t526 t527 t528 t529 t530 t531 t532 t533 t534 t535 t536 t537 t538 t539))
(step t541 (cl @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_578 @p_579) :rule reordering :premises (t540))
(step t542 (cl @p_578 @p_579) :rule contraction :premises (t541))
(step t543 (cl @p_621 @p_579) :rule resolution :premises (t514 t542))
(step t544 (cl @p_621 (! (not @p_579) :named @p_580)) :rule implies_neg2)
(step t545 (cl @p_621 @p_621) :rule resolution :premises (t543 t544))
(step t546 (cl @p_621) :rule contraction :premises (t545))
(step t547 (cl @p_578 @p_579) :rule implies :premises (t546))
(step t548 (cl (! (=> @p_579 false) :named @p_581) @p_579) :rule implies_neg1)
(anchor :step t549)
(assume t549.a0 @p_413)
(assume t549.a1 @p_476)
(assume t549.a2 @p_475)
(assume t549.a3 @p_409)
(assume t549.a4 @p_474)
(assume t549.a5 @p_473)
(assume t549.a6 @p_574)
(assume t549.a7 @p_267)
(step t549.t0 (cl (or (! (= (! (+ @p_4 (! (* -1/1 @p_248) :named @p_484)) :named @p_485) 0/1) :named @p_618) (! (not (! (<= @p_485 0/1) :named @p_488)) :named @p_567) (! (not (<= 0/1 @p_485)) :named @p_616))) :rule la_disequality)
(step t549.t1 (cl @p_618 @p_567 @p_616) :rule or :premises (t549.t0))
(step t549.t2 (cl (not (! (= @p_574 (! (not @p_618) :named @p_619)) :named @p_620)) @p_575 @p_619) :rule equiv_pos2)
(step t549.t3 (cl (= (* 1/1 (- @p_485 0/1)) (* 1/1 (- @p_4 @p_248)))) :rule poly_simp)
(step t549.t4 (cl (= @p_618 @p_249)) :rule poly_simp_rel :premises (t549.t3))
(step t549.t5 (cl (= @p_619 @p_574)) :rule cong :premises (t549.t4))
(step t549.t6 (cl @p_620) :rule symm :premises (t549.t5))
(step t549.t7 (cl @p_619) :rule resolution :premises (t549.t2 t549.t6 t549.a6))
(step t549.t8 (cl (not (! (= @p_267 @p_488) :named @p_565)) @p_446 @p_488) :rule equiv_pos2)
(step t549.t9 (cl (= @p_488 (! (>= 0/1 @p_485) :named @p_566))) :rule rare_rewrite :args ("arith-elim-leq" @p_485 0/1))
(step t549.t10 (cl (= (* -1/1 (- 0/1 @p_485)) (* -1/1 (- @p_266 0/1)))) :rule poly_simp)
(step t549.t11 (cl (= @p_566 @p_267)) :rule poly_simp_rel :premises (t549.t10))
(step t549.t12 (cl (= @p_488 @p_267)) :rule trans :premises (t549.t9 t549.t11))
(step t549.t13 (cl @p_565) :rule symm :premises (t549.t12))
(step t549.t14 (cl @p_488) :rule resolution :premises (t549.t8 t549.t13 t549.a7))
(step t549.t15 (cl (not (! (= (! (< @p_485 0/1) :named @p_582) @p_616) :named @p_617)) @p_582 (not @p_616)) :rule equiv_pos1)
(step t549.t16 (cl @p_617) :rule comp_simplify)
(step t549.t17 (cl @p_582) :rule resolution :premises (t549.t1 t549.t7 t549.t14 t549.t15 t549.t16))
(step t549.t18 (cl (not (! (= (! (>= @p_485 0/1) :named @p_584) (! (not @p_582) :named @p_583)) :named @p_615)) (! (not @p_584) :named @p_613) @p_583) :rule equiv_pos2)
(step t549.t19 (cl (= @p_582 @p_613)) :rule rare_rewrite :args ("arith-elim-lt" @p_485 0/1))
(step t549.t20 (cl (= @p_583 (! (not @p_613) :named @p_614))) :rule cong :premises (t549.t19))
(step t549.t21 (cl (= @p_614 @p_584)) :rule rare_rewrite :args ("bool-double-not-elim" @p_584))
(step t549.t22 (cl (! (= @p_583 @p_584) :named @p_612)) :rule trans :premises (t549.t20 t549.t21))
(step t549.t23 (cl @p_615) :rule symm :premises (t549.t22))
(step t549.t24 (cl (not @p_612) (not @p_583) @p_584) :rule equiv_pos2)
(step t549.t25 (cl (! (=> @p_582 false) :named @p_585) @p_582) :rule implies_neg1)
(anchor :step t549.t26)
(assume t549.t26.a0 @p_582)
(step t549.t26.t0 (cl (not (! (= (! (< (! (+ @p_485 (! (* -1/1 (! (+ @p_4 (! (* -1/2 @p_327) :named @p_505)) :named @p_506)) :named @p_592) (! (* -1/2 (! (+ @p_327 (* 2/1 @p_298)) :named @p_503)) :named @p_591) (! (* 2/1 (! (+ @p_6 @p_274) :named @p_501)) :named @p_590) (! (* -2/1 (! (+ @p_274 (* -1/2 @p_275)) :named @p_499)) :named @p_589) (! (+ @p_298 (! (* -1/1 @p_275) :named @p_496)) :named @p_497) (! (* -2/1 (! (+ @p_6 (* -1/2 @p_248)) :named @p_494)) :named @p_588)) :named @p_593) (! (+ 0/1 @p_175 @p_586 @p_490 @p_491 0/1 @p_491) :named @p_587)) :named @p_594) false) :named @p_607)) (not @p_594) false) :rule equiv_pos2)
(step t549.t26.t1 (cl (= @p_594 (! (not (! (>= @p_593 @p_587) :named @p_608)) :named @p_609))) :rule rare_rewrite :args ("arith-elim-lt" @p_593 @p_587))
(step t549.t26.t2 (cl (= @p_593 (! (+ @p_496 @p_275 @p_328 @p_313 @p_298 @p_505 @p_484 @p_248 (! (* 0/1 @p_274) :named @p_561) (! (* 0/1 @p_6) :named @p_560) (! (* 0/1 @p_4) :named @p_559)) :named @p_610))) :rule poly_simp)
(step t549.t26.t3 (cl (= @p_561 0/1)) :rule poly_simp)
(step t549.t26.t4 (cl (= @p_560 0/1)) :rule poly_simp)
(step t549.t26.t5 (cl (= @p_559 0/1)) :rule poly_simp)
(step t549.t26.t6 (cl (= @p_610 (! (+ @p_496 @p_275 @p_328 @p_313 @p_298 @p_505 @p_484 @p_248 0/1 0/1 0/1) :named @p_611))) :rule cong :premises (t549.t26.t3 t549.t26.t4 t549.t26.t5))
(step t549.t26.t7 (cl (= @p_611 0/1)) :rule poly_simp)
(step t549.t26.t8 (cl (= @p_610 0/1)) :rule trans :premises (t549.t26.t6 t549.t26.t7))
(step t549.t26.t9 (cl (= @p_593 0/1)) :rule trans :premises (t549.t26.t2 t549.t26.t8))
(step t549.t26.t10 (cl (= @p_175 0/1)) :rule evaluate)
(step t549.t26.t11 (cl (= @p_586 0/1)) :rule evaluate)
(step t549.t26.t12 (cl (= @p_490 0/1)) :rule evaluate)
(step t549.t26.t13 (cl (= @p_491 0/1)) :rule evaluate)
(step t549.t26.t14 (cl @p_60) :rule refl)
(step t549.t26.t15 (cl (= @p_587 (! (+ 0/1 0/1 0/1 0/1 0/1 0/1 0/1) :named @p_558))) :rule cong :premises (t549.t26.t10 t549.t26.t11 t549.t26.t12 t549.t26.t13 t549.t26.t14 t549.t26.t13))
(step t549.t26.t16 (cl (= @p_558 0/1)) :rule evaluate)
(step t549.t26.t17 (cl (= @p_587 0/1)) :rule trans :premises (t549.t26.t15 t549.t26.t16))
(step t549.t26.t18 (cl (= @p_608 @p_190)) :rule cong :premises (t549.t26.t9 t549.t26.t17))
(step t549.t26.t19 (cl @p_191) :rule evaluate)
(step t549.t26.t20 (cl (= @p_608 true)) :rule trans :premises (t549.t26.t18 t549.t26.t19))
(step t549.t26.t21 (cl (= @p_609 @p_189)) :rule cong :premises (t549.t26.t20))
(step t549.t26.t22 (cl (= @p_189 false)) :rule evaluate)
(step t549.t26.t23 (cl (= @p_609 false)) :rule trans :premises (t549.t26.t21 t549.t26.t22))
(step t549.t26.t24 (cl @p_607) :rule trans :premises (t549.t26.t1 t549.t26.t23))
(step t549.t26.t25 (cl @p_583 (not (! (= @p_592 @p_175) :named @p_605)) (not (! (= @p_591 @p_586) :named @p_601)) (not (! (= @p_590 @p_490) :named @p_599)) (not (! (= @p_589 @p_491) :named @p_597)) (not (! (= @p_497 0/1) :named @p_517)) (not (! (= @p_588 @p_491) :named @p_595)) @p_594) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t549.t26.t26 (cl (=> (! (and @p_183 (! (= @p_506 0/1) :named @p_545)) :named @p_606) @p_605)) :rule la_mult_neg)
(step t549.t26.t27 (cl (not @p_606) @p_605) :rule implies :premises (t549.t26.t26))
(step t549.t26.t28 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t549.t26.t29 (cl (not @p_185) @p_183) :rule equiv1 :premises (t549.t26.t28))
(step t549.t26.t30 (cl @p_185) :rule evaluate)
(step t549.t26.t31 (cl @p_183) :rule resolution :premises (t549.t26.t29 t549.t26.t30))
(step t549.t26.t32 (cl (! (not (! (= @p_473 @p_545) :named @p_546)) :named @p_547) (! (not @p_473) :named @p_483) @p_545) :rule equiv_pos2)
(step t549.t26.t33 (cl (= (* 1/1 (- @p_506 0/1)) (* 1/1 (- @p_4 @p_328)))) :rule poly_simp)
(step t549.t26.t34 (cl (= @p_545 @p_473)) :rule poly_simp_rel :premises (t549.t26.t33))
(step t549.t26.t35 (cl @p_546) :rule symm :premises (t549.t26.t34))
(step t549.t26.t36 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t549.t26.t37 (cl (= @p_388 true)) :rule evaluate)
(step t549.t26.t38 (cl (= @p_399 @p_404)) :rule cong :premises (t549.t26.t37))
(step t549.t26.t39 (cl (= @p_404 true)) :rule or_simplify)
(step t549.t26.t40 (cl (= @p_399 true)) :rule trans :premises (t549.t26.t38 t549.t26.t39))
(step t549.t26.t41 (cl (= @p_400 @p_403)) :rule cong :premises (t549.t26.t40))
(step t549.t26.t42 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t549.t26.t43 (cl (= @p_400 @p_396)) :rule trans :premises (t549.t26.t41 t549.t26.t42))
(step t549.t26.t44 (cl @p_402) :rule cong :premises (t549.t26.t43))
(step t549.t26.t45 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t549.t26.t46)
(assume t549.t26.t46.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t549.t26.t46.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t549.t26.t46.t1 (cl @p_397 @p_400) :rule or :premises (t549.t26.t46.t0))
(step t549.t26.t46.t2 (cl @p_400) :rule resolution :premises (t549.t26.t46.t1 t549.t26.t46.a0))
(step t549.t26.t46 (cl @p_397 @p_400) :rule subproof :discharge (t549.t26.t46.a0))
(step t549.t26.t47 (cl @p_401 @p_400) :rule resolution :premises (t549.t26.t45 t549.t26.t46))
(step t549.t26.t48 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t549.t26.t49 (cl @p_401 @p_401) :rule resolution :premises (t549.t26.t47 t549.t26.t48))
(step t549.t26.t50 (cl @p_401) :rule contraction :premises (t549.t26.t49))
(step t549.t26.t51 (cl @p_398) :rule resolution :premises (t549.t26.t36 t549.t26.t44 t549.t26.t50))
(step t549.t26.t52 (cl @p_397 @p_396) :rule implies :premises (t549.t26.t51))
(step t549.t26.t53 (cl @p_396) :rule resolution :premises (t549.t26.t52 a8))
(step t549.t26.t54 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t549.t26.t55 (cl (= @p_126 false)) :rule evaluate)
(step t549.t26.t56 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t549.t26.t57 (cl (= @p_364 @p_364)) :rule refl)
(step t549.t26.t58 (cl (= @p_378 @p_383)) :rule cong :premises (t549.t26.t56 t549.t26.t57))
(step t549.t26.t59 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t549.t26.t60 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t549.t26.t61 (cl (= @p_383 @p_364)) :rule trans :premises (t549.t26.t59 t549.t26.t60))
(step t549.t26.t62 (cl (= @p_378 @p_364)) :rule trans :premises (t549.t26.t58 t549.t26.t61))
(step t549.t26.t63 (cl (= @p_379 @p_382)) :rule cong :premises (t549.t26.t55 t549.t26.t62))
(step t549.t26.t64 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t549.t26.t65 (cl (= @p_379 @p_364)) :rule trans :premises (t549.t26.t63 t549.t26.t64))
(step t549.t26.t66 (cl @p_381) :rule cong :premises (t549.t26.t65))
(step t549.t26.t67 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t549.t26.t68)
(assume t549.t26.t68.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t549.t26.t68.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t549.t26.t68.t1 (cl @p_375 @p_379) :rule or :premises (t549.t26.t68.t0))
(step t549.t26.t68.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t549.t26.t68.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t549.t26.t68.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t549.t26.t68.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t549.t26.t68.t3.t0))
(step t549.t26.t68.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t549.t26.t68.t3.t1))
(step t549.t26.t68.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t549.t26.t68.t3.t2))
(step t549.t26.t68.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t549.t26.t68.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t549.t26.t68.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t549.t26.t68.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t549.t26.t68.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t549.t26.t68.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t549.t26.t68.t4.t1 t549.t26.t68.t4.t2))
(step t549.t26.t68.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t549.t26.t68.t4.t0 t549.t26.t68.t4.t3))
(step t549.t26.t68.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t549.t26.t68.t5 (cl @p_365) :rule trans :premises (t549.t26.t68.t3 t549.t26.t68.t4))
(step t549.t26.t68.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t549.t26.t68.t2 t549.t26.t68.t5 a17))
(step t549.t26.t68.t7 (cl @p_379) :rule resolution :premises (t549.t26.t68.t1 t549.t26.t68.t6))
(step t549.t26.t68 (cl @p_375 @p_379) :rule subproof :discharge (t549.t26.t68.a0))
(step t549.t26.t69 (cl @p_380 @p_379) :rule resolution :premises (t549.t26.t67 t549.t26.t68))
(step t549.t26.t70 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t549.t26.t71 (cl @p_380 @p_380) :rule resolution :premises (t549.t26.t69 t549.t26.t70))
(step t549.t26.t72 (cl @p_380) :rule contraction :premises (t549.t26.t71))
(step t549.t26.t73 (cl @p_376) :rule resolution :premises (t549.t26.t54 t549.t26.t66 t549.t26.t72))
(step t549.t26.t74 (cl @p_375 @p_364) :rule implies :premises (t549.t26.t73))
(step t549.t26.t75 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t549.t26.t76 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t549.t26.t76.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t549.t26.t76.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t549.t26.t76.t0))
(step t549.t26.t76.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t549.t26.t76.t1))
(step t549.t26.t76.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t549.t26.t76.t2))
(step t549.t26.t76 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t549.t26.t77 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t549.t26.t77.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t549.t26.t77.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t549.t26.t77.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t549.t26.t77.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t549.t26.t77.t1 t549.t26.t77.t2))
(step t549.t26.t77.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t549.t26.t77.t0 t549.t26.t77.t3))
(step t549.t26.t77 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t549.t26.t78 (cl @p_365) :rule trans :premises (t549.t26.t76 t549.t26.t77))
(step t549.t26.t79 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t549.t26.t75 t549.t26.t78 a17))
(step t549.t26.t80 (cl @p_364) :rule resolution :premises (t549.t26.t74 t549.t26.t79))
(step t549.t26.t81 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t549.t26.t82 (cl @p_312 @p_406) :rule or :premises (t549.t26.t81))
(step t549.t26.t83 (cl @p_406) :rule resolution :premises (t549.t26.t82 a27))
(step t549.t26.t84 (cl (= @p_362 @p_65)) :rule symm :premises (t549.t26.t83))
(step t549.t26.t85 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t549.t26.t86 (cl (= @p_362 @p_6)) :rule trans :premises (t549.t26.t84 t549.t26.t85))
(step t549.t26.t87 (cl (= 2/1 2/1)) :rule refl)
(step t549.t26.t88 (cl (= @p_363 @p_290)) :rule cong :premises (t549.t26.t86 t549.t26.t87))
(step t549.t26.t89 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t549.t26.t90 (cl @p_292 @p_291) :rule or :premises (t549.t26.t89))
(step t549.t26.t91 (cl @p_291) :rule resolution :premises (t549.t26.t90 a6))
(step t549.t26.t92 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t549.t26.t93 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t549.t26.t94 (cl @p_273 @p_295) :rule or :premises (t549.t26.t93))
(step t549.t26.t95 (cl @p_295) :rule resolution :premises (t549.t26.t94 a4))
(step t549.t26.t96 (cl (= @p_293 @p_294)) :rule symm :premises (t549.t26.t95))
(step t549.t26.t97 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t549.t26.t98 (cl @p_292 @p_305) :rule or :premises (t549.t26.t97))
(step t549.t26.t99 (cl @p_305) :rule resolution :premises (t549.t26.t98 a6))
(step t549.t26.t100 (cl (= @p_270 @p_304)) :rule symm :premises (t549.t26.t99))
(step t549.t26.t101 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t549.t26.t102 (cl (= @p_356 false)) :rule evaluate)
(step t549.t26.t103 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t549.t26.t104 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t549.t26.t103))
(step t549.t26.t105 (cl (= @p_357 @p_360)) :rule cong :premises (t549.t26.t102 t549.t26.t104))
(step t549.t26.t106 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t549.t26.t107 (cl (= @p_357 @p_344)) :rule trans :premises (t549.t26.t105 t549.t26.t106))
(step t549.t26.t108 (cl @p_359) :rule cong :premises (t549.t26.t107))
(step t549.t26.t109 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t549.t26.t110)
(assume t549.t26.t110.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t549.t26.t110.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t549.t26.t110.t1 (cl @p_353 @p_357) :rule or :premises (t549.t26.t110.t0))
(step t549.t26.t110.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t549.t26.t110.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t110.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t549.t26.t110.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t549.t26.t110.t3.t0))
(step t549.t26.t110.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t549.t26.t110.t3.t1))
(step t549.t26.t110.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t549.t26.t110.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t110.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t549.t26.t110.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t549.t26.t110.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t549.t26.t110.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t549.t26.t110.t4.t1 t549.t26.t110.t4.t2))
(step t549.t26.t110.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t549.t26.t110.t4.t0 t549.t26.t110.t4.t3))
(step t549.t26.t110.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t549.t26.t110.t5 (cl @p_345) :rule trans :premises (t549.t26.t110.t3 t549.t26.t110.t4))
(step t549.t26.t110.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t549.t26.t110.t2 t549.t26.t110.t5 a19))
(step t549.t26.t110.t7 (cl @p_357) :rule resolution :premises (t549.t26.t110.t1 t549.t26.t110.t6))
(step t549.t26.t110 (cl @p_353 @p_357) :rule subproof :discharge (t549.t26.t110.a0))
(step t549.t26.t111 (cl @p_358 @p_357) :rule resolution :premises (t549.t26.t109 t549.t26.t110))
(step t549.t26.t112 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t549.t26.t113 (cl @p_358 @p_358) :rule resolution :premises (t549.t26.t111 t549.t26.t112))
(step t549.t26.t114 (cl @p_358) :rule contraction :premises (t549.t26.t113))
(step t549.t26.t115 (cl @p_354) :rule resolution :premises (t549.t26.t101 t549.t26.t108 t549.t26.t114))
(step t549.t26.t116 (cl @p_353 @p_344) :rule implies :premises (t549.t26.t115))
(step t549.t26.t117 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t549.t26.t118 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t118.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t549.t26.t118.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t549.t26.t118.t0))
(step t549.t26.t118.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t549.t26.t118.t1))
(step t549.t26.t118 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t549.t26.t119 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t119.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t549.t26.t119.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t549.t26.t119.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t549.t26.t119.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t549.t26.t119.t1 t549.t26.t119.t2))
(step t549.t26.t119.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t549.t26.t119.t0 t549.t26.t119.t3))
(step t549.t26.t119 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t549.t26.t120 (cl @p_345) :rule trans :premises (t549.t26.t118 t549.t26.t119))
(step t549.t26.t121 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t549.t26.t117 t549.t26.t120 a19))
(step t549.t26.t122 (cl @p_344) :rule resolution :premises (t549.t26.t116 t549.t26.t121))
(step t549.t26.t123 (cl @p_355) :rule symm :premises (t549.t26.t122))
(step t549.t26.t124 (cl (= @p_304 @p_310)) :rule cong :premises (t549.t26.t123))
(step t549.t26.t125 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t549.t26.t126 (cl @p_312 @p_311) :rule or :premises (t549.t26.t125))
(step t549.t26.t127 (cl @p_311) :rule resolution :premises (t549.t26.t126 a27))
(step t549.t26.t128 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t549.t26.t129 (cl (= @p_389 @p_395)) :rule cong :premises (t549.t26.t55 t549.t26.t37))
(step t549.t26.t130 (cl (= @p_395 true)) :rule evaluate)
(step t549.t26.t131 (cl (= @p_389 true)) :rule trans :premises (t549.t26.t129 t549.t26.t130))
(step t549.t26.t132 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t549.t26.t133 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t549.t26.t132))
(step t549.t26.t134 (cl (= @p_390 @p_393)) :rule cong :premises (t549.t26.t131 t549.t26.t133))
(step t549.t26.t135 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t549.t26.t136 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t549.t26.t137 (cl (= @p_393 @p_385)) :rule trans :premises (t549.t26.t135 t549.t26.t136))
(step t549.t26.t138 (cl (= @p_390 @p_385)) :rule trans :premises (t549.t26.t134 t549.t26.t137))
(step t549.t26.t139 (cl @p_392) :rule cong :premises (t549.t26.t138))
(step t549.t26.t140 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t549.t26.t141)
(assume t549.t26.t141.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t549.t26.t141.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t549.t26.t141.t1 (cl @p_258 @p_390) :rule or :premises (t549.t26.t141.t0))
(step t549.t26.t141.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t549.t26.t141.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t141.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t549.t26.t141.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t549.t26.t141.t3.t0))
(step t549.t26.t141.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t549.t26.t141.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t549.t26.t141.t3.t1 t549.t26.t141.t3.t2))
(step t549.t26.t141.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t549.t26.t141.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t549.t26.t141.t3.t3 t549.t26.t141.t3.t4))
(step t549.t26.t141.t3 (cl @p_251) :rule bind)
(step t549.t26.t141.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t549.t26.t141.t2 t549.t26.t141.t3 a12))
(step t549.t26.t141.t5 (cl @p_390) :rule resolution :premises (t549.t26.t141.t1 t549.t26.t141.t4))
(step t549.t26.t141 (cl @p_258 @p_390) :rule subproof :discharge (t549.t26.t141.a0))
(step t549.t26.t142 (cl @p_391 @p_390) :rule resolution :premises (t549.t26.t140 t549.t26.t141))
(step t549.t26.t143 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t549.t26.t144 (cl @p_391 @p_391) :rule resolution :premises (t549.t26.t142 t549.t26.t143))
(step t549.t26.t145 (cl @p_391) :rule contraction :premises (t549.t26.t144))
(step t549.t26.t146 (cl @p_386) :rule resolution :premises (t549.t26.t128 t549.t26.t139 t549.t26.t145))
(step t549.t26.t147 (cl @p_258 @p_385) :rule implies :premises (t549.t26.t146))
(step t549.t26.t148 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t549.t26.t149 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t149.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t549.t26.t149.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t549.t26.t149.t0))
(step t549.t26.t149.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t549.t26.t149.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t549.t26.t149.t1 t549.t26.t149.t2))
(step t549.t26.t149.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t549.t26.t149.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t549.t26.t149.t3 t549.t26.t149.t4))
(step t549.t26.t149 (cl @p_251) :rule bind)
(step t549.t26.t150 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t549.t26.t148 t549.t26.t149 a12))
(step t549.t26.t151 (cl @p_385) :rule resolution :premises (t549.t26.t147 t549.t26.t150))
(step t549.t26.t152 (cl (= @p_307 @p_304)) :rule cong :premises (t549.t26.t151))
(step t549.t26.t153 (cl @p_388) :rule refl)
(step t549.t26.t154 (cl (= @p_308 @p_341)) :rule cong :premises (t549.t26.t152 t549.t26.t153))
(step t549.t26.t155 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t549.t26.t156 (cl @p_343 @p_342) :rule or :premises (t549.t26.t155))
(step t549.t26.t157 (cl @p_342) :rule resolution :premises (t549.t26.t156 a2))
(step t549.t26.t158 (cl (= @p_341 @p_296)) :rule symm :premises (t549.t26.t157))
(step t549.t26.t159 (cl (= @p_270 @p_296)) :rule trans :premises (t549.t26.t100 t549.t26.t124 t549.t26.t127 t549.t26.t154 t549.t26.t158))
(step t549.t26.t160 (cl (= @p_1 @p_1)) :rule refl)
(step t549.t26.t161 (cl (= @p_294 @p_339)) :rule cong :premises (t549.t26.t159 t549.t26.t160))
(step t549.t26.t162 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t549.t26.t163 (cl @p_292 @p_340) :rule or :premises (t549.t26.t162))
(step t549.t26.t164 (cl @p_340) :rule resolution :premises (t549.t26.t163 a6))
(step t549.t26.t165 (cl (= @p_339 @p_314)) :rule symm :premises (t549.t26.t164))
(step t549.t26.t166 (cl (not @p_336) (not @p_335) @p_330) :rule equiv_pos2)
(step t549.t26.t167 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t549.t26.t168 (cl (= @p_296 @p_296)) :rule refl)
(step t549.t26.t169 (cl (= @p_333 @p_327)) :rule cong :premises (t549.t26.t167 t549.t26.t168))
(step t549.t26.t170 (cl (= @p_331 @p_337)) :rule poly_simp)
(step t549.t26.t171 (cl (= @p_334 @p_338)) :rule cong :premises (t549.t26.t169 t549.t26.t170))
(step t549.t26.t172 (cl (= (* 1/1 (- @p_327 @p_337)) (* -2/1 (- @p_314 @p_328)))) :rule poly_simp)
(step t549.t26.t173 (cl (= @p_338 @p_329)) :rule poly_simp_rel :premises (t549.t26.t172))
(step t549.t26.t174 (cl (= @p_334 @p_329)) :rule trans :premises (t549.t26.t171 t549.t26.t173))
(step t549.t26.t175 (cl @p_336) :rule cong :premises (t549.t26.t174))
(step t549.t26.t176 (cl @p_335 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t549.t26.t177)
(assume t549.t26.t177.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t549.t26.t177.t0 (cl (or @p_279 @p_334)) :rule forall_inst :args (@p_1 @p_1 @p_296))
(step t549.t26.t177.t1 (cl @p_279 @p_334) :rule or :premises (t549.t26.t177.t0))
(step t549.t26.t177.t2 (cl @p_334) :rule resolution :premises (t549.t26.t177.t1 t549.t26.t177.a0))
(step t549.t26.t177 (cl @p_279 @p_334) :rule subproof :discharge (t549.t26.t177.a0))
(step t549.t26.t178 (cl @p_335 @p_334) :rule resolution :premises (t549.t26.t176 t549.t26.t177))
(step t549.t26.t179 (cl @p_335 (not @p_334)) :rule implies_neg2)
(step t549.t26.t180 (cl @p_335 @p_335) :rule resolution :premises (t549.t26.t178 t549.t26.t179))
(step t549.t26.t181 (cl @p_335) :rule contraction :premises (t549.t26.t180))
(step t549.t26.t182 (cl @p_330) :rule resolution :premises (t549.t26.t166 t549.t26.t175 t549.t26.t181))
(step t549.t26.t183 (cl @p_279 @p_329) :rule implies :premises (t549.t26.t182))
(step t549.t26.t184 (cl @p_329) :rule resolution :premises (t549.t26.t183 a1))
(step t549.t26.t185 (cl @p_473) :rule trans :premises (t549.t26.t53 t549.t26.t80 t549.t26.t88 t549.t26.t91 t549.t26.t92 t549.t26.t96 t549.t26.t161 t549.t26.t165 t549.t26.t184))
(step t549.t26.t186 (cl @p_545) :rule resolution :premises (t549.t26.t32 t549.t26.t35 t549.t26.t185))
(step t549.t26.t187 (cl @p_606) :rule and_intro :premises (t549.t26.t31 t549.t26.t186))
(step t549.t26.t188 (cl @p_605) :rule resolution :premises (t549.t26.t27 t549.t26.t187))
(step t549.t26.t189 (cl (=> (! (and @p_602 (! (= @p_503 0/1) :named @p_535)) :named @p_603) @p_601)) :rule la_mult_neg)
(step t549.t26.t190 (cl (not @p_603) @p_601) :rule implies :premises (t549.t26.t189))
(step t549.t26.t191 (cl (= @p_604 @p_602)) :rule equiv_simplify)
(step t549.t26.t192 (cl (not @p_604) @p_602) :rule equiv1 :premises (t549.t26.t191))
(step t549.t26.t193 (cl @p_604) :rule evaluate)
(step t549.t26.t194 (cl @p_602) :rule resolution :premises (t549.t26.t192 t549.t26.t193))
(step t549.t26.t195 (cl (not (! (= @p_474 @p_535) :named @p_538)) (! (not @p_474) :named @p_482) @p_535) :rule equiv_pos2)
(step t549.t26.t196 (cl (= (* 2/1 (- @p_328 @p_313)) (* 1/1 (! (- @p_327 (! (* -2/1 @p_298) :named @p_539)) :named @p_541)))) :rule poly_simp)
(step t549.t26.t197 (cl (= @p_474 (! (= @p_327 @p_539) :named @p_540))) :rule poly_simp_rel :premises (t549.t26.t196))
(step t549.t26.t198 (cl (= (* 2/1 (- @p_503 0/1)) (* 2/1 @p_541))) :rule poly_simp)
(step t549.t26.t199 (cl (= @p_535 @p_540)) :rule poly_simp_rel :premises (t549.t26.t198))
(step t549.t26.t200 (cl (= @p_540 @p_535)) :rule symm :premises (t549.t26.t199))
(step t549.t26.t201 (cl @p_538) :rule trans :premises (t549.t26.t197 t549.t26.t200))
(step t549.t26.t202 (cl (= @p_328 @p_314)) :rule symm :premises (t549.t26.t184))
(step t549.t26.t203 (cl (or @p_326 @p_315)) :rule forall_inst :args (@p_1 @p_296))
(step t549.t26.t204 (cl @p_326 @p_315) :rule or :premises (t549.t26.t203))
(step t549.t26.t205 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t549.t26.t206 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t549.t26.t206.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t549.t26.t206.t1 (cl @p_22) :rule refl)
(step t549.t26.t206.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t549.t26.t206.t0 t549.t26.t206.t1))
(step t549.t26.t206.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t549.t26.t206.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t549.t26.t206.t2 t549.t26.t206.t3))
(step t549.t26.t206.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t549.t26.t206.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t549.t26.t206.t5))
(step t549.t26.t206.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t549.t26.t206.t4 t549.t26.t206.t6))
(step t549.t26.t206 (cl @p_316) :rule bind)
(step t549.t26.t207 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t549.t26.t205 t549.t26.t206 a16))
(step t549.t26.t208 (cl @p_315) :rule resolution :premises (t549.t26.t204 t549.t26.t207))
(step t549.t26.t209 (cl @p_474) :rule trans :premises (t549.t26.t202 t549.t26.t208))
(step t549.t26.t210 (cl @p_535) :rule resolution :premises (t549.t26.t195 t549.t26.t201 t549.t26.t209))
(step t549.t26.t211 (cl @p_603) :rule and_intro :premises (t549.t26.t194 t549.t26.t210))
(step t549.t26.t212 (cl @p_601) :rule resolution :premises (t549.t26.t190 t549.t26.t211))
(step t549.t26.t213 (cl (=> (! (and @p_512 (! (= @p_501 0/1) :named @p_529)) :named @p_600) @p_599)) :rule la_mult_pos)
(step t549.t26.t214 (cl (not @p_600) @p_599) :rule implies :premises (t549.t26.t213))
(step t549.t26.t215 (cl (= @p_515 @p_512)) :rule equiv_simplify)
(step t549.t26.t216 (cl (not @p_515) @p_512) :rule equiv1 :premises (t549.t26.t215))
(step t549.t26.t217 (cl @p_515) :rule evaluate)
(step t549.t26.t218 (cl @p_512) :rule resolution :premises (t549.t26.t216 t549.t26.t217))
(step t549.t26.t219 (cl (not (! (= @p_409 @p_529) :named @p_532)) @p_425 @p_529) :rule equiv_pos2)
(step t549.t26.t220 (cl (= (* 1/1 (- @p_501 0/1)) (* 1/1 (- @p_6 @p_408)))) :rule poly_simp)
(step t549.t26.t221 (cl (= @p_529 @p_409)) :rule poly_simp_rel :premises (t549.t26.t220))
(step t549.t26.t222 (cl @p_532) :rule symm :premises (t549.t26.t221))
(step t549.t26.t223 (cl (or @p_326 @p_409)) :rule forall_inst :args (@p_1 @p_4))
(step t549.t26.t224 (cl @p_326 @p_409) :rule or :premises (t549.t26.t223))
(step t549.t26.t225 (cl @p_409) :rule resolution :premises (t549.t26.t224 t549.t26.t207))
(step t549.t26.t226 (cl @p_529) :rule resolution :premises (t549.t26.t219 t549.t26.t222 t549.t26.t225))
(step t549.t26.t227 (cl @p_600) :rule and_intro :premises (t549.t26.t218 t549.t26.t226))
(step t549.t26.t228 (cl @p_599) :rule resolution :premises (t549.t26.t214 t549.t26.t227))
(step t549.t26.t229 (cl (=> (! (and @p_530 (! (= @p_499 0/1) :named @p_523)) :named @p_598) @p_597)) :rule la_mult_neg)
(step t549.t26.t230 (cl (not @p_598) @p_597) :rule implies :premises (t549.t26.t229))
(step t549.t26.t231 (cl (= @p_533 @p_530)) :rule equiv_simplify)
(step t549.t26.t232 (cl (not @p_533) @p_530) :rule equiv1 :premises (t549.t26.t231))
(step t549.t26.t233 (cl @p_533) :rule evaluate)
(step t549.t26.t234 (cl @p_530) :rule resolution :premises (t549.t26.t232 t549.t26.t233))
(step t549.t26.t235 (cl (not (! (= @p_475 @p_523) :named @p_525)) (! (not @p_475) :named @p_481) @p_523) :rule equiv_pos2)
(step t549.t26.t236 (cl (= (* 1/1 (- @p_499 0/1)) (* 1/1 (- @p_274 @p_276)))) :rule poly_simp)
(step t549.t26.t237 (cl (= @p_523 @p_475)) :rule poly_simp_rel :premises (t549.t26.t236))
(step t549.t26.t238 (cl @p_525) :rule symm :premises (t549.t26.t237))
(step t549.t26.t239 (cl (or @p_292 @p_407)) :rule forall_inst :args (@p_139 @p_4))
(step t549.t26.t240 (cl @p_292 @p_407) :rule or :premises (t549.t26.t239))
(step t549.t26.t241 (cl @p_407) :rule resolution :premises (t549.t26.t240 a6))
(step t549.t26.t242 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t549.t26.t243 (cl @p_292 @p_405) :rule or :premises (t549.t26.t242))
(step t549.t26.t244 (cl @p_405) :rule resolution :premises (t549.t26.t243 a6))
(step t549.t26.t245 (cl (= @p_361 @p_301)) :rule symm :premises (t549.t26.t244))
(step t549.t26.t246 (cl (= @p_4 @p_301)) :rule trans :premises (t549.t26.t53 t549.t26.t245))
(step t549.t26.t247 (cl (= @p_139 @p_139)) :rule refl)
(step t549.t26.t248 (cl (= @p_268 @p_302)) :rule cong :premises (t549.t26.t246 t549.t26.t247))
(step t549.t26.t249 (cl (or @p_273 @p_303)) :rule forall_inst :args (1/1 @p_4 @p_139))
(step t549.t26.t250 (cl @p_273 @p_303) :rule or :premises (t549.t26.t249))
(step t549.t26.t251 (cl @p_303) :rule resolution :premises (t549.t26.t250 a4))
(step t549.t26.t252 (cl (= @p_268 @p_274)) :rule symm :premises (t549.t26.t241))
(step t549.t26.t253 (cl (= @p_300 @p_277)) :rule cong :premises (t549.t26.t252))
(step t549.t26.t254 (cl (not @p_286) (not @p_285) @p_280) :rule equiv_pos2)
(step t549.t26.t255 (cl (= @p_282 2/1)) :rule evaluate)
(step t549.t26.t256 (cl (= @p_274 @p_274)) :rule refl)
(step t549.t26.t257 (cl (= @p_283 @p_275)) :rule cong :premises (t549.t26.t255 t549.t26.t256))
(step t549.t26.t258 (cl (= @p_281 @p_287)) :rule poly_simp)
(step t549.t26.t259 (cl (= @p_284 @p_288)) :rule cong :premises (t549.t26.t257 t549.t26.t258))
(step t549.t26.t260 (cl (= (* -1/2 (- @p_275 @p_287)) (* 1/1 (- @p_277 @p_276)))) :rule poly_simp)
(step t549.t26.t261 (cl (= @p_288 @p_278)) :rule poly_simp_rel :premises (t549.t26.t260))
(step t549.t26.t262 (cl (= @p_284 @p_278)) :rule trans :premises (t549.t26.t259 t549.t26.t261))
(step t549.t26.t263 (cl @p_286) :rule cong :premises (t549.t26.t262))
(step t549.t26.t264 (cl @p_285 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t549.t26.t265)
(assume t549.t26.t265.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t549.t26.t265.t0 (cl (or @p_279 @p_284)) :rule forall_inst :args (1/1 1/1 @p_274))
(step t549.t26.t265.t1 (cl @p_279 @p_284) :rule or :premises (t549.t26.t265.t0))
(step t549.t26.t265.t2 (cl @p_284) :rule resolution :premises (t549.t26.t265.t1 t549.t26.t265.a0))
(step t549.t26.t265 (cl @p_279 @p_284) :rule subproof :discharge (t549.t26.t265.a0))
(step t549.t26.t266 (cl @p_285 @p_284) :rule resolution :premises (t549.t26.t264 t549.t26.t265))
(step t549.t26.t267 (cl @p_285 (not @p_284)) :rule implies_neg2)
(step t549.t26.t268 (cl @p_285 @p_285) :rule resolution :premises (t549.t26.t266 t549.t26.t267))
(step t549.t26.t269 (cl @p_285) :rule contraction :premises (t549.t26.t268))
(step t549.t26.t270 (cl @p_280) :rule resolution :premises (t549.t26.t254 t549.t26.t263 t549.t26.t269))
(step t549.t26.t271 (cl @p_279 @p_278) :rule implies :premises (t549.t26.t270))
(step t549.t26.t272 (cl @p_278) :rule resolution :premises (t549.t26.t271 a1))
(step t549.t26.t273 (cl @p_475) :rule trans :premises (t549.t26.t241 t549.t26.t248 t549.t26.t251 t549.t26.t253 t549.t26.t272))
(step t549.t26.t274 (cl @p_523) :rule resolution :premises (t549.t26.t235 t549.t26.t238 t549.t26.t273))
(step t549.t26.t275 (cl @p_598) :rule and_intro :premises (t549.t26.t234 t549.t26.t274))
(step t549.t26.t276 (cl @p_597) :rule resolution :premises (t549.t26.t230 t549.t26.t275))
(step t549.t26.t277 (cl (not (! (= @p_476 @p_517) :named @p_519)) (! (not @p_476) :named @p_480) @p_517) :rule equiv_pos2)
(step t549.t26.t278 (cl (= (* -1/1 (- @p_497 0/1)) (* -1/1 (- @p_298 @p_275)))) :rule poly_simp)
(step t549.t26.t279 (cl (= @p_517 @p_476)) :rule poly_simp_rel :premises (t549.t26.t278))
(step t549.t26.t280 (cl @p_519) :rule symm :premises (t549.t26.t279))
(step t549.t26.t281 (cl (or @p_292 @p_299)) :rule forall_inst :args (@p_139 @p_296))
(step t549.t26.t282 (cl @p_292 @p_299) :rule or :premises (t549.t26.t281))
(step t549.t26.t283 (cl @p_299) :rule resolution :premises (t549.t26.t282 a6))
(step t549.t26.t284 (cl @p_387) :rule symm :premises (t549.t26.t151))
(step t549.t26.t285 (cl (= @p_304 @p_307)) :rule cong :premises (t549.t26.t284))
(step t549.t26.t286 (cl (= @p_341 @p_308)) :rule cong :premises (t549.t26.t285 t549.t26.t153))
(step t549.t26.t287 (cl (= @p_308 @p_310)) :rule symm :premises (t549.t26.t127))
(step t549.t26.t288 (cl (= @p_310 @p_304)) :rule cong :premises (t549.t26.t122))
(step t549.t26.t289 (cl (= @p_296 @p_270)) :rule trans :premises (t549.t26.t157 t549.t26.t286 t549.t26.t287 t549.t26.t288 t549.t26.t99))
(step t549.t26.t290 (cl (= @p_297 @p_271)) :rule cong :premises (t549.t26.t289 t549.t26.t247))
(step t549.t26.t291 (cl (or @p_273 @p_272)) :rule forall_inst :args (2/1 @p_4 @p_139))
(step t549.t26.t292 (cl @p_273 @p_272) :rule or :premises (t549.t26.t291))
(step t549.t26.t293 (cl @p_272) :rule resolution :premises (t549.t26.t292 a4))
(step t549.t26.t294 (cl (= @p_269 @p_275)) :rule cong :premises (t549.t26.t252))
(step t549.t26.t295 (cl @p_476) :rule trans :premises (t549.t26.t283 t549.t26.t290 t549.t26.t293 t549.t26.t294))
(step t549.t26.t296 (cl @p_517) :rule resolution :premises (t549.t26.t277 t549.t26.t280 t549.t26.t295))
(step t549.t26.t297 (cl (=> (! (and @p_530 (! (= @p_494 0/1) :named @p_511)) :named @p_596) @p_595)) :rule la_mult_neg)
(step t549.t26.t298 (cl (not @p_596) @p_595) :rule implies :premises (t549.t26.t297))
(step t549.t26.t299 (cl (not (! (= @p_413 @p_511) :named @p_514)) @p_423 @p_511) :rule equiv_pos2)
(step t549.t26.t300 (cl (= (* 1/1 (- @p_494 0/1)) (* 1/1 @p_422))) :rule poly_simp)
(step t549.t26.t301 (cl (= @p_511 @p_413)) :rule poly_simp_rel :premises (t549.t26.t300))
(step t549.t26.t302 (cl @p_514) :rule symm :premises (t549.t26.t301))
(step t549.t26.t303 (cl (not @p_419) (not @p_418) @p_414) :rule equiv_pos2)
(step t549.t26.t304 (cl (= @p_4 @p_4)) :rule refl)
(step t549.t26.t305 (cl (= @p_416 @p_248)) :rule cong :premises (t549.t26.t167 t549.t26.t304))
(step t549.t26.t306 (cl (= @p_415 @p_420)) :rule poly_simp)
(step t549.t26.t307 (cl (= @p_417 @p_421)) :rule cong :premises (t549.t26.t305 t549.t26.t306))
(step t549.t26.t308 (cl (= (* 1/1 (- @p_248 @p_420)) (* -2/1 @p_422))) :rule poly_simp)
(step t549.t26.t309 (cl (= @p_421 @p_413)) :rule poly_simp_rel :premises (t549.t26.t308))
(step t549.t26.t310 (cl (= @p_417 @p_413)) :rule trans :premises (t549.t26.t307 t549.t26.t309))
(step t549.t26.t311 (cl @p_419) :rule cong :premises (t549.t26.t310))
(step t549.t26.t312 (cl @p_418 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t549.t26.t313)
(assume t549.t26.t313.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t549.t26.t313.t0 (cl (or @p_279 @p_417)) :rule forall_inst :args (@p_1 @p_1 @p_4))
(step t549.t26.t313.t1 (cl @p_279 @p_417) :rule or :premises (t549.t26.t313.t0))
(step t549.t26.t313.t2 (cl @p_417) :rule resolution :premises (t549.t26.t313.t1 t549.t26.t313.a0))
(step t549.t26.t313 (cl @p_279 @p_417) :rule subproof :discharge (t549.t26.t313.a0))
(step t549.t26.t314 (cl @p_418 @p_417) :rule resolution :premises (t549.t26.t312 t549.t26.t313))
(step t549.t26.t315 (cl @p_418 (not @p_417)) :rule implies_neg2)
(step t549.t26.t316 (cl @p_418 @p_418) :rule resolution :premises (t549.t26.t314 t549.t26.t315))
(step t549.t26.t317 (cl @p_418) :rule contraction :premises (t549.t26.t316))
(step t549.t26.t318 (cl @p_414) :rule resolution :premises (t549.t26.t303 t549.t26.t311 t549.t26.t317))
(step t549.t26.t319 (cl @p_279 @p_413) :rule implies :premises (t549.t26.t318))
(step t549.t26.t320 (cl @p_413) :rule resolution :premises (t549.t26.t319 a1))
(step t549.t26.t321 (cl @p_511) :rule resolution :premises (t549.t26.t299 t549.t26.t302 t549.t26.t320))
(step t549.t26.t322 (cl @p_596) :rule and_intro :premises (t549.t26.t234 t549.t26.t321))
(step t549.t26.t323 (cl @p_595) :rule resolution :premises (t549.t26.t298 t549.t26.t322))
(step t549.t26.t324 (cl @p_594) :rule resolution :premises (t549.t26.t25 t549.t26.a0 t549.t26.t188 t549.t26.t212 t549.t26.t228 t549.t26.t276 t549.t26.t296 t549.t26.t323))
(step t549.t26.t325 (cl false) :rule resolution :premises (t549.t26.t0 t549.t26.t24 t549.t26.t324))
(step t549.t26 (cl @p_583 false) :rule subproof :discharge (t549.t26.a0))
(step t549.t27 (cl @p_585 false) :rule resolution :premises (t549.t25 t549.t26))
(step t549.t28 (cl @p_585 @p_133) :rule implies_neg2)
(step t549.t29 (cl @p_585 @p_585) :rule resolution :premises (t549.t27 t549.t28))
(step t549.t30 (cl @p_585) :rule contraction :premises (t549.t29))
(step t549.t31 (cl (= @p_585 @p_583)) :rule implies_simplify)
(step t549.t32 (cl (not @p_585) @p_583) :rule equiv1 :premises (t549.t31))
(step t549.t33 (cl @p_583) :rule resolution :premises (t549.t30 t549.t32))
(step t549.t34 (cl @p_584) :rule resolution :premises (t549.t24 t549.t22 t549.t33))
(step t549.t35 (cl @p_583) :rule resolution :premises (t549.t18 t549.t23 t549.t34))
(step t549.t36 (cl) :rule resolution :premises (t549.t17 t549.t35))
(step t549 (cl @p_423 @p_480 @p_481 @p_425 @p_482 @p_483 @p_575 @p_446 false) :rule subproof :discharge (t549.a0 t549.a1 t549.a2 t549.a3 t549.a4 t549.a5 t549.a6 t549.a7))
(step t550 (cl @p_580 @p_413) :rule and_pos :args (0))
(step t551 (cl @p_580 @p_476) :rule and_pos :args (1))
(step t552 (cl @p_580 @p_475) :rule and_pos :args (2))
(step t553 (cl @p_580 @p_409) :rule and_pos :args (3))
(step t554 (cl @p_580 @p_474) :rule and_pos :args (4))
(step t555 (cl @p_580 @p_473) :rule and_pos :args (5))
(step t556 (cl @p_580 @p_574) :rule and_pos :args (6))
(step t557 (cl @p_580 @p_267) :rule and_pos :args (7))
(step t558 (cl false @p_580 @p_580 @p_580 @p_580 @p_580 @p_580 @p_580 @p_580) :rule resolution :premises (t549 t550 t551 t552 t553 t554 t555 t556 t557))
(step t559 (cl @p_580 @p_580 @p_580 @p_580 @p_580 @p_580 @p_580 @p_580 false) :rule reordering :premises (t558))
(step t560 (cl @p_580 false) :rule contraction :premises (t559))
(step t561 (cl @p_581 false) :rule resolution :premises (t548 t560))
(step t562 (cl @p_581 @p_133) :rule implies_neg2)
(step t563 (cl @p_581 @p_581) :rule resolution :premises (t561 t562))
(step t564 (cl @p_581) :rule contraction :premises (t563))
(step t565 (cl (= @p_581 @p_580)) :rule implies_simplify)
(step t566 (cl (not @p_581) @p_580) :rule equiv1 :premises (t565))
(step t567 (cl @p_580) :rule resolution :premises (t564 t566))
(step t568 (cl @p_578) :rule resolution :premises (t547 t567))
(step t569 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_575 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_446) :rule not_and :premises (t568))
(step t570 (cl @p_576 (! (not @p_423) :named @p_470)) :rule or_neg :args (0))
(step t571 (cl @p_576 @p_469) :rule or_neg :args (1))
(step t572 (cl @p_576 (! (not @p_425) :named @p_468)) :rule or_neg :args (2))
(step t573 (cl @p_576 (! (not @p_426) :named @p_467)) :rule or_neg :args (3))
(step t574 (cl @p_576 @p_466) :rule or_neg :args (4))
(step t575 (cl @p_576 (not @p_575)) :rule or_neg :args (5))
(step t576 (cl @p_576 @p_465) :rule or_neg :args (6))
(step t577 (cl @p_576 @p_464) :rule or_neg :args (7))
(step t578 (cl @p_576 @p_463) :rule or_neg :args (8))
(step t579 (cl @p_576 @p_462) :rule or_neg :args (9))
(step t580 (cl @p_576 @p_461) :rule or_neg :args (10))
(step t581 (cl @p_576 @p_460) :rule or_neg :args (11))
(step t582 (cl @p_576 @p_459) :rule or_neg :args (12))
(step t583 (cl @p_576 (! (not @p_435) :named @p_458)) :rule or_neg :args (13))
(step t584 (cl @p_576 (! (not @p_436) :named @p_457)) :rule or_neg :args (14))
(step t585 (cl @p_576 @p_456) :rule or_neg :args (15))
(step t586 (cl @p_576 @p_455) :rule or_neg :args (16))
(step t587 (cl @p_576 (! (not @p_439) :named @p_454)) :rule or_neg :args (17))
(step t588 (cl @p_576 (! (not @p_440) :named @p_453)) :rule or_neg :args (18))
(step t589 (cl @p_576 @p_452) :rule or_neg :args (19))
(step t590 (cl @p_576 @p_451) :rule or_neg :args (20))
(step t591 (cl @p_576 (! (not @p_443) :named @p_450)) :rule or_neg :args (21))
(step t592 (cl @p_576 (! (not @p_444) :named @p_449)) :rule or_neg :args (22))
(step t593 (cl @p_576 (! (not @p_446) :named @p_447)) :rule or_neg :args (23))
(step t594 (cl @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576 @p_576) :rule resolution :premises (t569 t570 t571 t572 t573 t574 t575 t576 t577 t578 t579 t580 t581 t582 t583 t584 t585 t586 t587 t588 t589 t590 t591 t592 t593))
(step t595 (cl @p_576) :rule contraction :premises (t594))
(step t596 (cl @p_573) :rule resolution :premises (t504 t513 t595))
(step t597 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_249 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_446) :rule or :premises (t596))
(step t598 (cl @p_423 @p_424 @p_425 @p_249 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_446) :rule reordering :premises (t597))
(step t599 (cl (not @p_419) (not @p_418) @p_414) :rule equiv_pos2)
(step t600 (cl (= @p_332 @p_247)) :rule poly_simp)
(step t601 (cl (= @p_4 @p_4)) :rule refl)
(step t602 (cl (= @p_416 @p_248)) :rule cong :premises (t600 t601))
(step t603 (cl (= @p_415 @p_420)) :rule poly_simp)
(step t604 (cl (= @p_417 @p_421)) :rule cong :premises (t602 t603))
(step t605 (cl (= (* 1/1 (- @p_248 @p_420)) (* -2/1 @p_422))) :rule poly_simp)
(step t606 (cl (= @p_421 @p_413)) :rule poly_simp_rel :premises (t605))
(step t607 (cl (= @p_417 @p_413)) :rule trans :premises (t604 t606))
(step t608 (cl @p_419) :rule cong :premises (t607))
(step t609 (cl @p_418 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t610)
(assume t610.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t610.t0 (cl (or @p_279 @p_417)) :rule forall_inst :args (@p_1 @p_1 @p_4))
(step t610.t1 (cl @p_279 @p_417) :rule or :premises (t610.t0))
(step t610.t2 (cl @p_417) :rule resolution :premises (t610.t1 t610.a0))
(step t610 (cl @p_279 @p_417) :rule subproof :discharge (t610.a0))
(step t611 (cl @p_418 @p_417) :rule resolution :premises (t609 t610))
(step t612 (cl @p_418 (not @p_417)) :rule implies_neg2)
(step t613 (cl @p_418 @p_418) :rule resolution :premises (t611 t612))
(step t614 (cl @p_418) :rule contraction :premises (t613))
(step t615 (cl @p_414) :rule resolution :premises (t599 t608 t614))
(step t616 (cl @p_279 @p_413) :rule implies :premises (t615))
(step t617 (cl @p_413) :rule resolution :premises (t616 a1))
(step t618 (cl (or @p_326 @p_409)) :rule forall_inst :args (@p_1 @p_4))
(step t619 (cl @p_326 @p_409) :rule or :premises (t618))
(step t620 (cl (not @p_316) (not (forall ((?v0 Real) (?v1 Real)) (= (times$a (- ?v0) ?v1) (- (times$a ?v0 ?v1))))) (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule equiv_pos2)
(anchor :step t621 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t621.t0 (cl (= @p_321 @p_85)) :rule poly_simp)
(step t621.t1 (cl @p_22) :rule refl)
(step t621.t2 (cl (= @p_322 @p_317)) :rule cong :premises (t621.t0 t621.t1))
(step t621.t3 (cl (= @p_320 @p_324)) :rule poly_simp)
(step t621.t4 (cl (= @p_323 @p_325)) :rule cong :premises (t621.t2 t621.t3))
(step t621.t5 (cl (= (* 1/1 (- @p_317 @p_324)) (* 1/1 (- @p_79 @p_318)))) :rule poly_simp)
(step t621.t6 (cl (= @p_325 @p_319)) :rule poly_simp_rel :premises (t621.t5))
(step t621.t7 (cl (= @p_323 @p_319)) :rule trans :premises (t621.t4 t621.t6))
(step t621 (cl @p_316) :rule bind)
(step t622 (cl (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule resolution :premises (t620 t621 a16))
(step t623 (cl @p_409) :rule resolution :premises (t619 t622))
(step t624 (cl (or @p_292 @p_407)) :rule forall_inst :args (@p_139 @p_4))
(step t625 (cl @p_292 @p_407) :rule or :premises (t624))
(step t626 (cl @p_407) :rule resolution :premises (t625 a6))
(step t627 (cl (or @p_312 @p_406)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t628 (cl @p_312 @p_406) :rule or :premises (t627))
(step t629 (cl @p_406) :rule resolution :premises (t628 a27))
(step t630 (cl (or @p_292 @p_405)) :rule forall_inst :args (1/1 @p_4))
(step t631 (cl @p_292 @p_405) :rule or :premises (t630))
(step t632 (cl @p_405) :rule resolution :premises (t631 a6))
(step t633 (cl (not @p_402) (not @p_401) @p_398) :rule equiv_pos2)
(step t634 (cl (= @p_388 true)) :rule evaluate)
(step t635 (cl (= @p_399 @p_404)) :rule cong :premises (t634))
(step t636 (cl (= @p_404 true)) :rule or_simplify)
(step t637 (cl (= @p_399 true)) :rule trans :premises (t635 t636))
(step t638 (cl (= @p_400 @p_403)) :rule cong :premises (t637))
(step t639 (cl (= @p_403 @p_396)) :rule rare_rewrite :args ("bool-eq-true" @p_396))
(step t640 (cl (= @p_400 @p_396)) :rule trans :premises (t638 t639))
(step t641 (cl @p_402) :rule cong :premises (t640))
(step t642 (cl @p_401 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t643)
(assume t643.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t643.t0 (cl (or @p_397 @p_400)) :rule forall_inst :args (@p_4 1/1))
(step t643.t1 (cl @p_397 @p_400) :rule or :premises (t643.t0))
(step t643.t2 (cl @p_400) :rule resolution :premises (t643.t1 t643.a0))
(step t643 (cl @p_397 @p_400) :rule subproof :discharge (t643.a0))
(step t644 (cl @p_401 @p_400) :rule resolution :premises (t642 t643))
(step t645 (cl @p_401 (not @p_400)) :rule implies_neg2)
(step t646 (cl @p_401 @p_401) :rule resolution :premises (t644 t645))
(step t647 (cl @p_401) :rule contraction :premises (t646))
(step t648 (cl @p_398) :rule resolution :premises (t633 t641 t647))
(step t649 (cl @p_397 @p_396) :rule implies :premises (t648))
(step t650 (cl @p_396) :rule resolution :premises (t649 a8))
(step t651 (cl (not @p_392) (not @p_391) @p_386) :rule equiv_pos2)
(step t652 (cl (= @p_126 false)) :rule evaluate)
(step t653 (cl (= @p_389 @p_395)) :rule cong :premises (t652 t634))
(step t654 (cl (= @p_395 true)) :rule evaluate)
(step t655 (cl (= @p_389 true)) :rule trans :premises (t653 t654))
(step t656 (cl (= (* -2/1 (- 2/1 @p_306)) (* 2/1 (- @p_306 2/1)))) :rule poly_simp)
(step t657 (cl (= @p_387 @p_385)) :rule poly_simp_rel :premises (t656))
(step t658 (cl (= @p_390 @p_393)) :rule cong :premises (t655 t657))
(step t659 (cl (= @p_393 @p_394)) :rule rare_rewrite :args ("eq-symm" true @p_385))
(step t660 (cl (= @p_394 @p_385)) :rule rare_rewrite :args ("bool-eq-true" @p_385))
(step t661 (cl (= @p_393 @p_385)) :rule trans :premises (t659 t660))
(step t662 (cl (= @p_390 @p_385)) :rule trans :premises (t658 t661))
(step t663 (cl @p_392) :rule cong :premises (t662))
(step t664 (cl @p_391 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t665)
(assume t665.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t665.t0 (cl (or @p_258 @p_390)) :rule forall_inst :args (1/1 2/1))
(step t665.t1 (cl @p_258 @p_390) :rule or :premises (t665.t0))
(step t665.t2 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t665.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t665.t3.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t665.t3.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t665.t3.t0))
(step t665.t3.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t665.t3.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t665.t3.t1 t665.t3.t2))
(step t665.t3.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t665.t3.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t665.t3.t3 t665.t3.t4))
(step t665.t3 (cl @p_251) :rule bind)
(step t665.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t665.t2 t665.t3 a12))
(step t665.t5 (cl @p_390) :rule resolution :premises (t665.t1 t665.t4))
(step t665 (cl @p_258 @p_390) :rule subproof :discharge (t665.a0))
(step t666 (cl @p_391 @p_390) :rule resolution :premises (t664 t665))
(step t667 (cl @p_391 (not @p_390)) :rule implies_neg2)
(step t668 (cl @p_391 @p_391) :rule resolution :premises (t666 t667))
(step t669 (cl @p_391) :rule contraction :premises (t668))
(step t670 (cl @p_386) :rule resolution :premises (t651 t663 t669))
(step t671 (cl @p_258 @p_385) :rule implies :premises (t670))
(step t672 (cl (not @p_251) (not (forall ((?v0 Real) (?v1 Real)) (= (= (times$a ?v0 ?v1) ?v1) (or (= ?v1 0/1) (= ?v0 1/1))))) (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t673 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t673.t0 (cl (= (* 1/1 (- @p_79 ?v1)) (* -1/1 (- ?v1 @p_79)))) :rule poly_simp)
(step t673.t1 (cl (= @p_255 @p_252)) :rule poly_simp_rel :premises (t673.t0))
(step t673.t2 (cl (= @p_253 @p_253)) :rule refl)
(step t673.t3 (cl (= @p_256 @p_257)) :rule cong :premises (t673.t1 t673.t2))
(step t673.t4 (cl (= @p_257 @p_254)) :rule rare_rewrite :args ("eq-symm" @p_252 @p_253))
(step t673.t5 (cl (= @p_256 @p_254)) :rule trans :premises (t673.t3 t673.t4))
(step t673 (cl @p_251) :rule bind)
(step t674 (cl (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule resolution :premises (t672 t673 a12))
(step t675 (cl @p_385) :rule resolution :premises (t671 t674))
(step t676 (cl (not @p_381) (not @p_380) @p_376) :rule equiv_pos2)
(step t677 (cl (= @p_377 true)) :rule rare_rewrite :args ("eq-refl" @p_362))
(step t678 (cl (= @p_364 @p_364)) :rule refl)
(step t679 (cl (= @p_378 @p_383)) :rule cong :premises (t677 t678))
(step t680 (cl (= @p_383 @p_384)) :rule rare_rewrite :args ("eq-symm" true @p_364))
(step t681 (cl (= @p_384 @p_364)) :rule rare_rewrite :args ("bool-eq-true" @p_364))
(step t682 (cl (= @p_383 @p_364)) :rule trans :premises (t680 t681))
(step t683 (cl (= @p_378 @p_364)) :rule trans :premises (t679 t682))
(step t684 (cl (= @p_379 @p_382)) :rule cong :premises (t652 t683))
(step t685 (cl (= @p_382 @p_364)) :rule aci_simp)
(step t686 (cl (= @p_379 @p_364)) :rule trans :premises (t684 t685))
(step t687 (cl @p_381) :rule cong :premises (t686))
(step t688 (cl @p_380 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t689)
(assume t689.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t689.t0 (cl (or @p_375 @p_379)) :rule forall_inst :args (2/1 @p_362 @p_361))
(step t689.t1 (cl @p_375 @p_379) :rule or :premises (t689.t0))
(step t689.t2 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t689.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t689.t3.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t689.t3.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t689.t3.t0))
(step t689.t3.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t689.t3.t1))
(step t689.t3.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t689.t3.t2))
(step t689.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t689.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t689.t4.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t689.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t689.t4.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t689.t4.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t689.t4.t1 t689.t4.t2))
(step t689.t4.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t689.t4.t0 t689.t4.t3))
(step t689.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t689.t5 (cl @p_365) :rule trans :premises (t689.t3 t689.t4))
(step t689.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t689.t2 t689.t5 a17))
(step t689.t7 (cl @p_379) :rule resolution :premises (t689.t1 t689.t6))
(step t689 (cl @p_375 @p_379) :rule subproof :discharge (t689.a0))
(step t690 (cl @p_380 @p_379) :rule resolution :premises (t688 t689))
(step t691 (cl @p_380 (not @p_379)) :rule implies_neg2)
(step t692 (cl @p_380 @p_380) :rule resolution :premises (t690 t691))
(step t693 (cl @p_380) :rule contraction :premises (t692))
(step t694 (cl @p_376) :rule resolution :premises (t676 t687 t693))
(step t695 (cl @p_375 @p_364) :rule implies :premises (t694))
(step t696 (cl (not @p_365) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule equiv_pos2)
(anchor :step t697 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t697.t0 (cl (= (* 1/1 (- @p_366 ?v2)) (* -1/1 (- ?v2 @p_366)))) :rule poly_simp)
(step t697.t1 (cl (= @p_373 @p_367)) :rule poly_simp_rel :premises (t697.t0))
(step t697.t2 (cl (= @p_374 @p_369)) :rule cong :premises (t697.t1))
(step t697.t3 (cl (= (=> @p_117 @p_374) @p_371)) :rule cong :premises (t697.t2))
(step t697 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= (times$a ?v1 ?v0) ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(anchor :step t698 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t698.t0 (cl (= @p_371 @p_372)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_369))
(step t698.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t698.t2 (cl (= @p_369 @p_369)) :rule refl)
(step t698.t3 (cl (= @p_372 @p_370)) :rule cong :premises (t698.t1 t698.t2))
(step t698.t4 (cl (= @p_371 @p_370)) :rule trans :premises (t698.t0 t698.t3))
(step t698 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (= ?v0 0/1)) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))) :rule bind)
(step t699 (cl @p_365) :rule trans :premises (t697 t698))
(step t700 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule resolution :premises (t696 t699 a17))
(step t701 (cl @p_364) :rule resolution :premises (t695 t700))
(step t702 (cl (not @p_359) (not @p_358) @p_354) :rule equiv_pos2)
(step t703 (cl (= @p_356 false)) :rule evaluate)
(step t704 (cl (= (* -2/1 (- 2/1 @p_309)) (* 2/1 (- @p_309 2/1)))) :rule poly_simp)
(step t705 (cl (= @p_355 @p_344)) :rule poly_simp_rel :premises (t704))
(step t706 (cl (= @p_357 @p_360)) :rule cong :premises (t703 t705))
(step t707 (cl (= @p_360 @p_344)) :rule aci_simp)
(step t708 (cl (= @p_357 @p_344)) :rule trans :premises (t706 t707))
(step t709 (cl @p_359) :rule cong :premises (t708))
(step t710 (cl @p_358 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t711)
(assume t711.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t711.t0 (cl (or @p_353 @p_357)) :rule forall_inst :args (1/1 2/1))
(step t711.t1 (cl @p_353 @p_357) :rule or :premises (t711.t0))
(step t711.t2 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t711.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t711.t3.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t711.t3.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t711.t3.t0))
(step t711.t3.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t711.t3.t1))
(step t711.t3 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t711.t4 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t711.t4.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t711.t4.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t711.t4.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t711.t4.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t711.t4.t1 t711.t4.t2))
(step t711.t4.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t711.t4.t0 t711.t4.t3))
(step t711.t4 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t711.t5 (cl @p_345) :rule trans :premises (t711.t3 t711.t4))
(step t711.t6 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t711.t2 t711.t5 a19))
(step t711.t7 (cl @p_357) :rule resolution :premises (t711.t1 t711.t6))
(step t711 (cl @p_353 @p_357) :rule subproof :discharge (t711.a0))
(step t712 (cl @p_358 @p_357) :rule resolution :premises (t710 t711))
(step t713 (cl @p_358 (not @p_357)) :rule implies_neg2)
(step t714 (cl @p_358 @p_358) :rule resolution :premises (t712 t713))
(step t715 (cl @p_358) :rule contraction :premises (t714))
(step t716 (cl @p_354) :rule resolution :premises (t702 t709 t715))
(step t717 (cl @p_353 @p_344) :rule implies :premises (t716))
(step t718 (cl (not @p_345) (not (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule equiv_pos2)
(anchor :step t719 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t719.t0 (cl (= (* 1/1 (- @p_346 ?v1)) (* -1/1 (- ?v1 @p_346)))) :rule poly_simp)
(step t719.t1 (cl (= @p_352 @p_347)) :rule poly_simp_rel :premises (t719.t0))
(step t719.t2 (cl (= (=> @p_117 @p_352) @p_349)) :rule cong :premises (t719.t1))
(step t719 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= (divide$ (times$a ?v0 ?v1) ?v0) ?v1))) (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(anchor :step t720 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t720.t0 (cl (= @p_349 @p_351)) :rule rare_rewrite :args ("bool-impl-elim" @p_117 @p_347))
(step t720.t1 (cl (= @p_350 @p_116)) :rule rare_rewrite :args ("bool-double-not-elim" @p_116))
(step t720.t2 (cl (= @p_347 @p_347)) :rule refl)
(step t720.t3 (cl (= @p_351 @p_348)) :rule cong :premises (t720.t1 t720.t2))
(step t720.t4 (cl (= @p_349 @p_348)) :rule trans :premises (t720.t0 t720.t3))
(step t720 (cl (= (forall ((?v0 Real) (?v1 Real)) (=> (not (= ?v0 0/1)) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))) :rule bind)
(step t721 (cl @p_345) :rule trans :premises (t719 t720))
(step t722 (cl (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule resolution :premises (t718 t721 a19))
(step t723 (cl @p_344) :rule resolution :premises (t717 t722))
(step t724 (cl (or @p_343 @p_342)) :rule forall_inst :args (@p_4 1/1 2/1))
(step t725 (cl @p_343 @p_342) :rule or :premises (t724))
(step t726 (cl @p_342) :rule resolution :premises (t725 a2))
(step t727 (cl (or @p_292 @p_340)) :rule forall_inst :args (@p_1 @p_296))
(step t728 (cl @p_292 @p_340) :rule or :premises (t727))
(step t729 (cl @p_340) :rule resolution :premises (t728 a6))
(step t730 (cl (not @p_336) (not @p_335) @p_330) :rule equiv_pos2)
(step t731 (cl (= @p_296 @p_296)) :rule refl)
(step t732 (cl (= @p_333 @p_327)) :rule cong :premises (t600 t731))
(step t733 (cl (= @p_331 @p_337)) :rule poly_simp)
(step t734 (cl (= @p_334 @p_338)) :rule cong :premises (t732 t733))
(step t735 (cl (= (* 1/1 (- @p_327 @p_337)) (* -2/1 (- @p_314 @p_328)))) :rule poly_simp)
(step t736 (cl (= @p_338 @p_329)) :rule poly_simp_rel :premises (t735))
(step t737 (cl (= @p_334 @p_329)) :rule trans :premises (t734 t736))
(step t738 (cl @p_336) :rule cong :premises (t737))
(step t739 (cl @p_335 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t740)
(assume t740.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t740.t0 (cl (or @p_279 @p_334)) :rule forall_inst :args (@p_1 @p_1 @p_296))
(step t740.t1 (cl @p_279 @p_334) :rule or :premises (t740.t0))
(step t740.t2 (cl @p_334) :rule resolution :premises (t740.t1 t740.a0))
(step t740 (cl @p_279 @p_334) :rule subproof :discharge (t740.a0))
(step t741 (cl @p_335 @p_334) :rule resolution :premises (t739 t740))
(step t742 (cl @p_335 (not @p_334)) :rule implies_neg2)
(step t743 (cl @p_335 @p_335) :rule resolution :premises (t741 t742))
(step t744 (cl @p_335) :rule contraction :premises (t743))
(step t745 (cl @p_330) :rule resolution :premises (t730 t738 t744))
(step t746 (cl @p_279 @p_329) :rule implies :premises (t745))
(step t747 (cl @p_329) :rule resolution :premises (t746 a1))
(step t748 (cl (or @p_326 @p_315)) :rule forall_inst :args (@p_1 @p_296))
(step t749 (cl @p_326 @p_315) :rule or :premises (t748))
(step t750 (cl @p_315) :rule resolution :premises (t749 t622))
(step t751 (cl (or @p_312 @p_311)) :rule forall_inst :args (@p_4 @p_306 1/1))
(step t752 (cl @p_312 @p_311) :rule or :premises (t751))
(step t753 (cl @p_311) :rule resolution :premises (t752 a27))
(step t754 (cl (or @p_292 @p_305)) :rule forall_inst :args (@p_4 2/1))
(step t755 (cl @p_292 @p_305) :rule or :premises (t754))
(step t756 (cl @p_305) :rule resolution :premises (t755 a6))
(step t757 (cl (or @p_273 @p_303)) :rule forall_inst :args (1/1 @p_4 @p_139))
(step t758 (cl @p_273 @p_303) :rule or :premises (t757))
(step t759 (cl @p_303) :rule resolution :premises (t758 a4))
(step t760 (cl (or @p_292 @p_299)) :rule forall_inst :args (@p_139 @p_296))
(step t761 (cl @p_292 @p_299) :rule or :premises (t760))
(step t762 (cl @p_299) :rule resolution :premises (t761 a6))
(step t763 (cl (or @p_273 @p_295)) :rule forall_inst :args (2/1 @p_4 @p_1))
(step t764 (cl @p_273 @p_295) :rule or :premises (t763))
(step t765 (cl @p_295) :rule resolution :premises (t764 a4))
(step t766 (cl (or @p_292 @p_291)) :rule forall_inst :args (@p_6 2/1))
(step t767 (cl @p_292 @p_291) :rule or :premises (t766))
(step t768 (cl @p_291) :rule resolution :premises (t767 a6))
(step t769 (cl (not @p_286) (not @p_285) @p_280) :rule equiv_pos2)
(step t770 (cl (= @p_282 2/1)) :rule evaluate)
(step t771 (cl (= @p_274 @p_274)) :rule refl)
(step t772 (cl (= @p_283 @p_275)) :rule cong :premises (t770 t771))
(step t773 (cl (= @p_281 @p_287)) :rule poly_simp)
(step t774 (cl (= @p_284 @p_288)) :rule cong :premises (t772 t773))
(step t775 (cl (= (* -1/2 (- @p_275 @p_287)) (* 1/1 (- @p_277 @p_276)))) :rule poly_simp)
(step t776 (cl (= @p_288 @p_278)) :rule poly_simp_rel :premises (t775))
(step t777 (cl (= @p_284 @p_278)) :rule trans :premises (t774 t776))
(step t778 (cl @p_286) :rule cong :premises (t777))
(step t779 (cl @p_285 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t780)
(assume t780.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t780.t0 (cl (or @p_279 @p_284)) :rule forall_inst :args (1/1 1/1 @p_274))
(step t780.t1 (cl @p_279 @p_284) :rule or :premises (t780.t0))
(step t780.t2 (cl @p_284) :rule resolution :premises (t780.t1 t780.a0))
(step t780 (cl @p_279 @p_284) :rule subproof :discharge (t780.a0))
(step t781 (cl @p_285 @p_284) :rule resolution :premises (t779 t780))
(step t782 (cl @p_285 (not @p_284)) :rule implies_neg2)
(step t783 (cl @p_285 @p_285) :rule resolution :premises (t781 t782))
(step t784 (cl @p_285) :rule contraction :premises (t783))
(step t785 (cl @p_280) :rule resolution :premises (t769 t778 t784))
(step t786 (cl @p_279 @p_278) :rule implies :premises (t785))
(step t787 (cl @p_278) :rule resolution :premises (t786 a1))
(step t788 (cl (or @p_273 @p_272)) :rule forall_inst :args (2/1 @p_4 @p_139))
(step t789 (cl @p_273 @p_272) :rule or :premises (t788))
(step t790 (cl @p_272) :rule resolution :premises (t789 a4))
(step t791 (cl (not (! (= (! (or @p_423 @p_424 @p_425 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_447) :named @p_448) (! (or @p_423 @p_424 @p_425 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_267) :named @p_445)) :named @p_572)) (not @p_448) @p_445) :rule equiv_pos2)
(step t792 (cl (= @p_447 @p_267)) :rule rare_rewrite :args ("bool-double-not-elim" @p_267))
(step t793 (cl @p_572) :rule cong :premises (t792))
(step t794 (cl (! (=> (! (and @p_413 @p_410 @p_409 @p_407 @p_406 @p_405 @p_396 @p_385 @p_364 @p_344 @p_342 @p_340 @p_329 @p_315 @p_311 @p_305 @p_303 @p_299 @p_295 @p_291 @p_278 @p_272 @p_446) :named @p_471) (! (and @p_413 @p_476 @p_475 @p_409 @p_474 @p_473 @p_446) :named @p_477)) :named @p_571) @p_471) :rule implies_neg1)
(anchor :step t795)
(assume t795.a0 @p_413)
(assume t795.a1 @p_410)
(assume t795.a2 @p_409)
(assume t795.a3 @p_407)
(assume t795.a4 @p_406)
(assume t795.a5 @p_405)
(assume t795.a6 @p_396)
(assume t795.a7 @p_385)
(assume t795.a8 @p_364)
(assume t795.a9 @p_344)
(assume t795.a10 @p_342)
(assume t795.a11 @p_340)
(assume t795.a12 @p_329)
(assume t795.a13 @p_315)
(assume t795.a14 @p_311)
(assume t795.a15 @p_305)
(assume t795.a16 @p_303)
(assume t795.a17 @p_299)
(assume t795.a18 @p_295)
(assume t795.a19 @p_291)
(assume t795.a20 @p_278)
(assume t795.a21 @p_272)
(assume t795.a22 @p_446)
(step t795.t0 (cl @p_387) :rule symm :premises (t675))
(step t795.t1 (cl (= @p_304 @p_307)) :rule cong :premises (t795.t0))
(step t795.t2 (cl @p_388) :rule refl)
(step t795.t3 (cl (= @p_341 @p_308)) :rule cong :premises (t795.t1 t795.t2))
(step t795.t4 (cl (= @p_308 @p_310)) :rule symm :premises (t753))
(step t795.t5 (cl (= @p_310 @p_304)) :rule cong :premises (t723))
(step t795.t6 (cl (= @p_296 @p_270)) :rule trans :premises (t726 t795.t3 t795.t4 t795.t5 t756))
(step t795.t7 (cl (= @p_139 @p_139)) :rule refl)
(step t795.t8 (cl (= @p_297 @p_271)) :rule cong :premises (t795.t6 t795.t7))
(step t795.t9 (cl (= @p_268 @p_274)) :rule symm :premises (t626))
(step t795.t10 (cl (= @p_269 @p_275)) :rule cong :premises (t795.t9))
(step t795.t11 (cl @p_476) :rule trans :premises (t762 t795.t8 t790 t795.t10))
(step t795.t12 (cl (= @p_361 @p_301)) :rule symm :premises (t632))
(step t795.t13 (cl (= @p_4 @p_301)) :rule trans :premises (t650 t795.t12))
(step t795.t14 (cl (= @p_268 @p_302)) :rule cong :premises (t795.t13 t795.t7))
(step t795.t15 (cl (= @p_300 @p_277)) :rule cong :premises (t795.t9))
(step t795.t16 (cl @p_475) :rule trans :premises (t626 t795.t14 t759 t795.t15 t787))
(step t795.t17 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t795.t18 (cl @p_474) :rule trans :premises (t795.t17 t750))
(step t795.t19 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t795.t20 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t795.t21 (cl (= @p_362 @p_6)) :rule trans :premises (t795.t19 t795.t20))
(step t795.t22 (cl (= 2/1 2/1)) :rule refl)
(step t795.t23 (cl (= @p_363 @p_290)) :rule cong :premises (t795.t21 t795.t22))
(step t795.t24 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t795.t25 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t795.t26 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t795.t27 (cl @p_355) :rule symm :premises (t723))
(step t795.t28 (cl (= @p_304 @p_310)) :rule cong :premises (t795.t27))
(step t795.t29 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t795.t30 (cl (= @p_308 @p_341)) :rule cong :premises (t795.t29 t795.t2))
(step t795.t31 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t795.t32 (cl (= @p_270 @p_296)) :rule trans :premises (t795.t26 t795.t28 t753 t795.t30 t795.t31))
(step t795.t33 (cl (= @p_1 @p_1)) :rule refl)
(step t795.t34 (cl (= @p_294 @p_339)) :rule cong :premises (t795.t32 t795.t33))
(step t795.t35 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t795.t36 (cl @p_473) :rule trans :premises (t650 t701 t795.t23 t768 t795.t24 t795.t25 t795.t34 t795.t35 t747))
(step t795.t37 (cl @p_477) :rule and_intro :premises (t617 t795.t11 t795.t16 t623 t795.t18 t795.t36 t795.a22))
(step t795 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_447 @p_477) :rule subproof :discharge (t795.a0 t795.a1 t795.a2 t795.a3 t795.a4 t795.a5 t795.a6 t795.a7 t795.a8 t795.a9 t795.a10 t795.a11 t795.a12 t795.a13 t795.a14 t795.a15 t795.a16 t795.a17 t795.a18 t795.a19 t795.a20 t795.a21 t795.a22))
(step t796 (cl (! (not @p_471) :named @p_472) @p_413) :rule and_pos :args (0))
(step t797 (cl @p_472 @p_410) :rule and_pos :args (1))
(step t798 (cl @p_472 @p_409) :rule and_pos :args (2))
(step t799 (cl @p_472 @p_407) :rule and_pos :args (3))
(step t800 (cl @p_472 @p_406) :rule and_pos :args (4))
(step t801 (cl @p_472 @p_405) :rule and_pos :args (5))
(step t802 (cl @p_472 @p_396) :rule and_pos :args (6))
(step t803 (cl @p_472 @p_385) :rule and_pos :args (7))
(step t804 (cl @p_472 @p_364) :rule and_pos :args (8))
(step t805 (cl @p_472 @p_344) :rule and_pos :args (9))
(step t806 (cl @p_472 @p_342) :rule and_pos :args (10))
(step t807 (cl @p_472 @p_340) :rule and_pos :args (11))
(step t808 (cl @p_472 @p_329) :rule and_pos :args (12))
(step t809 (cl @p_472 @p_315) :rule and_pos :args (13))
(step t810 (cl @p_472 @p_311) :rule and_pos :args (14))
(step t811 (cl @p_472 @p_305) :rule and_pos :args (15))
(step t812 (cl @p_472 @p_303) :rule and_pos :args (16))
(step t813 (cl @p_472 @p_299) :rule and_pos :args (17))
(step t814 (cl @p_472 @p_295) :rule and_pos :args (18))
(step t815 (cl @p_472 @p_291) :rule and_pos :args (19))
(step t816 (cl @p_472 @p_278) :rule and_pos :args (20))
(step t817 (cl @p_472 @p_272) :rule and_pos :args (21))
(step t818 (cl @p_472 @p_446) :rule and_pos :args (22))
(step t819 (cl @p_477 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472) :rule resolution :premises (t795 t796 t797 t798 t799 t800 t801 t802 t803 t804 t805 t806 t807 t808 t809 t810 t811 t812 t813 t814 t815 t816 t817 t818))
(step t820 (cl @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_472 @p_477) :rule reordering :premises (t819))
(step t821 (cl @p_472 @p_477) :rule contraction :premises (t820))
(step t822 (cl @p_571 @p_477) :rule resolution :premises (t794 t821))
(step t823 (cl @p_571 (! (not @p_477) :named @p_478)) :rule implies_neg2)
(step t824 (cl @p_571 @p_571) :rule resolution :premises (t822 t823))
(step t825 (cl @p_571) :rule contraction :premises (t824))
(step t826 (cl @p_472 @p_477) :rule implies :premises (t825))
(step t827 (cl (! (=> @p_477 false) :named @p_479) @p_477) :rule implies_neg1)
(anchor :step t828)
(assume t828.a0 @p_413)
(assume t828.a1 @p_476)
(assume t828.a2 @p_475)
(assume t828.a3 @p_409)
(assume t828.a4 @p_474)
(assume t828.a5 @p_473)
(assume t828.a6 @p_446)
(step t828.t0 (cl (not (! (= @p_446 (! (> @p_485 0/1) :named @p_486)) :named @p_570)) @p_447 @p_486) :rule equiv_pos2)
(step t828.t1 (cl (= @p_486 (! (not @p_566) :named @p_568))) :rule rare_rewrite :args ("arith-elim-gt" @p_485 0/1))
(step t828.t2 (cl (= @p_488 @p_566)) :rule rare_rewrite :args ("arith-elim-leq" @p_485 0/1))
(step t828.t3 (cl (= @p_566 @p_488)) :rule symm :premises (t828.t2))
(step t828.t4 (cl (= @p_568 @p_567)) :rule cong :premises (t828.t3))
(step t828.t5 (cl (= @p_486 @p_567)) :rule trans :premises (t828.t1 t828.t4))
(step t828.t6 (cl (= (* -1/1 (- 0/1 @p_485)) (* -1/1 (- @p_266 0/1)))) :rule poly_simp)
(step t828.t7 (cl (= @p_566 @p_267)) :rule poly_simp_rel :premises (t828.t6))
(step t828.t8 (cl (= @p_488 @p_267)) :rule trans :premises (t828.t2 t828.t7))
(step t828.t9 (cl (= @p_567 @p_446)) :rule cong :premises (t828.t8))
(step t828.t10 (cl (= @p_486 @p_446)) :rule trans :premises (t828.t5 t828.t9))
(step t828.t11 (cl @p_570) :rule symm :premises (t828.t10))
(step t828.t12 (cl @p_486) :rule resolution :premises (t828.t0 t828.t11 t828.a6))
(step t828.t13 (cl (not (! (= @p_488 (! (not @p_486) :named @p_487)) :named @p_569)) @p_567 @p_487) :rule equiv_pos2)
(step t828.t14 (cl (= @p_487 @p_447)) :rule cong :premises (t828.t10))
(step t828.t15 (cl (= @p_487 @p_267)) :rule trans :premises (t828.t14 t792))
(step t828.t16 (cl (= @p_267 @p_487)) :rule symm :premises (t828.t15))
(step t828.t17 (cl @p_569) :rule trans :premises (t828.t8 t828.t16))
(step t828.t18 (cl (not (! (= @p_487 @p_488) :named @p_564)) (not @p_487) @p_488) :rule equiv_pos2)
(step t828.t19 (cl @p_565) :rule symm :premises (t828.t8))
(step t828.t20 (cl @p_564) :rule trans :premises (t828.t15 t828.t19))
(step t828.t21 (cl (! (=> @p_486 false) :named @p_489) @p_486) :rule implies_neg1)
(anchor :step t828.t22)
(assume t828.t22.a0 @p_486)
(step t828.t22.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_485) :named @p_507) @p_506 (! (* 1/2 @p_503) :named @p_504) (! (* -2/1 @p_501) :named @p_502) (! (* 2/1 @p_499) :named @p_500) (! (* -1/1 @p_497) :named @p_498) (! (* 2/1 @p_494) :named @p_495)) :named @p_508) (! (+ @p_175 0/1 @p_492 @p_491 @p_490 @p_175 @p_490) :named @p_493)) :named @p_509) false) :named @p_555)) (not @p_509) false) :rule equiv_pos2)
(step t828.t22.t1 (cl (= @p_509 (! (not (! (>= @p_508 @p_493) :named @p_556)) :named @p_557))) :rule rare_rewrite :args ("arith-elim-lt" @p_508 @p_493))
(step t828.t22.t2 (cl (= @p_508 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 @p_248 @p_484 @p_561 @p_560 @p_559) :named @p_562))) :rule poly_simp)
(step t828.t22.t3 (cl (= @p_561 0/1)) :rule poly_simp)
(step t828.t22.t4 (cl (= @p_560 0/1)) :rule poly_simp)
(step t828.t22.t5 (cl (= @p_559 0/1)) :rule poly_simp)
(step t828.t22.t6 (cl (= @p_562 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 @p_248 @p_484 0/1 0/1 0/1) :named @p_563))) :rule cong :premises (t828.t22.t3 t828.t22.t4 t828.t22.t5))
(step t828.t22.t7 (cl (= @p_563 0/1)) :rule poly_simp)
(step t828.t22.t8 (cl (= @p_562 0/1)) :rule trans :premises (t828.t22.t6 t828.t22.t7))
(step t828.t22.t9 (cl (= @p_508 0/1)) :rule trans :premises (t828.t22.t2 t828.t22.t8))
(step t828.t22.t10 (cl (= @p_175 0/1)) :rule evaluate)
(step t828.t22.t11 (cl @p_60) :rule refl)
(step t828.t22.t12 (cl (= @p_492 0/1)) :rule evaluate)
(step t828.t22.t13 (cl (= @p_491 0/1)) :rule evaluate)
(step t828.t22.t14 (cl (= @p_490 0/1)) :rule evaluate)
(step t828.t22.t15 (cl (= @p_493 @p_558)) :rule cong :premises (t828.t22.t10 t828.t22.t11 t828.t22.t12 t828.t22.t13 t828.t22.t14 t828.t22.t10 t828.t22.t14))
(step t828.t22.t16 (cl (= @p_558 0/1)) :rule evaluate)
(step t828.t22.t17 (cl (= @p_493 0/1)) :rule trans :premises (t828.t22.t15 t828.t22.t16))
(step t828.t22.t18 (cl (= @p_556 @p_190)) :rule cong :premises (t828.t22.t9 t828.t22.t17))
(step t828.t22.t19 (cl @p_191) :rule evaluate)
(step t828.t22.t20 (cl (= @p_556 true)) :rule trans :premises (t828.t22.t18 t828.t22.t19))
(step t828.t22.t21 (cl (= @p_557 @p_189)) :rule cong :premises (t828.t22.t20))
(step t828.t22.t22 (cl (= @p_189 false)) :rule evaluate)
(step t828.t22.t23 (cl (= @p_557 false)) :rule trans :premises (t828.t22.t21 t828.t22.t22))
(step t828.t22.t24 (cl @p_555) :rule trans :premises (t828.t22.t1 t828.t22.t23))
(step t828.t22.t25 (cl (not (! (< @p_507 @p_175) :named @p_548)) (! (not @p_545) :named @p_550) (! (not (! (= @p_504 @p_492) :named @p_534)) :named @p_551) (! (not (! (= @p_502 @p_491) :named @p_528)) :named @p_552) (! (not (! (= @p_500 @p_490) :named @p_522)) :named @p_553) (! (not (! (= @p_498 @p_175) :named @p_516)) :named @p_554) (not (! (= @p_495 @p_490) :named @p_510)) @p_509) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1))
(step t828.t22.t26 (cl (=> (! (and @p_183 @p_486) :named @p_549) @p_548)) :rule la_mult_neg)
(step t828.t22.t27 (cl (not @p_549) @p_548) :rule implies :premises (t828.t22.t26))
(step t828.t22.t28 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t828.t22.t29 (cl (not @p_185) @p_183) :rule equiv1 :premises (t828.t22.t28))
(step t828.t22.t30 (cl @p_185) :rule evaluate)
(step t828.t22.t31 (cl @p_183) :rule resolution :premises (t828.t22.t29 t828.t22.t30))
(step t828.t22.t32 (cl @p_549) :rule and_intro :premises (t828.t22.t31 t828.t22.a0))
(step t828.t22.t33 (cl @p_548) :rule resolution :premises (t828.t22.t27 t828.t22.t32))
(step t828.t22.t34 (cl @p_547 @p_483 @p_545) :rule equiv_pos2)
(step t828.t22.t35 (cl (= (* 1/1 (- @p_506 0/1)) (* 1/1 (- @p_4 @p_328)))) :rule poly_simp)
(step t828.t22.t36 (cl (= @p_545 @p_473)) :rule poly_simp_rel :premises (t828.t22.t35))
(step t828.t22.t37 (cl @p_546) :rule symm :premises (t828.t22.t36))
(step t828.t22.t38 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t828.t22.t39 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t828.t22.t40 (cl (= @p_362 @p_6)) :rule trans :premises (t828.t22.t38 t828.t22.t39))
(step t828.t22.t41 (cl (= 2/1 2/1)) :rule refl)
(step t828.t22.t42 (cl (= @p_363 @p_290)) :rule cong :premises (t828.t22.t40 t828.t22.t41))
(step t828.t22.t43 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t828.t22.t44 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t828.t22.t45 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t828.t22.t46 (cl @p_355) :rule symm :premises (t723))
(step t828.t22.t47 (cl (= @p_304 @p_310)) :rule cong :premises (t828.t22.t46))
(step t828.t22.t48 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t828.t22.t49 (cl @p_388) :rule refl)
(step t828.t22.t50 (cl (= @p_308 @p_341)) :rule cong :premises (t828.t22.t48 t828.t22.t49))
(step t828.t22.t51 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t828.t22.t52 (cl (= @p_270 @p_296)) :rule trans :premises (t828.t22.t45 t828.t22.t47 t753 t828.t22.t50 t828.t22.t51))
(step t828.t22.t53 (cl (= @p_1 @p_1)) :rule refl)
(step t828.t22.t54 (cl (= @p_294 @p_339)) :rule cong :premises (t828.t22.t52 t828.t22.t53))
(step t828.t22.t55 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t828.t22.t56 (cl @p_473) :rule trans :premises (t650 t701 t828.t22.t42 t768 t828.t22.t43 t828.t22.t44 t828.t22.t54 t828.t22.t55 t747))
(step t828.t22.t57 (cl @p_545) :rule resolution :premises (t828.t22.t34 t828.t22.t37 t828.t22.t56))
(step t828.t22.t58 (cl (! (=> (! (and @p_536 @p_535) :named @p_537) @p_534) :named @p_544)) :rule la_mult_pos)
(step t828.t22.t59 (cl (! (not @p_537) :named @p_543) @p_534) :rule implies :premises (t828.t22.t58))
(step t828.t22.t60 (cl (= @p_542 @p_536)) :rule equiv_simplify)
(step t828.t22.t61 (cl (not @p_542) @p_536) :rule equiv1 :premises (t828.t22.t60))
(step t828.t22.t62 (cl @p_542) :rule evaluate)
(step t828.t22.t63 (cl @p_536) :rule resolution :premises (t828.t22.t61 t828.t22.t62))
(step t828.t22.t64 (cl (not @p_538) @p_482 @p_535) :rule equiv_pos2)
(step t828.t22.t65 (cl (= (* 2/1 (- @p_328 @p_313)) (* 1/1 @p_541))) :rule poly_simp)
(step t828.t22.t66 (cl (= @p_474 @p_540)) :rule poly_simp_rel :premises (t828.t22.t65))
(step t828.t22.t67 (cl (= (* 2/1 (- @p_503 0/1)) (* 2/1 @p_541))) :rule poly_simp)
(step t828.t22.t68 (cl (= @p_535 @p_540)) :rule poly_simp_rel :premises (t828.t22.t67))
(step t828.t22.t69 (cl (= @p_540 @p_535)) :rule symm :premises (t828.t22.t68))
(step t828.t22.t70 (cl @p_538) :rule trans :premises (t828.t22.t66 t828.t22.t69))
(step t828.t22.t71 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t828.t22.t72 (cl @p_474) :rule trans :premises (t828.t22.t71 t750))
(step t828.t22.t73 (cl @p_535) :rule resolution :premises (t828.t22.t64 t828.t22.t70 t828.t22.t72))
(step t828.t22.t74 (cl @p_537) :rule and_intro :premises (t828.t22.t63 t828.t22.t73))
(step t828.t22.t75 (cl @p_534) :rule resolution :premises (t828.t22.t59 t828.t22.t74))
(step t828.t22.t76 (cl (=> (! (and @p_530 @p_529) :named @p_531) @p_528)) :rule la_mult_neg)
(step t828.t22.t77 (cl (not @p_531) @p_528) :rule implies :premises (t828.t22.t76))
(step t828.t22.t78 (cl (= @p_533 @p_530)) :rule equiv_simplify)
(step t828.t22.t79 (cl (not @p_533) @p_530) :rule equiv1 :premises (t828.t22.t78))
(step t828.t22.t80 (cl @p_533) :rule evaluate)
(step t828.t22.t81 (cl @p_530) :rule resolution :premises (t828.t22.t79 t828.t22.t80))
(step t828.t22.t82 (cl (not @p_532) @p_425 @p_529) :rule equiv_pos2)
(step t828.t22.t83 (cl (= (* 1/1 (- @p_501 0/1)) (* 1/1 (- @p_6 @p_408)))) :rule poly_simp)
(step t828.t22.t84 (cl (= @p_529 @p_409)) :rule poly_simp_rel :premises (t828.t22.t83))
(step t828.t22.t85 (cl @p_532) :rule symm :premises (t828.t22.t84))
(step t828.t22.t86 (cl @p_529) :rule resolution :premises (t828.t22.t82 t828.t22.t85 t623))
(step t828.t22.t87 (cl @p_531) :rule and_intro :premises (t828.t22.t81 t828.t22.t86))
(step t828.t22.t88 (cl @p_528) :rule resolution :premises (t828.t22.t77 t828.t22.t87))
(step t828.t22.t89 (cl (! (=> (! (and @p_512 @p_523) :named @p_524) @p_522) :named @p_527)) :rule la_mult_pos)
(step t828.t22.t90 (cl (! (not @p_524) :named @p_526) @p_522) :rule implies :premises (t828.t22.t89))
(step t828.t22.t91 (cl (= @p_515 @p_512)) :rule equiv_simplify)
(step t828.t22.t92 (cl (not @p_515) @p_512) :rule equiv1 :premises (t828.t22.t91))
(step t828.t22.t93 (cl @p_515) :rule evaluate)
(step t828.t22.t94 (cl @p_512) :rule resolution :premises (t828.t22.t92 t828.t22.t93))
(step t828.t22.t95 (cl (not @p_525) @p_481 @p_523) :rule equiv_pos2)
(step t828.t22.t96 (cl (= (* 1/1 (- @p_499 0/1)) (* 1/1 (- @p_274 @p_276)))) :rule poly_simp)
(step t828.t22.t97 (cl (= @p_523 @p_475)) :rule poly_simp_rel :premises (t828.t22.t96))
(step t828.t22.t98 (cl @p_525) :rule symm :premises (t828.t22.t97))
(step t828.t22.t99 (cl (= @p_361 @p_301)) :rule symm :premises (t632))
(step t828.t22.t100 (cl (= @p_4 @p_301)) :rule trans :premises (t650 t828.t22.t99))
(step t828.t22.t101 (cl (= @p_139 @p_139)) :rule refl)
(step t828.t22.t102 (cl (= @p_268 @p_302)) :rule cong :premises (t828.t22.t100 t828.t22.t101))
(step t828.t22.t103 (cl (= @p_268 @p_274)) :rule symm :premises (t626))
(step t828.t22.t104 (cl (= @p_300 @p_277)) :rule cong :premises (t828.t22.t103))
(step t828.t22.t105 (cl @p_475) :rule trans :premises (t626 t828.t22.t102 t759 t828.t22.t104 t787))
(step t828.t22.t106 (cl @p_523) :rule resolution :premises (t828.t22.t95 t828.t22.t98 t828.t22.t105))
(step t828.t22.t107 (cl @p_524) :rule and_intro :premises (t828.t22.t94 t828.t22.t106))
(step t828.t22.t108 (cl @p_522) :rule resolution :premises (t828.t22.t90 t828.t22.t107))
(step t828.t22.t109 (cl (! (=> (! (and @p_183 @p_517) :named @p_518) @p_516) :named @p_521)) :rule la_mult_neg)
(step t828.t22.t110 (cl (! (not @p_518) :named @p_520) @p_516) :rule implies :premises (t828.t22.t109))
(step t828.t22.t111 (cl (not @p_519) @p_480 @p_517) :rule equiv_pos2)
(step t828.t22.t112 (cl (= (* -1/1 (- @p_497 0/1)) (* -1/1 (- @p_298 @p_275)))) :rule poly_simp)
(step t828.t22.t113 (cl (= @p_517 @p_476)) :rule poly_simp_rel :premises (t828.t22.t112))
(step t828.t22.t114 (cl @p_519) :rule symm :premises (t828.t22.t113))
(step t828.t22.t115 (cl @p_387) :rule symm :premises (t675))
(step t828.t22.t116 (cl (= @p_304 @p_307)) :rule cong :premises (t828.t22.t115))
(step t828.t22.t117 (cl (= @p_341 @p_308)) :rule cong :premises (t828.t22.t116 t828.t22.t49))
(step t828.t22.t118 (cl (= @p_308 @p_310)) :rule symm :premises (t753))
(step t828.t22.t119 (cl (= @p_310 @p_304)) :rule cong :premises (t723))
(step t828.t22.t120 (cl (= @p_296 @p_270)) :rule trans :premises (t726 t828.t22.t117 t828.t22.t118 t828.t22.t119 t756))
(step t828.t22.t121 (cl (= @p_297 @p_271)) :rule cong :premises (t828.t22.t120 t828.t22.t101))
(step t828.t22.t122 (cl (= @p_269 @p_275)) :rule cong :premises (t828.t22.t103))
(step t828.t22.t123 (cl @p_476) :rule trans :premises (t762 t828.t22.t121 t790 t828.t22.t122))
(step t828.t22.t124 (cl @p_517) :rule resolution :premises (t828.t22.t111 t828.t22.t114 t828.t22.t123))
(step t828.t22.t125 (cl @p_518) :rule and_intro :premises (t828.t22.t31 t828.t22.t124))
(step t828.t22.t126 (cl @p_516) :rule resolution :premises (t828.t22.t110 t828.t22.t125))
(step t828.t22.t127 (cl (=> (! (and @p_512 @p_511) :named @p_513) @p_510)) :rule la_mult_pos)
(step t828.t22.t128 (cl (not @p_513) @p_510) :rule implies :premises (t828.t22.t127))
(step t828.t22.t129 (cl (not @p_514) @p_423 @p_511) :rule equiv_pos2)
(step t828.t22.t130 (cl (= (* 1/1 (- @p_494 0/1)) (* 1/1 @p_422))) :rule poly_simp)
(step t828.t22.t131 (cl (= @p_511 @p_413)) :rule poly_simp_rel :premises (t828.t22.t130))
(step t828.t22.t132 (cl @p_514) :rule symm :premises (t828.t22.t131))
(step t828.t22.t133 (cl @p_511) :rule resolution :premises (t828.t22.t129 t828.t22.t132 t617))
(step t828.t22.t134 (cl @p_513) :rule and_intro :premises (t828.t22.t94 t828.t22.t133))
(step t828.t22.t135 (cl @p_510) :rule resolution :premises (t828.t22.t128 t828.t22.t134))
(step t828.t22.t136 (cl @p_509) :rule resolution :premises (t828.t22.t25 t828.t22.t33 t828.t22.t57 t828.t22.t75 t828.t22.t88 t828.t22.t108 t828.t22.t126 t828.t22.t135))
(step t828.t22.t137 (cl false) :rule resolution :premises (t828.t22.t0 t828.t22.t24 t828.t22.t136))
(step t828.t22 (cl @p_487 false) :rule subproof :discharge (t828.t22.a0))
(step t828.t23 (cl @p_489 false) :rule resolution :premises (t828.t21 t828.t22))
(step t828.t24 (cl @p_489 @p_133) :rule implies_neg2)
(step t828.t25 (cl @p_489 @p_489) :rule resolution :premises (t828.t23 t828.t24))
(step t828.t26 (cl @p_489) :rule contraction :premises (t828.t25))
(step t828.t27 (cl (= @p_489 @p_487)) :rule implies_simplify)
(step t828.t28 (cl (not @p_489) @p_487) :rule equiv1 :premises (t828.t27))
(step t828.t29 (cl @p_487) :rule resolution :premises (t828.t26 t828.t28))
(step t828.t30 (cl @p_488) :rule resolution :premises (t828.t18 t828.t20 t828.t29))
(step t828.t31 (cl @p_487) :rule resolution :premises (t828.t13 t828.t17 t828.t30))
(step t828.t32 (cl) :rule resolution :premises (t828.t12 t828.t31))
(step t828 (cl @p_423 @p_480 @p_481 @p_425 @p_482 @p_483 @p_447 false) :rule subproof :discharge (t828.a0 t828.a1 t828.a2 t828.a3 t828.a4 t828.a5 t828.a6))
(step t829 (cl @p_478 @p_413) :rule and_pos :args (0))
(step t830 (cl @p_478 @p_476) :rule and_pos :args (1))
(step t831 (cl @p_478 @p_475) :rule and_pos :args (2))
(step t832 (cl @p_478 @p_409) :rule and_pos :args (3))
(step t833 (cl @p_478 @p_474) :rule and_pos :args (4))
(step t834 (cl @p_478 @p_473) :rule and_pos :args (5))
(step t835 (cl @p_478 @p_446) :rule and_pos :args (6))
(step t836 (cl false @p_478 @p_478 @p_478 @p_478 @p_478 @p_478 @p_478) :rule resolution :premises (t828 t829 t830 t831 t832 t833 t834 t835))
(step t837 (cl @p_478 @p_478 @p_478 @p_478 @p_478 @p_478 @p_478 false) :rule reordering :premises (t836))
(step t838 (cl @p_478 false) :rule contraction :premises (t837))
(step t839 (cl @p_479 false) :rule resolution :premises (t827 t838))
(step t840 (cl @p_479 @p_133) :rule implies_neg2)
(step t841 (cl @p_479 @p_479) :rule resolution :premises (t839 t840))
(step t842 (cl @p_479) :rule contraction :premises (t841))
(step t843 (cl (= @p_479 @p_478)) :rule implies_simplify)
(step t844 (cl (not @p_479) @p_478) :rule equiv1 :premises (t843))
(step t845 (cl @p_478) :rule resolution :premises (t842 t844))
(step t846 (cl @p_472) :rule resolution :premises (t826 t845))
(step t847 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_447) :rule not_and :premises (t846))
(step t848 (cl @p_448 @p_470) :rule or_neg :args (0))
(step t849 (cl @p_448 @p_469) :rule or_neg :args (1))
(step t850 (cl @p_448 @p_468) :rule or_neg :args (2))
(step t851 (cl @p_448 @p_467) :rule or_neg :args (3))
(step t852 (cl @p_448 @p_466) :rule or_neg :args (4))
(step t853 (cl @p_448 @p_465) :rule or_neg :args (5))
(step t854 (cl @p_448 @p_464) :rule or_neg :args (6))
(step t855 (cl @p_448 @p_463) :rule or_neg :args (7))
(step t856 (cl @p_448 @p_462) :rule or_neg :args (8))
(step t857 (cl @p_448 @p_461) :rule or_neg :args (9))
(step t858 (cl @p_448 @p_460) :rule or_neg :args (10))
(step t859 (cl @p_448 @p_459) :rule or_neg :args (11))
(step t860 (cl @p_448 @p_458) :rule or_neg :args (12))
(step t861 (cl @p_448 @p_457) :rule or_neg :args (13))
(step t862 (cl @p_448 @p_456) :rule or_neg :args (14))
(step t863 (cl @p_448 @p_455) :rule or_neg :args (15))
(step t864 (cl @p_448 @p_454) :rule or_neg :args (16))
(step t865 (cl @p_448 @p_453) :rule or_neg :args (17))
(step t866 (cl @p_448 @p_452) :rule or_neg :args (18))
(step t867 (cl @p_448 @p_451) :rule or_neg :args (19))
(step t868 (cl @p_448 @p_450) :rule or_neg :args (20))
(step t869 (cl @p_448 @p_449) :rule or_neg :args (21))
(step t870 (cl @p_448 (not @p_447)) :rule or_neg :args (22))
(step t871 (cl @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448 @p_448) :rule resolution :premises (t847 t848 t849 t850 t851 t852 t853 t854 t855 t856 t857 t858 t859 t860 t861 t862 t863 t864 t865 t866 t867 t868 t869 t870))
(step t872 (cl @p_448) :rule contraction :premises (t871))
(step t873 (cl @p_445) :rule resolution :premises (t791 t793 t872))
(step t874 (cl @p_423 @p_424 @p_425 @p_426 @p_427 @p_428 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_439 @p_440 @p_441 @p_442 @p_443 @p_444 @p_267) :rule or :premises (t873))
(step t875 (cl @p_267) :rule resolution :premises (t874 t617 t240 t623 t626 t629 t632 t650 t675 t701 t723 t726 t729 t747 t750 t753 t756 t759 t762 t765 t768 t787 t790))
(step t876 (cl @p_249) :rule resolution :premises (t598 t617 t240 t623 t626 t629 t632 t650 t675 t701 t723 t726 t729 t747 t750 t753 t756 t759 t762 t765 t768 t787 t790 t875))
(step t877 (cl (! (not (! (or @p_245 @p_244) :named @p_246)) :named @p_675) @p_245 @p_244) :rule or_pos)
(step t878 (cl @p_245 @p_244 @p_675) :rule reordering :premises (t877))
(step t879 (cl (! (not (! (= @p_249 @p_246) :named @p_250)) :named @p_623) @p_574 @p_246) :rule equiv_pos2)
(step t880 (cl @p_246 @p_574 @p_623) :rule reordering :premises (t879))
(step t881 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) (! (= (! (or @p_245 (! (= @p_247 1/1) :named @p_260)) :named @p_261) @p_249) :named @p_262)) :named @p_263) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) @p_250) :named @p_259)) :named @p_264)) (not @p_263) @p_259) :rule equiv_pos2)
(step t882 (cl (= (* -1/2 (- @p_247 1/1)) (* -1/1 (- @p_1 1/2)))) :rule poly_simp)
(step t883 (cl (= @p_260 @p_244)) :rule poly_simp_rel :premises (t882))
(step t884 (cl (= @p_261 @p_246)) :rule cong :premises (t883))
(step t885 (cl (= @p_249 @p_249)) :rule refl)
(step t886 (cl (= @p_262 (! (= @p_246 @p_249) :named @p_265))) :rule cong :premises (t884 t885))
(step t887 (cl (= @p_265 @p_250)) :rule rare_rewrite :args ("eq-symm" @p_246 @p_249))
(step t888 (cl (= @p_262 @p_250)) :rule trans :premises (t886 t887))
(step t889 (cl @p_264) :rule cong :premises (t888))
(step t890 (cl @p_263 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t891)
(assume t891.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t891.t0 (cl (or @p_258 @p_262)) :rule forall_inst :args (@p_247 @p_4))
(step t891.t1 (cl @p_258 @p_262) :rule or :premises (t891.t0))
(step t891.t2 (cl @p_262) :rule resolution :premises (t891.t1 t674))
(step t891 (cl @p_258 @p_262) :rule subproof :discharge (t891.a0))
(step t892 (cl @p_263 @p_262) :rule resolution :premises (t890 t891))
(step t893 (cl @p_263 (not @p_262)) :rule implies_neg2)
(step t894 (cl @p_263 @p_263) :rule resolution :premises (t892 t893))
(step t895 (cl @p_263) :rule contraction :premises (t894))
(step t896 (cl @p_259) :rule resolution :premises (t881 t889 t895))
(step t897 (cl @p_258 @p_250) :rule implies :premises (t896))
(step t898 (cl @p_250) :rule resolution :premises (t897 t674))
(step t899 (cl @p_246) :rule resolution :premises (t880 t876 t898))
(step t900 (cl @p_244) :rule resolution :premises (t878 t287 t899))
(step t901 (cl (! (not (! (or (! (= @p_1 0/1) :named @p_979) @p_1176) :named @p_1177)) :named @p_1183) @p_979 @p_1176) :rule or_pos)
(step t902 (cl @p_979 @p_1176 @p_1183) :rule reordering :premises (t901))
(step t903 (cl (! (or @p_979 (! (= @p_296 1/1) :named @p_982)) :named @p_983) (! (not @p_979) :named @p_981)) :rule or_neg :args (0))
(step t904 (cl @p_981 @p_983) :rule reordering :premises (t903))
(step t905 (cl (! (not (! (= @p_983 (! (= @p_1 @p_313) :named @p_985)) :named @p_986)) :named @p_1028) (! (not @p_983) :named @p_984) @p_985) :rule equiv_pos2)
(step t906 (cl @p_984 @p_985 @p_1028) :rule reordering :premises (t905))
(step t907 (cl (not (! (= (! (or @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 (! (not (! (not (! (>= (! (+ @p_1 @p_71) :named @p_687) 0/1) :named @p_688)) :named @p_700)) :named @p_823) (! (not @p_985) :named @p_996)) :named @p_998) (! (or @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 @p_688 @p_996) :named @p_997)) :named @p_1027)) (not @p_998) @p_997) :rule equiv_pos2)
(step t908 (cl (= @p_823 @p_688)) :rule rare_rewrite :args ("bool-double-not-elim" @p_688))
(step t909 (cl (= @p_996 @p_996)) :rule refl)
(step t910 (cl @p_1027) :rule cong :premises (t908 t909))
(step t911 (cl (! (and @p_410 @p_406 @p_396 @p_385 @p_364 @p_344 @p_342 @p_340 @p_329 @p_315 @p_311 @p_305 @p_295 @p_291 @p_700) :named @p_1000) @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 @p_823) :rule and_neg)
(step t912 (cl (! (=> @p_1000 @p_996) :named @p_1002) @p_1000) :rule implies_neg1)
(anchor :step t913)
(assume t913.a0 @p_410)
(assume t913.a1 @p_406)
(assume t913.a2 @p_396)
(assume t913.a3 @p_385)
(assume t913.a4 @p_364)
(assume t913.a5 @p_344)
(assume t913.a6 @p_342)
(assume t913.a7 @p_340)
(assume t913.a8 @p_329)
(assume t913.a9 @p_315)
(assume t913.a10 @p_311)
(assume t913.a11 @p_305)
(assume t913.a12 @p_295)
(assume t913.a13 @p_291)
(assume t913.a14 @p_700)
(step t913.t0 (cl (! (=> (! (and (! (not (! (= @p_1 @p_4) :named @p_1003)) :named @p_1004) @p_473 @p_329 @p_315) :named @p_1005) @p_996) :named @p_1024) @p_1005) :rule implies_neg1)
(anchor :step t913.t1)
(assume t913.t1.a0 @p_1004)
(assume t913.t1.a1 @p_473)
(assume t913.t1.a2 @p_329)
(assume t913.t1.a3 @p_315)
(step t913.t1.t0 (cl (= (! (= @p_985 false) :named @p_1025) @p_996)) :rule equiv_simplify)
(step t913.t1.t1 (cl (not @p_1025) @p_996) :rule equiv1 :premises (t913.t1.t0))
(step t913.t1.t2 (cl (= @p_313 @p_314)) :rule symm :premises (t750))
(step t913.t1.t3 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t913.t1.t4 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t913.t1.t5 (cl (= @p_362 @p_6)) :rule trans :premises (t913.t1.t3 t913.t1.t4))
(step t913.t1.t6 (cl (= 2/1 2/1)) :rule refl)
(step t913.t1.t7 (cl (= @p_363 @p_290)) :rule cong :premises (t913.t1.t5 t913.t1.t6))
(step t913.t1.t8 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t913.t1.t9 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t913.t1.t10 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t913.t1.t11 (cl @p_355) :rule symm :premises (t723))
(step t913.t1.t12 (cl (= @p_304 @p_310)) :rule cong :premises (t913.t1.t11))
(step t913.t1.t13 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t913.t1.t14 (cl @p_388) :rule refl)
(step t913.t1.t15 (cl (= @p_308 @p_341)) :rule cong :premises (t913.t1.t13 t913.t1.t14))
(step t913.t1.t16 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t913.t1.t17 (cl (= @p_270 @p_296)) :rule trans :premises (t913.t1.t10 t913.t1.t12 t753 t913.t1.t15 t913.t1.t16))
(step t913.t1.t18 (cl (= @p_1 @p_1)) :rule refl)
(step t913.t1.t19 (cl (= @p_294 @p_339)) :rule cong :premises (t913.t1.t17 t913.t1.t18))
(step t913.t1.t20 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t913.t1.t21 (cl @p_473) :rule trans :premises (t650 t701 t913.t1.t7 t768 t913.t1.t8 t913.t1.t9 t913.t1.t19 t913.t1.t20 t747))
(step t913.t1.t22 (cl (= @p_328 @p_4)) :rule symm :premises (t913.t1.t21))
(step t913.t1.t23 (cl (= @p_313 @p_4)) :rule trans :premises (t913.t1.t2 t747 t913.t1.t22))
(step t913.t1.t24 (cl (= @p_985 @p_1003)) :rule cong :premises (t913.t1.t23))
(step t913.t1.t25 (cl (= (! (= @p_1003 false) :named @p_1026) @p_1004)) :rule equiv_simplify)
(step t913.t1.t26 (cl @p_1026 (! (not @p_1004) :named @p_1007)) :rule equiv2 :premises (t913.t1.t25))
(step t913.t1.t27 (cl (not @p_1007) @p_1003) :rule not_not)
(step t913.t1.t28 (cl @p_1026 @p_1003) :rule resolution :premises (t913.t1.t26 t913.t1.t27))
(step t913.t1.t29 (cl @p_1026) :rule resolution :premises (t913.t1.t28 t913.t1.a0))
(step t913.t1.t30 (cl @p_1025) :rule trans :premises (t913.t1.t24 t913.t1.t29))
(step t913.t1.t31 (cl @p_996) :rule resolution :premises (t913.t1.t1 t913.t1.t30))
(step t913.t1 (cl @p_1007 @p_483 @p_435 @p_436 @p_996) :rule subproof :discharge (t913.t1.a0 t913.t1.a1 t913.t1.a2 t913.t1.a3))
(step t913.t2 (cl (! (not @p_1005) :named @p_1023) @p_1004) :rule and_pos :args (0))
(step t913.t3 (cl @p_1023 @p_473) :rule and_pos :args (1))
(step t913.t4 (cl @p_1023 @p_329) :rule and_pos :args (2))
(step t913.t5 (cl @p_1023 @p_315) :rule and_pos :args (3))
(step t913.t6 (cl @p_996 @p_1023 @p_1023 @p_1023 @p_1023) :rule resolution :premises (t913.t1 t913.t2 t913.t3 t913.t4 t913.t5))
(step t913.t7 (cl @p_1023 @p_1023 @p_1023 @p_1023 @p_996) :rule reordering :premises (t913.t6))
(step t913.t8 (cl @p_1023 @p_996) :rule contraction :premises (t913.t7))
(step t913.t9 (cl @p_1024 @p_996) :rule resolution :premises (t913.t0 t913.t8))
(step t913.t10 (cl @p_1024 (! (not @p_996) :named @p_999)) :rule implies_neg2)
(step t913.t11 (cl @p_1024 @p_1024) :rule resolution :premises (t913.t9 t913.t10))
(step t913.t12 (cl @p_1024) :rule contraction :premises (t913.t11))
(step t913.t13 (cl @p_1023 @p_996) :rule implies :premises (t913.t12))
(step t913.t14 (cl (! (=> @p_700 @p_1004) :named @p_1006) @p_700) :rule implies_neg1)
(anchor :step t913.t15)
(assume t913.t15.a0 @p_700)
(step t913.t15.t0 (cl (! (=> @p_1003 false) :named @p_1008) @p_1003) :rule implies_neg1)
(anchor :step t913.t15.t1)
(assume t913.t15.t1.a0 @p_1003)
(step t913.t15.t1.t0 (cl (not (! (= (! (< (! (+ @p_139 @p_687) :named @p_1010) (! (+ @p_71 0/1) :named @p_1009)) :named @p_1011) false) :named @p_1016)) (not @p_1011) false) :rule equiv_pos2)
(step t913.t15.t1.t1 (cl (= @p_1011 (! (not (! (>= @p_1010 @p_1009) :named @p_1017)) :named @p_1018))) :rule rare_rewrite :args ("arith-elim-lt" @p_1010 @p_1009))
(step t913.t15.t1.t2 (cl (= @p_1010 (! (+ @p_71 @p_139 @p_1) :named @p_1022))) :rule poly_simp)
(step t913.t15.t1.t3 (cl (= @p_1022 @p_71)) :rule poly_simp)
(step t913.t15.t1.t4 (cl (= @p_1010 @p_71)) :rule trans :premises (t913.t15.t1.t2 t913.t15.t1.t3))
(step t913.t15.t1.t5 (cl (= @p_1009 @p_71)) :rule poly_simp)
(step t913.t15.t1.t6 (cl (= @p_1017 (! (>= @p_71 @p_71) :named @p_1019))) :rule cong :premises (t913.t15.t1.t4 t913.t15.t1.t5))
(step t913.t15.t1.t7 (cl (= @p_1019 (! (>= (! (- @p_71 @p_71) :named @p_1020) 0/1) :named @p_1021))) :rule rare_rewrite :args ("arith-geq-norm1-real" @p_71 @p_71))
(step t913.t15.t1.t8 (cl (= @p_1020 0/1)) :rule poly_simp)
(step t913.t15.t1.t9 (cl @p_60) :rule refl)
(step t913.t15.t1.t10 (cl (= @p_1021 @p_190)) :rule cong :premises (t913.t15.t1.t8 t913.t15.t1.t9))
(step t913.t15.t1.t11 (cl @p_191) :rule evaluate)
(step t913.t15.t1.t12 (cl (= @p_1021 true)) :rule trans :premises (t913.t15.t1.t10 t913.t15.t1.t11))
(step t913.t15.t1.t13 (cl (= @p_1019 true)) :rule trans :premises (t913.t15.t1.t7 t913.t15.t1.t12))
(step t913.t15.t1.t14 (cl (= @p_1017 true)) :rule trans :premises (t913.t15.t1.t6 t913.t15.t1.t13))
(step t913.t15.t1.t15 (cl (= @p_1018 @p_189)) :rule cong :premises (t913.t15.t1.t14))
(step t913.t15.t1.t16 (cl (= @p_189 false)) :rule evaluate)
(step t913.t15.t1.t17 (cl (= @p_1018 false)) :rule trans :premises (t913.t15.t1.t15 t913.t15.t1.t16))
(step t913.t15.t1.t18 (cl @p_1016) :rule trans :premises (t913.t15.t1.t1 t913.t15.t1.t17))
(step t913.t15.t1.t19 (cl (not (! (= @p_139 @p_71) :named @p_1014)) (not (! (< @p_687 0/1) :named @p_1012)) @p_1011) :rule la_generic :args (-1/1 1/1 1/1))
(step t913.t15.t1.t20 (cl (=> (! (and @p_183 @p_1003) :named @p_1015) @p_1014)) :rule la_mult_neg)
(step t913.t15.t1.t21 (cl (not @p_1015) @p_1014) :rule implies :premises (t913.t15.t1.t20))
(step t913.t15.t1.t22 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t913.t15.t1.t23 (cl (not @p_185) @p_183) :rule equiv1 :premises (t913.t15.t1.t22))
(step t913.t15.t1.t24 (cl @p_185) :rule evaluate)
(step t913.t15.t1.t25 (cl @p_183) :rule resolution :premises (t913.t15.t1.t23 t913.t15.t1.t24))
(step t913.t15.t1.t26 (cl @p_1015) :rule and_intro :premises (t913.t15.t1.t25 t913.t15.t1.a0))
(step t913.t15.t1.t27 (cl @p_1014) :rule resolution :premises (t913.t15.t1.t21 t913.t15.t1.t26))
(step t913.t15.t1.t28 (cl (not (! (= @p_700 @p_1012) :named @p_1013)) @p_823 @p_1012) :rule equiv_pos2)
(step t913.t15.t1.t29 (cl (= @p_1012 @p_700)) :rule rare_rewrite :args ("arith-elim-lt" @p_687 0/1))
(step t913.t15.t1.t30 (cl @p_1013) :rule symm :premises (t913.t15.t1.t29))
(step t913.t15.t1.t31 (cl @p_1012) :rule resolution :premises (t913.t15.t1.t28 t913.t15.t1.t30 t913.t15.a0))
(step t913.t15.t1.t32 (cl @p_1011) :rule resolution :premises (t913.t15.t1.t19 t913.t15.t1.t27 t913.t15.t1.t31))
(step t913.t15.t1.t33 (cl false) :rule resolution :premises (t913.t15.t1.t0 t913.t15.t1.t18 t913.t15.t1.t32))
(step t913.t15.t1 (cl @p_1004 false) :rule subproof :discharge (t913.t15.t1.a0))
(step t913.t15.t2 (cl @p_1008 false) :rule resolution :premises (t913.t15.t0 t913.t15.t1))
(step t913.t15.t3 (cl @p_1008 @p_133) :rule implies_neg2)
(step t913.t15.t4 (cl @p_1008 @p_1008) :rule resolution :premises (t913.t15.t2 t913.t15.t3))
(step t913.t15.t5 (cl @p_1008) :rule contraction :premises (t913.t15.t4))
(step t913.t15.t6 (cl (= @p_1008 @p_1004)) :rule implies_simplify)
(step t913.t15.t7 (cl (not @p_1008) @p_1004) :rule equiv1 :premises (t913.t15.t6))
(step t913.t15.t8 (cl @p_1004) :rule resolution :premises (t913.t15.t5 t913.t15.t7))
(step t913.t15 (cl @p_823 @p_1004) :rule subproof :discharge (t913.t15.a0))
(step t913.t16 (cl @p_1006 @p_1004) :rule resolution :premises (t913.t14 t913.t15))
(step t913.t17 (cl @p_1006 @p_1007) :rule implies_neg2)
(step t913.t18 (cl @p_1006 @p_1006) :rule resolution :premises (t913.t16 t913.t17))
(step t913.t19 (cl @p_1006) :rule contraction :premises (t913.t18))
(step t913.t20 (cl @p_823 @p_1004) :rule implies :premises (t913.t19))
(step t913.t21 (cl @p_1004) :rule resolution :premises (t913.t20 t913.a14))
(step t913.t22 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t913.t23 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t913.t24 (cl (= @p_362 @p_6)) :rule trans :premises (t913.t22 t913.t23))
(step t913.t25 (cl (= 2/1 2/1)) :rule refl)
(step t913.t26 (cl (= @p_363 @p_290)) :rule cong :premises (t913.t24 t913.t25))
(step t913.t27 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t913.t28 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t913.t29 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t913.t30 (cl @p_355) :rule symm :premises (t723))
(step t913.t31 (cl (= @p_304 @p_310)) :rule cong :premises (t913.t30))
(step t913.t32 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t913.t33 (cl @p_388) :rule refl)
(step t913.t34 (cl (= @p_308 @p_341)) :rule cong :premises (t913.t32 t913.t33))
(step t913.t35 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t913.t36 (cl (= @p_270 @p_296)) :rule trans :premises (t913.t29 t913.t31 t753 t913.t34 t913.t35))
(step t913.t37 (cl (= @p_1 @p_1)) :rule refl)
(step t913.t38 (cl (= @p_294 @p_339)) :rule cong :premises (t913.t36 t913.t37))
(step t913.t39 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t913.t40 (cl @p_473) :rule trans :premises (t650 t701 t913.t26 t768 t913.t27 t913.t28 t913.t38 t913.t39 t747))
(step t913.t41 (cl @p_1005) :rule and_intro :premises (t913.t21 t913.t40 t747 t750))
(step t913.t42 (cl @p_996) :rule resolution :premises (t913.t13 t913.t41))
(step t913 (cl @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 @p_823 @p_996) :rule subproof :discharge (t913.a0 t913.a1 t913.a2 t913.a3 t913.a4 t913.a5 t913.a6 t913.a7 t913.a8 t913.a9 t913.a10 t913.a11 t913.a12 t913.a13 t913.a14))
(step t914 (cl (! (not @p_1000) :named @p_1001) @p_410) :rule and_pos :args (0))
(step t915 (cl @p_1001 @p_406) :rule and_pos :args (1))
(step t916 (cl @p_1001 @p_396) :rule and_pos :args (2))
(step t917 (cl @p_1001 @p_385) :rule and_pos :args (3))
(step t918 (cl @p_1001 @p_364) :rule and_pos :args (4))
(step t919 (cl @p_1001 @p_344) :rule and_pos :args (5))
(step t920 (cl @p_1001 @p_342) :rule and_pos :args (6))
(step t921 (cl @p_1001 @p_340) :rule and_pos :args (7))
(step t922 (cl @p_1001 @p_329) :rule and_pos :args (8))
(step t923 (cl @p_1001 @p_315) :rule and_pos :args (9))
(step t924 (cl @p_1001 @p_311) :rule and_pos :args (10))
(step t925 (cl @p_1001 @p_305) :rule and_pos :args (11))
(step t926 (cl @p_1001 @p_295) :rule and_pos :args (12))
(step t927 (cl @p_1001 @p_291) :rule and_pos :args (13))
(step t928 (cl @p_1001 @p_700) :rule and_pos :args (14))
(step t929 (cl @p_996 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001) :rule resolution :premises (t913 t914 t915 t916 t917 t918 t919 t920 t921 t922 t923 t924 t925 t926 t927 t928))
(step t930 (cl @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_1001 @p_996) :rule reordering :premises (t929))
(step t931 (cl @p_1001 @p_996) :rule contraction :premises (t930))
(step t932 (cl @p_1002 @p_996) :rule resolution :premises (t912 t931))
(step t933 (cl @p_1002 @p_999) :rule implies_neg2)
(step t934 (cl @p_1002 @p_1002) :rule resolution :premises (t932 t933))
(step t935 (cl @p_1002) :rule contraction :premises (t934))
(step t936 (cl @p_1001 @p_996) :rule implies :premises (t935))
(step t937 (cl @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 @p_823 @p_996) :rule resolution :premises (t911 t936))
(step t938 (cl @p_998 @p_469) :rule or_neg :args (0))
(step t939 (cl @p_998 @p_466) :rule or_neg :args (1))
(step t940 (cl @p_998 @p_464) :rule or_neg :args (2))
(step t941 (cl @p_998 @p_463) :rule or_neg :args (3))
(step t942 (cl @p_998 @p_462) :rule or_neg :args (4))
(step t943 (cl @p_998 @p_461) :rule or_neg :args (5))
(step t944 (cl @p_998 @p_460) :rule or_neg :args (6))
(step t945 (cl @p_998 @p_459) :rule or_neg :args (7))
(step t946 (cl @p_998 @p_458) :rule or_neg :args (8))
(step t947 (cl @p_998 @p_457) :rule or_neg :args (9))
(step t948 (cl @p_998 @p_456) :rule or_neg :args (10))
(step t949 (cl @p_998 @p_455) :rule or_neg :args (11))
(step t950 (cl @p_998 @p_452) :rule or_neg :args (12))
(step t951 (cl @p_998 @p_451) :rule or_neg :args (13))
(step t952 (cl @p_998 (not @p_823)) :rule or_neg :args (14))
(step t953 (cl @p_998 @p_999) :rule or_neg :args (15))
(step t954 (cl @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998 @p_998) :rule resolution :premises (t937 t938 t939 t940 t941 t942 t943 t944 t945 t946 t947 t948 t949 t950 t951 t952 t953))
(step t955 (cl @p_998) :rule contraction :premises (t954))
(step t956 (cl @p_997) :rule resolution :premises (t907 t910 t955))
(step t957 (cl @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_441 @p_442 @p_688 @p_996) :rule or :premises (t956))
(step t958 (cl @p_424 @p_427 @p_429 @p_430 @p_431 @p_432 @p_433 @p_434 @p_435 @p_436 @p_437 @p_438 @p_688 @p_996 @p_441 @p_442) :rule reordering :premises (t957))
(step t959 (cl (not (! (= (! (or (! (= 1/1 @p_1) :named @p_818) (! (not (! (>= @p_139 -1/1) :named @p_714)) :named @p_715) @p_480 @p_483 @p_482 @p_425 @p_481 (! (not (! (>= (! (+ @p_4 @p_638) :named @p_731) 1/1) :named @p_732)) :named @p_740) @p_700) :named @p_819) (! (or (! (= @p_1 1/1) :named @p_789) (! (not (! (>= @p_139 -1/1) :named @p_714)) :named @p_715) @p_480 @p_483 (! (not @p_540) :named @p_702) @p_425 @p_481 (! (not (! (>= (! (+ @p_4 @p_638) :named @p_731) 1/1) :named @p_732)) :named @p_740) @p_700) :named @p_817)) :named @p_858)) (not @p_819) @p_817) :rule equiv_pos2)
(step t960 (cl (= (* -1/1 (! (- 1/1 @p_1) :named @p_845)) (* 1/1 (- @p_1 1/1)))) :rule poly_simp)
(step t961 (cl (= @p_818 @p_789)) :rule poly_simp_rel :premises (t960))
(step t962 (cl (= @p_715 @p_715)) :rule refl)
(step t963 (cl (= @p_480 @p_480)) :rule refl)
(step t964 (cl (= @p_483 @p_483)) :rule refl)
(step t965 (cl (= (* 2/1 (- @p_328 @p_313)) (* 1/1 @p_541))) :rule poly_simp)
(step t966 (cl (= @p_474 @p_540)) :rule poly_simp_rel :premises (t965))
(step t967 (cl (= @p_482 @p_702)) :rule cong :premises (t966))
(step t968 (cl (= @p_425 @p_425)) :rule refl)
(step t969 (cl (= @p_481 @p_481)) :rule refl)
(step t970 (cl (= @p_740 @p_740)) :rule refl)
(step t971 (cl (= @p_700 @p_700)) :rule refl)
(step t972 (cl @p_858) :rule cong :premises (t961 t962 t963 t964 t967 t968 t969 t970 t971))
(step t973 (cl (not (! (= (! (or (! (not (! (not @p_818) :named @p_820)) :named @p_821) @p_715 @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_700) :named @p_822) @p_819) :named @p_857)) (not @p_822) @p_819) :rule equiv_pos2)
(step t974 (cl (= @p_821 @p_818)) :rule rare_rewrite :args ("bool-double-not-elim" @p_818))
(step t975 (cl (= @p_821 @p_789)) :rule trans :premises (t974 t961))
(step t976 (cl (= @p_822 @p_817)) :rule cong :premises (t975 t962 t963 t964 t967 t968 t969 t970 t971))
(step t977 (cl (= @p_817 @p_819)) :rule symm :premises (t972))
(step t978 (cl @p_857) :rule trans :premises (t976 t977))
(step t979 (cl (! (=> (! (and @p_820 @p_714 @p_476 @p_473 @p_474 @p_409 @p_475 @p_732 @p_688) :named @p_828) false) :named @p_830) @p_828) :rule implies_neg1)
(anchor :step t980)
(assume t980.a0 @p_820)
(assume t980.a1 @p_714)
(assume t980.a2 @p_476)
(assume t980.a3 @p_473)
(assume t980.a4 @p_474)
(assume t980.a5 @p_409)
(assume t980.a6 @p_475)
(assume t980.a7 @p_732)
(assume t980.a8 @p_688)
(step t980.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_687) :named @p_834) @p_1 @p_498 @p_506 @p_504 @p_502 @p_500 (! (* -2/1 @p_731) :named @p_833)) :named @p_835) (! (+ @p_175 1/1 @p_175 0/1 @p_492 @p_491 @p_490 (! (* -2/1 1/1) :named @p_831)) :named @p_832)) :named @p_836) false) :named @p_849)) (not @p_836) false) :rule equiv_pos2)
(step t980.t1 (cl (= @p_836 (! (not (! (>= @p_835 @p_832) :named @p_850)) :named @p_851))) :rule rare_rewrite :args ("arith-elim-lt" @p_835 @p_832))
(step t980.t2 (cl (= @p_835 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 @p_561 @p_4 @p_420 (! (* -2/1 @p_6) :named @p_854) @p_71 (! (* 0/1 @p_1) :named @p_853)) :named @p_855))) :rule poly_simp)
(step t980.t3 (cl (= @p_561 0/1)) :rule poly_simp)
(step t980.t4 (cl (= @p_420 @p_420)) :rule refl)
(step t980.t5 (cl (= @p_854 @p_854)) :rule refl)
(step t980.t6 (cl (= @p_71 @p_71)) :rule refl)
(step t980.t7 (cl (= @p_853 0/1)) :rule poly_simp)
(step t980.t8 (cl (= @p_855 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 0/1 @p_4 @p_420 @p_854 @p_71 0/1) :named @p_856))) :rule cong :premises (t980.t3 t601 t980.t4 t980.t5 t980.t6 t980.t7))
(step t980.t9 (cl (= @p_856 0/1)) :rule poly_simp)
(step t980.t10 (cl (= @p_855 0/1)) :rule trans :premises (t980.t8 t980.t9))
(step t980.t11 (cl (= @p_835 0/1)) :rule trans :premises (t980.t2 t980.t10))
(step t980.t12 (cl (= @p_175 0/1)) :rule evaluate)
(step t980.t13 (cl @p_388) :rule refl)
(step t980.t14 (cl @p_60) :rule refl)
(step t980.t15 (cl (= @p_492 0/1)) :rule evaluate)
(step t980.t16 (cl (= @p_491 0/1)) :rule evaluate)
(step t980.t17 (cl (= @p_490 0/1)) :rule evaluate)
(step t980.t18 (cl (= @p_831 -2/1)) :rule evaluate)
(step t980.t19 (cl (= @p_832 (! (+ 0/1 1/1 0/1 0/1 0/1 0/1 0/1 -2/1) :named @p_852))) :rule cong :premises (t980.t12 t980.t13 t980.t12 t980.t14 t980.t15 t980.t16 t980.t17 t980.t18))
(step t980.t20 (cl (= @p_852 -1/1)) :rule evaluate)
(step t980.t21 (cl (= @p_832 -1/1)) :rule trans :premises (t980.t19 t980.t20))
(step t980.t22 (cl (= @p_850 (! (>= 0/1 -1/1) :named @p_778))) :rule cong :premises (t980.t11 t980.t21))
(step t980.t23 (cl (= @p_778 true)) :rule evaluate)
(step t980.t24 (cl (= @p_850 true)) :rule trans :premises (t980.t22 t980.t23))
(step t980.t25 (cl (= @p_851 @p_189)) :rule cong :premises (t980.t24))
(step t980.t26 (cl (= @p_189 false)) :rule evaluate)
(step t980.t27 (cl (= @p_851 false)) :rule trans :premises (t980.t25 t980.t26))
(step t980.t28 (cl @p_849) :rule trans :premises (t980.t1 t980.t27))
(step t980.t29 (cl (not (! (<= @p_834 @p_175) :named @p_847)) (not (! (< @p_1 1/1) :named @p_839)) @p_554 @p_550 @p_551 @p_552 @p_553 (not (! (<= @p_833 @p_831) :named @p_837)) @p_836) :rule la_generic :args (1/1 1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1 1/1))
(step t980.t30 (cl (=> (! (and @p_183 @p_688) :named @p_848) @p_847)) :rule la_mult_neg)
(step t980.t31 (cl (not @p_848) @p_847) :rule implies :premises (t980.t30))
(step t980.t32 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t980.t33 (cl (not @p_185) @p_183) :rule equiv1 :premises (t980.t32))
(step t980.t34 (cl @p_185) :rule evaluate)
(step t980.t35 (cl @p_183) :rule resolution :premises (t980.t33 t980.t34))
(step t980.t36 (cl @p_848) :rule and_intro :premises (t980.t35 t980.a8))
(step t980.t37 (cl @p_847) :rule resolution :premises (t980.t31 t980.t36))
(step t980.t38 (cl (or @p_789 (! (not (! (<= @p_1 1/1) :named @p_842)) :named @p_846) (! (not (<= 1/1 @p_1)) :named @p_840))) :rule la_disequality)
(step t980.t39 (cl @p_789 @p_846 @p_840) :rule or :premises (t980.t38))
(step t980.t40 (cl (! (not @p_789) :named @p_790)) :rule not_symm :premises (t980.a0))
(step t980.t41 (cl (not (! (= @p_714 @p_842) :named @p_843)) @p_715 @p_842) :rule equiv_pos2)
(step t980.t42 (cl (= @p_842 (! (>= 1/1 @p_1) :named @p_844))) :rule rare_rewrite :args ("arith-elim-leq" @p_1 1/1))
(step t980.t43 (cl (= (* 1/1 @p_845) (! (* 1/1 (- @p_139 -1/1)) :named @p_729))) :rule poly_simp)
(step t980.t44 (cl (= @p_844 @p_714)) :rule poly_simp_rel :premises (t980.t43))
(step t980.t45 (cl (= @p_842 @p_714)) :rule trans :premises (t980.t42 t980.t44))
(step t980.t46 (cl @p_843) :rule symm :premises (t980.t45))
(step t980.t47 (cl @p_842) :rule resolution :premises (t980.t41 t980.t46 t980.a1))
(step t980.t48 (cl (not (! (= @p_839 @p_840) :named @p_841)) @p_839 (not @p_840)) :rule equiv_pos1)
(step t980.t49 (cl @p_841) :rule comp_simplify)
(step t980.t50 (cl @p_839) :rule resolution :premises (t980.t39 t980.t40 t980.t47 t980.t48 t980.t49))
(step t980.t51 (cl @p_521) :rule la_mult_neg)
(step t980.t52 (cl @p_520 @p_516) :rule implies :premises (t980.t51))
(step t980.t53 (cl (not @p_519) @p_480 @p_517) :rule equiv_pos2)
(step t980.t54 (cl (= (* -1/1 (- @p_497 0/1)) (* -1/1 (- @p_298 @p_275)))) :rule poly_simp)
(step t980.t55 (cl (= @p_517 @p_476)) :rule poly_simp_rel :premises (t980.t54))
(step t980.t56 (cl @p_519) :rule symm :premises (t980.t55))
(step t980.t57 (cl @p_387) :rule symm :premises (t675))
(step t980.t58 (cl (= @p_304 @p_307)) :rule cong :premises (t980.t57))
(step t980.t59 (cl (= @p_341 @p_308)) :rule cong :premises (t980.t58 t980.t13))
(step t980.t60 (cl (= @p_308 @p_310)) :rule symm :premises (t753))
(step t980.t61 (cl (= @p_310 @p_304)) :rule cong :premises (t723))
(step t980.t62 (cl (= @p_296 @p_270)) :rule trans :premises (t726 t980.t59 t980.t60 t980.t61 t756))
(step t980.t63 (cl (= @p_139 @p_139)) :rule refl)
(step t980.t64 (cl (= @p_297 @p_271)) :rule cong :premises (t980.t62 t980.t63))
(step t980.t65 (cl (= @p_268 @p_274)) :rule symm :premises (t626))
(step t980.t66 (cl (= @p_269 @p_275)) :rule cong :premises (t980.t65))
(step t980.t67 (cl @p_476) :rule trans :premises (t762 t980.t64 t790 t980.t66))
(step t980.t68 (cl @p_517) :rule resolution :premises (t980.t53 t980.t56 t980.t67))
(step t980.t69 (cl @p_518) :rule and_intro :premises (t980.t35 t980.t68))
(step t980.t70 (cl @p_516) :rule resolution :premises (t980.t52 t980.t69))
(step t980.t71 (cl @p_547 @p_483 @p_545) :rule equiv_pos2)
(step t980.t72 (cl (= (* 1/1 (- @p_506 0/1)) (* 1/1 (- @p_4 @p_328)))) :rule poly_simp)
(step t980.t73 (cl (= @p_545 @p_473)) :rule poly_simp_rel :premises (t980.t72))
(step t980.t74 (cl @p_546) :rule symm :premises (t980.t73))
(step t980.t75 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t980.t76 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t980.t77 (cl (= @p_362 @p_6)) :rule trans :premises (t980.t75 t980.t76))
(step t980.t78 (cl (= 2/1 2/1)) :rule refl)
(step t980.t79 (cl (= @p_363 @p_290)) :rule cong :premises (t980.t77 t980.t78))
(step t980.t80 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t980.t81 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t980.t82 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t980.t83 (cl @p_355) :rule symm :premises (t723))
(step t980.t84 (cl (= @p_304 @p_310)) :rule cong :premises (t980.t83))
(step t980.t85 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t980.t86 (cl (= @p_308 @p_341)) :rule cong :premises (t980.t85 t980.t13))
(step t980.t87 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t980.t88 (cl (= @p_270 @p_296)) :rule trans :premises (t980.t82 t980.t84 t753 t980.t86 t980.t87))
(step t980.t89 (cl (= @p_1 @p_1)) :rule refl)
(step t980.t90 (cl (= @p_294 @p_339)) :rule cong :premises (t980.t88 t980.t89))
(step t980.t91 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t980.t92 (cl @p_473) :rule trans :premises (t650 t701 t980.t79 t768 t980.t80 t980.t81 t980.t90 t980.t91 t747))
(step t980.t93 (cl @p_545) :rule resolution :premises (t980.t71 t980.t74 t980.t92))
(step t980.t94 (cl @p_544) :rule la_mult_pos)
(step t980.t95 (cl @p_543 @p_534) :rule implies :premises (t980.t94))
(step t980.t96 (cl (= @p_542 @p_536)) :rule equiv_simplify)
(step t980.t97 (cl (not @p_542) @p_536) :rule equiv1 :premises (t980.t96))
(step t980.t98 (cl @p_542) :rule evaluate)
(step t980.t99 (cl @p_536) :rule resolution :premises (t980.t97 t980.t98))
(step t980.t100 (cl (not @p_538) @p_482 @p_535) :rule equiv_pos2)
(step t980.t101 (cl (= (* 2/1 (- @p_503 0/1)) (* 2/1 @p_541))) :rule poly_simp)
(step t980.t102 (cl (= @p_535 @p_540)) :rule poly_simp_rel :premises (t980.t101))
(step t980.t103 (cl (= @p_540 @p_535)) :rule symm :premises (t980.t102))
(step t980.t104 (cl @p_538) :rule trans :premises (t966 t980.t103))
(step t980.t105 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t980.t106 (cl @p_474) :rule trans :premises (t980.t105 t750))
(step t980.t107 (cl @p_535) :rule resolution :premises (t980.t100 t980.t104 t980.t106))
(step t980.t108 (cl @p_537) :rule and_intro :premises (t980.t99 t980.t107))
(step t980.t109 (cl @p_534) :rule resolution :premises (t980.t95 t980.t108))
(step t980.t110 (cl (=> @p_531 @p_528)) :rule la_mult_neg)
(step t980.t111 (cl (not @p_531) @p_528) :rule implies :premises (t980.t110))
(step t980.t112 (cl (= @p_533 @p_530)) :rule equiv_simplify)
(step t980.t113 (cl (not @p_533) @p_530) :rule equiv1 :premises (t980.t112))
(step t980.t114 (cl @p_533) :rule evaluate)
(step t980.t115 (cl @p_530) :rule resolution :premises (t980.t113 t980.t114))
(step t980.t116 (cl (not @p_532) @p_425 @p_529) :rule equiv_pos2)
(step t980.t117 (cl (= (* 1/1 (- @p_501 0/1)) (* 1/1 (- @p_6 @p_408)))) :rule poly_simp)
(step t980.t118 (cl (= @p_529 @p_409)) :rule poly_simp_rel :premises (t980.t117))
(step t980.t119 (cl @p_532) :rule symm :premises (t980.t118))
(step t980.t120 (cl @p_529) :rule resolution :premises (t980.t116 t980.t119 t623))
(step t980.t121 (cl @p_531) :rule and_intro :premises (t980.t115 t980.t120))
(step t980.t122 (cl @p_528) :rule resolution :premises (t980.t111 t980.t121))
(step t980.t123 (cl @p_527) :rule la_mult_pos)
(step t980.t124 (cl @p_526 @p_522) :rule implies :premises (t980.t123))
(step t980.t125 (cl (= @p_515 @p_512)) :rule equiv_simplify)
(step t980.t126 (cl (not @p_515) @p_512) :rule equiv1 :premises (t980.t125))
(step t980.t127 (cl @p_515) :rule evaluate)
(step t980.t128 (cl @p_512) :rule resolution :premises (t980.t126 t980.t127))
(step t980.t129 (cl (not @p_525) @p_481 @p_523) :rule equiv_pos2)
(step t980.t130 (cl (= (* 1/1 (- @p_499 0/1)) (* 1/1 (- @p_274 @p_276)))) :rule poly_simp)
(step t980.t131 (cl (= @p_523 @p_475)) :rule poly_simp_rel :premises (t980.t130))
(step t980.t132 (cl @p_525) :rule symm :premises (t980.t131))
(step t980.t133 (cl (= @p_361 @p_301)) :rule symm :premises (t632))
(step t980.t134 (cl (= @p_4 @p_301)) :rule trans :premises (t650 t980.t133))
(step t980.t135 (cl (= @p_268 @p_302)) :rule cong :premises (t980.t134 t980.t63))
(step t980.t136 (cl (= @p_300 @p_277)) :rule cong :premises (t980.t65))
(step t980.t137 (cl @p_475) :rule trans :premises (t626 t980.t135 t759 t980.t136 t787))
(step t980.t138 (cl @p_523) :rule resolution :premises (t980.t129 t980.t132 t980.t137))
(step t980.t139 (cl @p_524) :rule and_intro :premises (t980.t128 t980.t138))
(step t980.t140 (cl @p_522) :rule resolution :premises (t980.t124 t980.t139))
(step t980.t141 (cl (=> (! (and @p_530 @p_732) :named @p_838) @p_837)) :rule la_mult_neg)
(step t980.t142 (cl (not @p_838) @p_837) :rule implies :premises (t980.t141))
(step t980.t143 (cl (not (! (= @p_7 @p_732) :named @p_733)) (not @p_7) @p_732) :rule equiv_pos2)
(step t980.t144 (cl (= @p_5 (! (+ @p_4 @p_737) :named @p_738))) :rule poly_simp)
(step t980.t145 (cl (= @p_737 -1/1)) :rule evaluate)
(step t980.t146 (cl (= @p_738 (! (+ @p_4 -1/1) :named @p_739))) :rule cong :premises (t980.t145))
(step t980.t147 (cl (= @p_739 (! (+ -1/1 @p_4) :named @p_734))) :rule poly_simp)
(step t980.t148 (cl (= @p_738 @p_734)) :rule trans :premises (t980.t146 t980.t147))
(step t980.t149 (cl (= @p_5 @p_734)) :rule trans :premises (t980.t144 t980.t148))
(step t980.t150 (cl (= @p_7 (! (<= @p_6 @p_734) :named @p_735))) :rule cong :premises (t980.t149))
(step t980.t151 (cl (= @p_735 (! (>= @p_734 @p_6) :named @p_736))) :rule rare_rewrite :args ("arith-elim-leq" @p_6 @p_734))
(step t980.t152 (cl (= (* -1/1 (- @p_734 @p_6)) (* -1/1 (- @p_731 1/1)))) :rule poly_simp)
(step t980.t153 (cl (= @p_736 @p_732)) :rule poly_simp_rel :premises (t980.t152))
(step t980.t154 (cl (= @p_735 @p_732)) :rule trans :premises (t980.t151 t980.t153))
(step t980.t155 (cl @p_733) :rule trans :premises (t980.t150 t980.t154))
(step t980.t156 (cl @p_732) :rule resolution :premises (t980.t143 t980.t155 a30))
(step t980.t157 (cl @p_838) :rule and_intro :premises (t980.t115 t980.t156))
(step t980.t158 (cl @p_837) :rule resolution :premises (t980.t142 t980.t157))
(step t980.t159 (cl @p_836) :rule resolution :premises (t980.t29 t980.t37 t980.t50 t980.t70 t980.t93 t980.t109 t980.t122 t980.t140 t980.t158))
(step t980.t160 (cl false) :rule resolution :premises (t980.t0 t980.t28 t980.t159))
(step t980 (cl @p_821 @p_715 @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_700 false) :rule subproof :discharge (t980.a0 t980.a1 t980.a2 t980.a3 t980.a4 t980.a5 t980.a6 t980.a7 t980.a8))
(step t981 (cl (! (not @p_828) :named @p_829) @p_820) :rule and_pos :args (0))
(step t982 (cl @p_829 @p_714) :rule and_pos :args (1))
(step t983 (cl @p_829 @p_476) :rule and_pos :args (2))
(step t984 (cl @p_829 @p_473) :rule and_pos :args (3))
(step t985 (cl @p_829 @p_474) :rule and_pos :args (4))
(step t986 (cl @p_829 @p_409) :rule and_pos :args (5))
(step t987 (cl @p_829 @p_475) :rule and_pos :args (6))
(step t988 (cl @p_829 @p_732) :rule and_pos :args (7))
(step t989 (cl @p_829 @p_688) :rule and_pos :args (8))
(step t990 (cl false @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829) :rule resolution :premises (t980 t981 t982 t983 t984 t985 t986 t987 t988 t989))
(step t991 (cl @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 @p_829 false) :rule reordering :premises (t990))
(step t992 (cl @p_829 false) :rule contraction :premises (t991))
(step t993 (cl @p_830 false) :rule resolution :premises (t979 t992))
(step t994 (cl @p_830 @p_133) :rule implies_neg2)
(step t995 (cl @p_830 @p_830) :rule resolution :premises (t993 t994))
(step t996 (cl @p_830) :rule contraction :premises (t995))
(step t997 (cl (= @p_830 @p_829)) :rule implies_simplify)
(step t998 (cl (not @p_830) @p_829) :rule equiv1 :premises (t997))
(step t999 (cl @p_829) :rule resolution :premises (t996 t998))
(step t1000 (cl @p_821 @p_715 @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_700) :rule not_and :premises (t999))
(step t1001 (cl @p_822 (not @p_821)) :rule or_neg :args (0))
(step t1002 (cl @p_822 (! (not @p_715) :named @p_786)) :rule or_neg :args (1))
(step t1003 (cl @p_822 (! (not @p_480) :named @p_827)) :rule or_neg :args (2))
(step t1004 (cl @p_822 (! (not @p_483) :named @p_826)) :rule or_neg :args (3))
(step t1005 (cl @p_822 (! (not @p_482) :named @p_825)) :rule or_neg :args (4))
(step t1006 (cl @p_822 @p_468) :rule or_neg :args (5))
(step t1007 (cl @p_822 (! (not @p_481) :named @p_824)) :rule or_neg :args (6))
(step t1008 (cl @p_822 (! (not @p_740) :named @p_744)) :rule or_neg :args (7))
(step t1009 (cl @p_822 @p_823) :rule or_neg :args (8))
(step t1010 (cl @p_822 @p_822 @p_822 @p_822 @p_822 @p_822 @p_822 @p_822 @p_822) :rule resolution :premises (t1000 t1001 t1002 t1003 t1004 t1005 t1006 t1007 t1008 t1009))
(step t1011 (cl @p_822) :rule contraction :premises (t1010))
(step t1012 (cl @p_819) :rule resolution :premises (t973 t978 t1011))
(step t1013 (cl @p_817) :rule resolution :premises (t959 t972 t1012))
(step t1014 (cl @p_789 @p_715 @p_480 @p_483 @p_702 @p_425 @p_481 @p_740 @p_700) :rule or :premises (t1013))
(step t1015 (cl @p_740 @p_789 @p_425 @p_715 @p_702 @p_483 @p_700 @p_481 @p_480) :rule reordering :premises (t1014))
(step t1016 (cl (not @p_733) (not @p_7) @p_732) :rule equiv_pos2)
(step t1017 (cl (= @p_5 @p_738)) :rule poly_simp)
(step t1018 (cl (= @p_737 -1/1)) :rule evaluate)
(step t1019 (cl (= @p_738 @p_739)) :rule cong :premises (t1018))
(step t1020 (cl (= @p_739 @p_734)) :rule poly_simp)
(step t1021 (cl (= @p_738 @p_734)) :rule trans :premises (t1019 t1020))
(step t1022 (cl (= @p_5 @p_734)) :rule trans :premises (t1017 t1021))
(step t1023 (cl (= @p_7 @p_735)) :rule cong :premises (t1022))
(step t1024 (cl (= @p_735 @p_736)) :rule rare_rewrite :args ("arith-elim-leq" @p_6 @p_734))
(step t1025 (cl (= (* -1/1 (- @p_734 @p_6)) (* -1/1 (- @p_731 1/1)))) :rule poly_simp)
(step t1026 (cl (= @p_736 @p_732)) :rule poly_simp_rel :premises (t1025))
(step t1027 (cl (= @p_735 @p_732)) :rule trans :premises (t1024 t1026))
(step t1028 (cl @p_733) :rule trans :premises (t1023 t1027))
(step t1029 (cl @p_732) :rule resolution :premises (t1016 t1028 a30))
(step t1030 (cl (! (or @p_245 @p_789) :named @p_791) @p_790) :rule or_neg :args (1))
(step t1031 (cl (! (not (! (= (! (= @p_4 @p_6) :named @p_793) @p_791) :named @p_794)) :named @p_816) @p_793 (! (not @p_791) :named @p_792)) :rule equiv_pos1)
(step t1032 (cl @p_793 @p_792 @p_816) :rule reordering :premises (t1031))
(step t1033 (cl (! (=> @p_732 (! (not @p_793) :named @p_799)) :named @p_800) @p_732) :rule implies_neg1)
(anchor :step t1034)
(assume t1034.a0 @p_732)
(step t1034.t0 (cl @p_800 @p_732) :rule implies_neg1)
(anchor :step t1034.t1)
(assume t1034.t1.a0 @p_732)
(step t1034.t1.t0 (cl (! (=> @p_793 false) :named @p_802) @p_793) :rule implies_neg1)
(anchor :step t1034.t1.t1)
(assume t1034.t1.t1.a0 @p_793)
(step t1034.t1.t1.t0 (cl (not (! (= (! (<= (! (+ @p_4 (! (* -1/1 @p_731) :named @p_749)) :named @p_804) (! (+ @p_6 @p_737) :named @p_803)) :named @p_805) false) :named @p_806)) (not @p_805) false) :rule equiv_pos2)
(step t1034.t1.t1.t1 (cl (= @p_749 (! (+ @p_71 @p_6) :named @p_814))) :rule poly_simp)
(step t1034.t1.t1.t2 (cl (= @p_804 (! (+ @p_4 @p_814) :named @p_815))) :rule cong :premises (t1034.t1.t1.t1))
(step t1034.t1.t1.t3 (cl (= @p_815 @p_6)) :rule poly_simp)
(step t1034.t1.t1.t4 (cl (= @p_804 @p_6)) :rule trans :premises (t1034.t1.t1.t2 t1034.t1.t1.t3))
(step t1034.t1.t1.t5 (cl (= @p_803 (! (+ @p_6 -1/1) :named @p_813))) :rule cong :premises (t1018))
(step t1034.t1.t1.t6 (cl (= @p_813 (! (+ -1/1 @p_6) :named @p_807))) :rule poly_simp)
(step t1034.t1.t1.t7 (cl (= @p_803 @p_807)) :rule trans :premises (t1034.t1.t1.t5 t1034.t1.t1.t6))
(step t1034.t1.t1.t8 (cl (= @p_805 (! (<= @p_6 @p_807) :named @p_808))) :rule cong :premises (t1034.t1.t1.t4 t1034.t1.t1.t7))
(step t1034.t1.t1.t9 (cl (= @p_808 (! (>= @p_807 @p_6) :named @p_809))) :rule rare_rewrite :args ("arith-elim-leq" @p_6 @p_807))
(step t1034.t1.t1.t10 (cl (= @p_809 (! (>= (! (- @p_807 @p_6) :named @p_810) 0/1) :named @p_811))) :rule rare_rewrite :args ("arith-geq-norm1-real" @p_807 @p_6))
(step t1034.t1.t1.t11 (cl (= @p_810 -1/1)) :rule poly_simp)
(step t1034.t1.t1.t12 (cl @p_60) :rule refl)
(step t1034.t1.t1.t13 (cl (= @p_811 (! (>= -1/1 0/1) :named @p_812))) :rule cong :premises (t1034.t1.t1.t11 t1034.t1.t1.t12))
(step t1034.t1.t1.t14 (cl (= @p_812 false)) :rule evaluate)
(step t1034.t1.t1.t15 (cl (= @p_811 false)) :rule trans :premises (t1034.t1.t1.t13 t1034.t1.t1.t14))
(step t1034.t1.t1.t16 (cl (= @p_809 false)) :rule trans :premises (t1034.t1.t1.t10 t1034.t1.t1.t15))
(step t1034.t1.t1.t17 (cl (= @p_808 false)) :rule trans :premises (t1034.t1.t1.t9 t1034.t1.t1.t16))
(step t1034.t1.t1.t18 (cl @p_806) :rule trans :premises (t1034.t1.t1.t8 t1034.t1.t1.t17))
(step t1034.t1.t1.t19 (cl @p_799 (! (not (! (<= @p_749 @p_737) :named @p_758)) :named @p_774) @p_805) :rule la_generic :args (-1/1 1/1 1/1))
(step t1034.t1.t1.t20 (cl (=> (! (and @p_183 @p_732) :named @p_759) @p_758)) :rule la_mult_neg)
(step t1034.t1.t1.t21 (cl (not @p_759) @p_758) :rule implies :premises (t1034.t1.t1.t20))
(step t1034.t1.t1.t22 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t1034.t1.t1.t23 (cl (not @p_185) @p_183) :rule equiv1 :premises (t1034.t1.t1.t22))
(step t1034.t1.t1.t24 (cl @p_185) :rule evaluate)
(step t1034.t1.t1.t25 (cl @p_183) :rule resolution :premises (t1034.t1.t1.t23 t1034.t1.t1.t24))
(step t1034.t1.t1.t26 (cl @p_759) :rule and_intro :premises (t1034.t1.t1.t25 t1029))
(step t1034.t1.t1.t27 (cl @p_758) :rule resolution :premises (t1034.t1.t1.t21 t1034.t1.t1.t26))
(step t1034.t1.t1.t28 (cl @p_805) :rule resolution :premises (t1034.t1.t1.t19 t1034.t1.t1.a0 t1034.t1.t1.t27))
(step t1034.t1.t1.t29 (cl false) :rule resolution :premises (t1034.t1.t1.t0 t1034.t1.t1.t18 t1034.t1.t1.t28))
(step t1034.t1.t1 (cl @p_799 false) :rule subproof :discharge (t1034.t1.t1.a0))
(step t1034.t1.t2 (cl @p_802 false) :rule resolution :premises (t1034.t1.t0 t1034.t1.t1))
(step t1034.t1.t3 (cl @p_802 @p_133) :rule implies_neg2)
(step t1034.t1.t4 (cl @p_802 @p_802) :rule resolution :premises (t1034.t1.t2 t1034.t1.t3))
(step t1034.t1.t5 (cl @p_802) :rule contraction :premises (t1034.t1.t4))
(step t1034.t1.t6 (cl (= @p_802 @p_799)) :rule implies_simplify)
(step t1034.t1.t7 (cl (not @p_802) @p_799) :rule equiv1 :premises (t1034.t1.t6))
(step t1034.t1.t8 (cl @p_799) :rule resolution :premises (t1034.t1.t5 t1034.t1.t7))
(step t1034.t1 (cl @p_740 @p_799) :rule subproof :discharge (t1034.t1.a0))
(step t1034.t2 (cl @p_800 @p_799) :rule resolution :premises (t1034.t0 t1034.t1))
(step t1034.t3 (cl @p_800 (! (not @p_799) :named @p_801)) :rule implies_neg2)
(step t1034.t4 (cl @p_800 @p_800) :rule resolution :premises (t1034.t2 t1034.t3))
(step t1034.t5 (cl @p_800) :rule contraction :premises (t1034.t4))
(step t1034.t6 (cl @p_740 @p_799) :rule implies :premises (t1034.t5))
(step t1034.t7 (cl @p_799) :rule resolution :premises (t1034.t6 t1029))
(step t1034 (cl @p_740 @p_799) :rule subproof :discharge (t1034.a0))
(step t1035 (cl @p_800 @p_799) :rule resolution :premises (t1033 t1034))
(step t1036 (cl @p_800 @p_801) :rule implies_neg2)
(step t1037 (cl @p_800 @p_800) :rule resolution :premises (t1035 t1036))
(step t1038 (cl @p_800) :rule contraction :premises (t1037))
(step t1039 (cl @p_740 @p_799) :rule implies :premises (t1038))
(step t1040 (cl @p_799) :rule resolution :premises (t1039 t1029))
(step t1041 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) (! (= @p_791 @p_793) :named @p_796)) :named @p_797) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) @p_794) :named @p_795)) :named @p_798)) (not @p_797) @p_795) :rule equiv_pos2)
(step t1042 (cl (= @p_796 @p_794)) :rule rare_rewrite :args ("eq-symm" @p_791 @p_793))
(step t1043 (cl @p_798) :rule cong :premises (t1042))
(step t1044 (cl @p_797 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t1045)
(assume t1045.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t1045.t0 (cl (or @p_258 @p_796)) :rule forall_inst :args (@p_1 @p_4))
(step t1045.t1 (cl @p_258 @p_796) :rule or :premises (t1045.t0))
(step t1045.t2 (cl @p_796) :rule resolution :premises (t1045.t1 t674))
(step t1045 (cl @p_258 @p_796) :rule subproof :discharge (t1045.a0))
(step t1046 (cl @p_797 @p_796) :rule resolution :premises (t1044 t1045))
(step t1047 (cl @p_797 (not @p_796)) :rule implies_neg2)
(step t1048 (cl @p_797 @p_797) :rule resolution :premises (t1046 t1047))
(step t1049 (cl @p_797) :rule contraction :premises (t1048))
(step t1050 (cl @p_795) :rule resolution :premises (t1041 t1043 t1049))
(step t1051 (cl @p_258 @p_794) :rule implies :premises (t1050))
(step t1052 (cl @p_794) :rule resolution :premises (t1051 t674))
(step t1053 (cl @p_792) :rule resolution :premises (t1032 t1040 t1052))
(step t1054 (cl @p_790) :rule resolution :premises (t1030 t1053))
(step t1055 (cl (not (! (= (! (or (! (not (! (= (! (not (! (>= (! (+ (! (* -1/1 @p_65) :named @p_135) @p_361) :named @p_716) 0/1) :named @p_717)) :named @p_718) @p_715) :named @p_719)) :named @p_784) @p_718 @p_786) :named @p_787) (! (or @p_784 @p_718 @p_714) :named @p_785)) :named @p_788)) (not @p_787) @p_785) :rule equiv_pos2)
(step t1056 (cl (= @p_786 @p_714)) :rule rare_rewrite :args ("bool-double-not-elim" @p_714))
(step t1057 (cl @p_788) :rule cong :premises (t1056))
(step t1058 (cl @p_784 @p_718 @p_786) :rule equiv_pos1)
(step t1059 (cl @p_787 (not @p_784)) :rule or_neg :args (0))
(step t1060 (cl @p_787 (! (not @p_718) :named @p_742)) :rule or_neg :args (1))
(step t1061 (cl @p_787 (not @p_786)) :rule or_neg :args (2))
(step t1062 (cl @p_787 @p_787 @p_787) :rule resolution :premises (t1058 t1059 t1060 t1061))
(step t1063 (cl @p_787) :rule contraction :premises (t1062))
(step t1064 (cl @p_785) :rule resolution :premises (t1055 t1057 t1063))
(step t1065 (cl @p_784 @p_718 @p_714) :rule or :premises (t1064))
(step t1066 (cl @p_718 @p_714 @p_784) :rule reordering :premises (t1065))
(step t1067 (cl (not (! (= (! (or @p_429 @p_424 @p_740 @p_742) :named @p_743) (! (or @p_429 @p_424 @p_740 @p_717) :named @p_741)) :named @p_783)) (not @p_743) @p_741) :rule equiv_pos2)
(step t1068 (cl (= @p_742 @p_717)) :rule rare_rewrite :args ("bool-double-not-elim" @p_717))
(step t1069 (cl @p_783) :rule cong :premises (t1068))
(step t1070 (cl (! (=> (! (and @p_396 @p_410 @p_732 @p_718) :named @p_745) false) :named @p_747) @p_745) :rule implies_neg1)
(anchor :step t1071)
(assume t1071.a0 @p_396)
(assume t1071.a1 @p_410)
(assume t1071.a2 @p_732)
(assume t1071.a3 @p_718)
(step t1071.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 (! (+ @p_65 (! (* -1/1 @p_361) :named @p_752)) :named @p_754)) :named @p_755) (! (+ @p_4 @p_752) :named @p_753) (! (* -1/1 (! (+ @p_6 @p_135) :named @p_750)) :named @p_751) @p_749) :named @p_756) (! (+ @p_175 0/1 @p_175 @p_737) :named @p_748)) :named @p_757) false) :named @p_775)) (not @p_757) false) :rule equiv_pos2)
(step t1071.t1 (cl (= @p_757 (! (not (! (>= @p_756 @p_748) :named @p_776)) :named @p_777))) :rule rare_rewrite :args ("arith-elim-lt" @p_756 @p_748))
(step t1071.t2 (cl (= @p_756 (! (+ (! (* 0/1 @p_361) :named @p_780) @p_65 @p_135 @p_6 @p_638 @p_559) :named @p_781))) :rule poly_simp)
(step t1071.t3 (cl (= @p_780 0/1)) :rule poly_simp)
(step t1071.t4 (cl (= @p_65 @p_65)) :rule refl)
(step t1071.t5 (cl (= @p_135 @p_135)) :rule refl)
(step t1071.t6 (cl (= @p_6 @p_6)) :rule refl)
(step t1071.t7 (cl (= @p_638 @p_638)) :rule refl)
(step t1071.t8 (cl (= @p_559 0/1)) :rule poly_simp)
(step t1071.t9 (cl (= @p_781 (! (+ 0/1 @p_65 @p_135 @p_6 @p_638 0/1) :named @p_782))) :rule cong :premises (t1071.t3 t1071.t4 t1071.t5 t1071.t6 t1071.t7 t1071.t8))
(step t1071.t10 (cl (= @p_782 0/1)) :rule poly_simp)
(step t1071.t11 (cl (= @p_781 0/1)) :rule trans :premises (t1071.t9 t1071.t10))
(step t1071.t12 (cl (= @p_756 0/1)) :rule trans :premises (t1071.t2 t1071.t11))
(step t1071.t13 (cl (= @p_175 0/1)) :rule evaluate)
(step t1071.t14 (cl @p_60) :rule refl)
(step t1071.t15 (cl (= @p_748 (! (+ 0/1 0/1 0/1 -1/1) :named @p_779))) :rule cong :premises (t1071.t13 t1071.t14 t1071.t13 t1018))
(step t1071.t16 (cl (= @p_779 -1/1)) :rule evaluate)
(step t1071.t17 (cl (= @p_748 -1/1)) :rule trans :premises (t1071.t15 t1071.t16))
(step t1071.t18 (cl (= @p_776 @p_778)) :rule cong :premises (t1071.t12 t1071.t17))
(step t1071.t19 (cl (= @p_778 true)) :rule evaluate)
(step t1071.t20 (cl (= @p_776 true)) :rule trans :premises (t1071.t18 t1071.t19))
(step t1071.t21 (cl (= @p_777 @p_189)) :rule cong :premises (t1071.t20))
(step t1071.t22 (cl (= @p_189 false)) :rule evaluate)
(step t1071.t23 (cl (= @p_777 false)) :rule trans :premises (t1071.t21 t1071.t22))
(step t1071.t24 (cl @p_775) :rule trans :premises (t1071.t1 t1071.t23))
(step t1071.t25 (cl (not (! (< @p_755 @p_175) :named @p_766)) (not (! (= @p_753 0/1) :named @p_764)) (not (! (= @p_751 @p_175) :named @p_760)) @p_774 @p_757) :rule la_generic :args (1/1 -1/1 -1/1 1/1 1/1))
(step t1071.t26 (cl (=> (! (and @p_183 (! (> @p_754 0/1) :named @p_767)) :named @p_768) @p_766)) :rule la_mult_neg)
(step t1071.t27 (cl (not @p_768) @p_766) :rule implies :premises (t1071.t26))
(step t1071.t28 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t1071.t29 (cl (not @p_185) @p_183) :rule equiv1 :premises (t1071.t28))
(step t1071.t30 (cl @p_185) :rule evaluate)
(step t1071.t31 (cl @p_183) :rule resolution :premises (t1071.t29 t1071.t30))
(step t1071.t32 (cl (not (! (= @p_718 @p_767) :named @p_769)) @p_742 @p_767) :rule equiv_pos2)
(step t1071.t33 (cl (= @p_767 (! (not (! (>= 0/1 @p_754) :named @p_772)) :named @p_773))) :rule rare_rewrite :args ("arith-elim-gt" @p_754 0/1))
(step t1071.t34 (cl (= (! (<= @p_754 0/1) :named @p_770) @p_772)) :rule rare_rewrite :args ("arith-elim-leq" @p_754 0/1))
(step t1071.t35 (cl (= @p_772 @p_770)) :rule symm :premises (t1071.t34))
(step t1071.t36 (cl (= @p_773 (! (not @p_770) :named @p_771))) :rule cong :premises (t1071.t35))
(step t1071.t37 (cl (= @p_767 @p_771)) :rule trans :premises (t1071.t33 t1071.t36))
(step t1071.t38 (cl (= (* -1/1 (- 0/1 @p_754)) (* -1/1 (- @p_716 0/1)))) :rule poly_simp)
(step t1071.t39 (cl (= @p_772 @p_717)) :rule poly_simp_rel :premises (t1071.t38))
(step t1071.t40 (cl (= @p_770 @p_717)) :rule trans :premises (t1071.t34 t1071.t39))
(step t1071.t41 (cl (= @p_771 @p_718)) :rule cong :premises (t1071.t40))
(step t1071.t42 (cl (= @p_767 @p_718)) :rule trans :premises (t1071.t37 t1071.t41))
(step t1071.t43 (cl @p_769) :rule symm :premises (t1071.t42))
(step t1071.t44 (cl @p_767) :rule resolution :premises (t1071.t32 t1071.t43 t1071.a3))
(step t1071.t45 (cl @p_768) :rule and_intro :premises (t1071.t31 t1071.t44))
(step t1071.t46 (cl @p_766) :rule resolution :premises (t1071.t27 t1071.t45))
(step t1071.t47 (cl (not (! (= @p_396 @p_764) :named @p_765)) @p_429 @p_764) :rule equiv_pos2)
(step t1071.t48 (cl (= (* 1/1 (- @p_753 0/1)) (* 1/1 (- @p_4 @p_361)))) :rule poly_simp)
(step t1071.t49 (cl (= @p_764 @p_396)) :rule poly_simp_rel :premises (t1071.t48))
(step t1071.t50 (cl @p_765) :rule symm :premises (t1071.t49))
(step t1071.t51 (cl @p_764) :rule resolution :premises (t1071.t47 t1071.t50 t650))
(step t1071.t52 (cl (=> (! (and @p_183 (! (= @p_750 0/1) :named @p_761)) :named @p_762) @p_760)) :rule la_mult_neg)
(step t1071.t53 (cl (not @p_762) @p_760) :rule implies :premises (t1071.t52))
(step t1071.t54 (cl (not (! (= @p_410 @p_761) :named @p_763)) @p_424 @p_761) :rule equiv_pos2)
(step t1071.t55 (cl (= (* 1/1 (- @p_750 0/1)) (* 1/1 (- @p_6 @p_65)))) :rule poly_simp)
(step t1071.t56 (cl (= @p_761 @p_410)) :rule poly_simp_rel :premises (t1071.t55))
(step t1071.t57 (cl @p_763) :rule symm :premises (t1071.t56))
(step t1071.t58 (cl @p_761) :rule resolution :premises (t1071.t54 t1071.t57 t240))
(step t1071.t59 (cl @p_762) :rule and_intro :premises (t1071.t31 t1071.t58))
(step t1071.t60 (cl @p_760) :rule resolution :premises (t1071.t53 t1071.t59))
(step t1071.t61 (cl (=> @p_759 @p_758)) :rule la_mult_neg)
(step t1071.t62 (cl (not @p_759) @p_758) :rule implies :premises (t1071.t61))
(step t1071.t63 (cl @p_759) :rule and_intro :premises (t1071.t31 t1029))
(step t1071.t64 (cl @p_758) :rule resolution :premises (t1071.t62 t1071.t63))
(step t1071.t65 (cl @p_757) :rule resolution :premises (t1071.t25 t1071.t46 t1071.t51 t1071.t60 t1071.t64))
(step t1071.t66 (cl false) :rule resolution :premises (t1071.t0 t1071.t24 t1071.t65))
(step t1071 (cl @p_429 @p_424 @p_740 @p_742 false) :rule subproof :discharge (t1071.a0 t1071.a1 t1071.a2 t1071.a3))
(step t1072 (cl (! (not @p_745) :named @p_746) @p_396) :rule and_pos :args (0))
(step t1073 (cl @p_746 @p_410) :rule and_pos :args (1))
(step t1074 (cl @p_746 @p_732) :rule and_pos :args (2))
(step t1075 (cl @p_746 @p_718) :rule and_pos :args (3))
(step t1076 (cl false @p_746 @p_746 @p_746 @p_746) :rule resolution :premises (t1071 t1072 t1073 t1074 t1075))
(step t1077 (cl @p_746 @p_746 @p_746 @p_746 false) :rule reordering :premises (t1076))
(step t1078 (cl @p_746 false) :rule contraction :premises (t1077))
(step t1079 (cl @p_747 false) :rule resolution :premises (t1070 t1078))
(step t1080 (cl @p_747 @p_133) :rule implies_neg2)
(step t1081 (cl @p_747 @p_747) :rule resolution :premises (t1079 t1080))
(step t1082 (cl @p_747) :rule contraction :premises (t1081))
(step t1083 (cl (= @p_747 @p_746)) :rule implies_simplify)
(step t1084 (cl (not @p_747) @p_746) :rule equiv1 :premises (t1083))
(step t1085 (cl @p_746) :rule resolution :premises (t1082 t1084))
(step t1086 (cl @p_429 @p_424 @p_740 @p_742) :rule not_and :premises (t1085))
(step t1087 (cl @p_743 @p_464) :rule or_neg :args (0))
(step t1088 (cl @p_743 @p_469) :rule or_neg :args (1))
(step t1089 (cl @p_743 @p_744) :rule or_neg :args (2))
(step t1090 (cl @p_743 (not @p_742)) :rule or_neg :args (3))
(step t1091 (cl @p_743 @p_743 @p_743 @p_743) :rule resolution :premises (t1086 t1087 t1088 t1089 t1090))
(step t1092 (cl @p_743) :rule contraction :premises (t1091))
(step t1093 (cl @p_741) :rule resolution :premises (t1067 t1069 t1092))
(step t1094 (cl @p_429 @p_424 @p_740 @p_717) :rule or :premises (t1093))
(step t1095 (cl @p_740 @p_424 @p_429 @p_717) :rule reordering :premises (t1094))
(step t1096 (cl @p_717) :rule resolution :premises (t1095 t1029 t240 t650))
(step t1097 (cl (! (not (! (or (! (>= @p_71 0/1) :named @p_72) @p_719) :named @p_720)) :named @p_730) @p_72 @p_719) :rule or_pos)
(step t1098 (cl @p_72 @p_719 @p_730) :rule reordering :premises (t1097))
(step t1099 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1)))) (! (= (! (not @p_126) :named @p_127) (! (not @p_72) :named @p_111)) :named @p_128)) :named @p_129) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1)))) @p_111) :named @p_125)) :named @p_130)) (not @p_129) @p_125) :rule equiv_pos2)
(step t1100 (cl (= @p_127 @p_133)) :rule cong :premises (t652))
(step t1101 (cl (= @p_133 true)) :rule evaluate)
(step t1102 (cl (= @p_127 true)) :rule trans :premises (t1100 t1101))
(step t1103 (cl (= @p_111 @p_111)) :rule refl)
(step t1104 (cl (= @p_128 (! (= true @p_111) :named @p_131))) :rule cong :premises (t1102 t1103))
(step t1105 (cl (= @p_131 (! (= @p_111 true) :named @p_132))) :rule rare_rewrite :args ("eq-symm" true @p_111))
(step t1106 (cl (= @p_132 @p_111)) :rule rare_rewrite :args ("bool-eq-true" @p_111))
(step t1107 (cl (= @p_131 @p_111)) :rule trans :premises (t1105 t1106))
(step t1108 (cl (= @p_128 @p_111)) :rule trans :premises (t1104 t1107))
(step t1109 (cl @p_130) :rule cong :premises (t1108))
(step t1110 (cl @p_129 (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :rule implies_neg1)
(anchor :step t1111)
(assume t1111.a0 (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1)))))
(step t1111.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :named @p_124) @p_128)) :rule forall_inst :args (2/1 @p_3))
(step t1111.t1 (cl @p_124 @p_128) :rule or :premises (t1111.t0))
(step t1111.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real)) (= (< 0/1 (powr$ ?v0 ?v1)) (not (= ?v0 0/1)))) (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :named @p_112)) (not (forall ((?v0 Real) (?v1 Real)) (= (< 0/1 (powr$ ?v0 ?v1)) (not (= ?v0 0/1))))) (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :rule equiv_pos2)
(anchor :step t1111.t3 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t1111.t3.t0 (cl (= (! (= (! (< 0/1 @p_25) :named @p_119) @p_117) :named @p_120) (! (= @p_117 @p_119) :named @p_121))) :rule rare_rewrite :args ("eq-symm" @p_119 @p_117))
(step t1111.t3.t1 (cl (= @p_119 (! (not (! (>= 0/1 @p_25) :named @p_122)) :named @p_123))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_25))
(step t1111.t3.t2 (cl (= (* -1/1 (- 0/1 @p_25)) (* -1/1 (- (! (* -1/1 @p_25) :named @p_113) 0/1)))) :rule poly_simp)
(step t1111.t3.t3 (cl (= @p_122 (! (>= @p_113 0/1) :named @p_114))) :rule poly_simp_rel :premises (t1111.t3.t2))
(step t1111.t3.t4 (cl (= @p_123 (! (not @p_114) :named @p_115))) :rule cong :premises (t1111.t3.t3))
(step t1111.t3.t5 (cl (= @p_119 @p_115)) :rule trans :premises (t1111.t3.t1 t1111.t3.t4))
(step t1111.t3.t6 (cl (= @p_121 (! (= @p_117 @p_115) :named @p_118))) :rule cong :premises (t1111.t3.t5))
(step t1111.t3.t7 (cl (= @p_120 @p_118)) :rule trans :premises (t1111.t3.t0 t1111.t3.t6))
(step t1111.t3 (cl @p_112) :rule bind)
(step t1111.t4 (cl (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :rule resolution :premises (t1111.t2 t1111.t3 a22))
(step t1111.t5 (cl @p_128) :rule resolution :premises (t1111.t1 t1111.t4))
(step t1111 (cl @p_124 @p_128) :rule subproof :discharge (t1111.a0))
(step t1112 (cl @p_129 @p_128) :rule resolution :premises (t1110 t1111))
(step t1113 (cl @p_129 (not @p_128)) :rule implies_neg2)
(step t1114 (cl @p_129 @p_129) :rule resolution :premises (t1112 t1113))
(step t1115 (cl @p_129) :rule contraction :premises (t1114))
(step t1116 (cl @p_125) :rule resolution :premises (t1099 t1109 t1115))
(step t1117 (cl @p_124 @p_111) :rule implies :premises (t1116))
(step t1118 (cl (not @p_112) (not (forall ((?v0 Real) (?v1 Real)) (= (< 0/1 (powr$ ?v0 ?v1)) (not (= ?v0 0/1))))) (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :rule equiv_pos2)
(anchor :step t1119 :args ((?v0 Real) (?v1 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1)))
(step t1119.t0 (cl (= @p_120 @p_121)) :rule rare_rewrite :args ("eq-symm" @p_119 @p_117))
(step t1119.t1 (cl (= @p_119 @p_123)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 @p_25))
(step t1119.t2 (cl (= (* -1/1 (- 0/1 @p_25)) (* -1/1 (- @p_113 0/1)))) :rule poly_simp)
(step t1119.t3 (cl (= @p_122 @p_114)) :rule poly_simp_rel :premises (t1119.t2))
(step t1119.t4 (cl (= @p_123 @p_115)) :rule cong :premises (t1119.t3))
(step t1119.t5 (cl (= @p_119 @p_115)) :rule trans :premises (t1119.t1 t1119.t4))
(step t1119.t6 (cl (= @p_121 @p_118)) :rule cong :premises (t1119.t5))
(step t1119.t7 (cl (= @p_120 @p_118)) :rule trans :premises (t1119.t0 t1119.t6))
(step t1119 (cl @p_112) :rule bind)
(step t1120 (cl (forall ((?v0 Real) (?v1 Real)) (= (not (= ?v0 0/1)) (not (>= (* -1/1 (powr$ ?v0 ?v1)) 0/1))))) :rule resolution :premises (t1118 t1119 a22))
(step t1121 (cl @p_111) :rule resolution :premises (t1117 t1120))
(step t1122 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (! (or @p_72 (! (= @p_718 (! (not (! (>= (! (+ 1/1 @p_139) :named @p_722) 0/1) :named @p_723)) :named @p_724)) :named @p_725)) :named @p_726)) :named @p_727) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) @p_720) :named @p_721)) :named @p_728)) (not @p_727) @p_721) :rule equiv_pos2)
(step t1123 (cl (= (* 1/1 (- @p_722 0/1)) @p_729)) :rule poly_simp)
(step t1124 (cl (= @p_723 @p_714)) :rule poly_simp_rel :premises (t1123))
(step t1125 (cl (= @p_724 @p_715)) :rule cong :premises (t1124))
(step t1126 (cl (= @p_725 @p_719)) :rule cong :premises (t1125))
(step t1127 (cl (= @p_726 @p_720)) :rule cong :premises (t1126))
(step t1128 (cl @p_728) :rule cong :premises (t1127))
(step t1129 (cl @p_727 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1130)
(assume t1130.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1130.t0 (cl (or (! (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :named @p_102) @p_726)) :rule forall_inst :args (@p_4 1/1 @p_1))
(step t1130.t1 (cl @p_102 @p_726) :rule or :premises (t1130.t0))
(step t1130.t2 (cl (not (! (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :named @p_74)) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule equiv_pos2)
(anchor :step t1130.t3 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t1130.t3.t0 (cl (= (! (< 0/1 ?v0) :named @p_95) (! (not (! (>= 0/1 ?v0) :named @p_100)) :named @p_101))) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v0))
(step t1130.t3.t1 (cl (= (* -1/1 (- 0/1 ?v0)) (* -1/1 (- @p_85 0/1)))) :rule poly_simp)
(step t1130.t3.t2 (cl (= @p_100 (! (>= @p_85 0/1) :named @p_86))) :rule poly_simp_rel :premises (t1130.t3.t1))
(step t1130.t3.t3 (cl (= @p_101 (! (not @p_86) :named @p_88))) :rule cong :premises (t1130.t3.t2))
(step t1130.t3.t4 (cl (= @p_95 @p_88)) :rule trans :premises (t1130.t3.t0 t1130.t3.t3))
(step t1130.t3.t5 (cl (= (! (< @p_79 (! (times$a ?v0 ?v2) :named @p_80)) :named @p_93) (! (not (! (>= @p_79 @p_80) :named @p_98)) :named @p_99))) :rule rare_rewrite :args ("arith-elim-lt" @p_79 @p_80))
(step t1130.t3.t6 (cl (= (* -1/1 (- @p_79 @p_80)) (* -1/1 (- (! (+ (* -1/1 @p_80) @p_79) :named @p_81) 0/1)))) :rule poly_simp)
(step t1130.t3.t7 (cl (= @p_98 (! (>= @p_81 0/1) :named @p_82))) :rule poly_simp_rel :premises (t1130.t3.t6))
(step t1130.t3.t8 (cl (= @p_99 (! (not @p_82) :named @p_83))) :rule cong :premises (t1130.t3.t7))
(step t1130.t3.t9 (cl (= @p_93 @p_83)) :rule trans :premises (t1130.t3.t5 t1130.t3.t8))
(step t1130.t3.t10 (cl (= (! (< ?v1 ?v2) :named @p_92) (! (not (! (>= ?v1 ?v2) :named @p_96)) :named @p_97))) :rule rare_rewrite :args ("arith-elim-lt" ?v1 ?v2))
(step t1130.t3.t11 (cl (= (* 1/1 (- ?v1 ?v2)) (* 1/1 (- (! (+ ?v1 (* -1/1 ?v2)) :named @p_76) 0/1)))) :rule poly_simp)
(step t1130.t3.t12 (cl (= @p_96 (! (>= @p_76 0/1) :named @p_77))) :rule poly_simp_rel :premises (t1130.t3.t11))
(step t1130.t3.t13 (cl (= @p_97 (! (not @p_77) :named @p_78))) :rule cong :premises (t1130.t3.t12))
(step t1130.t3.t14 (cl (= @p_92 @p_78)) :rule trans :premises (t1130.t3.t10 t1130.t3.t13))
(step t1130.t3.t15 (cl (= (! (= @p_93 @p_92) :named @p_94) (! (= @p_83 @p_78) :named @p_84))) :rule cong :premises (t1130.t3.t9 t1130.t3.t14))
(step t1130.t3.t16 (cl (= (=> @p_95 @p_94) (! (=> @p_88 @p_84) :named @p_89))) :rule cong :premises (t1130.t3.t4 t1130.t3.t15))
(step t1130.t3 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (>= (* -1/1 ?v0) 0/1)) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))) :rule bind)
(anchor :step t1130.t4 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t1130.t4.t0 (cl (= @p_89 (! (or (! (not @p_88) :named @p_90) @p_84) :named @p_91))) :rule rare_rewrite :args ("bool-impl-elim" @p_88 @p_84))
(step t1130.t4.t1 (cl (= @p_90 @p_86)) :rule rare_rewrite :args ("bool-double-not-elim" @p_86))
(step t1130.t4.t2 (cl (= @p_84 @p_84)) :rule refl)
(step t1130.t4.t3 (cl (= @p_91 (! (or @p_86 @p_84) :named @p_87))) :rule cong :premises (t1130.t4.t1 t1130.t4.t2))
(step t1130.t4.t4 (cl (= @p_89 @p_87)) :rule trans :premises (t1130.t4.t0 t1130.t4.t3))
(step t1130.t4 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (>= (* -1/1 ?v0) 0/1)) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))) :rule bind)
(step t1130.t5 (cl @p_74) :rule trans :premises (t1130.t3 t1130.t4))
(step t1130.t6 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule resolution :premises (t1130.t2 t1130.t5 a13))
(step t1130.t7 (cl @p_726) :rule resolution :premises (t1130.t1 t1130.t6))
(step t1130 (cl @p_102 @p_726) :rule subproof :discharge (t1130.a0))
(step t1131 (cl @p_727 @p_726) :rule resolution :premises (t1129 t1130))
(step t1132 (cl @p_727 (not @p_726)) :rule implies_neg2)
(step t1133 (cl @p_727 @p_727) :rule resolution :premises (t1131 t1132))
(step t1134 (cl @p_727) :rule contraction :premises (t1133))
(step t1135 (cl @p_721) :rule resolution :premises (t1122 t1128 t1134))
(step t1136 (cl @p_102 @p_720) :rule implies :premises (t1135))
(step t1137 (cl (not @p_74) (not (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule equiv_pos2)
(anchor :step t1138 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t1138.t0 (cl (= @p_95 @p_101)) :rule rare_rewrite :args ("arith-elim-lt" 0/1 ?v0))
(step t1138.t1 (cl (= (* -1/1 (- 0/1 ?v0)) (* -1/1 (- @p_85 0/1)))) :rule poly_simp)
(step t1138.t2 (cl (= @p_100 @p_86)) :rule poly_simp_rel :premises (t1138.t1))
(step t1138.t3 (cl (= @p_101 @p_88)) :rule cong :premises (t1138.t2))
(step t1138.t4 (cl (= @p_95 @p_88)) :rule trans :premises (t1138.t0 t1138.t3))
(step t1138.t5 (cl (= @p_93 @p_99)) :rule rare_rewrite :args ("arith-elim-lt" @p_79 @p_80))
(step t1138.t6 (cl (= (* -1/1 (- @p_79 @p_80)) (* -1/1 (- @p_81 0/1)))) :rule poly_simp)
(step t1138.t7 (cl (= @p_98 @p_82)) :rule poly_simp_rel :premises (t1138.t6))
(step t1138.t8 (cl (= @p_99 @p_83)) :rule cong :premises (t1138.t7))
(step t1138.t9 (cl (= @p_93 @p_83)) :rule trans :premises (t1138.t5 t1138.t8))
(step t1138.t10 (cl (= @p_92 @p_97)) :rule rare_rewrite :args ("arith-elim-lt" ?v1 ?v2))
(step t1138.t11 (cl (= (* 1/1 (- ?v1 ?v2)) (* 1/1 (- @p_76 0/1)))) :rule poly_simp)
(step t1138.t12 (cl (= @p_96 @p_77)) :rule poly_simp_rel :premises (t1138.t11))
(step t1138.t13 (cl (= @p_97 @p_78)) :rule cong :premises (t1138.t12))
(step t1138.t14 (cl (= @p_92 @p_78)) :rule trans :premises (t1138.t10 t1138.t13))
(step t1138.t15 (cl (= @p_94 @p_84)) :rule cong :premises (t1138.t9 t1138.t14))
(step t1138.t16 (cl (= (=> @p_95 @p_94) @p_89)) :rule cong :premises (t1138.t4 t1138.t15))
(step t1138 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (< 0/1 ?v0) (= (< (times$a ?v0 ?v1) (times$a ?v0 ?v2)) (< ?v1 ?v2)))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (>= (* -1/1 ?v0) 0/1)) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))) :rule bind)
(anchor :step t1139 :args ((?v0 Real) (?v1 Real) (?v2 Real) (:= (?v0 Real) ?v0) (:= (?v1 Real) ?v1) (:= (?v2 Real) ?v2)))
(step t1139.t0 (cl (= @p_89 @p_91)) :rule rare_rewrite :args ("bool-impl-elim" @p_88 @p_84))
(step t1139.t1 (cl (= @p_90 @p_86)) :rule rare_rewrite :args ("bool-double-not-elim" @p_86))
(step t1139.t2 (cl (= @p_84 @p_84)) :rule refl)
(step t1139.t3 (cl (= @p_91 @p_87)) :rule cong :premises (t1139.t1 t1139.t2))
(step t1139.t4 (cl (= @p_89 @p_87)) :rule trans :premises (t1139.t0 t1139.t3))
(step t1139 (cl (= (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (=> (not (>= (* -1/1 ?v0) 0/1)) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))) :rule bind)
(step t1140 (cl @p_74) :rule trans :premises (t1138 t1139))
(step t1141 (cl (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule resolution :premises (t1137 t1140 a13))
(step t1142 (cl @p_720) :rule resolution :premises (t1136 t1141))
(step t1143 (cl @p_719) :rule resolution :premises (t1098 t1121 t1142))
(step t1144 (cl @p_714) :rule resolution :premises (t1066 t1096 t1143))
(step t1145 (cl (not (! (= (! (or @p_435 @p_436 (! (not @p_702) :named @p_703)) :named @p_704) (! (or @p_435 @p_436 @p_540) :named @p_701)) :named @p_713)) (not @p_704) @p_701) :rule equiv_pos2)
(step t1146 (cl (= @p_703 @p_540)) :rule rare_rewrite :args ("bool-double-not-elim" @p_540))
(step t1147 (cl @p_713) :rule cong :premises (t1146))
(step t1148 (cl (! (=> (! (and @p_329 @p_315 @p_702) :named @p_705) (! (and @p_474 @p_702) :named @p_707)) :named @p_712) @p_705) :rule implies_neg1)
(anchor :step t1149)
(assume t1149.a0 @p_329)
(assume t1149.a1 @p_315)
(assume t1149.a2 @p_702)
(step t1149.t0 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t1149.t1 (cl @p_474) :rule trans :premises (t1149.t0 t750))
(step t1149.t2 (cl @p_707) :rule and_intro :premises (t1149.t1 t1149.a2))
(step t1149 (cl @p_435 @p_436 @p_703 @p_707) :rule subproof :discharge (t1149.a0 t1149.a1 t1149.a2))
(step t1150 (cl (! (not @p_705) :named @p_706) @p_329) :rule and_pos :args (0))
(step t1151 (cl @p_706 @p_315) :rule and_pos :args (1))
(step t1152 (cl @p_706 @p_702) :rule and_pos :args (2))
(step t1153 (cl @p_707 @p_706 @p_706 @p_706) :rule resolution :premises (t1149 t1150 t1151 t1152))
(step t1154 (cl @p_706 @p_706 @p_706 @p_707) :rule reordering :premises (t1153))
(step t1155 (cl @p_706 @p_707) :rule contraction :premises (t1154))
(step t1156 (cl @p_712 @p_707) :rule resolution :premises (t1148 t1155))
(step t1157 (cl @p_712 (! (not @p_707) :named @p_708)) :rule implies_neg2)
(step t1158 (cl @p_712 @p_712) :rule resolution :premises (t1156 t1157))
(step t1159 (cl @p_712) :rule contraction :premises (t1158))
(step t1160 (cl @p_706 @p_707) :rule implies :premises (t1159))
(step t1161 (cl (! (=> @p_707 false) :named @p_709) @p_707) :rule implies_neg1)
(anchor :step t1162)
(assume t1162.a0 @p_474)
(assume t1162.a1 @p_702)
(step t1162.t0 (cl (not @p_538) @p_482 @p_535) :rule equiv_pos2)
(step t1162.t1 (cl (= (* 2/1 (- @p_503 0/1)) (* 2/1 @p_541))) :rule poly_simp)
(step t1162.t2 (cl (= @p_535 @p_540)) :rule poly_simp_rel :premises (t1162.t1))
(step t1162.t3 (cl (= @p_540 @p_535)) :rule symm :premises (t1162.t2))
(step t1162.t4 (cl @p_538) :rule trans :premises (t966 t1162.t3))
(step t1162.t5 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t1162.t6 (cl @p_474) :rule trans :premises (t1162.t5 t750))
(step t1162.t7 (cl @p_535) :rule resolution :premises (t1162.t0 t1162.t4 t1162.t6))
(step t1162.t8 (cl (not (! (= @p_702 (! (not @p_535) :named @p_710)) :named @p_711)) @p_703 @p_710) :rule equiv_pos2)
(step t1162.t9 (cl (= @p_710 @p_702)) :rule cong :premises (t1162.t2))
(step t1162.t10 (cl @p_711) :rule symm :premises (t1162.t9))
(step t1162.t11 (cl @p_710) :rule resolution :premises (t1162.t8 t1162.t10 t1162.a1))
(step t1162.t12 (cl) :rule resolution :premises (t1162.t7 t1162.t11))
(step t1162 (cl @p_482 @p_703 false) :rule subproof :discharge (t1162.a0 t1162.a1))
(step t1163 (cl @p_708 @p_474) :rule and_pos :args (0))
(step t1164 (cl @p_708 @p_702) :rule and_pos :args (1))
(step t1165 (cl false @p_708 @p_708) :rule resolution :premises (t1162 t1163 t1164))
(step t1166 (cl @p_708 @p_708 false) :rule reordering :premises (t1165))
(step t1167 (cl @p_708 false) :rule contraction :premises (t1166))
(step t1168 (cl @p_709 false) :rule resolution :premises (t1161 t1167))
(step t1169 (cl @p_709 @p_133) :rule implies_neg2)
(step t1170 (cl @p_709 @p_709) :rule resolution :premises (t1168 t1169))
(step t1171 (cl @p_709) :rule contraction :premises (t1170))
(step t1172 (cl (= @p_709 @p_708)) :rule implies_simplify)
(step t1173 (cl (not @p_709) @p_708) :rule equiv1 :premises (t1172))
(step t1174 (cl @p_708) :rule resolution :premises (t1171 t1173))
(step t1175 (cl @p_706) :rule resolution :premises (t1160 t1174))
(step t1176 (cl @p_435 @p_436 @p_703) :rule not_and :premises (t1175))
(step t1177 (cl @p_704 @p_458) :rule or_neg :args (0))
(step t1178 (cl @p_704 @p_457) :rule or_neg :args (1))
(step t1179 (cl @p_704 (not @p_703)) :rule or_neg :args (2))
(step t1180 (cl @p_704 @p_704 @p_704) :rule resolution :premises (t1176 t1177 t1178 t1179))
(step t1181 (cl @p_704) :rule contraction :premises (t1180))
(step t1182 (cl @p_701) :rule resolution :premises (t1145 t1147 t1181))
(step t1183 (cl @p_435 @p_436 @p_540) :rule or :premises (t1182))
(step t1184 (cl @p_540) :rule resolution :premises (t1183 t747 t750))
(step t1185 (cl (= @p_362 @p_65)) :rule symm :premises (t629))
(step t1186 (cl (= @p_65 @p_6)) :rule symm :premises (t240))
(step t1187 (cl (= @p_362 @p_6)) :rule trans :premises (t1185 t1186))
(step t1188 (cl (= 2/1 2/1)) :rule refl)
(step t1189 (cl (= @p_363 @p_290)) :rule cong :premises (t1187 t1188))
(step t1190 (cl (= @p_289 @p_293)) :rule cong :premises (t240))
(step t1191 (cl (= @p_293 @p_294)) :rule symm :premises (t765))
(step t1192 (cl (= @p_270 @p_304)) :rule symm :premises (t756))
(step t1193 (cl @p_355) :rule symm :premises (t723))
(step t1194 (cl (= @p_304 @p_310)) :rule cong :premises (t1193))
(step t1195 (cl (= @p_307 @p_304)) :rule cong :premises (t675))
(step t1196 (cl @p_388) :rule refl)
(step t1197 (cl (= @p_308 @p_341)) :rule cong :premises (t1195 t1196))
(step t1198 (cl (= @p_341 @p_296)) :rule symm :premises (t726))
(step t1199 (cl (= @p_270 @p_296)) :rule trans :premises (t1192 t1194 t753 t1197 t1198))
(step t1200 (cl (= @p_1 @p_1)) :rule refl)
(step t1201 (cl (= @p_294 @p_339)) :rule cong :premises (t1199 t1200))
(step t1202 (cl (= @p_339 @p_314)) :rule symm :premises (t729))
(step t1203 (cl @p_473) :rule trans :premises (t650 t701 t1189 t768 t1190 t1191 t1201 t1202 t747))
(step t1204 (cl (= @p_361 @p_301)) :rule symm :premises (t632))
(step t1205 (cl (= @p_4 @p_301)) :rule trans :premises (t650 t1204))
(step t1206 (cl (= @p_139 @p_139)) :rule refl)
(step t1207 (cl (= @p_268 @p_302)) :rule cong :premises (t1205 t1206))
(step t1208 (cl (= @p_268 @p_274)) :rule symm :premises (t626))
(step t1209 (cl (= @p_300 @p_277)) :rule cong :premises (t1208))
(step t1210 (cl @p_475) :rule trans :premises (t626 t1207 t759 t1209 t787))
(step t1211 (cl @p_387) :rule symm :premises (t675))
(step t1212 (cl (= @p_304 @p_307)) :rule cong :premises (t1211))
(step t1213 (cl (= @p_341 @p_308)) :rule cong :premises (t1212 t1196))
(step t1214 (cl (= @p_308 @p_310)) :rule symm :premises (t753))
(step t1215 (cl (= @p_310 @p_304)) :rule cong :premises (t723))
(step t1216 (cl (= @p_296 @p_270)) :rule trans :premises (t726 t1213 t1214 t1215 t756))
(step t1217 (cl (= @p_297 @p_271)) :rule cong :premises (t1216 t1206))
(step t1218 (cl (= @p_269 @p_275)) :rule cong :premises (t1208))
(step t1219 (cl @p_476) :rule trans :premises (t762 t1217 t790 t1218))
(step t1220 (cl @p_700) :rule resolution :premises (t1015 t1029 t1054 t623 t1144 t1184 t1203 t1210 t1219))
(step t1221 (cl @p_996) :rule resolution :premises (t958 t1220 t768 t765 t756 t753 t750 t747 t729 t726 t723 t701 t675 t650 t629 t240))
(step t1222 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))) (! (= (! (= @p_139 @p_298) :named @p_990) (! (or (! (= @p_139 0/1) :named @p_988) @p_982) :named @p_989)) :named @p_991)) :named @p_992) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))) @p_986) :named @p_987)) :named @p_993)) (not @p_992) @p_987) :rule equiv_pos2)
(step t1223 (cl (= (* 1/1 (- @p_139 @p_298)) (* -1/1 (- @p_1 @p_313)))) :rule poly_simp)
(step t1224 (cl (= @p_990 @p_985)) :rule poly_simp_rel :premises (t1223))
(step t1225 (cl (= (* 1/1 (- @p_139 0/1)) (* -1/1 (! (- @p_1 0/1) :named @p_995)))) :rule poly_simp)
(step t1226 (cl (= @p_988 @p_979)) :rule poly_simp_rel :premises (t1225))
(step t1227 (cl (= @p_982 @p_982)) :rule refl)
(step t1228 (cl (= @p_989 @p_983)) :rule cong :premises (t1226 t1227))
(step t1229 (cl (= @p_991 (! (= @p_985 @p_983) :named @p_994))) :rule cong :premises (t1224 t1228))
(step t1230 (cl (= @p_994 @p_986)) :rule rare_rewrite :args ("eq-symm" @p_985 @p_983))
(step t1231 (cl (= @p_991 @p_986)) :rule trans :premises (t1229 t1230))
(step t1232 (cl @p_993) :rule cong :premises (t1231))
(step t1233 (cl @p_992 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1))))) :rule implies_neg1)
(anchor :step t1234)
(assume t1234.a0 (forall ((?v0 Real) (?v1 Real)) (= (= ?v0 (times$a ?v0 ?v1)) (or (= ?v0 0/1) (= ?v1 1/1)))))
(step t1234.t0 (cl (or @p_397 @p_991)) :rule forall_inst :args (@p_139 @p_296))
(step t1234.t1 (cl @p_397 @p_991) :rule or :premises (t1234.t0))
(step t1234.t2 (cl @p_991) :rule resolution :premises (t1234.t1 t1234.a0))
(step t1234 (cl @p_397 @p_991) :rule subproof :discharge (t1234.a0))
(step t1235 (cl @p_992 @p_991) :rule resolution :premises (t1233 t1234))
(step t1236 (cl @p_992 (not @p_991)) :rule implies_neg2)
(step t1237 (cl @p_992 @p_992) :rule resolution :premises (t1235 t1236))
(step t1238 (cl @p_992) :rule contraction :premises (t1237))
(step t1239 (cl @p_987) :rule resolution :premises (t1222 t1232 t1238))
(step t1240 (cl @p_397 @p_986) :rule implies :premises (t1239))
(step t1241 (cl @p_986) :rule resolution :premises (t1240 a8))
(step t1242 (cl @p_984) :rule resolution :premises (t906 t1221 t1241))
(step t1243 (cl @p_981) :rule resolution :premises (t904 t1242))
(step t1244 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (! (or (! (= @p_247 0/1) :named @p_1179) @p_1176) :named @p_1180)) :named @p_1181) (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) @p_1177) :named @p_1178)) :named @p_1182)) (not @p_1181) @p_1178) :rule equiv_pos2)
(step t1245 (cl (= (* 1/1 (- @p_247 0/1)) (* 2/1 @p_995))) :rule poly_simp)
(step t1246 (cl (= @p_1179 @p_979)) :rule poly_simp_rel :premises (t1245))
(step t1247 (cl (= @p_1176 @p_1176)) :rule refl)
(step t1248 (cl (= @p_1180 @p_1177)) :rule cong :premises (t1246 t1247))
(step t1249 (cl @p_1182) :rule cong :premises (t1248))
(step t1250 (cl @p_1181 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1251)
(assume t1251.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t1251.t0 (cl (or @p_353 @p_1180)) :rule forall_inst :args (@p_247 @p_4))
(step t1251.t1 (cl @p_353 @p_1180) :rule or :premises (t1251.t0))
(step t1251.t2 (cl @p_1180) :rule resolution :premises (t1251.t1 t722))
(step t1251 (cl @p_353 @p_1180) :rule subproof :discharge (t1251.a0))
(step t1252 (cl @p_1181 @p_1180) :rule resolution :premises (t1250 t1251))
(step t1253 (cl @p_1181 (not @p_1180)) :rule implies_neg2)
(step t1254 (cl @p_1181 @p_1181) :rule resolution :premises (t1252 t1253))
(step t1255 (cl @p_1181) :rule contraction :premises (t1254))
(step t1256 (cl @p_1178) :rule resolution :premises (t1244 t1249 t1255))
(step t1257 (cl @p_353 @p_1177) :rule implies :premises (t1256))
(step t1258 (cl @p_1177) :rule resolution :premises (t1257 t722))
(step t1259 (cl @p_1176) :rule resolution :premises (t902 t1243 t1258))
(step t1260 (cl (or @p_312 @p_1175)) :rule forall_inst :args (@p_247 1/1 @p_4))
(step t1261 (cl @p_312 @p_1175) :rule or :premises (t1260))
(step t1262 (cl @p_1175) :rule resolution :premises (t1261 a27))
(step t1263 (cl (or @p_312 @p_1173)) :rule forall_inst :args (@p_139 1/1 @p_4))
(step t1264 (cl @p_312 @p_1173) :rule or :premises (t1263))
(step t1265 (cl @p_1173) :rule resolution :premises (t1264 a27))
(step t1266 (cl (not @p_973) (not @p_972) @p_970) :rule equiv_pos2)
(step t1267 (cl (= (* 1/1 (- @p_314 @p_932)) (* -1/1 (- @p_932 @p_314)))) :rule poly_simp)
(step t1268 (cl (= @p_971 @p_969)) :rule poly_simp_rel :premises (t1267))
(step t1269 (cl @p_973) :rule cong :premises (t1268))
(step t1270 (cl @p_972 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t1271)
(assume t1271.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t1271.t0 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t1271.t1 (cl @p_312 @p_971) :rule or :premises (t1271.t0))
(step t1271.t2 (cl @p_971) :rule resolution :premises (t1271.t1 t1271.a0))
(step t1271 (cl @p_312 @p_971) :rule subproof :discharge (t1271.a0))
(step t1272 (cl @p_972 @p_971) :rule resolution :premises (t1270 t1271))
(step t1273 (cl @p_972 (not @p_971)) :rule implies_neg2)
(step t1274 (cl @p_972 @p_972) :rule resolution :premises (t1272 t1273))
(step t1275 (cl @p_972) :rule contraction :premises (t1274))
(step t1276 (cl @p_970) :rule resolution :premises (t1266 t1269 t1275))
(step t1277 (cl @p_312 @p_969) :rule implies :premises (t1276))
(step t1278 (cl @p_969) :rule resolution :premises (t1277 a27))
(step t1279 (cl (not @p_1121) (not @p_1120) @p_1118) :rule equiv_pos2)
(step t1280 (cl (= (* 1/1 (- @p_1099 @p_1116)) (* -1/1 (- @p_1116 @p_1099)))) :rule poly_simp)
(step t1281 (cl (= @p_1119 @p_1117)) :rule poly_simp_rel :premises (t1280))
(step t1282 (cl @p_1121) :rule cong :premises (t1281))
(step t1283 (cl @p_1120 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2)))) :rule implies_neg1)
(anchor :step t1284)
(assume t1284.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v1) ?v2))))
(step t1284.t0 (cl (or @p_312 @p_1119)) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t1284.t1 (cl @p_312 @p_1119) :rule or :premises (t1284.t0))
(step t1284.t2 (cl @p_1119) :rule resolution :premises (t1284.t1 t1284.a0))
(step t1284 (cl @p_312 @p_1119) :rule subproof :discharge (t1284.a0))
(step t1285 (cl @p_1120 @p_1119) :rule resolution :premises (t1283 t1284))
(step t1286 (cl @p_1120 (not @p_1119)) :rule implies_neg2)
(step t1287 (cl @p_1120 @p_1120) :rule resolution :premises (t1285 t1286))
(step t1288 (cl @p_1120) :rule contraction :premises (t1287))
(step t1289 (cl @p_1118) :rule resolution :premises (t1279 t1282 t1288))
(step t1290 (cl @p_312 @p_1117) :rule implies :premises (t1289))
(step t1291 (cl @p_1117) :rule resolution :premises (t1290 a27))
(step t1292 (cl (not @p_1172) (not @p_1171) @p_1169) :rule equiv_pos2)
(step t1293 (cl (= (* -1/1 (- @p_1166 @p_1167)) (* 1/1 (- @p_1167 @p_1166)))) :rule poly_simp)
(step t1294 (cl (= @p_1170 @p_1168)) :rule poly_simp_rel :premises (t1293))
(step t1295 (cl @p_1172) :rule cong :premises (t1294))
(step t1296 (cl @p_1171 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1)))) :rule implies_neg1)
(anchor :step t1297)
(assume t1297.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (divide$ ?v0 (divide$ ?v1 ?v2)) (divide$ (times$a ?v0 ?v2) ?v1))))
(step t1297.t0 (cl (or @p_343 @p_1170)) :rule forall_inst :args (@p_139 @p_4 1/1))
(step t1297.t1 (cl @p_343 @p_1170) :rule or :premises (t1297.t0))
(step t1297.t2 (cl @p_1170) :rule resolution :premises (t1297.t1 t1297.a0))
(step t1297 (cl @p_343 @p_1170) :rule subproof :discharge (t1297.a0))
(step t1298 (cl @p_1171 @p_1170) :rule resolution :premises (t1296 t1297))
(step t1299 (cl @p_1171 (not @p_1170)) :rule implies_neg2)
(step t1300 (cl @p_1171 @p_1171) :rule resolution :premises (t1298 t1299))
(step t1301 (cl @p_1171) :rule contraction :premises (t1300))
(step t1302 (cl @p_1169) :rule resolution :premises (t1292 t1295 t1301))
(step t1303 (cl @p_343 @p_1168) :rule implies :premises (t1302))
(step t1304 (cl @p_1168) :rule resolution :premises (t1303 a2))
(step t1305 (cl (! (not (! (= @p_1103 (! (or (! (= @p_18 0/1) :named @p_1104) @p_244) :named @p_1105)) :named @p_1106)) :named @p_1115) @p_1103 (! (not @p_1105) :named @p_1114)) :rule equiv_pos1)
(step t1306 (cl @p_1103 @p_1114 @p_1115) :rule reordering :premises (t1305))
(step t1307 (cl @p_1105 @p_1113) :rule or_neg :args (1))
(step t1308 (cl @p_1113 @p_1105) :rule reordering :premises (t1307))
(step t1309 (cl @p_1105) :rule resolution :premises (t1308 t900))
(step t1310 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) (! (= (! (or @p_1104 @p_260) :named @p_1108) @p_1103) :named @p_1109)) :named @p_1110) (! (=> (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))) @p_1106) :named @p_1107)) :named @p_1111)) (not @p_1110) @p_1107) :rule equiv_pos2)
(step t1311 (cl (= @p_1108 @p_1105)) :rule cong :premises (t883))
(step t1312 (cl (= @p_1103 @p_1103)) :rule refl)
(step t1313 (cl (= @p_1109 (! (= @p_1105 @p_1103) :named @p_1112))) :rule cong :premises (t1311 t1312))
(step t1314 (cl (= @p_1112 @p_1106)) :rule rare_rewrite :args ("eq-symm" @p_1105 @p_1103))
(step t1315 (cl (= @p_1109 @p_1106)) :rule trans :premises (t1313 t1314))
(step t1316 (cl @p_1111) :rule cong :premises (t1315))
(step t1317 (cl @p_1110 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t1318)
(assume t1318.a0 (forall ((?v0 Real) (?v1 Real)) (= (or (= ?v1 0/1) (= ?v0 1/1)) (= ?v1 (times$a ?v0 ?v1)))))
(step t1318.t0 (cl (or @p_258 @p_1109)) :rule forall_inst :args (@p_247 @p_18))
(step t1318.t1 (cl @p_258 @p_1109) :rule or :premises (t1318.t0))
(step t1318.t2 (cl @p_1109) :rule resolution :premises (t1318.t1 t674))
(step t1318 (cl @p_258 @p_1109) :rule subproof :discharge (t1318.a0))
(step t1319 (cl @p_1110 @p_1109) :rule resolution :premises (t1317 t1318))
(step t1320 (cl @p_1110 (not @p_1109)) :rule implies_neg2)
(step t1321 (cl @p_1110 @p_1110) :rule resolution :premises (t1319 t1320))
(step t1322 (cl @p_1110) :rule contraction :premises (t1321))
(step t1323 (cl @p_1107) :rule resolution :premises (t1310 t1316 t1322))
(step t1324 (cl @p_258 @p_1106) :rule implies :premises (t1323))
(step t1325 (cl @p_1106) :rule resolution :premises (t1324 t674))
(step t1326 (cl @p_1103) :rule resolution :premises (t1306 t1309 t1325))
(step t1327 (cl (or @p_273 @p_1102)) :rule forall_inst :args (@p_4 @p_1 @p_1098))
(step t1328 (cl @p_273 @p_1102) :rule or :premises (t1327))
(step t1329 (cl @p_1102) :rule resolution :premises (t1328 a4))
(step t1330 (cl (or @p_273 @p_1164)) :rule forall_inst :args (@p_139 @p_247 @p_18))
(step t1331 (cl @p_273 @p_1164) :rule or :premises (t1330))
(step t1332 (cl @p_1164) :rule resolution :premises (t1331 a4))
(step t1333 (cl (not @p_1086) (not @p_1085) @p_1082) :rule equiv_pos2)
(step t1334 (cl (= (* 1/1 (- @p_680 @p_1083)) (* -1/1 @p_1087))) :rule poly_simp)
(step t1335 (cl (= @p_1084 @p_1081)) :rule poly_simp_rel :premises (t1334))
(step t1336 (cl @p_1086) :rule cong :premises (t1335))
(step t1337 (cl @p_1085 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t1338)
(assume t1338.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t1338.t0 (cl (or @p_279 @p_1084)) :rule forall_inst :args (@p_139 @p_4 @p_18))
(step t1338.t1 (cl @p_279 @p_1084) :rule or :premises (t1338.t0))
(step t1338.t2 (cl @p_1084) :rule resolution :premises (t1338.t1 t1338.a0))
(step t1338 (cl @p_279 @p_1084) :rule subproof :discharge (t1338.a0))
(step t1339 (cl @p_1085 @p_1084) :rule resolution :premises (t1337 t1338))
(step t1340 (cl @p_1085 (not @p_1084)) :rule implies_neg2)
(step t1341 (cl @p_1085 @p_1085) :rule resolution :premises (t1339 t1340))
(step t1342 (cl @p_1085) :rule contraction :premises (t1341))
(step t1343 (cl @p_1082) :rule resolution :premises (t1333 t1336 t1342))
(step t1344 (cl @p_279 @p_1081) :rule implies :premises (t1343))
(step t1345 (cl @p_1081) :rule resolution :premises (t1344 a1))
(step t1346 (cl (not @p_1076) (not @p_1075) @p_1070) :rule equiv_pos2)
(step t1347 (cl (= @p_1072 @p_1066)) :rule poly_simp)
(step t1348 (cl (= @p_18 @p_18)) :rule refl)
(step t1349 (cl (= @p_1073 @p_1067)) :rule cong :premises (t1347 t1348))
(step t1350 (cl (= @p_1071 @p_1077)) :rule poly_simp)
(step t1351 (cl (= @p_1074 @p_1078)) :rule cong :premises (t1349 t1350))
(step t1352 (cl (= (* 1/1 (- @p_1067 @p_1077)) (* -2/1 @p_1079))) :rule poly_simp)
(step t1353 (cl (= @p_1078 @p_1069)) :rule poly_simp_rel :premises (t1352))
(step t1354 (cl (= @p_1074 @p_1069)) :rule trans :premises (t1351 t1353))
(step t1355 (cl @p_1076) :rule cong :premises (t1354))
(step t1356 (cl @p_1075 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t1357)
(assume t1357.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t1357.t0 (cl (or @p_279 @p_1074)) :rule forall_inst :args (@p_247 @p_247 @p_18))
(step t1357.t1 (cl @p_279 @p_1074) :rule or :premises (t1357.t0))
(step t1357.t2 (cl @p_1074) :rule resolution :premises (t1357.t1 t1357.a0))
(step t1357 (cl @p_279 @p_1074) :rule subproof :discharge (t1357.a0))
(step t1358 (cl @p_1075 @p_1074) :rule resolution :premises (t1356 t1357))
(step t1359 (cl @p_1075 (not @p_1074)) :rule implies_neg2)
(step t1360 (cl @p_1075 @p_1075) :rule resolution :premises (t1358 t1359))
(step t1361 (cl @p_1075) :rule contraction :premises (t1360))
(step t1362 (cl @p_1070) :rule resolution :premises (t1346 t1355 t1361))
(step t1363 (cl @p_279 @p_1069) :rule implies :premises (t1362))
(step t1364 (cl @p_1069) :rule resolution :premises (t1363 a1))
(step t1365 (cl (not @p_1063) (not @p_1062) @p_1058) :rule equiv_pos2)
(step t1366 (cl (= @p_1060 @p_1055)) :rule cong :premises (t600 t1348))
(step t1367 (cl (= @p_1059 @p_1064)) :rule poly_simp)
(step t1368 (cl (= @p_1061 @p_1065)) :rule cong :premises (t1366 t1367))
(step t1369 (cl (= (* 1/1 (- @p_1055 @p_1064)) (* -2/1 (- @p_1053 @p_1056)))) :rule poly_simp)
(step t1370 (cl (= @p_1065 @p_1057)) :rule poly_simp_rel :premises (t1369))
(step t1371 (cl (= @p_1061 @p_1057)) :rule trans :premises (t1368 t1370))
(step t1372 (cl @p_1063) :rule cong :premises (t1371))
(step t1373 (cl @p_1062 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t1374)
(assume t1374.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t1374.t0 (cl (or @p_279 @p_1061)) :rule forall_inst :args (@p_1 @p_1 @p_18))
(step t1374.t1 (cl @p_279 @p_1061) :rule or :premises (t1374.t0))
(step t1374.t2 (cl @p_1061) :rule resolution :premises (t1374.t1 t1374.a0))
(step t1374 (cl @p_279 @p_1061) :rule subproof :discharge (t1374.a0))
(step t1375 (cl @p_1062 @p_1061) :rule resolution :premises (t1373 t1374))
(step t1376 (cl @p_1062 (not @p_1061)) :rule implies_neg2)
(step t1377 (cl @p_1062 @p_1062) :rule resolution :premises (t1375 t1376))
(step t1378 (cl @p_1062) :rule contraction :premises (t1377))
(step t1379 (cl @p_1058) :rule resolution :premises (t1365 t1372 t1378))
(step t1380 (cl @p_279 @p_1057) :rule implies :premises (t1379))
(step t1381 (cl @p_1057) :rule resolution :premises (t1380 a1))
(step t1382 (cl (or @p_326 @p_1054)) :rule forall_inst :args (@p_1 @p_18))
(step t1383 (cl @p_326 @p_1054) :rule or :premises (t1382))
(step t1384 (cl @p_1054) :rule resolution :premises (t1383 t622))
(step t1385 (cl (! (not (! (or (! (= @p_296 0/1) :named @p_961) @p_960) :named @p_962)) :named @p_1050) @p_961 @p_960) :rule or_pos)
(step t1386 (cl @p_961 @p_960 @p_1050) :rule reordering :premises (t1385))
(step t1387 (cl (! (or @p_961 @p_789) :named @p_964) (! (not @p_961) :named @p_963)) :rule or_neg :args (0))
(step t1388 (cl (! (not (! (= @p_964 (! (= @p_296 @p_314) :named @p_966)) :named @p_967)) :named @p_1049) (! (not @p_964) :named @p_965) @p_966) :rule equiv_pos2)
(step t1389 (cl @p_966 @p_965 @p_1049) :rule reordering :premises (t1388))
(step t1390 (cl (! (and @p_974 @p_969 @p_966) :named @p_1043) (! (not @p_974) :named @p_1041) @p_1042 (! (not @p_966) :named @p_968)) :rule and_neg)
(step t1391 (cl (! (=> @p_1043 (! (= @p_4 @p_296) :named @p_975)) :named @p_1045) @p_1043) :rule implies_neg1)
(anchor :step t1392)
(assume t1392.a0 @p_974)
(assume t1392.a1 @p_969)
(assume t1392.a2 @p_966)
(step t1392.t0 (cl (! (=> (! (and @p_966 @p_969 @p_974) :named @p_1046) @p_975) :named @p_1048) @p_1046) :rule implies_neg1)
(anchor :step t1392.t1)
(assume t1392.t1.a0 @p_966)
(assume t1392.t1.a1 @p_969)
(assume t1392.t1.a2 @p_974)
(step t1392.t1.t0 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t1392.t1.t1 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t1392.t1.t2 (cl @p_312 @p_971) :rule or :premises (t1392.t1.t1))
(step t1392.t1.t3 (cl @p_971) :rule resolution :premises (t1392.t1.t2 a27))
(step t1392.t1.t4 (cl @p_974) :rule trans :premises (t1203 t1392.t1.t0 t1392.t1.t3))
(step t1392.t1.t5 (cl (= @p_314 @p_296)) :rule symm :premises (t1392.t1.a0))
(step t1392.t1.t6 (cl @p_975) :rule trans :premises (t1392.t1.t4 t1278 t1392.t1.t5))
(step t1392.t1 (cl @p_968 @p_1042 @p_1041 @p_975) :rule subproof :discharge (t1392.t1.a0 t1392.t1.a1 t1392.t1.a2))
(step t1392.t2 (cl (! (not @p_1046) :named @p_1047) @p_966) :rule and_pos :args (0))
(step t1392.t3 (cl @p_1047 @p_969) :rule and_pos :args (1))
(step t1392.t4 (cl @p_1047 @p_974) :rule and_pos :args (2))
(step t1392.t5 (cl @p_975 @p_1047 @p_1047 @p_1047) :rule resolution :premises (t1392.t1 t1392.t2 t1392.t3 t1392.t4))
(step t1392.t6 (cl @p_1047 @p_1047 @p_1047 @p_975) :rule reordering :premises (t1392.t5))
(step t1392.t7 (cl @p_1047 @p_975) :rule contraction :premises (t1392.t6))
(step t1392.t8 (cl @p_1048 @p_975) :rule resolution :premises (t1392.t0 t1392.t7))
(step t1392.t9 (cl @p_1048 (! (not @p_975) :named @p_976)) :rule implies_neg2)
(step t1392.t10 (cl @p_1048 @p_1048) :rule resolution :premises (t1392.t8 t1392.t9))
(step t1392.t11 (cl @p_1048) :rule contraction :premises (t1392.t10))
(step t1392.t12 (cl @p_1047 @p_975) :rule implies :premises (t1392.t11))
(step t1392.t13 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t1392.t14 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t1392.t15 (cl @p_312 @p_971) :rule or :premises (t1392.t14))
(step t1392.t16 (cl @p_971) :rule resolution :premises (t1392.t15 a27))
(step t1392.t17 (cl @p_974) :rule trans :premises (t1203 t1392.t13 t1392.t16))
(step t1392.t18 (cl @p_1046) :rule and_intro :premises (t1392.a2 t1278 t1392.t17))
(step t1392.t19 (cl @p_975) :rule resolution :premises (t1392.t12 t1392.t18))
(step t1392 (cl @p_1041 @p_1042 @p_968 @p_975) :rule subproof :discharge (t1392.a0 t1392.a1 t1392.a2))
(step t1393 (cl (! (not @p_1043) :named @p_1044) @p_974) :rule and_pos :args (0))
(step t1394 (cl @p_1044 @p_969) :rule and_pos :args (1))
(step t1395 (cl @p_1044 @p_966) :rule and_pos :args (2))
(step t1396 (cl @p_975 @p_1044 @p_1044 @p_1044) :rule resolution :premises (t1392 t1393 t1394 t1395))
(step t1397 (cl @p_1044 @p_1044 @p_1044 @p_975) :rule reordering :premises (t1396))
(step t1398 (cl @p_1044 @p_975) :rule contraction :premises (t1397))
(step t1399 (cl @p_1045 @p_975) :rule resolution :premises (t1391 t1398))
(step t1400 (cl @p_1045 @p_976) :rule implies_neg2)
(step t1401 (cl @p_1045 @p_1045) :rule resolution :premises (t1399 t1400))
(step t1402 (cl @p_1045) :rule contraction :premises (t1401))
(step t1403 (cl @p_1044 @p_975) :rule implies :premises (t1402))
(step t1404 (cl @p_1041 @p_1042 @p_968 @p_975) :rule resolution :premises (t1390 t1403))
(step t1405 (cl @p_1041 @p_1042 @p_975 @p_968) :rule reordering :premises (t1404))
(step t1406 (cl (! (not (! (= @p_975 (! (= @p_4 @p_65) :named @p_977)) :named @p_978)) :named @p_1040) @p_976 @p_977) :rule equiv_pos2)
(step t1407 (cl @p_977 @p_976 @p_1040) :rule reordering :premises (t1406))
(step t1408 (cl (! (and @p_732 @p_410) :named @p_1031) @p_740 @p_424) :rule and_neg)
(step t1409 (cl (! (=> @p_1031 (! (not @p_977) :named @p_1030)) :named @p_1033) @p_1031) :rule implies_neg1)
(anchor :step t1410)
(assume t1410.a0 @p_732)
(assume t1410.a1 @p_410)
(step t1410.t0 (cl (! (=> (! (and @p_799 @p_410) :named @p_1035) @p_1030) :named @p_1037) @p_1035) :rule implies_neg1)
(anchor :step t1410.t1)
(assume t1410.t1.a0 @p_799)
(assume t1410.t1.a1 @p_410)
(step t1410.t1.t0 (cl (= (! (= @p_977 false) :named @p_1038) @p_1030)) :rule equiv_simplify)
(step t1410.t1.t1 (cl (not @p_1038) @p_1030) :rule equiv1 :premises (t1410.t1.t0))
(step t1410.t1.t2 (cl (= @p_977 @p_793)) :rule cong :premises (t1186))
(step t1410.t1.t3 (cl (= (! (= @p_793 false) :named @p_1039) @p_799)) :rule equiv_simplify)
(step t1410.t1.t4 (cl @p_1039 @p_801) :rule equiv2 :premises (t1410.t1.t3))
(step t1410.t1.t5 (cl (not @p_801) @p_793) :rule not_not)
(step t1410.t1.t6 (cl @p_1039 @p_793) :rule resolution :premises (t1410.t1.t4 t1410.t1.t5))
(step t1410.t1.t7 (cl @p_1039) :rule resolution :premises (t1410.t1.t6 t1410.t1.a0))
(step t1410.t1.t8 (cl @p_1038) :rule trans :premises (t1410.t1.t2 t1410.t1.t7))
(step t1410.t1.t9 (cl @p_1030) :rule resolution :premises (t1410.t1.t1 t1410.t1.t8))
(step t1410.t1 (cl @p_801 @p_424 @p_1030) :rule subproof :discharge (t1410.t1.a0 t1410.t1.a1))
(step t1410.t2 (cl (! (not @p_1035) :named @p_1036) @p_799) :rule and_pos :args (0))
(step t1410.t3 (cl @p_1036 @p_410) :rule and_pos :args (1))
(step t1410.t4 (cl @p_1030 @p_1036 @p_1036) :rule resolution :premises (t1410.t1 t1410.t2 t1410.t3))
(step t1410.t5 (cl @p_1036 @p_1036 @p_1030) :rule reordering :premises (t1410.t4))
(step t1410.t6 (cl @p_1036 @p_1030) :rule contraction :premises (t1410.t5))
(step t1410.t7 (cl @p_1037 @p_1030) :rule resolution :premises (t1410.t0 t1410.t6))
(step t1410.t8 (cl @p_1037 (! (not @p_1030) :named @p_1034)) :rule implies_neg2)
(step t1410.t9 (cl @p_1037 @p_1037) :rule resolution :premises (t1410.t7 t1410.t8))
(step t1410.t10 (cl @p_1037) :rule contraction :premises (t1410.t9))
(step t1410.t11 (cl @p_1036 @p_1030) :rule implies :premises (t1410.t10))
(step t1410.t12 (cl @p_800 @p_732) :rule implies_neg1)
(anchor :step t1410.t13)
(assume t1410.t13.a0 @p_732)
(step t1410.t13.t0 (cl @p_802 @p_793) :rule implies_neg1)
(anchor :step t1410.t13.t1)
(assume t1410.t13.t1.a0 @p_793)
(step t1410.t13.t1.t0 (cl (not @p_806) (not @p_805) false) :rule equiv_pos2)
(step t1410.t13.t1.t1 (cl (= @p_749 @p_814)) :rule poly_simp)
(step t1410.t13.t1.t2 (cl (= @p_804 @p_815)) :rule cong :premises (t1410.t13.t1.t1))
(step t1410.t13.t1.t3 (cl (= @p_815 @p_6)) :rule poly_simp)
(step t1410.t13.t1.t4 (cl (= @p_804 @p_6)) :rule trans :premises (t1410.t13.t1.t2 t1410.t13.t1.t3))
(step t1410.t13.t1.t5 (cl (= @p_803 @p_813)) :rule cong :premises (t1018))
(step t1410.t13.t1.t6 (cl (= @p_813 @p_807)) :rule poly_simp)
(step t1410.t13.t1.t7 (cl (= @p_803 @p_807)) :rule trans :premises (t1410.t13.t1.t5 t1410.t13.t1.t6))
(step t1410.t13.t1.t8 (cl (= @p_805 @p_808)) :rule cong :premises (t1410.t13.t1.t4 t1410.t13.t1.t7))
(step t1410.t13.t1.t9 (cl (= @p_808 @p_809)) :rule rare_rewrite :args ("arith-elim-leq" @p_6 @p_807))
(step t1410.t13.t1.t10 (cl (= @p_809 @p_811)) :rule rare_rewrite :args ("arith-geq-norm1-real" @p_807 @p_6))
(step t1410.t13.t1.t11 (cl (= @p_810 -1/1)) :rule poly_simp)
(step t1410.t13.t1.t12 (cl @p_60) :rule refl)
(step t1410.t13.t1.t13 (cl (= @p_811 @p_812)) :rule cong :premises (t1410.t13.t1.t11 t1410.t13.t1.t12))
(step t1410.t13.t1.t14 (cl (= @p_812 false)) :rule evaluate)
(step t1410.t13.t1.t15 (cl (= @p_811 false)) :rule trans :premises (t1410.t13.t1.t13 t1410.t13.t1.t14))
(step t1410.t13.t1.t16 (cl (= @p_809 false)) :rule trans :premises (t1410.t13.t1.t10 t1410.t13.t1.t15))
(step t1410.t13.t1.t17 (cl (= @p_808 false)) :rule trans :premises (t1410.t13.t1.t9 t1410.t13.t1.t16))
(step t1410.t13.t1.t18 (cl @p_806) :rule trans :premises (t1410.t13.t1.t8 t1410.t13.t1.t17))
(step t1410.t13.t1.t19 (cl @p_799 @p_774 @p_805) :rule la_generic :args (-1/1 1/1 1/1))
(step t1410.t13.t1.t20 (cl (=> @p_759 @p_758)) :rule la_mult_neg)
(step t1410.t13.t1.t21 (cl (not @p_759) @p_758) :rule implies :premises (t1410.t13.t1.t20))
(step t1410.t13.t1.t22 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t1410.t13.t1.t23 (cl (not @p_185) @p_183) :rule equiv1 :premises (t1410.t13.t1.t22))
(step t1410.t13.t1.t24 (cl @p_185) :rule evaluate)
(step t1410.t13.t1.t25 (cl @p_183) :rule resolution :premises (t1410.t13.t1.t23 t1410.t13.t1.t24))
(step t1410.t13.t1.t26 (cl @p_759) :rule and_intro :premises (t1410.t13.t1.t25 t1029))
(step t1410.t13.t1.t27 (cl @p_758) :rule resolution :premises (t1410.t13.t1.t21 t1410.t13.t1.t26))
(step t1410.t13.t1.t28 (cl @p_805) :rule resolution :premises (t1410.t13.t1.t19 t1410.t13.t1.a0 t1410.t13.t1.t27))
(step t1410.t13.t1.t29 (cl false) :rule resolution :premises (t1410.t13.t1.t0 t1410.t13.t1.t18 t1410.t13.t1.t28))
(step t1410.t13.t1 (cl @p_799 false) :rule subproof :discharge (t1410.t13.t1.a0))
(step t1410.t13.t2 (cl @p_802 false) :rule resolution :premises (t1410.t13.t0 t1410.t13.t1))
(step t1410.t13.t3 (cl @p_802 @p_133) :rule implies_neg2)
(step t1410.t13.t4 (cl @p_802 @p_802) :rule resolution :premises (t1410.t13.t2 t1410.t13.t3))
(step t1410.t13.t5 (cl @p_802) :rule contraction :premises (t1410.t13.t4))
(step t1410.t13.t6 (cl (= @p_802 @p_799)) :rule implies_simplify)
(step t1410.t13.t7 (cl (not @p_802) @p_799) :rule equiv1 :premises (t1410.t13.t6))
(step t1410.t13.t8 (cl @p_799) :rule resolution :premises (t1410.t13.t5 t1410.t13.t7))
(step t1410.t13 (cl @p_740 @p_799) :rule subproof :discharge (t1410.t13.a0))
(step t1410.t14 (cl @p_800 @p_799) :rule resolution :premises (t1410.t12 t1410.t13))
(step t1410.t15 (cl @p_800 @p_801) :rule implies_neg2)
(step t1410.t16 (cl @p_800 @p_800) :rule resolution :premises (t1410.t14 t1410.t15))
(step t1410.t17 (cl @p_800) :rule contraction :premises (t1410.t16))
(step t1410.t18 (cl @p_740 @p_799) :rule implies :premises (t1410.t17))
(step t1410.t19 (cl @p_799) :rule resolution :premises (t1410.t18 t1029))
(step t1410.t20 (cl @p_1035) :rule and_intro :premises (t1410.t19 t240))
(step t1410.t21 (cl @p_1030) :rule resolution :premises (t1410.t11 t1410.t20))
(step t1410 (cl @p_740 @p_424 @p_1030) :rule subproof :discharge (t1410.a0 t1410.a1))
(step t1411 (cl (! (not @p_1031) :named @p_1032) @p_732) :rule and_pos :args (0))
(step t1412 (cl @p_1032 @p_410) :rule and_pos :args (1))
(step t1413 (cl @p_1030 @p_1032 @p_1032) :rule resolution :premises (t1410 t1411 t1412))
(step t1414 (cl @p_1032 @p_1032 @p_1030) :rule reordering :premises (t1413))
(step t1415 (cl @p_1032 @p_1030) :rule contraction :premises (t1414))
(step t1416 (cl @p_1033 @p_1030) :rule resolution :premises (t1409 t1415))
(step t1417 (cl @p_1033 @p_1034) :rule implies_neg2)
(step t1418 (cl @p_1033 @p_1033) :rule resolution :premises (t1416 t1417))
(step t1419 (cl @p_1033) :rule contraction :premises (t1418))
(step t1420 (cl @p_1032 @p_1030) :rule implies :premises (t1419))
(step t1421 (cl @p_740 @p_424 @p_1030) :rule resolution :premises (t1408 t1420))
(step t1422 (cl @p_1030) :rule resolution :premises (t1421 t240 t1029))
(step t1423 (cl (! (not (! (or @p_979 @p_978) :named @p_980)) :named @p_1029) @p_979 @p_978) :rule or_pos)
(step t1424 (cl @p_979 @p_978 @p_1029) :rule reordering :premises (t1423))
(step t1425 (cl (or @p_375 @p_980)) :rule forall_inst :args (@p_1 @p_4 @p_4))
(step t1426 (cl @p_375 @p_980) :rule or :premises (t1425))
(step t1427 (cl @p_980) :rule resolution :premises (t1426 t700))
(step t1428 (cl @p_978) :rule resolution :premises (t1424 t1243 t1427))
(step t1429 (cl @p_976) :rule resolution :premises (t1407 t1422 t1428))
(step t1430 (cl (= @p_328 @p_314)) :rule symm :premises (t747))
(step t1431 (cl (or @p_312 @p_971)) :rule forall_inst :args (@p_1 @p_4 @p_1))
(step t1432 (cl @p_312 @p_971) :rule or :premises (t1431))
(step t1433 (cl @p_971) :rule resolution :premises (t1432 a27))
(step t1434 (cl @p_974) :rule trans :premises (t1203 t1430 t1433))
(step t1435 (cl @p_968) :rule resolution :premises (t1405 t1429 t1434 t1278))
(step t1436 (cl (or @p_258 @p_967)) :rule forall_inst :args (@p_1 @p_296))
(step t1437 (cl @p_258 @p_967) :rule or :premises (t1436))
(step t1438 (cl @p_967) :rule resolution :premises (t1437 t674))
(step t1439 (cl @p_965) :rule resolution :premises (t1389 t1435 t1438))
(step t1440 (cl @p_963) :rule resolution :premises (t1387 t1439))
(step t1441 (cl (or @p_883 @p_962)) :rule forall_inst :args (@p_296 @p_1))
(step t1442 (cl @p_883 @p_962) :rule or :premises (t1441))
(step t1443 (cl @p_962) :rule resolution :premises (t1442 t294))
(step t1444 (cl @p_960) :rule resolution :premises (t1386 t1440 t1443))
(step t1445 (cl (not @p_226) (not @p_225) @p_220) :rule equiv_pos2)
(step t1446 (cl (= @p_221 x$)) :rule poly_simp)
(step t1447 (cl (= @p_222 @p_33)) :rule cong :premises (t1446))
(step t1448 (cl (= @p_223 @p_227)) :rule cong :premises (t1447))
(step t1449 (cl (= @p_224 @p_228)) :rule cong :premises (t1448))
(step t1450 (cl (= (* 1/1 (- @p_208 @p_227)) @p_229)) :rule poly_simp)
(step t1451 (cl (= @p_228 @p_210)) :rule poly_simp_rel :premises (t1450))
(step t1452 (cl (= @p_224 @p_210)) :rule trans :premises (t1449 t1451))
(step t1453 (cl @p_226) :rule cong :premises (t1452))
(step t1454 (cl @p_225 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule implies_neg1)
(anchor :step t1455)
(assume t1455.a0 (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1))))))
(step t1455.t0 (cl (or @p_219 @p_224)) :rule forall_inst :args (p$ @p_61))
(step t1455.t1 (cl @p_219 @p_224) :rule or :premises (t1455.t0))
(step t1455.t2 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t1455.t3 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t1455.t3.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t1455.t3.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t1455.t3.t0))
(step t1455.t3.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t1455.t3.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t1455.t3.t1 t1455.t3.t2))
(step t1455.t3.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t1455.t3.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t1455.t3.t4))
(step t1455.t3.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t1455.t3.t3 t1455.t3.t5))
(step t1455.t3 (cl @p_211) :rule bind)
(step t1455.t4 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t1455.t2 t1455.t3 a24))
(step t1455.t5 (cl @p_224) :rule resolution :premises (t1455.t1 t1455.t4))
(step t1455 (cl @p_219 @p_224) :rule subproof :discharge (t1455.a0))
(step t1456 (cl @p_225 @p_224) :rule resolution :premises (t1454 t1455))
(step t1457 (cl @p_225 (not @p_224)) :rule implies_neg2)
(step t1458 (cl @p_225 @p_225) :rule resolution :premises (t1456 t1457))
(step t1459 (cl @p_225) :rule contraction :premises (t1458))
(step t1460 (cl @p_220) :rule resolution :premises (t1445 t1453 t1459))
(step t1461 (cl @p_219 @p_210) :rule implies :premises (t1460))
(step t1462 (cl (not @p_211) (not (forall ((?v0 Int) (?v1 Real)) (= (round_down$ ?v0 (- ?v1)) (- (round_up$ ?v0 ?v1))))) (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule equiv_pos2)
(anchor :step t1463 :args ((?v0 Int) (?v1 Real) (:= (?v0 Int) ?v0) (:= (?v1 Real) ?v1)))
(step t1463.t0 (cl (= @p_28 @p_23)) :rule poly_simp)
(step t1463.t1 (cl (= @p_216 @p_212)) :rule cong :premises (t1463.t0))
(step t1463.t2 (cl (= @p_215 @p_44)) :rule poly_simp)
(step t1463.t3 (cl (= @p_217 @p_218)) :rule cong :premises (t1463.t1 t1463.t2))
(step t1463.t4 (cl (= (* 1/1 (- @p_212 @p_44)) (* 1/1 (- @p_43 @p_213)))) :rule poly_simp)
(step t1463.t5 (cl (= @p_218 @p_214)) :rule poly_simp_rel :premises (t1463.t4))
(step t1463.t6 (cl (= @p_217 @p_214)) :rule trans :premises (t1463.t3 t1463.t5))
(step t1463 (cl @p_211) :rule bind)
(step t1464 (cl (forall ((?v0 Int) (?v1 Real)) (= (round_up$ ?v0 ?v1) (* -1/1 (round_down$ ?v0 (* -1/1 ?v1)))))) :rule resolution :premises (t1462 t1463 a24))
(step t1465 (cl @p_210) :rule resolution :premises (t1461 t1464))
(step t1466 (cl (not @p_243) (not @p_242) @p_239) :rule equiv_pos2)
(step t1467 (cl (= @p_208 @p_208)) :rule refl)
(step t1468 (cl (= @p_240 @p_230)) :rule cong :premises (t1446 t1467))
(step t1469 (cl @p_60) :rule refl)
(step t1470 (cl (= @p_241 @p_231)) :rule cong :premises (t1468 t1469))
(step t1471 (cl @p_243) :rule cong :premises (t1470))
(step t1472 (cl @p_242 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule implies_neg1)
(anchor :step t1473)
(assume t1473.a0 (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1)))
(step t1473.t0 (cl (or @p_238 @p_241)) :rule forall_inst :args (@p_61 p$))
(step t1473.t1 (cl @p_238 @p_241) :rule or :premises (t1473.t0))
(step t1473.t2 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t1473.t3 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t1473.t3.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t1473.t3.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t1473.t3.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t1473.t3.t1))
(step t1473.t3.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t1473.t3.t0 t1473.t3.t2))
(step t1473.t3 (cl @p_232) :rule bind)
(step t1473.t4 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t1473.t2 t1473.t3 a25))
(step t1473.t5 (cl @p_241) :rule resolution :premises (t1473.t1 t1473.t4))
(step t1473 (cl @p_238 @p_241) :rule subproof :discharge (t1473.a0))
(step t1474 (cl @p_242 @p_241) :rule resolution :premises (t1472 t1473))
(step t1475 (cl @p_242 (not @p_241)) :rule implies_neg2)
(step t1476 (cl @p_242 @p_242) :rule resolution :premises (t1474 t1475))
(step t1477 (cl @p_242) :rule contraction :premises (t1476))
(step t1478 (cl @p_239) :rule resolution :premises (t1466 t1471 t1477))
(step t1479 (cl @p_238 @p_231) :rule implies :premises (t1478))
(step t1480 (cl (not @p_232) (not (forall ((?v0 Real) (?v1 Int)) (<= ?v0 (round_up$ ?v1 ?v0)))) (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule equiv_pos2)
(anchor :step t1481 :args ((?v0 Real) (?v1 Int) (:= (?v0 Real) ?v0) (:= (?v1 Int) ?v1)))
(step t1481.t0 (cl (= @p_236 @p_237)) :rule rare_rewrite :args ("arith-elim-leq" ?v0 @p_233))
(step t1481.t1 (cl (= (* -1/1 (- @p_233 ?v0)) (* -1/1 (- @p_234 0/1)))) :rule poly_simp)
(step t1481.t2 (cl (= @p_237 @p_235)) :rule poly_simp_rel :premises (t1481.t1))
(step t1481.t3 (cl (= @p_236 @p_235)) :rule trans :premises (t1481.t0 t1481.t2))
(step t1481 (cl @p_232) :rule bind)
(step t1482 (cl (forall ((?v0 Real) (?v1 Int)) (>= (+ (* -1/1 ?v0) (round_up$ ?v1 ?v0)) 0/1))) :rule resolution :premises (t1480 t1481 a25))
(step t1483 (cl @p_231) :rule resolution :premises (t1479 t1482))
(step t1484 (cl (or @p_312 @p_937)) :rule forall_inst :args (@p_4 1/1 @p_4))
(step t1485 (cl @p_312 @p_937) :rule or :premises (t1484))
(step t1486 (cl @p_937) :rule resolution :premises (t1485 a27))
(step t1487 (cl (or @p_343 @p_1161)) :rule forall_inst :args (@p_247 @p_301 1/1))
(step t1488 (cl @p_343 @p_1161) :rule or :premises (t1487))
(step t1489 (cl @p_1161) :rule resolution :premises (t1488 a2))
(step t1490 (cl (or @p_292 @p_1156)) :rule forall_inst :args (@p_247 @p_139))
(step t1491 (cl @p_292 @p_1156) :rule or :premises (t1490))
(step t1492 (cl @p_1156) :rule resolution :premises (t1491 a6))
(step t1493 (cl (or @p_343 @p_934)) :rule forall_inst :args (@p_4 @p_6 @p_1))
(step t1494 (cl @p_343 @p_934) :rule or :premises (t1493))
(step t1495 (cl @p_934) :rule resolution :premises (t1494 a2))
(step t1496 (cl (or @p_343 @p_930)) :rule forall_inst :args (@p_6 @p_361 2/1))
(step t1497 (cl @p_343 @p_930) :rule or :premises (t1496))
(step t1498 (cl @p_930) :rule resolution :premises (t1497 a2))
(step t1499 (cl (not @p_926) (not @p_925) @p_923) :rule equiv_pos2)
(step t1500 (cl (= @p_922 @p_922)) :rule refl)
(step t1501 (cl (= @p_924 @p_927)) :rule cong :premises (t652 t1500))
(step t1502 (cl (= @p_927 @p_922)) :rule aci_simp)
(step t1503 (cl (= @p_924 @p_922)) :rule trans :premises (t1501 t1502))
(step t1504 (cl @p_926) :rule cong :premises (t1503))
(step t1505 (cl @p_925 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1506)
(assume t1506.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t1506.t0 (cl (or @p_353 @p_924)) :rule forall_inst :args (2/1 @p_4))
(step t1506.t1 (cl @p_353 @p_924) :rule or :premises (t1506.t0))
(step t1506.t2 (cl @p_924) :rule resolution :premises (t1506.t1 t722))
(step t1506 (cl @p_353 @p_924) :rule subproof :discharge (t1506.a0))
(step t1507 (cl @p_925 @p_924) :rule resolution :premises (t1505 t1506))
(step t1508 (cl @p_925 (not @p_924)) :rule implies_neg2)
(step t1509 (cl @p_925 @p_925) :rule resolution :premises (t1507 t1508))
(step t1510 (cl @p_925) :rule contraction :premises (t1509))
(step t1511 (cl @p_923) :rule resolution :premises (t1499 t1504 t1510))
(step t1512 (cl @p_353 @p_922) :rule implies :premises (t1511))
(step t1513 (cl @p_922) :rule resolution :premises (t1512 t722))
(step t1514 (cl (! (not (! (or @p_245 @p_913) :named @p_914)) :named @p_920) @p_245 @p_913) :rule or_pos)
(step t1515 (cl @p_245 @p_913 @p_920) :rule reordering :premises (t1514))
(step t1516 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) (! (or @p_245 @p_916) :named @p_917)) :named @p_918) (! (=> (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))) @p_914) :named @p_915)) :named @p_919)) (not @p_918) @p_915) :rule equiv_pos2)
(step t1517 (cl (= (* -2/1 (- 2/1 @p_912)) (* 2/1 (- @p_912 2/1)))) :rule poly_simp)
(step t1518 (cl (= @p_916 @p_913)) :rule poly_simp_rel :premises (t1517))
(step t1519 (cl (= @p_917 @p_914)) :rule cong :premises (t1518))
(step t1520 (cl @p_919) :rule cong :premises (t1519))
(step t1521 (cl @p_918 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0))))) :rule implies_neg1)
(anchor :step t1522)
(assume t1522.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v0 ?v1) ?v0)))))
(step t1522.t0 (cl (or @p_353 @p_917)) :rule forall_inst :args (@p_4 2/1))
(step t1522.t1 (cl @p_353 @p_917) :rule or :premises (t1522.t0))
(step t1522.t2 (cl @p_917) :rule resolution :premises (t1522.t1 t722))
(step t1522 (cl @p_353 @p_917) :rule subproof :discharge (t1522.a0))
(step t1523 (cl @p_918 @p_917) :rule resolution :premises (t1521 t1522))
(step t1524 (cl @p_918 (not @p_917)) :rule implies_neg2)
(step t1525 (cl @p_918 @p_918) :rule resolution :premises (t1523 t1524))
(step t1526 (cl @p_918) :rule contraction :premises (t1525))
(step t1527 (cl @p_915) :rule resolution :premises (t1516 t1520 t1526))
(step t1528 (cl @p_353 @p_914) :rule implies :premises (t1527))
(step t1529 (cl @p_914) :rule resolution :premises (t1528 t722))
(step t1530 (cl @p_913) :rule resolution :premises (t1515 t287 t1529))
(step t1531 (cl (or @p_273 @p_1155)) :rule forall_inst :args (@p_247 @p_139 @p_1))
(step t1532 (cl @p_273 @p_1155) :rule or :premises (t1531))
(step t1533 (cl @p_1155) :rule resolution :premises (t1532 a4))
(step t1534 (cl (not @p_908) (not @p_907) @p_903) :rule equiv_pos2)
(step t1535 (cl (= @p_905 @p_900)) :rule cong :premises (t600 t1200))
(step t1536 (cl (= @p_904 @p_909)) :rule poly_simp)
(step t1537 (cl (= @p_906 @p_910)) :rule cong :premises (t1535 t1536))
(step t1538 (cl (= (* 1/1 (- @p_900 @p_909)) (* -2/1 @p_911))) :rule poly_simp)
(step t1539 (cl (= @p_910 @p_902)) :rule poly_simp_rel :premises (t1538))
(step t1540 (cl (= @p_906 @p_902)) :rule trans :premises (t1537 t1539))
(step t1541 (cl @p_908) :rule cong :premises (t1540))
(step t1542 (cl @p_907 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t1543)
(assume t1543.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t1543.t0 (cl (or @p_279 @p_906)) :rule forall_inst :args (@p_1 @p_1 @p_1))
(step t1543.t1 (cl @p_279 @p_906) :rule or :premises (t1543.t0))
(step t1543.t2 (cl @p_906) :rule resolution :premises (t1543.t1 t1543.a0))
(step t1543 (cl @p_279 @p_906) :rule subproof :discharge (t1543.a0))
(step t1544 (cl @p_907 @p_906) :rule resolution :premises (t1542 t1543))
(step t1545 (cl @p_907 (not @p_906)) :rule implies_neg2)
(step t1546 (cl @p_907 @p_907) :rule resolution :premises (t1544 t1545))
(step t1547 (cl @p_907) :rule contraction :premises (t1546))
(step t1548 (cl @p_903) :rule resolution :premises (t1534 t1541 t1547))
(step t1549 (cl @p_279 @p_902) :rule implies :premises (t1548))
(step t1550 (cl @p_902) :rule resolution :premises (t1549 a1))
(step t1551 (cl (not @p_898) (not @p_897) @p_894) :rule equiv_pos2)
(step t1552 (cl (= (* 1/1 (- @p_890 @p_895)) @p_899)) :rule poly_simp)
(step t1553 (cl (= @p_896 @p_893)) :rule poly_simp_rel :premises (t1552))
(step t1554 (cl @p_898) :rule cong :premises (t1553))
(step t1555 (cl @p_897 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1))))) :rule implies_neg1)
(anchor :step t1556)
(assume t1556.a0 (forall ((?v0 Real) (?v1 Real)) (= (times$a ?v0 ?v1) (* -1/1 (times$a (* -1/1 ?v0) ?v1)))))
(step t1556.t0 (cl (or @p_326 @p_896)) :rule forall_inst :args (@p_1 @p_1))
(step t1556.t1 (cl @p_326 @p_896) :rule or :premises (t1556.t0))
(step t1556.t2 (cl @p_896) :rule resolution :premises (t1556.t1 t622))
(step t1556 (cl @p_326 @p_896) :rule subproof :discharge (t1556.a0))
(step t1557 (cl @p_897 @p_896) :rule resolution :premises (t1555 t1556))
(step t1558 (cl @p_897 (not @p_896)) :rule implies_neg2)
(step t1559 (cl @p_897 @p_897) :rule resolution :premises (t1557 t1558))
(step t1560 (cl @p_897) :rule contraction :premises (t1559))
(step t1561 (cl @p_894) :rule resolution :premises (t1551 t1554 t1560))
(step t1562 (cl @p_326 @p_893) :rule implies :premises (t1561))
(step t1563 (cl @p_893) :rule resolution :premises (t1562 t622))
(step t1564 (cl (not @p_888) (not @p_887) @p_884) :rule equiv_pos2)
(step t1565 (cl (= (* -1/1 (- 1/1 @p_874)) (* 1/1 (- @p_874 1/1)))) :rule poly_simp)
(step t1566 (cl (= @p_885 @p_875)) :rule poly_simp_rel :premises (t1565))
(step t1567 (cl (= @p_886 @p_889)) :rule cong :premises (t652 t1566))
(step t1568 (cl (= @p_889 @p_875)) :rule aci_simp)
(step t1569 (cl (= @p_886 @p_875)) :rule trans :premises (t1567 t1568))
(step t1570 (cl @p_888) :rule cong :premises (t1569))
(step t1571 (cl @p_887 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0))))) :rule implies_neg1)
(anchor :step t1572)
(assume t1572.a0 (forall ((?v0 Real) (?v1 Real)) (or (= ?v0 0/1) (= ?v1 (divide$ (times$a ?v1 ?v0) ?v0)))))
(step t1572.t0 (cl (or @p_883 @p_886)) :rule forall_inst :args (2/1 1/1))
(step t1572.t1 (cl @p_883 @p_886) :rule or :premises (t1572.t0))
(step t1572.t2 (cl @p_886) :rule resolution :premises (t1572.t1 t294))
(step t1572 (cl @p_883 @p_886) :rule subproof :discharge (t1572.a0))
(step t1573 (cl @p_887 @p_886) :rule resolution :premises (t1571 t1572))
(step t1574 (cl @p_887 (not @p_886)) :rule implies_neg2)
(step t1575 (cl @p_887 @p_887) :rule resolution :premises (t1573 t1574))
(step t1576 (cl @p_887) :rule contraction :premises (t1575))
(step t1577 (cl @p_884) :rule resolution :premises (t1564 t1570 t1576))
(step t1578 (cl @p_883 @p_875) :rule implies :premises (t1577))
(step t1579 (cl @p_875) :rule resolution :premises (t1578 t294))
(step t1580 (cl (or @p_343 @p_873)) :rule forall_inst :args (@p_306 @p_270 @p_4))
(step t1581 (cl @p_343 @p_873) :rule or :premises (t1580))
(step t1582 (cl @p_873) :rule resolution :premises (t1581 a2))
(step t1583 (cl (or @p_343 @p_868)) :rule forall_inst :args (@p_4 @p_304 2/1))
(step t1584 (cl @p_343 @p_868) :rule or :premises (t1583))
(step t1585 (cl @p_868) :rule resolution :premises (t1584 a2))
(step t1586 (cl (or @p_343 @p_1152)) :rule forall_inst :args (@p_139 @p_248 @p_247))
(step t1587 (cl @p_343 @p_1152) :rule or :premises (t1586))
(step t1588 (cl @p_1152) :rule resolution :premises (t1587 a2))
(step t1589 (cl (or @p_312 @p_1148)) :rule forall_inst :args (@p_139 @p_247 @p_1143))
(step t1590 (cl @p_312 @p_1148) :rule or :premises (t1589))
(step t1591 (cl @p_1148) :rule resolution :premises (t1590 a27))
(step t1592 (cl (or @p_312 @p_864)) :rule forall_inst :args (@p_247 @p_314 @p_296))
(step t1593 (cl @p_312 @p_864) :rule or :premises (t1592))
(step t1594 (cl @p_864) :rule resolution :premises (t1593 a27))
(step t1595 (cl (or @p_273 @p_1142)) :rule forall_inst :args (@p_139 @p_1 @p_247))
(step t1596 (cl @p_273 @p_1142) :rule or :premises (t1595))
(step t1597 (cl @p_1142) :rule resolution :premises (t1596 a4))
(step t1598 (cl (or @p_292 @p_1140)) :rule forall_inst :args (@p_1 @p_247))
(step t1599 (cl @p_292 @p_1140) :rule or :premises (t1598))
(step t1600 (cl @p_1140) :rule resolution :premises (t1599 a6))
(step t1601 (cl (or @p_292 @p_1138)) :rule forall_inst :args (@p_247 @p_892))
(step t1602 (cl @p_292 @p_1138) :rule or :premises (t1601))
(step t1603 (cl @p_1138) :rule resolution :premises (t1602 a6))
(step t1604 (cl @p_1135) :rule resolution :premises (t497 t231 t237 t240 t296 t302 t319 t500 t503 t876 t900 t1259 t1262 t629 t1265 t1278 t1291 t632 t650 t675 t701 t723 t726 t1304 t1326 t729 t1329 t1332 t1345 t1364 t1381 t1384 t1444 t1465 t1483 t1486 t753 t1489 t756 t1492 t1495 t1498 t1513 t1530 t765 t1533 t768 t1550 t1563 t1579 t1582 t1585 t1588 t1591 t1594 t1597 t1600 t1603))
(step t1605 (cl (! (not (! (or @p_245 @p_1125) :named @p_1126)) :named @p_1134) @p_245 @p_1125) :rule or_pos)
(step t1606 (cl @p_245 @p_1125 @p_1134) :rule reordering :premises (t1605))
(step t1607 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) (! (or @p_245 (! (= @p_1124 @p_1128) :named @p_1129)) :named @p_1130)) :named @p_1131) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))) @p_1126) :named @p_1127)) :named @p_1132)) (not @p_1131) @p_1127) :rule equiv_pos2)
(step t1608 (cl (= (* -1/1 @p_1133) (* 1/1 (- @p_6 1/1)))) :rule poly_simp)
(step t1609 (cl (= @p_1128 @p_1122)) :rule poly_simp_rel :premises (t1608))
(step t1610 (cl (= @p_1129 @p_1125)) :rule cong :premises (t1609))
(step t1611 (cl (= @p_1130 @p_1126)) :rule cong :premises (t1610))
(step t1612 (cl @p_1132) :rule cong :premises (t1611))
(step t1613 (cl @p_1131 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0)))))) :rule implies_neg1)
(anchor :step t1614)
(assume t1614.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (= ?v0 0/1) (= (= ?v1 (divide$ ?v2 ?v0)) (= ?v2 (times$a ?v1 ?v0))))))
(step t1614.t0 (cl (or @p_375 @p_1130)) :rule forall_inst :args (@p_4 @p_1 1/1))
(step t1614.t1 (cl @p_375 @p_1130) :rule or :premises (t1614.t0))
(step t1614.t2 (cl @p_1130) :rule resolution :premises (t1614.t1 t700))
(step t1614 (cl @p_375 @p_1130) :rule subproof :discharge (t1614.a0))
(step t1615 (cl @p_1131 @p_1130) :rule resolution :premises (t1613 t1614))
(step t1616 (cl @p_1131 (not @p_1130)) :rule implies_neg2)
(step t1617 (cl @p_1131 @p_1131) :rule resolution :premises (t1615 t1616))
(step t1618 (cl @p_1131) :rule contraction :premises (t1617))
(step t1619 (cl @p_1127) :rule resolution :premises (t1607 t1612 t1618))
(step t1620 (cl @p_375 @p_1126) :rule implies :premises (t1619))
(step t1621 (cl @p_1126) :rule resolution :premises (t1620 t700))
(step t1622 (cl @p_1125) :rule resolution :premises (t1606 t287 t1621))
(step t1623 (cl @p_1123) :rule resolution :premises (t321 t1604 t1622))
(step t1624 (cl (not @p_1096) (not @p_1095) @p_1090) :rule equiv_pos2)
(step t1625 (cl (= @p_1092 @p_679)) :rule poly_simp)
(step t1626 (cl (= @p_1093 @p_681)) :rule cong :premises (t1625 t1200))
(step t1627 (cl (= @p_1091 @p_1091)) :rule refl)
(step t1628 (cl (= @p_1094 @p_1097)) :rule cong :premises (t1626 t1627))
(step t1629 (cl (= (* 1/1 (- @p_681 @p_1091)) (* -1/1 (- @p_65 @p_1088)))) :rule poly_simp)
(step t1630 (cl (= @p_1097 @p_1089)) :rule poly_simp_rel :premises (t1629))
(step t1631 (cl (= @p_1094 @p_1089)) :rule trans :premises (t1628 t1630))
(step t1632 (cl @p_1096) :rule cong :premises (t1631))
(step t1633 (cl @p_1095 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2))))) :rule implies_neg1)
(anchor :step t1634)
(assume t1634.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (= (times$a (+ ?v0 ?v1) ?v2) (+ (times$a ?v0 ?v2) (times$a ?v1 ?v2)))))
(step t1634.t0 (cl (or @p_279 @p_1094)) :rule forall_inst :args (@p_4 @p_139 @p_1))
(step t1634.t1 (cl @p_279 @p_1094) :rule or :premises (t1634.t0))
(step t1634.t2 (cl @p_1094) :rule resolution :premises (t1634.t1 t1634.a0))
(step t1634 (cl @p_279 @p_1094) :rule subproof :discharge (t1634.a0))
(step t1635 (cl @p_1095 @p_1094) :rule resolution :premises (t1633 t1634))
(step t1636 (cl @p_1095 (not @p_1094)) :rule implies_neg2)
(step t1637 (cl @p_1095 @p_1095) :rule resolution :premises (t1635 t1636))
(step t1638 (cl @p_1095) :rule contraction :premises (t1637))
(step t1639 (cl @p_1090) :rule resolution :premises (t1624 t1632 t1638))
(step t1640 (cl @p_279 @p_1089) :rule implies :premises (t1639))
(step t1641 (cl @p_1089) :rule resolution :premises (t1640 a1))
(step t1642 (cl (not (! (= (! (or @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_938) :named @p_940) (! (or @p_480 @p_483 @p_702 @p_425 @p_481 @p_740 @p_938) :named @p_939)) :named @p_959)) (not @p_940) @p_939) :rule equiv_pos2)
(step t1643 (cl (= @p_938 @p_938)) :rule refl)
(step t1644 (cl @p_959) :rule cong :premises (t967 t968 t969 t970 t1643))
(step t1645 (cl (not (! (= (! (or @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_942) :named @p_943) @p_940) :named @p_958)) (not @p_943) @p_940) :rule equiv_pos2)
(step t1646 (cl (= @p_942 @p_938)) :rule rare_rewrite :args ("bool-double-not-elim" @p_938))
(step t1647 (cl (= @p_943 @p_939)) :rule cong :premises (t967 t968 t969 t970 t1646))
(step t1648 (cl (= @p_939 @p_940)) :rule symm :premises (t1644))
(step t1649 (cl @p_958) :rule trans :premises (t1647 t1648))
(step t1650 (cl (! (=> (! (and @p_476 @p_473 @p_474 @p_409 @p_475 @p_732 @p_941) :named @p_944) false) :named @p_946) @p_944) :rule implies_neg1)
(anchor :step t1651)
(assume t1651.a0 @p_476)
(assume t1651.a1 @p_473)
(assume t1651.a2 @p_474)
(assume t1651.a3 @p_409)
(assume t1651.a4 @p_475)
(assume t1651.a5 @p_732)
(assume t1651.a6 @p_941)
(step t1651.t0 (cl (not (! (= (! (< (! (+ @p_6 @p_498 @p_506 @p_504 @p_502 @p_500 @p_749) :named @p_948) (! (+ 1/1 @p_175 0/1 @p_492 @p_491 @p_490 @p_737) :named @p_947)) :named @p_949) false) :named @p_952)) (not @p_949) false) :rule equiv_pos2)
(step t1651.t1 (cl (= @p_949 (! (not (! (>= @p_948 @p_947) :named @p_953)) :named @p_954))) :rule rare_rewrite :args ("arith-elim-lt" @p_948 @p_947))
(step t1651.t2 (cl (= @p_948 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 @p_561 @p_6 @p_638 @p_559) :named @p_956))) :rule poly_simp)
(step t1651.t3 (cl (= @p_561 0/1)) :rule poly_simp)
(step t1651.t4 (cl (= @p_6 @p_6)) :rule refl)
(step t1651.t5 (cl (= @p_638 @p_638)) :rule refl)
(step t1651.t6 (cl (= @p_559 0/1)) :rule poly_simp)
(step t1651.t7 (cl (= @p_956 (! (+ @p_275 @p_496 @p_505 @p_298 @p_313 @p_328 0/1 @p_6 @p_638 0/1) :named @p_957))) :rule cong :premises (t1651.t3 t1651.t4 t1651.t5 t1651.t6))
(step t1651.t8 (cl (= @p_957 0/1)) :rule poly_simp)
(step t1651.t9 (cl (= @p_956 0/1)) :rule trans :premises (t1651.t7 t1651.t8))
(step t1651.t10 (cl (= @p_948 0/1)) :rule trans :premises (t1651.t2 t1651.t9))
(step t1651.t11 (cl (= @p_175 0/1)) :rule evaluate)
(step t1651.t12 (cl @p_60) :rule refl)
(step t1651.t13 (cl (= @p_492 0/1)) :rule evaluate)
(step t1651.t14 (cl (= @p_491 0/1)) :rule evaluate)
(step t1651.t15 (cl (= @p_490 0/1)) :rule evaluate)
(step t1651.t16 (cl (= @p_947 (! (+ 1/1 0/1 0/1 0/1 0/1 0/1 -1/1) :named @p_955))) :rule cong :premises (t1651.t11 t1651.t12 t1651.t13 t1651.t14 t1651.t15 t1018))
(step t1651.t17 (cl (= @p_955 0/1)) :rule evaluate)
(step t1651.t18 (cl (= @p_947 0/1)) :rule trans :premises (t1651.t16 t1651.t17))
(step t1651.t19 (cl (= @p_953 @p_190)) :rule cong :premises (t1651.t10 t1651.t18))
(step t1651.t20 (cl @p_191) :rule evaluate)
(step t1651.t21 (cl (= @p_953 true)) :rule trans :premises (t1651.t19 t1651.t20))
(step t1651.t22 (cl (= @p_954 @p_189)) :rule cong :premises (t1651.t21))
(step t1651.t23 (cl (= @p_189 false)) :rule evaluate)
(step t1651.t24 (cl (= @p_954 false)) :rule trans :premises (t1651.t22 t1651.t23))
(step t1651.t25 (cl @p_952) :rule trans :premises (t1651.t1 t1651.t24))
(step t1651.t26 (cl (not (! (< @p_6 1/1) :named @p_950)) @p_554 @p_550 @p_551 @p_552 @p_553 @p_774 @p_949) :rule la_generic :args (1/1 -1/1 -1/1 -1/1 -1/1 -1/1 1/1 1/1))
(step t1651.t27 (cl (not (! (= @p_941 @p_950) :named @p_951)) @p_942 @p_950) :rule equiv_pos2)
(step t1651.t28 (cl (= @p_950 @p_941)) :rule rare_rewrite :args ("arith-elim-lt" @p_6 1/1))
(step t1651.t29 (cl @p_951) :rule symm :premises (t1651.t28))
(step t1651.t30 (cl @p_950) :rule resolution :premises (t1651.t27 t1651.t29 t1651.a6))
(step t1651.t31 (cl @p_521) :rule la_mult_neg)
(step t1651.t32 (cl @p_520 @p_516) :rule implies :premises (t1651.t31))
(step t1651.t33 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t1651.t34 (cl (not @p_185) @p_183) :rule equiv1 :premises (t1651.t33))
(step t1651.t35 (cl @p_185) :rule evaluate)
(step t1651.t36 (cl @p_183) :rule resolution :premises (t1651.t34 t1651.t35))
(step t1651.t37 (cl (not @p_519) @p_480 @p_517) :rule equiv_pos2)
(step t1651.t38 (cl (= (* -1/1 (- @p_497 0/1)) (* -1/1 (- @p_298 @p_275)))) :rule poly_simp)
(step t1651.t39 (cl (= @p_517 @p_476)) :rule poly_simp_rel :premises (t1651.t38))
(step t1651.t40 (cl @p_519) :rule symm :premises (t1651.t39))
(step t1651.t41 (cl @p_517) :rule resolution :premises (t1651.t37 t1651.t40 t1219))
(step t1651.t42 (cl @p_518) :rule and_intro :premises (t1651.t36 t1651.t41))
(step t1651.t43 (cl @p_516) :rule resolution :premises (t1651.t32 t1651.t42))
(step t1651.t44 (cl @p_547 @p_483 @p_545) :rule equiv_pos2)
(step t1651.t45 (cl (= (* 1/1 (- @p_506 0/1)) (* 1/1 (- @p_4 @p_328)))) :rule poly_simp)
(step t1651.t46 (cl (= @p_545 @p_473)) :rule poly_simp_rel :premises (t1651.t45))
(step t1651.t47 (cl @p_546) :rule symm :premises (t1651.t46))
(step t1651.t48 (cl @p_545) :rule resolution :premises (t1651.t44 t1651.t47 t1203))
(step t1651.t49 (cl @p_544) :rule la_mult_pos)
(step t1651.t50 (cl @p_543 @p_534) :rule implies :premises (t1651.t49))
(step t1651.t51 (cl (= @p_542 @p_536)) :rule equiv_simplify)
(step t1651.t52 (cl (not @p_542) @p_536) :rule equiv1 :premises (t1651.t51))
(step t1651.t53 (cl @p_542) :rule evaluate)
(step t1651.t54 (cl @p_536) :rule resolution :premises (t1651.t52 t1651.t53))
(step t1651.t55 (cl (not @p_538) @p_482 @p_535) :rule equiv_pos2)
(step t1651.t56 (cl (= (* 2/1 (- @p_503 0/1)) (* 2/1 @p_541))) :rule poly_simp)
(step t1651.t57 (cl (= @p_535 @p_540)) :rule poly_simp_rel :premises (t1651.t56))
(step t1651.t58 (cl (= @p_540 @p_535)) :rule symm :premises (t1651.t57))
(step t1651.t59 (cl @p_538) :rule trans :premises (t966 t1651.t58))
(step t1651.t60 (cl @p_474) :rule trans :premises (t1430 t750))
(step t1651.t61 (cl @p_535) :rule resolution :premises (t1651.t55 t1651.t59 t1651.t60))
(step t1651.t62 (cl @p_537) :rule and_intro :premises (t1651.t54 t1651.t61))
(step t1651.t63 (cl @p_534) :rule resolution :premises (t1651.t50 t1651.t62))
(step t1651.t64 (cl (=> @p_531 @p_528)) :rule la_mult_neg)
(step t1651.t65 (cl (not @p_531) @p_528) :rule implies :premises (t1651.t64))
(step t1651.t66 (cl (= @p_533 @p_530)) :rule equiv_simplify)
(step t1651.t67 (cl (not @p_533) @p_530) :rule equiv1 :premises (t1651.t66))
(step t1651.t68 (cl @p_533) :rule evaluate)
(step t1651.t69 (cl @p_530) :rule resolution :premises (t1651.t67 t1651.t68))
(step t1651.t70 (cl (not @p_532) @p_425 @p_529) :rule equiv_pos2)
(step t1651.t71 (cl (= (* 1/1 (- @p_501 0/1)) (* 1/1 (- @p_6 @p_408)))) :rule poly_simp)
(step t1651.t72 (cl (= @p_529 @p_409)) :rule poly_simp_rel :premises (t1651.t71))
(step t1651.t73 (cl @p_532) :rule symm :premises (t1651.t72))
(step t1651.t74 (cl @p_529) :rule resolution :premises (t1651.t70 t1651.t73 t623))
(step t1651.t75 (cl @p_531) :rule and_intro :premises (t1651.t69 t1651.t74))
(step t1651.t76 (cl @p_528) :rule resolution :premises (t1651.t65 t1651.t75))
(step t1651.t77 (cl @p_527) :rule la_mult_pos)
(step t1651.t78 (cl @p_526 @p_522) :rule implies :premises (t1651.t77))
(step t1651.t79 (cl (= @p_515 @p_512)) :rule equiv_simplify)
(step t1651.t80 (cl (not @p_515) @p_512) :rule equiv1 :premises (t1651.t79))
(step t1651.t81 (cl @p_515) :rule evaluate)
(step t1651.t82 (cl @p_512) :rule resolution :premises (t1651.t80 t1651.t81))
(step t1651.t83 (cl (not @p_525) @p_481 @p_523) :rule equiv_pos2)
(step t1651.t84 (cl (= (* 1/1 (- @p_499 0/1)) (* 1/1 (- @p_274 @p_276)))) :rule poly_simp)
(step t1651.t85 (cl (= @p_523 @p_475)) :rule poly_simp_rel :premises (t1651.t84))
(step t1651.t86 (cl @p_525) :rule symm :premises (t1651.t85))
(step t1651.t87 (cl @p_523) :rule resolution :premises (t1651.t83 t1651.t86 t1210))
(step t1651.t88 (cl @p_524) :rule and_intro :premises (t1651.t82 t1651.t87))
(step t1651.t89 (cl @p_522) :rule resolution :premises (t1651.t78 t1651.t88))
(step t1651.t90 (cl (=> @p_759 @p_758)) :rule la_mult_neg)
(step t1651.t91 (cl (not @p_759) @p_758) :rule implies :premises (t1651.t90))
(step t1651.t92 (cl @p_759) :rule and_intro :premises (t1651.t36 t1029))
(step t1651.t93 (cl @p_758) :rule resolution :premises (t1651.t91 t1651.t92))
(step t1651.t94 (cl @p_949) :rule resolution :premises (t1651.t26 t1651.t30 t1651.t43 t1651.t48 t1651.t63 t1651.t76 t1651.t89 t1651.t93))
(step t1651.t95 (cl false) :rule resolution :premises (t1651.t0 t1651.t25 t1651.t94))
(step t1651 (cl @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_942 false) :rule subproof :discharge (t1651.a0 t1651.a1 t1651.a2 t1651.a3 t1651.a4 t1651.a5 t1651.a6))
(step t1652 (cl (! (not @p_944) :named @p_945) @p_476) :rule and_pos :args (0))
(step t1653 (cl @p_945 @p_473) :rule and_pos :args (1))
(step t1654 (cl @p_945 @p_474) :rule and_pos :args (2))
(step t1655 (cl @p_945 @p_409) :rule and_pos :args (3))
(step t1656 (cl @p_945 @p_475) :rule and_pos :args (4))
(step t1657 (cl @p_945 @p_732) :rule and_pos :args (5))
(step t1658 (cl @p_945 @p_941) :rule and_pos :args (6))
(step t1659 (cl false @p_945 @p_945 @p_945 @p_945 @p_945 @p_945 @p_945) :rule resolution :premises (t1651 t1652 t1653 t1654 t1655 t1656 t1657 t1658))
(step t1660 (cl @p_945 @p_945 @p_945 @p_945 @p_945 @p_945 @p_945 false) :rule reordering :premises (t1659))
(step t1661 (cl @p_945 false) :rule contraction :premises (t1660))
(step t1662 (cl @p_946 false) :rule resolution :premises (t1650 t1661))
(step t1663 (cl @p_946 @p_133) :rule implies_neg2)
(step t1664 (cl @p_946 @p_946) :rule resolution :premises (t1662 t1663))
(step t1665 (cl @p_946) :rule contraction :premises (t1664))
(step t1666 (cl (= @p_946 @p_945)) :rule implies_simplify)
(step t1667 (cl (not @p_946) @p_945) :rule equiv1 :premises (t1666))
(step t1668 (cl @p_945) :rule resolution :premises (t1665 t1667))
(step t1669 (cl @p_480 @p_483 @p_482 @p_425 @p_481 @p_740 @p_942) :rule not_and :premises (t1668))
(step t1670 (cl @p_943 @p_827) :rule or_neg :args (0))
(step t1671 (cl @p_943 @p_826) :rule or_neg :args (1))
(step t1672 (cl @p_943 @p_825) :rule or_neg :args (2))
(step t1673 (cl @p_943 @p_468) :rule or_neg :args (3))
(step t1674 (cl @p_943 @p_824) :rule or_neg :args (4))
(step t1675 (cl @p_943 @p_744) :rule or_neg :args (5))
(step t1676 (cl @p_943 (not @p_942)) :rule or_neg :args (6))
(step t1677 (cl @p_943 @p_943 @p_943 @p_943 @p_943 @p_943 @p_943) :rule resolution :premises (t1669 t1670 t1671 t1672 t1673 t1674 t1675 t1676))
(step t1678 (cl @p_943) :rule contraction :premises (t1677))
(step t1679 (cl @p_940) :rule resolution :premises (t1645 t1649 t1678))
(step t1680 (cl @p_939) :rule resolution :premises (t1642 t1644 t1679))
(step t1681 (cl @p_480 @p_483 @p_702 @p_425 @p_481 @p_740 @p_938) :rule or :premises (t1680))
(step t1682 (cl @p_740 @p_425 @p_702 @p_483 @p_938 @p_481 @p_480) :rule reordering :premises (t1681))
(step t1683 (cl @p_938) :rule resolution :premises (t1682 t1029 t623 t1184 t1203 t1210 t1219))
(step t1684 (cl @p_685) :rule resolution :premises (t224 t231 t237 t240 t296 t302 t319 t1623 t876 t900 t629 t1278 t1291 t632 t650 t675 t701 t723 t726 t1326 t729 t1329 t1641 t1345 t1364 t1381 t1384 t1444 t1465 t1483 t1683 t1486 t753 t756 t1495 t1498 t1513 t1530 t765 t768 t1550 t1563 t1579 t1582 t1585 t1594))
(step t1685 (cl (! (not (! (or @p_688 @p_686) :named @p_689)) :named @p_859) @p_688 @p_686) :rule or_pos)
(step t1686 (cl @p_688 @p_686 @p_859) :rule reordering :premises (t1685))
(step t1687 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (! (or (! (>= (! (* -1/1 @p_679) :named @p_695) 0/1) :named @p_696) (! (= @p_685 (! (not (! (>= (! (+ @p_18 @p_139) :named @p_691) 0/1) :named @p_692)) :named @p_693)) :named @p_694)) :named @p_697)) :named @p_698) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) @p_689) :named @p_690)) :named @p_699)) (not @p_698) @p_690) :rule equiv_pos2)
(step t1688 (cl (= @p_695 @p_687)) :rule poly_simp)
(step t1689 (cl @p_60) :rule refl)
(step t1690 (cl (= @p_696 @p_688)) :rule cong :premises (t1688 t1689))
(step t1691 (cl (= @p_691 @p_676)) :rule poly_simp)
(step t1692 (cl @p_60) :rule refl)
(step t1693 (cl (= @p_692 @p_677)) :rule cong :premises (t1691 t1692))
(step t1694 (cl (= @p_693 @p_678)) :rule cong :premises (t1693))
(step t1695 (cl (= @p_694 @p_686)) :rule cong :premises (t1694))
(step t1696 (cl (= @p_697 @p_689)) :rule cong :premises (t1690 t1695))
(step t1697 (cl @p_699) :rule cong :premises (t1696))
(step t1698 (cl @p_698 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1699)
(assume t1699.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1699.t0 (cl (or @p_102 @p_697)) :rule forall_inst :args (@p_679 @p_18 @p_1))
(step t1699.t1 (cl @p_102 @p_697) :rule or :premises (t1699.t0))
(step t1699.t2 (cl @p_697) :rule resolution :premises (t1699.t1 t1141))
(step t1699 (cl @p_102 @p_697) :rule subproof :discharge (t1699.a0))
(step t1700 (cl @p_698 @p_697) :rule resolution :premises (t1698 t1699))
(step t1701 (cl @p_698 (not @p_697)) :rule implies_neg2)
(step t1702 (cl @p_698 @p_698) :rule resolution :premises (t1700 t1701))
(step t1703 (cl @p_698) :rule contraction :premises (t1702))
(step t1704 (cl @p_690) :rule resolution :premises (t1687 t1697 t1703))
(step t1705 (cl @p_102 @p_689) :rule implies :premises (t1704))
(step t1706 (cl @p_689) :rule resolution :premises (t1705 t1141))
(step t1707 (cl @p_686) :rule resolution :premises (t1686 t1220 t1706))
(step t1708 (cl @p_678) :rule resolution :premises (t68 t1684 t1707))
(step t1709 (cl (not (! (= (! (or (! (not (! (= (! (not (! (>= (! (+ (* -1/1 (! (times$a @p_4 x$) :named @p_66)) @p_65) :named @p_67) 0/1) :named @p_68)) :named @p_69) @p_64) :named @p_70)) :named @p_203) @p_69 @p_205) :named @p_206) (! (or @p_203 @p_69 @p_63) :named @p_204)) :named @p_207)) (not @p_206) @p_204) :rule equiv_pos2)
(step t1710 (cl (= @p_205 @p_63)) :rule rare_rewrite :args ("bool-double-not-elim" @p_63))
(step t1711 (cl @p_207) :rule cong :premises (t1710))
(step t1712 (cl @p_203 @p_69 @p_205) :rule equiv_pos1)
(step t1713 (cl @p_206 (not @p_203)) :rule or_neg :args (0))
(step t1714 (cl @p_206 (! (not @p_69) :named @p_199)) :rule or_neg :args (1))
(step t1715 (cl @p_206 (not @p_205)) :rule or_neg :args (2))
(step t1716 (cl @p_206 @p_206 @p_206) :rule resolution :premises (t1712 t1713 t1714 t1715))
(step t1717 (cl @p_206) :rule contraction :premises (t1716))
(step t1718 (cl @p_204) :rule resolution :premises (t1709 t1711 t1717))
(step t1719 (cl @p_203 @p_69 @p_63) :rule or :premises (t1718))
(step t1720 (cl @p_69 @p_63 @p_203) :rule reordering :premises (t1719))
(step t1721 (cl (not (! (= (! (or (! (not (! (not (! (>= (! (+ @p_66 @p_135) :named @p_136) 0/1) :named @p_137)) :named @p_138)) :named @p_165) @p_68) :named @p_169) (! (or @p_137 @p_68) :named @p_168)) :named @p_202)) (not @p_169) @p_168) :rule equiv_pos2)
(step t1722 (cl (= @p_165 @p_137)) :rule rare_rewrite :args ("bool-double-not-elim" @p_137))
(step t1723 (cl (= @p_68 @p_68)) :rule refl)
(step t1724 (cl @p_202) :rule cong :premises (t1722 t1723))
(step t1725 (cl (! (=> @p_138 @p_68) :named @p_170) @p_138) :rule implies_neg1)
(anchor :step t1726)
(assume t1726.a0 @p_138)
(step t1726.t0 (cl @p_170 @p_138) :rule implies_neg1)
(anchor :step t1726.t1)
(assume t1726.t1.a0 @p_138)
(step t1726.t1.t0 (cl (not (! (= (! (<= @p_136 0/1) :named @p_171) @p_68) :named @p_197)) (! (not @p_171) :named @p_200) @p_68) :rule equiv_pos2)
(step t1726.t1.t1 (cl (= @p_171 (! (>= 0/1 @p_136) :named @p_198))) :rule rare_rewrite :args ("arith-elim-leq" @p_136 0/1))
(step t1726.t1.t2 (cl (= (* -1/1 (- 0/1 @p_136)) (* -1/1 (- @p_67 0/1)))) :rule poly_simp)
(step t1726.t1.t3 (cl (= @p_198 @p_68)) :rule poly_simp_rel :premises (t1726.t1.t2))
(step t1726.t1.t4 (cl @p_197) :rule trans :premises (t1726.t1.t1 t1726.t1.t3))
(step t1726.t1.t5 (cl (not (! (= (! (not (! (> @p_136 0/1) :named @p_172)) :named @p_173) @p_171) :named @p_196)) (not @p_173) @p_171) :rule equiv_pos2)
(step t1726.t1.t6 (cl (= @p_172 (! (not @p_198) :named @p_201))) :rule rare_rewrite :args ("arith-elim-gt" @p_136 0/1))
(step t1726.t1.t7 (cl (= @p_198 @p_171)) :rule symm :premises (t1726.t1.t1))
(step t1726.t1.t8 (cl (= @p_201 @p_200)) :rule cong :premises (t1726.t1.t7))
(step t1726.t1.t9 (cl (= @p_172 @p_200)) :rule trans :premises (t1726.t1.t6 t1726.t1.t8))
(step t1726.t1.t10 (cl (= @p_200 @p_69)) :rule cong :premises (t1726.t1.t4))
(step t1726.t1.t11 (cl (= @p_172 @p_69)) :rule trans :premises (t1726.t1.t9 t1726.t1.t10))
(step t1726.t1.t12 (cl (= @p_173 @p_199)) :rule cong :premises (t1726.t1.t11))
(step t1726.t1.t13 (cl (= @p_199 @p_68)) :rule rare_rewrite :args ("bool-double-not-elim" @p_68))
(step t1726.t1.t14 (cl (= @p_173 @p_68)) :rule trans :premises (t1726.t1.t12 t1726.t1.t13))
(step t1726.t1.t15 (cl (= @p_68 @p_171)) :rule symm :premises (t1726.t1.t4))
(step t1726.t1.t16 (cl @p_196) :rule trans :premises (t1726.t1.t14 t1726.t1.t15))
(step t1726.t1.t17 (cl (! (=> @p_172 false) :named @p_174) @p_172) :rule implies_neg1)
(anchor :step t1726.t1.t18)
(assume t1726.t1.t18.a0 @p_172)
(step t1726.t1.t18.t0 (cl (not (! (= (! (< (! (+ (! (* -1/1 @p_136) :named @p_177) @p_136) :named @p_178) (! (+ @p_175 0/1) :named @p_176)) :named @p_179) false) :named @p_186)) (not @p_179) false) :rule equiv_pos2)
(step t1726.t1.t18.t1 (cl (= @p_179 (! (not (! (>= @p_178 @p_176) :named @p_187)) :named @p_188))) :rule rare_rewrite :args ("arith-elim-lt" @p_178 @p_176))
(step t1726.t1.t18.t2 (cl (= @p_178 (! (+ (! (* 0/1 @p_65) :named @p_194) (! (* 0/1 @p_66) :named @p_193)) :named @p_195))) :rule poly_simp)
(step t1726.t1.t18.t3 (cl (= @p_194 0/1)) :rule poly_simp)
(step t1726.t1.t18.t4 (cl (= @p_193 0/1)) :rule poly_simp)
(step t1726.t1.t18.t5 (cl (= @p_195 (! (+ 0/1 0/1) :named @p_192))) :rule cong :premises (t1726.t1.t18.t3 t1726.t1.t18.t4))
(step t1726.t1.t18.t6 (cl (= @p_192 0/1)) :rule evaluate)
(step t1726.t1.t18.t7 (cl (= @p_195 0/1)) :rule trans :premises (t1726.t1.t18.t5 t1726.t1.t18.t6))
(step t1726.t1.t18.t8 (cl (= @p_178 0/1)) :rule trans :premises (t1726.t1.t18.t2 t1726.t1.t18.t7))
(step t1726.t1.t18.t9 (cl (= @p_175 0/1)) :rule evaluate)
(step t1726.t1.t18.t10 (cl @p_60) :rule refl)
(step t1726.t1.t18.t11 (cl (= @p_176 @p_192)) :rule cong :premises (t1726.t1.t18.t9 t1726.t1.t18.t10))
(step t1726.t1.t18.t12 (cl (= @p_176 0/1)) :rule trans :premises (t1726.t1.t18.t11 t1726.t1.t18.t6))
(step t1726.t1.t18.t13 (cl (= @p_187 @p_190)) :rule cong :premises (t1726.t1.t18.t8 t1726.t1.t18.t12))
(step t1726.t1.t18.t14 (cl @p_191) :rule evaluate)
(step t1726.t1.t18.t15 (cl (= @p_187 true)) :rule trans :premises (t1726.t1.t18.t13 t1726.t1.t18.t14))
(step t1726.t1.t18.t16 (cl (= @p_188 @p_189)) :rule cong :premises (t1726.t1.t18.t15))
(step t1726.t1.t18.t17 (cl (= @p_189 false)) :rule evaluate)
(step t1726.t1.t18.t18 (cl (= @p_188 false)) :rule trans :premises (t1726.t1.t18.t16 t1726.t1.t18.t17))
(step t1726.t1.t18.t19 (cl @p_186) :rule trans :premises (t1726.t1.t18.t1 t1726.t1.t18.t18))
(step t1726.t1.t18.t20 (cl (not (! (< @p_177 @p_175) :named @p_182)) (not (! (< @p_136 0/1) :named @p_180)) @p_179) :rule la_generic :args (1/1 1/1 1/1))
(step t1726.t1.t18.t21 (cl (=> (! (and @p_183 @p_172) :named @p_184) @p_182)) :rule la_mult_neg)
(step t1726.t1.t18.t22 (cl (not @p_184) @p_182) :rule implies :premises (t1726.t1.t18.t21))
(step t1726.t1.t18.t23 (cl (= @p_185 @p_183)) :rule equiv_simplify)
(step t1726.t1.t18.t24 (cl (not @p_185) @p_183) :rule equiv1 :premises (t1726.t1.t18.t23))
(step t1726.t1.t18.t25 (cl @p_185) :rule evaluate)
(step t1726.t1.t18.t26 (cl @p_183) :rule resolution :premises (t1726.t1.t18.t24 t1726.t1.t18.t25))
(step t1726.t1.t18.t27 (cl @p_184) :rule and_intro :premises (t1726.t1.t18.t26 t1726.t1.t18.a0))
(step t1726.t1.t18.t28 (cl @p_182) :rule resolution :premises (t1726.t1.t18.t22 t1726.t1.t18.t27))
(step t1726.t1.t18.t29 (cl (not (! (= @p_138 @p_180) :named @p_181)) @p_165 @p_180) :rule equiv_pos2)
(step t1726.t1.t18.t30 (cl (= @p_180 @p_138)) :rule rare_rewrite :args ("arith-elim-lt" @p_136 0/1))
(step t1726.t1.t18.t31 (cl @p_181) :rule symm :premises (t1726.t1.t18.t30))
(step t1726.t1.t18.t32 (cl (not (! (= (! (or (! (not (! (= @p_142 @p_138) :named @p_143)) :named @p_161) @p_163 @p_138) :named @p_164) (! (or @p_161 @p_141 @p_138) :named @p_162)) :named @p_167)) (not @p_164) @p_162) :rule equiv_pos2)
(step t1726.t1.t18.t33 (cl (= @p_138 @p_138)) :rule refl)
(step t1726.t1.t18.t34 (cl @p_167) :rule cong :premises (t70 t1726.t1.t18.t33))
(step t1726.t1.t18.t35 (cl @p_161 @p_163 @p_138) :rule equiv_pos2)
(step t1726.t1.t18.t36 (cl @p_164 (not @p_161)) :rule or_neg :args (0))
(step t1726.t1.t18.t37 (cl @p_164 @p_166) :rule or_neg :args (1))
(step t1726.t1.t18.t38 (cl @p_164 @p_165) :rule or_neg :args (2))
(step t1726.t1.t18.t39 (cl @p_164 @p_164 @p_164) :rule resolution :premises (t1726.t1.t18.t35 t1726.t1.t18.t36 t1726.t1.t18.t37 t1726.t1.t18.t38))
(step t1726.t1.t18.t40 (cl @p_164) :rule contraction :premises (t1726.t1.t18.t39))
(step t1726.t1.t18.t41 (cl @p_162) :rule resolution :premises (t1726.t1.t18.t32 t1726.t1.t18.t34 t1726.t1.t18.t40))
(step t1726.t1.t18.t42 (cl @p_161 @p_141 @p_138) :rule or :premises (t1726.t1.t18.t41))
(step t1726.t1.t18.t43 (cl @p_141 @p_138 @p_161) :rule reordering :premises (t1726.t1.t18.t42))
(step t1726.t1.t18.t44 (cl (! (not (! (or @p_72 @p_143) :named @p_144)) :named @p_154) @p_72 @p_143) :rule or_pos)
(step t1726.t1.t18.t45 (cl @p_72 @p_143 @p_154) :rule reordering :premises (t1726.t1.t18.t44))
(step t1726.t1.t18.t46 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (! (or @p_72 (! (= (! (not (! (>= (! (+ @p_135 @p_66) :named @p_146) 0/1) :named @p_147)) :named @p_148) @p_142) :named @p_149)) :named @p_150)) :named @p_151) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) @p_144) :named @p_145)) :named @p_152)) (not @p_151) @p_145) :rule equiv_pos2)
(step t1726.t1.t18.t47 (cl (= @p_149 (! (= @p_142 @p_148) :named @p_153))) :rule rare_rewrite :args ("eq-symm" @p_148 @p_142))
(step t1726.t1.t18.t48 (cl (= @p_146 @p_136)) :rule poly_simp)
(step t1726.t1.t18.t49 (cl @p_60) :rule refl)
(step t1726.t1.t18.t50 (cl (= @p_147 @p_137)) :rule cong :premises (t1726.t1.t18.t48 t1726.t1.t18.t49))
(step t1726.t1.t18.t51 (cl (= @p_148 @p_138)) :rule cong :premises (t1726.t1.t18.t50))
(step t1726.t1.t18.t52 (cl (= @p_153 @p_143)) :rule cong :premises (t1726.t1.t18.t51))
(step t1726.t1.t18.t53 (cl (= @p_149 @p_143)) :rule trans :premises (t1726.t1.t18.t47 t1726.t1.t18.t52))
(step t1726.t1.t18.t54 (cl (= @p_150 @p_144)) :rule cong :premises (t1726.t1.t18.t53))
(step t1726.t1.t18.t55 (cl @p_152) :rule cong :premises (t1726.t1.t18.t54))
(step t1726.t1.t18.t56 (cl @p_151 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1726.t1.t18.t57)
(assume t1726.t1.t18.t57.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1726.t1.t18.t57.t0 (cl (or @p_102 @p_150)) :rule forall_inst :args (@p_4 x$ @p_1))
(step t1726.t1.t18.t57.t1 (cl @p_102 @p_150) :rule or :premises (t1726.t1.t18.t57.t0))
(step t1726.t1.t18.t57.t2 (cl @p_150) :rule resolution :premises (t1726.t1.t18.t57.t1 t1141))
(step t1726.t1.t18.t57 (cl @p_102 @p_150) :rule subproof :discharge (t1726.t1.t18.t57.a0))
(step t1726.t1.t18.t58 (cl @p_151 @p_150) :rule resolution :premises (t1726.t1.t18.t56 t1726.t1.t18.t57))
(step t1726.t1.t18.t59 (cl @p_151 (not @p_150)) :rule implies_neg2)
(step t1726.t1.t18.t60 (cl @p_151 @p_151) :rule resolution :premises (t1726.t1.t18.t58 t1726.t1.t18.t59))
(step t1726.t1.t18.t61 (cl @p_151) :rule contraction :premises (t1726.t1.t18.t60))
(step t1726.t1.t18.t62 (cl @p_145) :rule resolution :premises (t1726.t1.t18.t46 t1726.t1.t18.t55 t1726.t1.t18.t61))
(step t1726.t1.t18.t63 (cl @p_102 @p_144) :rule implies :premises (t1726.t1.t18.t62))
(step t1726.t1.t18.t64 (cl @p_144) :rule resolution :premises (t1726.t1.t18.t63 t1141))
(step t1726.t1.t18.t65 (cl @p_143) :rule resolution :premises (t1726.t1.t18.t45 t1121 t1726.t1.t18.t64))
(step t1726.t1.t18.t66 (cl @p_138) :rule resolution :premises (t1726.t1.t18.t43 t231 t1726.t1.t18.t65))
(step t1726.t1.t18.t67 (cl @p_180) :rule resolution :premises (t1726.t1.t18.t29 t1726.t1.t18.t31 t1726.t1.t18.t66))
(step t1726.t1.t18.t68 (cl @p_179) :rule resolution :premises (t1726.t1.t18.t20 t1726.t1.t18.t28 t1726.t1.t18.t67))
(step t1726.t1.t18.t69 (cl false) :rule resolution :premises (t1726.t1.t18.t0 t1726.t1.t18.t19 t1726.t1.t18.t68))
(step t1726.t1.t18 (cl @p_173 false) :rule subproof :discharge (t1726.t1.t18.a0))
(step t1726.t1.t19 (cl @p_174 false) :rule resolution :premises (t1726.t1.t17 t1726.t1.t18))
(step t1726.t1.t20 (cl @p_174 @p_133) :rule implies_neg2)
(step t1726.t1.t21 (cl @p_174 @p_174) :rule resolution :premises (t1726.t1.t19 t1726.t1.t20))
(step t1726.t1.t22 (cl @p_174) :rule contraction :premises (t1726.t1.t21))
(step t1726.t1.t23 (cl (= @p_174 @p_173)) :rule implies_simplify)
(step t1726.t1.t24 (cl (not @p_174) @p_173) :rule equiv1 :premises (t1726.t1.t23))
(step t1726.t1.t25 (cl @p_173) :rule resolution :premises (t1726.t1.t22 t1726.t1.t24))
(step t1726.t1.t26 (cl @p_171) :rule resolution :premises (t1726.t1.t5 t1726.t1.t16 t1726.t1.t25))
(step t1726.t1.t27 (cl @p_68) :rule resolution :premises (t1726.t1.t0 t1726.t1.t4 t1726.t1.t26))
(step t1726.t1 (cl @p_165 @p_68) :rule subproof :discharge (t1726.t1.a0))
(step t1726.t2 (cl @p_170 @p_68) :rule resolution :premises (t1726.t0 t1726.t1))
(step t1726.t3 (cl @p_170 @p_69) :rule implies_neg2)
(step t1726.t4 (cl @p_170 @p_170) :rule resolution :premises (t1726.t2 t1726.t3))
(step t1726.t5 (cl @p_170) :rule contraction :premises (t1726.t4))
(step t1726.t6 (cl @p_165 @p_68) :rule implies :premises (t1726.t5))
(step t1726.t7 (cl (not @p_167) (not @p_164) @p_162) :rule equiv_pos2)
(step t1726.t8 (cl (= @p_138 @p_138)) :rule refl)
(step t1726.t9 (cl @p_167) :rule cong :premises (t70 t1726.t8))
(step t1726.t10 (cl @p_161 @p_163 @p_138) :rule equiv_pos2)
(step t1726.t11 (cl @p_164 (not @p_161)) :rule or_neg :args (0))
(step t1726.t12 (cl @p_164 @p_166) :rule or_neg :args (1))
(step t1726.t13 (cl @p_164 @p_165) :rule or_neg :args (2))
(step t1726.t14 (cl @p_164 @p_164 @p_164) :rule resolution :premises (t1726.t10 t1726.t11 t1726.t12 t1726.t13))
(step t1726.t15 (cl @p_164) :rule contraction :premises (t1726.t14))
(step t1726.t16 (cl @p_162) :rule resolution :premises (t1726.t7 t1726.t9 t1726.t15))
(step t1726.t17 (cl @p_161 @p_141 @p_138) :rule or :premises (t1726.t16))
(step t1726.t18 (cl @p_141 @p_138 @p_161) :rule reordering :premises (t1726.t17))
(step t1726.t19 (cl @p_154 @p_72 @p_143) :rule or_pos)
(step t1726.t20 (cl @p_72 @p_143 @p_154) :rule reordering :premises (t1726.t19))
(step t1726.t21 (cl (not @p_152) (not @p_151) @p_145) :rule equiv_pos2)
(step t1726.t22 (cl (= @p_149 @p_153)) :rule rare_rewrite :args ("eq-symm" @p_148 @p_142))
(step t1726.t23 (cl (= @p_146 @p_136)) :rule poly_simp)
(step t1726.t24 (cl @p_60) :rule refl)
(step t1726.t25 (cl (= @p_147 @p_137)) :rule cong :premises (t1726.t23 t1726.t24))
(step t1726.t26 (cl (= @p_148 @p_138)) :rule cong :premises (t1726.t25))
(step t1726.t27 (cl (= @p_153 @p_143)) :rule cong :premises (t1726.t26))
(step t1726.t28 (cl (= @p_149 @p_143)) :rule trans :premises (t1726.t22 t1726.t27))
(step t1726.t29 (cl (= @p_150 @p_144)) :rule cong :premises (t1726.t28))
(step t1726.t30 (cl @p_152) :rule cong :premises (t1726.t29))
(step t1726.t31 (cl @p_151 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1726.t32)
(assume t1726.t32.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1726.t32.t0 (cl (or @p_102 @p_150)) :rule forall_inst :args (@p_4 x$ @p_1))
(step t1726.t32.t1 (cl @p_102 @p_150) :rule or :premises (t1726.t32.t0))
(step t1726.t32.t2 (cl @p_150) :rule resolution :premises (t1726.t32.t1 t1141))
(step t1726.t32 (cl @p_102 @p_150) :rule subproof :discharge (t1726.t32.a0))
(step t1726.t33 (cl @p_151 @p_150) :rule resolution :premises (t1726.t31 t1726.t32))
(step t1726.t34 (cl @p_151 (not @p_150)) :rule implies_neg2)
(step t1726.t35 (cl @p_151 @p_151) :rule resolution :premises (t1726.t33 t1726.t34))
(step t1726.t36 (cl @p_151) :rule contraction :premises (t1726.t35))
(step t1726.t37 (cl @p_145) :rule resolution :premises (t1726.t21 t1726.t30 t1726.t36))
(step t1726.t38 (cl @p_102 @p_144) :rule implies :premises (t1726.t37))
(step t1726.t39 (cl @p_144) :rule resolution :premises (t1726.t38 t1141))
(step t1726.t40 (cl @p_143) :rule resolution :premises (t1726.t20 t1121 t1726.t39))
(step t1726.t41 (cl @p_138) :rule resolution :premises (t1726.t18 t231 t1726.t40))
(step t1726.t42 (cl @p_68) :rule resolution :premises (t1726.t6 t1726.t41))
(step t1726 (cl @p_165 @p_68) :rule subproof :discharge (t1726.a0))
(step t1727 (cl @p_170 @p_68) :rule resolution :premises (t1725 t1726))
(step t1728 (cl @p_170 @p_69) :rule implies_neg2)
(step t1729 (cl @p_170 @p_170) :rule resolution :premises (t1727 t1728))
(step t1730 (cl @p_170) :rule contraction :premises (t1729))
(step t1731 (cl @p_165 @p_68) :rule implies :premises (t1730))
(step t1732 (cl @p_169 (not @p_165)) :rule or_neg :args (0))
(step t1733 (cl @p_169 @p_69) :rule or_neg :args (1))
(step t1734 (cl @p_169 @p_169) :rule resolution :premises (t1731 t1732 t1733))
(step t1735 (cl @p_169) :rule contraction :premises (t1734))
(step t1736 (cl @p_168) :rule resolution :premises (t1721 t1724 t1735))
(step t1737 (cl @p_137 @p_68) :rule or :premises (t1736))
(step t1738 (cl @p_68 @p_137) :rule reordering :premises (t1737))
(step t1739 (cl (not @p_167) (not @p_164) @p_162) :rule equiv_pos2)
(step t1740 (cl (= @p_138 @p_138)) :rule refl)
(step t1741 (cl @p_167) :rule cong :premises (t70 t1740))
(step t1742 (cl @p_161 @p_163 @p_138) :rule equiv_pos2)
(step t1743 (cl @p_164 (not @p_161)) :rule or_neg :args (0))
(step t1744 (cl @p_164 @p_166) :rule or_neg :args (1))
(step t1745 (cl @p_164 @p_165) :rule or_neg :args (2))
(step t1746 (cl @p_164 @p_164 @p_164) :rule resolution :premises (t1742 t1743 t1744 t1745))
(step t1747 (cl @p_164) :rule contraction :premises (t1746))
(step t1748 (cl @p_162) :rule resolution :premises (t1739 t1741 t1747))
(step t1749 (cl @p_161 @p_141 @p_138) :rule or :premises (t1748))
(step t1750 (cl @p_141 @p_138 @p_161) :rule reordering :premises (t1749))
(step t1751 (cl @p_154 @p_72 @p_143) :rule or_pos)
(step t1752 (cl @p_72 @p_143 @p_154) :rule reordering :premises (t1751))
(step t1753 (cl (not @p_152) (not @p_151) @p_145) :rule equiv_pos2)
(step t1754 (cl (= @p_149 @p_153)) :rule rare_rewrite :args ("eq-symm" @p_148 @p_142))
(step t1755 (cl (= @p_146 @p_136)) :rule poly_simp)
(step t1756 (cl @p_60) :rule refl)
(step t1757 (cl (= @p_147 @p_137)) :rule cong :premises (t1755 t1756))
(step t1758 (cl (= @p_148 @p_138)) :rule cong :premises (t1757))
(step t1759 (cl (= @p_153 @p_143)) :rule cong :premises (t1758))
(step t1760 (cl (= @p_149 @p_143)) :rule trans :premises (t1754 t1759))
(step t1761 (cl (= @p_150 @p_144)) :rule cong :premises (t1760))
(step t1762 (cl @p_152) :rule cong :premises (t1761))
(step t1763 (cl @p_151 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1764)
(assume t1764.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1764.t0 (cl (or @p_102 @p_150)) :rule forall_inst :args (@p_4 x$ @p_1))
(step t1764.t1 (cl @p_102 @p_150) :rule or :premises (t1764.t0))
(step t1764.t2 (cl @p_150) :rule resolution :premises (t1764.t1 t1141))
(step t1764 (cl @p_102 @p_150) :rule subproof :discharge (t1764.a0))
(step t1765 (cl @p_151 @p_150) :rule resolution :premises (t1763 t1764))
(step t1766 (cl @p_151 (not @p_150)) :rule implies_neg2)
(step t1767 (cl @p_151 @p_151) :rule resolution :premises (t1765 t1766))
(step t1768 (cl @p_151) :rule contraction :premises (t1767))
(step t1769 (cl @p_145) :rule resolution :premises (t1753 t1762 t1768))
(step t1770 (cl @p_102 @p_144) :rule implies :premises (t1769))
(step t1771 (cl @p_144) :rule resolution :premises (t1770 t1141))
(step t1772 (cl @p_143) :rule resolution :premises (t1752 t1121 t1771))
(step t1773 (cl @p_138) :rule resolution :premises (t1750 t231 t1772))
(step t1774 (cl @p_68) :rule resolution :premises (t1738 t1773))
(step t1775 (cl (! (not (! (or @p_72 @p_70) :named @p_73)) :named @p_134) @p_72 @p_70) :rule or_pos)
(step t1776 (cl @p_72 @p_70 @p_134) :rule reordering :premises (t1775))
(step t1777 (cl (not (! (= (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) (! (or @p_72 (! (= @p_69 (! (not (! (>= (! (+ @p_1 @p_61) :named @p_104) 0/1) :named @p_105)) :named @p_106)) :named @p_107)) :named @p_108)) :named @p_109) (! (=> (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))) @p_73) :named @p_103)) :named @p_110)) (not @p_109) @p_103) :rule equiv_pos2)
(step t1778 (cl (= @p_104 @p_62)) :rule poly_simp)
(step t1779 (cl @p_60) :rule refl)
(step t1780 (cl (= @p_105 @p_63)) :rule cong :premises (t1778 t1779))
(step t1781 (cl (= @p_106 @p_64)) :rule cong :premises (t1780))
(step t1782 (cl (= @p_107 @p_70)) :rule cong :premises (t1781))
(step t1783 (cl (= @p_108 @p_73)) :rule cong :premises (t1782))
(step t1784 (cl @p_110) :rule cong :premises (t1783))
(step t1785 (cl @p_109 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1)))))) :rule implies_neg1)
(anchor :step t1786)
(assume t1786.a0 (forall ((?v0 Real) (?v1 Real) (?v2 Real)) (or (>= (* -1/1 ?v0) 0/1) (= (not (>= (+ (* -1/1 (times$a ?v0 ?v2)) (times$a ?v0 ?v1)) 0/1)) (not (>= (+ ?v1 (* -1/1 ?v2)) 0/1))))))
(step t1786.t0 (cl (or @p_102 @p_108)) :rule forall_inst :args (@p_4 @p_1 x$))
(step t1786.t1 (cl @p_102 @p_108) :rule or :premises (t1786.t0))
(step t1786.t2 (cl @p_108) :rule resolution :premises (t1786.t1 t1141))
(step t1786 (cl @p_102 @p_108) :rule subproof :discharge (t1786.a0))
(step t1787 (cl @p_109 @p_108) :rule resolution :premises (t1785 t1786))
(step t1788 (cl @p_109 (not @p_108)) :rule implies_neg2)
(step t1789 (cl @p_109 @p_109) :rule resolution :premises (t1787 t1788))
(step t1790 (cl @p_109) :rule contraction :premises (t1789))
(step t1791 (cl @p_103) :rule resolution :premises (t1777 t1784 t1790))
(step t1792 (cl @p_102 @p_73) :rule implies :premises (t1791))
(step t1793 (cl @p_73) :rule resolution :premises (t1792 t1141))
(step t1794 (cl @p_70) :rule resolution :premises (t1776 t1121 t1793))
(step t1795 (cl @p_63) :rule resolution :premises (t1720 t1774 t1794))
(step t1796 (cl) :rule resolution :premises (t55 t1708 t900 t1483 t1465 t1795 t319 t302 t237))
)
00f950cd0246ba710daee1ee712da18e5feb8a65 535 0
unsat
(
(define-fun @quantifiers_skolemize_33 () I_a_state$ (choice ((?v3 I_a_state$)) (not (or (not (member$d (pair$g s$ ?v3) (rtrancl$ (collect$d (case_prod$f uu$))))) (not (member$d (pair$g ?v3 s$a) (collect$d (case_prod$f uu$))))))))
(define-fun @quantifiers_skolemize_34 () I_a_state$ (choice ((?v2 I_a_state$)) (not (forall ((?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))))))
(define-fun @quantifiers_skolemize_35 () I_a_state$ (choice ((?v3 I_a_state$)) (not (or (not (= (pair$g @quantifiers_skolemize_34 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ @quantifiers_skolemize_34) ?v3))))))
(assume a0 (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (and (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))))))))
(assume a7 (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)))
(assume a12 (forall ((?v0 I_a_state_i_a_state_prod$) (?v1 I_a_state_i_a_state_prod_bool_fun$)) (= (member$d ?v0 (collect$d ?v1)) (fun_app$p ?v1 ?v0))))
(assume a13 (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (= (pair$g ?v0 ?v1) (pair$g ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))))
(assume a20 (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))))))
(assume a31 (! (member$d (pair$g s$ s$a) (trancl$ (! (collect$d (! (case_prod$f uu$) :named @p_1)) :named @p_2))) :named @p_3))
(assume a32 (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a)))))
(assume a33 (! (not (! (normalized_tableau$ (t$ s$a)) :named @p_4)) :named @p_5))
(step t0 (cl (! (not (! (or (! (not (! (normalized_tableau$ (t$ @quantifiers_skolemize_33)) :named @p_22)) :named @p_23) (! (not (! (bounds_consistent$ @quantifiers_skolemize_33) :named @p_20)) :named @p_21) (! (not (! (curr_val_satisfies_no_lhs$ @quantifiers_skolemize_33) :named @p_18)) :named @p_19) (! (not (! (tableau_valuated$ @quantifiers_skolemize_33) :named @p_16)) :named @p_17) (! (not (! (fun_app$ (fun_app$a gt_state$ @quantifiers_skolemize_33) s$a) :named @p_14)) :named @p_15) (! (not (! (= (! (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) :named @p_11) (! (pair$ (b_i_l$ @quantifiers_skolemize_33) (b_i_u$ @quantifiers_skolemize_33)) :named @p_10)) :named @p_12)) :named @p_13) (! (not (! (= (! (u_c$ s$a) :named @p_7) (! (u_c$ @quantifiers_skolemize_33) :named @p_6)) :named @p_8)) :named @p_9)) :named @p_24)) :named @p_235) @p_23 @p_21 @p_19 @p_17 @p_15 @p_13 @p_9) :rule or_pos)
(step t1 (cl @p_23 @p_21 @p_19 @p_17 @p_15 @p_13 @p_9 @p_235) :rule reordering :premises (t0))
(step t2 (cl (! (not (! (and @p_22 @p_20 @p_18 @p_16 @p_14 @p_12 @p_8) :named @p_94)) :named @p_234) @p_8) :rule and_pos :args (6))
(step t3 (cl @p_8 @p_234) :rule reordering :premises (t2))
(step t4 (cl (! (not (! (= (! (fun_app$ (! (fun_app$a uu$ @quantifiers_skolemize_33) :named @p_95) s$a) :named @p_96) @p_94) :named @p_97)) :named @p_233) (! (not @p_96) :named @p_232) @p_94) :rule equiv_pos2)
(step t5 (cl @p_94 @p_232 @p_233) :rule reordering :premises (t4))
(step t6 (cl (= (! (= @p_96 true) :named @p_119) @p_96)) :rule equiv_simplify)
(step t7 (cl (not @p_119) @p_96) :rule equiv1 :premises (t6))
(step t8 (cl (! (not (! (and (! (= @quantifiers_skolemize_33 @quantifiers_skolemize_34) :named @p_207) (! (= s$a @quantifiers_skolemize_35) :named @p_206)) :named @p_208)) :named @p_231) @p_207) :rule and_pos :args (0))
(step t9 (cl @p_207 @p_231) :rule reordering :premises (t8))
(step t10 (cl (! (not (! (= (! (= (! (pair$g @quantifiers_skolemize_33 s$a) :named @p_125) (! (pair$g @quantifiers_skolemize_34 @quantifiers_skolemize_35) :named @p_124)) :named @p_126) @p_208) :named @p_209)) :named @p_230) (! (not @p_126) :named @p_127) @p_208) :rule equiv_pos2)
(step t11 (cl @p_127 @p_208 @p_230) :rule reordering :premises (t10))
(step t12 (cl (not (! (= (! (or (! (or @p_127 (! (not (! (fun_app$ (! (fun_app$a uu$ @quantifiers_skolemize_34) :named @p_120) @quantifiers_skolemize_35) :named @p_121)) :named @p_123)) :named @p_128) (! (not @p_127) :named @p_227)) :named @p_228) (! (or @p_128 @p_126) :named @p_226)) :named @p_229)) (not @p_228) @p_226) :rule equiv_pos2)
(step t13 (cl (= @p_227 @p_126)) :rule rare_rewrite :args ("bool-double-not-elim" @p_126))
(step t14 (cl @p_229) :rule cong :premises (t13))
(step t15 (cl @p_128 @p_227) :rule or_neg :args (0))
(step t16 (cl @p_228 (! (not @p_128) :named @p_129)) :rule or_neg :args (0))
(step t17 (cl @p_228 (not @p_227)) :rule or_neg :args (1))
(step t18 (cl @p_228 @p_228) :rule resolution :premises (t15 t16 t17))
(step t19 (cl @p_228) :rule contraction :premises (t18))
(step t20 (cl @p_226) :rule resolution :premises (t12 t14 t19))
(step t21 (cl @p_128 @p_126) :rule or :premises (t20))
(step t22 (cl @p_126 @p_128) :rule reordering :premises (t21))
(step t23 (cl (not (! (= (! (or (! (not (! (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3))))) :named @p_130)) :named @p_191) @p_129) :named @p_192) (! (or (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))) @p_129) :named @p_190)) :named @p_201)) (not @p_192) @p_190) :rule equiv_pos2)
(step t24 (cl (= @p_191 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))))) :rule rare_rewrite :args ("bool-double-not-elim" (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3))))))
(step t25 (cl (= @p_129 @p_129)) :rule refl)
(step t26 (cl @p_201) :rule cong :premises (t24 t25))
(step t27 (cl (not (! (= (! (=> @p_130 (! (not (! (or (! (not (! (= @p_124 @p_125) :named @p_194)) :named @p_195) @p_123) :named @p_196)) :named @p_197)) :named @p_198) (! (=> @p_130 @p_129) :named @p_193)) :named @p_200)) (not @p_198) @p_193) :rule equiv_pos2)
(step t28 (cl (= @p_194 @p_126)) :rule rare_rewrite :args ("eq-symm" @p_124 @p_125))
(step t29 (cl (= @p_195 @p_127)) :rule cong :premises (t28))
(step t30 (cl (= @p_123 @p_123)) :rule refl)
(step t31 (cl (= @p_196 @p_128)) :rule cong :premises (t29 t30))
(step t32 (cl (= @p_197 @p_129)) :rule cong :premises (t31))
(step t33 (cl @p_200) :rule cong :premises (t32))
(step t34 (cl @p_198 @p_130) :rule implies_neg1)
(anchor :step t35)
(assume t35.a0 @p_130)
(step t35.t0 (cl (not (! (= @p_130 @p_197) :named @p_199)) @p_191 @p_197) :rule equiv_pos2)
(anchor :step t35.t1 :args ((:= (?v2 I_a_state$) @quantifiers_skolemize_34) (:= (?v3 I_a_state$) @quantifiers_skolemize_35)))
(step t35.t1.t0 (cl (= (! (or (! (not (! (= (! (pair$g ?v2 ?v3) :named @p_146) @p_125) :named @p_157)) :named @p_158) (! (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)) :named @p_156)) :named @p_159) @p_196)) :rule refl)
(step t35.t1 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))) @p_196)) :rule sko_forall)
(step t35.t2 (cl @p_199) :rule cong :premises (t35.t1))
(step t35.t3 (cl (! (not (! (or (! (not (! (fun_app$p @p_1 @p_125) :named @p_131)) :named @p_132) @p_130) :named @p_133)) :named @p_189) @p_132 @p_130) :rule or_pos)
(step t35.t4 (cl @p_132 @p_130 @p_189) :rule reordering :premises (t35.t3))
(step t35.t5 (cl (! (not (! (= (! (member$d @p_125 @p_2) :named @p_162) @p_131) :named @p_163)) :named @p_188) (! (not @p_162) :named @p_165) @p_131) :rule equiv_pos2)
(step t35.t6 (cl @p_165 @p_131 @p_188) :rule reordering :premises (t35.t5))
(step t35.t7 (cl (not (! (= (! (or (! (or (not (member$d (pair$g s$ @quantifiers_skolemize_33) (! (rtrancl$ @p_2) :named @p_166))) @p_165) :named @p_167) (! (not @p_165) :named @p_185)) :named @p_186) (! (or @p_167 @p_162) :named @p_184)) :named @p_187)) (not @p_186) @p_184) :rule equiv_pos2)
(step t35.t8 (cl (= @p_185 @p_162)) :rule rare_rewrite :args ("bool-double-not-elim" @p_162))
(step t35.t9 (cl @p_187) :rule cong :premises (t35.t8))
(step t35.t10 (cl @p_167 @p_185) :rule or_neg :args (1))
(step t35.t11 (cl @p_186 (! (not @p_167) :named @p_168)) :rule or_neg :args (0))
(step t35.t12 (cl @p_186 (not @p_185)) :rule or_neg :args (1))
(step t35.t13 (cl @p_186 @p_186) :rule resolution :premises (t35.t10 t35.t11 t35.t12))
(step t35.t14 (cl @p_186) :rule contraction :premises (t35.t13))
(step t35.t15 (cl @p_184) :rule resolution :premises (t35.t7 t35.t9 t35.t14))
(step t35.t16 (cl @p_167 @p_162) :rule or :premises (t35.t15))
(step t35.t17 (cl @p_162 @p_167) :rule reordering :premises (t35.t16))
(step t35.t18 (cl (not (! (= (! (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g s$ ?v3) (rtrancl$ (collect$d (case_prod$f uu$))))) (not (member$d (pair$g ?v3 s$a) (collect$d (case_prod$f uu$))))))) :named @p_169) @p_168) :named @p_183)) (not @p_169) @p_168) :rule equiv_pos2)
(anchor :step t35.t19 :args ((:= (?v3 I_a_state$) @quantifiers_skolemize_33)))
(step t35.t19.t0 (cl (= (or (not (member$d (pair$g s$ ?v3) @p_166)) (not (member$d (pair$g ?v3 s$a) @p_2))) @p_167)) :rule refl)
(step t35.t19 (cl (= (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g s$ ?v3) (rtrancl$ (collect$d (case_prod$f uu$))))) (not (member$d (pair$g ?v3 s$a) (collect$d (case_prod$f uu$)))))) @p_167)) :rule sko_forall)
(step t35.t20 (cl @p_183) :rule cong :premises (t35.t19))
(step t35.t21 (cl (! (not (! (or (! (not @p_3) :named @p_170) @p_169) :named @p_171)) :named @p_182) @p_170 @p_169) :rule or_pos)
(step t35.t22 (cl @p_170 @p_169 @p_182) :rule reordering :premises (t35.t21))
(step t35.t23 (cl (or (! (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :named @p_181) @p_171)) :rule forall_inst :args (s$ s$a @p_2))
(step t35.t24 (cl @p_181 @p_171) :rule or :premises (t35.t23))
(step t35.t25 (cl (not (! (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :named @p_172)) (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :rule equiv_pos2)
(anchor :step t35.t26 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state_i_a_state_prod_set$) ?v2)))
(step t35.t26.t0 (cl (= (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))) (! (not (forall ((?v3 I_a_state$)) (not (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))))) :named @p_178))) :rule connective_def)
(anchor :step t35.t26.t1 :args ((?v3 I_a_state$) (:= (?v3 I_a_state$) ?v3)))
(step t35.t26.t1.t0 (cl (= (not (and (! (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) :named @p_180) (! (member$d (pair$g ?v3 ?v1) ?v2) :named @p_179))) (or (not @p_180) (not @p_179)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_180 @p_179 rare-list))
(step t35.t26.t1 (cl (= (forall ((?v3 I_a_state$)) (not (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))) (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))) :rule bind)
(step t35.t26.t2 (cl (= @p_178 (! (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))) :named @p_174))) :rule cong :premises (t35.t26.t1))
(step t35.t26.t3 (cl (= (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))) @p_174)) :rule trans :premises (t35.t26.t0 t35.t26.t2))
(step t35.t26.t4 (cl (= (=> (! (member$d (! (pair$g ?v0 ?v1) :named @p_175) (trancl$ ?v2)) :named @p_176) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))) (! (=> @p_176 @p_174) :named @p_177))) :rule cong :premises (t35.t26.t3))
(step t35.t26 (cl (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))))) :rule bind)
(anchor :step t35.t27 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state_i_a_state_prod_set$) ?v2)))
(step t35.t27.t0 (cl (= @p_177 (or (not @p_176) @p_174))) :rule rare_rewrite :args ("bool-impl-elim" @p_176 @p_174))
(step t35.t27 (cl (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))))) :rule bind)
(step t35.t28 (cl @p_172) :rule trans :premises (t35.t26 t35.t27))
(step t35.t29 (cl (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :rule resolution :premises (t35.t25 t35.t28 a20))
(step t35.t30 (cl @p_171) :rule resolution :premises (t35.t24 t35.t29))
(step t35.t31 (cl @p_169) :rule resolution :premises (t35.t22 a31 t35.t30))
(step t35.t32 (cl @p_168) :rule resolution :premises (t35.t18 t35.t20 t35.t31))
(step t35.t33 (cl @p_162) :rule resolution :premises (t35.t17 t35.t32))
(step t35.t34 (cl (or (! (not (forall ((?v0 I_a_state_i_a_state_prod$) (?v1 I_a_state_i_a_state_prod_bool_fun$)) (= (member$d ?v0 (collect$d ?v1)) (fun_app$p ?v1 ?v0)))) :named @p_164) @p_163)) :rule forall_inst :args (@p_125 @p_1))
(step t35.t35 (cl @p_164 @p_163) :rule or :premises (t35.t34))
(step t35.t36 (cl @p_163) :rule resolution :premises (t35.t35 a12))
(step t35.t37 (cl @p_131) :rule resolution :premises (t35.t6 t35.t33 t35.t36))
(step t35.t38 (cl (not (! (= (! (=> (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) (! (or @p_132 (! (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g @quantifiers_skolemize_33 s$a) (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3))))) :named @p_152)) :named @p_153)) :named @p_154) (! (=> (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) @p_133) :named @p_151)) :named @p_155)) (not @p_154) @p_151) :rule equiv_pos2)
(anchor :step t35.t39 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t35.t39.t0 (cl (= (! (= @p_125 @p_146) :named @p_160) @p_157)) :rule rare_rewrite :args ("eq-symm" @p_125 @p_146))
(step t35.t39.t1 (cl (= (! (not @p_160) :named @p_161) @p_158)) :rule cong :premises (t35.t39.t0))
(step t35.t39.t2 (cl (= @p_156 @p_156)) :rule refl)
(step t35.t39.t3 (cl (= (or @p_161 @p_156) @p_159)) :rule cong :premises (t35.t39.t1 t35.t39.t2))
(step t35.t39 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g @quantifiers_skolemize_33 s$a) (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))))) :rule bind)
(step t35.t40 (cl (= @p_152 @p_130)) :rule cong :premises (t35.t39))
(step t35.t41 (cl (= @p_153 @p_133)) :rule cong :premises (t35.t40))
(step t35.t42 (cl @p_155) :rule cong :premises (t35.t41))
(step t35.t43 (cl @p_154 (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule implies_neg1)
(anchor :step t35.t44)
(assume t35.t44.a0 (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))
(step t35.t44.t0 (cl (or (! (not (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :named @p_150) @p_153)) :rule forall_inst :args (uu$ @p_125))
(step t35.t44.t1 (cl @p_150 @p_153) :rule or :premises (t35.t44.t0))
(step t35.t44.t2 (cl (not (! (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :named @p_134)) (not (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule equiv_pos2)
(anchor :step t35.t44.t3 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t35.t44.t3.t0 (cl (= (! (=> (! (and (! (fun_app$p (case_prod$f ?v0) ?v1) :named @p_137) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) :named @p_140) false) :named @p_141) (! (not @p_140) :named @p_142))) :rule rare_rewrite :args ("bool-impl-false1" @p_140))
(anchor :step t35.t44.t3.t1 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t35.t44.t3.t1.t0 (cl (= (=> (! (and (! (= ?v1 @p_146) :named @p_147) (! (fun_app$ (fun_app$a ?v0 ?v2) ?v3) :named @p_145)) :named @p_148) false) (! (not @p_148) :named @p_149))) :rule rare_rewrite :args ("bool-impl-false1" @p_148))
(step t35.t44.t3.t1 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(anchor :step t35.t44.t3.t2 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t35.t44.t3.t2.t0 (cl (= @p_149 (or (not @p_147) (not @p_145)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_147 @p_145 rare-list))
(step t35.t44.t3.t2 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(step t35.t44.t3.t3 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule trans :premises (t35.t44.t3.t1 t35.t44.t3.t2))
(step t35.t44.t3.t4 (cl (= @p_140 (! (and @p_137 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))) :named @p_138))) :rule cong :premises (t35.t44.t3.t3))
(step t35.t44.t3.t5 (cl (= @p_142 (! (not @p_138) :named @p_139))) :rule cong :premises (t35.t44.t3.t4))
(step t35.t44.t3.t6 (cl (= @p_141 @p_139)) :rule trans :premises (t35.t44.t3.t0 t35.t44.t3.t5))
(step t35.t44.t3 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(anchor :step t35.t44.t4 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t35.t44.t4.t0 (cl (= @p_139 (or (not @p_137) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_137 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) rare-list))
(step t35.t44.t4 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(step t35.t44.t5 (cl @p_134) :rule trans :premises (t35.t44.t3 t35.t44.t4))
(step t35.t44.t6 (cl (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule resolution :premises (t35.t44.t2 t35.t44.t5 a7))
(step t35.t44.t7 (cl @p_153) :rule resolution :premises (t35.t44.t1 t35.t44.t6))
(step t35.t44 (cl @p_150 @p_153) :rule subproof :discharge (t35.t44.a0))
(step t35.t45 (cl @p_154 @p_153) :rule resolution :premises (t35.t43 t35.t44))
(step t35.t46 (cl @p_154 (not @p_153)) :rule implies_neg2)
(step t35.t47 (cl @p_154 @p_154) :rule resolution :premises (t35.t45 t35.t46))
(step t35.t48 (cl @p_154) :rule contraction :premises (t35.t47))
(step t35.t49 (cl @p_151) :rule resolution :premises (t35.t38 t35.t42 t35.t48))
(step t35.t50 (cl @p_150 @p_133) :rule implies :premises (t35.t49))
(step t35.t51 (cl (not @p_134) (not (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule equiv_pos2)
(anchor :step t35.t52 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t35.t52.t0 (cl (= @p_141 @p_142)) :rule rare_rewrite :args ("bool-impl-false1" @p_140))
(anchor :step t35.t52.t1 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t35.t52.t1.t0 (cl (= (=> @p_148 false) @p_149)) :rule rare_rewrite :args ("bool-impl-false1" @p_148))
(step t35.t52.t1 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(anchor :step t35.t52.t2 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t35.t52.t2.t0 (cl (= @p_149 (or (not @p_147) (not @p_145)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_147 @p_145 rare-list))
(step t35.t52.t2 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(step t35.t52.t3 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule trans :premises (t35.t52.t1 t35.t52.t2))
(step t35.t52.t4 (cl (= @p_140 @p_138)) :rule cong :premises (t35.t52.t3))
(step t35.t52.t5 (cl (= @p_142 @p_139)) :rule cong :premises (t35.t52.t4))
(step t35.t52.t6 (cl (= @p_141 @p_139)) :rule trans :premises (t35.t52.t0 t35.t52.t5))
(step t35.t52 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(anchor :step t35.t53 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t35.t53.t0 (cl (= @p_139 (or (not @p_137) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_137 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) rare-list))
(step t35.t53 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(step t35.t54 (cl @p_134) :rule trans :premises (t35.t52 t35.t53))
(step t35.t55 (cl (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule resolution :premises (t35.t51 t35.t54 a7))
(step t35.t56 (cl @p_133) :rule resolution :premises (t35.t50 t35.t55))
(step t35.t57 (cl @p_130) :rule resolution :premises (t35.t4 t35.t37 t35.t56))
(step t35.t58 (cl @p_197) :rule resolution :premises (t35.t0 t35.t2 t35.t57))
(step t35 (cl @p_191 @p_197) :rule subproof :discharge (t35.a0))
(step t36 (cl @p_198 @p_197) :rule resolution :premises (t34 t35))
(step t37 (cl @p_198 (not @p_197)) :rule implies_neg2)
(step t38 (cl @p_198 @p_198) :rule resolution :premises (t36 t37))
(step t39 (cl @p_198) :rule contraction :premises (t38))
(step t40 (cl @p_193) :rule resolution :premises (t27 t33 t39))
(step t41 (cl @p_191 @p_129) :rule implies :premises (t40))
(step t42 (cl @p_192 (not @p_191)) :rule or_neg :args (0))
(step t43 (cl @p_192 (not @p_129)) :rule or_neg :args (1))
(step t44 (cl @p_192 @p_192) :rule resolution :premises (t41 t42 t43))
(step t45 (cl @p_192) :rule contraction :premises (t44))
(step t46 (cl @p_190) :rule resolution :premises (t23 t26 t45))
(step t47 (cl (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))) @p_129) :rule or :premises (t46))
(step t48 (cl @p_189 @p_132 @p_130) :rule or_pos)
(step t49 (cl @p_132 @p_130 @p_189) :rule reordering :premises (t48))
(step t50 (cl @p_188 @p_165 @p_131) :rule equiv_pos2)
(step t51 (cl @p_165 @p_131 @p_188) :rule reordering :premises (t50))
(step t52 (cl (not @p_187) (not @p_186) @p_184) :rule equiv_pos2)
(step t53 (cl (= @p_185 @p_162)) :rule rare_rewrite :args ("bool-double-not-elim" @p_162))
(step t54 (cl @p_187) :rule cong :premises (t53))
(step t55 (cl @p_167 @p_185) :rule or_neg :args (1))
(step t56 (cl @p_186 @p_168) :rule or_neg :args (0))
(step t57 (cl @p_186 (not @p_185)) :rule or_neg :args (1))
(step t58 (cl @p_186 @p_186) :rule resolution :premises (t55 t56 t57))
(step t59 (cl @p_186) :rule contraction :premises (t58))
(step t60 (cl @p_184) :rule resolution :premises (t52 t54 t59))
(step t61 (cl @p_167 @p_162) :rule or :premises (t60))
(step t62 (cl @p_162 @p_167) :rule reordering :premises (t61))
(step t63 (cl (not @p_183) (not @p_169) @p_168) :rule equiv_pos2)
(anchor :step t64 :args ((:= (?v3 I_a_state$) @quantifiers_skolemize_33)))
(step t64.t0 (cl (= (or (not (member$d (pair$g s$ ?v3) @p_166)) (not (member$d (pair$g ?v3 s$a) @p_2))) @p_167)) :rule refl)
(step t64 (cl (= (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g s$ ?v3) (rtrancl$ (collect$d (case_prod$f uu$))))) (not (member$d (pair$g ?v3 s$a) (collect$d (case_prod$f uu$)))))) @p_167)) :rule sko_forall)
(step t65 (cl @p_183) :rule cong :premises (t64))
(step t66 (cl @p_182 @p_170 @p_169) :rule or_pos)
(step t67 (cl @p_170 @p_169 @p_182) :rule reordering :premises (t66))
(step t68 (cl (or @p_181 @p_171)) :rule forall_inst :args (s$ s$a @p_2))
(step t69 (cl @p_181 @p_171) :rule or :premises (t68))
(step t70 (cl (not @p_172) (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :rule equiv_pos2)
(anchor :step t71 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state_i_a_state_prod_set$) ?v2)))
(step t71.t0 (cl (= (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))) @p_178)) :rule connective_def)
(anchor :step t71.t1 :args ((?v3 I_a_state$) (:= (?v3 I_a_state$) ?v3)))
(step t71.t1.t0 (cl (= (not (and @p_180 @p_179)) (or (not @p_180) (not @p_179)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_180 @p_179 rare-list))
(step t71.t1 (cl (= (forall ((?v3 I_a_state$)) (not (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))) (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))) :rule bind)
(step t71.t2 (cl (= @p_178 @p_174)) :rule cong :premises (t71.t1))
(step t71.t3 (cl (= (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))) @p_174)) :rule trans :premises (t71.t0 t71.t2))
(step t71.t4 (cl (= (=> @p_176 (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2)))) @p_177)) :rule cong :premises (t71.t3))
(step t71 (cl (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (exists ((?v3 I_a_state$)) (and (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2)) (member$d (pair$g ?v3 ?v1) ?v2))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))))) :rule bind)
(anchor :step t72 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state_i_a_state_prod_set$) ?v2)))
(step t72.t0 (cl (= @p_177 (or (not @p_176) @p_174))) :rule rare_rewrite :args ("bool-impl-elim" @p_176 @p_174))
(step t72 (cl (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (=> (member$d (pair$g ?v0 ?v1) (trancl$ ?v2)) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2))))))))) :rule bind)
(step t73 (cl @p_172) :rule trans :premises (t71 t72))
(step t74 (cl (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state_i_a_state_prod_set$)) (or (not (member$d (pair$g ?v0 ?v1) (trancl$ ?v2))) (not (forall ((?v3 I_a_state$)) (or (not (member$d (pair$g ?v0 ?v3) (rtrancl$ ?v2))) (not (member$d (pair$g ?v3 ?v1) ?v2)))))))) :rule resolution :premises (t70 t73 a20))
(step t75 (cl @p_171) :rule resolution :premises (t69 t74))
(step t76 (cl @p_169) :rule resolution :premises (t67 a31 t75))
(step t77 (cl @p_168) :rule resolution :premises (t63 t65 t76))
(step t78 (cl @p_162) :rule resolution :premises (t62 t77))
(step t79 (cl (or @p_164 @p_163)) :rule forall_inst :args (@p_125 @p_1))
(step t80 (cl @p_164 @p_163) :rule or :premises (t79))
(step t81 (cl @p_163) :rule resolution :premises (t80 a12))
(step t82 (cl @p_131) :rule resolution :premises (t51 t78 t81))
(step t83 (cl (not @p_155) (not @p_154) @p_151) :rule equiv_pos2)
(anchor :step t84 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t84.t0 (cl (= @p_160 @p_157)) :rule rare_rewrite :args ("eq-symm" @p_125 @p_146))
(step t84.t1 (cl (= @p_161 @p_158)) :rule cong :premises (t84.t0))
(step t84.t2 (cl (= @p_156 @p_156)) :rule refl)
(step t84.t3 (cl (= (or @p_161 @p_156) @p_159)) :rule cong :premises (t84.t1 t84.t2))
(step t84 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g @quantifiers_skolemize_33 s$a) (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= (pair$g ?v2 ?v3) (pair$g @quantifiers_skolemize_33 s$a))) (not (fun_app$ (fun_app$a uu$ ?v2) ?v3)))))) :rule bind)
(step t85 (cl (= @p_152 @p_130)) :rule cong :premises (t84))
(step t86 (cl (= @p_153 @p_133)) :rule cong :premises (t85))
(step t87 (cl @p_155) :rule cong :premises (t86))
(step t88 (cl @p_154 (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule implies_neg1)
(anchor :step t89)
(assume t89.a0 (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))
(step t89.t0 (cl (or @p_150 @p_153)) :rule forall_inst :args (uu$ @p_125))
(step t89.t1 (cl @p_150 @p_153) :rule or :premises (t89.t0))
(step t89.t2 (cl (not @p_134) (not (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule equiv_pos2)
(anchor :step t89.t3 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t89.t3.t0 (cl (= @p_141 @p_142)) :rule rare_rewrite :args ("bool-impl-false1" @p_140))
(anchor :step t89.t3.t1 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t89.t3.t1.t0 (cl (= (=> @p_148 false) @p_149)) :rule rare_rewrite :args ("bool-impl-false1" @p_148))
(step t89.t3.t1 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(anchor :step t89.t3.t2 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t89.t3.t2.t0 (cl (= @p_149 (or (not @p_147) (not @p_145)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_147 @p_145 rare-list))
(step t89.t3.t2 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(step t89.t3.t3 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule trans :premises (t89.t3.t1 t89.t3.t2))
(step t89.t3.t4 (cl (= @p_140 @p_138)) :rule cong :premises (t89.t3.t3))
(step t89.t3.t5 (cl (= @p_142 @p_139)) :rule cong :premises (t89.t3.t4))
(step t89.t3.t6 (cl (= @p_141 @p_139)) :rule trans :premises (t89.t3.t0 t89.t3.t5))
(step t89.t3 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(anchor :step t89.t4 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t89.t4.t0 (cl (= @p_139 (or (not @p_137) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_137 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) rare-list))
(step t89.t4 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(step t89.t5 (cl @p_134) :rule trans :premises (t89.t3 t89.t4))
(step t89.t6 (cl (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule resolution :premises (t89.t2 t89.t5 a7))
(step t89.t7 (cl @p_153) :rule resolution :premises (t89.t1 t89.t6))
(step t89 (cl @p_150 @p_153) :rule subproof :discharge (t89.a0))
(step t90 (cl @p_154 @p_153) :rule resolution :premises (t88 t89))
(step t91 (cl @p_154 (not @p_153)) :rule implies_neg2)
(step t92 (cl @p_154 @p_154) :rule resolution :premises (t90 t91))
(step t93 (cl @p_154) :rule contraction :premises (t92))
(step t94 (cl @p_151) :rule resolution :premises (t83 t87 t93))
(step t95 (cl @p_150 @p_133) :rule implies :premises (t94))
(step t96 (cl (not @p_134) (not (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule equiv_pos2)
(anchor :step t97 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t97.t0 (cl (= @p_141 @p_142)) :rule rare_rewrite :args ("bool-impl-false1" @p_140))
(anchor :step t97.t1 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t97.t1.t0 (cl (= (=> @p_148 false) @p_149)) :rule rare_rewrite :args ("bool-impl-false1" @p_148))
(step t97.t1 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(anchor :step t97.t2 :args ((?v2 I_a_state$) (?v3 I_a_state$) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t97.t2.t0 (cl (= @p_149 (or (not @p_147) (not @p_145)))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_147 @p_145 rare-list))
(step t97.t2 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (not (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule bind)
(step t97.t3 (cl (= (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false)) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))) :rule trans :premises (t97.t1 t97.t2))
(step t97.t4 (cl (= @p_140 @p_138)) :rule cong :premises (t97.t3))
(step t97.t5 (cl (= @p_142 @p_139)) :rule cong :premises (t97.t4))
(step t97.t6 (cl (= @p_141 @p_139)) :rule trans :premises (t97.t0 t97.t5))
(step t97 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (=> (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (=> (and (= ?v1 (pair$g ?v2 ?v3)) (fun_app$ (fun_app$a ?v0 ?v2) ?v3)) false))) false)) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(anchor :step t98 :args ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$) (:= (?v0 I_a_state_i_a_state_bool_fun_fun$) ?v0) (:= (?v1 I_a_state_i_a_state_prod$) ?v1)))
(step t98.t0 (cl (= @p_139 (or (not @p_137) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_137 (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))) rare-list))
(step t98 (cl (= (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (not (and (fun_app$p (case_prod$f ?v0) ?v1) (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))) (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3))))))))) :rule bind)
(step t99 (cl @p_134) :rule trans :premises (t97 t98))
(step t100 (cl (forall ((?v0 I_a_state_i_a_state_bool_fun_fun$) (?v1 I_a_state_i_a_state_prod$)) (or (not (fun_app$p (case_prod$f ?v0) ?v1)) (not (forall ((?v2 I_a_state$) (?v3 I_a_state$)) (or (not (= ?v1 (pair$g ?v2 ?v3))) (not (fun_app$ (fun_app$a ?v0 ?v2) ?v3)))))))) :rule resolution :premises (t96 t99 a7))
(step t101 (cl @p_133) :rule resolution :premises (t95 t100))
(step t102 (cl @p_130) :rule resolution :premises (t49 t82 t101))
(step t103 (cl @p_129) :rule resolution :premises (t47 t102))
(step t104 (cl @p_126) :rule resolution :premises (t22 t103))
(step t105 (cl (not (! (= (! (=> (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1)))) (! (= (! (and (! (= @quantifiers_skolemize_34 @quantifiers_skolemize_33) :named @p_220) (! (= @quantifiers_skolemize_35 s$a) :named @p_219)) :named @p_221) @p_126) :named @p_222)) :named @p_223) (! (=> (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1)))) @p_209) :named @p_218)) :named @p_224)) (not @p_223) @p_218) :rule equiv_pos2)
(step t106 (cl (= @p_222 (! (= @p_126 @p_221) :named @p_225))) :rule rare_rewrite :args ("eq-symm" @p_221 @p_126))
(step t107 (cl (= @p_220 @p_207)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_34 @quantifiers_skolemize_33))
(step t108 (cl (= @p_219 @p_206)) :rule rare_rewrite :args ("eq-symm" @quantifiers_skolemize_35 s$a))
(step t109 (cl (= @p_221 @p_208)) :rule cong :premises (t107 t108))
(step t110 (cl (= @p_225 @p_209)) :rule cong :premises (t109))
(step t111 (cl (= @p_222 @p_209)) :rule trans :premises (t106 t110))
(step t112 (cl @p_224) :rule cong :premises (t111))
(step t113 (cl @p_223 (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :rule implies_neg1)
(anchor :step t114)
(assume t114.a0 (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1)))))
(step t114.t0 (cl (or (! (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :named @p_217) @p_222)) :rule forall_inst :args (@quantifiers_skolemize_34 @quantifiers_skolemize_35 @quantifiers_skolemize_33 s$a))
(step t114.t1 (cl @p_217 @p_222) :rule or :premises (t114.t0))
(step t114.t2 (cl (not (! (= (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (= (pair$g ?v0 ?v1) (pair$g ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3)))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :named @p_210)) (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (= (pair$g ?v0 ?v1) (pair$g ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t114.t3 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t114.t3.t0 (cl (= (! (= @p_175 @p_146) :named @p_214) (! (= @p_146 @p_175) :named @p_211))) :rule rare_rewrite :args ("eq-symm" @p_175 @p_146))
(step t114.t3.t1 (cl (= (! (and (= ?v0 ?v2) (= ?v1 ?v3)) :named @p_212) @p_212)) :rule refl)
(step t114.t3.t2 (cl (= (! (= @p_214 @p_212) :named @p_215) (! (= @p_211 @p_212) :named @p_216))) :rule cong :premises (t114.t3.t0 t114.t3.t1))
(step t114.t3.t3 (cl (= @p_216 (! (= @p_212 @p_211) :named @p_213))) :rule rare_rewrite :args ("eq-symm" @p_211 @p_212))
(step t114.t3.t4 (cl (= @p_215 @p_213)) :rule trans :premises (t114.t3.t2 t114.t3.t3))
(step t114.t3 (cl @p_210) :rule bind)
(step t114.t4 (cl (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :rule resolution :premises (t114.t2 t114.t3 a13))
(step t114.t5 (cl @p_222) :rule resolution :premises (t114.t1 t114.t4))
(step t114 (cl @p_217 @p_222) :rule subproof :discharge (t114.a0))
(step t115 (cl @p_223 @p_222) :rule resolution :premises (t113 t114))
(step t116 (cl @p_223 (not @p_222)) :rule implies_neg2)
(step t117 (cl @p_223 @p_223) :rule resolution :premises (t115 t116))
(step t118 (cl @p_223) :rule contraction :premises (t117))
(step t119 (cl @p_218) :rule resolution :premises (t105 t112 t118))
(step t120 (cl @p_217 @p_209) :rule implies :premises (t119))
(step t121 (cl (not @p_210) (not (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (= (pair$g ?v0 ?v1) (pair$g ?v2 ?v3)) (and (= ?v0 ?v2) (= ?v1 ?v3))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :rule equiv_pos2)
(anchor :step t122 :args ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1) (:= (?v2 I_a_state$) ?v2) (:= (?v3 I_a_state$) ?v3)))
(step t122.t0 (cl (= @p_214 @p_211)) :rule rare_rewrite :args ("eq-symm" @p_175 @p_146))
(step t122.t1 (cl (= @p_212 @p_212)) :rule refl)
(step t122.t2 (cl (= @p_215 @p_216)) :rule cong :premises (t122.t0 t122.t1))
(step t122.t3 (cl (= @p_216 @p_213)) :rule rare_rewrite :args ("eq-symm" @p_211 @p_212))
(step t122.t4 (cl (= @p_215 @p_213)) :rule trans :premises (t122.t2 t122.t3))
(step t122 (cl @p_210) :rule bind)
(step t123 (cl (forall ((?v0 I_a_state$) (?v1 I_a_state$) (?v2 I_a_state$) (?v3 I_a_state$)) (= (and (= ?v0 ?v2) (= ?v1 ?v3)) (= (pair$g ?v2 ?v3) (pair$g ?v0 ?v1))))) :rule resolution :premises (t121 t122 a13))
(step t124 (cl @p_209) :rule resolution :premises (t120 t123))
(step t125 (cl @p_208) :rule resolution :premises (t11 t104 t124))
(step t126 (cl @p_207) :rule resolution :premises (t9 t125))
(step t127 (cl (= @p_95 @p_120)) :rule cong :premises (t126))
(step t128 (cl @p_231 @p_206) :rule and_pos :args (1))
(step t129 (cl @p_206 @p_231) :rule reordering :premises (t128))
(step t130 (cl @p_206) :rule resolution :premises (t129 t125))
(step t131 (cl (= @p_96 @p_121)) :rule cong :premises (t127 t130))
(step t132 (cl (= (! (= @p_121 true) :named @p_122) @p_121)) :rule equiv_simplify)
(step t133 (cl @p_122 @p_123) :rule equiv2 :premises (t132))
(step t134 (cl (not (! (= (! (or @p_128 (! (not @p_123) :named @p_203)) :named @p_204) (! (or @p_128 @p_121) :named @p_202)) :named @p_205)) (not @p_204) @p_202) :rule equiv_pos2)
(step t135 (cl (= @p_203 @p_121)) :rule rare_rewrite :args ("bool-double-not-elim" @p_121))
(step t136 (cl @p_205) :rule cong :premises (t135))
(step t137 (cl @p_128 @p_203) :rule or_neg :args (1))
(step t138 (cl @p_204 @p_129) :rule or_neg :args (0))
(step t139 (cl @p_204 (not @p_203)) :rule or_neg :args (1))
(step t140 (cl @p_204 @p_204) :rule resolution :premises (t137 t138 t139))
(step t141 (cl @p_204) :rule contraction :premises (t140))
(step t142 (cl @p_202) :rule resolution :premises (t134 t136 t141))
(step t143 (cl @p_128 @p_121) :rule or :premises (t142))
(step t144 (cl @p_121 @p_128) :rule reordering :premises (t143))
(step t145 (cl @p_121) :rule resolution :premises (t144 t103))
(step t146 (cl @p_122) :rule resolution :premises (t133 t145))
(step t147 (cl @p_119) :rule trans :premises (t131 t146))
(step t148 (cl @p_96) :rule resolution :premises (t7 t147))
(step t149 (cl (or (! (not (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))) :named @p_118) @p_97)) :rule forall_inst :args (@quantifiers_skolemize_33 s$a))
(step t150 (cl @p_118 @p_97) :rule or :premises (t149))
(step t151 (cl (not (! (= (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (and (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))) :named @p_98)) (not (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (and (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0))))))))))) (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))) :rule equiv_pos2)
(anchor :step t152 :args ((?v0 I_a_state$) (?v1 I_a_state$) (:= (?v0 I_a_state$) ?v0) (:= (?v1 I_a_state$) ?v1)))
(step t152.t0 (cl (= (! (and (! (fun_app$ (! (fun_app$a gt_state$ ?v0) :named @p_34) ?v1) :named @p_102) (and (! (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (! (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) :named @p_31)) :named @p_101) (! (= (u_c$ ?v1) (! (u_c$ ?v0) :named @p_28)) :named @p_100))) :named @p_105) (! (and @p_102 @p_101 @p_100) :named @p_116))) :rule aci_simp)
(step t152.t1 (cl (= (! (and (! (tableau_valuated$ ?v0) :named @p_37) @p_105) :named @p_106) (! (and @p_37 @p_116) :named @p_117))) :rule cong :premises (t152.t0))
(step t152.t2 (cl (= @p_117 (! (and @p_37 @p_102 @p_101 @p_100) :named @p_114))) :rule aci_simp)
(step t152.t3 (cl (= @p_106 @p_114)) :rule trans :premises (t152.t1 t152.t2))
(step t152.t4 (cl (= (! (and (! (curr_val_satisfies_no_lhs$ ?v0) :named @p_39) @p_106) :named @p_107) (! (and @p_39 @p_114) :named @p_115))) :rule cong :premises (t152.t3))
(step t152.t5 (cl (= @p_115 (! (and @p_39 @p_37 @p_102 @p_101 @p_100) :named @p_112))) :rule aci_simp)
(step t152.t6 (cl (= @p_107 @p_112)) :rule trans :premises (t152.t4 t152.t5))
(step t152.t7 (cl (= (! (and (! (bounds_consistent$ ?v0) :named @p_41) @p_107) :named @p_108) (! (and @p_41 @p_112) :named @p_113))) :rule cong :premises (t152.t6))
(step t152.t8 (cl (= @p_113 (! (and @p_41 @p_39 @p_37 @p_102 @p_101 @p_100) :named @p_110))) :rule aci_simp)
(step t152.t9 (cl (= @p_108 @p_110)) :rule trans :premises (t152.t7 t152.t8))
(step t152.t10 (cl (= (! (and (! (normalized_tableau$ (t$ ?v0)) :named @p_43) @p_108) :named @p_109) (! (and @p_43 @p_110) :named @p_111))) :rule cong :premises (t152.t9))
(step t152.t11 (cl (= @p_111 (! (and @p_43 @p_41 @p_39 @p_37 @p_102 @p_101 @p_100) :named @p_103))) :rule aci_simp)
(step t152.t12 (cl (= @p_109 @p_103)) :rule trans :premises (t152.t10 t152.t11))
(step t152.t13 (cl (= (= (! (fun_app$ (fun_app$a uu$ ?v0) ?v1) :named @p_104) @p_109) (= @p_104 @p_103))) :rule cong :premises (t152.t12))
(step t152 (cl @p_98) :rule bind)
(step t153 (cl (forall ((?v0 I_a_state$) (?v1 I_a_state$)) (= (fun_app$ (fun_app$a uu$ ?v0) ?v1) (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) ?v1) (= (pair$ (b_i_l$ ?v1) (b_i_u$ ?v1)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ ?v1) (u_c$ ?v0)))))) :rule resolution :premises (t151 t152 a0))
(step t154 (cl @p_97) :rule resolution :premises (t150 t153))
(step t155 (cl @p_94) :rule resolution :premises (t5 t148 t154))
(step t156 (cl @p_8) :rule resolution :premises (t3 t155))
(step t157 (cl @p_234 @p_12) :rule and_pos :args (5))
(step t158 (cl @p_12 @p_234) :rule reordering :premises (t157))
(step t159 (cl @p_12) :rule resolution :premises (t158 t155))
(step t160 (cl @p_234 @p_22) :rule and_pos :args (0))
(step t161 (cl @p_22 @p_234) :rule reordering :premises (t160))
(step t162 (cl @p_22) :rule resolution :premises (t161 t155))
(step t163 (cl @p_234 @p_20) :rule and_pos :args (1))
(step t164 (cl @p_20 @p_234) :rule reordering :premises (t163))
(step t165 (cl @p_20) :rule resolution :premises (t164 t155))
(step t166 (cl @p_234 @p_18) :rule and_pos :args (2))
(step t167 (cl @p_18 @p_234) :rule reordering :premises (t166))
(step t168 (cl @p_18) :rule resolution :premises (t167 t155))
(step t169 (cl @p_234 @p_16) :rule and_pos :args (3))
(step t170 (cl @p_16 @p_234) :rule reordering :premises (t169))
(step t171 (cl @p_16) :rule resolution :premises (t170 t155))
(step t172 (cl @p_234 @p_14) :rule and_pos :args (4))
(step t173 (cl @p_14 @p_234) :rule reordering :premises (t172))
(step t174 (cl @p_14) :rule resolution :premises (t173 t155))
(step t175 (cl (not (! (= (! (=> (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))))) (! (or @p_23 @p_21 @p_19 @p_17 @p_15 (! (not (! (= @p_10 @p_11) :named @p_89)) :named @p_90) (! (not (! (= @p_6 @p_7) :named @p_87)) :named @p_88)) :named @p_91)) :named @p_92) (! (=> (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))))) @p_24) :named @p_86)) :named @p_93)) (not @p_92) @p_86) :rule equiv_pos2)
(step t176 (cl (= @p_89 @p_12)) :rule rare_rewrite :args ("eq-symm" @p_10 @p_11))
(step t177 (cl (= @p_90 @p_13)) :rule cong :premises (t176))
(step t178 (cl (= @p_87 @p_8)) :rule rare_rewrite :args ("eq-symm" @p_6 @p_7))
(step t179 (cl (= @p_88 @p_9)) :rule cong :premises (t178))
(step t180 (cl (= @p_91 @p_24)) :rule cong :premises (t177 t179))
(step t181 (cl @p_93) :rule cong :premises (t180))
(step t182 (cl @p_92 (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :rule implies_neg1)
(anchor :step t183)
(assume t183.a0 (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))))))
(step t183.t0 (cl (or (! (not (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :named @p_85) @p_91)) :rule forall_inst :args (@quantifiers_skolemize_33))
(step t183.t1 (cl @p_85 @p_91) :rule or :premises (t183.t0))
(step t183.t2 (cl (not (! (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a)))) (! (or @p_4 (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :named @p_25)) :named @p_26)) (not (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a))))) @p_25) :rule equiv_pos2)
(anchor :step t183.t3 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t183.t3.t0 (cl (= (! (and (! (fun_app$ @p_34 s$a) :named @p_35) (and (! (= @p_11 @p_31) :named @p_70) (! (= @p_7 @p_28) :named @p_69))) :named @p_71) (! (and @p_35 @p_70 @p_69) :named @p_83))) :rule aci_simp)
(step t183.t3.t1 (cl (= (! (and @p_37 @p_71) :named @p_72) (! (and @p_37 @p_83) :named @p_84))) :rule cong :premises (t183.t3.t0))
(step t183.t3.t2 (cl (= @p_84 (! (and @p_37 @p_35 @p_70 @p_69) :named @p_81))) :rule aci_simp)
(step t183.t3.t3 (cl (= @p_72 @p_81)) :rule trans :premises (t183.t3.t1 t183.t3.t2))
(step t183.t3.t4 (cl (= (! (and @p_39 @p_72) :named @p_73) (! (and @p_39 @p_81) :named @p_82))) :rule cong :premises (t183.t3.t3))
(step t183.t3.t5 (cl (= @p_82 (! (and @p_39 @p_37 @p_35 @p_70 @p_69) :named @p_79))) :rule aci_simp)
(step t183.t3.t6 (cl (= @p_73 @p_79)) :rule trans :premises (t183.t3.t4 t183.t3.t5))
(step t183.t3.t7 (cl (= (! (and @p_41 @p_73) :named @p_74) (! (and @p_41 @p_79) :named @p_80))) :rule cong :premises (t183.t3.t6))
(step t183.t3.t8 (cl (= @p_80 (! (and @p_41 @p_39 @p_37 @p_35 @p_70 @p_69) :named @p_77))) :rule aci_simp)
(step t183.t3.t9 (cl (= @p_74 @p_77)) :rule trans :premises (t183.t3.t7 t183.t3.t8))
(step t183.t3.t10 (cl (= (! (and @p_43 @p_74) :named @p_75) (! (and @p_43 @p_77) :named @p_78))) :rule cong :premises (t183.t3.t9))
(step t183.t3.t11 (cl (= @p_78 (! (and @p_43 @p_41 @p_39 @p_37 @p_35 @p_70 @p_69) :named @p_76))) :rule aci_simp)
(step t183.t3.t12 (cl (= @p_75 @p_76)) :rule trans :premises (t183.t3.t10 t183.t3.t11))
(step t183.t3.t13 (cl (= @p_70 (! (= @p_31 @p_11) :named @p_32))) :rule rare_rewrite :args ("eq-symm" @p_11 @p_31))
(step t183.t3.t14 (cl (= @p_69 (! (= @p_28 @p_7) :named @p_29))) :rule rare_rewrite :args ("eq-symm" @p_7 @p_28))
(step t183.t3.t15 (cl (= @p_76 (! (and @p_43 @p_41 @p_39 @p_37 @p_35 @p_32 @p_29) :named @p_47))) :rule cong :premises (t183.t3.t13 t183.t3.t14))
(step t183.t3.t16 (cl (= @p_75 @p_47)) :rule trans :premises (t183.t3.t12 t183.t3.t15))
(step t183.t3.t17 (cl (! (= @p_4 @p_4) :named @p_52)) :rule refl)
(step t183.t3.t18 (cl (= (=> @p_75 @p_4) (! (=> @p_47 @p_4) :named @p_48))) :rule cong :premises (t183.t3.t16 t183.t3.t17))
(step t183.t3 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))))) :rule bind)
(anchor :step t183.t4 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t183.t4.t0 (cl (= @p_48 (! (or (! (not @p_47) :named @p_49) @p_4) :named @p_50))) :rule rare_rewrite :args ("bool-impl-elim" @p_47 @p_4))
(step t183.t4.t1 (cl (= @p_49 (! (or (! (not @p_43) :named @p_44) (! (not (and @p_41 @p_39 @p_37 @p_35 @p_32 @p_29)) :named @p_59)) :named @p_60))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_43 @p_41 (rare-list @p_39 @p_37 @p_35 @p_32 @p_29)))
(step t183.t4.t2 (cl (= @p_59 (! (or (! (not @p_41) :named @p_42) (! (not (and @p_39 @p_37 @p_35 @p_32 @p_29)) :named @p_61)) :named @p_62))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_41 @p_39 (rare-list @p_37 @p_35 @p_32 @p_29)))
(step t183.t4.t3 (cl (= @p_61 (! (or (! (not @p_39) :named @p_40) (! (not (and @p_37 @p_35 @p_32 @p_29)) :named @p_63)) :named @p_64))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_39 @p_37 (rare-list @p_35 @p_32 @p_29)))
(step t183.t4.t4 (cl (= @p_63 (! (or (! (not @p_37) :named @p_38) (! (not (and @p_35 @p_32 @p_29)) :named @p_65)) :named @p_66))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_37 @p_35 (rare-list @p_32 @p_29)))
(step t183.t4.t5 (cl (= @p_65 (! (or (! (not @p_35) :named @p_36) (! (not (and @p_32 @p_29)) :named @p_67)) :named @p_68))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_35 @p_32 (rare-list @p_29)))
(step t183.t4.t6 (cl (= @p_67 (! (or (! (not @p_32) :named @p_33) (! (not @p_29) :named @p_30)) :named @p_53))) :rule rare_rewrite :args ("bool-and-de-morgan" @p_32 @p_29 rare-list))
(step t183.t4.t7 (cl (= @p_68 (! (or @p_36 @p_53) :named @p_54))) :rule cong :premises (t183.t4.t6))
(step t183.t4.t8 (cl (= @p_65 @p_54)) :rule trans :premises (t183.t4.t5 t183.t4.t7))
(step t183.t4.t9 (cl (= @p_66 (! (or @p_38 @p_54) :named @p_55))) :rule cong :premises (t183.t4.t8))
(step t183.t4.t10 (cl (= @p_63 @p_55)) :rule trans :premises (t183.t4.t4 t183.t4.t9))
(step t183.t4.t11 (cl (= @p_64 (! (or @p_40 @p_55) :named @p_56))) :rule cong :premises (t183.t4.t10))
(step t183.t4.t12 (cl (= @p_61 @p_56)) :rule trans :premises (t183.t4.t3 t183.t4.t11))
(step t183.t4.t13 (cl (= @p_62 (! (or @p_42 @p_56) :named @p_57))) :rule cong :premises (t183.t4.t12))
(step t183.t4.t14 (cl (= @p_59 @p_57)) :rule trans :premises (t183.t4.t2 t183.t4.t13))
(step t183.t4.t15 (cl (= @p_60 (! (or @p_44 @p_57) :named @p_58))) :rule cong :premises (t183.t4.t14))
(step t183.t4.t16 (cl (= @p_49 @p_58)) :rule trans :premises (t183.t4.t1 t183.t4.t15))
(step t183.t4.t17 (cl (= @p_58 (! (or @p_44 @p_42 @p_40 @p_38 @p_36 @p_33 @p_30) :named @p_45))) :rule aci_simp)
(step t183.t4.t18 (cl (= @p_49 @p_45)) :rule trans :premises (t183.t4.t16 t183.t4.t17))
(step t183.t4.t19 (cl @p_52) :rule refl)
(step t183.t4.t20 (cl (= @p_50 (! (or @p_45 @p_4) :named @p_51))) :rule cong :premises (t183.t4.t18 t183.t4.t19))
(step t183.t4.t21 (cl (= @p_51 (! (or @p_44 @p_42 @p_40 @p_38 @p_36 @p_33 @p_30 @p_4) :named @p_46))) :rule aci_simp)
(step t183.t4.t22 (cl (= @p_50 @p_46)) :rule trans :premises (t183.t4.t20 t183.t4.t21))
(step t183.t4.t23 (cl (= @p_48 @p_46)) :rule trans :premises (t183.t4.t0 t183.t4.t22))
(step t183.t4 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))))) :rule bind)
(anchor :step t183.t5 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t183.t5.t0 (cl (= @p_46 (or @p_4 @p_45))) :rule aci_simp)
(step t183.t5 (cl (= (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (or (normalized_tableau$ (t$ s$a)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))))) :rule bind)
(step t183.t6 (cl (= (forall ((?v0 I_a_state$)) (or (normalized_tableau$ (t$ s$a)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) @p_25)) :rule miniscope_split)
(step t183.t7 (cl (= (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) @p_25)) :rule trans :premises (t183.t5 t183.t6))
(step t183.t8 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) @p_25)) :rule trans :premises (t183.t4 t183.t7))
(step t183.t9 (cl @p_26) :rule trans :premises (t183.t3 t183.t8))
(step t183.t10 (cl @p_25) :rule resolution :premises (t183.t2 t183.t9 a32))
(step t183.t11 (cl @p_4 (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :rule or :premises (t183.t10))
(step t183.t12 (cl (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :rule resolution :premises (t183.t11 a33))
(step t183.t13 (cl @p_91) :rule resolution :premises (t183.t1 t183.t12))
(step t183 (cl @p_85 @p_91) :rule subproof :discharge (t183.a0))
(step t184 (cl @p_92 @p_91) :rule resolution :premises (t182 t183))
(step t185 (cl @p_92 (not @p_91)) :rule implies_neg2)
(step t186 (cl @p_92 @p_92) :rule resolution :premises (t184 t185))
(step t187 (cl @p_92) :rule contraction :premises (t186))
(step t188 (cl @p_86) :rule resolution :premises (t175 t181 t187))
(step t189 (cl @p_85 @p_24) :rule implies :premises (t188))
(step t190 (cl (not @p_26) (not (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a))))) @p_25) :rule equiv_pos2)
(anchor :step t191 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t191.t0 (cl (= @p_71 @p_83)) :rule aci_simp)
(step t191.t1 (cl (= @p_72 @p_84)) :rule cong :premises (t191.t0))
(step t191.t2 (cl (= @p_84 @p_81)) :rule aci_simp)
(step t191.t3 (cl (= @p_72 @p_81)) :rule trans :premises (t191.t1 t191.t2))
(step t191.t4 (cl (= @p_73 @p_82)) :rule cong :premises (t191.t3))
(step t191.t5 (cl (= @p_82 @p_79)) :rule aci_simp)
(step t191.t6 (cl (= @p_73 @p_79)) :rule trans :premises (t191.t4 t191.t5))
(step t191.t7 (cl (= @p_74 @p_80)) :rule cong :premises (t191.t6))
(step t191.t8 (cl (= @p_80 @p_77)) :rule aci_simp)
(step t191.t9 (cl (= @p_74 @p_77)) :rule trans :premises (t191.t7 t191.t8))
(step t191.t10 (cl (= @p_75 @p_78)) :rule cong :premises (t191.t9))
(step t191.t11 (cl (= @p_78 @p_76)) :rule aci_simp)
(step t191.t12 (cl (= @p_75 @p_76)) :rule trans :premises (t191.t10 t191.t11))
(step t191.t13 (cl (= @p_70 @p_32)) :rule rare_rewrite :args ("eq-symm" @p_11 @p_31))
(step t191.t14 (cl (= @p_69 @p_29)) :rule rare_rewrite :args ("eq-symm" @p_7 @p_28))
(step t191.t15 (cl (= @p_76 @p_47)) :rule cong :premises (t191.t13 t191.t14))
(step t191.t16 (cl (= @p_75 @p_47)) :rule trans :premises (t191.t12 t191.t15))
(step t191.t17 (cl @p_52) :rule refl)
(step t191.t18 (cl (= (=> @p_75 @p_4) @p_48)) :rule cong :premises (t191.t16 t191.t17))
(step t191 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (and (bounds_consistent$ ?v0) (and (curr_val_satisfies_no_lhs$ ?v0) (and (tableau_valuated$ ?v0) (and (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (and (= (pair$ (b_i_l$ s$a) (b_i_u$ s$a)) (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0))) (= (u_c$ s$a) (u_c$ ?v0)))))))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))))) :rule bind)
(anchor :step t192 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t192.t0 (cl (= @p_48 @p_50)) :rule rare_rewrite :args ("bool-impl-elim" @p_47 @p_4))
(step t192.t1 (cl (= @p_49 @p_60)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_43 @p_41 (rare-list @p_39 @p_37 @p_35 @p_32 @p_29)))
(step t192.t2 (cl (= @p_59 @p_62)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_41 @p_39 (rare-list @p_37 @p_35 @p_32 @p_29)))
(step t192.t3 (cl (= @p_61 @p_64)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_39 @p_37 (rare-list @p_35 @p_32 @p_29)))
(step t192.t4 (cl (= @p_63 @p_66)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_37 @p_35 (rare-list @p_32 @p_29)))
(step t192.t5 (cl (= @p_65 @p_68)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_35 @p_32 (rare-list @p_29)))
(step t192.t6 (cl (= @p_67 @p_53)) :rule rare_rewrite :args ("bool-and-de-morgan" @p_32 @p_29 rare-list))
(step t192.t7 (cl (= @p_68 @p_54)) :rule cong :premises (t192.t6))
(step t192.t8 (cl (= @p_65 @p_54)) :rule trans :premises (t192.t5 t192.t7))
(step t192.t9 (cl (= @p_66 @p_55)) :rule cong :premises (t192.t8))
(step t192.t10 (cl (= @p_63 @p_55)) :rule trans :premises (t192.t4 t192.t9))
(step t192.t11 (cl (= @p_64 @p_56)) :rule cong :premises (t192.t10))
(step t192.t12 (cl (= @p_61 @p_56)) :rule trans :premises (t192.t3 t192.t11))
(step t192.t13 (cl (= @p_62 @p_57)) :rule cong :premises (t192.t12))
(step t192.t14 (cl (= @p_59 @p_57)) :rule trans :premises (t192.t2 t192.t13))
(step t192.t15 (cl (= @p_60 @p_58)) :rule cong :premises (t192.t14))
(step t192.t16 (cl (= @p_49 @p_58)) :rule trans :premises (t192.t1 t192.t15))
(step t192.t17 (cl (= @p_58 @p_45)) :rule aci_simp)
(step t192.t18 (cl (= @p_49 @p_45)) :rule trans :premises (t192.t16 t192.t17))
(step t192.t19 (cl @p_52) :rule refl)
(step t192.t20 (cl (= @p_50 @p_51)) :rule cong :premises (t192.t18 t192.t19))
(step t192.t21 (cl (= @p_51 @p_46)) :rule aci_simp)
(step t192.t22 (cl (= @p_50 @p_46)) :rule trans :premises (t192.t20 t192.t21))
(step t192.t23 (cl (= @p_48 @p_46)) :rule trans :premises (t192.t0 t192.t22))
(step t192 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))))) :rule bind)
(anchor :step t193 :args ((?v0 I_a_state$) (:= (?v0 I_a_state$) ?v0)))
(step t193.t0 (cl (= @p_46 (or @p_4 @p_45))) :rule aci_simp)
(step t193 (cl (= (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) (forall ((?v0 I_a_state$)) (or (normalized_tableau$ (t$ s$a)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))))) :rule bind)
(step t194 (cl (= (forall ((?v0 I_a_state$)) (or (normalized_tableau$ (t$ s$a)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) @p_25)) :rule miniscope_split)
(step t195 (cl (= (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) @p_25)) :rule trans :premises (t193 t194))
(step t196 (cl (= (forall ((?v0 I_a_state$)) (=> (and (normalized_tableau$ (t$ ?v0)) (bounds_consistent$ ?v0) (curr_val_satisfies_no_lhs$ ?v0) (tableau_valuated$ ?v0) (fun_app$ (fun_app$a gt_state$ ?v0) s$a) (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a))) (= (u_c$ ?v0) (u_c$ s$a))) (normalized_tableau$ (t$ s$a)))) @p_25)) :rule trans :premises (t192 t195))
(step t197 (cl @p_26) :rule trans :premises (t191 t196))
(step t198 (cl @p_25) :rule resolution :premises (t190 t197 a32))
(step t199 (cl @p_4 (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :rule or :premises (t198))
(step t200 (cl (forall ((?v0 I_a_state$)) (or (not (normalized_tableau$ (t$ ?v0))) (not (bounds_consistent$ ?v0)) (not (curr_val_satisfies_no_lhs$ ?v0)) (not (tableau_valuated$ ?v0)) (not (fun_app$ (fun_app$a gt_state$ ?v0) s$a)) (not (= (pair$ (b_i_l$ ?v0) (b_i_u$ ?v0)) (pair$ (b_i_l$ s$a) (b_i_u$ s$a)))) (not (= (u_c$ ?v0) (u_c$ s$a)))))) :rule resolution :premises (t199 a33))
(step t201 (cl @p_24) :rule resolution :premises (t189 t200))
(step t202 (cl) :rule resolution :premises (t1 t156 t159 t162 t165 t168 t171 t174 t201))
)