src/HOL/SMT_Examples/SMT_Examples_Verit.certs

--- a/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Fri Oct 01 12:45:47 2021 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Fri Oct 01 22:35:32 2021 +0200
@@ -111,6 +111,45 @@
 (step t26 (cl false) :rule th_resolution :premises (a0 t22 t25))
 (step t27 (cl (not false)) :rule false)
 (step t28 (cl) :rule resolution :premises (t26 t27))
+a331481eed4f18a666baadda4e1010ca7a295ccf 38 0
+unsat
+(assume a0 (! (forall ((?v0 A$) (?v1 A$)) (! (= (! (symm_f$ ?v0 ?v1) :named @p_2) (! (symm_f$ ?v1 ?v0) :named @p_6)) :named @p_8)) :named @p_1))
+(assume a1 (! (not (! (and (! (= a$ a$) :named @p_19) (! (= (symm_f$ a$ b$) (symm_f$ b$ a$)) :named @p_21)) :named @p_20)) :named @p_24))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 A$) veriT_vr1)))
+(step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl)
+(step t3.t2 (cl (! (= ?v1 veriT_vr1) :named @p_4)) :rule refl)
+(step t3.t3 (cl (= @p_2 (! (symm_f$ veriT_vr0 veriT_vr1) :named @p_3))) :rule cong :premises (t3.t1 t3.t2))
+(step t3.t4 (cl @p_4) :rule refl)
+(step t3.t5 (cl @p_5) :rule refl)
+(step t3.t6 (cl (= @p_6 (! (symm_f$ veriT_vr1 veriT_vr0) :named @p_7))) :rule cong :premises (t3.t4 t3.t5))
+(step t3.t7 (cl (= @p_8 (! (= @p_3 @p_7) :named @p_9))) :rule cong :premises (t3.t3 t3.t6))
+(step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$) (veriT_vr1 A$)) @p_9) :named @p_11)) :named @p_10)) :rule bind)
+(step t4 (cl (not @p_10) (not @p_1) @p_11) :rule equiv_pos2)
+(step t5 (cl @p_11) :rule th_resolution :premises (a0 t3 t4))
+(anchor :step t6 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 A$) veriT_vr3)))
+(step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_14)) :rule refl)
+(step t6.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_13)) :rule refl)
+(step t6.t3 (cl (= @p_3 (! (symm_f$ veriT_vr2 veriT_vr3) :named @p_12))) :rule cong :premises (t6.t1 t6.t2))
+(step t6.t4 (cl @p_13) :rule refl)
+(step t6.t5 (cl @p_14) :rule refl)
+(step t6.t6 (cl (= @p_7 (! (symm_f$ veriT_vr3 veriT_vr2) :named @p_15))) :rule cong :premises (t6.t4 t6.t5))
+(step t6.t7 (cl (= @p_9 (! (= @p_12 @p_15) :named @p_16))) :rule cong :premises (t6.t3 t6.t6))
+(step t6 (cl (! (= @p_11 (! (forall ((veriT_vr2 A$) (veriT_vr3 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
+(step t7 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2)
+(step t8 (cl @p_18) :rule th_resolution :premises (t5 t6 t7))
+(step t9 (cl (= @p_19 true)) :rule eq_simplify)
+(step t10 (cl (= @p_20 (! (and true @p_21) :named @p_22))) :rule cong :premises (t9))
+(step t11 (cl (= @p_22 (! (and @p_21) :named @p_23))) :rule and_simplify)
+(step t12 (cl (= @p_23 @p_21)) :rule and_simplify)
+(step t13 (cl (= @p_20 @p_21)) :rule trans :premises (t10 t11 t12))
+(step t14 (cl (! (= @p_24 (! (not @p_21) :named @p_26)) :named @p_25)) :rule cong :premises (t13))
+(step t15 (cl (! (not @p_25) :named @p_28) (! (not @p_24) :named @p_27) @p_26) :rule equiv_pos2)
+(step t16 (cl (not @p_27) @p_20) :rule not_not)
+(step t17 (cl @p_28 @p_20 @p_26) :rule th_resolution :premises (t16 t15))
+(step t18 (cl @p_26) :rule th_resolution :premises (a1 t14 t17))
+(step t19 (cl (or (! (not @p_18) :named @p_29) @p_21)) :rule forall_inst :args ((:= veriT_vr2 a$) (:= veriT_vr3 b$)))
+(step t20 (cl @p_29 @p_21) :rule or :premises (t19))
+(step t21 (cl) :rule resolution :premises (t20 t8 t18))
 ef250e7a4e9499952e8416cff69ed029a37c7aa3 59 0
 unsat
 (assume a0 (! (or a$ (or b$ (or c$ d$))) :named @p_1))
@@ -171,45 +210,71 @@
 (step t56 (cl @p_26) :rule resolution :premises (t54 t50))
 (step t57 (cl a$) :rule resolution :premises (t51 t55 t50 t56))
 (step t58 (cl) :rule resolution :premises (t52 t55 t57))
-a331481eed4f18a666baadda4e1010ca7a295ccf 38 0
+a73b15b00e6e103b31fc48e963d878be9038a417 64 0
 unsat
-(assume a0 (! (forall ((?v0 A$) (?v1 A$)) (! (= (! (symm_f$ ?v0 ?v1) :named @p_2) (! (symm_f$ ?v1 ?v0) :named @p_6)) :named @p_8)) :named @p_1))
-(assume a1 (! (not (! (and (! (= a$ a$) :named @p_19) (! (= (symm_f$ a$ b$) (symm_f$ b$ a$)) :named @p_21)) :named @p_20)) :named @p_24))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
-(step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl)
-(step t3.t2 (cl (! (= ?v1 veriT_vr1) :named @p_4)) :rule refl)
-(step t3.t3 (cl (= @p_2 (! (symm_f$ veriT_vr0 veriT_vr1) :named @p_3))) :rule cong :premises (t3.t1 t3.t2))
-(step t3.t4 (cl @p_4) :rule refl)
-(step t3.t5 (cl @p_5) :rule refl)
-(step t3.t6 (cl (= @p_6 (! (symm_f$ veriT_vr1 veriT_vr0) :named @p_7))) :rule cong :premises (t3.t4 t3.t5))
-(step t3.t7 (cl (= @p_8 (! (= @p_3 @p_7) :named @p_9))) :rule cong :premises (t3.t3 t3.t6))
-(step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$) (veriT_vr1 A$)) @p_9) :named @p_11)) :named @p_10)) :rule bind)
-(step t4 (cl (not @p_10) (not @p_1) @p_11) :rule equiv_pos2)
-(step t5 (cl @p_11) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
-(step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_14)) :rule refl)
-(step t6.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_13)) :rule refl)
-(step t6.t3 (cl (= @p_3 (! (symm_f$ veriT_vr2 veriT_vr3) :named @p_12))) :rule cong :premises (t6.t1 t6.t2))
-(step t6.t4 (cl @p_13) :rule refl)
-(step t6.t5 (cl @p_14) :rule refl)
-(step t6.t6 (cl (= @p_7 (! (symm_f$ veriT_vr3 veriT_vr2) :named @p_15))) :rule cong :premises (t6.t4 t6.t5))
-(step t6.t7 (cl (= @p_9 (! (= @p_12 @p_15) :named @p_16))) :rule cong :premises (t6.t3 t6.t6))
-(step t6 (cl (! (= @p_11 (! (forall ((veriT_vr2 A$) (veriT_vr3 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
-(step t7 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2)
-(step t8 (cl @p_18) :rule th_resolution :premises (t5 t6 t7))
-(step t9 (cl (= @p_19 true)) :rule eq_simplify)
-(step t10 (cl (= @p_20 (! (and true @p_21) :named @p_22))) :rule cong :premises (t9))
-(step t11 (cl (= @p_22 (! (and @p_21) :named @p_23))) :rule and_simplify)
-(step t12 (cl (= @p_23 @p_21)) :rule and_simplify)
-(step t13 (cl (= @p_20 @p_21)) :rule trans :premises (t10 t11 t12))
-(step t14 (cl (! (= @p_24 (! (not @p_21) :named @p_26)) :named @p_25)) :rule cong :premises (t13))
-(step t15 (cl (! (not @p_25) :named @p_28) (! (not @p_24) :named @p_27) @p_26) :rule equiv_pos2)
-(step t16 (cl (not @p_27) @p_20) :rule not_not)
-(step t17 (cl @p_28 @p_20 @p_26) :rule th_resolution :premises (t16 t15))
-(step t18 (cl @p_26) :rule th_resolution :premises (a1 t14 t17))
-(step t19 (cl (or (! (not @p_18) :named @p_29) @p_21)) :rule forall_inst :args ((:= veriT_vr2 a$) (:= veriT_vr3 b$)))
-(step t20 (cl @p_29 @p_21) :rule or :premises (t19))
-(step t21 (cl) :rule resolution :premises (t20 t8 t18))
+(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (! (=> (! (p$ veriT_vr2) :named @p_20) (! (forall ((veriT_vr3 Int)) (! (or @p_20 (! (p$ veriT_vr3) :named @p_24)) :named @p_25)) :named @p_21)) :named @p_26))) :named @p_33))
+(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (p$ @p_33) @p_24))) :named @p_37))
+(assume a0 (! (not (! (forall ((?v0 Int)) (! (=> (! (p$ ?v0) :named @p_1) (! (forall ((?v1 Int)) (! (or @p_1 (! (p$ ?v1) :named @p_8)) :named @p_10)) :named @p_4)) :named @p_12)) :named @p_2)) :named @p_14))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
+(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
+(step t2.t2 (cl (! (= @p_1 (! (p$ veriT_vr0) :named @p_3)) :named @p_7)) :rule cong :premises (t2.t1))
+(anchor :step t2.t3 :args ((:= (?v1 Int) veriT_vr1)))
+(step t2.t3.t1 (cl @p_6) :rule refl)
+(step t2.t3.t2 (cl @p_7) :rule cong :premises (t2.t3.t1))
+(step t2.t3.t3 (cl (= ?v1 veriT_vr1)) :rule refl)
+(step t2.t3.t4 (cl (= @p_8 (! (p$ veriT_vr1) :named @p_9))) :rule cong :premises (t2.t3.t3))
+(step t2.t3.t5 (cl (= @p_10 (! (or @p_3 @p_9) :named @p_11))) :rule cong :premises (t2.t3.t2 t2.t3.t4))
+(step t2.t3 (cl (= @p_4 (! (forall ((veriT_vr1 Int)) @p_11) :named @p_5))) :rule bind)
+(step t2.t4 (cl (= @p_12 (! (=> @p_3 @p_5) :named @p_13))) :rule cong :premises (t2.t2 t2.t3))
+(step t2 (cl (= @p_2 (! (forall ((veriT_vr0 Int)) @p_13) :named @p_15))) :rule bind)
+(step t3 (cl (! (= @p_14 (! (not @p_15) :named @p_17)) :named @p_16)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_16) :named @p_19) (! (not @p_14) :named @p_18) @p_17) :rule equiv_pos2)
+(step t5 (cl (not @p_18) @p_2) :rule not_not)
+(step t6 (cl @p_19 @p_2 @p_17) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_17) :rule th_resolution :premises (a0 t3 t6))
+(anchor :step t8 :args ((:= (veriT_vr0 Int) veriT_vr2)))
+(step t8.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_22)) :rule refl)
+(step t8.t2 (cl (! (= @p_3 @p_20) :named @p_23)) :rule cong :premises (t8.t1))
+(anchor :step t8.t3 :args ((:= (veriT_vr1 Int) veriT_vr3)))
+(step t8.t3.t1 (cl @p_22) :rule refl)
+(step t8.t3.t2 (cl @p_23) :rule cong :premises (t8.t3.t1))
+(step t8.t3.t3 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
+(step t8.t3.t4 (cl (= @p_9 @p_24)) :rule cong :premises (t8.t3.t3))
+(step t8.t3.t5 (cl (= @p_11 @p_25)) :rule cong :premises (t8.t3.t2 t8.t3.t4))
+(step t8.t3 (cl (= @p_5 @p_21)) :rule bind)
+(step t8.t4 (cl (= @p_13 @p_26)) :rule cong :premises (t8.t2 t8.t3))
+(step t8 (cl (= @p_15 (! (forall ((veriT_vr2 Int)) @p_26) :named @p_27))) :rule bind)
+(step t9 (cl (! (= @p_17 (! (not @p_27) :named @p_29)) :named @p_28)) :rule cong :premises (t8))
+(step t10 (cl (! (not @p_28) :named @p_31) (! (not @p_17) :named @p_30) @p_29) :rule equiv_pos2)
+(step t11 (cl (not @p_30) @p_15) :rule not_not)
+(step t12 (cl @p_31 @p_15 @p_29) :rule th_resolution :premises (t11 t10))
+(step t13 (cl @p_29) :rule th_resolution :premises (t7 t9 t12))
+(anchor :step t14 :args ((:= (veriT_vr2 Int) veriT_sk0)))
+(step t14.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_35)) :rule refl)
+(step t14.t2 (cl (! (= @p_20 (! (p$ veriT_sk0) :named @p_32)) :named @p_36)) :rule cong :premises (t14.t1))
+(anchor :step t14.t3 :args ((:= (veriT_vr3 Int) veriT_sk1)))
+(step t14.t3.t1 (cl @p_35) :rule refl)
+(step t14.t3.t2 (cl @p_36) :rule cong :premises (t14.t3.t1))
+(step t14.t3.t3 (cl (= veriT_vr3 veriT_sk1)) :rule refl)
+(step t14.t3.t4 (cl (= @p_24 (! (p$ veriT_sk1) :named @p_38))) :rule cong :premises (t14.t3.t3))
+(step t14.t3.t5 (cl (= @p_25 (! (or @p_32 @p_38) :named @p_34))) :rule cong :premises (t14.t3.t2 t14.t3.t4))
+(step t14.t3 (cl (= @p_21 @p_34)) :rule sko_forall)
+(step t14.t4 (cl (= @p_26 (! (=> @p_32 @p_34) :named @p_39))) :rule cong :premises (t14.t2 t14.t3))
+(step t14 (cl (= @p_27 @p_39)) :rule sko_forall)
+(step t15 (cl (! (= @p_29 (! (not @p_39) :named @p_41)) :named @p_40)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_40) :named @p_43) (! (not @p_29) :named @p_42) @p_41) :rule equiv_pos2)
+(step t17 (cl (not @p_42) @p_27) :rule not_not)
+(step t18 (cl @p_43 @p_27 @p_41) :rule th_resolution :premises (t17 t16))
+(step t19 (cl @p_41) :rule th_resolution :premises (t13 t15 t18))
+(step t20 (cl (! (= @p_41 (! (and @p_32 (! (not @p_34) :named @p_48)) :named @p_45)) :named @p_44)) :rule bool_simplify)
+(step t21 (cl (! (not @p_44) :named @p_47) (! (not @p_41) :named @p_46) @p_45) :rule equiv_pos2)
+(step t22 (cl (not @p_46) @p_39) :rule not_not)
+(step t23 (cl @p_47 @p_39 @p_45) :rule th_resolution :premises (t22 t21))
+(step t24 (cl @p_45) :rule th_resolution :premises (t19 t20 t23))
+(step t25 (cl @p_32) :rule and :premises (t24))
+(step t26 (cl @p_48) :rule and :premises (t24))
+(step t27 (cl (not @p_32)) :rule not_or :premises (t26))
+(step t28 (cl) :rule resolution :premises (t27 t25))
 a5b152c08be1e0a4da353f094af8f11f36a16f52 333 0
 unsat
 (assume a0 (not x0$))
@@ -544,71 +609,6 @@
 (step t330 (cl x36$) :rule resolution :premises (t159 t328))
 (step t331 (cl x42$) :rule resolution :premises (t287 t329))
 (step t332 (cl) :rule resolution :premises (t201 t330 t331))
-a73b15b00e6e103b31fc48e963d878be9038a417 64 0
-unsat
-(define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (! (=> (! (p$ veriT_vr2) :named @p_20) (! (forall ((veriT_vr3 Int)) (! (or @p_20 (! (p$ veriT_vr3) :named @p_24)) :named @p_25)) :named @p_21)) :named @p_26))) :named @p_33))
-(define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (p$ @p_33) @p_24))) :named @p_37))
-(assume a0 (! (not (! (forall ((?v0 Int)) (! (=> (! (p$ ?v0) :named @p_1) (! (forall ((?v1 Int)) (! (or @p_1 (! (p$ ?v1) :named @p_8)) :named @p_10)) :named @p_4)) :named @p_12)) :named @p_2)) :named @p_14))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0)))
-(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
-(step t2.t2 (cl (! (= @p_1 (! (p$ veriT_vr0) :named @p_3)) :named @p_7)) :rule cong :premises (t2.t1))
-(anchor :step t2.t3 :args ((:= ?v1 veriT_vr1)))
-(step t2.t3.t1 (cl @p_6) :rule refl)
-(step t2.t3.t2 (cl @p_7) :rule cong :premises (t2.t3.t1))
-(step t2.t3.t3 (cl (= ?v1 veriT_vr1)) :rule refl)
-(step t2.t3.t4 (cl (= @p_8 (! (p$ veriT_vr1) :named @p_9))) :rule cong :premises (t2.t3.t3))
-(step t2.t3.t5 (cl (= @p_10 (! (or @p_3 @p_9) :named @p_11))) :rule cong :premises (t2.t3.t2 t2.t3.t4))
-(step t2.t3 (cl (= @p_4 (! (forall ((veriT_vr1 Int)) @p_11) :named @p_5))) :rule bind)
-(step t2.t4 (cl (= @p_12 (! (=> @p_3 @p_5) :named @p_13))) :rule cong :premises (t2.t2 t2.t3))
-(step t2 (cl (= @p_2 (! (forall ((veriT_vr0 Int)) @p_13) :named @p_15))) :rule bind)
-(step t3 (cl (! (= @p_14 (! (not @p_15) :named @p_17)) :named @p_16)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_16) :named @p_19) (! (not @p_14) :named @p_18) @p_17) :rule equiv_pos2)
-(step t5 (cl (not @p_18) @p_2) :rule not_not)
-(step t6 (cl @p_19 @p_2 @p_17) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_17) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args ((:= veriT_vr0 veriT_vr2)))
-(step t8.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_22)) :rule refl)
-(step t8.t2 (cl (! (= @p_3 @p_20) :named @p_23)) :rule cong :premises (t8.t1))
-(anchor :step t8.t3 :args ((:= veriT_vr1 veriT_vr3)))
-(step t8.t3.t1 (cl @p_22) :rule refl)
-(step t8.t3.t2 (cl @p_23) :rule cong :premises (t8.t3.t1))
-(step t8.t3.t3 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
-(step t8.t3.t4 (cl (= @p_9 @p_24)) :rule cong :premises (t8.t3.t3))
-(step t8.t3.t5 (cl (= @p_11 @p_25)) :rule cong :premises (t8.t3.t2 t8.t3.t4))
-(step t8.t3 (cl (= @p_5 @p_21)) :rule bind)
-(step t8.t4 (cl (= @p_13 @p_26)) :rule cong :premises (t8.t2 t8.t3))
-(step t8 (cl (= @p_15 (! (forall ((veriT_vr2 Int)) @p_26) :named @p_27))) :rule bind)
-(step t9 (cl (! (= @p_17 (! (not @p_27) :named @p_29)) :named @p_28)) :rule cong :premises (t8))
-(step t10 (cl (! (not @p_28) :named @p_31) (! (not @p_17) :named @p_30) @p_29) :rule equiv_pos2)
-(step t11 (cl (not @p_30) @p_15) :rule not_not)
-(step t12 (cl @p_31 @p_15 @p_29) :rule th_resolution :premises (t11 t10))
-(step t13 (cl @p_29) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr2 veriT_sk0)))
-(step t14.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_35)) :rule refl)
-(step t14.t2 (cl (! (= @p_20 (! (p$ veriT_sk0) :named @p_32)) :named @p_36)) :rule cong :premises (t14.t1))
-(anchor :step t14.t3 :args ((:= veriT_vr3 veriT_sk1)))
-(step t14.t3.t1 (cl @p_35) :rule refl)
-(step t14.t3.t2 (cl @p_36) :rule cong :premises (t14.t3.t1))
-(step t14.t3.t3 (cl (= veriT_vr3 veriT_sk1)) :rule refl)
-(step t14.t3.t4 (cl (= @p_24 (! (p$ veriT_sk1) :named @p_38))) :rule cong :premises (t14.t3.t3))
-(step t14.t3.t5 (cl (= @p_25 (! (or @p_32 @p_38) :named @p_34))) :rule cong :premises (t14.t3.t2 t14.t3.t4))
-(step t14.t3 (cl (= @p_21 @p_34)) :rule sko_forall)
-(step t14.t4 (cl (= @p_26 (! (=> @p_32 @p_34) :named @p_39))) :rule cong :premises (t14.t2 t14.t3))
-(step t14 (cl (= @p_27 @p_39)) :rule sko_forall)
-(step t15 (cl (! (= @p_29 (! (not @p_39) :named @p_41)) :named @p_40)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_40) :named @p_43) (! (not @p_29) :named @p_42) @p_41) :rule equiv_pos2)
-(step t17 (cl (not @p_42) @p_27) :rule not_not)
-(step t18 (cl @p_43 @p_27 @p_41) :rule th_resolution :premises (t17 t16))
-(step t19 (cl @p_41) :rule th_resolution :premises (t13 t15 t18))
-(step t20 (cl (! (= @p_41 (! (and @p_32 (! (not @p_34) :named @p_48)) :named @p_45)) :named @p_44)) :rule bool_simplify)
-(step t21 (cl (! (not @p_44) :named @p_47) (! (not @p_41) :named @p_46) @p_45) :rule equiv_pos2)
-(step t22 (cl (not @p_46) @p_39) :rule not_not)
-(step t23 (cl @p_47 @p_39 @p_45) :rule th_resolution :premises (t22 t21))
-(step t24 (cl @p_45) :rule th_resolution :premises (t19 t20 t23))
-(step t25 (cl @p_32) :rule and :premises (t24))
-(step t26 (cl @p_48) :rule and :premises (t24))
-(step t27 (cl (not @p_32)) :rule not_or :premises (t26))
-(step t28 (cl) :rule resolution :premises (t27 t25))
 9024ca3fa3536be727200e6a5ffc1df778e7e505 155 0
 unsat
 (define-fun veriT_sk0 () A$ (! (choice ((veriT_vr3 A$)) (! (ite x$ (! (p$ true veriT_vr3) :named @p_48) (! (p$ false veriT_vr3) :named @p_50)) :named @p_51)) :named @p_62))
@@ -616,7 +616,7 @@
 (assume a1 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
 (step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (a0))
 (step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (! (p$ false c$) :named @p_93)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (a1))
-(anchor :step t5 :args ((:= ?v1 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v1 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v1 veriT_vr0) :named @p_6)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (p$ false veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
 (step t5.t3 (cl (= @p_4 (! (= @p_3 false) :named @p_5))) :rule cong :premises (t5.t2))
@@ -627,14 +627,14 @@
 (step t5 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$)) @p_12) :named @p_14)) :named @p_13)) :rule bind)
 (step t6 (cl (not @p_13) (not @p_1) @p_14) :rule equiv_pos2)
 (step t7 (cl @p_14) :rule th_resolution :premises (t3 t5 t6))
-(anchor :step t8 :args (veriT_vr0))
+(anchor :step t8 :args ((veriT_vr0 A$)))
 (step t8.t1 (cl (= @p_5 (! (not @p_3) :named @p_15))) :rule equiv_simplify)
 (step t8.t2 (cl (= @p_10 @p_8)) :rule equiv_simplify)
 (step t8.t3 (cl (= @p_12 (! (and @p_15 @p_8) :named @p_16))) :rule cong :premises (t8.t1 t8.t2))
 (step t8 (cl (! (= @p_14 (! (forall ((veriT_vr0 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
 (step t9 (cl (not @p_17) (not @p_14) @p_18) :rule equiv_pos2)
 (step t10 (cl @p_18) :rule th_resolution :premises (t7 t8 t9))
-(anchor :step t11 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t11 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t11.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_21)) :rule refl)
 (step t11.t2 (cl (= @p_3 (! (p$ false veriT_vr1) :named @p_19))) :rule cong :premises (t11.t1))
 (step t11.t3 (cl (= @p_15 (! (not @p_19) :named @p_20))) :rule cong :premises (t11.t2))
@@ -644,7 +644,7 @@
 (step t11 (cl (! (= @p_18 (! (forall ((veriT_vr1 A$)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
 (step t12 (cl (not @p_24) (not @p_18) @p_25) :rule equiv_pos2)
 (step t13 (cl @p_25) :rule th_resolution :premises (t10 t11 t12))
-(anchor :step t14 :args ((:= ?v0 veriT_vr2)))
+(anchor :step t14 :args ((:= (?v0 A$) veriT_vr2)))
 (step t14.t1 (cl (! (= ?v0 veriT_vr2) :named @p_29)) :rule refl)
 (step t14.t2 (cl (= @p_27 (! (p$ true veriT_vr2) :named @p_28))) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_29) :rule refl)
@@ -663,7 +663,7 @@
 (step t24 (cl (not @p_46) @p_38) :rule not_not)
 (step t25 (cl @p_47 @p_38 @p_45) :rule th_resolution :premises (t24 t23))
 (step t26 (cl @p_45) :rule th_resolution :premises (t20 t22 t25))
-(anchor :step t27 :args ((:= veriT_vr2 veriT_vr3)))
+(anchor :step t27 :args ((:= (veriT_vr2 A$) veriT_vr3)))
 (step t27.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_49)) :rule refl)
 (step t27.t2 (cl (= @p_28 @p_48)) :rule cong :premises (t27.t1))
 (step t27.t3 (cl @p_49) :rule refl)
@@ -678,7 +678,7 @@
 (step t33 (cl (not @p_60) @p_43) :rule not_not)
 (step t34 (cl @p_61 @p_43 @p_59) :rule th_resolution :premises (t33 t32))
 (step t35 (cl @p_59) :rule th_resolution :premises (t26 t31 t34))
-(anchor :step t36 :args ((:= veriT_vr3 veriT_sk0)))
+(anchor :step t36 :args ((:= (veriT_vr3 A$) veriT_sk0)))
 (step t36.t1 (cl (! (= veriT_vr3 veriT_sk0) :named @p_64)) :rule refl)
 (step t36.t2 (cl (= @p_48 (! (p$ true veriT_sk0) :named @p_63))) :rule cong :premises (t36.t1))
 (step t36.t3 (cl @p_64) :rule refl)
@@ -692,7 +692,7 @@
 (step t41 (cl (not @p_71) @p_57) :rule not_not)
 (step t42 (cl @p_72 @p_57 @p_70) :rule th_resolution :premises (t41 t40))
 (step t43 (cl @p_70) :rule th_resolution :premises (t35 t39 t42))
-(anchor :step t44 :args ((:= veriT_vr3 veriT_vr4)))
+(anchor :step t44 :args ((:= (veriT_vr3 A$) veriT_vr4)))
 (step t44.t1 (cl (! (= veriT_vr3 veriT_vr4) :named @p_74)) :rule refl)
 (step t44.t2 (cl (= @p_48 (! (p$ true veriT_vr4) :named @p_73))) :rule cong :premises (t44.t1))
 (step t44.t3 (cl @p_74) :rule refl)
@@ -772,7 +772,7 @@
 (assume a2 (not (= (exists ((?v0 A$)) (p$ x$ ?v0)) (p$ x$ c$))))
 (step t3 (cl (! (forall ((?v1 A$)) (! (and (! (= (! (p$ false ?v1) :named @p_2) false) :named @p_4) (! (= (! (p$ true ?v1) :named @p_7) true) :named @p_9)) :named @p_11)) :named @p_1)) :rule bfun_elim :premises (a0))
 (step t4 (cl (! (not (! (= (! (exists ((?v0 A$)) (! (ite x$ (! (p$ true ?v0) :named @p_27) (! (p$ false ?v0) :named @p_30)) :named @p_32)) :named @p_26) (! (ite x$ (! (p$ true c$) :named @p_91) (p$ false c$)) :named @p_36)) :named @p_34)) :named @p_37)) :rule bfun_elim :premises (a2))
-(anchor :step t5 :args ((:= ?v1 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v1 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v1 veriT_vr0) :named @p_6)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (p$ false veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
 (step t5.t3 (cl (= @p_4 (! (= @p_3 false) :named @p_5))) :rule cong :premises (t5.t2))
@@ -783,14 +783,14 @@
 (step t5 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$)) @p_12) :named @p_14)) :named @p_13)) :rule bind)
 (step t6 (cl (not @p_13) (not @p_1) @p_14) :rule equiv_pos2)
 (step t7 (cl @p_14) :rule th_resolution :premises (t3 t5 t6))
-(anchor :step t8 :args (veriT_vr0))
+(anchor :step t8 :args ((veriT_vr0 A$)))
 (step t8.t1 (cl (= @p_5 (! (not @p_3) :named @p_15))) :rule equiv_simplify)
 (step t8.t2 (cl (= @p_10 @p_8)) :rule equiv_simplify)
 (step t8.t3 (cl (= @p_12 (! (and @p_15 @p_8) :named @p_16))) :rule cong :premises (t8.t1 t8.t2))
 (step t8 (cl (! (= @p_14 (! (forall ((veriT_vr0 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
 (step t9 (cl (not @p_17) (not @p_14) @p_18) :rule equiv_pos2)
 (step t10 (cl @p_18) :rule th_resolution :premises (t7 t8 t9))
-(anchor :step t11 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t11 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t11.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_21)) :rule refl)
 (step t11.t2 (cl (= @p_3 (! (p$ false veriT_vr1) :named @p_19))) :rule cong :premises (t11.t1))
 (step t11.t3 (cl (= @p_15 (! (not @p_19) :named @p_20))) :rule cong :premises (t11.t2))
@@ -800,7 +800,7 @@
 (step t11 (cl (! (= @p_18 (! (forall ((veriT_vr1 A$)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
 (step t12 (cl (not @p_24) (not @p_18) @p_25) :rule equiv_pos2)
 (step t13 (cl @p_25) :rule th_resolution :premises (t10 t11 t12))
-(anchor :step t14 :args ((:= ?v0 veriT_vr8)))
+(anchor :step t14 :args ((:= (?v0 A$) veriT_vr8)))
 (step t14.t1 (cl (! (= ?v0 veriT_vr8) :named @p_29)) :rule refl)
 (step t14.t2 (cl (= @p_27 (! (p$ true veriT_vr8) :named @p_28))) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_29) :rule refl)
@@ -819,7 +819,7 @@
 (step t24 (cl (not @p_46) @p_38) :rule not_not)
 (step t25 (cl @p_47 @p_38 @p_45) :rule th_resolution :premises (t24 t23))
 (step t26 (cl @p_45) :rule th_resolution :premises (t20 t22 t25))
-(anchor :step t27 :args ((:= veriT_vr8 veriT_vr9)))
+(anchor :step t27 :args ((:= (veriT_vr8 A$) veriT_vr9)))
 (step t27.t1 (cl (! (= veriT_vr8 veriT_vr9) :named @p_49)) :rule refl)
 (step t27.t2 (cl (= @p_28 @p_48)) :rule cong :premises (t27.t1))
 (step t27.t3 (cl @p_49) :rule refl)
@@ -834,7 +834,7 @@
 (step t33 (cl (not @p_60) @p_43) :rule not_not)
 (step t34 (cl @p_61 @p_43 @p_59) :rule th_resolution :premises (t33 t32))
 (step t35 (cl @p_59) :rule th_resolution :premises (t26 t31 t34))
-(anchor :step t36 :args ((:= veriT_vr9 veriT_sk2)))
+(anchor :step t36 :args ((:= (veriT_vr9 A$) veriT_sk2)))
 (step t36.t1 (cl (! (= veriT_vr9 veriT_sk2) :named @p_64)) :rule refl)
 (step t36.t2 (cl (= @p_48 (! (p$ true veriT_sk2) :named @p_63))) :rule cong :premises (t36.t1))
 (step t36.t3 (cl @p_64) :rule refl)
@@ -848,7 +848,7 @@
 (step t41 (cl (not @p_71) @p_57) :rule not_not)
 (step t42 (cl @p_72 @p_57 @p_70) :rule th_resolution :premises (t41 t40))
 (step t43 (cl @p_70) :rule th_resolution :premises (t35 t39 t42))
-(anchor :step t44 :args ((:= veriT_vr9 veriT_vr10)))
+(anchor :step t44 :args ((:= (veriT_vr9 A$) veriT_vr10)))
 (step t44.t1 (cl (! (= veriT_vr9 veriT_vr10) :named @p_74)) :rule refl)
 (step t44.t2 (cl (= @p_48 (! (p$ true veriT_vr10) :named @p_73))) :rule cong :premises (t44.t1))
 (step t44.t3 (cl @p_74) :rule refl)
@@ -913,12 +913,12 @@
 unsat
 (assume a0 (! (ite (! (p$ x$) :named @p_2) (! (not (! (exists ((?v0 A$)) (! (p$ ?v0) :named @p_1)) :named @p_3)) :named @p_5) (! (forall ((?v0 A$)) (! (not @p_1) :named @p_10)) :named @p_7)) :named @p_12))
 (assume a1 (! (not (! (=> @p_2 (! (p$ y$) :named @p_35)) :named @p_39)) :named @p_34))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_8)) :rule refl)
 (step t3.t2 (cl (! (= @p_1 (! (p$ veriT_vr0) :named @p_4)) :named @p_9)) :rule cong :premises (t3.t1))
 (step t3 (cl (= @p_3 (! (exists ((veriT_vr0 A$)) @p_4) :named @p_6))) :rule bind)
 (step t4 (cl (= @p_5 (! (not @p_6) :named @p_13))) :rule cong :premises (t3))
-(anchor :step t5 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v0 A$) veriT_vr0)))
 (step t5.t1 (cl @p_8) :rule refl)
 (step t5.t2 (cl @p_9) :rule cong :premises (t5.t1))
 (step t5.t3 (cl (= @p_10 (! (not @p_4) :named @p_11))) :rule cong :premises (t5.t2))
@@ -926,7 +926,7 @@
 (step t6 (cl (! (= @p_12 (! (ite @p_2 @p_13 @p_14) :named @p_16)) :named @p_15)) :rule cong :premises (t4 t5))
 (step t7 (cl (not @p_15) (not @p_12) @p_16) :rule equiv_pos2)
 (step t8 (cl @p_16) :rule th_resolution :premises (a0 t6 t7))
-(anchor :step t9 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t9 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t9.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl)
 (step t9.t2 (cl (= @p_4 (! (p$ veriT_vr1) :named @p_17))) :rule cong :premises (t9.t1))
 (step t9.t3 (cl (= @p_11 (! (not @p_17) :named @p_18))) :rule cong :premises (t9.t2))
@@ -934,12 +934,12 @@
 (step t10 (cl (! (= @p_16 (! (ite @p_2 @p_13 @p_19) :named @p_21)) :named @p_20)) :rule cong :premises (t9))
 (step t11 (cl (not @p_20) (not @p_16) @p_21) :rule equiv_pos2)
 (step t12 (cl @p_21) :rule th_resolution :premises (t8 t10 t11))
-(anchor :step t13 :args ((:= veriT_vr0 veriT_vr2)))
+(anchor :step t13 :args ((:= (veriT_vr0 A$) veriT_vr2)))
 (step t13.t1 (cl (= veriT_vr0 veriT_vr2)) :rule refl)
 (step t13.t2 (cl (= @p_4 (! (p$ veriT_vr2) :named @p_22))) :rule cong :premises (t13.t1))
 (step t13 (cl (= @p_6 (! (exists ((veriT_vr2 A$)) @p_22) :named @p_23))) :rule bind)
 (step t14 (cl (= @p_13 (! (not @p_23) :named @p_26))) :rule cong :premises (t13))
-(anchor :step t15 :args ((:= veriT_vr1 veriT_vr3)))
+(anchor :step t15 :args ((:= (veriT_vr1 A$) veriT_vr3)))
 (step t15.t1 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
 (step t15.t2 (cl (= @p_17 (! (p$ veriT_vr3) :named @p_24))) :rule cong :premises (t15.t1))
 (step t15.t3 (cl (= @p_18 (! (not @p_24) :named @p_25))) :rule cong :premises (t15.t2))
@@ -1688,7 +1688,7 @@
 17b588accea82f232f85c0c80edac2592c83c741 44 0
 unsat
 (assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (and (! (= 0 ?v0) :named @p_2) (! (= 1 ?v1) :named @p_4)) :named @p_6) (! (not (! (= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_1)) :named @p_14))
-(anchor :step t2 :args ((:= ?v0 0) (:= ?v1 1)))
+(anchor :step t2 :args ((:= (?v0 Int) 0) (:= (?v1 Int) 1)))
 (step t2.t1 (cl @p_2) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (= 0 0) :named @p_3))) :rule cong :premises (t2.t1))
 (step t2.t3 (cl @p_4) :rule refl)
@@ -1735,7 +1735,7 @@
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (=> (! (< veriT_vr2 veriT_vr3) :named @p_30) (! (< (! (+ 1 (! (* 2 veriT_vr2) :named @p_32)) :named @p_33) (! (* 2 veriT_vr3) :named @p_35)) :named @p_36)) :named @p_37)))) :named @p_43))
 (define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (=> (< @p_43 veriT_vr3) (< (+ 1 (* 2 @p_43)) @p_35)))) :named @p_44))
 (assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (=> (! (< ?v0 ?v1) :named @p_2) (! (< (! (+ (! (* 2 ?v0) :named @p_5) 1) :named @p_7) (! (* 2 ?v1) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_1)) :named @p_16))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_9)) :rule refl)
 (step t2.t3 (cl (= @p_2 (! (< veriT_vr0 veriT_vr1) :named @p_3))) :rule cong :premises (t2.t1 t2.t2))
@@ -1752,7 +1752,7 @@
 (step t5 (cl (not @p_20) @p_1) :rule not_not)
 (step t6 (cl @p_21 @p_1 @p_19) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_19) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args (veriT_vr0 veriT_vr1))
+(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
 (step t8.t1 (cl (= @p_8 (! (+ 1 @p_6) :named @p_22))) :rule sum_simplify)
 (step t8.t2 (cl (= @p_13 (! (< @p_22 @p_11) :named @p_23))) :rule cong :premises (t8.t1))
 (step t8.t3 (cl (= @p_15 (! (=> @p_3 @p_23) :named @p_24))) :rule cong :premises (t8.t2))
@@ -1762,7 +1762,7 @@
 (step t11 (cl (not @p_28) @p_17) :rule not_not)
 (step t12 (cl @p_29 @p_17 @p_27) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_27) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
 (step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
 (step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_34)) :rule refl)
 (step t14.t3 (cl (= @p_3 @p_30)) :rule cong :premises (t14.t1 t14.t2))
@@ -1779,7 +1779,7 @@
 (step t17 (cl (not @p_41) @p_25) :rule not_not)
 (step t18 (cl @p_42 @p_25 @p_40) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_40) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr2 veriT_sk0) (:= veriT_vr3 veriT_sk1)))
+(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
 (step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_46)) :rule refl)
 (step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_49)) :rule refl)
 (step t20.t3 (cl (= @p_30 (! (< veriT_sk0 veriT_sk1) :named @p_45))) :rule cong :premises (t20.t1 t20.t2))
@@ -1810,7 +1810,7 @@
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (or (! (< 2 (! (+ veriT_vr2 veriT_vr3) :named @p_29)) :named @p_30) (! (= 2 @p_29) :named @p_34) (! (< @p_29 2) :named @p_35)) :named @p_36)))) :named @p_42))
 (define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (or (< 2 (! (+ @p_42 veriT_vr3) :named @p_43)) (= 2 @p_43) (< @p_43 2)))) :named @p_45))
 (assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 2 (! (+ ?v0 ?v1) :named @p_1)) :named @p_4) (! (or (! (= 2 @p_1) :named @p_9) (! (< @p_1 2) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2)) :named @p_17))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
 (step t2.t2 (cl (! (= ?v1 veriT_vr1) :named @p_7)) :rule refl)
 (step t2.t3 (cl (! (= @p_1 (! (+ veriT_vr0 veriT_vr1) :named @p_3)) :named @p_8)) :rule cong :premises (t2.t1 t2.t2))
@@ -1831,7 +1831,7 @@
 (step t5 (cl (not @p_21) @p_2) :rule not_not)
 (step t6 (cl @p_22 @p_2 @p_20) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_20) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args (veriT_vr0 veriT_vr1))
+(anchor :step t8 :args ((veriT_vr0 Int) (veriT_vr1 Int)))
 (step t8.t1 (cl (= @p_16 (! (or @p_5 @p_10 @p_12) :named @p_23))) :rule ac_simp)
 (step t8 (cl (= @p_18 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_23) :named @p_24))) :rule bind)
 (step t9 (cl (! (= @p_20 (! (not @p_24) :named @p_26)) :named @p_25)) :rule cong :premises (t8))
@@ -1839,7 +1839,7 @@
 (step t11 (cl (not @p_27) @p_18) :rule not_not)
 (step t12 (cl @p_28 @p_18 @p_26) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_26) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
 (step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_31)) :rule refl)
 (step t14.t2 (cl (! (= veriT_vr1 veriT_vr3) :named @p_32)) :rule refl)
 (step t14.t3 (cl (! (= @p_3 @p_29) :named @p_33)) :rule cong :premises (t14.t1 t14.t2))
@@ -1859,7 +1859,7 @@
 (step t17 (cl (not @p_40) @p_24) :rule not_not)
 (step t18 (cl @p_41 @p_24 @p_39) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_39) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr2 veriT_sk0) (:= veriT_vr3 veriT_sk1)))
+(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
 (step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_47)) :rule refl)
 (step t20.t2 (cl (! (= veriT_vr3 veriT_sk1) :named @p_48)) :rule refl)
 (step t20.t3 (cl (! (= @p_29 (! (+ veriT_sk0 veriT_sk1) :named @p_44)) :named @p_49)) :rule cong :premises (t20.t1 t20.t2))
@@ -1894,7 +1894,7 @@
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (ite (! (< 0 veriT_vr1) :named @p_27) (! (< 0 (! (+ 1 veriT_vr1) :named @p_29)) :named @p_30) (! (< veriT_vr1 1) :named @p_31)) :named @p_32))) :named @p_38))
 (assume a0 (! (not (! (forall ((?v0 Int)) (! (ite (! (< 0 ?v0) :named @p_2) (! (< 0 (! (+ ?v0 1) :named @p_5)) :named @p_7) (! (< ?v0 1) :named @p_9)) :named @p_11)) :named @p_1)) :named @p_13))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (< 0 veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1))
 (step t2.t3 (cl @p_4) :rule refl)
@@ -1909,7 +1909,7 @@
 (step t5 (cl (not @p_17) @p_1) :rule not_not)
 (step t6 (cl @p_18 @p_1 @p_16) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_16) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args (veriT_vr0))
+(anchor :step t8 :args ((veriT_vr0 Int)))
 (step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_19))) :rule sum_simplify)
 (step t8.t2 (cl (= @p_8 (! (< 0 @p_19) :named @p_20))) :rule cong :premises (t8.t1))
 (step t8.t3 (cl (= @p_12 (! (ite @p_3 @p_20 @p_10) :named @p_21))) :rule cong :premises (t8.t2))
@@ -1919,7 +1919,7 @@
 (step t11 (cl (not @p_25) @p_14) :rule not_not)
 (step t12 (cl @p_26 @p_14 @p_24) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_24) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t14.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_28)) :rule refl)
 (step t14.t2 (cl (= @p_3 @p_27)) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_28) :rule refl)
@@ -1934,7 +1934,7 @@
 (step t17 (cl (not @p_36) @p_22) :rule not_not)
 (step t18 (cl @p_37 @p_22 @p_35) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_35) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr1 veriT_sk0)))
+(anchor :step t20 :args ((:= (veriT_vr1 Int) veriT_sk0)))
 (step t20.t1 (cl (! (= veriT_vr1 veriT_sk0) :named @p_40)) :rule refl)
 (step t20.t2 (cl (= @p_27 (! (< 0 veriT_sk0) :named @p_39))) :rule cong :premises (t20.t1))
 (step t20.t3 (cl @p_40) :rule refl)
@@ -1962,7 +1962,7 @@
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (or (! (< veriT_vr1 0) :named @p_37) (! (< 0 veriT_vr1) :named @p_39)) :named @p_40))) :named @p_51))
 (assume a0 (! (not (! (< 0 (! (ite (! (forall ((?v0 Int)) (! (or (! (< ?v0 0) :named @p_2) (! (< 0 ?v0) :named @p_5)) :named @p_7)) :named @p_1) (! (- 1) :named @p_11) 3) :named @p_9)) :named @p_12)) :named @p_14))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0)))
 (step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (< veriT_vr0 0) :named @p_3))) :rule cong :premises (t2.t1))
 (step t2.t3 (cl @p_4) :rule refl)
@@ -1993,7 +1993,7 @@
 (step t24 (cl (! (= @p_27 (! (and @p_33 @p_34) :named @p_36)) :named @p_35)) :rule cong :premises (t23))
 (step t25 (cl (not @p_35) (not @p_27) @p_36) :rule equiv_pos2)
 (step t26 (cl @p_36) :rule th_resolution :premises (t22 t24 t25))
-(anchor :step t27 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t27 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t27.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_38)) :rule refl)
 (step t27.t2 (cl (= @p_3 @p_37)) :rule cong :premises (t27.t1))
 (step t27.t3 (cl @p_38) :rule refl)
@@ -2007,7 +2007,7 @@
 (step t32 (cl (! (= @p_36 (! (and @p_33 @p_48) :named @p_50)) :named @p_49)) :rule cong :premises (t31))
 (step t33 (cl (not @p_49) (not @p_36) @p_50) :rule equiv_pos2)
 (step t34 (cl @p_50) :rule th_resolution :premises (t26 t32 t33))
-(anchor :step t35 :args ((:= veriT_vr1 veriT_sk0)))
+(anchor :step t35 :args ((:= (veriT_vr1 Int) veriT_sk0)))
 (step t35.t1 (cl (! (= veriT_vr1 veriT_sk0) :named @p_53)) :rule refl)
 (step t35.t2 (cl (= @p_37 (! (< veriT_sk0 0) :named @p_52))) :rule cong :premises (t35.t1))
 (step t35.t3 (cl @p_53) :rule refl)
@@ -2019,7 +2019,7 @@
 (step t38 (cl (! (= @p_50 (! (and @p_33 @p_57) :named @p_59)) :named @p_58)) :rule cong :premises (t37))
 (step t39 (cl (not @p_58) (not @p_50) @p_59) :rule equiv_pos2)
 (step t40 (cl @p_59) :rule th_resolution :premises (t34 t38 t39))
-(anchor :step t41 :args ((:= veriT_vr1 veriT_vr2)))
+(anchor :step t41 :args ((:= (veriT_vr1 Int) veriT_vr2)))
 (step t41.t1 (cl (! (= veriT_vr1 veriT_vr2) :named @p_61)) :rule refl)
 (step t41.t2 (cl (= @p_37 (! (< veriT_vr2 0) :named @p_60))) :rule cong :premises (t41.t1))
 (step t41.t3 (cl @p_61) :rule refl)
@@ -2077,7 +2077,7 @@
 (step t5 (cl (not @p_6) @p_1) :rule not_not)
 (step t6 (cl @p_7 @p_1 @p_5) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_5) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args ((:= ?v1 veriT_vr0) (:= ?v2 veriT_vr1)))
+(anchor :step t8 :args ((:= (?v1 Int) veriT_vr0) (:= (?v2 Int) veriT_vr1)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_14)) :rule refl)
 (step t8.t2 (cl (= @p_8 (! (< 0 veriT_vr0) :named @p_9))) :rule cong :premises (t8.t1))
 (step t8.t3 (cl (! (= ?v2 veriT_vr1) :named @p_15)) :rule refl)
@@ -2094,7 +2094,7 @@
 (step t11 (cl (not @p_25) @p_2) :rule not_not)
 (step t12 (cl @p_26 @p_2 @p_24) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_24) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
 (step t14.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_30)) :rule refl)
 (step t14.t2 (cl (= @p_9 @p_27)) :rule cong :premises (t14.t1))
 (step t14.t3 (cl (! (= veriT_vr1 veriT_vr3) :named @p_31)) :rule refl)
@@ -2111,7 +2111,7 @@
 (step t17 (cl (not @p_38) @p_22) :rule not_not)
 (step t18 (cl @p_39 @p_22 @p_37) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_37) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr2 veriT_sk0) (:= veriT_vr3 veriT_sk1)))
+(anchor :step t20 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Int) veriT_sk1)))
 (step t20.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_45)) :rule refl)
 (step t20.t2 (cl (= @p_27 (! (< 0 veriT_sk0) :named @p_42))) :rule cong :premises (t20.t1))
 (step t20.t3 (cl (! (= veriT_vr3 veriT_sk1) :named @p_46)) :rule refl)
@@ -2152,7 +2152,7 @@
 (step t5 (cl (not @p_6) @p_1) :rule not_not)
 (step t6 (cl @p_7 @p_1 @p_5) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_5) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args ((:= ?v1 veriT_vr0) (:= ?v2 veriT_vr1)))
+(anchor :step t8 :args ((:= (?v1 Int) veriT_vr0) (:= (?v2 Real) veriT_vr1)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_15)) :rule refl)
 (step t8.t2 (cl (= @p_9 (! (< 0 veriT_vr0) :named @p_10))) :rule cong :premises (t8.t1))
 (step t8.t3 (cl (= ?v2 veriT_vr1)) :rule refl)
@@ -2167,7 +2167,7 @@
 (step t11 (cl (not @p_23) @p_2) :rule not_not)
 (step t12 (cl @p_24 @p_2 @p_22) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_22) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args (veriT_vr0 veriT_vr1))
+(anchor :step t14 :args ((veriT_vr0 Int) (veriT_vr1 Real)))
 (step t14.t1 (cl (= @p_8 (- 1))) :rule minus_simplify)
 (step t14.t2 (cl (= @p_17 (! (< (- 1) veriT_vr0) :named @p_25))) :rule cong :premises (t14.t1))
 (step t14.t3 (cl (= @p_19 (! (=> @p_14 @p_25) :named @p_26))) :rule cong :premises (t14.t2))
@@ -2177,7 +2177,7 @@
 (step t17 (cl (not @p_30) @p_20) :rule not_not)
 (step t18 (cl @p_31 @p_20 @p_29) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_29) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t20 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Real) veriT_vr3)))
 (step t20.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_35)) :rule refl)
 (step t20.t2 (cl (= @p_10 @p_32)) :rule cong :premises (t20.t1))
 (step t20.t3 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
@@ -2192,7 +2192,7 @@
 (step t23 (cl (not @p_41) @p_27) :rule not_not)
 (step t24 (cl @p_42 @p_27 @p_40) :rule th_resolution :premises (t23 t22))
 (step t25 (cl @p_40) :rule th_resolution :premises (t19 t21 t24))
-(anchor :step t26 :args ((:= veriT_vr2 veriT_sk0) (:= veriT_vr3 veriT_sk1)))
+(anchor :step t26 :args ((:= (veriT_vr2 Int) veriT_sk0) (:= (veriT_vr3 Real) veriT_sk1)))
 (step t26.t1 (cl (! (= veriT_vr2 veriT_sk0) :named @p_48)) :rule refl)
 (step t26.t2 (cl (= @p_32 (! (< 0 veriT_sk0) :named @p_44))) :rule cong :premises (t26.t1))
 (step t26.t3 (cl (= veriT_vr3 veriT_sk1)) :rule refl)
@@ -2229,7 +2229,7 @@
 (step t5 (cl (not @p_7) @p_1) :rule not_not)
 (step t6 (cl @p_8 @p_1 @p_6) :rule th_resolution :premises (t5 t4))
 (step t7 (cl @p_6) :rule th_resolution :premises (a0 t3 t6))
-(anchor :step t8 :args ((:= ?v1 veriT_vr0)))
+(anchor :step t8 :args ((:= (?v1 Int) veriT_vr0)))
 (step t8.t1 (cl (! (= ?v1 veriT_vr0) :named @p_11)) :rule refl)
 (step t8.t2 (cl (= @p_9 (! (< 0 veriT_vr0) :named @p_10))) :rule cong :premises (t8.t1))
 (step t8.t3 (cl @p_11) :rule refl)
@@ -2241,7 +2241,7 @@
 (step t11 (cl (not @p_18) @p_4) :rule not_not)
 (step t12 (cl @p_19 @p_4 @p_17) :rule th_resolution :premises (t11 t10))
 (step t13 (cl @p_17) :rule th_resolution :premises (t7 t9 t12))
-(anchor :step t14 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t14.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_21)) :rule refl)
 (step t14.t2 (cl (= @p_10 @p_20)) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_21) :rule refl)
@@ -2253,7 +2253,7 @@
 (step t17 (cl (not @p_27) @p_15) :rule not_not)
 (step t18 (cl @p_28 @p_15 @p_26) :rule th_resolution :premises (t17 t16))
 (step t19 (cl @p_26) :rule th_resolution :premises (t13 t15 t18))
-(anchor :step t20 :args ((:= veriT_vr1 veriT_sk0)))
+(anchor :step t20 :args ((:= (veriT_vr1 Int) veriT_sk0)))
 (step t20.t1 (cl (! (= veriT_vr1 veriT_sk0) :named @p_31)) :rule refl)
 (step t20.t2 (cl (= @p_20 (! (< 0 veriT_sk0) :named @p_30))) :rule cong :premises (t20.t1))
 (step t20.t3 (cl @p_31) :rule refl)
@@ -2349,7 +2349,7 @@
 unsat
 (assume a4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_3)) :named @p_5) (! (ite (! (<= 0 ?v0) :named @p_8) ?v0 0) :named @p_10)) :named @p_12)) :named @p_2))
 (assume a1 (! (not (! (= (! (ite (! (< x$ 0) :named @p_25) (! (- x$) :named @p_26) x$) :named @p_1) (of_nat$ (nat$ @p_1))) :named @p_30)) :named @p_24))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t3 :args ((:= (?v0 Int) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_7)) :rule refl)
 (step t3.t2 (cl (= @p_3 (! (nat$ veriT_vr0) :named @p_4))) :rule cong :premises (t3.t1))
 (step t3.t3 (cl (= @p_5 (! (of_nat$ @p_4) :named @p_6))) :rule cong :premises (t3.t2))
@@ -2361,7 +2361,7 @@
 (step t3 (cl (! (= @p_2 (! (forall ((veriT_vr0 Int)) @p_13) :named @p_15)) :named @p_14)) :rule bind)
 (step t4 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2)
 (step t5 (cl @p_15) :rule th_resolution :premises (a4 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_18)) :rule refl)
 (step t6.t2 (cl (= @p_4 (! (nat$ veriT_vr1) :named @p_16))) :rule cong :premises (t6.t1))
 (step t6.t3 (cl (= @p_6 (! (of_nat$ @p_16) :named @p_17))) :rule cong :premises (t6.t2))
@@ -2429,13 +2429,13 @@
 (assume a1 (! (not (! (=> (! (prime_nat$ (! (nat$ (! (+ @p_117 1) :named @p_116)) :named @p_118)) :named @p_109) (! (<= 1 @p_3) :named @p_110)) :named @p_114)) :named @p_108))
 (assume a2 (! (forall ((?v0 Nat$)) (! (<= 0 @p_1) :named @p_127)) :named @p_125))
 (assume a4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (nat$ ?v0) :named @p_136)) :named @p_138) (! (ite (! (<= 0 ?v0) :named @p_141) ?v0 0) :named @p_143)) :named @p_145)) :named @p_135))
-(anchor :step t5 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v0 Nat$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
 (step t5.t2 (cl (= @p_7 (! (prime_nat$ veriT_vr0) :named @p_8))) :rule cong :premises (t5.t1))
 (step t5.t3 (cl @p_9) :rule refl)
 (step t5.t4 (cl (! (= @p_1 (! (of_nat$ veriT_vr0) :named @p_5)) :named @p_19)) :rule cong :premises (t5.t3))
 (step t5.t5 (cl (= @p_10 (! (< 1 @p_5) :named @p_11))) :rule cong :premises (t5.t4))
-(anchor :step t5.t6 :args ((:= ?v1 veriT_vr1)))
+(anchor :step t5.t6 :args ((:= (?v1 Nat$) veriT_vr1)))
 (step t5.t6.t1 (cl (! (= ?v1 veriT_vr1) :named @p_16)) :rule refl)
 (step t5.t6.t2 (cl @p_9) :rule refl)
 (step t5.t6.t3 (cl (= @p_14 (! (dvd$ veriT_vr1 veriT_vr0) :named @p_15))) :rule cong :premises (t5.t6.t1 t5.t6.t2))
@@ -2455,18 +2455,18 @@
 (step t5 (cl (! (= @p_4 (! (forall ((veriT_vr0 Nat$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
 (step t6 (cl (not @p_31) (not @p_4) @p_32) :rule equiv_pos2)
 (step t7 (cl @p_32) :rule th_resolution :premises (a0 t5 t6))
-(anchor :step t8 :args (veriT_vr0))
+(anchor :step t8 :args ((veriT_vr0 Nat$)))
 (step t8.t1 (cl (= @p_30 (! (and (! (=> @p_8 @p_28) :named @p_52) (! (=> @p_28 @p_8) :named @p_65)) :named @p_33))) :rule connective_def)
 (step t8 (cl (! (= @p_32 (! (forall ((veriT_vr0 Nat$)) @p_33) :named @p_35)) :named @p_34)) :rule bind)
 (step t9 (cl (not @p_34) (not @p_32) @p_35) :rule equiv_pos2)
 (step t10 (cl @p_35) :rule th_resolution :premises (t7 t8 t9))
-(anchor :step t11 :args ((:= veriT_vr0 veriT_vr2)))
+(anchor :step t11 :args ((:= (veriT_vr0 Nat$) veriT_vr2)))
 (step t11.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_41)) :rule refl)
 (step t11.t2 (cl (! (= @p_8 (! (prime_nat$ veriT_vr2) :named @p_40)) :named @p_64)) :rule cong :premises (t11.t1))
 (step t11.t3 (cl @p_41) :rule refl)
 (step t11.t4 (cl (! (= @p_5 (! (of_nat$ veriT_vr2) :named @p_36)) :named @p_46)) :rule cong :premises (t11.t3))
 (step t11.t5 (cl (! (= @p_11 (! (< 1 @p_36) :named @p_38)) :named @p_54)) :rule cong :premises (t11.t4))
-(anchor :step t11.t6 :args ((:= veriT_vr1 veriT_vr3)))
+(anchor :step t11.t6 :args ((:= (veriT_vr1 Nat$) veriT_vr3)))
 (step t11.t6.t1 (cl (! (= veriT_vr1 veriT_vr3) :named @p_44)) :rule refl)
 (step t11.t6.t2 (cl @p_41) :rule refl)
 (step t11.t6.t3 (cl (= @p_15 (! (dvd$ veriT_vr3 veriT_vr2) :named @p_43))) :rule cong :premises (t11.t6.t1 t11.t6.t2))
@@ -2486,7 +2486,7 @@
 (step t11.t9 (cl @p_41) :rule refl)
 (step t11.t10 (cl @p_46) :rule cong :premises (t11.t9))
 (step t11.t11 (cl @p_54) :rule cong :premises (t11.t10))
-(anchor :step t11.t12 :args ((:= veriT_vr1 veriT_vr4)))
+(anchor :step t11.t12 :args ((:= (veriT_vr1 Nat$) veriT_vr4)))
 (step t11.t12.t1 (cl (! (= veriT_vr1 veriT_vr4) :named @p_57)) :rule refl)
 (step t11.t12.t2 (cl @p_41) :rule refl)
 (step t11.t12.t3 (cl (= @p_15 (! (dvd$ veriT_vr4 veriT_vr2) :named @p_56))) :rule cong :premises (t11.t12.t1 t11.t12.t2))
@@ -2509,13 +2509,13 @@
 (step t11 (cl (! (= @p_35 (! (forall ((veriT_vr2 Nat$)) @p_67) :named @p_69)) :named @p_68)) :rule bind)
 (step t12 (cl (not @p_68) (not @p_35) @p_69) :rule equiv_pos2)
 (step t13 (cl @p_69) :rule th_resolution :premises (t10 t11 t12))
-(anchor :step t14 :args ((:= veriT_vr2 veriT_vr5)))
+(anchor :step t14 :args ((:= (veriT_vr2 Nat$) veriT_vr5)))
 (step t14.t1 (cl (! (= veriT_vr2 veriT_vr5) :named @p_74)) :rule refl)
 (step t14.t2 (cl (! (= @p_40 (! (prime_nat$ veriT_vr5) :named @p_73)) :named @p_89)) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_74) :rule refl)
 (step t14.t4 (cl (! (= @p_36 (! (of_nat$ veriT_vr5) :named @p_70)) :named @p_80)) :rule cong :premises (t14.t3))
 (step t14.t5 (cl (! (= @p_38 (! (< 1 @p_70) :named @p_75)) :named @p_86)) :rule cong :premises (t14.t4))
-(anchor :step t14.t6 :args ((:= veriT_vr3 veriT_vr6)))
+(anchor :step t14.t6 :args ((:= (veriT_vr3 Nat$) veriT_vr6)))
 (step t14.t6.t1 (cl (! (= veriT_vr3 veriT_vr6) :named @p_78)) :rule refl)
 (step t14.t6.t2 (cl @p_74) :rule refl)
 (step t14.t6.t3 (cl (= @p_43 (! (dvd$ veriT_vr6 veriT_vr5) :named @p_77))) :rule cong :premises (t14.t6.t1 t14.t6.t2))
@@ -2535,7 +2535,7 @@
 (step t14.t9 (cl @p_74) :rule refl)
 (step t14.t10 (cl @p_80) :rule cong :premises (t14.t9))
 (step t14.t11 (cl @p_86) :rule cong :premises (t14.t10))
-(anchor :step t14.t12 :args ((:= veriT_vr4 veriT_vr6)))
+(anchor :step t14.t12 :args ((:= (veriT_vr4 Nat$) veriT_vr6)))
 (step t14.t12.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_87)) :rule refl)
 (step t14.t12.t2 (cl @p_74) :rule refl)
 (step t14.t12.t3 (cl (= @p_56 @p_77)) :rule cong :premises (t14.t12.t1 t14.t12.t2))
@@ -2558,8 +2558,8 @@
 (step t14 (cl (! (= @p_69 (! (forall ((veriT_vr5 Nat$)) @p_91) :named @p_93)) :named @p_92)) :rule bind)
 (step t15 (cl (not @p_92) (not @p_69) @p_93) :rule equiv_pos2)
 (step t16 (cl @p_93) :rule th_resolution :premises (t13 t14 t15))
-(anchor :step t17 :args ((:= veriT_vr5 veriT_vr5)))
-(anchor :step t17.t1 :args ((:= veriT_vr6 veriT_vr7)))
+(anchor :step t17 :args ((:= (veriT_vr5 Nat$) veriT_vr5)))
+(anchor :step t17.t1 :args ((:= (veriT_vr6 Nat$) veriT_vr7)))
 (step t17.t1.t1 (cl (! (= veriT_vr6 veriT_vr7) :named @p_97)) :rule refl)
 (step t17.t1.t2 (cl (= @p_77 (! (dvd$ veriT_vr7 veriT_vr5) :named @p_96))) :rule cong :premises (t17.t1.t1))
 (step t17.t1.t3 (cl @p_97) :rule refl)
@@ -2588,21 +2588,21 @@
 (step t28 (cl (! (= @p_112 (! (and @p_121 @p_122) :named @p_124)) :named @p_123)) :rule cong :premises (t27))
 (step t29 (cl (not @p_123) (not @p_112) @p_124) :rule equiv_pos2)
 (step t30 (cl @p_124) :rule th_resolution :premises (t24 t28 t29))
-(anchor :step t31 :args ((:= ?v0 veriT_vr8)))
+(anchor :step t31 :args ((:= (?v0 Nat$) veriT_vr8)))
 (step t31.t1 (cl (= ?v0 veriT_vr8)) :rule refl)
 (step t31.t2 (cl (= @p_1 (! (of_nat$ veriT_vr8) :named @p_126))) :rule cong :premises (t31.t1))
 (step t31.t3 (cl (= @p_127 (! (<= 0 @p_126) :named @p_128))) :rule cong :premises (t31.t2))
 (step t31 (cl (! (= @p_125 (! (forall ((veriT_vr8 Nat$)) @p_128) :named @p_130)) :named @p_129)) :rule bind)
 (step t32 (cl (not @p_129) (not @p_125) @p_130) :rule equiv_pos2)
 (step t33 (cl @p_130) :rule th_resolution :premises (a2 t31 t32))
-(anchor :step t34 :args ((:= veriT_vr8 veriT_vr9)))
+(anchor :step t34 :args ((:= (veriT_vr8 Nat$) veriT_vr9)))
 (step t34.t1 (cl (= veriT_vr8 veriT_vr9)) :rule refl)
 (step t34.t2 (cl (= @p_126 (! (of_nat$ veriT_vr9) :named @p_131))) :rule cong :premises (t34.t1))
 (step t34.t3 (cl (= @p_128 (! (<= 0 @p_131) :named @p_132))) :rule cong :premises (t34.t2))
 (step t34 (cl (! (= @p_130 (! (forall ((veriT_vr9 Nat$)) @p_132) :named @p_134)) :named @p_133)) :rule bind)
 (step t35 (cl (not @p_133) (not @p_130) @p_134) :rule equiv_pos2)
 (step t36 (cl @p_134) :rule th_resolution :premises (t33 t34 t35))
-(anchor :step t37 :args ((:= ?v0 veriT_vr12)))
+(anchor :step t37 :args ((:= (?v0 Int) veriT_vr12)))
 (step t37.t1 (cl (! (= ?v0 veriT_vr12) :named @p_140)) :rule refl)
 (step t37.t2 (cl (= @p_136 (! (nat$ veriT_vr12) :named @p_137))) :rule cong :premises (t37.t1))
 (step t37.t3 (cl (= @p_138 (! (of_nat$ @p_137) :named @p_139))) :rule cong :premises (t37.t2))
@@ -2614,7 +2614,7 @@
 (step t37 (cl (! (= @p_135 (! (forall ((veriT_vr12 Int)) @p_146) :named @p_148)) :named @p_147)) :rule bind)
 (step t38 (cl (not @p_147) (not @p_135) @p_148) :rule equiv_pos2)
 (step t39 (cl @p_148) :rule th_resolution :premises (a4 t37 t38))
-(anchor :step t40 :args ((:= veriT_vr12 veriT_vr13)))
+(anchor :step t40 :args ((:= (veriT_vr12 Int) veriT_vr13)))
 (step t40.t1 (cl (! (= veriT_vr12 veriT_vr13) :named @p_151)) :rule refl)
 (step t40.t2 (cl (= @p_137 (! (nat$ veriT_vr13) :named @p_149))) :rule cong :premises (t40.t1))
 (step t40.t3 (cl (= @p_139 (! (of_nat$ @p_149) :named @p_150))) :rule cong :premises (t40.t2))
@@ -2646,7 +2646,7 @@
 (step t55 (cl (or @p_167 (! (and (! (=> @p_121 (! (and (! (< 1 @p_158) :named @p_168) (! (forall ((veriT_vr6 Nat$)) (! (=> (! (dvd$ veriT_vr6 @p_120) :named @p_176) (! (or @p_79 (! (= @p_71 @p_158) :named @p_181)) :named @p_183)) :named @p_185)) :named @p_174)) :named @p_187)) :named @p_189) (! (=> (! (and @p_168 (! (forall ((veriT_vr7 Nat$)) (! (=> (! (dvd$ veriT_vr7 @p_120) :named @p_192) (! (or @p_98 (! (= @p_94 @p_158) :named @p_195)) :named @p_196)) :named @p_197)) :named @p_191)) :named @p_198) @p_121) :named @p_199)) :named @p_169))) :rule forall_inst :args ((:= veriT_vr5 @p_120)))
 (anchor :step t56)
 (assume t56.h1 @p_169)
-(anchor :step t56.t2 :args ((:= veriT_vr6 veriT_vr17)))
+(anchor :step t56.t2 :args ((:= (veriT_vr6 Nat$) veriT_vr17)))
 (step t56.t2.t1 (cl (! (= veriT_vr6 veriT_vr17) :named @p_178)) :rule refl)
 (step t56.t2.t2 (cl (= @p_176 (! (dvd$ veriT_vr17 @p_120) :named @p_177))) :rule cong :premises (t56.t2.t1))
 (step t56.t2.t3 (cl @p_178) :rule refl)
@@ -2660,7 +2660,7 @@
 (step t56.t2 (cl (= @p_174 (! (forall ((veriT_vr17 Nat$)) @p_186) :named @p_188))) :rule bind)
 (step t56.t3 (cl (= @p_187 (! (and @p_168 @p_188) :named @p_190))) :rule cong :premises (t56.t2))
 (step t56.t4 (cl (= @p_189 (! (=> @p_121 @p_190) :named @p_200))) :rule cong :premises (t56.t3))
-(anchor :step t56.t5 :args ((:= veriT_vr7 veriT_vr17)))
+(anchor :step t56.t5 :args ((:= (veriT_vr7 Nat$) veriT_vr17)))
 (step t56.t5.t1 (cl (! (= veriT_vr7 veriT_vr17) :named @p_193)) :rule refl)
 (step t56.t5.t2 (cl (= @p_192 @p_177)) :rule cong :premises (t56.t5.t1))
 (step t56.t5.t3 (cl @p_193) :rule refl)
@@ -2677,7 +2677,7 @@
 (step t56.t8 (cl (! (= @p_169 (! (and @p_200 @p_201) :named @p_204)) :named @p_202)) :rule cong :premises (t56.t4 t56.t7))
 (step t56.t9 (cl (not @p_202) (! (not @p_169) :named @p_203) @p_204) :rule equiv_pos2)
 (step t56.t10 (cl @p_204) :rule th_resolution :premises (t56.h1 t56.t8 t56.t9))
-(anchor :step t56.t11 :args ((:= veriT_vr17 veriT_vr18)))
+(anchor :step t56.t11 :args ((:= (veriT_vr17 Nat$) veriT_vr18)))
 (step t56.t11.t1 (cl (! (= veriT_vr17 veriT_vr18) :named @p_207)) :rule refl)
 (step t56.t11.t2 (cl (= @p_177 @p_206)) :rule cong :premises (t56.t11.t1))
 (step t56.t11.t3 (cl @p_207) :rule refl)
@@ -2695,7 +2695,7 @@
 (step t56.t15 (cl (! (= @p_204 (! (and @p_214 @p_215) :named @p_217)) :named @p_216)) :rule cong :premises (t56.t13 t56.t14))
 (step t56.t16 (cl (not @p_216) (not @p_204) @p_217) :rule equiv_pos2)
 (step t56.t17 (cl @p_217) :rule th_resolution :premises (t56.t10 t56.t15 t56.t16))
-(anchor :step t56.t18 :args ((:= veriT_vr18 veriT_sk1)))
+(anchor :step t56.t18 :args ((:= (veriT_vr18 Nat$) veriT_sk1)))
 (step t56.t18.t1 (cl (! (= veriT_vr18 veriT_sk1) :named @p_220)) :rule refl)
 (step t56.t18.t2 (cl (= @p_206 (! (dvd$ veriT_sk1 @p_120) :named @p_219))) :rule cong :premises (t56.t18.t1))
 (step t56.t18.t3 (cl @p_220) :rule refl)
@@ -2712,7 +2712,7 @@
 (step t56.t21 (cl (! (= @p_217 (! (and @p_214 @p_226) :named @p_228)) :named @p_227)) :rule cong :premises (t56.t20))
 (step t56.t22 (cl (not @p_227) (not @p_217) @p_228) :rule equiv_pos2)
 (step t56.t23 (cl @p_228) :rule th_resolution :premises (t56.t17 t56.t21 t56.t22))
-(anchor :step t56.t24 :args ((:= veriT_vr18 veriT_vr19)))
+(anchor :step t56.t24 :args ((:= (veriT_vr18 Nat$) veriT_vr19)))
 (step t56.t24.t1 (cl (! (= veriT_vr18 veriT_vr19) :named @p_231)) :rule refl)
 (step t56.t24.t2 (cl (= @p_206 (! (dvd$ veriT_vr19 @p_120) :named @p_230))) :rule cong :premises (t56.t24.t1))
 (step t56.t24.t3 (cl @p_231) :rule refl)
@@ -2772,7 +2772,7 @@
 unsat
 (assume a0 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$ (! (pair$ ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
 (assume a1 (! (not (! (=> (! (= (! (fst$ (pair$ x$ y$)) :named @p_26) a$) :named @p_18) (! (= x$ a$) :named @p_19)) :named @p_23)) :named @p_17))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 B$) veriT_vr1)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_2)) :rule refl)
 (step t3.t2 (cl @p_2) :rule refl)
 (step t3.t3 (cl (= ?v1 veriT_vr1)) :rule refl)
@@ -2782,7 +2782,7 @@
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 A$) (veriT_vr1 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
 (step t4 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
 (step t5 (cl @p_10) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t6 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 B$) veriT_vr3)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_11)) :rule refl)
 (step t6.t2 (cl @p_11) :rule refl)
 (step t6.t3 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
@@ -2804,79 +2804,11 @@
 (step t18 (cl @p_28) :rule resolution :premises (t17 t8))
 (step t19 (cl (not @p_28) (not @p_18) @p_19) :rule eq_transitive)
 (step t20 (cl) :rule resolution :premises (t19 t14 t15 t18))
-22e3ad7a3ba163eb9b2786d30a493e2c63cf8f81 67 0
-unsat
-(assume a1 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$a (! (pair$a ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
-(assume a3 (! (forall ((?v0 B$) (?v1 A$)) (! (= ?v1 (! (snd$a (! (pair$ ?v0 ?v1) :named @p_19)) :named @p_21)) :named @p_23)) :named @p_17))
-(assume a4 (! (not (! (=> (! (and (! (= p1$ (! (pair$a x$ y$) :named @p_47)) :named @p_41) (! (= p2$ (! (pair$ y$ x$) :named @p_46)) :named @p_42)) :named @p_34) (! (= (! (fst$a p1$) :named @p_52) (! (snd$a p2$) :named @p_54)) :named @p_35)) :named @p_39)) :named @p_33))
-(anchor :step t4 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5)))
-(step t4.t1 (cl (! (= ?v0 veriT_vr4) :named @p_2)) :rule refl)
-(step t4.t2 (cl @p_2) :rule refl)
-(step t4.t3 (cl (= ?v1 veriT_vr5)) :rule refl)
-(step t4.t4 (cl (= @p_3 (! (pair$a veriT_vr4 veriT_vr5) :named @p_4))) :rule cong :premises (t4.t2 t4.t3))
-(step t4.t5 (cl (= @p_5 (! (fst$a @p_4) :named @p_6))) :rule cong :premises (t4.t4))
-(step t4.t6 (cl (= @p_7 (! (= veriT_vr4 @p_6) :named @p_8))) :rule cong :premises (t4.t1 t4.t5))
-(step t4 (cl (! (= @p_1 (! (forall ((veriT_vr4 A$) (veriT_vr5 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
-(step t5 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
-(step t6 (cl @p_10) :rule th_resolution :premises (a1 t4 t5))
-(anchor :step t7 :args ((:= veriT_vr4 veriT_vr6) (:= veriT_vr5 veriT_vr7)))
-(step t7.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_11)) :rule refl)
-(step t7.t2 (cl @p_11) :rule refl)
-(step t7.t3 (cl (= veriT_vr5 veriT_vr7)) :rule refl)
-(step t7.t4 (cl (= @p_4 (! (pair$a veriT_vr6 veriT_vr7) :named @p_12))) :rule cong :premises (t7.t2 t7.t3))
-(step t7.t5 (cl (= @p_6 (! (fst$a @p_12) :named @p_13))) :rule cong :premises (t7.t4))
-(step t7.t6 (cl (= @p_8 (! (= veriT_vr6 @p_13) :named @p_14))) :rule cong :premises (t7.t1 t7.t5))
-(step t7 (cl (! (= @p_10 (! (forall ((veriT_vr6 A$) (veriT_vr7 B$)) @p_14) :named @p_16)) :named @p_15)) :rule bind)
-(step t8 (cl (not @p_15) (not @p_10) @p_16) :rule equiv_pos2)
-(step t9 (cl @p_16) :rule th_resolution :premises (t6 t7 t8))
-(anchor :step t10 :args ((:= ?v0 veriT_vr12) (:= ?v1 veriT_vr13)))
-(step t10.t1 (cl (! (= ?v1 veriT_vr13) :named @p_18)) :rule refl)
-(step t10.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
-(step t10.t3 (cl @p_18) :rule refl)
-(step t10.t4 (cl (= @p_19 (! (pair$ veriT_vr12 veriT_vr13) :named @p_20))) :rule cong :premises (t10.t2 t10.t3))
-(step t10.t5 (cl (= @p_21 (! (snd$a @p_20) :named @p_22))) :rule cong :premises (t10.t4))
-(step t10.t6 (cl (= @p_23 (! (= veriT_vr13 @p_22) :named @p_24))) :rule cong :premises (t10.t1 t10.t5))
-(step t10 (cl (! (= @p_17 (! (forall ((veriT_vr12 B$) (veriT_vr13 A$)) @p_24) :named @p_26)) :named @p_25)) :rule bind)
-(step t11 (cl (not @p_25) (not @p_17) @p_26) :rule equiv_pos2)
-(step t12 (cl @p_26) :rule th_resolution :premises (a3 t10 t11))
-(anchor :step t13 :args ((:= veriT_vr12 veriT_vr14) (:= veriT_vr13 veriT_vr15)))
-(step t13.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_27)) :rule refl)
-(step t13.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
-(step t13.t3 (cl @p_27) :rule refl)
-(step t13.t4 (cl (= @p_20 (! (pair$ veriT_vr14 veriT_vr15) :named @p_28))) :rule cong :premises (t13.t2 t13.t3))
-(step t13.t5 (cl (= @p_22 (! (snd$a @p_28) :named @p_29))) :rule cong :premises (t13.t4))
-(step t13.t6 (cl (= @p_24 (! (= veriT_vr15 @p_29) :named @p_30))) :rule cong :premises (t13.t1 t13.t5))
-(step t13 (cl (! (= @p_26 (! (forall ((veriT_vr14 B$) (veriT_vr15 A$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
-(step t14 (cl (not @p_31) (not @p_26) @p_32) :rule equiv_pos2)
-(step t15 (cl @p_32) :rule th_resolution :premises (t12 t13 t14))
-(step t16 (cl (! (= @p_33 (! (and @p_34 (! (not @p_35) :named @p_43)) :named @p_37)) :named @p_36)) :rule bool_simplify)
-(step t17 (cl (! (not @p_36) :named @p_40) (! (not @p_33) :named @p_38) @p_37) :rule equiv_pos2)
-(step t18 (cl (not @p_38) @p_39) :rule not_not)
-(step t19 (cl @p_40 @p_39 @p_37) :rule th_resolution :premises (t18 t17))
-(step t20 (cl @p_37) :rule th_resolution :premises (a4 t16 t19))
-(step t21 (cl (! (= @p_37 (! (and @p_41 @p_42 @p_43) :named @p_45)) :named @p_44)) :rule ac_simp)
-(step t22 (cl (not @p_44) (not @p_37) @p_45) :rule equiv_pos2)
-(step t23 (cl @p_45) :rule th_resolution :premises (t20 t21 t22))
-(step t24 (cl @p_41) :rule and :premises (t23))
-(step t25 (cl @p_42) :rule and :premises (t23))
-(step t26 (cl @p_43) :rule and :premises (t23))
-(step t27 (cl (or (! (not @p_32) :named @p_48) (! (= x$ (! (snd$a @p_46) :named @p_55)) :named @p_49))) :rule forall_inst :args ((:= veriT_vr14 y$) (:= veriT_vr15 x$)))
-(step t28 (cl (or (! (not @p_16) :named @p_50) (! (= x$ (! (fst$a @p_47) :named @p_53)) :named @p_51))) :rule forall_inst :args ((:= veriT_vr6 x$) (:= veriT_vr7 y$)))
-(step t29 (cl @p_48 @p_49) :rule or :premises (t27))
-(step t30 (cl @p_49) :rule resolution :premises (t29 t15))
-(step t31 (cl @p_50 @p_51) :rule or :premises (t28))
-(step t32 (cl @p_51) :rule resolution :premises (t31 t9))
-(step t33 (cl (! (not (! (= @p_52 @p_53) :named @p_61)) :named @p_57) (! (not @p_51) :named @p_58) (! (not @p_49) :named @p_59) (not (! (= @p_54 @p_55) :named @p_56)) @p_35) :rule eq_transitive)
-(step t34 (cl (! (not @p_42) :named @p_60) @p_56) :rule eq_congruent)
-(step t35 (cl @p_57 @p_58 @p_59 @p_35 @p_60) :rule th_resolution :premises (t33 t34))
-(step t36 (cl (! (not @p_41) :named @p_62) @p_61) :rule eq_congruent)
-(step t37 (cl @p_58 @p_59 @p_35 @p_60 @p_62) :rule th_resolution :premises (t35 t36))
-(step t38 (cl) :rule resolution :premises (t37 t24 t25 t26 t30 t32))
 323770b82ef8fd021b5433671b6c4077843fd9d7 97 0
 unsat
 (assume a1 (! (forall ((?v0 A_b_fun$) (?v1 A$) (?v2 B$) (?v3 A$)) (! (= (! (fun_app$ (! (fun_upd$ ?v0 ?v1 ?v2) :named @p_2) ?v3) :named @p_4) (! (ite (! (= ?v1 ?v3) :named @p_8) ?v2 (! (fun_app$ ?v0 ?v3) :named @p_12)) :named @p_14)) :named @p_16)) :named @p_1))
 (assume a2 (! (not (! (=> (! (and (! (not (! (= i$ i1$) :named @p_62)) :named @p_40) (! (not (! (= i$ i2$) :named @p_46)) :named @p_41)) :named @p_33) (! (= (! (fun_app$ (fun_upd$ (! (fun_upd$ f$ i1$ v1$) :named @p_47) i2$ v2$) i$) :named @p_45) (! (fun_app$ f$ i$) :named @p_63)) :named @p_34)) :named @p_38)) :named @p_32))
-(anchor :step t3 :args ((:= ?v0 veriT_vr6) (:= ?v1 veriT_vr7) (:= ?v2 veriT_vr8) (:= ?v3 veriT_vr9)))
+(anchor :step t3 :args ((:= (?v0 A_b_fun$) veriT_vr6) (:= (?v1 A$) veriT_vr7) (:= (?v2 B$) veriT_vr8) (:= (?v3 A$) veriT_vr9)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr6) :named @p_11)) :rule refl)
 (step t3.t2 (cl (! (= ?v1 veriT_vr7) :named @p_6)) :rule refl)
 (step t3.t3 (cl (! (= ?v2 veriT_vr8) :named @p_10)) :rule refl)
@@ -2895,7 +2827,7 @@
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr6 A_b_fun$) (veriT_vr7 A$) (veriT_vr8 B$) (veriT_vr9 A$)) @p_17) :named @p_19)) :named @p_18)) :rule bind)
 (step t4 (cl (not @p_18) (not @p_1) @p_19) :rule equiv_pos2)
 (step t5 (cl @p_19) :rule th_resolution :premises (a1 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr6 veriT_vr10) (:= veriT_vr7 veriT_vr11) (:= veriT_vr8 veriT_vr12) (:= veriT_vr9 veriT_vr13)))
+(anchor :step t6 :args ((:= (veriT_vr6 A_b_fun$) veriT_vr10) (:= (veriT_vr7 A$) veriT_vr11) (:= (veriT_vr8 B$) veriT_vr12) (:= (veriT_vr9 A$) veriT_vr13)))
 (step t6.t1 (cl (! (= veriT_vr6 veriT_vr10) :named @p_26)) :rule refl)
 (step t6.t2 (cl (! (= veriT_vr7 veriT_vr11) :named @p_22)) :rule refl)
 (step t6.t3 (cl (! (= veriT_vr8 veriT_vr12) :named @p_25)) :rule refl)
@@ -2970,6 +2902,74 @@
 (step t52 (cl @p_73) :rule resolution :premises (t48 t51))
 (step t53 (cl (not @p_58) (not @p_60) (not @p_71) (not @p_73) @p_34) :rule eq_transitive)
 (step t54 (cl) :rule resolution :premises (t53 t19 t34 t36 t50 t52))
+22e3ad7a3ba163eb9b2786d30a493e2c63cf8f81 67 0
+unsat
+(assume a1 (! (forall ((?v0 A$) (?v1 B$)) (! (= ?v0 (! (fst$a (! (pair$a ?v0 ?v1) :named @p_3)) :named @p_5)) :named @p_7)) :named @p_1))
+(assume a3 (! (forall ((?v0 B$) (?v1 A$)) (! (= ?v1 (! (snd$a (! (pair$ ?v0 ?v1) :named @p_19)) :named @p_21)) :named @p_23)) :named @p_17))
+(assume a4 (! (not (! (=> (! (and (! (= p1$ (! (pair$a x$ y$) :named @p_47)) :named @p_41) (! (= p2$ (! (pair$ y$ x$) :named @p_46)) :named @p_42)) :named @p_34) (! (= (! (fst$a p1$) :named @p_52) (! (snd$a p2$) :named @p_54)) :named @p_35)) :named @p_39)) :named @p_33))
+(anchor :step t4 :args ((:= (?v0 A$) veriT_vr4) (:= (?v1 B$) veriT_vr5)))
+(step t4.t1 (cl (! (= ?v0 veriT_vr4) :named @p_2)) :rule refl)
+(step t4.t2 (cl @p_2) :rule refl)
+(step t4.t3 (cl (= ?v1 veriT_vr5)) :rule refl)
+(step t4.t4 (cl (= @p_3 (! (pair$a veriT_vr4 veriT_vr5) :named @p_4))) :rule cong :premises (t4.t2 t4.t3))
+(step t4.t5 (cl (= @p_5 (! (fst$a @p_4) :named @p_6))) :rule cong :premises (t4.t4))
+(step t4.t6 (cl (= @p_7 (! (= veriT_vr4 @p_6) :named @p_8))) :rule cong :premises (t4.t1 t4.t5))
+(step t4 (cl (! (= @p_1 (! (forall ((veriT_vr4 A$) (veriT_vr5 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
+(step t5 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
+(step t6 (cl @p_10) :rule th_resolution :premises (a1 t4 t5))
+(anchor :step t7 :args ((:= (veriT_vr4 A$) veriT_vr6) (:= (veriT_vr5 B$) veriT_vr7)))
+(step t7.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_11)) :rule refl)
+(step t7.t2 (cl @p_11) :rule refl)
+(step t7.t3 (cl (= veriT_vr5 veriT_vr7)) :rule refl)
+(step t7.t4 (cl (= @p_4 (! (pair$a veriT_vr6 veriT_vr7) :named @p_12))) :rule cong :premises (t7.t2 t7.t3))
+(step t7.t5 (cl (= @p_6 (! (fst$a @p_12) :named @p_13))) :rule cong :premises (t7.t4))
+(step t7.t6 (cl (= @p_8 (! (= veriT_vr6 @p_13) :named @p_14))) :rule cong :premises (t7.t1 t7.t5))
+(step t7 (cl (! (= @p_10 (! (forall ((veriT_vr6 A$) (veriT_vr7 B$)) @p_14) :named @p_16)) :named @p_15)) :rule bind)
+(step t8 (cl (not @p_15) (not @p_10) @p_16) :rule equiv_pos2)
+(step t9 (cl @p_16) :rule th_resolution :premises (t6 t7 t8))
+(anchor :step t10 :args ((:= (?v0 B$) veriT_vr12) (:= (?v1 A$) veriT_vr13)))
+(step t10.t1 (cl (! (= ?v1 veriT_vr13) :named @p_18)) :rule refl)
+(step t10.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
+(step t10.t3 (cl @p_18) :rule refl)
+(step t10.t4 (cl (= @p_19 (! (pair$ veriT_vr12 veriT_vr13) :named @p_20))) :rule cong :premises (t10.t2 t10.t3))
+(step t10.t5 (cl (= @p_21 (! (snd$a @p_20) :named @p_22))) :rule cong :premises (t10.t4))
+(step t10.t6 (cl (= @p_23 (! (= veriT_vr13 @p_22) :named @p_24))) :rule cong :premises (t10.t1 t10.t5))
+(step t10 (cl (! (= @p_17 (! (forall ((veriT_vr12 B$) (veriT_vr13 A$)) @p_24) :named @p_26)) :named @p_25)) :rule bind)
+(step t11 (cl (not @p_25) (not @p_17) @p_26) :rule equiv_pos2)
+(step t12 (cl @p_26) :rule th_resolution :premises (a3 t10 t11))
+(anchor :step t13 :args ((:= (veriT_vr12 B$) veriT_vr14) (:= (veriT_vr13 A$) veriT_vr15)))
+(step t13.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_27)) :rule refl)
+(step t13.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
+(step t13.t3 (cl @p_27) :rule refl)
+(step t13.t4 (cl (= @p_20 (! (pair$ veriT_vr14 veriT_vr15) :named @p_28))) :rule cong :premises (t13.t2 t13.t3))
+(step t13.t5 (cl (= @p_22 (! (snd$a @p_28) :named @p_29))) :rule cong :premises (t13.t4))
+(step t13.t6 (cl (= @p_24 (! (= veriT_vr15 @p_29) :named @p_30))) :rule cong :premises (t13.t1 t13.t5))
+(step t13 (cl (! (= @p_26 (! (forall ((veriT_vr14 B$) (veriT_vr15 A$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
+(step t14 (cl (not @p_31) (not @p_26) @p_32) :rule equiv_pos2)
+(step t15 (cl @p_32) :rule th_resolution :premises (t12 t13 t14))
+(step t16 (cl (! (= @p_33 (! (and @p_34 (! (not @p_35) :named @p_43)) :named @p_37)) :named @p_36)) :rule bool_simplify)
+(step t17 (cl (! (not @p_36) :named @p_40) (! (not @p_33) :named @p_38) @p_37) :rule equiv_pos2)
+(step t18 (cl (not @p_38) @p_39) :rule not_not)
+(step t19 (cl @p_40 @p_39 @p_37) :rule th_resolution :premises (t18 t17))
+(step t20 (cl @p_37) :rule th_resolution :premises (a4 t16 t19))
+(step t21 (cl (! (= @p_37 (! (and @p_41 @p_42 @p_43) :named @p_45)) :named @p_44)) :rule ac_simp)
+(step t22 (cl (not @p_44) (not @p_37) @p_45) :rule equiv_pos2)
+(step t23 (cl @p_45) :rule th_resolution :premises (t20 t21 t22))
+(step t24 (cl @p_41) :rule and :premises (t23))
+(step t25 (cl @p_42) :rule and :premises (t23))
+(step t26 (cl @p_43) :rule and :premises (t23))
+(step t27 (cl (or (! (not @p_32) :named @p_48) (! (= x$ (! (snd$a @p_46) :named @p_55)) :named @p_49))) :rule forall_inst :args ((:= veriT_vr14 y$) (:= veriT_vr15 x$)))
+(step t28 (cl (or (! (not @p_16) :named @p_50) (! (= x$ (! (fst$a @p_47) :named @p_53)) :named @p_51))) :rule forall_inst :args ((:= veriT_vr6 x$) (:= veriT_vr7 y$)))
+(step t29 (cl @p_48 @p_49) :rule or :premises (t27))
+(step t30 (cl @p_49) :rule resolution :premises (t29 t15))
+(step t31 (cl @p_50 @p_51) :rule or :premises (t28))
+(step t32 (cl @p_51) :rule resolution :premises (t31 t9))
+(step t33 (cl (! (not (! (= @p_52 @p_53) :named @p_61)) :named @p_57) (! (not @p_51) :named @p_58) (! (not @p_49) :named @p_59) (not (! (= @p_54 @p_55) :named @p_56)) @p_35) :rule eq_transitive)
+(step t34 (cl (! (not @p_42) :named @p_60) @p_56) :rule eq_congruent)
+(step t35 (cl @p_57 @p_58 @p_59 @p_35 @p_60) :rule th_resolution :premises (t33 t34))
+(step t36 (cl (! (not @p_41) :named @p_62) @p_61) :rule eq_congruent)
+(step t37 (cl @p_58 @p_59 @p_35 @p_60 @p_62) :rule th_resolution :premises (t35 t36))
+(step t38 (cl) :rule resolution :premises (t37 t24 t25 t26 t30 t32))
 5c8ad736381ed7e2bc55bcefd8a06994784b278f 25 0
 unsat
 (assume a0 (! (not (! (or (! (= (! (f$ g$ x$) :named @p_1) (! (and (! (fun_app$ g$ x$) :named @p_2) true) :named @p_13)) :named @p_4) (or (! (= @p_1 true) :named @p_5) (! (= @p_2 true) :named @p_6))) :named @p_3)) :named @p_7))
@@ -3002,7 +3002,7 @@
 (assume a1 (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)))
 (assume a2 (! (not (! (and (! (= x$ (id$ x$)) :named @p_23) (! (= (! (id$a true) :named @p_17) true) :named @p_1)) :named @p_22)) :named @p_24))
 (step t4 (cl (! (and (! (= (! (id$a false) :named @p_16) false) :named @p_15) @p_1) :named @p_18)) :rule bfun_elim :premises (a1))
-(anchor :step t5 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v0 A$) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_3)) :rule refl)
 (step t5.t2 (cl @p_3) :rule refl)
 (step t5.t3 (cl (= @p_4 (! (id$ veriT_vr0) :named @p_5))) :rule cong :premises (t5.t2))
@@ -3010,7 +3010,7 @@
 (step t5 (cl (! (= @p_2 (! (forall ((veriT_vr0 A$)) @p_7) :named @p_9)) :named @p_8)) :rule bind)
 (step t6 (cl (not @p_8) (not @p_2) @p_9) :rule equiv_pos2)
 (step t7 (cl @p_9) :rule th_resolution :premises (a0 t5 t6))
-(anchor :step t8 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t8 :args ((:= (veriT_vr0 A$) veriT_vr1)))
 (step t8.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_10)) :rule refl)
 (step t8.t2 (cl @p_10) :rule refl)
 (step t8.t3 (cl (= @p_5 (! (id$ veriT_vr1) :named @p_11))) :rule cong :premises (t8.t2))
@@ -3039,7 +3039,7 @@
 unsat
 (assume a0 (not (=> (f$ (! (exists ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
 (step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
 (step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
 (step t3 (cl (= @p_1 (! (exists ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
@@ -3063,39 +3063,11 @@
 (step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
 (step t22 (cl (not false)) :rule false)
 (step t23 (cl) :rule resolution :premises (t21 t22))
-c16c43a541a3283a006315d4b74b5196ee73be5b 27 0
-unsat
-(assume a0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
-(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0)))
-(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
-(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
-(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3))
-(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2)
-(step t8 (cl (not @p_14) @p_8) :rule not_not)
-(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7))
-(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9))
-(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify)
-(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2)
-(step t13 (cl (not @p_18) @p_11) :rule not_not)
-(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12))
-(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14))
-(step t16 (cl (= @p_20 false)) :rule not_simplify)
-(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16))
-(step t18 (cl (= @p_21 false)) :rule and_simplify)
-(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18))
-(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2)
-(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
-(step t22 (cl (not false)) :rule false)
-(step t23 (cl) :rule resolution :premises (t21 t22))
 bfe8d775ab64ce32fa8986be49dfdcae57d75099 60 0
 unsat
 (assume a0 (! (forall ((?v0 Int) (?v1 Int)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_2) ?v1) :named @p_4) (! (<= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_1))
 (assume a1 (! (not (! (=> (! (= uu$ le$) :named @p_23) (! (fun_app$ (! (fun_app$a le$ 3) :named @p_40) 42) :named @p_24)) :named @p_28)) :named @p_22))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t3 :args ((:= (?v0 Int) veriT_vr0) (:= (?v1 Int) veriT_vr1)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_6)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (fun_app$a uu$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
 (step t3.t3 (cl (! (= ?v1 veriT_vr1) :named @p_7)) :rule refl)
@@ -3107,7 +3079,7 @@
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_11) :named @p_13)) :named @p_12)) :rule bind)
 (step t4 (cl (not @p_12) (not @p_1) @p_13) :rule equiv_pos2)
 (step t5 (cl @p_13) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr2) (:= (veriT_vr1 Int) veriT_vr3)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_16)) :rule refl)
 (step t6.t2 (cl (= @p_3 (! (fun_app$a uu$ veriT_vr2) :named @p_14))) :rule cong :premises (t6.t1))
 (step t6.t3 (cl (! (= veriT_vr1 veriT_vr3) :named @p_17)) :rule refl)
@@ -3152,13 +3124,41 @@
 (step t31 (cl @p_47) :rule eq_reflexive)
 (step t32 (cl @p_42 @p_24 @p_45) :rule th_resolution :premises (t30 t31))
 (step t33 (cl) :rule resolution :premises (t32 t14 t15 t25))
+c16c43a541a3283a006315d4b74b5196ee73be5b 27 0
+unsat
+(assume a0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true)))
+(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0))
+(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0)))
+(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
+(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
+(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3))
+(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2)
+(step t8 (cl (not @p_14) @p_8) :rule not_not)
+(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7))
+(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9))
+(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify)
+(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2)
+(step t13 (cl (not @p_18) @p_11) :rule not_not)
+(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12))
+(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14))
+(step t16 (cl (= @p_20 false)) :rule not_simplify)
+(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16))
+(step t18 (cl (= @p_21 false)) :rule and_simplify)
+(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18))
+(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2)
+(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
+(step t22 (cl (not false)) :rule false)
+(step t23 (cl) :rule resolution :premises (t21 t22))
 2224e31ba45ff13284551d05730c64492fbe999c 125 0
 unsat
 (assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_2) (! (+ ?v0 1) :named @p_5)) :named @p_7)) :named @p_1))
 (assume a1 (! (forall ((?v0 Int_int_fun$)) (! (= nil$ (! (map$ ?v0 nil$) :named @p_22)) :named @p_24)) :named @p_21))
 (assume a2 (! (forall ((?v0 Int_int_fun$) (?v1 Int) (?v2 Int_list$)) (! (= (! (map$ ?v0 (! (cons$ ?v1 ?v2) :named @p_33)) :named @p_35) (! (cons$ (! (fun_app$ ?v0 ?v1) :named @p_39) (! (map$ ?v0 ?v2) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_32))
 (assume a3 (not (! (= (! (map$ uu$ (cons$ 0 (! (cons$ 1 nil$) :named @p_62))) :named @p_61) (! (cons$ 1 (! (cons$ 2 nil$) :named @p_90)) :named @p_86)) :named @p_88)))
-(anchor :step t5 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t5 :args ((:= (?v0 Int) veriT_vr0)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t5.t2 (cl (= @p_2 (! (fun_app$ uu$ veriT_vr0) :named @p_3))) :rule cong :premises (t5.t1))
 (step t5.t3 (cl @p_4) :rule refl)
@@ -3167,13 +3167,13 @@
 (step t5 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
 (step t6 (cl (not @p_9) (not @p_1) @p_10) :rule equiv_pos2)
 (step t7 (cl @p_10) :rule th_resolution :premises (a0 t5 t6))
-(anchor :step t8 :args (veriT_vr0))
+(anchor :step t8 :args ((veriT_vr0 Int)))
 (step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_11))) :rule sum_simplify)
 (step t8.t2 (cl (= @p_8 (! (= @p_3 @p_11) :named @p_12))) :rule cong :premises (t8.t1))
 (step t8 (cl (! (= @p_10 (! (forall ((veriT_vr0 Int)) @p_12) :named @p_14)) :named @p_13)) :rule bind)
 (step t9 (cl (not @p_13) (not @p_10) @p_14) :rule equiv_pos2)
 (step t10 (cl @p_14) :rule th_resolution :premises (t7 t8 t9))
-(anchor :step t11 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t11 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t11.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_16)) :rule refl)
 (step t11.t2 (cl (= @p_3 (! (fun_app$ uu$ veriT_vr1) :named @p_15))) :rule cong :premises (t11.t1))
 (step t11.t3 (cl @p_16) :rule refl)
@@ -3182,21 +3182,21 @@
 (step t11 (cl (! (= @p_14 (! (forall ((veriT_vr1 Int)) @p_18) :named @p_20)) :named @p_19)) :rule bind)
 (step t12 (cl (not @p_19) (not @p_14) @p_20) :rule equiv_pos2)
 (step t13 (cl @p_20) :rule th_resolution :premises (t10 t11 t12))
-(anchor :step t14 :args ((:= ?v0 veriT_vr2)))
+(anchor :step t14 :args ((:= (?v0 Int_int_fun$) veriT_vr2)))
 (step t14.t1 (cl (= ?v0 veriT_vr2)) :rule refl)
 (step t14.t2 (cl (= @p_22 (! (map$ veriT_vr2 nil$) :named @p_23))) :rule cong :premises (t14.t1))
 (step t14.t3 (cl (= @p_24 (! (= nil$ @p_23) :named @p_25))) :rule cong :premises (t14.t2))
 (step t14 (cl (! (= @p_21 (! (forall ((veriT_vr2 Int_int_fun$)) @p_25) :named @p_27)) :named @p_26)) :rule bind)
 (step t15 (cl (not @p_26) (not @p_21) @p_27) :rule equiv_pos2)
 (step t16 (cl @p_27) :rule th_resolution :premises (a1 t14 t15))
-(anchor :step t17 :args ((:= veriT_vr2 veriT_vr3)))
+(anchor :step t17 :args ((:= (veriT_vr2 Int_int_fun$) veriT_vr3)))
 (step t17.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl)
 (step t17.t2 (cl (= @p_23 (! (map$ veriT_vr3 nil$) :named @p_28))) :rule cong :premises (t17.t1))
 (step t17.t3 (cl (= @p_25 (! (= nil$ @p_28) :named @p_29))) :rule cong :premises (t17.t2))
 (step t17 (cl (! (= @p_27 (! (forall ((veriT_vr3 Int_int_fun$)) @p_29) :named @p_31)) :named @p_30)) :rule bind)
 (step t18 (cl (not @p_30) (not @p_27) @p_31) :rule equiv_pos2)
 (step t19 (cl @p_31) :rule th_resolution :premises (t16 t17 t18))
-(anchor :step t20 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5) (:= ?v2 veriT_vr6)))
+(anchor :step t20 :args ((:= (?v0 Int_int_fun$) veriT_vr4) (:= (?v1 Int) veriT_vr5) (:= (?v2 Int_list$) veriT_vr6)))
 (step t20.t1 (cl (! (= ?v0 veriT_vr4) :named @p_37)) :rule refl)
 (step t20.t2 (cl (! (= ?v1 veriT_vr5) :named @p_38)) :rule refl)
 (step t20.t3 (cl (! (= ?v2 veriT_vr6) :named @p_41)) :rule refl)
@@ -3213,7 +3213,7 @@
 (step t20 (cl (! (= @p_32 (! (forall ((veriT_vr4 Int_int_fun$) (veriT_vr5 Int) (veriT_vr6 Int_list$)) @p_47) :named @p_49)) :named @p_48)) :rule bind)
 (step t21 (cl (not @p_48) (not @p_32) @p_49) :rule equiv_pos2)
 (step t22 (cl @p_49) :rule th_resolution :premises (a2 t20 t21))
-(anchor :step t23 :args ((:= veriT_vr4 veriT_vr7) (:= veriT_vr5 veriT_vr8) (:= veriT_vr6 veriT_vr9)))
+(anchor :step t23 :args ((:= (veriT_vr4 Int_int_fun$) veriT_vr7) (:= (veriT_vr5 Int) veriT_vr8) (:= (veriT_vr6 Int_list$) veriT_vr9)))
 (step t23.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_52)) :rule refl)
 (step t23.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_53)) :rule refl)
 (step t23.t3 (cl (! (= veriT_vr6 veriT_vr9) :named @p_55)) :rule refl)
@@ -3281,7 +3281,7 @@
 9bfeafd531163b7b5dc1f3e29f35b01c7ed668dc 23 0
 unsat
 (assume a0 (! (not (! (or (! (forall ((?v0 A$)) (! (p$ ?v0) :named @p_2)) :named @p_1) (! (not @p_1) :named @p_4)) :named @p_6)) :named @p_8))
-(anchor :step t2 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t2 :args ((:= (?v0 A$) veriT_vr0)))
 (step t2.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t2.t2 (cl (= @p_2 (! (p$ veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1))
 (step t2 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind)
@@ -3306,7 +3306,7 @@
 unsat
 (assume a0 (! (forall ((?v0 Int)) (! (= (! (dec_10$ ?v0) :named @p_2) (! (ite (! (< ?v0 10) :named @p_5) ?v0 (! (dec_10$ (! (- ?v0 10) :named @p_7)) :named @p_9)) :named @p_11)) :named @p_13)) :named @p_1))
 (assume a1 (not (! (= (! (dec_10$ (! (* 4 (! (dec_10$ 4) :named @p_38)) :named @p_27)) :named @p_26) 6) :named @p_74)))
-(anchor :step t3 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t3 :args ((:= (?v0 Int) veriT_vr0)))
 (step t3.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl)
 (step t3.t2 (cl (= @p_2 (! (dec_10$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1))
 (step t3.t3 (cl @p_4) :rule refl)
@@ -3320,7 +3320,7 @@
 (step t3 (cl (! (= @p_1 (! (forall ((veriT_vr0 Int)) @p_14) :named @p_16)) :named @p_15)) :rule bind)
 (step t4 (cl (not @p_15) (not @p_1) @p_16) :rule equiv_pos2)
 (step t5 (cl @p_16) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t6 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t6.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_18)) :rule refl)
 (step t6.t2 (cl (= @p_3 (! (dec_10$ veriT_vr1) :named @p_17))) :rule cong :premises (t6.t1))
 (step t6.t3 (cl @p_18) :rule refl)
@@ -3416,7 +3416,7 @@
 (assume a3 (! (less_eq$ (! (sup$ (collect$ uu$)) :named @p_2) (! (sup$ (collect$ uua$)) :named @p_1)) :named @p_31))
 (assume a4 (! (less_eq$ @p_1 @p_2) :named @p_32))
 (assume a5 (not (! (less_eq$ @p_2 @p_2) :named @p_33)))
-(anchor :step t5 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5) (:= ?v2 veriT_vr6)))
+(anchor :step t5 :args ((:= (?v0 A$) veriT_vr4) (:= (?v1 A$) veriT_vr5) (:= (?v2 A$) veriT_vr6)))
 (step t5.t1 (cl (! (= ?v0 veriT_vr4) :named @p_11)) :rule refl)
 (step t5.t2 (cl (! (= ?v1 veriT_vr5) :named @p_6)) :rule refl)
 (step t5.t3 (cl (= @p_4 (! (less_eq$ veriT_vr4 veriT_vr5) :named @p_5))) :rule cong :premises (t5.t1 t5.t2))
@@ -3431,7 +3431,7 @@
 (step t5 (cl (! (= @p_3 (! (forall ((veriT_vr4 A$) (veriT_vr5 A$) (veriT_vr6 A$)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
 (step t6 (cl (not @p_17) (not @p_3) @p_18) :rule equiv_pos2)
 (step t7 (cl @p_18) :rule th_resolution :premises (a2 t5 t6))
-(anchor :step t8 :args ((:= veriT_vr4 veriT_vr7) (:= veriT_vr5 veriT_vr8) (:= veriT_vr6 veriT_vr9)))
+(anchor :step t8 :args ((:= (veriT_vr4 A$) veriT_vr7) (:= (veriT_vr5 A$) veriT_vr8) (:= (veriT_vr6 A$) veriT_vr9)))
 (step t8.t1 (cl (! (= veriT_vr4 veriT_vr7) :named @p_23)) :rule refl)
 (step t8.t2 (cl (! (= veriT_vr5 veriT_vr8) :named @p_20)) :rule refl)
 (step t8.t3 (cl (= @p_5 (! (less_eq$ veriT_vr7 veriT_vr8) :named @p_19))) :rule cong :premises (t8.t1 t8.t2))
@@ -3494,7 +3494,7 @@
 (assume a26 (! (forall ((?v0 A_set$) (?v1 A_set$)) (! (=> @p_18 @p_13) :named @p_602)) :named @p_593))
 (assume a27 (! (forall ((?v0 A_set$) (?v1 A_list$)) (! (= (! (fun_app$ @p_19 (! (coset$ ?v1) :named @p_619)) :named @p_621) (! (forall ((?v2 A$)) (! (=> (! (member$ ?v2 @p_20) :named @p_627) (! (not @p_15) :named @p_632)) :named @p_634)) :named @p_623)) :named @p_636)) :named @p_617))
 (assume a28 (not (= (! (fun_app$ (! (fun_app$a eq_set$ @p_21) :named @p_1097) (! (set$ ys$) :named @p_713)) :named @p_711) rhs$)))
-(anchor :step t28 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t28 :args ((:= (?v0 A_set$) veriT_vr0) (:= (?v1 A_set$) veriT_vr1)))
 (step t28.t1 (cl (! (= ?v0 veriT_vr0) :named @p_27)) :rule refl)
 (step t28.t2 (cl (= @p_23 (! (fun_app$a uu$ veriT_vr0) :named @p_24))) :rule cong :premises (t28.t1))
 (step t28.t3 (cl (! (= ?v1 veriT_vr1) :named @p_28)) :rule refl)
@@ -3506,7 +3506,7 @@
 (step t28 (cl (! (= @p_22 (! (forall ((veriT_vr0 A_set$) (veriT_vr1 A_set$)) @p_31) :named @p_33)) :named @p_32)) :rule bind)
 (step t29 (cl (not @p_32) (not @p_22) @p_33) :rule equiv_pos2)
 (step t30 (cl @p_33) :rule th_resolution :premises (a0 t28 t29))
-(anchor :step t31 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t31 :args ((:= (veriT_vr0 A_set$) veriT_vr2) (:= (veriT_vr1 A_set$) veriT_vr3)))
 (step t31.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_36)) :rule refl)
 (step t31.t2 (cl (= @p_24 (! (fun_app$a uu$ veriT_vr2) :named @p_34))) :rule cong :premises (t31.t1))
 (step t31.t3 (cl (! (= veriT_vr1 veriT_vr3) :named @p_37)) :rule refl)
@@ -3518,7 +3518,7 @@
 (step t31 (cl (! (= @p_33 (! (forall ((veriT_vr2 A_set$) (veriT_vr3 A_set$)) @p_39) :named @p_41)) :named @p_40)) :rule bind)
 (step t32 (cl (not @p_40) (not @p_33) @p_41) :rule equiv_pos2)
 (step t33 (cl @p_41) :rule th_resolution :premises (t30 t31 t32))
-(anchor :step t34 :args ((:= ?v0 veriT_vr4)))
+(anchor :step t34 :args ((:= (?v0 A_list$) veriT_vr4)))
 (step t34.t1 (cl (! (= ?v0 veriT_vr4) :named @p_48)) :rule refl)
 (step t34.t2 (cl (= @p_2 (! (set$ veriT_vr4) :named @p_45))) :rule cong :premises (t34.t1))
 (step t34.t3 (cl (= @p_46 (! (fun_app$ @p_43 @p_45) :named @p_47))) :rule cong :premises (t34.t2))
@@ -3532,7 +3532,7 @@
 (step t34 (cl (! (= @p_42 (! (forall ((veriT_vr4 A_list$)) @p_60) :named @p_62)) :named @p_61)) :rule bind)
 (step t35 (cl (not @p_61) (not @p_42) @p_62) :rule equiv_pos2)
 (step t36 (cl @p_62) :rule th_resolution :premises (a1 t34 t35))
-(anchor :step t37 :args ((:= veriT_vr4 veriT_vr5)))
+(anchor :step t37 :args ((:= (veriT_vr4 A_list$) veriT_vr5)))
 (step t37.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_65)) :rule refl)
 (step t37.t2 (cl (= @p_45 (! (set$ veriT_vr5) :named @p_63))) :rule cong :premises (t37.t1))
 (step t37.t3 (cl (= @p_47 (! (fun_app$ @p_43 @p_63) :named @p_64))) :rule cong :premises (t37.t2))
@@ -3546,7 +3546,7 @@
 (step t37 (cl (! (= @p_62 (! (forall ((veriT_vr5 A_list$)) @p_71) :named @p_73)) :named @p_72)) :rule bind)
 (step t38 (cl (not @p_72) (not @p_62) @p_73) :rule equiv_pos2)
 (step t39 (cl @p_73) :rule th_resolution :premises (t36 t37 t38))
-(anchor :step t40 :args ((:= ?v0 veriT_vr6) (:= ?v1 veriT_vr7)))
+(anchor :step t40 :args ((:= (?v0 A$) veriT_vr6) (:= (?v1 A_set$) veriT_vr7)))
 (step t40.t1 (cl (! (= ?v0 veriT_vr6) :named @p_79)) :rule refl)
 (step t40.t2 (cl (! (= ?v1 veriT_vr7) :named @p_80)) :rule refl)
 (step t40.t3 (cl (= @p_75 (! (uminus$ veriT_vr7) :named @p_76))) :rule cong :premises (t40.t2))
@@ -3559,7 +3559,7 @@
 (step t40 (cl (! (= @p_74 (! (forall ((veriT_vr6 A$) (veriT_vr7 A_set$)) @p_86) :named @p_88)) :named @p_87)) :rule bind)
 (step t41 (cl (not @p_87) (not @p_74) @p_88) :rule equiv_pos2)
 (step t42 (cl @p_88) :rule th_resolution :premises (a2 t40 t41))
-(anchor :step t43 :args ((:= veriT_vr6 veriT_vr8) (:= veriT_vr7 veriT_vr9)))
+(anchor :step t43 :args ((:= (veriT_vr6 A$) veriT_vr8) (:= (veriT_vr7 A_set$) veriT_vr9)))
 (step t43.t1 (cl (! (= veriT_vr6 veriT_vr8) :named @p_91)) :rule refl)
 (step t43.t2 (cl (! (= veriT_vr7 veriT_vr9) :named @p_92)) :rule refl)
 (step t43.t3 (cl (= @p_76 (! (uminus$ veriT_vr9) :named @p_89))) :rule cong :premises (t43.t2))
@@ -3572,7 +3572,7 @@
 (step t43 (cl (! (= @p_88 (! (forall ((veriT_vr8 A$) (veriT_vr9 A_set$)) @p_95) :named @p_97)) :named @p_96)) :rule bind)
 (step t44 (cl (not @p_96) (not @p_88) @p_97) :rule equiv_pos2)
 (step t45 (cl @p_97) :rule th_resolution :premises (t42 t43 t44))
-(anchor :step t46 :args ((:= ?v0 veriT_vr10)))
+(anchor :step t46 :args ((:= (?v0 A_list$) veriT_vr10)))
 (step t46.t1 (cl (! (= ?v0 veriT_vr10) :named @p_102)) :rule refl)
 (step t46.t2 (cl (= @p_2 (! (set$ veriT_vr10) :named @p_99))) :rule cong :premises (t46.t1))
 (step t46.t3 (cl (= @p_100 (! (fun_app$b card$ @p_99) :named @p_101))) :rule cong :premises (t46.t2))
@@ -3583,7 +3583,7 @@
 (step t46 (cl (! (= @p_98 (! (forall ((veriT_vr10 A_list$)) @p_107) :named @p_109)) :named @p_108)) :rule bind)
 (step t47 (cl (not @p_108) (not @p_98) @p_109) :rule equiv_pos2)
 (step t48 (cl @p_109) :rule th_resolution :premises (a3 t46 t47))
-(anchor :step t49 :args ((:= veriT_vr10 veriT_vr11)))
+(anchor :step t49 :args ((:= (veriT_vr10 A_list$) veriT_vr11)))
 (step t49.t1 (cl (! (= veriT_vr10 veriT_vr11) :named @p_112)) :rule refl)
 (step t49.t2 (cl (= @p_99 (! (set$ veriT_vr11) :named @p_110))) :rule cong :premises (t49.t1))
 (step t49.t3 (cl (= @p_101 (! (fun_app$b card$ @p_110) :named @p_111))) :rule cong :premises (t49.t2))
@@ -3594,33 +3594,33 @@
 (step t49 (cl (! (= @p_109 (! (forall ((veriT_vr11 A_list$)) @p_115) :named @p_117)) :named @p_116)) :rule bind)
 (step t50 (cl (not @p_116) (not @p_109) @p_117) :rule equiv_pos2)
 (step t51 (cl @p_117) :rule th_resolution :premises (t48 t49 t50))
-(anchor :step t52 :args ((:= ?v0 veriT_vr12)))
+(anchor :step t52 :args ((:= (?v0 A_list$) veriT_vr12)))
 (step t52.t1 (cl (= ?v0 veriT_vr12)) :rule refl)
 (step t52.t2 (cl (= @p_2 (! (set$ veriT_vr12) :named @p_119))) :rule cong :premises (t52.t1))
 (step t52.t3 (cl (= @p_120 (! (finite$ @p_119) :named @p_121))) :rule cong :premises (t52.t2))
 (step t52 (cl (! (= @p_118 (! (forall ((veriT_vr12 A_list$)) @p_121) :named @p_123)) :named @p_122)) :rule bind)
 (step t53 (cl (not @p_122) (not @p_118) @p_123) :rule equiv_pos2)
 (step t54 (cl @p_123) :rule th_resolution :premises (a4 t52 t53))
-(anchor :step t55 :args ((:= veriT_vr12 veriT_vr13)))
+(anchor :step t55 :args ((:= (veriT_vr12 A_list$) veriT_vr13)))
 (step t55.t1 (cl (= veriT_vr12 veriT_vr13)) :rule refl)
 (step t55.t2 (cl (= @p_119 (! (set$ veriT_vr13) :named @p_124))) :rule cong :premises (t55.t1))
 (step t55.t3 (cl (= @p_121 (! (finite$ @p_124) :named @p_125))) :rule cong :premises (t55.t2))
 (step t55 (cl (! (= @p_123 (! (forall ((veriT_vr13 A_list$)) @p_125) :named @p_127)) :named @p_126)) :rule bind)
 (step t56 (cl (not @p_126) (not @p_123) @p_127) :rule equiv_pos2)
 (step t57 (cl @p_127) :rule th_resolution :premises (t54 t55 t56))
-(anchor :step t58 :args ((:= ?v0 veriT_vr14)))
+(anchor :step t58 :args ((:= (?v0 A$) veriT_vr14)))
 (step t58.t1 (cl (= ?v0 veriT_vr14)) :rule refl)
 (step t58.t2 (cl (= @p_129 (! (member$ veriT_vr14 top$) :named @p_130))) :rule cong :premises (t58.t1))
 (step t58 (cl (! (= @p_128 (! (forall ((veriT_vr14 A$)) @p_130) :named @p_132)) :named @p_131)) :rule bind)
 (step t59 (cl (not @p_131) (not @p_128) @p_132) :rule equiv_pos2)
 (step t60 (cl @p_132) :rule th_resolution :premises (a5 t58 t59))
-(anchor :step t61 :args ((:= veriT_vr14 veriT_vr15)))
+(anchor :step t61 :args ((:= (veriT_vr14 A$) veriT_vr15)))
 (step t61.t1 (cl (= veriT_vr14 veriT_vr15)) :rule refl)
 (step t61.t2 (cl (= @p_130 (! (member$ veriT_vr15 top$) :named @p_133))) :rule cong :premises (t61.t1))
 (step t61 (cl (! (= @p_132 (! (forall ((veriT_vr15 A$)) @p_133) :named @p_135)) :named @p_134)) :rule bind)
 (step t62 (cl (not @p_134) (not @p_132) @p_135) :rule equiv_pos2)
 (step t63 (cl @p_135) :rule th_resolution :premises (t60 t61 t62))
-(anchor :step t64 :args ((:= ?v0 veriT_vr26) (:= ?v1 veriT_vr27)))
+(anchor :step t64 :args ((:= (?v0 Nat$) veriT_vr26) (:= (?v1 Nat$) veriT_vr27)))
 (step t64.t1 (cl (! (= ?v0 veriT_vr26) :named @p_137)) :rule refl)
 (step t64.t2 (cl @p_137) :rule refl)
 (step t64.t3 (cl (! (= ?v1 veriT_vr27) :named @p_142)) :rule refl)
@@ -3632,7 +3632,7 @@
 (step t64 (cl (! (= @p_136 (! (forall ((veriT_vr26 Nat$) (veriT_vr27 Nat$)) @p_146) :named @p_148)) :named @p_147)) :rule bind)
 (step t65 (cl (not @p_147) (not @p_136) @p_148) :rule equiv_pos2)
 (step t66 (cl @p_148) :rule th_resolution :premises (a9 t64 t65))
-(anchor :step t67 :args ((:= veriT_vr26 veriT_vr28) (:= veriT_vr27 veriT_vr29)))
+(anchor :step t67 :args ((:= (veriT_vr26 Nat$) veriT_vr28) (:= (veriT_vr27 Nat$) veriT_vr29)))
 (step t67.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_149)) :rule refl)
 (step t67.t2 (cl @p_149) :rule refl)
 (step t67.t3 (cl (! (= veriT_vr27 veriT_vr29) :named @p_152)) :rule refl)
@@ -3644,7 +3644,7 @@
 (step t67 (cl (! (= @p_148 (! (forall ((veriT_vr28 Nat$) (veriT_vr29 Nat$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
 (step t68 (cl (not @p_155) (not @p_148) @p_156) :rule equiv_pos2)
 (step t69 (cl @p_156) :rule th_resolution :premises (t66 t67 t68))
-(anchor :step t70 :args ((:= ?v0 veriT_vr30) (:= ?v1 veriT_vr31)))
+(anchor :step t70 :args ((:= (?v0 A_set$) veriT_vr30) (:= (?v1 A_set$) veriT_vr31)))
 (step t70.t1 (cl (! (= ?v0 veriT_vr30) :named @p_163)) :rule refl)
 (step t70.t2 (cl (= @p_4 (! (finite$ veriT_vr30) :named @p_158))) :rule cong :premises (t70.t1))
 (step t70.t3 (cl (! (= ?v1 veriT_vr31) :named @p_165)) :rule refl)
@@ -3669,7 +3669,7 @@
 (step t70 (cl (! (= @p_157 (! (forall ((veriT_vr30 A_set$) (veriT_vr31 A_set$)) @p_182) :named @p_184)) :named @p_183)) :rule bind)
 (step t71 (cl (not @p_183) (not @p_157) @p_184) :rule equiv_pos2)
 (step t72 (cl @p_184) :rule th_resolution :premises (a12 t70 t71))
-(anchor :step t73 :args ((:= veriT_vr30 veriT_vr32) (:= veriT_vr31 veriT_vr33)))
+(anchor :step t73 :args ((:= (veriT_vr30 A_set$) veriT_vr32) (:= (veriT_vr31 A_set$) veriT_vr33)))
 (step t73.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_188)) :rule refl)
 (step t73.t2 (cl (= @p_158 (! (finite$ veriT_vr32) :named @p_185))) :rule cong :premises (t73.t1))
 (step t73.t3 (cl (! (= veriT_vr31 veriT_vr33) :named @p_190)) :rule refl)
@@ -3694,7 +3694,7 @@
 (step t73 (cl (! (= @p_184 (! (forall ((veriT_vr32 A_set$) (veriT_vr33 A_set$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
 (step t74 (cl (not @p_200) (not @p_184) @p_201) :rule equiv_pos2)
 (step t75 (cl @p_201) :rule th_resolution :premises (t72 t73 t74))
-(anchor :step t76 :args ((:= ?v0 veriT_vr34)))
+(anchor :step t76 :args ((:= (?v0 A_set$) veriT_vr34)))
 (step t76.t1 (cl (! (= ?v0 veriT_vr34) :named @p_206)) :rule refl)
 (step t76.t2 (cl (= @p_3 (! (fun_app$b card$ veriT_vr34) :named @p_203))) :rule cong :premises (t76.t1))
 (step t76.t3 (cl (= @p_204 (! (= zero$ @p_203) :named @p_205))) :rule cong :premises (t76.t2))
@@ -3708,7 +3708,7 @@
 (step t76 (cl (! (= @p_202 (! (forall ((veriT_vr34 A_set$)) @p_215) :named @p_217)) :named @p_216)) :rule bind)
 (step t77 (cl (not @p_216) (not @p_202) @p_217) :rule equiv_pos2)
 (step t78 (cl @p_217) :rule th_resolution :premises (a13 t76 t77))
-(anchor :step t79 :args ((:= veriT_vr34 veriT_vr35)))
+(anchor :step t79 :args ((:= (veriT_vr34 A_set$) veriT_vr35)))
 (step t79.t1 (cl (! (= veriT_vr34 veriT_vr35) :named @p_220)) :rule refl)
 (step t79.t2 (cl (= @p_203 (! (fun_app$b card$ veriT_vr35) :named @p_218))) :rule cong :premises (t79.t1))
 (step t79.t3 (cl (= @p_205 (! (= zero$ @p_218) :named @p_219))) :rule cong :premises (t79.t2))
@@ -3722,7 +3722,7 @@
 (step t79 (cl (! (= @p_217 (! (forall ((veriT_vr35 A_set$)) @p_225) :named @p_227)) :named @p_226)) :rule bind)
 (step t80 (cl (not @p_226) (not @p_217) @p_227) :rule equiv_pos2)
 (step t81 (cl @p_227) :rule th_resolution :premises (t78 t79 t80))
-(anchor :step t82 :args ((:= ?v0 veriT_vr36)))
+(anchor :step t82 :args ((:= (?v0 A_set$) veriT_vr36)))
 (step t82.t1 (cl (! (= ?v0 veriT_vr36) :named @p_234)) :rule refl)
 (step t82.t2 (cl (= @p_3 (! (fun_app$b card$ veriT_vr36) :named @p_229))) :rule cong :premises (t82.t1))
 (step t82.t3 (cl (= @p_230 (! (= @p_1 @p_229) :named @p_231))) :rule cong :premises (t82.t2))
@@ -3733,7 +3733,7 @@
 (step t82 (cl (! (= @p_228 (! (forall ((veriT_vr36 A_set$)) @p_238) :named @p_240)) :named @p_239)) :rule bind)
 (step t83 (cl (not @p_239) (not @p_228) @p_240) :rule equiv_pos2)
 (step t84 (cl @p_240) :rule th_resolution :premises (a14 t82 t83))
-(anchor :step t85 :args ((:= veriT_vr36 veriT_vr37)))
+(anchor :step t85 :args ((:= (veriT_vr36 A_set$) veriT_vr37)))
 (step t85.t1 (cl (! (= veriT_vr36 veriT_vr37) :named @p_244)) :rule refl)
 (step t85.t2 (cl (= @p_229 (! (fun_app$b card$ veriT_vr37) :named @p_241))) :rule cong :premises (t85.t1))
 (step t85.t3 (cl (= @p_231 (! (= @p_1 @p_241) :named @p_242))) :rule cong :premises (t85.t2))
@@ -3744,7 +3744,7 @@
 (step t85 (cl (! (= @p_240 (! (forall ((veriT_vr37 A_set$)) @p_246) :named @p_248)) :named @p_247)) :rule bind)
 (step t86 (cl (not @p_247) (not @p_240) @p_248) :rule equiv_pos2)
 (step t87 (cl @p_248) :rule th_resolution :premises (t84 t85 t86))
-(anchor :step t88 :args ((:= ?v0 veriT_vr38)))
+(anchor :step t88 :args ((:= (?v0 A_list$) veriT_vr38)))
 (step t88.t1 (cl (! (= ?v0 veriT_vr38) :named @p_251)) :rule refl)
 (step t88.t2 (cl (= @p_2 (! (set$ veriT_vr38) :named @p_250))) :rule cong :premises (t88.t1))
 (step t88.t3 (cl @p_251) :rule refl)
@@ -3754,7 +3754,7 @@
 (step t88 (cl (! (= @p_249 (! (forall ((veriT_vr38 A_list$)) @p_256) :named @p_258)) :named @p_257)) :rule bind)
 (step t89 (cl (not @p_257) (not @p_249) @p_258) :rule equiv_pos2)
 (step t90 (cl @p_258) :rule th_resolution :premises (a15 t88 t89))
-(anchor :step t91 :args ((:= veriT_vr38 veriT_vr39)))
+(anchor :step t91 :args ((:= (veriT_vr38 A_list$) veriT_vr39)))
 (step t91.t1 (cl (! (= veriT_vr38 veriT_vr39) :named @p_260)) :rule refl)
 (step t91.t2 (cl (= @p_250 (! (set$ veriT_vr39) :named @p_259))) :rule cong :premises (t91.t1))
 (step t91.t3 (cl @p_260) :rule refl)
@@ -3764,7 +3764,7 @@
 (step t91 (cl (! (= @p_258 (! (forall ((veriT_vr39 A_list$)) @p_263) :named @p_265)) :named @p_264)) :rule bind)
 (step t92 (cl (not @p_264) (not @p_258) @p_265) :rule equiv_pos2)
 (step t93 (cl @p_265) :rule th_resolution :premises (t90 t91 t92))
-(anchor :step t94 :args ((:= ?v0 veriT_vr40)))
+(anchor :step t94 :args ((:= (?v0 A_list$) veriT_vr40)))
 (step t94.t1 (cl (! (= ?v0 veriT_vr40) :named @p_268)) :rule refl)
 (step t94.t2 (cl (= @p_5 (! (coset$ veriT_vr40) :named @p_267))) :rule cong :premises (t94.t1))
 (step t94.t3 (cl @p_268) :rule refl)
@@ -3774,7 +3774,7 @@
 (step t94 (cl (! (= @p_266 (! (forall ((veriT_vr40 A_list$)) @p_273) :named @p_275)) :named @p_274)) :rule bind)
 (step t95 (cl (not @p_274) (not @p_266) @p_275) :rule equiv_pos2)
 (step t96 (cl @p_275) :rule th_resolution :premises (a16 t94 t95))
-(anchor :step t97 :args ((:= veriT_vr40 veriT_vr41)))
+(anchor :step t97 :args ((:= (veriT_vr40 A_list$) veriT_vr41)))
 (step t97.t1 (cl (! (= veriT_vr40 veriT_vr41) :named @p_277)) :rule refl)
 (step t97.t2 (cl (= @p_267 (! (coset$ veriT_vr41) :named @p_276))) :rule cong :premises (t97.t1))
 (step t97.t3 (cl @p_277) :rule refl)
@@ -3784,12 +3784,12 @@
 (step t97 (cl (! (= @p_275 (! (forall ((veriT_vr41 A_list$)) @p_280) :named @p_282)) :named @p_281)) :rule bind)
 (step t98 (cl (not @p_281) (not @p_275) @p_282) :rule equiv_pos2)
 (step t99 (cl @p_282) :rule th_resolution :premises (t96 t97 t98))
-(anchor :step t100 :args ((:= ?v0 veriT_vr42) (:= ?v1 veriT_vr43)))
+(anchor :step t100 :args ((:= (?v0 A_set$) veriT_vr42) (:= (?v1 A_set$) veriT_vr43)))
 (step t100.t1 (cl (! (= ?v0 veriT_vr42) :named @p_289)) :rule refl)
 (step t100.t2 (cl (! (= ?v1 veriT_vr43) :named @p_292)) :rule refl)
 (step t100.t3 (cl (= @p_6 (! (inf$ veriT_vr42 veriT_vr43) :named @p_284))) :rule cong :premises (t100.t1 t100.t2))
 (step t100.t4 (cl (= @p_285 (! (= bot$ @p_284) :named @p_286))) :rule cong :premises (t100.t3))
-(anchor :step t100.t5 :args ((:= ?v2 veriT_vr44)))
+(anchor :step t100.t5 :args ((:= (?v2 A$) veriT_vr44)))
 (step t100.t5.t1 (cl (! (= ?v2 veriT_vr44) :named @p_291)) :rule refl)
 (step t100.t5.t2 (cl @p_289) :rule refl)
 (step t100.t5.t3 (cl (= @p_15 (! (member$ veriT_vr44 veriT_vr42) :named @p_290))) :rule cong :premises (t100.t5.t1 t100.t5.t2))
@@ -3803,17 +3803,17 @@
 (step t100 (cl (! (= @p_283 (! (forall ((veriT_vr42 A_set$) (veriT_vr43 A_set$)) @p_299) :named @p_301)) :named @p_300)) :rule bind)
 (step t101 (cl (not @p_300) (not @p_283) @p_301) :rule equiv_pos2)
 (step t102 (cl @p_301) :rule th_resolution :premises (a17 t100 t101))
-(anchor :step t103 :args (veriT_vr42 veriT_vr43))
+(anchor :step t103 :args ((veriT_vr42 A_set$) (veriT_vr43 A_set$)))
 (step t103.t1 (cl (= @p_299 (! (and (! (=> @p_286 @p_288) :named @p_315) (! (=> @p_288 @p_286) :named @p_325)) :named @p_302))) :rule connective_def)
 (step t103 (cl (! (= @p_301 (! (forall ((veriT_vr42 A_set$) (veriT_vr43 A_set$)) @p_302) :named @p_304)) :named @p_303)) :rule bind)
 (step t104 (cl (not @p_303) (not @p_301) @p_304) :rule equiv_pos2)
 (step t105 (cl @p_304) :rule th_resolution :premises (t102 t103 t104))
-(anchor :step t106 :args ((:= veriT_vr42 veriT_vr45) (:= veriT_vr43 veriT_vr46)))
+(anchor :step t106 :args ((:= (veriT_vr42 A_set$) veriT_vr45) (:= (veriT_vr43 A_set$) veriT_vr46)))
 (step t106.t1 (cl (! (= veriT_vr42 veriT_vr45) :named @p_308)) :rule refl)
 (step t106.t2 (cl (! (= veriT_vr43 veriT_vr46) :named @p_311)) :rule refl)
 (step t106.t3 (cl (! (= @p_284 (! (inf$ veriT_vr45 veriT_vr46) :named @p_306)) :named @p_323)) :rule cong :premises (t106.t1 t106.t2))
 (step t106.t4 (cl (! (= @p_286 (! (= bot$ @p_306) :named @p_305)) :named @p_324)) :rule cong :premises (t106.t3))
-(anchor :step t106.t5 :args ((:= veriT_vr44 veriT_vr47)))
+(anchor :step t106.t5 :args ((:= (veriT_vr44 A$) veriT_vr47)))
 (step t106.t5.t1 (cl (! (= veriT_vr44 veriT_vr47) :named @p_310)) :rule refl)
 (step t106.t5.t2 (cl @p_308) :rule refl)
 (step t106.t5.t3 (cl (= @p_290 (! (member$ veriT_vr47 veriT_vr45) :named @p_309))) :rule cong :premises (t106.t5.t1 t106.t5.t2))
@@ -3824,7 +3824,7 @@
 (step t106.t5.t8 (cl (= @p_297 (! (=> @p_309 @p_313) :named @p_314))) :rule cong :premises (t106.t5.t3 t106.t5.t7))
 (step t106.t5 (cl (= @p_288 (! (forall ((veriT_vr47 A$)) @p_314) :named @p_307))) :rule bind)
 (step t106.t6 (cl (= @p_315 (! (=> @p_305 @p_307) :named @p_316))) :rule cong :premises (t106.t4 t106.t5))
-(anchor :step t106.t7 :args ((:= veriT_vr44 veriT_vr48)))
+(anchor :step t106.t7 :args ((:= (veriT_vr44 A$) veriT_vr48)))
 (step t106.t7.t1 (cl (! (= veriT_vr44 veriT_vr48) :named @p_319)) :rule refl)
 (step t106.t7.t2 (cl @p_308) :rule refl)
 (step t106.t7.t3 (cl (= @p_290 (! (member$ veriT_vr48 veriT_vr45) :named @p_318))) :rule cong :premises (t106.t7.t1 t106.t7.t2))
@@ -3843,12 +3843,12 @@
 (step t106 (cl (! (= @p_304 (! (forall ((veriT_vr45 A_set$) (veriT_vr46 A_set$)) @p_327) :named @p_329)) :named @p_328)) :rule bind)
 (step t107 (cl (not @p_328) (not @p_304) @p_329) :rule equiv_pos2)
 (step t108 (cl @p_329) :rule th_resolution :premises (t105 t106 t107))
-(anchor :step t109 :args ((:= veriT_vr45 veriT_vr49) (:= veriT_vr46 veriT_vr50)))
+(anchor :step t109 :args ((:= (veriT_vr45 A_set$) veriT_vr49) (:= (veriT_vr46 A_set$) veriT_vr50)))
 (step t109.t1 (cl (! (= veriT_vr45 veriT_vr49) :named @p_333)) :rule refl)
 (step t109.t2 (cl (! (= veriT_vr46 veriT_vr50) :named @p_336)) :rule refl)
 (step t109.t3 (cl (! (= @p_306 (! (inf$ veriT_vr49 veriT_vr50) :named @p_332)) :named @p_342)) :rule cong :premises (t109.t1 t109.t2))
 (step t109.t4 (cl (! (= @p_305 (! (= bot$ @p_332) :named @p_331)) :named @p_343)) :rule cong :premises (t109.t3))
-(anchor :step t109.t5 :args ((:= veriT_vr47 veriT_vr51)))
+(anchor :step t109.t5 :args ((:= (veriT_vr47 A$) veriT_vr51)))
 (step t109.t5.t1 (cl (! (= veriT_vr47 veriT_vr51) :named @p_335)) :rule refl)
 (step t109.t5.t2 (cl @p_333) :rule refl)
 (step t109.t5.t3 (cl (= @p_309 (! (member$ veriT_vr51 veriT_vr49) :named @p_334))) :rule cong :premises (t109.t5.t1 t109.t5.t2))
@@ -3859,7 +3859,7 @@
 (step t109.t5.t8 (cl (= @p_314 (! (=> @p_334 @p_338) :named @p_339))) :rule cong :premises (t109.t5.t3 t109.t5.t7))
 (step t109.t5 (cl (= @p_307 (! (forall ((veriT_vr51 A$)) @p_339) :named @p_330))) :rule bind)
 (step t109.t6 (cl (= @p_316 (! (=> @p_331 @p_330) :named @p_340))) :rule cong :premises (t109.t4 t109.t5))
-(anchor :step t109.t7 :args ((:= veriT_vr48 veriT_vr51)))
+(anchor :step t109.t7 :args ((:= (veriT_vr48 A$) veriT_vr51)))
 (step t109.t7.t1 (cl (! (= veriT_vr48 veriT_vr51) :named @p_341)) :rule refl)
 (step t109.t7.t2 (cl @p_333) :rule refl)
 (step t109.t7.t3 (cl (= @p_318 @p_334)) :rule cong :premises (t109.t7.t1 t109.t7.t2))
@@ -3878,8 +3878,8 @@
 (step t109 (cl (! (= @p_329 (! (forall ((veriT_vr49 A_set$) (veriT_vr50 A_set$)) @p_345) :named @p_347)) :named @p_346)) :rule bind)
 (step t110 (cl (not @p_346) (not @p_329) @p_347) :rule equiv_pos2)
 (step t111 (cl @p_347) :rule th_resolution :premises (t108 t109 t110))
-(anchor :step t112 :args ((:= veriT_vr49 veriT_vr49) (:= veriT_vr50 veriT_vr50)))
-(anchor :step t112.t1 :args ((:= veriT_vr51 veriT_vr52)))
+(anchor :step t112 :args ((:= (veriT_vr49 A_set$) veriT_vr49) (:= (veriT_vr50 A_set$) veriT_vr50)))
+(anchor :step t112.t1 :args ((:= (veriT_vr51 A$) veriT_vr52)))
 (step t112.t1.t1 (cl (! (= veriT_vr51 veriT_vr52) :named @p_350)) :rule refl)
 (step t112.t1.t2 (cl (= @p_334 (! (member$ veriT_vr52 veriT_vr49) :named @p_349))) :rule cong :premises (t112.t1.t1))
 (step t112.t1.t3 (cl @p_350) :rule refl)
@@ -3892,7 +3892,7 @@
 (step t112 (cl (! (= @p_347 (! (forall ((veriT_vr49 A_set$) (veriT_vr50 A_set$)) @p_355) :named @p_357)) :named @p_356)) :rule bind)
 (step t113 (cl (not @p_356) (not @p_347) @p_357) :rule equiv_pos2)
 (step t114 (cl @p_357) :rule th_resolution :premises (t111 t112 t113))
-(anchor :step t115 :args ((:= ?v0 veriT_vr53)))
+(anchor :step t115 :args ((:= (?v0 A_set$) veriT_vr53)))
 (step t115.t1 (cl (! (= ?v0 veriT_vr53) :named @p_360)) :rule refl)
 (step t115.t2 (cl (= @p_4 (! (finite$ veriT_vr53) :named @p_359))) :rule cong :premises (t115.t1))
 (step t115.t3 (cl @p_360) :rule refl)
@@ -3903,7 +3903,7 @@
 (step t115 (cl (! (= @p_358 (! (forall ((veriT_vr53 A_set$)) @p_368) :named @p_370)) :named @p_369)) :rule bind)
 (step t116 (cl (not @p_369) (not @p_358) @p_370) :rule equiv_pos2)
 (step t117 (cl @p_370) :rule th_resolution :premises (a19 t115 t116))
-(anchor :step t118 :args ((:= veriT_vr53 veriT_vr54)))
+(anchor :step t118 :args ((:= (veriT_vr53 A_set$) veriT_vr54)))
 (step t118.t1 (cl (! (= veriT_vr53 veriT_vr54) :named @p_372)) :rule refl)
 (step t118.t2 (cl (= @p_359 (! (finite$ veriT_vr54) :named @p_371))) :rule cong :premises (t118.t1))
 (step t118.t3 (cl @p_372) :rule refl)
@@ -3914,7 +3914,7 @@
 (step t118 (cl (! (= @p_370 (! (forall ((veriT_vr54 A_set$)) @p_376) :named @p_378)) :named @p_377)) :rule bind)
 (step t119 (cl (not @p_377) (not @p_370) @p_378) :rule equiv_pos2)
 (step t120 (cl @p_378) :rule th_resolution :premises (t117 t118 t119))
-(anchor :step t121 :args ((:= ?v0 veriT_vr55)))
+(anchor :step t121 :args ((:= (?v0 A$) veriT_vr55)))
 (step t121.t1 (cl (! (= ?v0 veriT_vr55) :named @p_383)) :rule refl)
 (step t121.t2 (cl (! (= @p_12 (! (member$ veriT_vr55 @p_380) :named @p_382)) :named @p_391)) :rule cong :premises (t121.t1))
 (step t121.t3 (cl @p_383) :rule refl)
@@ -3922,7 +3922,7 @@
 (step t121.t5 (cl (= @p_385 (! (not @p_384) :named @p_386))) :rule cong :premises (t121.t4))
 (step t121.t6 (cl (= @p_387 (! (=> @p_382 @p_386) :named @p_388))) :rule cong :premises (t121.t2 t121.t5))
 (step t121 (cl (= @p_379 (! (forall ((veriT_vr55 A$)) @p_388) :named @p_397))) :rule bind)
-(anchor :step t122 :args ((:= ?v0 veriT_vr55)))
+(anchor :step t122 :args ((:= (?v0 A$) veriT_vr55)))
 (step t122.t1 (cl @p_383) :rule refl)
 (step t122.t2 (cl @p_390) :rule cong :premises (t122.t1))
 (step t122.t3 (cl @p_383) :rule refl)
@@ -3945,7 +3945,7 @@
 (step t135 (cl (! (= @p_412 (! (= rhs$ @p_413) :named @p_415)) :named @p_414)) :rule cong :premises (t134))
 (step t136 (cl (not @p_414) (not @p_412) @p_415) :rule equiv_pos2)
 (step t137 (cl @p_415) :rule th_resolution :premises (t133 t135 t136))
-(anchor :step t138 :args ((:= veriT_vr55 veriT_vr56)))
+(anchor :step t138 :args ((:= (veriT_vr55 A$) veriT_vr56)))
 (step t138.t1 (cl (! (= veriT_vr55 veriT_vr56) :named @p_417)) :rule refl)
 (step t138.t2 (cl (= @p_384 (! (member$ veriT_vr56 @p_381) :named @p_416))) :rule cong :premises (t138.t1))
 (step t138.t3 (cl @p_417) :rule refl)
@@ -3961,7 +3961,7 @@
 (step t144 (cl (! (= @p_426 (! (and (! (=> rhs$ @p_424) :named @p_442) (! (=> @p_424 rhs$) :named @p_444)) :named @p_428)) :named @p_427)) :rule connective_def)
 (step t145 (cl (not @p_427) (not @p_426) @p_428) :rule equiv_pos2)
 (step t146 (cl @p_428) :rule th_resolution :premises (t143 t144 t145))
-(anchor :step t147 :args ((:= veriT_vr55 veriT_vr57)))
+(anchor :step t147 :args ((:= (veriT_vr55 A$) veriT_vr57)))
 (step t147.t1 (cl (! (= veriT_vr55 veriT_vr57) :named @p_430)) :rule refl)
 (step t147.t2 (cl (= @p_382 @p_429)) :rule cong :premises (t147.t1))
 (step t147.t3 (cl @p_430) :rule refl)
@@ -3969,7 +3969,7 @@
 (step t147.t5 (cl (= @p_386 @p_432)) :rule cong :premises (t147.t4))
 (step t147.t6 (cl (= @p_388 @p_433)) :rule cong :premises (t147.t2 t147.t5))
 (step t147 (cl (= @p_397 (! (forall ((veriT_vr57 A$)) @p_433) :named @p_439))) :rule bind)
-(anchor :step t148 :args ((:= veriT_vr56 veriT_vr58)))
+(anchor :step t148 :args ((:= (veriT_vr56 A$) veriT_vr58)))
 (step t148.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_435)) :rule refl)
 (step t148.t2 (cl (= @p_416 @p_434)) :rule cong :premises (t148.t1))
 (step t148.t3 (cl @p_435) :rule refl)
@@ -3984,7 +3984,7 @@
 (step t153 (cl (! (= @p_428 (! (and @p_445 @p_446) :named @p_448)) :named @p_447)) :rule cong :premises (t151 t152))
 (step t154 (cl (not @p_447) (not @p_428) @p_448) :rule equiv_pos2)
 (step t155 (cl @p_448) :rule th_resolution :premises (t146 t153 t154))
-(anchor :step t156 :args ((:= veriT_vr57 veriT_sk0)))
+(anchor :step t156 :args ((:= (veriT_vr57 A$) veriT_sk0)))
 (step t156.t1 (cl (! (= veriT_vr57 veriT_sk0) :named @p_451)) :rule refl)
 (step t156.t2 (cl (= @p_429 (! (member$ veriT_sk0 @p_380) :named @p_450))) :rule cong :premises (t156.t1))
 (step t156.t3 (cl @p_451) :rule refl)
@@ -3992,7 +3992,7 @@
 (step t156.t5 (cl (= @p_432 (! (not @p_452) :named @p_453))) :rule cong :premises (t156.t4))
 (step t156.t6 (cl (= @p_433 (! (=> @p_450 @p_453) :named @p_454))) :rule cong :premises (t156.t2 t156.t5))
 (step t156 (cl (= @p_439 @p_454)) :rule sko_forall)
-(anchor :step t157 :args ((:= veriT_vr58 veriT_sk1)))
+(anchor :step t157 :args ((:= (veriT_vr58 A$) veriT_sk1)))
 (step t157.t1 (cl (! (= veriT_vr58 veriT_sk1) :named @p_457)) :rule refl)
 (step t157.t2 (cl (= @p_434 (! (member$ veriT_sk1 @p_381) :named @p_456))) :rule cong :premises (t157.t1))
 (step t157.t3 (cl @p_457) :rule refl)
@@ -4006,7 +4006,7 @@
 (step t161 (cl (! (= @p_448 (! (and @p_445 @p_463) :named @p_465)) :named @p_464)) :rule cong :premises (t160))
 (step t162 (cl (not @p_464) (not @p_448) @p_465) :rule equiv_pos2)
 (step t163 (cl @p_465) :rule th_resolution :premises (t155 t161 t162))
-(anchor :step t164 :args ((:= veriT_vr57 veriT_vr59)))
+(anchor :step t164 :args ((:= (veriT_vr57 A$) veriT_vr59)))
 (step t164.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_467)) :rule refl)
 (step t164.t2 (cl (= @p_429 (! (member$ veriT_vr59 @p_380) :named @p_466))) :rule cong :premises (t164.t1))
 (step t164.t3 (cl @p_467) :rule refl)
@@ -4014,7 +4014,7 @@
 (step t164.t5 (cl (= @p_432 (! (not @p_468) :named @p_469))) :rule cong :premises (t164.t4))
 (step t164.t6 (cl (= @p_433 (! (=> @p_466 @p_469) :named @p_470))) :rule cong :premises (t164.t2 t164.t5))
 (step t164 (cl (= @p_439 (! (forall ((veriT_vr59 A$)) @p_470) :named @p_474))) :rule bind)
-(anchor :step t165 :args ((:= veriT_vr58 veriT_vr59)))
+(anchor :step t165 :args ((:= (veriT_vr58 A$) veriT_vr59)))
 (step t165.t1 (cl (! (= veriT_vr58 veriT_vr59) :named @p_471)) :rule refl)
 (step t165.t2 (cl (= @p_434 @p_468)) :rule cong :premises (t165.t1))
 (step t165.t3 (cl @p_471) :rule refl)
@@ -4035,7 +4035,7 @@
 (step t176 (cl (! (= @p_480 (! (and @p_483 @p_484) :named @p_486)) :named @p_485)) :rule ac_simp :premises (t173 t175))
 (step t177 (cl (not @p_485) (not @p_480) @p_486) :rule equiv_pos2)
 (step t178 (cl @p_486) :rule th_resolution :premises (t171 t176 t177))
-(anchor :step t179 :args ((:= veriT_vr59 veriT_vr60)))
+(anchor :step t179 :args ((:= (veriT_vr59 A$) veriT_vr60)))
 (step t179.t1 (cl (! (= veriT_vr59 veriT_vr60) :named @p_488)) :rule refl)
 (step t179.t2 (cl (= @p_468 (! (member$ veriT_vr60 @p_381) :named @p_487))) :rule cong :premises (t179.t1))
 (step t179.t3 (cl @p_488) :rule refl)
@@ -4048,7 +4048,7 @@
 (step t182 (cl (! (= @p_486 (! (and @p_494 @p_484) :named @p_496)) :named @p_495)) :rule cong :premises (t181))
 (step t183 (cl (not @p_495) (not @p_486) @p_496) :rule equiv_pos2)
 (step t184 (cl @p_496) :rule th_resolution :premises (t178 t182 t183))
-(anchor :step t185 :args ((:= ?v0 veriT_vr61) (:= ?v1 veriT_vr62)))
+(anchor :step t185 :args ((:= (?v0 A_list$) veriT_vr61) (:= (?v1 A_list$) veriT_vr62)))
 (step t185.t1 (cl (! (= ?v0 veriT_vr61) :named @p_502)) :rule refl)
 (step t185.t2 (cl (! (= ?v1 veriT_vr62) :named @p_504)) :rule refl)
 (step t185.t3 (cl (= @p_498 (! (append$ veriT_vr61 veriT_vr62) :named @p_499))) :rule cong :premises (t185.t1 t185.t2))
@@ -4062,7 +4062,7 @@
 (step t185 (cl (! (= @p_497 (! (forall ((veriT_vr61 A_list$) (veriT_vr62 A_list$)) @p_509) :named @p_511)) :named @p_510)) :rule bind)
 (step t186 (cl (not @p_510) (not @p_497) @p_511) :rule equiv_pos2)
 (step t187 (cl @p_511) :rule th_resolution :premises (a21 t185 t186))
-(anchor :step t188 :args ((:= veriT_vr61 veriT_vr63) (:= veriT_vr62 veriT_vr64)))
+(anchor :step t188 :args ((:= (veriT_vr61 A_list$) veriT_vr63) (:= (veriT_vr62 A_list$) veriT_vr64)))
 (step t188.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_514)) :rule refl)
 (step t188.t2 (cl (! (= veriT_vr62 veriT_vr64) :named @p_516)) :rule refl)
 (step t188.t3 (cl (= @p_499 (! (append$ veriT_vr63 veriT_vr64) :named @p_512))) :rule cong :premises (t188.t1 t188.t2))
@@ -4076,7 +4076,7 @@
 (step t188 (cl (! (= @p_511 (! (forall ((veriT_vr63 A_list$) (veriT_vr64 A_list$)) @p_519) :named @p_521)) :named @p_520)) :rule bind)
 (step t189 (cl (not @p_520) (not @p_511) @p_521) :rule equiv_pos2)
 (step t190 (cl @p_521) :rule th_resolution :premises (t187 t188 t189))
-(anchor :step t191 :args ((:= ?v0 veriT_vr65) (:= ?v1 veriT_vr66)))
+(anchor :step t191 :args ((:= (?v0 A_set$) veriT_vr65) (:= (?v1 A_set$) veriT_vr66)))
 (step t191.t1 (cl (! (= ?v0 veriT_vr65) :named @p_524)) :rule refl)
 (step t191.t2 (cl (! (= ?v1 veriT_vr66) :named @p_526)) :rule refl)
 (step t191.t3 (cl (= @p_13 (! (= veriT_vr65 veriT_vr66) :named @p_523))) :rule cong :premises (t191.t1 t191.t2))
@@ -4093,7 +4093,7 @@
 (step t191 (cl (! (= @p_522 (! (forall ((veriT_vr65 A_set$) (veriT_vr66 A_set$)) @p_534) :named @p_536)) :named @p_535)) :rule bind)
 (step t192 (cl (not @p_535) (not @p_522) @p_536) :rule equiv_pos2)
 (step t193 (cl @p_536) :rule th_resolution :premises (a22 t191 t192))
-(anchor :step t194 :args ((:= veriT_vr65 veriT_vr67) (:= veriT_vr66 veriT_vr68)))
+(anchor :step t194 :args ((:= (veriT_vr65 A_set$) veriT_vr67) (:= (veriT_vr66 A_set$) veriT_vr68)))
 (step t194.t1 (cl (! (= veriT_vr65 veriT_vr67) :named @p_538)) :rule refl)
 (step t194.t2 (cl (! (= veriT_vr66 veriT_vr68) :named @p_540)) :rule refl)
 (step t194.t3 (cl (= @p_523 (! (= veriT_vr67 veriT_vr68) :named @p_537))) :rule cong :premises (t194.t1 t194.t2))
@@ -4110,7 +4110,7 @@
 (step t194 (cl (! (= @p_536 (! (forall ((veriT_vr67 A_set$) (veriT_vr68 A_set$)) @p_545) :named @p_547)) :named @p_546)) :rule bind)
 (step t195 (cl (not @p_546) (not @p_536) @p_547) :rule equiv_pos2)
 (step t196 (cl @p_547) :rule th_resolution :premises (t193 t194 t195))
-(anchor :step t197 :args ((:= ?v0 veriT_vr69)))
+(anchor :step t197 :args ((:= (?v0 A_list$) veriT_vr69)))
 (step t197.t1 (cl (! (= ?v0 veriT_vr69) :named @p_550)) :rule refl)
 (step t197.t2 (cl (= @p_2 (! (set$ veriT_vr69) :named @p_549))) :rule cong :premises (t197.t1))
 (step t197.t3 (cl @p_550) :rule refl)
@@ -4120,7 +4120,7 @@
 (step t197 (cl (! (= @p_548 (! (forall ((veriT_vr69 A_list$)) @p_555) :named @p_557)) :named @p_556)) :rule bind)
 (step t198 (cl (not @p_556) (not @p_548) @p_557) :rule equiv_pos2)
 (step t199 (cl @p_557) :rule th_resolution :premises (a23 t197 t198))
-(anchor :step t200 :args ((:= veriT_vr69 veriT_vr70)))
+(anchor :step t200 :args ((:= (veriT_vr69 A_list$) veriT_vr70)))
 (step t200.t1 (cl (! (= veriT_vr69 veriT_vr70) :named @p_559)) :rule refl)
 (step t200.t2 (cl (= @p_549 (! (set$ veriT_vr70) :named @p_558))) :rule cong :premises (t200.t1))
 (step t200.t3 (cl @p_559) :rule refl)
@@ -4130,8 +4130,8 @@
 (step t200 (cl (! (= @p_557 (! (forall ((veriT_vr70 A_list$)) @p_562) :named @p_564)) :named @p_563)) :rule bind)
 (step t201 (cl (not @p_563) (not @p_557) @p_564) :rule equiv_pos2)
 (step t202 (cl @p_564) :rule th_resolution :premises (t199 t200 t201))
-(anchor :step t203 :args ((:= ?v0 veriT_vr71) (:= ?v1 veriT_vr72)))
-(anchor :step t203.t1 :args ((:= ?v2 veriT_vr73)))
+(anchor :step t203 :args ((:= (?v0 A_set$) veriT_vr71) (:= (?v1 A_set$) veriT_vr72)))
+(anchor :step t203.t1 :args ((:= (?v2 A$) veriT_vr73)))
 (step t203.t1.t1 (cl (! (= ?v2 veriT_vr73) :named @p_569)) :rule refl)
 (step t203.t1.t2 (cl (! (= ?v0 veriT_vr71) :named @p_573)) :rule refl)
 (step t203.t1.t3 (cl (= @p_15 (! (member$ veriT_vr73 veriT_vr71) :named @p_568))) :rule cong :premises (t203.t1.t1 t203.t1.t2))
@@ -4148,8 +4148,8 @@
 (step t203 (cl (! (= @p_565 (! (forall ((veriT_vr71 A_set$) (veriT_vr72 A_set$)) @p_578) :named @p_580)) :named @p_579)) :rule bind)
 (step t204 (cl (not @p_579) (not @p_565) @p_580) :rule equiv_pos2)
 (step t205 (cl @p_580) :rule th_resolution :premises (a25 t203 t204))
-(anchor :step t206 :args ((:= veriT_vr71 veriT_vr74) (:= veriT_vr72 veriT_vr75)))
-(anchor :step t206.t1 :args ((:= veriT_vr73 veriT_vr76)))
+(anchor :step t206 :args ((:= (veriT_vr71 A_set$) veriT_vr74) (:= (veriT_vr72 A_set$) veriT_vr75)))
+(anchor :step t206.t1 :args ((:= (veriT_vr73 A$) veriT_vr76)))
 (step t206.t1.t1 (cl (! (= veriT_vr73 veriT_vr76) :named @p_583)) :rule refl)
 (step t206.t1.t2 (cl (! (= veriT_vr71 veriT_vr74) :named @p_586)) :rule refl)
 (step t206.t1.t3 (cl (= @p_568 (! (member$ veriT_vr76 veriT_vr74) :named @p_582))) :rule cong :premises (t206.t1.t1 t206.t1.t2))
@@ -4166,7 +4166,7 @@
 (step t206 (cl (! (= @p_580 (! (forall ((veriT_vr74 A_set$) (veriT_vr75 A_set$)) @p_590) :named @p_592)) :named @p_591)) :rule bind)
 (step t207 (cl (not @p_591) (not @p_580) @p_592) :rule equiv_pos2)
 (step t208 (cl @p_592) :rule th_resolution :premises (t205 t206 t207))
-(anchor :step t209 :args ((:= ?v0 veriT_vr77) (:= ?v1 veriT_vr78)))
+(anchor :step t209 :args ((:= (?v0 A_set$) veriT_vr77) (:= (?v1 A_set$) veriT_vr78)))
 (step t209.t1 (cl (! (= ?v0 veriT_vr77) :named @p_598)) :rule refl)
 (step t209.t2 (cl (= @p_19 (! (fun_app$a less_eq$ veriT_vr77) :named @p_594))) :rule cong :premises (t209.t1))
 (step t209.t3 (cl (! (= ?v1 veriT_vr78) :named @p_596)) :rule refl)
@@ -4183,7 +4183,7 @@
 (step t209 (cl (! (= @p_593 (! (forall ((veriT_vr77 A_set$) (veriT_vr78 A_set$)) @p_603) :named @p_605)) :named @p_604)) :rule bind)
 (step t210 (cl (not @p_604) (not @p_593) @p_605) :rule equiv_pos2)
 (step t211 (cl @p_605) :rule th_resolution :premises (a26 t209 t210))
-(anchor :step t212 :args ((:= veriT_vr77 veriT_vr79) (:= veriT_vr78 veriT_vr80)))
+(anchor :step t212 :args ((:= (veriT_vr77 A_set$) veriT_vr79) (:= (veriT_vr78 A_set$) veriT_vr80)))
 (step t212.t1 (cl (! (= veriT_vr77 veriT_vr79) :named @p_610)) :rule refl)
 (step t212.t2 (cl (= @p_594 (! (fun_app$a less_eq$ veriT_vr79) :named @p_606))) :rule cong :premises (t212.t1))
 (step t212.t3 (cl (! (= veriT_vr78 veriT_vr80) :named @p_608)) :rule refl)
@@ -4200,13 +4200,13 @@
 (step t212 (cl (! (= @p_605 (! (forall ((veriT_vr79 A_set$) (veriT_vr80 A_set$)) @p_614) :named @p_616)) :named @p_615)) :rule bind)
 (step t213 (cl (not @p_615) (not @p_605) @p_616) :rule equiv_pos2)
 (step t214 (cl @p_616) :rule th_resolution :premises (t211 t212 t213))
-(anchor :step t215 :args ((:= ?v0 veriT_vr81) (:= ?v1 veriT_vr82)))
+(anchor :step t215 :args ((:= (?v0 A_set$) veriT_vr81) (:= (?v1 A_list$) veriT_vr82)))
 (step t215.t1 (cl (! (= ?v0 veriT_vr81) :named @p_630)) :rule refl)
 (step t215.t2 (cl (= @p_19 (! (fun_app$a less_eq$ veriT_vr81) :named @p_618))) :rule cong :premises (t215.t1))
 (step t215.t3 (cl (! (= ?v1 veriT_vr82) :named @p_625)) :rule refl)
 (step t215.t4 (cl (= @p_619 (! (coset$ veriT_vr82) :named @p_620))) :rule cong :premises (t215.t3))
 (step t215.t5 (cl (= @p_621 (! (fun_app$ @p_618 @p_620) :named @p_622))) :rule cong :premises (t215.t2 t215.t4))
-(anchor :step t215.t6 :args ((:= ?v2 veriT_vr83)))
+(anchor :step t215.t6 :args ((:= (?v2 A$) veriT_vr83)))
 (step t215.t6.t1 (cl (! (= ?v2 veriT_vr83) :named @p_629)) :rule refl)
 (step t215.t6.t2 (cl @p_625) :rule refl)
 (step t215.t6.t3 (cl (= @p_20 (! (set$ veriT_vr82) :named @p_626))) :rule cong :premises (t215.t6.t2))
@@ -4221,18 +4221,18 @@
 (step t215 (cl (! (= @p_617 (! (forall ((veriT_vr81 A_set$) (veriT_vr82 A_list$)) @p_637) :named @p_639)) :named @p_638)) :rule bind)
 (step t216 (cl (not @p_638) (not @p_617) @p_639) :rule equiv_pos2)
 (step t217 (cl @p_639) :rule th_resolution :premises (a27 t215 t216))
-(anchor :step t218 :args (veriT_vr81 veriT_vr82))
+(anchor :step t218 :args ((veriT_vr81 A_set$) (veriT_vr82 A_list$)))
 (step t218.t1 (cl (= @p_637 (! (and (! (=> @p_622 @p_624) :named @p_655) (! (=> @p_624 @p_622) :named @p_667)) :named @p_640))) :rule connective_def)
 (step t218 (cl (! (= @p_639 (! (forall ((veriT_vr81 A_set$) (veriT_vr82 A_list$)) @p_640) :named @p_642)) :named @p_641)) :rule bind)
 (step t219 (cl (not @p_641) (not @p_639) @p_642) :rule equiv_pos2)
 (step t220 (cl @p_642) :rule th_resolution :premises (t217 t218 t219))
-(anchor :step t221 :args ((:= veriT_vr81 veriT_vr84) (:= veriT_vr82 veriT_vr85)))
+(anchor :step t221 :args ((:= (veriT_vr81 A_set$) veriT_vr84) (:= (veriT_vr82 A_list$) veriT_vr85)))
 (step t221.t1 (cl (! (= veriT_vr81 veriT_vr84) :named @p_651)) :rule refl)
 (step t221.t2 (cl (! (= @p_618 (! (fun_app$a less_eq$ veriT_vr84) :named @p_645)) :named @p_664)) :rule cong :premises (t221.t1))
 (step t221.t3 (cl (! (= veriT_vr82 veriT_vr85) :named @p_648)) :rule refl)
 (step t221.t4 (cl (! (= @p_620 (! (coset$ veriT_vr85) :named @p_646)) :named @p_665)) :rule cong :premises (t221.t3))
 (step t221.t5 (cl (! (= @p_622 (! (fun_app$ @p_645 @p_646) :named @p_644)) :named @p_666)) :rule cong :premises (t221.t2 t221.t4))
-(anchor :step t221.t6 :args ((:= veriT_vr83 veriT_vr86)))
+(anchor :step t221.t6 :args ((:= (veriT_vr83 A$) veriT_vr86)))
 (step t221.t6.t1 (cl (! (= veriT_vr83 veriT_vr86) :named @p_650)) :rule refl)
 (step t221.t6.t2 (cl @p_648) :rule refl)
 (step t221.t6.t3 (cl (! (= @p_626 (! (set$ veriT_vr85) :named @p_643)) :named @p_658)) :rule cong :premises (t221.t6.t2))
@@ -4244,7 +4244,7 @@
 (step t221.t6.t9 (cl (= @p_635 (! (=> @p_649 @p_653) :named @p_654))) :rule cong :premises (t221.t6.t4 t221.t6.t8))
 (step t221.t6 (cl (= @p_624 (! (forall ((veriT_vr86 A$)) @p_654) :named @p_647))) :rule bind)
 (step t221.t7 (cl (= @p_655 (! (=> @p_644 @p_647) :named @p_656))) :rule cong :premises (t221.t5 t221.t6))
-(anchor :step t221.t8 :args ((:= veriT_vr83 veriT_vr87)))
+(anchor :step t221.t8 :args ((:= (veriT_vr83 A$) veriT_vr87)))
 (step t221.t8.t1 (cl (! (= veriT_vr83 veriT_vr87) :named @p_660)) :rule refl)
 (step t221.t8.t2 (cl @p_648) :rule refl)
 (step t221.t8.t3 (cl @p_658) :rule cong :premises (t221.t8.t2))
@@ -4265,13 +4265,13 @@
 (step t221 (cl (! (= @p_642 (! (forall ((veriT_vr84 A_set$) (veriT_vr85 A_list$)) @p_669) :named @p_671)) :named @p_670)) :rule bind)
 (step t222 (cl (not @p_670) (not @p_642) @p_671) :rule equiv_pos2)
 (step t223 (cl @p_671) :rule th_resolution :premises (t220 t221 t222))
-(anchor :step t224 :args ((:= veriT_vr84 veriT_vr88) (:= veriT_vr85 veriT_vr89)))
+(anchor :step t224 :args ((:= (veriT_vr84 A_set$) veriT_vr88) (:= (veriT_vr85 A_list$) veriT_vr89)))
 (step t224.t1 (cl (! (= veriT_vr84 veriT_vr88) :named @p_680)) :rule refl)
 (step t224.t2 (cl (! (= @p_645 (! (fun_app$a less_eq$ veriT_vr88) :named @p_674)) :named @p_687)) :rule cong :premises (t224.t1))
 (step t224.t3 (cl (! (= veriT_vr85 veriT_vr89) :named @p_676)) :rule refl)
 (step t224.t4 (cl (! (= @p_646 (! (coset$ veriT_vr89) :named @p_675)) :named @p_688)) :rule cong :premises (t224.t3))
 (step t224.t5 (cl (! (= @p_644 (! (fun_app$ @p_674 @p_675) :named @p_673)) :named @p_689)) :rule cong :premises (t224.t2 t224.t4))
-(anchor :step t224.t6 :args ((:= veriT_vr86 veriT_vr90)))
+(anchor :step t224.t6 :args ((:= (veriT_vr86 A$) veriT_vr90)))
 (step t224.t6.t1 (cl (! (= veriT_vr86 veriT_vr90) :named @p_679)) :rule refl)
 (step t224.t6.t2 (cl @p_676) :rule refl)
 (step t224.t6.t3 (cl (! (= @p_643 (! (set$ veriT_vr89) :named @p_677)) :named @p_685)) :rule cong :premises (t224.t6.t2))
@@ -4283,7 +4283,7 @@
 (step t224.t6.t9 (cl (= @p_654 (! (=> @p_678 @p_682) :named @p_683))) :rule cong :premises (t224.t6.t4 t224.t6.t8))
 (step t224.t6 (cl (= @p_647 (! (forall ((veriT_vr90 A$)) @p_683) :named @p_672))) :rule bind)
 (step t224.t7 (cl (= @p_656 (! (=> @p_673 @p_672) :named @p_684))) :rule cong :premises (t224.t5 t224.t6))
-(anchor :step t224.t8 :args ((:= veriT_vr87 veriT_vr90)))
+(anchor :step t224.t8 :args ((:= (veriT_vr87 A$) veriT_vr90)))
 (step t224.t8.t1 (cl (! (= veriT_vr87 veriT_vr90) :named @p_686)) :rule refl)
 (step t224.t8.t2 (cl @p_676) :rule refl)
 (step t224.t8.t3 (cl @p_685) :rule cong :premises (t224.t8.t2))
@@ -4304,8 +4304,8 @@
 (step t224 (cl (! (= @p_671 (! (forall ((veriT_vr88 A_set$) (veriT_vr89 A_list$)) @p_691) :named @p_693)) :named @p_692)) :rule bind)
 (step t225 (cl (not @p_692) (not @p_671) @p_693) :rule equiv_pos2)
 (step t226 (cl @p_693) :rule th_resolution :premises (t223 t224 t225))
-(anchor :step t227 :args ((:= veriT_vr88 veriT_vr88) (:= veriT_vr89 veriT_vr89)))
-(anchor :step t227.t1 :args ((:= veriT_vr90 veriT_vr91)))
+(anchor :step t227 :args ((:= (veriT_vr88 A_set$) veriT_vr88) (:= (veriT_vr89 A_list$) veriT_vr89)))
+(anchor :step t227.t1 :args ((:= (veriT_vr90 A$) veriT_vr91)))
 (step t227.t1.t1 (cl (! (= veriT_vr90 veriT_vr91) :named @p_696)) :rule refl)
 (step t227.t1.t2 (cl (= @p_678 (! (member$ veriT_vr91 @p_677) :named @p_695))) :rule cong :premises (t227.t1.t1))
 (step t227.t1.t3 (cl @p_696) :rule refl)
@@ -4444,7 +4444,7 @@
 (step t353 (cl (or @p_798 (! (and (! (=> (! (fun_app$ @p_799 @p_792) :named @p_800) (! (forall ((veriT_vr90 A$)) (! (=> (! (member$ veriT_vr90 @p_380) :named @p_804) (! (not (! (member$ veriT_vr90 @p_381) :named @p_807)) :named @p_809)) :named @p_811)) :named @p_803)) :named @p_813) (! (=> (! (forall ((veriT_vr91 A$)) (! (=> (! (member$ veriT_vr91 @p_380) :named @p_816) (! (not (! (member$ veriT_vr91 @p_381) :named @p_818)) :named @p_819)) :named @p_820)) :named @p_815) @p_800) :named @p_821)) :named @p_801))) :rule forall_inst :args ((:= veriT_vr88 @p_381) (:= veriT_vr89 @p_9)))
 (anchor :step t354)
 (assume t354.h1 @p_801)
-(anchor :step t354.t2 :args ((:= veriT_vr90 veriT_vr99)))
+(anchor :step t354.t2 :args ((:= (veriT_vr90 A$) veriT_vr99)))
 (step t354.t2.t1 (cl (! (= veriT_vr90 veriT_vr99) :named @p_806)) :rule refl)
 (step t354.t2.t2 (cl (= @p_804 (! (member$ veriT_vr99 @p_380) :named @p_805))) :rule cong :premises (t354.t2.t1))
 (step t354.t2.t3 (cl @p_806) :rule refl)
@@ -4453,7 +4453,7 @@
 (step t354.t2.t6 (cl (= @p_811 (! (=> @p_805 @p_810) :named @p_812))) :rule cong :premises (t354.t2.t2 t354.t2.t5))
 (step t354.t2 (cl (= @p_803 (! (forall ((veriT_vr99 A$)) @p_812) :named @p_814))) :rule bind)
 (step t354.t3 (cl (= @p_813 (! (=> @p_800 @p_814) :named @p_822))) :rule cong :premises (t354.t2))
-(anchor :step t354.t4 :args ((:= veriT_vr91 veriT_vr99)))
+(anchor :step t354.t4 :args ((:= (veriT_vr91 A$) veriT_vr99)))
 (step t354.t4.t1 (cl (! (= veriT_vr91 veriT_vr99) :named @p_817)) :rule refl)
 (step t354.t4.t2 (cl (= @p_816 @p_805)) :rule cong :premises (t354.t4.t1))
 (step t354.t4.t3 (cl @p_817) :rule refl)
@@ -4465,7 +4465,7 @@
 (step t354.t6 (cl (! (= @p_801 (! (and @p_822 @p_823) :named @p_826)) :named @p_824)) :rule cong :premises (t354.t3 t354.t5))
 (step t354.t7 (cl (not @p_824) (! (not @p_801) :named @p_825) @p_826) :rule equiv_pos2)
 (step t354.t8 (cl @p_826) :rule th_resolution :premises (t354.h1 t354.t6 t354.t7))
-(anchor :step t354.t9 :args ((:= veriT_vr99 veriT_vr100)))
+(anchor :step t354.t9 :args ((:= (veriT_vr99 A$) veriT_vr100)))
 (step t354.t9.t1 (cl (! (= veriT_vr99 veriT_vr100) :named @p_829)) :rule refl)
 (step t354.t9.t2 (cl (= @p_805 @p_828)) :rule cong :premises (t354.t9.t1))
 (step t354.t9.t3 (cl @p_829) :rule refl)
@@ -4478,7 +4478,7 @@
 (step t354.t12 (cl (! (= @p_826 (! (and @p_833 @p_834) :named @p_836)) :named @p_835)) :rule cong :premises (t354.t10 t354.t11))
 (step t354.t13 (cl (not @p_835) (not @p_826) @p_836) :rule equiv_pos2)
 (step t354.t14 (cl @p_836) :rule th_resolution :premises (t354.t8 t354.t12 t354.t13))
-(anchor :step t354.t15 :args ((:= veriT_vr100 veriT_sk5)))
+(anchor :step t354.t15 :args ((:= (veriT_vr100 A$) veriT_sk5)))
 (step t354.t15.t1 (cl (! (= veriT_vr100 veriT_sk5) :named @p_839)) :rule refl)
 (step t354.t15.t2 (cl (= @p_828 (! (member$ veriT_sk5 @p_380) :named @p_838))) :rule cong :premises (t354.t15.t1))
 (step t354.t15.t3 (cl @p_839) :rule refl)
@@ -4490,7 +4490,7 @@
 (step t354.t17 (cl (! (= @p_836 (! (and @p_833 @p_842) :named @p_844)) :named @p_843)) :rule cong :premises (t354.t16))
 (step t354.t18 (cl (not @p_843) (not @p_836) @p_844) :rule equiv_pos2)
 (step t354.t19 (cl @p_844) :rule th_resolution :premises (t354.t14 t354.t17 t354.t18))
-(anchor :step t354.t20 :args ((:= veriT_vr100 veriT_vr101)))
+(anchor :step t354.t20 :args ((:= (veriT_vr100 A$) veriT_vr101)))
 (step t354.t20.t1 (cl (! (= veriT_vr100 veriT_vr101) :named @p_847)) :rule refl)
 (step t354.t20.t2 (cl (= @p_828 (! (member$ veriT_vr101 @p_380) :named @p_846))) :rule cong :premises (t354.t20.t1))
 (step t354.t20.t3 (cl @p_847) :rule refl)
@@ -4511,7 +4511,7 @@
 (step t360 (cl (or @p_798 (! (and (! (=> @p_762 (! (forall ((veriT_vr90 A$)) (! (=> (! (member$ veriT_vr90 @p_715) :named @p_859) @p_809) :named @p_864)) :named @p_858)) :named @p_866) (! (=> (! (forall ((veriT_vr91 A$)) (! (=> (! (member$ veriT_vr91 @p_715) :named @p_869) @p_819) :named @p_871)) :named @p_868) @p_762) :named @p_872)) :named @p_856))) :rule forall_inst :args ((:= veriT_vr88 @p_381) (:= veriT_vr89 xs$)))
 (anchor :step t361)
 (assume t361.h1 @p_856)
-(anchor :step t361.t2 :args ((:= veriT_vr90 veriT_vr102)))
+(anchor :step t361.t2 :args ((:= (veriT_vr90 A$) veriT_vr102)))
 (step t361.t2.t1 (cl (! (= veriT_vr90 veriT_vr102) :named @p_861)) :rule refl)
 (step t361.t2.t2 (cl (= @p_859 (! (member$ veriT_vr102 @p_715) :named @p_860))) :rule cong :premises (t361.t2.t1))
 (step t361.t2.t3 (cl @p_861) :rule refl)
@@ -4520,7 +4520,7 @@
 (step t361.t2.t6 (cl (= @p_864 (! (=> @p_860 @p_863) :named @p_865))) :rule cong :premises (t361.t2.t2 t361.t2.t5))
 (step t361.t2 (cl (= @p_858 (! (forall ((veriT_vr102 A$)) @p_865) :named @p_867))) :rule bind)
 (step t361.t3 (cl (= @p_866 (! (=> @p_762 @p_867) :named @p_873))) :rule cong :premises (t361.t2))
-(anchor :step t361.t4 :args ((:= veriT_vr91 veriT_vr102)))
+(anchor :step t361.t4 :args ((:= (veriT_vr91 A$) veriT_vr102)))
 (step t361.t4.t1 (cl (! (= veriT_vr91 veriT_vr102) :named @p_870)) :rule refl)
 (step t361.t4.t2 (cl (= @p_869 @p_860)) :rule cong :premises (t361.t4.t1))
 (step t361.t4.t3 (cl @p_870) :rule refl)
@@ -4532,7 +4532,7 @@
 (step t361.t6 (cl (! (= @p_856 (! (and @p_873 @p_874) :named @p_877)) :named @p_875)) :rule cong :premises (t361.t3 t361.t5))
 (step t361.t7 (cl (not @p_875) (! (not @p_856) :named @p_876) @p_877) :rule equiv_pos2)
 (step t361.t8 (cl @p_877) :rule th_resolution :premises (t361.h1 t361.t6 t361.t7))
-(anchor :step t361.t9 :args ((:= veriT_vr102 veriT_vr103)))
+(anchor :step t361.t9 :args ((:= (veriT_vr102 A$) veriT_vr103)))
 (step t361.t9.t1 (cl (! (= veriT_vr102 veriT_vr103) :named @p_880)) :rule refl)
 (step t361.t9.t2 (cl (= @p_860 @p_879)) :rule cong :premises (t361.t9.t1))
 (step t361.t9.t3 (cl @p_880) :rule refl)
@@ -4545,7 +4545,7 @@
 (step t361.t12 (cl (! (= @p_877 (! (and @p_884 @p_885) :named @p_887)) :named @p_886)) :rule cong :premises (t361.t10 t361.t11))
 (step t361.t13 (cl (not @p_886) (not @p_877) @p_887) :rule equiv_pos2)
 (step t361.t14 (cl @p_887) :rule th_resolution :premises (t361.t8 t361.t12 t361.t13))
-(anchor :step t361.t15 :args ((:= veriT_vr103 veriT_sk6)))
+(anchor :step t361.t15 :args ((:= (veriT_vr103 A$) veriT_sk6)))
 (step t361.t15.t1 (cl (! (= veriT_vr103 veriT_sk6) :named @p_890)) :rule refl)
 (step t361.t15.t2 (cl (= @p_879 (! (member$ veriT_sk6 @p_715) :named @p_889))) :rule cong :premises (t361.t15.t1))
 (step t361.t15.t3 (cl @p_890) :rule refl)
@@ -4557,7 +4557,7 @@
 (step t361.t17 (cl (! (= @p_887 (! (and @p_884 @p_893) :named @p_895)) :named @p_894)) :rule cong :premises (t361.t16))
 (step t361.t18 (cl (not @p_894) (not @p_887) @p_895) :rule equiv_pos2)
 (step t361.t19 (cl @p_895) :rule th_resolution :premises (t361.t14 t361.t17 t361.t18))
-(anchor :step t361.t20 :args ((:= veriT_vr103 veriT_vr104)))
+(anchor :step t361.t20 :args ((:= (veriT_vr103 A$) veriT_vr104)))
 (step t361.t20.t1 (cl (! (= veriT_vr103 veriT_vr104) :named @p_898)) :rule refl)
 (step t361.t20.t2 (cl (= @p_879 (! (member$ veriT_vr104 @p_715) :named @p_897))) :rule cong :premises (t361.t20.t1))
 (step t361.t20.t3 (cl @p_898) :rule refl)
@@ -4578,7 +4578,7 @@
 (step t367 (cl (or @p_906 (! (=> (! (forall ((veriT_vr76 A$)) (! (=> (! (member$ veriT_vr76 @p_21) :named @p_912) (! (member$ veriT_vr76 @p_760) :named @p_915)) :named @p_917)) :named @p_911) (! (fun_app$ @p_907 @p_760) :named @p_910)) :named @p_908))) :rule forall_inst :args ((:= veriT_vr74 @p_21) (:= veriT_vr75 @p_760)))
 (anchor :step t368)
 (assume t368.h1 @p_908)
-(anchor :step t368.t2 :args ((:= veriT_vr76 veriT_vr116)))
+(anchor :step t368.t2 :args ((:= (veriT_vr76 A$) veriT_vr116)))
 (step t368.t2.t1 (cl (! (= veriT_vr76 veriT_vr116) :named @p_914)) :rule refl)
 (step t368.t2.t2 (cl (= @p_912 (! (member$ veriT_vr116 @p_21) :named @p_913))) :rule cong :premises (t368.t2.t1))
 (step t368.t2.t3 (cl @p_914) :rule refl)
@@ -4588,7 +4588,7 @@
 (step t368.t3 (cl (! (= @p_908 (! (=> @p_919 @p_910) :named @p_922)) :named @p_920)) :rule cong :premises (t368.t2))
 (step t368.t4 (cl (not @p_920) (! (not @p_908) :named @p_921) @p_922) :rule equiv_pos2)
 (step t368.t5 (cl @p_922) :rule th_resolution :premises (t368.h1 t368.t3 t368.t4))
-(anchor :step t368.t6 :args ((:= veriT_vr116 veriT_vr117)))
+(anchor :step t368.t6 :args ((:= (veriT_vr116 A$) veriT_vr117)))
 (step t368.t6.t1 (cl (! (= veriT_vr116 veriT_vr117) :named @p_925)) :rule refl)
 (step t368.t6.t2 (cl (= @p_913 @p_924)) :rule cong :premises (t368.t6.t1))
 (step t368.t6.t3 (cl @p_925) :rule refl)
@@ -4598,7 +4598,7 @@
 (step t368.t7 (cl (! (= @p_922 (! (=> @p_927 @p_910) :named @p_929)) :named @p_928)) :rule cong :premises (t368.t6))
 (step t368.t8 (cl (not @p_928) (not @p_922) @p_929) :rule equiv_pos2)
 (step t368.t9 (cl @p_929) :rule th_resolution :premises (t368.t5 t368.t7 t368.t8))
-(anchor :step t368.t10 :args ((:= veriT_vr117 veriT_sk11)))
+(anchor :step t368.t10 :args ((:= (veriT_vr117 A$) veriT_sk11)))
 (step t368.t10.t1 (cl (! (= veriT_vr117 veriT_sk11) :named @p_932)) :rule refl)
 (step t368.t10.t2 (cl (= @p_924 (! (member$ veriT_sk11 @p_21) :named @p_931))) :rule cong :premises (t368.t10.t1))
 (step t368.t10.t3 (cl @p_932) :rule refl)
@@ -4618,7 +4618,7 @@
 (step t375 (cl (or (! (not @p_357) :named @p_995) (! (and (! (=> (! (= bot$ @p_940) :named @p_941) (! (forall ((veriT_vr51 A$)) (! (=> (! (member$ veriT_vr51 @p_715) :named @p_945) (! (not (! (member$ veriT_vr51 @p_381) :named @p_948)) :named @p_950)) :named @p_952)) :named @p_944)) :named @p_954) (! (=> (! (forall ((veriT_vr52 A$)) (! (=> (! (member$ veriT_vr52 @p_715) :named @p_957) (! (not (! (member$ veriT_vr52 @p_381) :named @p_959)) :named @p_960)) :named @p_961)) :named @p_956) @p_941) :named @p_962)) :named @p_942))) :rule forall_inst :args ((:= veriT_vr49 @p_715) (:= veriT_vr50 @p_381)))
 (anchor :step t376)
 (assume t376.h1 @p_942)
-(anchor :step t376.t2 :args ((:= veriT_vr51 veriT_vr122)))
+(anchor :step t376.t2 :args ((:= (veriT_vr51 A$) veriT_vr122)))
 (step t376.t2.t1 (cl (! (= veriT_vr51 veriT_vr122) :named @p_947)) :rule refl)
 (step t376.t2.t2 (cl (= @p_945 (! (member$ veriT_vr122 @p_715) :named @p_946))) :rule cong :premises (t376.t2.t1))
 (step t376.t2.t3 (cl @p_947) :rule refl)
@@ -4627,7 +4627,7 @@
 (step t376.t2.t6 (cl (= @p_952 (! (=> @p_946 @p_951) :named @p_953))) :rule cong :premises (t376.t2.t2 t376.t2.t5))
 (step t376.t2 (cl (= @p_944 (! (forall ((veriT_vr122 A$)) @p_953) :named @p_955))) :rule bind)
 (step t376.t3 (cl (= @p_954 (! (=> @p_941 @p_955) :named @p_963))) :rule cong :premises (t376.t2))
-(anchor :step t376.t4 :args ((:= veriT_vr52 veriT_vr122)))
+(anchor :step t376.t4 :args ((:= (veriT_vr52 A$) veriT_vr122)))
 (step t376.t4.t1 (cl (! (= veriT_vr52 veriT_vr122) :named @p_958)) :rule refl)
 (step t376.t4.t2 (cl (= @p_957 @p_946)) :rule cong :premises (t376.t4.t1))
 (step t376.t4.t3 (cl @p_958) :rule refl)
@@ -4639,7 +4639,7 @@
 (step t376.t6 (cl (! (= @p_942 (! (and @p_963 @p_964) :named @p_967)) :named @p_965)) :rule cong :premises (t376.t3 t376.t5))
 (step t376.t7 (cl (not @p_965) (! (not @p_942) :named @p_966) @p_967) :rule equiv_pos2)
 (step t376.t8 (cl @p_967) :rule th_resolution :premises (t376.h1 t376.t6 t376.t7))
-(anchor :step t376.t9 :args ((:= veriT_vr122 veriT_vr123)))
+(anchor :step t376.t9 :args ((:= (veriT_vr122 A$) veriT_vr123)))
 (step t376.t9.t1 (cl (! (= veriT_vr122 veriT_vr123) :named @p_970)) :rule refl)
 (step t376.t9.t2 (cl (= @p_946 @p_969)) :rule cong :premises (t376.t9.t1))
 (step t376.t9.t3 (cl @p_970) :rule refl)
@@ -4652,7 +4652,7 @@
 (step t376.t12 (cl (! (= @p_967 (! (and @p_974 @p_975) :named @p_977)) :named @p_976)) :rule cong :premises (t376.t10 t376.t11))
 (step t376.t13 (cl (not @p_976) (not @p_967) @p_977) :rule equiv_pos2)
 (step t376.t14 (cl @p_977) :rule th_resolution :premises (t376.t8 t376.t12 t376.t13))
-(anchor :step t376.t15 :args ((:= veriT_vr123 veriT_sk14)))
+(anchor :step t376.t15 :args ((:= (veriT_vr123 A$) veriT_sk14)))
 (step t376.t15.t1 (cl (! (= veriT_vr123 veriT_sk14) :named @p_980)) :rule refl)
 (step t376.t15.t2 (cl (= @p_969 (! (member$ veriT_sk14 @p_715) :named @p_979))) :rule cong :premises (t376.t15.t1))
 (step t376.t15.t3 (cl @p_980) :rule refl)
@@ -4664,7 +4664,7 @@
 (step t376.t17 (cl (! (= @p_977 (! (and @p_974 @p_983) :named @p_985)) :named @p_984)) :rule cong :premises (t376.t16))
 (step t376.t18 (cl (not @p_984) (not @p_977) @p_985) :rule equiv_pos2)
 (step t376.t19 (cl @p_985) :rule th_resolution :premises (t376.t14 t376.t17 t376.t18))
-(anchor :step t376.t20 :args ((:= veriT_vr123 veriT_vr124)))
+(anchor :step t376.t20 :args ((:= (veriT_vr123 A$) veriT_vr124)))
 (step t376.t20.t1 (cl (! (= veriT_vr123 veriT_vr124) :named @p_988)) :rule refl)
 (step t376.t20.t2 (cl (= @p_969 (! (member$ veriT_vr124 @p_715) :named @p_987))) :rule cong :premises (t376.t20.t1))
 (step t376.t20.t3 (cl @p_988) :rule refl)
@@ -4916,35 +4916,35 @@
 (assume a17 (! (and (! (= (one_chain_line_integral$ f$ @p_5 one_chain_typeI$) (one_chain_line_integral$ f$ @p_5 one_chain_typeII$)) :named @p_337) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeI$) :named @p_9) (! (case_prod$ uu$ ?v0) :named @p_6)) :named @p_326)) :named @p_322) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> (! (member$ ?v0 one_chain_typeII$) :named @p_8) @p_6) :named @p_331)) :named @p_328)) :named @p_333)) :named @p_336))
 (assume a18 (! (and (! (= (one_chain_line_integral$ f$ @p_7 one_chain_typeII$) (one_chain_line_integral$ f$ @p_7 one_chain_typeI$)) :named @p_377) (! (and (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_8 (! (case_prod$ uua$ ?v0) :named @p_10)) :named @p_366)) :named @p_362) (! (forall ((?v0 Int_real_real_real_prod_fun_prod$)) (! (=> @p_9 @p_10) :named @p_371)) :named @p_368)) :named @p_373)) :named @p_376))
 (assume a19 (not (! (= (! (line_integral$ f$ (! (insert$ i$ @p_7) :named @p_407) g$) :named @p_462) (! (+ (! (line_integral$ f$ @p_5 g$) :named @p_404) (! (line_integral$ f$ @p_7 g$) :named @p_405)) :named @p_463)) :named @p_410)))
-(anchor :step t21 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t21 :args ((:= (?v0 Int) veriT_vr0)))
 (step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1))
 (step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2))
 (step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
 (step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2)
 (step t23 (cl @p_18) :rule th_resolution :premises (a0 t21 t22))
-(anchor :step t24 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t24 :args ((:= (veriT_vr0 Int) veriT_vr1)))
 (step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl)
 (step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1))
 (step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2))
 (step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
 (step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2)
 (step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25))
-(anchor :step t27 :args ((:= ?v0 veriT_vr2)))
+(anchor :step t27 :args ((:= (?v0 Int) veriT_vr2)))
 (step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl)
 (step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1))
 (step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2))
 (step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind)
 (step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2)
 (step t29 (cl @p_30) :rule th_resolution :premises (a1 t27 t28))
-(anchor :step t30 :args ((:= veriT_vr2 veriT_vr3)))
+(anchor :step t30 :args ((:= (veriT_vr2 Int) veriT_vr3)))
 (step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl)
 (step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1))
 (step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2))
 (step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind)
 (step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2)
 (step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31))
-(anchor :step t33 :args ((:= ?v0 veriT_vr4) (:= ?v1 veriT_vr5)))
+(anchor :step t33 :args ((:= (?v0 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr4) (:= (?v1 Int_real_real_real_prod_fun_prod$) veriT_vr5)))
 (step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl)
 (step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl)
 (step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2))
@@ -4959,7 +4959,7 @@
 (step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
 (step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34))
-(anchor :step t36 :args ((:= veriT_vr4 veriT_vr6) (:= veriT_vr5 veriT_vr7)))
+(anchor :step t36 :args ((:= (veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr6) (:= (veriT_vr5 Int_real_real_real_prod_fun_prod$) veriT_vr7)))
 (step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl)
 (step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl)
 (step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2))
@@ -4974,7 +4974,7 @@
 (step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
 (step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2)
 (step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37))
-(anchor :step t39 :args ((:= ?v0 veriT_vr8) (:= ?v1 veriT_vr9)))
+(anchor :step t39 :args ((:= (?v0 Real_real_prod$) veriT_vr8) (:= (?v1 Real_real_prod$) veriT_vr9)))
 (step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl)
 (step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1))
 (step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl)
@@ -4987,7 +4987,7 @@
 (step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
 (step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2)
 (step t41 (cl @p_75) :rule th_resolution :premises (a3 t39 t40))
-(anchor :step t42 :args ((:= veriT_vr8 veriT_vr10) (:= veriT_vr9 veriT_vr11)))
+(anchor :step t42 :args ((:= (veriT_vr8 Real_real_prod$) veriT_vr10) (:= (veriT_vr9 Real_real_prod$) veriT_vr11)))
 (step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl)
 (step t42.t2 (cl (= @p_63 (! (insert$ veriT_vr10 bot$) :named @p_76))) :rule cong :premises (t42.t1))
 (step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl)
@@ -5000,7 +5000,7 @@
 (step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
 (step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
 (step t44 (cl @p_84) :rule th_resolution :premises (t41 t42 t43))
-(anchor :step t45 :args ((:= ?v0 veriT_vr12) (:= ?v1 veriT_vr13)))
+(anchor :step t45 :args ((:= (?v0 Int) veriT_vr12) (:= (?v1 Real_real_real_prod_fun$) veriT_vr13)))
 (step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl)
 (step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
 (step t45.t3 (cl @p_86) :rule refl)
@@ -5010,7 +5010,7 @@
 (step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
 (step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2)
 (step t47 (cl @p_94) :rule th_resolution :premises (a4 t45 t46))
-(anchor :step t48 :args ((:= veriT_vr12 veriT_vr14) (:= veriT_vr13 veriT_vr15)))
+(anchor :step t48 :args ((:= (veriT_vr12 Int) veriT_vr14) (:= (veriT_vr13 Real_real_real_prod_fun$) veriT_vr15)))
 (step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl)
 (step t48.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
 (step t48.t3 (cl @p_95) :rule refl)
@@ -5020,7 +5020,7 @@
 (step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind)
 (step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2)
 (step t50 (cl @p_100) :rule th_resolution :premises (t47 t48 t49))
-(anchor :step t51 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
+(anchor :step t51 :args ((:= (?v0 Real) veriT_vr16) (:= (?v1 Real) veriT_vr17)))
 (step t51.t1 (cl (! (= ?v1 veriT_vr17) :named @p_104)) :rule refl)
 (step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl)
 (step t51.t3 (cl (= @p_102 (! (pair$a veriT_vr16) :named @p_103))) :rule cong :premises (t51.t2))
@@ -5031,7 +5031,7 @@
 (step t51 (cl (! (= @p_101 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_110) :named @p_112)) :named @p_111)) :rule bind)
 (step t52 (cl (not @p_111) (not @p_101) @p_112) :rule equiv_pos2)
 (step t53 (cl @p_112) :rule th_resolution :premises (a5 t51 t52))
-(anchor :step t54 :args ((:= veriT_vr16 veriT_vr18) (:= veriT_vr17 veriT_vr19)))
+(anchor :step t54 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
 (step t54.t1 (cl (! (= veriT_vr17 veriT_vr19) :named @p_114)) :rule refl)
 (step t54.t2 (cl (= veriT_vr16 veriT_vr18)) :rule refl)
 (step t54.t3 (cl (= @p_103 (! (pair$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2))
@@ -5042,7 +5042,7 @@
 (step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind)
 (step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2)
 (step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55))
-(anchor :step t57 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21) (:= ?v2 veriT_vr22)))
+(anchor :step t57 :args ((:= (?v0 Real_real_prod_set$) veriT_vr20) (:= (?v1 Real_real_prod$) veriT_vr21) (:= (?v2 Real_real_prod_set$) veriT_vr22)))
 (step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl)
 (step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl)
 (step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl)
@@ -5062,7 +5062,7 @@
 (step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind)
 (step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2)
 (step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58))
-(anchor :step t60 :args ((:= veriT_vr20 veriT_vr23) (:= veriT_vr21 veriT_vr24) (:= veriT_vr22 veriT_vr25)))
+(anchor :step t60 :args ((:= (veriT_vr20 Real_real_prod_set$) veriT_vr23) (:= (veriT_vr21 Real_real_prod$) veriT_vr24) (:= (veriT_vr22 Real_real_prod_set$) veriT_vr25)))
 (step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl)
 (step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl)
 (step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl)
@@ -5082,7 +5082,7 @@
 (step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
 (step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2)
 (step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61))
-(anchor :step t63 :args ((:= ?v0 veriT_vr26) (:= ?v1 veriT_vr27)))
+(anchor :step t63 :args ((:= (?v0 Real_real_prod_set$) veriT_vr26) (:= (?v1 Real_real_prod$) veriT_vr27)))
 (step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl)
 (step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1))
 (step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl)
@@ -5093,7 +5093,7 @@
 (step t63 (cl (! (= @p_157 (! (forall ((veriT_vr26 Real_real_prod_set$) (veriT_vr27 Real_real_prod$)) @p_165) :named @p_167)) :named @p_166)) :rule bind)
 (step t64 (cl (not @p_166) (not @p_157) @p_167) :rule equiv_pos2)
 (step t65 (cl @p_167) :rule th_resolution :premises (a9 t63 t64))
-(anchor :step t66 :args ((:= veriT_vr26 veriT_vr28) (:= veriT_vr27 veriT_vr29)))
+(anchor :step t66 :args ((:= (veriT_vr26 Real_real_prod_set$) veriT_vr28) (:= (veriT_vr27 Real_real_prod$) veriT_vr29)))
 (step t66.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_169)) :rule refl)
 (step t66.t2 (cl (= @p_158 (! (finite$ veriT_vr28) :named @p_168))) :rule cong :premises (t66.t1))
 (step t66.t3 (cl (= veriT_vr27 veriT_vr29)) :rule refl)
@@ -5104,7 +5104,7 @@
 (step t66 (cl (! (= @p_167 (! (forall ((veriT_vr28 Real_real_prod_set$) (veriT_vr29 Real_real_prod$)) @p_172) :named @p_174)) :named @p_173)) :rule bind)
 (step t67 (cl (not @p_173) (not @p_167) @p_174) :rule equiv_pos2)
 (step t68 (cl @p_174) :rule th_resolution :premises (t65 t66 t67))
-(anchor :step t69 :args ((:= ?v0 veriT_vr30) (:= ?v1 veriT_vr31)))
+(anchor :step t69 :args ((:= (?v0 Real_real_prod$) veriT_vr30) (:= (?v1 Real_real_prod_set$) veriT_vr31)))
 (step t69.t1 (cl (! (= ?v0 veriT_vr30) :named @p_179)) :rule refl)
 (step t69.t2 (cl (! (= ?v1 veriT_vr31) :named @p_178)) :rule refl)
 (step t69.t3 (cl (= @p_176 (! (member$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2))
@@ -5117,7 +5117,7 @@
 (step t69 (cl (! (= @p_175 (! (forall ((veriT_vr30 Real_real_prod$) (veriT_vr31 Real_real_prod_set$)) @p_184) :named @p_186)) :named @p_185)) :rule bind)
 (step t70 (cl (not @p_185) (not @p_175) @p_186) :rule equiv_pos2)
 (step t71 (cl @p_186) :rule th_resolution :premises (a11 t69 t70))
-(anchor :step t72 :args ((:= veriT_vr30 veriT_vr32) (:= veriT_vr31 veriT_vr33)))
+(anchor :step t72 :args ((:= (veriT_vr30 Real_real_prod$) veriT_vr32) (:= (veriT_vr31 Real_real_prod_set$) veriT_vr33)))
 (step t72.t1 (cl (! (= veriT_vr30 veriT_vr32) :named @p_189)) :rule refl)
 (step t72.t2 (cl (! (= veriT_vr31 veriT_vr33) :named @p_188)) :rule refl)
 (step t72.t3 (cl (= @p_177 (! (member$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2))
@@ -5130,21 +5130,21 @@
 (step t72 (cl (! (= @p_186 (! (forall ((veriT_vr32 Real_real_prod$) (veriT_vr33 Real_real_prod_set$)) @p_192) :named @p_194)) :named @p_193)) :rule bind)
 (step t73 (cl (not @p_193) (not @p_186) @p_194) :rule equiv_pos2)
 (step t74 (cl @p_194) :rule th_resolution :premises (t71 t72 t73))
-(anchor :step t75 :args ((:= ?v0 veriT_vr34)))
+(anchor :step t75 :args ((:= (?v0 Real_real_prod_set$) veriT_vr34)))
 (step t75.t1 (cl (= ?v0 veriT_vr34)) :rule refl)
 (step t75.t2 (cl (= @p_196 (! (inf$ veriT_vr34 bot$) :named @p_197))) :rule cong :premises (t75.t1))
 (step t75.t3 (cl (= @p_198 (! (= bot$ @p_197) :named @p_199))) :rule cong :premises (t75.t2))
 (step t75 (cl (! (= @p_195 (! (forall ((veriT_vr34 Real_real_prod_set$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
 (step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2)
 (step t77 (cl @p_201) :rule th_resolution :premises (a13 t75 t76))
-(anchor :step t78 :args ((:= veriT_vr34 veriT_vr35)))
+(anchor :step t78 :args ((:= (veriT_vr34 Real_real_prod_set$) veriT_vr35)))
 (step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl)
 (step t78.t2 (cl (= @p_197 (! (inf$ veriT_vr35 bot$) :named @p_202))) :rule cong :premises (t78.t1))
 (step t78.t3 (cl (= @p_199 (! (= bot$ @p_202) :named @p_203))) :rule cong :premises (t78.t2))
 (step t78 (cl (! (= @p_201 (! (forall ((veriT_vr35 Real_real_prod_set$)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
 (step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2)
 (step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79))
-(anchor :step t81 :args ((:= ?v0 veriT_vr36) (:= ?v1 veriT_vr37) (:= ?v2 veriT_vr38)))
+(anchor :step t81 :args ((:= (?v0 Real_real_prod$) veriT_vr36) (:= (?v1 Real_real_prod$) veriT_vr37) (:= (?v2 Real_real_prod_set$) veriT_vr38)))
 (step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl)
 (step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl)
 (step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl)
@@ -5159,7 +5159,7 @@
 (step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind)
 (step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2)
 (step t83 (cl @p_220) :rule th_resolution :premises (a14 t81 t82))
-(anchor :step t84 :args ((:= veriT_vr36 veriT_vr39) (:= veriT_vr37 veriT_vr40) (:= veriT_vr38 veriT_vr41)))
+(anchor :step t84 :args ((:= (veriT_vr36 Real_real_prod$) veriT_vr39) (:= (veriT_vr37 Real_real_prod$) veriT_vr40) (:= (veriT_vr38 Real_real_prod_set$) veriT_vr41)))
 (step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl)
 (step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl)
 (step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl)
@@ -5174,7 +5174,7 @@
 (step t84 (cl (! (= @p_220 (! (forall ((veriT_vr39 Real_real_prod$) (veriT_vr40 Real_real_prod$) (veriT_vr41 Real_real_prod_set$)) @p_228) :named @p_230)) :named @p_229)) :rule bind)
 (step t85 (cl (not @p_229) (not @p_220) @p_230) :rule equiv_pos2)
 (step t86 (cl @p_230) :rule th_resolution :premises (t83 t84 t85))
-(anchor :step t87 :args ((:= ?v0 veriT_vr42) (:= ?v1 veriT_vr43)))
+(anchor :step t87 :args ((:= (?v0 Real_real_prod$) veriT_vr42) (:= (?v1 Real_real_prod_set$) veriT_vr43)))
 (step t87.t1 (cl (! (= ?v0 veriT_vr42) :named @p_233)) :rule refl)
 (step t87.t2 (cl (! (= ?v1 veriT_vr43) :named @p_235)) :rule refl)
 (step t87.t3 (cl (= @p_2 (! (insert$ veriT_vr42 veriT_vr43) :named @p_232))) :rule cong :premises (t87.t1 t87.t2))
@@ -5186,7 +5186,7 @@
 (step t87 (cl (! (= @p_231 (! (forall ((veriT_vr42 Real_real_prod$) (veriT_vr43 Real_real_prod_set$)) @p_239) :named @p_241)) :named @p_240)) :rule bind)
 (step t88 (cl (not @p_240) (not @p_231) @p_241) :rule equiv_pos2)
 (step t89 (cl @p_241) :rule th_resolution :premises (a15 t87 t88))
-(anchor :step t90 :args ((:= veriT_vr42 veriT_vr44) (:= veriT_vr43 veriT_vr45)))
+(anchor :step t90 :args ((:= (veriT_vr42 Real_real_prod$) veriT_vr44) (:= (veriT_vr43 Real_real_prod_set$) veriT_vr45)))
 (step t90.t1 (cl (! (= veriT_vr42 veriT_vr44) :named @p_243)) :rule refl)
 (step t90.t2 (cl (! (= veriT_vr43 veriT_vr45) :named @p_245)) :rule refl)
 (step t90.t3 (cl (= @p_232 (! (insert$ veriT_vr44 veriT_vr45) :named @p_242))) :rule cong :premises (t90.t1 t90.t2))
@@ -5198,7 +5198,7 @@
 (step t90 (cl (! (= @p_241 (! (forall ((veriT_vr44 Real_real_prod$) (veriT_vr45 Real_real_prod_set$)) @p_247) :named @p_249)) :named @p_248)) :rule bind)
 (step t91 (cl (not @p_248) (not @p_241) @p_249) :rule equiv_pos2)
 (step t92 (cl @p_249) :rule th_resolution :premises (t89 t90 t91))
-(anchor :step t93 :args ((:= ?v0 veriT_vr46) (:= ?v1 veriT_vr47) (:= ?v2 veriT_vr48) (:= ?v3 veriT_vr49) (:= ?v4 veriT_vr50)))
+(anchor :step t93 :args ((:= (?v0 Real_real_prod_set$) veriT_vr46) (:= (?v1 Real_real_prod_real_real_prod_fun$) veriT_vr47) (:= (?v2 Real_real_prod_set$) veriT_vr48) (:= (?v3 Real_real_real_prod_fun$) veriT_vr49) (:= (?v4 Real_real_prod_set$) veriT_vr50)))
 (step t93.t1 (cl (! (= ?v0 veriT_vr46) :named @p_262)) :rule refl)
 (step t93.t2 (cl (= @p_4 (! (finite$ veriT_vr46) :named @p_251))) :rule cong :premises (t93.t1))
 (step t93.t3 (cl (! (= ?v1 veriT_vr47) :named @p_256)) :rule refl)
@@ -5242,13 +5242,13 @@
 (step t93 (cl (! (= @p_250 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_292) :named @p_294)) :named @p_293)) :rule bind)
 (step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2)
 (step t95 (cl @p_294) :rule th_resolution :premises (a16 t93 t94))
-(anchor :step t96 :args (veriT_vr46 veriT_vr47 veriT_vr48 veriT_vr49 veriT_vr50))
+(anchor :step t96 :args ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)))
 (step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp)
 (step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1))
 (step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (veriT_vr47 Real_real_prod_real_real_prod_fun$) (veriT_vr48 Real_real_prod_set$) (veriT_vr49 Real_real_real_prod_fun$) (veriT_vr50 Real_real_prod_set$)) @p_296) :named @p_298)) :named @p_297)) :rule bind)
 (step t97 (cl (not @p_297) (not @p_294) @p_298) :rule equiv_pos2)
 (step t98 (cl @p_298) :rule th_resolution :premises (t95 t96 t97))
-(anchor :step t99 :args ((:= veriT_vr46 veriT_vr51) (:= veriT_vr47 veriT_vr52) (:= veriT_vr48 veriT_vr53) (:= veriT_vr49 veriT_vr54) (:= veriT_vr50 veriT_vr55)))
+(anchor :step t99 :args ((:= (veriT_vr46 Real_real_prod_set$) veriT_vr51) (:= (veriT_vr47 Real_real_prod_real_real_prod_fun$) veriT_vr52) (:= (veriT_vr48 Real_real_prod_set$) veriT_vr53) (:= (veriT_vr49 Real_real_real_prod_fun$) veriT_vr54) (:= (veriT_vr50 Real_real_prod_set$) veriT_vr55)))
 (step t99.t1 (cl (! (= veriT_vr46 veriT_vr51) :named @p_306)) :rule refl)
 (step t99.t2 (cl (= @p_251 (! (finite$ veriT_vr51) :named @p_299))) :rule cong :premises (t99.t1))
 (step t99.t3 (cl (! (= veriT_vr47 veriT_vr52) :named @p_302)) :rule refl)
@@ -5289,14 +5289,14 @@
 (step t99 (cl (! (= @p_298 (! (forall ((veriT_vr51 Real_real_prod_set$) (veriT_vr52 Real_real_prod_real_real_prod_fun$) (veriT_vr53 Real_real_prod_set$) (veriT_vr54 Real_real_real_prod_fun$) (veriT_vr55 Real_real_prod_set$)) @p_319) :named @p_321)) :named @p_320)) :rule bind)
 (step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2)
 (step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100))
-(anchor :step t102 :args ((:= ?v0 veriT_vr56)))
+(anchor :step t102 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
 (step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl)
 (step t102.t2 (cl (= @p_9 (! (member$ veriT_vr56 one_chain_typeI$) :named @p_323))) :rule cong :premises (t102.t1))
 (step t102.t3 (cl @p_324) :rule refl)
 (step t102.t4 (cl (! (= @p_6 (! (case_prod$ uu$ veriT_vr56) :named @p_325)) :named @p_330)) :rule cong :premises (t102.t3))
 (step t102.t5 (cl (= @p_326 (! (=> @p_323 @p_325) :named @p_327))) :rule cong :premises (t102.t2 t102.t4))
 (step t102 (cl (= @p_322 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_327) :named @p_334))) :rule bind)
-(anchor :step t103 :args ((:= ?v0 veriT_vr56)))
+(anchor :step t103 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr56)))
 (step t103.t1 (cl @p_324) :rule refl)
 (step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1))
 (step t103.t3 (cl @p_324) :rule refl)
@@ -5310,7 +5310,7 @@
 (step t108 (cl (! (= @p_340 (! (and @p_337 @p_334 @p_335) :named @p_342)) :named @p_341)) :rule ac_simp)
 (step t109 (cl (not @p_341) (not @p_340) @p_342) :rule equiv_pos2)
 (step t110 (cl @p_342) :rule th_resolution :premises (t107 t108 t109))
-(anchor :step t111 :args ((:= veriT_vr56 veriT_vr57)))
+(anchor :step t111 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr57)))
 (step t111.t1 (cl (! (= veriT_vr56 veriT_vr57) :named @p_344)) :rule refl)
 (step t111.t2 (cl (= @p_329 (! (member$ veriT_vr57 one_chain_typeII$) :named @p_343))) :rule cong :premises (t111.t1))
 (step t111.t3 (cl @p_344) :rule refl)
@@ -5320,14 +5320,14 @@
 (step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111))
 (step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2)
 (step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113))
-(anchor :step t115 :args ((:= veriT_vr56 veriT_vr58)))
+(anchor :step t115 :args ((:= (veriT_vr56 Int_real_real_real_prod_fun_prod$) veriT_vr58)))
 (step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl)
 (step t115.t2 (cl (= @p_323 (! (member$ veriT_vr58 one_chain_typeI$) :named @p_350))) :rule cong :premises (t115.t1))
 (step t115.t3 (cl @p_351) :rule refl)
 (step t115.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr58) :named @p_352))) :rule cong :premises (t115.t3))
 (step t115.t5 (cl (= @p_327 (! (=> @p_350 @p_352) :named @p_353))) :rule cong :premises (t115.t2 t115.t4))
 (step t115 (cl (= @p_334 (! (forall ((veriT_vr58 Int_real_real_real_prod_fun_prod$)) @p_353) :named @p_358))) :rule bind)
-(anchor :step t116 :args ((:= veriT_vr57 veriT_vr59)))
+(anchor :step t116 :args ((:= (veriT_vr57 Int_real_real_real_prod_fun_prod$) veriT_vr59)))
 (step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl)
 (step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1))
 (step t116.t3 (cl @p_355) :rule refl)
@@ -5337,14 +5337,14 @@
 (step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116))
 (step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2)
 (step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118))
-(anchor :step t120 :args ((:= ?v0 veriT_vr60)))
+(anchor :step t120 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
 (step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl)
 (step t120.t2 (cl (= @p_8 (! (member$ veriT_vr60 one_chain_typeII$) :named @p_363))) :rule cong :premises (t120.t1))
 (step t120.t3 (cl @p_364) :rule refl)
 (step t120.t4 (cl (! (= @p_10 (! (case_prod$ uua$ veriT_vr60) :named @p_365)) :named @p_370)) :rule cong :premises (t120.t3))
 (step t120.t5 (cl (= @p_366 (! (=> @p_363 @p_365) :named @p_367))) :rule cong :premises (t120.t2 t120.t4))
 (step t120 (cl (= @p_362 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_367) :named @p_374))) :rule bind)
-(anchor :step t121 :args ((:= ?v0 veriT_vr60)))
+(anchor :step t121 :args ((:= (?v0 Int_real_real_real_prod_fun_prod$) veriT_vr60)))
 (step t121.t1 (cl @p_364) :rule refl)
 (step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1))
 (step t121.t3 (cl @p_364) :rule refl)
@@ -5358,7 +5358,7 @@
 (step t126 (cl (! (= @p_380 (! (and @p_377 @p_374 @p_375) :named @p_382)) :named @p_381)) :rule ac_simp)
 (step t127 (cl (not @p_381) (not @p_380) @p_382) :rule equiv_pos2)
 (step t128 (cl @p_382) :rule th_resolution :premises (t125 t126 t127))
-(anchor :step t129 :args ((:= veriT_vr60 veriT_vr61)))
+(anchor :step t129 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr61)))
 (step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl)
 (step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1))
 (step t129.t3 (cl @p_384) :rule refl)
@@ -5368,14 +5368,14 @@
 (step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129))
 (step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2)
 (step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131))
-(anchor :step t133 :args ((:= veriT_vr60 veriT_vr62)))
+(anchor :step t133 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr62)))
 (step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl)
 (step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1))
 (step t133.t3 (cl @p_391) :rule refl)
 (step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3))
 (step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4))
 (step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind)
-(anchor :step t134 :args ((:= veriT_vr61 veriT_vr63)))
+(anchor :step t134 :args ((:= (veriT_vr61 Int_real_real_real_prod_fun_prod$) veriT_vr63)))
 (step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl)
 (step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1))
 (step t134.t3 (cl @p_395) :rule refl)
@@ -5567,7 +5567,7 @@
 (assume a9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
 (assume a10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
 (assume a11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
-(anchor :step t10 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t10 :args ((:= (?v0 Real) veriT_vr0)))
 (step t10.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
 (step t10.t2 (cl (= @p_9 (! (fun_app$ uuc$ veriT_vr0) :named @p_10))) :rule cong :premises (t10.t1))
 (step t10.t3 (cl @p_11) :rule refl)
@@ -5582,7 +5582,7 @@
 (step t10 (cl (! (= @p_6 (! (forall ((veriT_vr0 Real)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
 (step t11 (cl (not @p_22) (not @p_6) @p_23) :rule equiv_pos2)
 (step t12 (cl @p_23) :rule th_resolution :premises (a0 t10 t11))
-(anchor :step t13 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t13 :args ((:= (veriT_vr0 Real) veriT_vr1)))
 (step t13.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_26)) :rule refl)
 (step t13.t2 (cl (= @p_10 (! (fun_app$ uuc$ veriT_vr1) :named @p_25))) :rule cong :premises (t13.t1))
 (step t13.t3 (cl @p_26) :rule refl)
@@ -5597,7 +5597,7 @@
 (step t13 (cl (! (= @p_23 (! (forall ((veriT_vr1 Real)) @p_32) :named @p_34)) :named @p_33)) :rule bind)
 (step t14 (cl (not @p_33) (not @p_23) @p_34) :rule equiv_pos2)
 (step t15 (cl @p_34) :rule th_resolution :premises (t12 t13 t14))
-(anchor :step t16 :args ((:= ?v0 veriT_vr6)))
+(anchor :step t16 :args ((:= (?v0 Real) veriT_vr6)))
 (step t16.t1 (cl (! (= ?v0 veriT_vr6) :named @p_39)) :rule refl)
 (step t16.t2 (cl (= @p_37 (! (fun_app$ uub$ veriT_vr6) :named @p_38))) :rule cong :premises (t16.t1))
 (step t16.t3 (cl @p_39) :rule refl)
@@ -5609,7 +5609,7 @@
 (step t16 (cl (! (= @p_35 (! (forall ((veriT_vr6 Real)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t17 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
 (step t18 (cl @p_51) :rule th_resolution :premises (a3 t16 t17))
-(anchor :step t19 :args ((:= veriT_vr6 veriT_vr7)))
+(anchor :step t19 :args ((:= (veriT_vr6 Real) veriT_vr7)))
 (step t19.t1 (cl (! (= veriT_vr6 veriT_vr7) :named @p_53)) :rule refl)
 (step t19.t2 (cl (= @p_38 (! (fun_app$ uub$ veriT_vr7) :named @p_52))) :rule cong :premises (t19.t1))
 (step t19.t3 (cl @p_53) :rule refl)
@@ -5621,7 +5621,7 @@
 (step t19 (cl (! (= @p_51 (! (forall ((veriT_vr7 Real)) @p_58) :named @p_60)) :named @p_59)) :rule bind)
 (step t20 (cl (not @p_59) (not @p_51) @p_60) :rule equiv_pos2)
 (step t21 (cl @p_60) :rule th_resolution :premises (t18 t19 t20))
-(anchor :step t22 :args ((:= ?v0 veriT_vr8)))
+(anchor :step t22 :args ((:= (?v0 Real) veriT_vr8)))
 (step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_64)) :rule refl)
 (step t22.t2 (cl (= @p_62 (! (diamond_y$ veriT_vr8) :named @p_63))) :rule cong :premises (t22.t1))
 (step t22.t3 (cl @p_64) :rule refl)
@@ -5635,7 +5635,7 @@
 (step t22 (cl (! (= @p_61 (! (forall ((veriT_vr8 Real)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
 (step t23 (cl (not @p_74) (not @p_61) @p_75) :rule equiv_pos2)
 (step t24 (cl @p_75) :rule th_resolution :premises (a5 t22 t23))
-(anchor :step t25 :args ((:= veriT_vr8 veriT_vr9)))
+(anchor :step t25 :args ((:= (veriT_vr8 Real) veriT_vr9)))
 (step t25.t1 (cl (! (= veriT_vr8 veriT_vr9) :named @p_77)) :rule refl)
 (step t25.t2 (cl (= @p_63 (! (diamond_y$ veriT_vr9) :named @p_76))) :rule cong :premises (t25.t1))
 (step t25.t3 (cl @p_77) :rule refl)
@@ -5649,7 +5649,7 @@
 (step t25 (cl (! (= @p_75 (! (forall ((veriT_vr9 Real)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
 (step t26 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
 (step t27 (cl @p_84) :rule th_resolution :premises (t24 t25 t26))
-(anchor :step t28 :args ((:= ?v0 veriT_vr10) (:= ?v1 veriT_vr11) (:= ?v2 veriT_vr12)))
+(anchor :step t28 :args ((:= (?v0 Real) veriT_vr10) (:= (?v1 Real) veriT_vr11) (:= (?v2 Real) veriT_vr12)))
 (step t28.t1 (cl (! (= ?v0 veriT_vr10) :named @p_94)) :rule refl)
 (step t28.t2 (cl (! (= ?v1 veriT_vr11) :named @p_87)) :rule refl)
 (step t28.t3 (cl (= @p_5 (! (divide$ veriT_vr10 veriT_vr11) :named @p_86))) :rule cong :premises (t28.t1 t28.t2))
@@ -5678,13 +5678,13 @@
 (step t28 (cl (! (= @p_85 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_115) :named @p_117)) :named @p_116)) :rule bind)
 (step t29 (cl (not @p_116) (not @p_85) @p_117) :rule equiv_pos2)
 (step t30 (cl @p_117) :rule th_resolution :premises (a7 t28 t29))
-(anchor :step t31 :args (veriT_vr10 veriT_vr11 veriT_vr12))
+(anchor :step t31 :args ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)))
 (step t31.t1 (cl (= @p_113 (! (and @p_99 @p_105 @p_109) :named @p_118))) :rule ac_simp)
 (step t31.t2 (cl (= @p_115 (! (= @p_91 @p_118) :named @p_119))) :rule cong :premises (t31.t1))
 (step t31 (cl (! (= @p_117 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_119) :named @p_121)) :named @p_120)) :rule bind)
 (step t32 (cl (not @p_120) (not @p_117) @p_121) :rule equiv_pos2)
 (step t33 (cl @p_121) :rule th_resolution :premises (t30 t31 t32))
-(anchor :step t34 :args ((:= veriT_vr10 veriT_vr13) (:= veriT_vr11 veriT_vr14) (:= veriT_vr12 veriT_vr15)))
+(anchor :step t34 :args ((:= (veriT_vr10 Real) veriT_vr13) (:= (veriT_vr11 Real) veriT_vr14) (:= (veriT_vr12 Real) veriT_vr15)))
 (step t34.t1 (cl (! (= veriT_vr10 veriT_vr13) :named @p_127)) :rule refl)
 (step t34.t2 (cl (! (= veriT_vr11 veriT_vr14) :named @p_123)) :rule refl)
 (step t34.t3 (cl (= @p_86 (! (divide$ veriT_vr13 veriT_vr14) :named @p_122))) :rule cong :premises (t34.t1 t34.t2))
@@ -5712,7 +5712,7 @@
 (step t34 (cl (! (= @p_121 (! (forall ((veriT_vr13 Real) (veriT_vr14 Real) (veriT_vr15 Real)) @p_137) :named @p_139)) :named @p_138)) :rule bind)
 (step t35 (cl (not @p_138) (not @p_121) @p_139) :rule equiv_pos2)
 (step t36 (cl @p_139) :rule th_resolution :premises (t33 t34 t35))
-(anchor :step t37 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
+(anchor :step t37 :args ((:= (?v0 Real) veriT_vr16) (:= (?v1 Real) veriT_vr17)))
 (step t37.t1 (cl (! (= ?v0 veriT_vr16) :named @p_144)) :rule refl)
 (step t37.t2 (cl (= @p_4 (! (- veriT_vr16) :named @p_141))) :rule cong :premises (t37.t1))
 (step t37.t3 (cl (! (= ?v1 veriT_vr17) :named @p_145)) :rule refl)
@@ -5725,7 +5725,7 @@
 (step t37 (cl (! (= @p_140 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_150) :named @p_152)) :named @p_151)) :rule bind)
 (step t38 (cl (not @p_151) (not @p_140) @p_152) :rule equiv_pos2)
 (step t39 (cl @p_152) :rule th_resolution :premises (a8 t37 t38))
-(anchor :step t40 :args ((:= veriT_vr16 veriT_vr18) (:= veriT_vr17 veriT_vr19)))
+(anchor :step t40 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
 (step t40.t1 (cl (! (= veriT_vr16 veriT_vr18) :named @p_155)) :rule refl)
 (step t40.t2 (cl (= @p_141 (! (- veriT_vr18) :named @p_153))) :rule cong :premises (t40.t1))
 (step t40.t3 (cl (! (= veriT_vr17 veriT_vr19) :named @p_156)) :rule refl)
@@ -5738,7 +5738,7 @@
 (step t40 (cl (! (= @p_152 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_159) :named @p_161)) :named @p_160)) :rule bind)
 (step t41 (cl (not @p_160) (not @p_152) @p_161) :rule equiv_pos2)
 (step t42 (cl @p_161) :rule th_resolution :premises (t39 t40 t41))
-(anchor :step t43 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21)))
+(anchor :step t43 :args ((:= (?v0 Real) veriT_vr20) (:= (?v1 Real) veriT_vr21)))
 (step t43.t1 (cl (! (= ?v0 veriT_vr20) :named @p_166)) :rule refl)
 (step t43.t2 (cl (= @p_4 (! (- veriT_vr20) :named @p_163))) :rule cong :premises (t43.t1))
 (step t43.t3 (cl (! (= ?v1 veriT_vr21) :named @p_167)) :rule refl)
@@ -5751,7 +5751,7 @@
 (step t43 (cl (! (= @p_162 (! (forall ((veriT_vr20 Real) (veriT_vr21 Real)) @p_173) :named @p_175)) :named @p_174)) :rule bind)
 (step t44 (cl (not @p_174) (not @p_162) @p_175) :rule equiv_pos2)
 (step t45 (cl @p_175) :rule th_resolution :premises (a9 t43 t44))
-(anchor :step t46 :args ((:= veriT_vr20 veriT_vr22) (:= veriT_vr21 veriT_vr23)))
+(anchor :step t46 :args ((:= (veriT_vr20 Real) veriT_vr22) (:= (veriT_vr21 Real) veriT_vr23)))
 (step t46.t1 (cl (! (= veriT_vr20 veriT_vr22) :named @p_178)) :rule refl)
 (step t46.t2 (cl (= @p_163 (! (- veriT_vr22) :named @p_176))) :rule cong :premises (t46.t1))
 (step t46.t3 (cl (! (= veriT_vr21 veriT_vr23) :named @p_179)) :rule refl)
@@ -5764,7 +5764,7 @@
 (step t46 (cl (! (= @p_175 (! (forall ((veriT_vr22 Real) (veriT_vr23 Real)) @p_182) :named @p_184)) :named @p_183)) :rule bind)
 (step t47 (cl (not @p_183) (not @p_175) @p_184) :rule equiv_pos2)
 (step t48 (cl @p_184) :rule th_resolution :premises (t45 t46 t47))
-(anchor :step t49 :args ((:= ?v0 veriT_vr24) (:= ?v1 veriT_vr25) (:= ?v2 veriT_vr26) (:= ?v3 veriT_vr27)))
+(anchor :step t49 :args ((:= (?v0 Real) veriT_vr24) (:= (?v1 Real) veriT_vr25) (:= (?v2 Real) veriT_vr26) (:= (?v3 Real) veriT_vr27)))
 (step t49.t1 (cl (! (= ?v0 veriT_vr24) :named @p_192)) :rule refl)
 (step t49.t2 (cl (! (= ?v1 veriT_vr25) :named @p_196)) :rule refl)
 (step t49.t3 (cl (= @p_186 (! (pair$ veriT_vr24 veriT_vr25) :named @p_187))) :rule cong :premises (t49.t1 t49.t2))
@@ -5783,7 +5783,7 @@
 (step t49 (cl (! (= @p_185 (! (forall ((veriT_vr24 Real) (veriT_vr25 Real) (veriT_vr26 Real) (veriT_vr27 Real)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
 (step t50 (cl (not @p_204) (not @p_185) @p_205) :rule equiv_pos2)
 (step t51 (cl @p_205) :rule th_resolution :premises (a10 t49 t50))
-(anchor :step t52 :args ((:= veriT_vr24 veriT_vr28) (:= veriT_vr25 veriT_vr29) (:= veriT_vr26 veriT_vr30) (:= veriT_vr27 veriT_vr31)))
+(anchor :step t52 :args ((:= (veriT_vr24 Real) veriT_vr28) (:= (veriT_vr25 Real) veriT_vr29) (:= (veriT_vr26 Real) veriT_vr30) (:= (veriT_vr27 Real) veriT_vr31)))
 (step t52.t1 (cl (! (= veriT_vr24 veriT_vr28) :named @p_209)) :rule refl)
 (step t52.t2 (cl (! (= veriT_vr25 veriT_vr29) :named @p_212)) :rule refl)
 (step t52.t3 (cl (= @p_187 (! (pair$ veriT_vr28 veriT_vr29) :named @p_206))) :rule cong :premises (t52.t1 t52.t2))
@@ -6303,7 +6303,7 @@
 (assume a9 (! (forall ((?v0 Real) (?v1 Real)) (! (= (! (times$ @p_4 ?v1) :named @p_164) (! (- (! (times$ ?v0 ?v1) :named @p_168)) :named @p_170)) :named @p_172)) :named @p_162))
 (assume a10 (! (forall ((?v0 Real) (?v1 Real) (?v2 Real) (?v3 Real)) (! (= (! (= (! (pair$ ?v0 ?v1) :named @p_186) (! (pair$ ?v2 ?v3) :named @p_188)) :named @p_190) (! (and (! (= ?v0 ?v2) :named @p_194) (! (= ?v1 ?v3) :named @p_198)) :named @p_200)) :named @p_202)) :named @p_185))
 (assume a11 (! (not (! (=> (! (and (! (not (= uua$ uu$)) :named @p_226) (! (= uuc$ uub$) :named @p_227)) :named @p_220) false) :named @p_224)) :named @p_219))
-(anchor :step t10 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t10 :args ((:= (?v0 Real) veriT_vr0)))
 (step t10.t1 (cl (! (= ?v0 veriT_vr0) :named @p_11)) :rule refl)
 (step t10.t2 (cl (= @p_9 (! (fun_app$ uuc$ veriT_vr0) :named @p_10))) :rule cong :premises (t10.t1))
 (step t10.t3 (cl @p_11) :rule refl)
@@ -6318,7 +6318,7 @@
 (step t10 (cl (! (= @p_6 (! (forall ((veriT_vr0 Real)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
 (step t11 (cl (not @p_22) (not @p_6) @p_23) :rule equiv_pos2)
 (step t12 (cl @p_23) :rule th_resolution :premises (a0 t10 t11))
-(anchor :step t13 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t13 :args ((:= (veriT_vr0 Real) veriT_vr1)))
 (step t13.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_26)) :rule refl)
 (step t13.t2 (cl (= @p_10 (! (fun_app$ uuc$ veriT_vr1) :named @p_25))) :rule cong :premises (t13.t1))
 (step t13.t3 (cl @p_26) :rule refl)
@@ -6333,7 +6333,7 @@
 (step t13 (cl (! (= @p_23 (! (forall ((veriT_vr1 Real)) @p_32) :named @p_34)) :named @p_33)) :rule bind)
 (step t14 (cl (not @p_33) (not @p_23) @p_34) :rule equiv_pos2)
 (step t15 (cl @p_34) :rule th_resolution :premises (t12 t13 t14))
-(anchor :step t16 :args ((:= ?v0 veriT_vr6)))
+(anchor :step t16 :args ((:= (?v0 Real) veriT_vr6)))
 (step t16.t1 (cl (! (= ?v0 veriT_vr6) :named @p_39)) :rule refl)
 (step t16.t2 (cl (= @p_37 (! (fun_app$ uub$ veriT_vr6) :named @p_38))) :rule cong :premises (t16.t1))
 (step t16.t3 (cl @p_39) :rule refl)
@@ -6345,7 +6345,7 @@
 (step t16 (cl (! (= @p_35 (! (forall ((veriT_vr6 Real)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
 (step t17 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
 (step t18 (cl @p_51) :rule th_resolution :premises (a3 t16 t17))
-(anchor :step t19 :args ((:= veriT_vr6 veriT_vr7)))
+(anchor :step t19 :args ((:= (veriT_vr6 Real) veriT_vr7)))
 (step t19.t1 (cl (! (= veriT_vr6 veriT_vr7) :named @p_53)) :rule refl)
 (step t19.t2 (cl (= @p_38 (! (fun_app$ uub$ veriT_vr7) :named @p_52))) :rule cong :premises (t19.t1))
 (step t19.t3 (cl @p_53) :rule refl)
@@ -6357,7 +6357,7 @@
 (step t19 (cl (! (= @p_51 (! (forall ((veriT_vr7 Real)) @p_58) :named @p_60)) :named @p_59)) :rule bind)
 (step t20 (cl (not @p_59) (not @p_51) @p_60) :rule equiv_pos2)
 (step t21 (cl @p_60) :rule th_resolution :premises (t18 t19 t20))
-(anchor :step t22 :args ((:= ?v0 veriT_vr8)))
+(anchor :step t22 :args ((:= (?v0 Real) veriT_vr8)))
 (step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_64)) :rule refl)
 (step t22.t2 (cl (= @p_62 (! (diamond_y$ veriT_vr8) :named @p_63))) :rule cong :premises (t22.t1))
 (step t22.t3 (cl @p_64) :rule refl)
@@ -6371,7 +6371,7 @@
 (step t22 (cl (! (= @p_61 (! (forall ((veriT_vr8 Real)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
 (step t23 (cl (not @p_74) (not @p_61) @p_75) :rule equiv_pos2)
 (step t24 (cl @p_75) :rule th_resolution :premises (a5 t22 t23))
-(anchor :step t25 :args ((:= veriT_vr8 veriT_vr9)))
+(anchor :step t25 :args ((:= (veriT_vr8 Real) veriT_vr9)))
 (step t25.t1 (cl (! (= veriT_vr8 veriT_vr9) :named @p_77)) :rule refl)
 (step t25.t2 (cl (= @p_63 (! (diamond_y$ veriT_vr9) :named @p_76))) :rule cong :premises (t25.t1))
 (step t25.t3 (cl @p_77) :rule refl)
@@ -6385,7 +6385,7 @@
 (step t25 (cl (! (= @p_75 (! (forall ((veriT_vr9 Real)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
 (step t26 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
 (step t27 (cl @p_84) :rule th_resolution :premises (t24 t25 t26))
-(anchor :step t28 :args ((:= ?v0 veriT_vr10) (:= ?v1 veriT_vr11) (:= ?v2 veriT_vr12)))
+(anchor :step t28 :args ((:= (?v0 Real) veriT_vr10) (:= (?v1 Real) veriT_vr11) (:= (?v2 Real) veriT_vr12)))
 (step t28.t1 (cl (! (= ?v0 veriT_vr10) :named @p_94)) :rule refl)
 (step t28.t2 (cl (! (= ?v1 veriT_vr11) :named @p_87)) :rule refl)
 (step t28.t3 (cl (= @p_5 (! (divide$ veriT_vr10 veriT_vr11) :named @p_86))) :rule cong :premises (t28.t1 t28.t2))
@@ -6414,13 +6414,13 @@
 (step t28 (cl (! (= @p_85 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_115) :named @p_117)) :named @p_116)) :rule bind)
 (step t29 (cl (not @p_116) (not @p_85) @p_117) :rule equiv_pos2)
 (step t30 (cl @p_117) :rule th_resolution :premises (a7 t28 t29))
-(anchor :step t31 :args (veriT_vr10 veriT_vr11 veriT_vr12))
+(anchor :step t31 :args ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)))
 (step t31.t1 (cl (= @p_113 (! (and @p_99 @p_105 @p_109) :named @p_118))) :rule ac_simp)
 (step t31.t2 (cl (= @p_115 (! (= @p_91 @p_118) :named @p_119))) :rule cong :premises (t31.t1))
 (step t31 (cl (! (= @p_117 (! (forall ((veriT_vr10 Real) (veriT_vr11 Real) (veriT_vr12 Real)) @p_119) :named @p_121)) :named @p_120)) :rule bind)
 (step t32 (cl (not @p_120) (not @p_117) @p_121) :rule equiv_pos2)
 (step t33 (cl @p_121) :rule th_resolution :premises (t30 t31 t32))
-(anchor :step t34 :args ((:= veriT_vr10 veriT_vr13) (:= veriT_vr11 veriT_vr14) (:= veriT_vr12 veriT_vr15)))
+(anchor :step t34 :args ((:= (veriT_vr10 Real) veriT_vr13) (:= (veriT_vr11 Real) veriT_vr14) (:= (veriT_vr12 Real) veriT_vr15)))
 (step t34.t1 (cl (! (= veriT_vr10 veriT_vr13) :named @p_127)) :rule refl)
 (step t34.t2 (cl (! (= veriT_vr11 veriT_vr14) :named @p_123)) :rule refl)
 (step t34.t3 (cl (= @p_86 (! (divide$ veriT_vr13 veriT_vr14) :named @p_122))) :rule cong :premises (t34.t1 t34.t2))
@@ -6448,7 +6448,7 @@
 (step t34 (cl (! (= @p_121 (! (forall ((veriT_vr13 Real) (veriT_vr14 Real) (veriT_vr15 Real)) @p_137) :named @p_139)) :named @p_138)) :rule bind)
 (step t35 (cl (not @p_138) (not @p_121) @p_139) :rule equiv_pos2)
 (step t36 (cl @p_139) :rule th_resolution :premises (t33 t34 t35))
-(anchor :step t37 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
+(anchor :step t37 :args ((:= (?v0 Real) veriT_vr16) (:= (?v1 Real) veriT_vr17)))
 (step t37.t1 (cl (! (= ?v0 veriT_vr16) :named @p_144)) :rule refl)
 (step t37.t2 (cl (= @p_4 (! (- veriT_vr16) :named @p_141))) :rule cong :premises (t37.t1))
 (step t37.t3 (cl (! (= ?v1 veriT_vr17) :named @p_145)) :rule refl)
@@ -6461,7 +6461,7 @@
 (step t37 (cl (! (= @p_140 (! (forall ((veriT_vr16 Real) (veriT_vr17 Real)) @p_150) :named @p_152)) :named @p_151)) :rule bind)
 (step t38 (cl (not @p_151) (not @p_140) @p_152) :rule equiv_pos2)
 (step t39 (cl @p_152) :rule th_resolution :premises (a8 t37 t38))
-(anchor :step t40 :args ((:= veriT_vr16 veriT_vr18) (:= veriT_vr17 veriT_vr19)))
+(anchor :step t40 :args ((:= (veriT_vr16 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19)))
 (step t40.t1 (cl (! (= veriT_vr16 veriT_vr18) :named @p_155)) :rule refl)
 (step t40.t2 (cl (= @p_141 (! (- veriT_vr18) :named @p_153))) :rule cong :premises (t40.t1))
 (step t40.t3 (cl (! (= veriT_vr17 veriT_vr19) :named @p_156)) :rule refl)
@@ -6474,7 +6474,7 @@
 (step t40 (cl (! (= @p_152 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_159) :named @p_161)) :named @p_160)) :rule bind)
 (step t41 (cl (not @p_160) (not @p_152) @p_161) :rule equiv_pos2)
 (step t42 (cl @p_161) :rule th_resolution :premises (t39 t40 t41))
-(anchor :step t43 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21)))
+(anchor :step t43 :args ((:= (?v0 Real) veriT_vr20) (:= (?v1 Real) veriT_vr21)))
 (step t43.t1 (cl (! (= ?v0 veriT_vr20) :named @p_166)) :rule refl)
 (step t43.t2 (cl (= @p_4 (! (- veriT_vr20) :named @p_163))) :rule cong :premises (t43.t1))
 (step t43.t3 (cl (! (= ?v1 veriT_vr21) :named @p_167)) :rule refl)
@@ -6487,7 +6487,7 @@
 (step t43 (cl (! (= @p_162 (! (forall ((veriT_vr20 Real) (veriT_vr21 Real)) @p_173) :named @p_175)) :named @p_174)) :rule bind)
 (step t44 (cl (not @p_174) (not @p_162) @p_175) :rule equiv_pos2)
 (step t45 (cl @p_175) :rule th_resolution :premises (a9 t43 t44))
-(anchor :step t46 :args ((:= veriT_vr20 veriT_vr22) (:= veriT_vr21 veriT_vr23)))
+(anchor :step t46 :args ((:= (veriT_vr20 Real) veriT_vr22) (:= (veriT_vr21 Real) veriT_vr23)))
 (step t46.t1 (cl (! (= veriT_vr20 veriT_vr22) :named @p_178)) :rule refl)
 (step t46.t2 (cl (= @p_163 (! (- veriT_vr22) :named @p_176))) :rule cong :premises (t46.t1))
 (step t46.t3 (cl (! (= veriT_vr21 veriT_vr23) :named @p_179)) :rule refl)
@@ -6500,7 +6500,7 @@
 (step t46 (cl (! (= @p_175 (! (forall ((veriT_vr22 Real) (veriT_vr23 Real)) @p_182) :named @p_184)) :named @p_183)) :rule bind)
 (step t47 (cl (not @p_183) (not @p_175) @p_184) :rule equiv_pos2)
 (step t48 (cl @p_184) :rule th_resolution :premises (t45 t46 t47))
-(anchor :step t49 :args ((:= ?v0 veriT_vr24) (:= ?v1 veriT_vr25) (:= ?v2 veriT_vr26) (:= ?v3 veriT_vr27)))
+(anchor :step t49 :args ((:= (?v0 Real) veriT_vr24) (:= (?v1 Real) veriT_vr25) (:= (?v2 Real) veriT_vr26) (:= (?v3 Real) veriT_vr27)))
 (step t49.t1 (cl (! (= ?v0 veriT_vr24) :named @p_192)) :rule refl)
 (step t49.t2 (cl (! (= ?v1 veriT_vr25) :named @p_196)) :rule refl)
 (step t49.t3 (cl (= @p_186 (! (pair$ veriT_vr24 veriT_vr25) :named @p_187))) :rule cong :premises (t49.t1 t49.t2))
@@ -6519,7 +6519,7 @@
 (step t49 (cl (! (= @p_185 (! (forall ((veriT_vr24 Real) (veriT_vr25 Real) (veriT_vr26 Real) (veriT_vr27 Real)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
 (step t50 (cl (not @p_204) (not @p_185) @p_205) :rule equiv_pos2)
 (step t51 (cl @p_205) :rule th_resolution :premises (a10 t49 t50))
-(anchor :step t52 :args ((:= veriT_vr24 veriT_vr28) (:= veriT_vr25 veriT_vr29) (:= veriT_vr26 veriT_vr30) (:= veriT_vr27 veriT_vr31)))
+(anchor :step t52 :args ((:= (veriT_vr24 Real) veriT_vr28) (:= (veriT_vr25 Real) veriT_vr29) (:= (veriT_vr26 Real) veriT_vr30) (:= (veriT_vr27 Real) veriT_vr31)))
 (step t52.t1 (cl (! (= veriT_vr24 veriT_vr28) :named @p_209)) :rule refl)
 (step t52.t2 (cl (! (= veriT_vr25 veriT_vr29) :named @p_212)) :rule refl)
 (step t52.t3 (cl (= @p_187 (! (pair$ veriT_vr28 veriT_vr29) :named @p_206))) :rule cong :premises (t52.t1 t52.t2))
@@ -6784,14 +6784,14 @@
 (step t3 (cl (! (= @p_1 (! (forall ((?v0 A$) (?v1 B$)) @p_2) :named @p_4)) :named @p_3)) :rule qnt_rm_unused)
 (step t4 (cl (not @p_3) (not @p_1) @p_4) :rule equiv_pos2)
 (step t5 (cl @p_4) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t6 :args ((:= (?v0 A$) veriT_vr0) (:= (?v1 B$) veriT_vr1)))
 (step t6.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
 (step t6.t2 (cl (= ?v1 veriT_vr1)) :rule refl)
 (step t6.t3 (cl (= @p_2 (! (p$ veriT_vr0 veriT_vr1) :named @p_5))) :rule cong :premises (t6.t1 t6.t2))
 (step t6 (cl (! (= @p_4 (! (forall ((veriT_vr0 A$) (veriT_vr1 B$)) @p_5) :named @p_7)) :named @p_6)) :rule bind)
 (step t7 (cl (not @p_6) (not @p_4) @p_7) :rule equiv_pos2)
 (step t8 (cl @p_7) :rule th_resolution :premises (t5 t6 t7))
-(anchor :step t9 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t9 :args ((:= (veriT_vr0 A$) veriT_vr2) (:= (veriT_vr1 B$) veriT_vr3)))
 (step t9.t1 (cl (= veriT_vr0 veriT_vr2)) :rule refl)
 (step t9.t2 (cl (= veriT_vr1 veriT_vr3)) :rule refl)
 (step t9.t3 (cl (= @p_5 (! (p$ veriT_vr2 veriT_vr3) :named @p_8))) :rule cong :premises (t9.t1 t9.t2))
@@ -6846,7 +6846,7 @@
 (assume a26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_4) b$) :named @p_5) b$) :named @p_423))
 (assume a27 (! (not (! (exists ((?v0 A$)) (! (and (! (member$a ?v0 b$) :named @p_300) (! (less$ (! (fun_app$a @p_4 ?v0) :named @p_303) (! (fun_app$a @p_4 @p_5) :named @p_299)) :named @p_305)) :named @p_307)) :named @p_298)) :named @p_309))
 (assume a52 (not (! (= @p_336 (! (fun_app$b g$ @p_5) :named @p_333)) :named @p_355)))
-(anchor :step t16 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(anchor :step t16 :args ((:= (?v0 B_set$) veriT_vr0) (:= (?v1 B_c_fun$) veriT_vr1)))
 (step t16.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
 (step t16.t2 (cl (= @p_1 (! (finite$ veriT_vr0) :named @p_8))) :rule cong :premises (t16.t1))
 (step t16.t3 (cl @p_9) :rule refl)
@@ -6862,7 +6862,7 @@
 (step t16 (cl (! (= @p_7 (! (forall ((veriT_vr0 B_set$) (veriT_vr1 B_c_fun$)) @p_20) :named @p_22)) :named @p_21)) :rule bind)
 (step t17 (cl (not @p_21) (not @p_7) @p_22) :rule equiv_pos2)
 (step t18 (cl @p_22) :rule th_resolution :premises (a29 t16 t17))
-(anchor :step t19 :args ((:= veriT_vr0 veriT_vr2) (:= veriT_vr1 veriT_vr3)))
+(anchor :step t19 :args ((:= (veriT_vr0 B_set$) veriT_vr2) (:= (veriT_vr1 B_c_fun$) veriT_vr3)))
 (step t19.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_24)) :rule refl)
 (step t19.t2 (cl (= @p_8 (! (finite$ veriT_vr2) :named @p_23))) :rule cong :premises (t19.t1))
 (step t19.t3 (cl @p_24) :rule refl)
@@ -6878,7 +6878,7 @@
 (step t19 (cl (! (= @p_22 (! (forall ((veriT_vr2 B_set$) (veriT_vr3 B_c_fun$)) @p_30) :named @p_32)) :named @p_31)) :rule bind)
 (step t20 (cl (not @p_31) (not @p_22) @p_32) :rule equiv_pos2)
 (step t21 (cl @p_32) :rule th_resolution :premises (t18 t19 t20))
-(anchor :step t22 :args ((:= ?v0 veriT_vr8) (:= ?v1 veriT_vr9) (:= ?v2 veriT_vr10)))
+(anchor :step t22 :args ((:= (?v0 B_set$) veriT_vr8) (:= (?v1 B$) veriT_vr9) (:= (?v2 B_c_fun$) veriT_vr10)))
 (step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_35)) :rule refl)
 (step t22.t2 (cl (= @p_1 (! (finite$ veriT_vr8) :named @p_34))) :rule cong :premises (t22.t1))
 (step t22.t3 (cl @p_35) :rule refl)
@@ -6902,13 +6902,13 @@
 (step t22 (cl (! (= @p_33 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_55) :named @p_57)) :named @p_56)) :rule bind)
 (step t23 (cl (not @p_56) (not @p_33) @p_57) :rule equiv_pos2)
 (step t24 (cl @p_57) :rule th_resolution :premises (a31 t22 t23))
-(anchor :step t25 :args (veriT_vr8 veriT_vr9 veriT_vr10))
+(anchor :step t25 :args ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)))
 (step t25.t1 (cl (= @p_43 (! (and @p_34 @p_37 @p_39) :named @p_58))) :rule ac_simp)
 (step t25.t2 (cl (= @p_55 (! (=> @p_58 @p_53) :named @p_59))) :rule cong :premises (t25.t1))
 (step t25 (cl (! (= @p_57 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
 (step t26 (cl (not @p_60) (not @p_57) @p_61) :rule equiv_pos2)
 (step t27 (cl @p_61) :rule th_resolution :premises (t24 t25 t26))
-(anchor :step t28 :args ((:= veriT_vr8 veriT_vr11) (:= veriT_vr9 veriT_vr12) (:= veriT_vr10 veriT_vr13)))
+(anchor :step t28 :args ((:= (veriT_vr8 B_set$) veriT_vr11) (:= (veriT_vr9 B$) veriT_vr12) (:= (veriT_vr10 B_c_fun$) veriT_vr13)))
 (step t28.t1 (cl (! (= veriT_vr8 veriT_vr11) :named @p_63)) :rule refl)
 (step t28.t2 (cl (= @p_34 (! (finite$ veriT_vr11) :named @p_62))) :rule cong :premises (t28.t1))
 (step t28.t3 (cl @p_63) :rule refl)
@@ -6931,7 +6931,7 @@
 (step t28 (cl (! (= @p_61 (! (forall ((veriT_vr11 B_set$) (veriT_vr12 B$) (veriT_vr13 B_c_fun$)) @p_74) :named @p_76)) :named @p_75)) :rule bind)
 (step t29 (cl (not @p_75) (not @p_61) @p_76) :rule equiv_pos2)
 (step t30 (cl @p_76) :rule th_resolution :premises (t27 t28 t29))
-(anchor :step t31 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21) (:= ?v2 veriT_vr22)))
+(anchor :step t31 :args ((:= (?v0 B_c_fun$) veriT_vr20) (:= (?v1 A_b_fun$) veriT_vr21) (:= (?v2 A$) veriT_vr22)))
 (step t31.t1 (cl (! (= ?v0 veriT_vr20) :named @p_82)) :rule refl)
 (step t31.t2 (cl (! (= ?v1 veriT_vr21) :named @p_83)) :rule refl)
 (step t31.t3 (cl (= @p_78 (! (comp$ veriT_vr20 veriT_vr21) :named @p_79))) :rule cong :premises (t31.t1 t31.t2))
@@ -6946,7 +6946,7 @@
 (step t31 (cl (! (= @p_77 (! (forall ((veriT_vr20 B_c_fun$) (veriT_vr21 A_b_fun$) (veriT_vr22 A$)) @p_89) :named @p_91)) :named @p_90)) :rule bind)
 (step t32 (cl (not @p_90) (not @p_77) @p_91) :rule equiv_pos2)
 (step t33 (cl @p_91) :rule th_resolution :premises (a33 t31 t32))
-(anchor :step t34 :args ((:= veriT_vr20 veriT_vr23) (:= veriT_vr21 veriT_vr24) (:= veriT_vr22 veriT_vr25)))
+(anchor :step t34 :args ((:= (veriT_vr20 B_c_fun$) veriT_vr23) (:= (veriT_vr21 A_b_fun$) veriT_vr24) (:= (veriT_vr22 A$) veriT_vr25)))
 (step t34.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_94)) :rule refl)
 (step t34.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_95)) :rule refl)
 (step t34.t3 (cl (= @p_79 (! (comp$ veriT_vr23 veriT_vr24) :named @p_92))) :rule cong :premises (t34.t1 t34.t2))
@@ -6961,7 +6961,7 @@
 (step t34 (cl (! (= @p_91 (! (forall ((veriT_vr23 B_c_fun$) (veriT_vr24 A_b_fun$) (veriT_vr25 A$)) @p_99) :named @p_101)) :named @p_100)) :rule bind)
 (step t35 (cl (not @p_100) (not @p_91) @p_101) :rule equiv_pos2)
 (step t36 (cl @p_101) :rule th_resolution :premises (t33 t34 t35))
-(anchor :step t37 :args ((:= ?v0 veriT_vr34) (:= ?v1 veriT_vr35)))
+(anchor :step t37 :args ((:= (?v0 A_set$) veriT_vr34) (:= (?v1 A_b_fun$) veriT_vr35)))
 (step t37.t1 (cl (! (= ?v0 veriT_vr34) :named @p_105)) :rule refl)
 (step t37.t2 (cl (= @p_103 (! (finite$a veriT_vr34) :named @p_104))) :rule cong :premises (t37.t1))
 (step t37.t3 (cl (= ?v1 veriT_vr35)) :rule refl)
@@ -6972,7 +6972,7 @@
 (step t37 (cl (! (= @p_102 (! (forall ((veriT_vr34 A_set$) (veriT_vr35 A_b_fun$)) @p_111) :named @p_113)) :named @p_112)) :rule bind)
 (step t38 (cl (not @p_112) (not @p_102) @p_113) :rule equiv_pos2)
 (step t39 (cl @p_113) :rule th_resolution :premises (a36 t37 t38))
-(anchor :step t40 :args ((:= veriT_vr34 veriT_vr36) (:= veriT_vr35 veriT_vr37)))
+(anchor :step t40 :args ((:= (veriT_vr34 A_set$) veriT_vr36) (:= (veriT_vr35 A_b_fun$) veriT_vr37)))
 (step t40.t1 (cl (! (= veriT_vr34 veriT_vr36) :named @p_115)) :rule refl)
 (step t40.t2 (cl (= @p_104 (! (finite$a veriT_vr36) :named @p_114))) :rule cong :premises (t40.t1))
 (step t40.t3 (cl (= veriT_vr35 veriT_vr37)) :rule refl)
@@ -6983,13 +6983,13 @@
 (step t40 (cl (! (= @p_113 (! (forall ((veriT_vr36 A_set$) (veriT_vr37 A_b_fun$)) @p_118) :named @p_120)) :named @p_119)) :rule bind)
 (step t41 (cl (not @p_119) (not @p_113) @p_120) :rule equiv_pos2)
 (step t42 (cl @p_120) :rule th_resolution :premises (t39 t40 t41))
-(anchor :step t43 :args ((:= ?v0 veriT_vr58) (:= ?v1 veriT_vr59) (:= ?v2 veriT_vr60)))
+(anchor :step t43 :args ((:= (?v0 B$) veriT_vr58) (:= (?v1 A_b_fun$) veriT_vr59) (:= (?v2 A_set$) veriT_vr60)))
 (step t43.t1 (cl (! (= ?v0 veriT_vr58) :named @p_128)) :rule refl)
 (step t43.t2 (cl (! (= ?v1 veriT_vr59) :named @p_129)) :rule refl)
 (step t43.t3 (cl (! (= ?v2 veriT_vr60) :named @p_135)) :rule refl)
 (step t43.t4 (cl (= @p_122 (! (image$b veriT_vr59 veriT_vr60) :named @p_123))) :rule cong :premises (t43.t2 t43.t3))
 (step t43.t5 (cl (= @p_124 (! (member$ veriT_vr58 @p_123) :named @p_125))) :rule cong :premises (t43.t1 t43.t4))
-(anchor :step t43.t6 :args ((:= ?v3 veriT_vr61)))
+(anchor :step t43.t6 :args ((:= (?v3 A$) veriT_vr61)))
 (step t43.t6.t1 (cl @p_128) :rule refl)
 (step t43.t6.t2 (cl @p_129) :rule refl)
 (step t43.t6.t3 (cl (! (= ?v3 veriT_vr61) :named @p_134)) :rule refl)
@@ -7006,8 +7006,8 @@
 (step t43 (cl (! (= @p_121 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_145) :named @p_147)) :named @p_146)) :rule bind)
 (step t44 (cl (not @p_146) (not @p_121) @p_147) :rule equiv_pos2)
 (step t45 (cl @p_147) :rule th_resolution :premises (a40 t43 t44))
-(anchor :step t46 :args (veriT_vr58 veriT_vr59 veriT_vr60))
-(anchor :step t46.t1 :args (veriT_vr61))
+(anchor :step t46 :args ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)))
+(anchor :step t46.t1 :args ((veriT_vr61 A$)))
 (step t46.t1.t1 (cl (= @p_141 (! (not @p_139) :named @p_149))) :rule implies_simplify)
 (step t46.t1 (cl (= @p_127 (! (forall ((veriT_vr61 A$)) @p_149) :named @p_148))) :rule bind)
 (step t46.t2 (cl (= @p_143 (! (and @p_125 @p_148) :named @p_150))) :rule cong :premises (t46.t1))
@@ -7017,13 +7017,13 @@
 (step t46 (cl (! (= @p_147 (! (forall ((veriT_vr58 B$) (veriT_vr59 A_b_fun$) (veriT_vr60 A_set$)) @p_152) :named @p_154)) :named @p_153)) :rule bind)
 (step t47 (cl (not @p_153) (not @p_147) @p_154) :rule equiv_pos2)
 (step t48 (cl @p_154) :rule th_resolution :premises (t45 t46 t47))
-(anchor :step t49 :args ((:= veriT_vr58 veriT_vr62) (:= veriT_vr59 veriT_vr63) (:= veriT_vr60 veriT_vr64)))
+(anchor :step t49 :args ((:= (veriT_vr58 B$) veriT_vr62) (:= (veriT_vr59 A_b_fun$) veriT_vr63) (:= (veriT_vr60 A_set$) veriT_vr64)))
 (step t49.t1 (cl (! (= veriT_vr58 veriT_vr62) :named @p_158)) :rule refl)
 (step t49.t2 (cl (! (= veriT_vr59 veriT_vr63) :named @p_159)) :rule refl)
 (step t49.t3 (cl (! (= veriT_vr60 veriT_vr64) :named @p_163)) :rule refl)
 (step t49.t4 (cl (= @p_123 (! (image$b veriT_vr63 veriT_vr64) :named @p_155))) :rule cong :premises (t49.t2 t49.t3))
 (step t49.t5 (cl (= @p_125 (! (member$ veriT_vr62 @p_155) :named @p_156))) :rule cong :premises (t49.t1 t49.t4))
-(anchor :step t49.t6 :args ((:= veriT_vr61 veriT_vr65)))
+(anchor :step t49.t6 :args ((:= (veriT_vr61 A$) veriT_vr65)))
 (step t49.t6.t1 (cl @p_158) :rule refl)
 (step t49.t6.t2 (cl @p_159) :rule refl)
 (step t49.t6.t3 (cl (! (= veriT_vr61 veriT_vr65) :named @p_162)) :rule refl)
@@ -7040,7 +7040,7 @@
 (step t49 (cl (! (= @p_154 (! (forall ((veriT_vr62 B$) (veriT_vr63 A_b_fun$) (veriT_vr64 A_set$)) @p_168) :named @p_170)) :named @p_169)) :rule bind)
 (step t50 (cl (not @p_169) (not @p_154) @p_170) :rule equiv_pos2)
 (step t51 (cl @p_170) :rule th_resolution :premises (t48 t49 t50))
-(anchor :step t52 :args ((:= ?v0 veriT_vr90) (:= ?v1 veriT_vr91) (:= ?v2 veriT_vr92) (:= ?v3 veriT_vr93)))
+(anchor :step t52 :args ((:= (?v0 B$) veriT_vr90) (:= (?v1 A_b_fun$) veriT_vr91) (:= (?v2 A$) veriT_vr92) (:= (?v3 A_set$) veriT_vr93)))
 (step t52.t1 (cl (! (= ?v1 veriT_vr91) :named @p_181)) :rule refl)
 (step t52.t2 (cl (! (= ?v2 veriT_vr92) :named @p_175)) :rule refl)
 (step t52.t3 (cl (= @p_3 (! (fun_app$b veriT_vr91 veriT_vr92) :named @p_172))) :rule cong :premises (t52.t1 t52.t2))
@@ -7059,7 +7059,7 @@
 (step t52 (cl (! (= @p_171 (! (forall ((veriT_vr90 B$) (veriT_vr91 A_b_fun$) (veriT_vr92 A$) (veriT_vr93 A_set$)) @p_188) :named @p_190)) :named @p_189)) :rule bind)
 (step t53 (cl (not @p_189) (not @p_171) @p_190) :rule equiv_pos2)
 (step t54 (cl @p_190) :rule th_resolution :premises (a44 t52 t53))
-(anchor :step t55 :args ((:= veriT_vr90 veriT_vr94) (:= veriT_vr91 veriT_vr95) (:= veriT_vr92 veriT_vr96) (:= veriT_vr93 veriT_vr97)))
+(anchor :step t55 :args ((:= (veriT_vr90 B$) veriT_vr94) (:= (veriT_vr91 A_b_fun$) veriT_vr95) (:= (veriT_vr92 A$) veriT_vr96) (:= (veriT_vr93 A_set$) veriT_vr97)))
 (step t55.t1 (cl (! (= veriT_vr90 veriT_vr94) :named @p_196)) :rule refl)
 (step t55.t2 (cl (! (= veriT_vr91 veriT_vr95) :named @p_197)) :rule refl)
 (step t55.t3 (cl (! (= veriT_vr92 veriT_vr96) :named @p_193)) :rule refl)
@@ -7078,7 +7078,7 @@
 (step t55 (cl (! (= @p_190 (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) @p_201) :named @p_203)) :named @p_202)) :rule bind)
 (step t56 (cl (not @p_202) (not @p_190) @p_203) :rule equiv_pos2)
 (step t57 (cl @p_203) :rule th_resolution :premises (t54 t55 t56))
-(anchor :step t58 :args ((:= ?v0 veriT_vr114) (:= ?v1 veriT_vr115)))
+(anchor :step t58 :args ((:= (?v0 A_b_fun$) veriT_vr114) (:= (?v1 A_set$) veriT_vr115)))
 (step t58.t1 (cl (= ?v0 veriT_vr114)) :rule refl)
 (step t58.t2 (cl (! (= ?v1 veriT_vr115) :named @p_209)) :rule refl)
 (step t58.t3 (cl (= @p_205 (! (image$b veriT_vr114 veriT_vr115) :named @p_206))) :rule cong :premises (t58.t1 t58.t2))
@@ -7089,7 +7089,7 @@
 (step t58 (cl (! (= @p_204 (! (forall ((veriT_vr114 A_b_fun$) (veriT_vr115 A_set$)) @p_213) :named @p_215)) :named @p_214)) :rule bind)
 (step t59 (cl (not @p_214) (not @p_204) @p_215) :rule equiv_pos2)
 (step t60 (cl @p_215) :rule th_resolution :premises (a48 t58 t59))
-(anchor :step t61 :args ((:= veriT_vr114 veriT_vr116) (:= veriT_vr115 veriT_vr117)))
+(anchor :step t61 :args ((:= (veriT_vr114 A_b_fun$) veriT_vr116) (:= (veriT_vr115 A_set$) veriT_vr117)))
 (step t61.t1 (cl (= veriT_vr114 veriT_vr116)) :rule refl)
 (step t61.t2 (cl (! (= veriT_vr115 veriT_vr117) :named @p_218)) :rule refl)
 (step t61.t3 (cl (= @p_206 (! (image$b veriT_vr116 veriT_vr117) :named @p_216))) :rule cong :premises (t61.t1 t61.t2))
@@ -7100,7 +7100,7 @@
 (step t61 (cl (! (= @p_215 (! (forall ((veriT_vr116 A_b_fun$) (veriT_vr117 A_set$)) @p_220) :named @p_222)) :named @p_221)) :rule bind)
 (step t62 (cl (not @p_221) (not @p_215) @p_222) :rule equiv_pos2)
 (step t63 (cl @p_222) :rule th_resolution :premises (t60 t61 t62))
-(anchor :step t64 :args ((:= ?v0 veriT_vr122) (:= ?v1 veriT_vr123) (:= ?v2 veriT_vr124) (:= ?v3 veriT_vr125)))
+(anchor :step t64 :args ((:= (?v0 B_c_fun$) veriT_vr122) (:= (?v1 B_set$) veriT_vr123) (:= (?v2 B$) veriT_vr124) (:= (?v3 B$) veriT_vr125)))
 (step t64.t1 (cl (! (= ?v0 veriT_vr122) :named @p_226)) :rule refl)
 (step t64.t2 (cl (! (= ?v1 veriT_vr123) :named @p_234)) :rule refl)
 (step t64.t3 (cl (= @p_224 (! (inj_on$ veriT_vr122 veriT_vr123) :named @p_225))) :rule cong :premises (t64.t1 t64.t2))
@@ -7127,13 +7127,13 @@
 (step t64 (cl (! (= @p_223 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_249) :named @p_251)) :named @p_250)) :rule bind)
 (step t65 (cl (not @p_250) (not @p_223) @p_251) :rule equiv_pos2)
 (step t66 (cl @p_251) :rule th_resolution :premises (a50 t64 t65))
-(anchor :step t67 :args (veriT_vr122 veriT_vr123 veriT_vr124 veriT_vr125))
+(anchor :step t67 :args ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)))
 (step t67.t1 (cl (= @p_245 (! (and @p_225 @p_232 @p_236 @p_239) :named @p_252))) :rule ac_simp)
 (step t67.t2 (cl (= @p_249 (! (=> @p_252 @p_247) :named @p_253))) :rule cong :premises (t67.t1))
 (step t67 (cl (! (= @p_251 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_253) :named @p_255)) :named @p_254)) :rule bind)
 (step t68 (cl (not @p_254) (not @p_251) @p_255) :rule equiv_pos2)
 (step t69 (cl @p_255) :rule th_resolution :premises (t66 t67 t68))
-(anchor :step t70 :args ((:= veriT_vr122 veriT_vr126) (:= veriT_vr123 veriT_vr127) (:= veriT_vr124 veriT_vr128) (:= veriT_vr125 veriT_vr129)))
+(anchor :step t70 :args ((:= (veriT_vr122 B_c_fun$) veriT_vr126) (:= (veriT_vr123 B_set$) veriT_vr127) (:= (veriT_vr124 B$) veriT_vr128) (:= (veriT_vr125 B$) veriT_vr129)))
 (step t70.t1 (cl (! (= veriT_vr122 veriT_vr126) :named @p_257)) :rule refl)
 (step t70.t2 (cl (! (= veriT_vr123 veriT_vr127) :named @p_262)) :rule refl)
 (step t70.t3 (cl (= @p_225 (! (inj_on$ veriT_vr126 veriT_vr127) :named @p_256))) :rule cong :premises (t70.t1 t70.t2))
@@ -7158,7 +7158,7 @@
 (step t70 (cl (! (= @p_255 (! (forall ((veriT_vr126 B_c_fun$) (veriT_vr127 B_set$) (veriT_vr128 B$) (veriT_vr129 B$)) @p_268) :named @p_270)) :named @p_269)) :rule bind)
 (step t71 (cl (not @p_269) (not @p_255) @p_270) :rule equiv_pos2)
 (step t72 (cl @p_270) :rule th_resolution :premises (t69 t70 t71))
-(anchor :step t73 :args ((:= ?v0 veriT_vr130) (:= ?v1 veriT_vr131)))
+(anchor :step t73 :args ((:= (?v0 C$) veriT_vr130) (:= (?v1 C$) veriT_vr131)))
 (step t73.t1 (cl (! (= ?v0 veriT_vr130) :named @p_274)) :rule refl)
 (step t73.t2 (cl (! (= ?v1 veriT_vr131) :named @p_275)) :rule refl)
 (step t73.t3 (cl (= @p_272 (! (less$ veriT_vr130 veriT_vr131) :named @p_273))) :rule cong :premises (t73.t1 t73.t2))
@@ -7174,7 +7174,7 @@
 (step t73 (cl (! (= @p_271 (! (forall ((veriT_vr130 C$) (veriT_vr131 C$)) @p_285) :named @p_287)) :named @p_286)) :rule bind)
 (step t74 (cl (not @p_286) (not @p_271) @p_287) :rule equiv_pos2)
 (step t75 (cl @p_287) :rule th_resolution :premises (a51 t73 t74))
-(anchor :step t76 :args ((:= veriT_vr130 veriT_vr132) (:= veriT_vr131 veriT_vr133)))
+(anchor :step t76 :args ((:= (veriT_vr130 C$) veriT_vr132) (:= (veriT_vr131 C$) veriT_vr133)))
 (step t76.t1 (cl (! (= veriT_vr130 veriT_vr132) :named @p_289)) :rule refl)
 (step t76.t2 (cl (! (= veriT_vr131 veriT_vr133) :named @p_290)) :rule refl)
 (step t76.t3 (cl (= @p_273 (! (less$ veriT_vr132 veriT_vr133) :named @p_288))) :rule cong :premises (t76.t1 t76.t2))
@@ -7190,7 +7190,7 @@
 (step t76 (cl (! (= @p_287 (! (forall ((veriT_vr132 C$) (veriT_vr133 C$)) @p_295) :named @p_297)) :named @p_296)) :rule bind)
 (step t77 (cl (not @p_296) (not @p_287) @p_297) :rule equiv_pos2)
 (step t78 (cl @p_297) :rule th_resolution :premises (t75 t76 t77))
-(anchor :step t79 :args ((:= ?v0 veriT_vr134)))
+(anchor :step t79 :args ((:= (?v0 A$) veriT_vr134)))
 (step t79.t1 (cl (! (= ?v0 veriT_vr134) :named @p_302)) :rule refl)
 (step t79.t2 (cl (= @p_300 (! (member$a veriT_vr134 b$) :named @p_301))) :rule cong :premises (t79.t1))
 (step t79.t3 (cl @p_302) :rule refl)
@@ -7203,7 +7203,7 @@
 (step t82 (cl (not @p_313) @p_298) :rule not_not)
 (step t83 (cl @p_314 @p_298 @p_312) :rule th_resolution :premises (t82 t81))
 (step t84 (cl @p_312) :rule th_resolution :premises (a27 t80 t83))
-(anchor :step t85 :args ((:= veriT_vr134 veriT_vr135)))
+(anchor :step t85 :args ((:= (veriT_vr134 A$) veriT_vr135)))
 (step t85.t1 (cl (! (= veriT_vr134 veriT_vr135) :named @p_316)) :rule refl)
 (step t85.t2 (cl (= @p_301 (! (member$a veriT_vr135 b$) :named @p_315))) :rule cong :premises (t85.t1))
 (step t85.t3 (cl @p_316) :rule refl)
@@ -7255,7 +7255,7 @@
 (step t127 (cl (or (! (not @p_170) :named @p_401) (! (not (! (and @p_350 (! (forall ((veriT_vr65 A$)) (! (not (! (and (! (= @p_336 (! (fun_app$b g$ veriT_vr65) :named @p_359)) :named @p_361) (! (member$a veriT_vr65 b$) :named @p_364)) :named @p_366)) :named @p_368)) :named @p_358)) :named @p_370)) :named @p_356))) :rule forall_inst :args ((:= veriT_vr62 @p_336) (:= veriT_vr63 g$) (:= veriT_vr64 b$)))
 (anchor :step t128)
 (assume t128.h1 @p_356)
-(anchor :step t128.t2 :args ((:= veriT_vr65 veriT_vr144)))
+(anchor :step t128.t2 :args ((:= (veriT_vr65 A$) veriT_vr144)))
 (step t128.t2.t1 (cl (! (= veriT_vr65 veriT_vr144) :named @p_363)) :rule refl)
 (step t128.t2.t2 (cl (= @p_359 (! (fun_app$b g$ veriT_vr144) :named @p_360))) :rule cong :premises (t128.t2.t1))
 (step t128.t2.t3 (cl (= @p_361 (! (= @p_336 @p_360) :named @p_362))) :rule cong :premises (t128.t2.t2))
@@ -7270,7 +7270,7 @@
 (step t128.t6 (cl (! (not @p_374) :named @p_400) @p_370) :rule not_not)
 (step t128.t7 (cl @p_376 @p_370 @p_375) :rule th_resolution :premises (t128.t6 t128.t5))
 (step t128.t8 (cl @p_375) :rule th_resolution :premises (t128.h1 t128.t4 t128.t7))
-(anchor :step t128.t9 :args ((:= veriT_vr144 veriT_vr145)))
+(anchor :step t128.t9 :args ((:= (veriT_vr144 A$) veriT_vr145)))
 (step t128.t9.t1 (cl (! (= veriT_vr144 veriT_vr145) :named @p_380)) :rule refl)
 (step t128.t9.t2 (cl (= @p_360 @p_378)) :rule cong :premises (t128.t9.t1))
 (step t128.t9.t3 (cl (= @p_362 @p_379)) :rule cong :premises (t128.t9.t2))
@@ -7285,7 +7285,7 @@
 (step t128.t13 (cl (not @p_387) @p_372) :rule not_not)
 (step t128.t14 (cl @p_388 @p_372 @p_386) :rule th_resolution :premises (t128.t13 t128.t12))
 (step t128.t15 (cl @p_386) :rule th_resolution :premises (t128.t8 t128.t11 t128.t14))
-(anchor :step t128.t16 :args ((:= veriT_vr145 veriT_sk0)))
+(anchor :step t128.t16 :args ((:= (veriT_vr145 A$) veriT_sk0)))
 (step t128.t16.t1 (cl (! (= veriT_vr145 veriT_sk0) :named @p_392)) :rule refl)
 (step t128.t16.t2 (cl (= @p_378 (! (fun_app$b g$ veriT_sk0) :named @p_390))) :rule cong :premises (t128.t16.t1))
 (step t128.t16.t3 (cl (= @p_379 (! (= @p_336 @p_390) :named @p_391))) :rule cong :premises (t128.t16.t2))
@@ -7396,6 +7396,526 @@
 (step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209))
 (step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210))
 (step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204))
+ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0
+unsat
+(assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! (rec_join$ ?v0) :named @p_10) ?v1) :named @p_19) (! (and (! (=> (! (and (! (= nil$ ?v0) :named @p_11) (! (= uu$ ?v1) :named @p_20)) :named @p_22) false) :named @p_24) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= @p_8 ?v0) :named @p_17) (! (= @p_1 ?v1) :named @p_27)) :named @p_29) false) :named @p_31)) :named @p_25) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= @p_9 ?v0) :named @p_18) (! (= @p_7 ?v1) :named @p_35)) :named @p_37) false) :named @p_39)) :named @p_33)) :named @p_41)) :named @p_43)) :named @p_45) false) :named @p_47)) :named @p_14) (! (forall ((?v0 B_list$)) (! (=> (! (and (! (= @p_10 @p_10) :named @p_15) (! (and (! (=> (! (and @p_11 (! (= uu$ @p_10) :named @p_21)) :named @p_23) false) :named @p_16) (! (and (! (forall ((?v1 B$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 nil$) :named @p_162)) :named @p_163) (! (= @p_10 (! (coeff_cube_to_path$ ?v1) :named @p_12)) :named @p_165)) :named @p_166) false) :named @p_167)) :named @p_161) (! (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55))
+(anchor :step t2 :args ((?v0 B_list$) (:= (?v1 Real_a_fun$) @p_10)))
+(step t2.t1 (cl @p_19) :rule refl)
+(step t2.t2 (cl (= @p_19 @p_15)) :rule cong :premises (t2.t1))
+(step t2.t3 (cl @p_19) :rule refl)
+(step t2.t4 (cl (= @p_20 @p_21)) :rule cong :premises (t2.t3))
+(step t2.t5 (cl (= @p_22 @p_23)) :rule cong :premises (t2.t4))
+(step t2.t6 (cl (= @p_24 @p_16)) :rule cong :premises (t2.t5))
+(anchor :step t2.t7 :args ((?v2 B$)))
+(step t2.t7.t1 (cl @p_19) :rule refl)
+(step t2.t7.t2 (cl (= @p_27 (! (= @p_1 @p_10) :named @p_28))) :rule cong :premises (t2.t7.t1))
+(step t2.t7.t3 (cl (= @p_29 (! (and @p_17 @p_28) :named @p_30))) :rule cong :premises (t2.t7.t2))
+(step t2.t7.t4 (cl (= @p_31 (! (=> @p_30 false) :named @p_32))) :rule cong :premises (t2.t7.t3))
+(step t2.t7 (cl (= @p_25 (! (forall ((?v2 B$)) @p_32) :named @p_26))) :rule bind)
+(anchor :step t2.t8 :args ((?v2 B$) (?v3 B$) (?v4 B_list$)))
+(step t2.t8.t1 (cl @p_19) :rule refl)
+(step t2.t8.t2 (cl (= @p_35 (! (= @p_7 @p_10) :named @p_36))) :rule cong :premises (t2.t8.t1))
+(step t2.t8.t3 (cl (= @p_37 (! (and @p_18 @p_36) :named @p_38))) :rule cong :premises (t2.t8.t2))
+(step t2.t8.t4 (cl (= @p_39 (! (=> @p_38 false) :named @p_40))) :rule cong :premises (t2.t8.t3))
+(step t2.t8 (cl (= @p_33 (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) @p_40) :named @p_34))) :rule bind)
+(step t2.t9 (cl (= @p_41 (! (and @p_26 @p_34) :named @p_42))) :rule cong :premises (t2.t7 t2.t8))
+(step t2.t10 (cl (= @p_43 (! (and @p_16 @p_42) :named @p_44))) :rule cong :premises (t2.t6 t2.t9))
+(step t2.t11 (cl (= @p_45 (! (and @p_15 @p_44) :named @p_46))) :rule cong :premises (t2.t2 t2.t10))
+(step t2.t12 (cl (= @p_47 (! (=> @p_46 false) :named @p_48))) :rule cong :premises (t2.t11))
+(step t2 (cl (= @p_14 (! (forall ((?v0 B_list$)) @p_48) :named @p_50))) :rule onepoint)
+(step t3 (cl (= @p_49 (! (= @p_50 @p_51) :named @p_54))) :rule cong :premises (t2))
+(step t4 (cl (= @p_52 (! (=> @p_53 @p_54) :named @p_56))) :rule cong :premises (t3))
+(step t5 (cl (! (= @p_55 (! (not @p_56) :named @p_58)) :named @p_57)) :rule cong :premises (t4))
+(step t6 (cl (! (not @p_57) :named @p_60) (! (not @p_55) :named @p_59) @p_58) :rule equiv_pos2)
+(step t7 (cl (not @p_59) @p_52) :rule not_not)
+(step t8 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t7 t6))
+(step t9 (cl @p_58) :rule th_resolution :premises (a1 t5 t8))
+(anchor :step t10 :args ((:= (?v0 Real_a_fun$) veriT_vr2) (:= (?v1 B_list$) veriT_vr3)))
+(step t10.t1 (cl (! (= ?v1 veriT_vr3) :named @p_70)) :rule refl)
+(step t10.t2 (cl (! (= @p_3 (! (rec_join$ veriT_vr3) :named @p_63)) :named @p_111)) :rule cong :premises (t10.t1))
+(step t10.t3 (cl (! (= ?v0 veriT_vr2) :named @p_71)) :rule refl)
+(step t10.t4 (cl (= @p_68 (! (= veriT_vr2 @p_63) :named @p_69))) :rule cong :premises (t10.t2 t10.t3))
+(step t10.t5 (cl @p_70) :rule refl)
+(step t10.t6 (cl (! (= @p_4 (! (= nil$ veriT_vr3) :named @p_64)) :named @p_114)) :rule cong :premises (t10.t5))
+(step t10.t7 (cl @p_71) :rule refl)
+(step t10.t8 (cl (= @p_72 (! (= uu$ veriT_vr2) :named @p_73))) :rule cong :premises (t10.t7))
+(step t10.t9 (cl (= @p_74 (! (and @p_64 @p_73) :named @p_75))) :rule cong :premises (t10.t6 t10.t8))
+(step t10.t10 (cl (= @p_76 (! (=> @p_75 false) :named @p_77))) :rule cong :premises (t10.t9))
+(anchor :step t10.t11 :args ((:= (?v2 B$) veriT_vr4)))
+(step t10.t11.t1 (cl @p_70) :rule refl)
+(step t10.t11.t2 (cl (! (= ?v2 veriT_vr4) :named @p_81)) :rule refl)
+(step t10.t11.t3 (cl (! (= @p_8 (! (cons$ veriT_vr4 nil$) :named @p_80)) :named @p_123)) :rule cong :premises (t10.t11.t2))
+(step t10.t11.t4 (cl (! (= @p_5 (! (= veriT_vr3 @p_80) :named @p_65)) :named @p_124)) :rule cong :premises (t10.t11.t1 t10.t11.t3))
+(step t10.t11.t5 (cl @p_71) :rule refl)
+(step t10.t11.t6 (cl @p_81) :rule refl)
+(step t10.t11.t7 (cl (! (= @p_1 (! (coeff_cube_to_path$ veriT_vr4) :named @p_61)) :named @p_91)) :rule cong :premises (t10.t11.t6))
+(step t10.t11.t8 (cl (= @p_82 (! (= veriT_vr2 @p_61) :named @p_83))) :rule cong :premises (t10.t11.t5 t10.t11.t7))
+(step t10.t11.t9 (cl (= @p_84 (! (and @p_65 @p_83) :named @p_85))) :rule cong :premises (t10.t11.t4 t10.t11.t8))
+(step t10.t11.t10 (cl (= @p_86 (! (=> @p_85 false) :named @p_87))) :rule cong :premises (t10.t11.t9))
+(step t10.t11 (cl (= @p_78 (! (forall ((veriT_vr4 B$)) @p_87) :named @p_79))) :rule bind)
+(anchor :step t10.t12 :args ((:= (?v2 B$) veriT_vr4) (:= (?v3 B$) veriT_vr5) (:= (?v4 B_list$) veriT_vr6)))
+(step t10.t12.t1 (cl @p_70) :rule refl)
+(step t10.t12.t2 (cl @p_81) :rule refl)
+(step t10.t12.t3 (cl (! (= ?v3 veriT_vr5) :named @p_92)) :rule refl)
+(step t10.t12.t4 (cl (! (= ?v4 veriT_vr6) :named @p_93)) :rule refl)
+(step t10.t12.t5 (cl (! (= @p_2 (! (cons$ veriT_vr5 veriT_vr6) :named @p_62)) :named @p_94)) :rule cong :premises (t10.t12.t3 t10.t12.t4))
+(step t10.t12.t6 (cl (! (= @p_9 (! (cons$ veriT_vr4 @p_62) :named @p_90)) :named @p_133)) :rule cong :premises (t10.t12.t2 t10.t12.t5))
+(step t10.t12.t7 (cl (! (= @p_6 (! (= veriT_vr3 @p_90) :named @p_66)) :named @p_134)) :rule cong :premises (t10.t12.t1 t10.t12.t6))
+(step t10.t12.t8 (cl @p_71) :rule refl)
+(step t10.t12.t9 (cl @p_81) :rule refl)
+(step t10.t12.t10 (cl @p_91) :rule cong :premises (t10.t12.t9))
+(step t10.t12.t11 (cl @p_92) :rule refl)
+(step t10.t12.t12 (cl @p_93) :rule refl)
+(step t10.t12.t13 (cl @p_94) :rule cong :premises (t10.t12.t11 t10.t12.t12))
+(step t10.t12.t14 (cl (! (= @p_95 (! (rec_join$ @p_62) :named @p_96)) :named @p_135)) :rule cong :premises (t10.t12.t13))
+(step t10.t12.t15 (cl (! (= @p_7 (! (joinpaths$ @p_61 @p_96) :named @p_67)) :named @p_136)) :rule cong :premises (t10.t12.t10 t10.t12.t14))
+(step t10.t12.t16 (cl (= @p_97 (! (= veriT_vr2 @p_67) :named @p_98))) :rule cong :premises (t10.t12.t8 t10.t12.t15))
+(step t10.t12.t17 (cl (= @p_99 (! (and @p_66 @p_98) :named @p_100))) :rule cong :premises (t10.t12.t7 t10.t12.t16))
+(step t10.t12.t18 (cl (= @p_101 (! (=> @p_100 false) :named @p_102))) :rule cong :premises (t10.t12.t17))
+(step t10.t12 (cl (= @p_88 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_102) :named @p_89))) :rule bind)
+(step t10.t13 (cl (= @p_103 (! (and @p_79 @p_89) :named @p_104))) :rule cong :premises (t10.t11 t10.t12))
+(step t10.t14 (cl (= @p_105 (! (and @p_77 @p_104) :named @p_106))) :rule cong :premises (t10.t10 t10.t13))
+(step t10.t15 (cl (= @p_107 (! (and @p_69 @p_106) :named @p_108))) :rule cong :premises (t10.t4 t10.t14))
+(step t10.t16 (cl (= @p_109 (! (=> @p_108 false) :named @p_110))) :rule cong :premises (t10.t15))
+(step t10.t17 (cl @p_70) :rule refl)
+(step t10.t18 (cl @p_111) :rule cong :premises (t10.t17))
+(step t10.t19 (cl @p_70) :rule refl)
+(step t10.t20 (cl @p_111) :rule cong :premises (t10.t19))
+(step t10.t21 (cl (= @p_112 (! (= @p_63 @p_63) :named @p_113))) :rule cong :premises (t10.t18 t10.t20))
+(step t10.t22 (cl @p_70) :rule refl)
+(step t10.t23 (cl @p_114) :rule cong :premises (t10.t22))
+(step t10.t24 (cl @p_70) :rule refl)
+(step t10.t25 (cl @p_111) :rule cong :premises (t10.t24))
+(step t10.t26 (cl (= @p_115 (! (= uu$ @p_63) :named @p_116))) :rule cong :premises (t10.t25))
+(step t10.t27 (cl (= @p_117 (! (and @p_64 @p_116) :named @p_118))) :rule cong :premises (t10.t23 t10.t26))
+(step t10.t28 (cl (= @p_119 (! (=> @p_118 false) :named @p_120))) :rule cong :premises (t10.t27))
+(anchor :step t10.t29 :args ((:= (?v2 B$) veriT_vr4)))
+(step t10.t29.t1 (cl @p_70) :rule refl)
+(step t10.t29.t2 (cl @p_81) :rule refl)
+(step t10.t29.t3 (cl @p_123) :rule cong :premises (t10.t29.t2))
+(step t10.t29.t4 (cl @p_124) :rule cong :premises (t10.t29.t1 t10.t29.t3))
+(step t10.t29.t5 (cl @p_70) :rule refl)
+(step t10.t29.t6 (cl @p_111) :rule cong :premises (t10.t29.t5))
+(step t10.t29.t7 (cl @p_81) :rule refl)
+(step t10.t29.t8 (cl @p_91) :rule cong :premises (t10.t29.t7))
+(step t10.t29.t9 (cl (= @p_125 (! (= @p_63 @p_61) :named @p_126))) :rule cong :premises (t10.t29.t6 t10.t29.t8))
+(step t10.t29.t10 (cl (= @p_127 (! (and @p_65 @p_126) :named @p_128))) :rule cong :premises (t10.t29.t4 t10.t29.t9))
+(step t10.t29.t11 (cl (= @p_129 (! (=> @p_128 false) :named @p_130))) :rule cong :premises (t10.t29.t10))
+(step t10.t29 (cl (= @p_121 (! (forall ((veriT_vr4 B$)) @p_130) :named @p_122))) :rule bind)
+(anchor :step t10.t30 :args ((:= (?v2 B$) veriT_vr4) (:= (?v3 B$) veriT_vr5) (:= (?v4 B_list$) veriT_vr6)))
+(step t10.t30.t1 (cl @p_70) :rule refl)
+(step t10.t30.t2 (cl @p_81) :rule refl)
+(step t10.t30.t3 (cl @p_92) :rule refl)
+(step t10.t30.t4 (cl @p_93) :rule refl)
+(step t10.t30.t5 (cl @p_94) :rule cong :premises (t10.t30.t3 t10.t30.t4))
+(step t10.t30.t6 (cl @p_133) :rule cong :premises (t10.t30.t2 t10.t30.t5))
+(step t10.t30.t7 (cl @p_134) :rule cong :premises (t10.t30.t1 t10.t30.t6))
+(step t10.t30.t8 (cl @p_70) :rule refl)
+(step t10.t30.t9 (cl @p_111) :rule cong :premises (t10.t30.t8))
+(step t10.t30.t10 (cl @p_81) :rule refl)
+(step t10.t30.t11 (cl @p_91) :rule cong :premises (t10.t30.t10))
+(step t10.t30.t12 (cl @p_92) :rule refl)
+(step t10.t30.t13 (cl @p_93) :rule refl)
+(step t10.t30.t14 (cl @p_94) :rule cong :premises (t10.t30.t12 t10.t30.t13))
+(step t10.t30.t15 (cl @p_135) :rule cong :premises (t10.t30.t14))
+(step t10.t30.t16 (cl @p_136) :rule cong :premises (t10.t30.t11 t10.t30.t15))
+(step t10.t30.t17 (cl (= @p_137 (! (= @p_63 @p_67) :named @p_138))) :rule cong :premises (t10.t30.t9 t10.t30.t16))
+(step t10.t30.t18 (cl (= @p_139 (! (and @p_66 @p_138) :named @p_140))) :rule cong :premises (t10.t30.t7 t10.t30.t17))
+(step t10.t30.t19 (cl (= @p_141 (! (=> @p_140 false) :named @p_142))) :rule cong :premises (t10.t30.t18))
+(step t10.t30 (cl (= @p_131 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_142) :named @p_132))) :rule bind)
+(step t10.t31 (cl (= @p_143 (! (and @p_122 @p_132) :named @p_144))) :rule cong :premises (t10.t29 t10.t30))
+(step t10.t32 (cl (= @p_145 (! (and @p_120 @p_144) :named @p_146))) :rule cong :premises (t10.t28 t10.t31))
+(step t10.t33 (cl (= @p_147 (! (and @p_113 @p_146) :named @p_148))) :rule cong :premises (t10.t21 t10.t32))
+(step t10.t34 (cl (= @p_149 (! (=> @p_148 false) :named @p_150))) :rule cong :premises (t10.t33))
+(step t10.t35 (cl (= @p_151 (! (= @p_110 @p_150) :named @p_152))) :rule cong :premises (t10.t16 t10.t34))
+(step t10 (cl (= @p_53 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_152) :named @p_184))) :rule bind)
+(anchor :step t11 :args ((:= (?v0 B_list$) veriT_vr3)))
+(step t11.t1 (cl (! (= ?v0 veriT_vr3) :named @p_153)) :rule refl)
+(step t11.t2 (cl (! (= @p_10 @p_63) :named @p_154)) :rule cong :premises (t11.t1))
+(step t11.t3 (cl @p_153) :rule refl)
+(step t11.t4 (cl @p_154) :rule cong :premises (t11.t3))
+(step t11.t5 (cl (! (= @p_15 @p_113) :named @p_156)) :rule cong :premises (t11.t2 t11.t4))
+(step t11.t6 (cl @p_153) :rule refl)
+(step t11.t7 (cl (! (= @p_11 @p_64) :named @p_157)) :rule cong :premises (t11.t6))
+(step t11.t8 (cl @p_153) :rule refl)
+(step t11.t9 (cl @p_154) :rule cong :premises (t11.t8))
+(step t11.t10 (cl (! (= @p_21 @p_116) :named @p_158)) :rule cong :premises (t11.t9))
+(step t11.t11 (cl (! (= @p_23 @p_118) :named @p_159)) :rule cong :premises (t11.t7 t11.t10))
+(step t11.t12 (cl (! (= @p_16 @p_120) :named @p_160)) :rule cong :premises (t11.t11))
+(anchor :step t11.t13 :args ((:= (?v2 B$) veriT_vr4)))
+(step t11.t13.t1 (cl @p_81) :rule refl)
+(step t11.t13.t2 (cl @p_123) :rule cong :premises (t11.t13.t1))
+(step t11.t13.t3 (cl @p_153) :rule refl)
+(step t11.t13.t4 (cl (= @p_17 @p_65)) :rule cong :premises (t11.t13.t2 t11.t13.t3))
+(step t11.t13.t5 (cl @p_81) :rule refl)
+(step t11.t13.t6 (cl @p_91) :rule cong :premises (t11.t13.t5))
+(step t11.t13.t7 (cl @p_153) :rule refl)
+(step t11.t13.t8 (cl @p_154) :rule cong :premises (t11.t13.t7))
+(step t11.t13.t9 (cl (= @p_28 @p_126)) :rule cong :premises (t11.t13.t6 t11.t13.t8))
+(step t11.t13.t10 (cl (= @p_30 @p_128)) :rule cong :premises (t11.t13.t4 t11.t13.t9))
+(step t11.t13.t11 (cl (= @p_32 @p_130)) :rule cong :premises (t11.t13.t10))
+(step t11.t13 (cl (= @p_26 @p_122)) :rule bind)
+(anchor :step t11.t14 :args ((:= (?v2 B$) veriT_vr4) (:= (?v3 B$) veriT_vr5) (:= (?v4 B_list$) veriT_vr6)))
+(step t11.t14.t1 (cl @p_81) :rule refl)
+(step t11.t14.t2 (cl @p_92) :rule refl)
+(step t11.t14.t3 (cl @p_93) :rule refl)
+(step t11.t14.t4 (cl @p_94) :rule cong :premises (t11.t14.t2 t11.t14.t3))
+(step t11.t14.t5 (cl @p_133) :rule cong :premises (t11.t14.t1 t11.t14.t4))
+(step t11.t14.t6 (cl @p_153) :rule refl)
+(step t11.t14.t7 (cl (= @p_18 @p_66)) :rule cong :premises (t11.t14.t5 t11.t14.t6))
+(step t11.t14.t8 (cl @p_81) :rule refl)
+(step t11.t14.t9 (cl @p_91) :rule cong :premises (t11.t14.t8))
+(step t11.t14.t10 (cl @p_92) :rule refl)
+(step t11.t14.t11 (cl @p_93) :rule refl)
+(step t11.t14.t12 (cl @p_94) :rule cong :premises (t11.t14.t10 t11.t14.t11))
+(step t11.t14.t13 (cl @p_135) :rule cong :premises (t11.t14.t12))
+(step t11.t14.t14 (cl @p_136) :rule cong :premises (t11.t14.t9 t11.t14.t13))
+(step t11.t14.t15 (cl @p_153) :rule refl)
+(step t11.t14.t16 (cl @p_154) :rule cong :premises (t11.t14.t15))
+(step t11.t14.t17 (cl (= @p_36 @p_138)) :rule cong :premises (t11.t14.t14 t11.t14.t16))
+(step t11.t14.t18 (cl (= @p_38 @p_140)) :rule cong :premises (t11.t14.t7 t11.t14.t17))
+(step t11.t14.t19 (cl (= @p_40 @p_142)) :rule cong :premises (t11.t14.t18))
+(step t11.t14 (cl (= @p_34 @p_132)) :rule bind)
+(step t11.t15 (cl (= @p_42 @p_144)) :rule cong :premises (t11.t13 t11.t14))
+(step t11.t16 (cl (= @p_44 @p_146)) :rule cong :premises (t11.t12 t11.t15))
+(step t11.t17 (cl (= @p_46 @p_148)) :rule cong :premises (t11.t5 t11.t16))
+(step t11.t18 (cl (= @p_48 @p_150)) :rule cong :premises (t11.t17))
+(step t11 (cl (= @p_50 (! (forall ((veriT_vr3 B_list$)) @p_150) :named @p_155))) :rule bind)
+(anchor :step t12 :args ((:= (?v0 B_list$) veriT_vr3)))
+(step t12.t1 (cl @p_153) :rule refl)
+(step t12.t2 (cl @p_154) :rule cong :premises (t12.t1))
+(step t12.t3 (cl @p_153) :rule refl)
+(step t12.t4 (cl @p_154) :rule cong :premises (t12.t3))
+(step t12.t5 (cl @p_156) :rule cong :premises (t12.t2 t12.t4))
+(step t12.t6 (cl @p_153) :rule refl)
+(step t12.t7 (cl @p_157) :rule cong :premises (t12.t6))
+(step t12.t8 (cl @p_153) :rule refl)
+(step t12.t9 (cl @p_154) :rule cong :premises (t12.t8))
+(step t12.t10 (cl @p_158) :rule cong :premises (t12.t9))
+(step t12.t11 (cl @p_159) :rule cong :premises (t12.t7 t12.t10))
+(step t12.t12 (cl @p_160) :rule cong :premises (t12.t11))
+(anchor :step t12.t13 :args ((:= (?v1 B$) veriT_vr4)))
+(step t12.t13.t1 (cl @p_153) :rule refl)
+(step t12.t13.t2 (cl (! (= ?v1 veriT_vr4) :named @p_164)) :rule refl)
+(step t12.t13.t3 (cl (= @p_162 @p_80)) :rule cong :premises (t12.t13.t2))
+(step t12.t13.t4 (cl (= @p_163 @p_65)) :rule cong :premises (t12.t13.t1 t12.t13.t3))
+(step t12.t13.t5 (cl @p_153) :rule refl)
+(step t12.t13.t6 (cl @p_154) :rule cong :premises (t12.t13.t5))
+(step t12.t13.t7 (cl @p_164) :rule refl)
+(step t12.t13.t8 (cl (! (= @p_12 @p_61) :named @p_171)) :rule cong :premises (t12.t13.t7))
+(step t12.t13.t9 (cl (= @p_165 @p_126)) :rule cong :premises (t12.t13.t6 t12.t13.t8))
+(step t12.t13.t10 (cl (= @p_166 @p_128)) :rule cong :premises (t12.t13.t4 t12.t13.t9))
+(step t12.t13.t11 (cl (= @p_167 @p_130)) :rule cong :premises (t12.t13.t10))
+(step t12.t13 (cl (= @p_161 @p_122)) :rule bind)
+(anchor :step t12.t14 :args ((:= (?v1 B$) veriT_vr4) (:= (?v2 B$) veriT_vr5) (:= (?v3 B_list$) veriT_vr6)))
+(step t12.t14.t1 (cl @p_153) :rule refl)
+(step t12.t14.t2 (cl @p_164) :rule refl)
+(step t12.t14.t3 (cl (! (= ?v2 veriT_vr5) :named @p_172)) :rule refl)
+(step t12.t14.t4 (cl (! (= ?v3 veriT_vr6) :named @p_173)) :rule refl)
+(step t12.t14.t5 (cl (! (= @p_13 @p_62) :named @p_174)) :rule cong :premises (t12.t14.t3 t12.t14.t4))
+(step t12.t14.t6 (cl (= @p_169 @p_90)) :rule cong :premises (t12.t14.t2 t12.t14.t5))
+(step t12.t14.t7 (cl (= @p_170 @p_66)) :rule cong :premises (t12.t14.t1 t12.t14.t6))
+(step t12.t14.t8 (cl @p_153) :rule refl)
+(step t12.t14.t9 (cl @p_154) :rule cong :premises (t12.t14.t8))
+(step t12.t14.t10 (cl @p_164) :rule refl)
+(step t12.t14.t11 (cl @p_171) :rule cong :premises (t12.t14.t10))
+(step t12.t14.t12 (cl @p_172) :rule refl)
+(step t12.t14.t13 (cl @p_173) :rule refl)
+(step t12.t14.t14 (cl @p_174) :rule cong :premises (t12.t14.t12 t12.t14.t13))
+(step t12.t14.t15 (cl (= @p_175 @p_96)) :rule cong :premises (t12.t14.t14))
+(step t12.t14.t16 (cl (= @p_176 @p_67)) :rule cong :premises (t12.t14.t11 t12.t14.t15))
+(step t12.t14.t17 (cl (= @p_177 @p_138)) :rule cong :premises (t12.t14.t9 t12.t14.t16))
+(step t12.t14.t18 (cl (= @p_178 @p_140)) :rule cong :premises (t12.t14.t7 t12.t14.t17))
+(step t12.t14.t19 (cl (= @p_179 @p_142)) :rule cong :premises (t12.t14.t18))
+(step t12.t14 (cl (= @p_168 @p_132)) :rule bind)
+(step t12.t15 (cl (= @p_180 @p_144)) :rule cong :premises (t12.t13 t12.t14))
+(step t12.t16 (cl (= @p_181 @p_146)) :rule cong :premises (t12.t12 t12.t15))
+(step t12.t17 (cl (= @p_182 @p_148)) :rule cong :premises (t12.t5 t12.t16))
+(step t12.t18 (cl (= @p_183 @p_150)) :rule cong :premises (t12.t17))
+(step t12 (cl (= @p_51 @p_155)) :rule bind)
+(step t13 (cl (= @p_54 (! (= @p_155 @p_155) :named @p_185))) :rule cong :premises (t11 t12))
+(step t14 (cl (= @p_56 (! (=> @p_184 @p_185) :named @p_186))) :rule cong :premises (t10 t13))
+(step t15 (cl (! (= @p_58 (! (not @p_186) :named @p_188)) :named @p_187)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_187) :named @p_190) (! (not @p_58) :named @p_189) @p_188) :rule equiv_pos2)
+(step t17 (cl (not @p_189) @p_56) :rule not_not)
+(step t18 (cl @p_190 @p_56 @p_188) :rule th_resolution :premises (t17 t16))
+(step t19 (cl @p_188) :rule th_resolution :premises (t9 t15 t18))
+(step t20 (cl (! (= @p_188 (! (and @p_184 (! (not @p_185) :named @p_203)) :named @p_192)) :named @p_191)) :rule bool_simplify)
+(step t21 (cl (! (not @p_191) :named @p_194) (! (not @p_188) :named @p_193) @p_192) :rule equiv_pos2)
+(step t22 (cl (not @p_193) @p_186) :rule not_not)
+(step t23 (cl @p_194 @p_186 @p_192) :rule th_resolution :premises (t22 t21))
+(step t24 (cl @p_192) :rule th_resolution :premises (t19 t20 t23))
+(anchor :step t25 :args ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)))
+(step t25.t1 (cl (= @p_108 (! (and @p_69 @p_77 @p_79 @p_89) :named @p_195))) :rule ac_simp)
+(step t25.t2 (cl (= @p_110 (! (=> @p_195 false) :named @p_196))) :rule cong :premises (t25.t1))
+(step t25.t3 (cl (! (= @p_148 (! (and @p_113 @p_120 @p_122 @p_132) :named @p_197)) :named @p_200)) :rule ac_simp)
+(step t25.t4 (cl (! (= @p_150 (! (=> @p_197 false) :named @p_198)) :named @p_201)) :rule cong :premises (t25.t3))
+(step t25.t5 (cl (= @p_152 (! (= @p_196 @p_198) :named @p_199))) :rule cong :premises (t25.t2 t25.t4))
+(step t25 (cl (= @p_184 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_199) :named @p_205))) :rule bind)
+(anchor :step t26 :args ((veriT_vr3 B_list$)))
+(step t26.t1 (cl @p_200) :rule ac_simp)
+(step t26.t2 (cl @p_201) :rule cong :premises (t26.t1))
+(step t26 (cl (= @p_155 (! (forall ((veriT_vr3 B_list$)) @p_198) :named @p_202))) :rule bind)
+(step t27 (cl (= @p_185 (! (= @p_202 @p_202) :named @p_204))) :rule cong :premises (t26 t26))
+(step t28 (cl (= @p_203 (! (not @p_204) :named @p_206))) :rule cong :premises (t27))
+(step t29 (cl (! (= @p_192 (! (and @p_205 @p_206) :named @p_208)) :named @p_207)) :rule ac_simp :premises (t25 t28))
+(step t30 (cl (not @p_207) (not @p_192) @p_208) :rule equiv_pos2)
+(step t31 (cl @p_208) :rule th_resolution :premises (t24 t29 t30))
+(anchor :step t32 :args ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)))
+(step t32.t1 (cl (= @p_77 (! (not @p_75) :named @p_209))) :rule implies_simplify)
+(anchor :step t32.t2 :args ((veriT_vr4 B$)))
+(step t32.t2.t1 (cl (= @p_87 (! (not @p_85) :named @p_211))) :rule implies_simplify)
+(step t32.t2 (cl (= @p_79 (! (forall ((veriT_vr4 B$)) @p_211) :named @p_210))) :rule bind)
+(anchor :step t32.t3 :args ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)))
+(step t32.t3.t1 (cl (= @p_102 (! (not @p_100) :named @p_213))) :rule implies_simplify)
+(step t32.t3 (cl (= @p_89 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_213) :named @p_212))) :rule bind)
+(step t32.t4 (cl (= @p_195 (! (and @p_69 @p_209 @p_210 @p_212) :named @p_214))) :rule cong :premises (t32.t1 t32.t2 t32.t3))
+(step t32.t5 (cl (= @p_196 (! (=> @p_214 false) :named @p_215))) :rule cong :premises (t32.t4))
+(step t32.t6 (cl (= @p_215 (! (not @p_214) :named @p_216))) :rule implies_simplify)
+(step t32.t7 (cl (= @p_196 @p_216)) :rule trans :premises (t32.t5 t32.t6))
+(step t32.t8 (cl (! (= @p_113 true) :named @p_228)) :rule eq_simplify)
+(step t32.t9 (cl (! (= @p_120 (! (not @p_118) :named @p_217)) :named @p_229)) :rule implies_simplify)
+(anchor :step t32.t10 :args ((veriT_vr4 B$)))
+(step t32.t10.t1 (cl (! (= @p_130 (! (not @p_128) :named @p_219)) :named @p_231)) :rule implies_simplify)
+(step t32.t10 (cl (! (= @p_122 (! (forall ((veriT_vr4 B$)) @p_219) :named @p_218)) :named @p_230)) :rule bind)
+(anchor :step t32.t11 :args ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)))
+(step t32.t11.t1 (cl (! (= @p_142 (! (not @p_140) :named @p_221)) :named @p_233)) :rule implies_simplify)
+(step t32.t11 (cl (! (= @p_132 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_221) :named @p_220)) :named @p_232)) :rule bind)
+(step t32.t12 (cl (! (= @p_197 (! (and true @p_217 @p_218 @p_220) :named @p_222)) :named @p_234)) :rule cong :premises (t32.t8 t32.t9 t32.t10 t32.t11))
+(step t32.t13 (cl (! (= @p_222 (! (and @p_217 @p_218 @p_220) :named @p_223)) :named @p_235)) :rule and_simplify)
+(step t32.t14 (cl (! (= @p_197 @p_223) :named @p_236)) :rule trans :premises (t32.t12 t32.t13))
+(step t32.t15 (cl (! (= @p_198 (! (=> @p_223 false) :named @p_224)) :named @p_237)) :rule cong :premises (t32.t14))
+(step t32.t16 (cl (! (= @p_224 (! (not @p_223) :named @p_225)) :named @p_238)) :rule implies_simplify)
+(step t32.t17 (cl (! (= @p_198 @p_225) :named @p_239)) :rule trans :premises (t32.t15 t32.t16))
+(step t32.t18 (cl (= @p_199 (! (= @p_216 @p_225) :named @p_226))) :rule cong :premises (t32.t7 t32.t17))
+(step t32.t19 (cl (= @p_226 (! (= @p_214 @p_223) :named @p_227))) :rule equiv_simplify)
+(step t32.t20 (cl (= @p_199 @p_227)) :rule trans :premises (t32.t18 t32.t19))
+(step t32 (cl (= @p_205 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_227) :named @p_243))) :rule bind)
+(anchor :step t33 :args ((veriT_vr3 B_list$)))
+(step t33.t1 (cl @p_228) :rule eq_simplify)
+(step t33.t2 (cl @p_229) :rule implies_simplify)
+(anchor :step t33.t3 :args ((veriT_vr4 B$)))
+(step t33.t3.t1 (cl @p_231) :rule implies_simplify)
+(step t33.t3 (cl @p_230) :rule bind)
+(anchor :step t33.t4 :args ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)))
+(step t33.t4.t1 (cl @p_233) :rule implies_simplify)
+(step t33.t4 (cl @p_232) :rule bind)
+(step t33.t5 (cl @p_234) :rule cong :premises (t33.t1 t33.t2 t33.t3 t33.t4))
+(step t33.t6 (cl @p_235) :rule and_simplify)
+(step t33.t7 (cl @p_236) :rule trans :premises (t33.t5 t33.t6))
+(step t33.t8 (cl @p_237) :rule cong :premises (t33.t7))
+(step t33.t9 (cl @p_238) :rule implies_simplify)
+(step t33.t10 (cl @p_239) :rule trans :premises (t33.t8 t33.t9))
+(step t33 (cl (= @p_202 (! (forall ((veriT_vr3 B_list$)) @p_225) :named @p_240))) :rule bind)
+(step t34 (cl (= @p_204 (! (= @p_240 @p_240) :named @p_241))) :rule cong :premises (t33 t33))
+(step t35 (cl (= @p_241 true)) :rule equiv_simplify)
+(step t36 (cl (= @p_204 true)) :rule trans :premises (t34 t35))
+(step t37 (cl (= @p_206 (! (not true) :named @p_242))) :rule cong :premises (t36))
+(step t38 (cl (= @p_242 false)) :rule not_simplify)
+(step t39 (cl (= @p_206 false)) :rule trans :premises (t37 t38))
+(step t40 (cl (= @p_208 (! (and @p_243 false) :named @p_244))) :rule cong :premises (t32 t39))
+(step t41 (cl (= @p_244 false)) :rule and_simplify)
+(step t42 (cl (! (= @p_208 false) :named @p_245)) :rule trans :premises (t40 t41))
+(step t43 (cl (not @p_245) (not @p_208) false) :rule equiv_pos2)
+(step t44 (cl false) :rule th_resolution :premises (t31 t42 t43))
+(step t45 (cl (not false)) :rule false)
+(step t46 (cl) :rule resolution :premises (t44 t45))
+2da165964e2359aec5a20e66969cc8494006e9ba 36 0
+unsat
+(assume a4 (! (forall ((?v0 Int)) (! (and (! (pred$e ?v0) :named @p_4) (! (or (! (pred$d (! (cons$d ?v0 nil$d) :named @p_7)) :named @p_1) (! (not @p_1) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2))
+(assume a5 (not (! (pred$e 1) :named @p_26)))
+(anchor :step t3 :args ((:= (?v0 Int) veriT_vr8)))
+(step t3.t1 (cl (! (= ?v0 veriT_vr8) :named @p_6)) :rule refl)
+(step t3.t2 (cl (= @p_4 (! (pred$e veriT_vr8) :named @p_5))) :rule cong :premises (t3.t1))
+(step t3.t3 (cl @p_6) :rule refl)
+(step t3.t4 (cl (! (= @p_7 (! (cons$d veriT_vr8 nil$d) :named @p_8)) :named @p_9)) :rule cong :premises (t3.t3))
+(step t3.t5 (cl (! (= @p_1 (! (pred$d @p_8) :named @p_3)) :named @p_10)) :rule cong :premises (t3.t4))
+(step t3.t6 (cl @p_6) :rule refl)
+(step t3.t7 (cl @p_9) :rule cong :premises (t3.t6))
+(step t3.t8 (cl @p_10) :rule cong :premises (t3.t7))
+(step t3.t9 (cl (= @p_11 (! (not @p_3) :named @p_12))) :rule cong :premises (t3.t8))
+(step t3.t10 (cl (= @p_13 (! (or @p_3 @p_12) :named @p_14))) :rule cong :premises (t3.t5 t3.t9))
+(step t3.t11 (cl (= @p_15 (! (and @p_5 @p_14) :named @p_16))) :rule cong :premises (t3.t2 t3.t10))
+(step t3 (cl (! (= @p_2 (! (forall ((veriT_vr8 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
+(step t4 (cl (not @p_17) (not @p_2) @p_18) :rule equiv_pos2)
+(step t5 (cl @p_18) :rule th_resolution :premises (a4 t3 t4))
+(anchor :step t6 :args ((veriT_vr8 Int)))
+(step t6.t1 (cl (= @p_14 true)) :rule or_simplify)
+(step t6.t2 (cl (= @p_16 (! (and @p_5 true) :named @p_19))) :rule cong :premises (t6.t1))
+(step t6.t3 (cl (= @p_19 (! (and @p_5) :named @p_20))) :rule and_simplify)
+(step t6.t4 (cl (= @p_20 @p_5)) :rule and_simplify)
+(step t6.t5 (cl (= @p_16 @p_5)) :rule trans :premises (t6.t2 t6.t3 t6.t4))
+(step t6 (cl (! (= @p_18 (! (forall ((veriT_vr8 Int)) @p_5) :named @p_22)) :named @p_21)) :rule bind)
+(step t7 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2)
+(step t8 (cl @p_22) :rule th_resolution :premises (t5 t6 t7))
+(anchor :step t9 :args ((:= (veriT_vr8 Int) veriT_vr9)))
+(step t9.t1 (cl (= veriT_vr8 veriT_vr9)) :rule refl)
+(step t9.t2 (cl (= @p_5 (! (pred$e veriT_vr9) :named @p_23))) :rule cong :premises (t9.t1))
+(step t9 (cl (! (= @p_22 (! (forall ((veriT_vr9 Int)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
+(step t10 (cl (not @p_24) (not @p_22) @p_25) :rule equiv_pos2)
+(step t11 (cl @p_25) :rule th_resolution :premises (t8 t9 t10))
+(step t12 (cl (or (! (not @p_25) :named @p_27) @p_26)) :rule forall_inst :args ((:= veriT_vr9 1)))
+(step t13 (cl @p_27 @p_26) :rule or :premises (t12))
+(step t14 (cl) :rule resolution :premises (t13 t11 a5))
+f9bb7f97f8819ceceaefe0cdf934d0eda3431a5b 158 0
+unsat
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (some$ ?v0) :named @p_5)) :named @p_7) (! (g$a (! (cons$ ?v0 nil$) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_4))
+(assume a1 (forall ((?v0 Bool)) (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a)))))
+(assume a6 (! (forall ((?v0 Bool_list$)) (! (= (! (g$c ?v0) :named @p_27) (! (size$ ?v0) :named @p_30)) :named @p_32)) :named @p_26))
+(assume a7 (! (forall ((?v0 Int_list$)) (! (= (! (g$a ?v0) :named @p_43) (! (size$a ?v0) :named @p_46)) :named @p_48)) :named @p_42))
+(assume a12 (! (= zero$ (! (size$ nil$a) :named @p_118)) :named @p_143))
+(assume a13 (! (= zero$ (! (size$a nil$) :named @p_133)) :named @p_144))
+(assume a14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (size$ (cons$a ?v0 ?v1)) (! (plus$ (! (size$ ?v1) :named @p_60) (! (suc$ zero$) :named @p_1)) :named @p_3))))
+(assume a15 (! (forall ((?v0 Int) (?v1 Int_list$)) (! (= (! (size$a (! (cons$ ?v0 ?v1) :named @p_96)) :named @p_98) (! (plus$ (! (size$a ?v1) :named @p_101) @p_1) :named @p_103)) :named @p_105)) :named @p_95))
+(assume a16 (not (! (= (! (g$ (some$ 3)) :named @p_124) (! (g$b (some$a true)) :named @p_2)) :named @p_141)))
+(step t10 (cl (and (= (g$b (some$a false)) (g$c (! (cons$a false nil$a) :named @p_119))) (! (= @p_2 (! (g$c (! (cons$a true nil$a) :named @p_121)) :named @p_122)) :named @p_117))) :rule bfun_elim :premises (a1))
+(step t11 (cl (! (forall ((?v1 Bool_list$)) (! (and (! (= @p_3 (! (size$ (! (cons$a false ?v1) :named @p_63)) :named @p_65)) :named @p_67) (! (= @p_3 (! (size$ (! (cons$a true ?v1) :named @p_71)) :named @p_73)) :named @p_75)) :named @p_77)) :named @p_58)) :rule bfun_elim :premises (a14))
+(anchor :step t12 :args ((:= (?v0 Int) veriT_vr0)))
+(step t12.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
+(step t12.t2 (cl (= @p_5 (! (some$ veriT_vr0) :named @p_6))) :rule cong :premises (t12.t1))
+(step t12.t3 (cl (= @p_7 (! (g$ @p_6) :named @p_8))) :rule cong :premises (t12.t2))
+(step t12.t4 (cl @p_9) :rule refl)
+(step t12.t5 (cl (= @p_10 (! (cons$ veriT_vr0 nil$) :named @p_11))) :rule cong :premises (t12.t4))
+(step t12.t6 (cl (= @p_12 (! (g$a @p_11) :named @p_13))) :rule cong :premises (t12.t5))
+(step t12.t7 (cl (= @p_14 (! (= @p_8 @p_13) :named @p_15))) :rule cong :premises (t12.t3 t12.t6))
+(step t12 (cl (! (= @p_4 (! (forall ((veriT_vr0 Int)) @p_15) :named @p_17)) :named @p_16)) :rule bind)
+(step t13 (cl (not @p_16) (not @p_4) @p_17) :rule equiv_pos2)
+(step t14 (cl @p_17) :rule th_resolution :premises (a0 t12 t13))
+(anchor :step t15 :args ((:= (veriT_vr0 Int) veriT_vr1)))
+(step t15.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_20)) :rule refl)
+(step t15.t2 (cl (= @p_6 (! (some$ veriT_vr1) :named @p_18))) :rule cong :premises (t15.t1))
+(step t15.t3 (cl (= @p_8 (! (g$ @p_18) :named @p_19))) :rule cong :premises (t15.t2))
+(step t15.t4 (cl @p_20) :rule refl)
+(step t15.t5 (cl (= @p_11 (! (cons$ veriT_vr1 nil$) :named @p_21))) :rule cong :premises (t15.t4))
+(step t15.t6 (cl (= @p_13 (! (g$a @p_21) :named @p_22))) :rule cong :premises (t15.t5))
+(step t15.t7 (cl (= @p_15 (! (= @p_19 @p_22) :named @p_23))) :rule cong :premises (t15.t3 t15.t6))
+(step t15 (cl (! (= @p_17 (! (forall ((veriT_vr1 Int)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
+(step t16 (cl (not @p_24) (not @p_17) @p_25) :rule equiv_pos2)
+(step t17 (cl @p_25) :rule th_resolution :premises (t14 t15 t16))
+(anchor :step t18 :args ((:= (?v0 Bool_list$) veriT_vr2)))
+(step t18.t1 (cl (! (= ?v0 veriT_vr2) :named @p_29)) :rule refl)
+(step t18.t2 (cl (= @p_27 (! (g$c veriT_vr2) :named @p_28))) :rule cong :premises (t18.t1))
+(step t18.t3 (cl @p_29) :rule refl)
+(step t18.t4 (cl (= @p_30 (! (size$ veriT_vr2) :named @p_31))) :rule cong :premises (t18.t3))
+(step t18.t5 (cl (= @p_32 (! (= @p_28 @p_31) :named @p_33))) :rule cong :premises (t18.t2 t18.t4))
+(step t18 (cl (! (= @p_26 (! (forall ((veriT_vr2 Bool_list$)) @p_33) :named @p_35)) :named @p_34)) :rule bind)
+(step t19 (cl (not @p_34) (not @p_26) @p_35) :rule equiv_pos2)
+(step t20 (cl @p_35) :rule th_resolution :premises (a6 t18 t19))
+(anchor :step t21 :args ((:= (veriT_vr2 Bool_list$) veriT_vr3)))
+(step t21.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_37)) :rule refl)
+(step t21.t2 (cl (= @p_28 (! (g$c veriT_vr3) :named @p_36))) :rule cong :premises (t21.t1))
+(step t21.t3 (cl @p_37) :rule refl)
+(step t21.t4 (cl (= @p_31 (! (size$ veriT_vr3) :named @p_38))) :rule cong :premises (t21.t3))
+(step t21.t5 (cl (= @p_33 (! (= @p_36 @p_38) :named @p_39))) :rule cong :premises (t21.t2 t21.t4))
+(step t21 (cl (! (= @p_35 (! (forall ((veriT_vr3 Bool_list$)) @p_39) :named @p_41)) :named @p_40)) :rule bind)
+(step t22 (cl (not @p_40) (not @p_35) @p_41) :rule equiv_pos2)
+(step t23 (cl @p_41) :rule th_resolution :premises (t20 t21 t22))
+(anchor :step t24 :args ((:= (?v0 Int_list$) veriT_vr4)))
+(step t24.t1 (cl (! (= ?v0 veriT_vr4) :named @p_45)) :rule refl)
+(step t24.t2 (cl (= @p_43 (! (g$a veriT_vr4) :named @p_44))) :rule cong :premises (t24.t1))
+(step t24.t3 (cl @p_45) :rule refl)
+(step t24.t4 (cl (= @p_46 (! (size$a veriT_vr4) :named @p_47))) :rule cong :premises (t24.t3))
+(step t24.t5 (cl (= @p_48 (! (= @p_44 @p_47) :named @p_49))) :rule cong :premises (t24.t2 t24.t4))
+(step t24 (cl (! (= @p_42 (! (forall ((veriT_vr4 Int_list$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
+(step t25 (cl (not @p_50) (not @p_42) @p_51) :rule equiv_pos2)
+(step t26 (cl @p_51) :rule th_resolution :premises (a7 t24 t25))
+(anchor :step t27 :args ((:= (veriT_vr4 Int_list$) veriT_vr5)))
+(step t27.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_53)) :rule refl)
+(step t27.t2 (cl (= @p_44 (! (g$a veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1))
+(step t27.t3 (cl @p_53) :rule refl)
+(step t27.t4 (cl (= @p_47 (! (size$a veriT_vr5) :named @p_54))) :rule cong :premises (t27.t3))
+(step t27.t5 (cl (= @p_49 (! (= @p_52 @p_54) :named @p_55))) :rule cong :premises (t27.t2 t27.t4))
+(step t27 (cl (! (= @p_51 (! (forall ((veriT_vr5 Int_list$)) @p_55) :named @p_57)) :named @p_56)) :rule bind)
+(step t28 (cl (not @p_56) (not @p_51) @p_57) :rule equiv_pos2)
+(step t29 (cl @p_57) :rule th_resolution :premises (t26 t27 t28))
+(anchor :step t30 :args ((:= (?v1 Bool_list$) veriT_vr20)))
+(step t30.t1 (cl (! (= ?v1 veriT_vr20) :named @p_62)) :rule refl)
+(step t30.t2 (cl (! (= @p_60 (! (size$ veriT_vr20) :named @p_61)) :named @p_69)) :rule cong :premises (t30.t1))
+(step t30.t3 (cl (! (= @p_3 (! (plus$ @p_61 @p_1) :named @p_59)) :named @p_70)) :rule cong :premises (t30.t2))
+(step t30.t4 (cl @p_62) :rule refl)
+(step t30.t5 (cl (= @p_63 (! (cons$a false veriT_vr20) :named @p_64))) :rule cong :premises (t30.t4))
+(step t30.t6 (cl (= @p_65 (! (size$ @p_64) :named @p_66))) :rule cong :premises (t30.t5))
+(step t30.t7 (cl (= @p_67 (! (= @p_59 @p_66) :named @p_68))) :rule cong :premises (t30.t3 t30.t6))
+(step t30.t8 (cl @p_62) :rule refl)
+(step t30.t9 (cl @p_69) :rule cong :premises (t30.t8))
+(step t30.t10 (cl @p_70) :rule cong :premises (t30.t9))
+(step t30.t11 (cl @p_62) :rule refl)
+(step t30.t12 (cl (= @p_71 (! (cons$a true veriT_vr20) :named @p_72))) :rule cong :premises (t30.t11))
+(step t30.t13 (cl (= @p_73 (! (size$ @p_72) :named @p_74))) :rule cong :premises (t30.t12))
+(step t30.t14 (cl (= @p_75 (! (= @p_59 @p_74) :named @p_76))) :rule cong :premises (t30.t10 t30.t13))
+(step t30.t15 (cl (= @p_77 (! (and @p_68 @p_76) :named @p_78))) :rule cong :premises (t30.t7 t30.t14))
+(step t30 (cl (! (= @p_58 (! (forall ((veriT_vr20 Bool_list$)) @p_78) :named @p_80)) :named @p_79)) :rule bind)
+(step t31 (cl (not @p_79) (not @p_58) @p_80) :rule equiv_pos2)
+(step t32 (cl @p_80) :rule th_resolution :premises (t11 t30 t31))
+(anchor :step t33 :args ((:= (veriT_vr20 Bool_list$) veriT_vr21)))
+(step t33.t1 (cl (! (= veriT_vr20 veriT_vr21) :named @p_83)) :rule refl)
+(step t33.t2 (cl (! (= @p_61 (! (size$ veriT_vr21) :named @p_82)) :named @p_87)) :rule cong :premises (t33.t1))
+(step t33.t3 (cl (! (= @p_59 (! (plus$ @p_82 @p_1) :named @p_81)) :named @p_88)) :rule cong :premises (t33.t2))
+(step t33.t4 (cl @p_83) :rule refl)
+(step t33.t5 (cl (= @p_64 (! (cons$a false veriT_vr21) :named @p_84))) :rule cong :premises (t33.t4))
+(step t33.t6 (cl (= @p_66 (! (size$ @p_84) :named @p_85))) :rule cong :premises (t33.t5))
+(step t33.t7 (cl (= @p_68 (! (= @p_81 @p_85) :named @p_86))) :rule cong :premises (t33.t3 t33.t6))
+(step t33.t8 (cl @p_83) :rule refl)
+(step t33.t9 (cl @p_87) :rule cong :premises (t33.t8))
+(step t33.t10 (cl @p_88) :rule cong :premises (t33.t9))
+(step t33.t11 (cl @p_83) :rule refl)
+(step t33.t12 (cl (= @p_72 (! (cons$a true veriT_vr21) :named @p_89))) :rule cong :premises (t33.t11))
+(step t33.t13 (cl (= @p_74 (! (size$ @p_89) :named @p_90))) :rule cong :premises (t33.t12))
+(step t33.t14 (cl (= @p_76 (! (= @p_81 @p_90) :named @p_91))) :rule cong :premises (t33.t10 t33.t13))
+(step t33.t15 (cl (= @p_78 (! (and @p_86 @p_91) :named @p_92))) :rule cong :premises (t33.t7 t33.t14))
+(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr21 Bool_list$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
+(step t34 (cl (not @p_93) (not @p_80) @p_94) :rule equiv_pos2)
+(step t35 (cl @p_94) :rule th_resolution :premises (t32 t33 t34))
+(anchor :step t36 :args ((:= (?v0 Int) veriT_vr22) (:= (?v1 Int_list$) veriT_vr23)))
+(step t36.t1 (cl (= ?v0 veriT_vr22)) :rule refl)
+(step t36.t2 (cl (! (= ?v1 veriT_vr23) :named @p_100)) :rule refl)
+(step t36.t3 (cl (= @p_96 (! (cons$ veriT_vr22 veriT_vr23) :named @p_97))) :rule cong :premises (t36.t1 t36.t2))
+(step t36.t4 (cl (= @p_98 (! (size$a @p_97) :named @p_99))) :rule cong :premises (t36.t3))
+(step t36.t5 (cl @p_100) :rule refl)
+(step t36.t6 (cl (= @p_101 (! (size$a veriT_vr23) :named @p_102))) :rule cong :premises (t36.t5))
+(step t36.t7 (cl (= @p_103 (! (plus$ @p_102 @p_1) :named @p_104))) :rule cong :premises (t36.t6))
+(step t36.t8 (cl (= @p_105 (! (= @p_99 @p_104) :named @p_106))) :rule cong :premises (t36.t4 t36.t7))
+(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr22 Int) (veriT_vr23 Int_list$)) @p_106) :named @p_108)) :named @p_107)) :rule bind)
+(step t37 (cl (not @p_107) (not @p_95) @p_108) :rule equiv_pos2)
+(step t38 (cl @p_108) :rule th_resolution :premises (a15 t36 t37))
+(anchor :step t39 :args ((:= (veriT_vr22 Int) veriT_vr24) (:= (veriT_vr23 Int_list$) veriT_vr25)))
+(step t39.t1 (cl (= veriT_vr22 veriT_vr24)) :rule refl)
+(step t39.t2 (cl (! (= veriT_vr23 veriT_vr25) :named @p_111)) :rule refl)
+(step t39.t3 (cl (= @p_97 (! (cons$ veriT_vr24 veriT_vr25) :named @p_109))) :rule cong :premises (t39.t1 t39.t2))
+(step t39.t4 (cl (= @p_99 (! (size$a @p_109) :named @p_110))) :rule cong :premises (t39.t3))
+(step t39.t5 (cl @p_111) :rule refl)
+(step t39.t6 (cl (= @p_102 (! (size$a veriT_vr25) :named @p_112))) :rule cong :premises (t39.t5))
+(step t39.t7 (cl (= @p_104 (! (plus$ @p_112 @p_1) :named @p_113))) :rule cong :premises (t39.t6))
+(step t39.t8 (cl (= @p_106 (! (= @p_110 @p_113) :named @p_114))) :rule cong :premises (t39.t4 t39.t7))
+(step t39 (cl (! (= @p_108 (! (forall ((veriT_vr24 Int) (veriT_vr25 Int_list$)) @p_114) :named @p_116)) :named @p_115)) :rule bind)
+(step t40 (cl (not @p_115) (not @p_108) @p_116) :rule equiv_pos2)
+(step t41 (cl @p_116) :rule th_resolution :premises (t38 t39 t40))
+(step t42 (cl @p_117) :rule and :premises (t10))
+(step t43 (cl (or (! (not @p_94) :named @p_127) (! (and (= (! (plus$ @p_118 @p_1) :named @p_120) (size$ @p_119)) (! (= @p_120 (! (size$ @p_121) :named @p_123)) :named @p_126)) :named @p_125))) :rule forall_inst :args ((:= veriT_vr21 nil$a)))
+(step t44 (cl (or (! (not @p_41) :named @p_128) (! (= @p_122 @p_123) :named @p_129))) :rule forall_inst :args ((:= veriT_vr3 @p_121)))
+(step t45 (cl (or (! (not @p_25) :named @p_130) (! (= @p_124 (! (g$a (! (cons$ 3 nil$) :named @p_132)) :named @p_134)) :named @p_131))) :rule forall_inst :args ((:= veriT_vr1 3)))
+(step t46 (cl (not @p_125) @p_126) :rule and_pos)
+(step t47 (cl @p_127 @p_125) :rule or :premises (t43))
+(step t48 (cl @p_125) :rule resolution :premises (t47 t35))
+(step t49 (cl @p_126) :rule resolution :premises (t46 t48))
+(step t50 (cl @p_128 @p_129) :rule or :premises (t44))
+(step t51 (cl @p_129) :rule resolution :premises (t50 t23))
+(step t52 (cl @p_130 @p_131) :rule or :premises (t45))
+(step t53 (cl @p_131) :rule resolution :premises (t52 t17))
+(step t54 (cl (or (! (not @p_116) :named @p_136) (! (= (! (size$a @p_132) :named @p_135) (! (plus$ @p_133 @p_1) :named @p_140)) :named @p_137))) :rule forall_inst :args ((:= veriT_vr24 3) (:= veriT_vr25 nil$)))
+(step t55 (cl (or (! (not @p_57) :named @p_138) (! (= @p_134 @p_135) :named @p_139))) :rule forall_inst :args ((:= veriT_vr5 @p_132)))
+(step t56 (cl @p_136 @p_137) :rule or :premises (t54))
+(step t57 (cl @p_137) :rule resolution :premises (t56 t41))
+(step t58 (cl @p_138 @p_139) :rule or :premises (t55))
+(step t59 (cl @p_139) :rule resolution :premises (t58 t29))
+(step t60 (cl (! (not @p_131) :named @p_150) (! (not @p_139) :named @p_151) (! (not @p_137) :named @p_152) (not (! (= @p_120 @p_140) :named @p_142)) (! (not @p_126) :named @p_153) (! (not @p_129) :named @p_154) (! (not @p_117) :named @p_155) @p_141) :rule eq_transitive)
+(step t61 (cl (not (! (= @p_118 @p_133) :named @p_145)) (! (not (! (= @p_1 @p_1) :named @p_149)) :named @p_146) @p_142) :rule eq_congruent)
+(step t62 (cl (! (not @p_143) :named @p_147) (! (not @p_144) :named @p_148) @p_145) :rule eq_transitive)
+(step t63 (cl @p_146 @p_142 @p_147 @p_148) :rule th_resolution :premises (t61 t62))
+(step t64 (cl @p_149) :rule eq_reflexive)
+(step t65 (cl @p_142 @p_147 @p_148) :rule th_resolution :premises (t63 t64))
+(step t66 (cl @p_150 @p_151 @p_152 @p_153 @p_154 @p_155 @p_141 @p_147 @p_148) :rule th_resolution :premises (t60 t65))
+(step t67 (cl) :rule resolution :premises (t66 t42 a12 a13 a16 t49 t51 t53 t57 t59))
 672f5a048dc0215d5adebfbf2f0a3a36f69e286e 873 0
 unsat
 (define-fun veriT_sk0 () V$ (! (choice ((veriT_vr65 V$)) (not (! (not (! (= x2$ (! (rraise$ veriT_vr65) :named @p_369)) :named @p_370)) :named @p_368))) :named @p_382))
@@ -7416,7 +7936,7 @@
 (assume a11 (! (forall ((?v0 Astate$) (?v1 Astate$) (?v2 V_list_v_result$)) (! (= @p_2 (! (pair$ (! (update_clock$ (! (uu$ ?v0 ?v1) :named @p_263) ?v1) :named @p_265) ?v2) :named @p_268)) :named @p_270)) :named @p_258))
 (assume a12 (! (forall ((?v0 V_error_result$) (?v1 V$)) (! (=> (! (and (! (= r$ (! (rerr$ ?v0) :named @p_287)) :named @p_289) @p_3) :named @p_294) (! (less_eq$ (! (clock$ (! (fst$ (! (fun_app$ (! (fun_evaluate_match$ st$ env$ ?v1 pes$) :named @p_297) ?v1) :named @p_299)) :named @p_301)) :named @p_303) (! (clock$ st$) :named @p_286)) :named @p_305)) :named @p_307)) :named @p_285))
 (assume a13 (! (not (! (=> (! (= r$ (! (rerr$ x2$) :named @p_562)) :named @p_327) (! (less_eq$ (! (clock$ (! (fst$ @p_547) :named @p_565)) :named @p_338) @p_4) :named @p_328)) :named @p_332)) :named @p_326))
-(anchor :step t14 :args ((:= ?v0 veriT_vr0)))
+(anchor :step t14 :args ((:= (?v0 V$) veriT_vr0)))
 (step t14.t1 (cl (! (= ?v0 veriT_vr0) :named @p_8)) :rule refl)
 (step t14.t2 (cl (= @p_6 (! (fun_app$ uua$ veriT_vr0) :named @p_7))) :rule cong :premises (t14.t1))
 (step t14.t3 (cl @p_8) :rule refl)
@@ -7427,7 +7947,7 @@
 (step t14 (cl (! (= @p_5 (! (forall ((veriT_vr0 V$)) @p_14) :named @p_16)) :named @p_15)) :rule bind)
 (step t15 (cl (not @p_15) (not @p_5) @p_16) :rule equiv_pos2)
 (step t16 (cl @p_16) :rule th_resolution :premises (a0 t14 t15))
-(anchor :step t17 :args ((:= veriT_vr0 veriT_vr1)))
+(anchor :step t17 :args ((:= (veriT_vr0 V$) veriT_vr1)))
 (step t17.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_18)) :rule refl)
 (step t17.t2 (cl (= @p_7 (! (fun_app$ uua$ veriT_vr1) :named @p_17))) :rule cong :premises (t17.t1))
 (step t17.t3 (cl @p_18) :rule refl)
@@ -7438,7 +7958,7 @@
 (step t17 (cl (! (= @p_16 (! (forall ((veriT_vr1 V$)) @p_21) :named @p_23)) :named @p_22)) :rule bind)
 (step t18 (cl (not @p_22) (not @p_16) @p_23) :rule equiv_pos2)
 (step t19 (cl @p_23) :rule th_resolution :premises (t16 t17 t18))
-(anchor :step t20 :args ((:= ?v0 veriT_vr2)))
+(anchor :step t20 :args ((:= (?v0 Abort$) veriT_vr2)))
 (step t20.t1 (cl (! (= ?v0 veriT_vr2) :named @p_27)) :rule refl)
 (step t20.t2 (cl (= @p_25 (! (fun_app$a uub$ veriT_vr2) :named @p_26))) :rule cong :premises (t20.t1))
 (step t20.t3 (cl @p_27) :rule refl)
@@ -7449,7 +7969,7 @@
 (step t20 (cl (! (= @p_24 (! (forall ((veriT_vr2 Abort$)) @p_35) :named @p_37)) :named @p_36)) :rule bind)
 (step t21 (cl (not @p_36) (not @p_24) @p_37) :rule equiv_pos2)
 (step t22 (cl @p_37) :rule th_resolution :premises (a1 t20 t21))
-(anchor :step t23 :args ((:= veriT_vr2 veriT_vr3)))
+(anchor :step t23 :args ((:= (veriT_vr2 Abort$) veriT_vr3)))
 (step t23.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_39)) :rule refl)
 (step t23.t2 (cl (= @p_26 (! (fun_app$a uub$ veriT_vr3) :named @p_38))) :rule cong :premises (t23.t1))
 (step t23.t3 (cl @p_39) :rule refl)
@@ -7460,7 +7980,7 @@
 (step t23 (cl (! (= @p_37 (! (forall ((veriT_vr3 Abort$)) @p_43) :named @p_45)) :named @p_44)) :rule bind)
 (step t24 (cl (not @p_44) (not @p_37) @p_45) :rule equiv_pos2)
 (step t25 (cl @p_45) :rule th_resolution :premises (t22 t23 t24))
-(anchor :step t26 :args ((:= ?v0 veriT_vr10) (:= ?v1 veriT_vr11) (:= ?v2 veriT_vr12)))
+(anchor :step t26 :args ((:= (?v0 Nat$) veriT_vr10) (:= (?v1 Nat$) veriT_vr11) (:= (?v2 Nat$) veriT_vr12)))
 (step t26.t1 (cl (! (= ?v0 veriT_vr10) :named @p_49)) :rule refl)
 (step t26.t2 (cl (! (= ?v1 veriT_vr11) :named @p_55)) :rule refl)
 (step t26.t3 (cl (= @p_47 (! (less_eq$ veriT_vr10 veriT_vr11) :named @p_48))) :rule cong :premises (t26.t1 t26.t2))
@@ -7475,7 +7995,7 @@
 (step t26 (cl (! (= @p_46 (! (forall ((veriT_vr10 Nat$) (veriT_vr11 Nat$) (veriT_vr12 Nat$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
 (step t27 (cl (not @p_60) (not @p_46) @p_61) :rule equiv_pos2)
 (step t28 (cl @p_61) :rule th_resolution :premises (a5 t26 t27))
-(anchor :step t29 :args ((:= veriT_vr10 veriT_vr13) (:= veriT_vr11 veriT_vr14) (:= veriT_vr12 veriT_vr15)))
+(anchor :step t29 :args ((:= (veriT_vr10 Nat$) veriT_vr13) (:= (veriT_vr11 Nat$) veriT_vr14) (:= (veriT_vr12 Nat$) veriT_vr15)))
 (step t29.t1 (cl (! (= veriT_vr10 veriT_vr13) :named @p_63)) :rule refl)
 (step t29.t2 (cl (! (= veriT_vr11 veriT_vr14) :named @p_67)) :rule refl)
 (step t29.t3 (cl (= @p_48 (! (less_eq$ veriT_vr13 veriT_vr14) :named @p_62))) :rule cong :premises (t29.t1 t29.t2))
@@ -7490,12 +8010,12 @@
 (step t29 (cl (! (= @p_61 (! (forall ((veriT_vr13 Nat$) (veriT_vr14 Nat$) (veriT_vr15 Nat$)) @p_69) :named @p_71)) :named @p_70)) :rule bind)
 (step t30 (cl (not @p_70) (not @p_61) @p_71) :rule equiv_pos2)
 (step t31 (cl @p_71) :rule th_resolution :premises (t28 t29 t30))
-(anchor :step t32 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
+(anchor :step t32 :args ((:= (?v0 Astate$) veriT_vr16) (:= (?v1 Astate_v_list_v_result_prod$) veriT_vr17)))
 (step t32.t1 (cl (! (= ?v0 veriT_vr16) :named @p_80)) :rule refl)
 (step t32.t2 (cl (! (= ?v1 veriT_vr17) :named @p_79)) :rule refl)
 (step t32.t3 (cl (= @p_73 (! (fst$ veriT_vr17) :named @p_74))) :rule cong :premises (t32.t2))
 (step t32.t4 (cl (= @p_75 (! (= veriT_vr16 @p_74) :named @p_76))) :rule cong :premises (t32.t1 t32.t3))
-(anchor :step t32.t5 :args ((:= ?v2 veriT_vr18)))
+(anchor :step t32.t5 :args ((:= (?v2 V_list_v_result$) veriT_vr18)))
 (step t32.t5.t1 (cl @p_79) :rule refl)
 (step t32.t5.t2 (cl @p_80) :rule refl)
 (step t32.t5.t3 (cl (= ?v2 veriT_vr18)) :rule refl)
@@ -7506,17 +8026,17 @@
 (step t32 (cl (! (= @p_72 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_86) :named @p_88)) :named @p_87)) :rule bind)
 (step t33 (cl (not @p_87) (not @p_72) @p_88) :rule equiv_pos2)
 (step t34 (cl @p_88) :rule th_resolution :premises (a6 t32 t33))
-(anchor :step t35 :args (veriT_vr16 veriT_vr17))
+(anchor :step t35 :args ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)))
 (step t35.t1 (cl (= @p_86 (! (and (! (=> @p_76 @p_78) :named @p_99) (! (=> @p_78 @p_76) :named @p_106)) :named @p_89))) :rule connective_def)
 (step t35 (cl (! (= @p_88 (! (forall ((veriT_vr16 Astate$) (veriT_vr17 Astate_v_list_v_result_prod$)) @p_89) :named @p_91)) :named @p_90)) :rule bind)
 (step t36 (cl (not @p_90) (not @p_88) @p_91) :rule equiv_pos2)
 (step t37 (cl @p_91) :rule th_resolution :premises (t34 t35 t36))
-(anchor :step t38 :args ((:= veriT_vr16 veriT_vr19) (:= veriT_vr17 veriT_vr20)))
+(anchor :step t38 :args ((:= (veriT_vr16 Astate$) veriT_vr19) (:= (veriT_vr17 Astate_v_list_v_result_prod$) veriT_vr20)))
 (step t38.t1 (cl (! (= veriT_vr16 veriT_vr19) :named @p_96)) :rule refl)
 (step t38.t2 (cl (! (= veriT_vr17 veriT_vr20) :named @p_95)) :rule refl)
 (step t38.t3 (cl (! (= @p_74 (! (fst$ veriT_vr20) :named @p_93)) :named @p_104)) :rule cong :premises (t38.t2))
 (step t38.t4 (cl (! (= @p_76 (! (= veriT_vr19 @p_93) :named @p_92)) :named @p_105)) :rule cong :premises (t38.t1 t38.t3))
-(anchor :step t38.t5 :args ((:= veriT_vr18 veriT_vr21)))
+(anchor :step t38.t5 :args ((:= (veriT_vr18 V_list_v_result$) veriT_vr21)))
 (step t38.t5.t1 (cl @p_95) :rule refl)
 (step t38.t5.t2 (cl @p_96) :rule refl)
 (step t38.t5.t3 (cl (= veriT_vr18 veriT_vr21)) :rule refl)
@@ -7524,7 +8044,7 @@
 (step t38.t5.t5 (cl (= @p_84 (! (= veriT_vr20 @p_97) :named @p_98))) :rule cong :premises (t38.t5.t1 t38.t5.t4))
 (step t38.t5 (cl (= @p_78 (! (exists ((veriT_vr21 V_list_v_result$)) @p_98) :named @p_94))) :rule bind)
 (step t38.t6 (cl (= @p_99 (! (=> @p_92 @p_94) :named @p_100))) :rule cong :premises (t38.t4 t38.t5))
-(anchor :step t38.t7 :args ((:= veriT_vr18 veriT_vr22)))
+(anchor :step t38.t7 :args ((:= (veriT_vr18 V_list_v_result$) veriT_vr22)))
 (step t38.t7.t1 (cl @p_95) :rule refl)
 (step t38.t7.t2 (cl @p_96) :rule refl)
 (step t38.t7.t3 (cl (= veriT_vr18 veriT_vr22)) :rule refl)
@@ -7540,12 +8060,12 @@
 (step t38 (cl (! (= @p_91 (! (forall ((veriT_vr19 Astate$) (veriT_vr20 Astate_v_list_v_result_prod$)) @p_108) :named @p_110)) :named @p_109)) :rule bind)
 (step t39 (cl (not @p_109) (not @p_91) @p_110) :rule equiv_pos2)
 (step t40 (cl @p_110) :rule th_resolution :premises (t37 t38 t39))
-(anchor :step t41 :args ((:= veriT_vr19 veriT_vr23) (:= veriT_vr20 veriT_vr24)))
+(anchor :step t41 :args ((:= (veriT_vr19 Astate$) veriT_vr23) (:= (veriT_vr20 Astate_v_list_v_result_prod$) veriT_vr24)))
 (step t41.t1 (cl (! (= veriT_vr19 veriT_vr23) :named @p_115)) :rule refl)
 (step t41.t2 (cl (! (= veriT_vr20 veriT_vr24) :named @p_114)) :rule refl)
 (step t41.t3 (cl (! (= @p_93 (! (fst$ veriT_vr24) :named @p_113)) :named @p_119)) :rule cong :premises (t41.t2))
 (step t41.t4 (cl (! (= @p_92 (! (= veriT_vr23 @p_113) :named @p_112)) :named @p_120)) :rule cong :premises (t41.t1 t41.t3))
-(anchor :step t41.t5 :args ((:= veriT_vr21 veriT_vr25)))
+(anchor :step t41.t5 :args ((:= (veriT_vr21 V_list_v_result$) veriT_vr25)))
 (step t41.t5.t1 (cl @p_114) :rule refl)
 (step t41.t5.t2 (cl @p_115) :rule refl)
 (step t41.t5.t3 (cl (= veriT_vr21 veriT_vr25)) :rule refl)
@@ -7553,7 +8073,7 @@
 (step t41.t5.t5 (cl (= @p_98 (! (= veriT_vr24 @p_116) :named @p_117))) :rule cong :premises (t41.t5.t1 t41.t5.t4))
 (step t41.t5 (cl (= @p_94 (! (exists ((veriT_vr25 V_list_v_result$)) @p_117) :named @p_111))) :rule bind)
 (step t41.t6 (cl (= @p_100 (! (=> @p_112 @p_111) :named @p_118))) :rule cong :premises (t41.t4 t41.t5))
-(anchor :step t41.t7 :args ((:= veriT_vr22 veriT_vr25)))
+(anchor :step t41.t7 :args ((:= (veriT_vr22 V_list_v_result$) veriT_vr25)))
 (step t41.t7.t1 (cl @p_114) :rule refl)
 (step t41.t7.t2 (cl @p_115) :rule refl)
 (step t41.t7.t3 (cl (= veriT_vr22 veriT_vr25)) :rule refl)
@@ -7569,8 +8089,8 @@
 (step t41 (cl (! (= @p_110 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_122) :named @p_124)) :named @p_123)) :rule bind)
 (step t42 (cl (not @p_123) (not @p_110) @p_124) :rule equiv_pos2)
 (step t43 (cl @p_124) :rule th_resolution :premises (t40 t41 t42))
-(anchor :step t44 :args ((:= veriT_vr23 veriT_vr23) (:= veriT_vr24 veriT_vr24)))
-(anchor :step t44.t1 :args ((:= veriT_vr25 veriT_vr26)))
+(anchor :step t44 :args ((:= (veriT_vr23 Astate$) veriT_vr23) (:= (veriT_vr24 Astate_v_list_v_result_prod$) veriT_vr24)))
+(anchor :step t44.t1 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr26)))
 (step t44.t1.t1 (cl (= veriT_vr25 veriT_vr26)) :rule refl)
 (step t44.t1.t2 (cl (= @p_116 (! (pair$ veriT_vr23 veriT_vr26) :named @p_126))) :rule cong :premises (t44.t1.t1))
 (step t44.t1.t3 (cl (= @p_117 (! (= veriT_vr24 @p_126) :named @p_127))) :rule cong :premises (t44.t1.t2))
@@ -7580,22 +8100,22 @@
 (step t44 (cl (! (= @p_124 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_129) :named @p_131)) :named @p_130)) :rule bind)
 (step t45 (cl (not @p_130) (not @p_124) @p_131) :rule equiv_pos2)
 (step t46 (cl @p_131) :rule th_resolution :premises (t43 t44 t45))
-(anchor :step t47 :args (veriT_vr23 veriT_vr24))
+(anchor :step t47 :args ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)))
 (step t47.t1 (cl (= @p_125 (! (not (forall ((veriT_vr26 V_list_v_result$)) (! (not @p_127) :named @p_335))) :named @p_132))) :rule connective_def)
 (step t47.t2 (cl (= @p_128 (! (=> @p_132 @p_112) :named @p_133))) :rule cong :premises (t47.t1))
 (step t47.t3 (cl (= @p_129 (! (and @p_118 @p_133) :named @p_134))) :rule cong :premises (t47.t2))
 (step t47 (cl (! (= @p_131 (! (forall ((veriT_vr23 Astate$) (veriT_vr24 Astate_v_list_v_result_prod$)) @p_134) :named @p_136)) :named @p_135)) :rule bind)
 (step t48 (cl (not @p_135) (not @p_131) @p_136) :rule equiv_pos2)
 (step t49 (cl @p_136) :rule th_resolution :premises (t46 t47 t48))
-(anchor :step t50 :args ((:= ?v0 veriT_vr27)))
-(anchor :step t50.t1 :args ((:= ?v1 veriT_vr28)))
+(anchor :step t50 :args ((:= (?v0 V_error_result$) veriT_vr27)))
+(anchor :step t50.t1 :args ((:= (?v1 V$) veriT_vr28)))
 (step t50.t1.t1 (cl (! (= ?v0 veriT_vr27) :named @p_147)) :rule refl)
 (step t50.t1.t2 (cl (= ?v1 veriT_vr28)) :rule refl)
 (step t50.t1.t3 (cl (= @p_140 (! (rraise$ veriT_vr28) :named @p_141))) :rule cong :premises (t50.t1.t2))
 (step t50.t1.t4 (cl (= @p_3 (! (= veriT_vr27 @p_141) :named @p_142))) :rule cong :premises (t50.t1.t1 t50.t1.t3))
 (step t50.t1.t5 (cl (= @p_143 (! (=> @p_142 false) :named @p_144))) :rule cong :premises (t50.t1.t4))
 (step t50.t1 (cl (= @p_138 (! (forall ((veriT_vr28 V$)) @p_144) :named @p_139))) :rule bind)
-(anchor :step t50.t2 :args ((:= ?v1 veriT_vr29)))
+(anchor :step t50.t2 :args ((:= (?v1 Abort$) veriT_vr29)))
 (step t50.t2.t1 (cl @p_147) :rule refl)
 (step t50.t2.t2 (cl (= ?v1 veriT_vr29)) :rule refl)
 (step t50.t2.t3 (cl (= @p_148 (! (rabort$ veriT_vr29) :named @p_149))) :rule cong :premises (t50.t2.t2))
@@ -7607,11 +8127,11 @@
 (step t50 (cl (! (= @p_137 (! (forall ((veriT_vr27 V_error_result$)) @p_157) :named @p_159)) :named @p_158)) :rule bind)
 (step t51 (cl (not @p_158) (not @p_137) @p_159) :rule equiv_pos2)
 (step t52 (cl @p_159) :rule th_resolution :premises (a7 t50 t51))
-(anchor :step t53 :args (veriT_vr27))
-(anchor :step t53.t1 :args (veriT_vr28))
+(anchor :step t53 :args ((veriT_vr27 V_error_result$)))
+(anchor :step t53.t1 :args ((veriT_vr28 V$)))
 (step t53.t1.t1 (cl (= @p_144 (! (not @p_142) :named @p_161))) :rule implies_simplify)
 (step t53.t1 (cl (= @p_139 (! (forall ((veriT_vr28 V$)) @p_161) :named @p_160))) :rule bind)
-(anchor :step t53.t2 :args (veriT_vr29))
+(anchor :step t53.t2 :args ((veriT_vr29 Abort$)))
 (step t53.t2.t1 (cl (= @p_153 (! (not @p_151) :named @p_163))) :rule implies_simplify)
 (step t53.t2 (cl (= @p_146 (! (forall ((veriT_vr29 Abort$)) @p_163) :named @p_162))) :rule bind)
 (step t53.t3 (cl (= @p_155 (! (and @p_160 @p_162) :named @p_164))) :rule cong :premises (t53.t1 t53.t2))
@@ -7621,15 +8141,15 @@
 (step t53 (cl (! (= @p_159 (! (forall ((veriT_vr27 V_error_result$)) @p_166) :named @p_168)) :named @p_167)) :rule bind)
 (step t54 (cl (not @p_167) (not @p_159) @p_168) :rule equiv_pos2)
 (step t55 (cl @p_168) :rule th_resolution :premises (t52 t53 t54))
-(anchor :step t56 :args ((:= veriT_vr27 veriT_vr30)))
-(anchor :step t56.t1 :args ((:= veriT_vr28 veriT_vr31)))
+(anchor :step t56 :args ((:= (veriT_vr27 V_error_result$) veriT_vr30)))
+(anchor :step t56.t1 :args ((:= (veriT_vr28 V$) veriT_vr31)))
 (step t56.t1.t1 (cl (! (= veriT_vr27 veriT_vr30) :named @p_174)) :rule refl)
 (step t56.t1.t2 (cl (= veriT_vr28 veriT_vr31)) :rule refl)
 (step t56.t1.t3 (cl (= @p_141 (! (rraise$ veriT_vr31) :named @p_170))) :rule cong :premises (t56.t1.t2))
 (step t56.t1.t4 (cl (= @p_142 (! (= veriT_vr30 @p_170) :named @p_171))) :rule cong :premises (t56.t1.t1 t56.t1.t3))
 (step t56.t1.t5 (cl (= @p_161 (! (not @p_171) :named @p_172))) :rule cong :premises (t56.t1.t4))
 (step t56.t1 (cl (= @p_160 (! (forall ((veriT_vr31 V$)) @p_172) :named @p_169))) :rule bind)
-(anchor :step t56.t2 :args ((:= veriT_vr29 veriT_vr32)))
+(anchor :step t56.t2 :args ((:= (veriT_vr29 Abort$) veriT_vr32)))
 (step t56.t2.t1 (cl @p_174) :rule refl)
 (step t56.t2.t2 (cl (= veriT_vr29 veriT_vr32)) :rule refl)
 (step t56.t2.t3 (cl (= @p_149 (! (rabort$ veriT_vr32) :named @p_175))) :rule cong :premises (t56.t2.t2))
@@ -7641,7 +8161,7 @@
 (step t56 (cl (! (= @p_168 (! (forall ((veriT_vr30 V_error_result$)) @p_179) :named @p_181)) :named @p_180)) :rule bind)
 (step t57 (cl (not @p_180) (not @p_168) @p_181) :rule equiv_pos2)
 (step t58 (cl @p_181) :rule th_resolution :premises (t55 t56 t57))
-(anchor :step t59 :args ((:= ?v0 veriT_vr33) (:= ?v1 veriT_vr34) (:= ?v2 veriT_vr35)))
+(anchor :step t59 :args ((:= (?v0 V_astate_v_list_v_result_prod_fun$) veriT_vr33) (:= (?v1 Abort_astate_v_list_v_result_prod_fun$) veriT_vr34) (:= (?v2 V$) veriT_vr35)))
 (step t59.t1 (cl (! (= ?v0 veriT_vr33) :named @p_187)) :rule refl)
 (step t59.t2 (cl (= ?v1 veriT_vr34)) :rule refl)
 (step t59.t3 (cl (! (= ?v2 veriT_vr35) :named @p_188)) :rule refl)
@@ -7654,7 +8174,7 @@
 (step t59 (cl (! (= @p_182 (! (forall ((veriT_vr33 V_astate_v_list_v_result_prod_fun$) (veriT_vr34 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr35 V$)) @p_192) :named @p_194)) :named @p_193)) :rule bind)
 (step t60 (cl (not @p_193) (not @p_182) @p_194) :rule equiv_pos2)
 (step t61 (cl @p_194) :rule th_resolution :premises (a8 t59 t60))
-(anchor :step t62 :args ((:= veriT_vr33 veriT_vr36) (:= veriT_vr34 veriT_vr37) (:= veriT_vr35 veriT_vr38)))
+(anchor :step t62 :args ((:= (veriT_vr33 V_astate_v_list_v_result_prod_fun$) veriT_vr36) (:= (veriT_vr34 Abort_astate_v_list_v_result_prod_fun$) veriT_vr37) (:= (veriT_vr35 V$) veriT_vr38)))
 (step t62.t1 (cl (! (= veriT_vr33 veriT_vr36) :named @p_197)) :rule refl)
 (step t62.t2 (cl (= veriT_vr34 veriT_vr37)) :rule refl)
 (step t62.t3 (cl (! (= veriT_vr35 veriT_vr38) :named @p_198)) :rule refl)
@@ -7667,7 +8187,7 @@
 (step t62 (cl (! (= @p_194 (! (forall ((veriT_vr36 V_astate_v_list_v_result_prod_fun$) (veriT_vr37 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr38 V$)) @p_200) :named @p_202)) :named @p_201)) :rule bind)
 (step t63 (cl (not @p_201) (not @p_194) @p_202) :rule equiv_pos2)
 (step t64 (cl @p_202) :rule th_resolution :premises (t61 t62 t63))
-(anchor :step t65 :args ((:= ?v0 veriT_vr39) (:= ?v1 veriT_vr40) (:= ?v2 veriT_vr41)))
+(anchor :step t65 :args ((:= (?v0 V_astate_v_list_v_result_prod_fun$) veriT_vr39) (:= (?v1 Abort_astate_v_list_v_result_prod_fun$) veriT_vr40) (:= (?v2 Abort$) veriT_vr41)))
 (step t65.t1 (cl (= ?v0 veriT_vr39)) :rule refl)
 (step t65.t2 (cl (! (= ?v1 veriT_vr40) :named @p_208)) :rule refl)
 (step t65.t3 (cl (! (= ?v2 veriT_vr41) :named @p_209)) :rule refl)
@@ -7680,7 +8200,7 @@
 (step t65 (cl (! (= @p_203 (! (forall ((veriT_vr39 V_astate_v_list_v_result_prod_fun$) (veriT_vr40 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr41 Abort$)) @p_213) :named @p_215)) :named @p_214)) :rule bind)
 (step t66 (cl (not @p_214) (not @p_203) @p_215) :rule equiv_pos2)
 (step t67 (cl @p_215) :rule th_resolution :premises (a9 t65 t66))
-(anchor :step t68 :args ((:= veriT_vr39 veriT_vr42) (:= veriT_vr40 veriT_vr43) (:= veriT_vr41 veriT_vr44)))
+(anchor :step t68 :args ((:= (veriT_vr39 V_astate_v_list_v_result_prod_fun$) veriT_vr42) (:= (veriT_vr40 Abort_astate_v_list_v_result_prod_fun$) veriT_vr43) (:= (veriT_vr41 Abort$) veriT_vr44)))
 (step t68.t1 (cl (= veriT_vr39 veriT_vr42)) :rule refl)
 (step t68.t2 (cl (! (= veriT_vr40 veriT_vr43) :named @p_218)) :rule refl)
 (step t68.t3 (cl (! (= veriT_vr41 veriT_vr44) :named @p_219)) :rule refl)
@@ -7693,7 +8213,7 @@
 (step t68 (cl (! (= @p_215 (! (forall ((veriT_vr42 V_astate_v_list_v_result_prod_fun$) (veriT_vr43 Abort_astate_v_list_v_result_prod_fun$) (veriT_vr44 Abort$)) @p_221) :named @p_223)) :named @p_222)) :rule bind)
 (step t69 (cl (not @p_222) (not @p_215) @p_223) :rule equiv_pos2)
 (step t70 (cl @p_223) :rule th_resolution :premises (t67 t68 t69))
-(anchor :step t71 :args ((:= ?v0 veriT_vr45) (:= ?v1 veriT_vr46) (:= ?v2 veriT_vr47) (:= ?v3 veriT_vr48)))
+(anchor :step t71 :args ((:= (?v0 Astate$) veriT_vr45) (:= (?v1 Astate$) veriT_vr46) (:= (?v2 V_list_v_result$) veriT_vr47) (:= (?v3 Astate$) veriT_vr48)))
 (step t71.t1 (cl (= ?v0 veriT_vr45)) :rule refl)
 (step t71.t2 (cl (! (= ?v1 veriT_vr46) :named @p_236)) :rule refl)
 (step t71.t3 (cl (! (= ?v2 veriT_vr47) :named @p_228)) :rule refl)
@@ -7712,7 +8232,7 @@
 (step t71 (cl (! (= @p_224 (! (forall ((veriT_vr45 Astate$) (veriT_vr46 Astate$) (veriT_vr47 V_list_v_result$) (veriT_vr48 Astate$)) @p_242) :named @p_244)) :named @p_243)) :rule bind)
 (step t72 (cl (not @p_243) (not @p_224) @p_244) :rule equiv_pos2)
 (step t73 (cl @p_244) :rule th_resolution :premises (a10 t71 t72))
-(anchor :step t74 :args ((:= veriT_vr45 veriT_vr49) (:= veriT_vr46 veriT_vr50) (:= veriT_vr47 veriT_vr51) (:= veriT_vr48 veriT_vr52)))
+(anchor :step t74 :args ((:= (veriT_vr45 Astate$) veriT_vr49) (:= (veriT_vr46 Astate$) veriT_vr50) (:= (veriT_vr47 V_list_v_result$) veriT_vr51) (:= (veriT_vr48 Astate$) veriT_vr52)))
 (step t74.t1 (cl (= veriT_vr45 veriT_vr49)) :rule refl)
 (step t74.t2 (cl (! (= veriT_vr46 veriT_vr50) :named @p_252)) :rule refl)
 (step t74.t3 (cl (! (= veriT_vr47 veriT_vr51) :named @p_247)) :rule refl)
@@ -7731,7 +8251,7 @@
 (step t74 (cl (! (= @p_244 (! (forall ((veriT_vr49 Astate$) (veriT_vr50 Astate$) (veriT_vr51 V_list_v_result$) (veriT_vr52 Astate$)) @p_255) :named @p_257)) :named @p_256)) :rule bind)
 (step t75 (cl (not @p_256) (not @p_244) @p_257) :rule equiv_pos2)
 (step t76 (cl @p_257) :rule th_resolution :premises (t73 t74 t75))
-(anchor :step t77 :args ((:= ?v0 veriT_vr53) (:= ?v1 veriT_vr54) (:= ?v2 veriT_vr55)))
+(anchor :step t77 :args ((:= (?v0 Astate$) veriT_vr53) (:= (?v1 Astate$) veriT_vr54) (:= (?v2 V_list_v_result$) veriT_vr55)))
 (step t77.t1 (cl (! (= ?v0 veriT_vr53) :named @p_261)) :rule refl)
 (step t77.t2 (cl (! (= ?v1 veriT_vr54) :named @p_262)) :rule refl)
 (step t77.t3 (cl (! (= ?v2 veriT_vr55) :named @p_267)) :rule refl)
@@ -7748,7 +8268,7 @@
 (step t77 (cl (! (= @p_258 (! (forall ((veriT_vr53 Astate$) (veriT_vr54 Astate$) (veriT_vr55 V_list_v_result$)) @p_271) :named @p_273)) :named @p_272)) :rule bind)
 (step t78 (cl (not @p_272) (not @p_258) @p_273) :rule equiv_pos2)
 (step t79 (cl @p_273) :rule th_resolution :premises (a11 t77 t78))
-(anchor :step t80 :args ((:= veriT_vr53 veriT_vr56) (:= veriT_vr54 veriT_vr57) (:= veriT_vr55 veriT_vr58)))
+(anchor :step t80 :args ((:= (veriT_vr53 Astate$) veriT_vr56) (:= (veriT_vr54 Astate$) veriT_vr57) (:= (veriT_vr55 V_list_v_result$) veriT_vr58)))
 (step t80.t1 (cl (! (= veriT_vr53 veriT_vr56) :named @p_276)) :rule refl)
 (step t80.t2 (cl (! (= veriT_vr54 veriT_vr57) :named @p_277)) :rule refl)
 (step t80.t3 (cl (! (= veriT_vr55 veriT_vr58) :named @p_280)) :rule refl)
@@ -7765,7 +8285,7 @@
 (step t80 (cl (! (= @p_273 (! (forall ((veriT_vr56 Astate$) (veriT_vr57 Astate$) (veriT_vr58 V_list_v_result$)) @p_282) :named @p_284)) :named @p_283)) :rule bind)
 (step t81 (cl (not @p_283) (not @p_273) @p_284) :rule equiv_pos2)
 (step t82 (cl @p_284) :rule th_resolution :premises (t79 t80 t81))
-(anchor :step t83 :args ((:= ?v0 veriT_vr59) (:= ?v1 veriT_vr60)))
+(anchor :step t83 :args ((:= (?v0 V_error_result$) veriT_vr59) (:= (?v1 V$) veriT_vr60)))
 (step t83.t1 (cl (! (= ?v0 veriT_vr59) :named @p_291)) :rule refl)
 (step t83.t2 (cl (= @p_287 (! (rerr$ veriT_vr59) :named @p_288))) :rule cong :premises (t83.t1))
 (step t83.t3 (cl (= @p_289 (! (= r$ @p_288) :named @p_290))) :rule cong :premises (t83.t2))
@@ -7785,7 +8305,7 @@
 (step t83 (cl (! (= @p_285 (! (forall ((veriT_vr59 V_error_result$) (veriT_vr60 V$)) @p_308) :named @p_310)) :named @p_309)) :rule bind)
 (step t84 (cl (not @p_309) (not @p_285) @p_310) :rule equiv_pos2)
 (step t85 (cl @p_310) :rule th_resolution :premises (a12 t83 t84))
-(anchor :step t86 :args ((:= veriT_vr59 veriT_vr61) (:= veriT_vr60 veriT_vr62)))
+(anchor :step t86 :args ((:= (veriT_vr59 V_error_result$) veriT_vr61) (:= (veriT_vr60 V$) veriT_vr62)))
 (step t86.t1 (cl (! (= veriT_vr59 veriT_vr61) :named @p_313)) :rule refl)
 (step t86.t2 (cl (= @p_288 (! (rerr$ veriT_vr61) :named @p_311))) :rule cong :premises (t86.t1))
 (step t86.t3 (cl (= @p_290 (! (= r$ @p_311) :named @p_312))) :rule cong :premises (t86.t2))
@@ -7828,13 +8348,13 @@
 (step t109 (cl (or (! (not @p_181) :named @p_395) (! (not (! (and (! (forall ((veriT_vr31 V$)) (! (not (! (= x2$ @p_170) :named @p_350)) :named @p_352)) :named @p_348) (! (forall ((veriT_vr32 Abort$)) (! (not (! (= x2$ @p_175) :named @p_356)) :named @p_358)) :named @p_354)) :named @p_360)) :named @p_347))) :rule forall_inst :args ((:= veriT_vr30 x2$)))
 (anchor :step t110)
 (assume t110.h1 @p_347)
-(anchor :step t110.t2 :args ((:= veriT_vr31 veriT_vr63)))
+(anchor :step t110.t2 :args ((:= (veriT_vr31 V$) veriT_vr63)))
 (step t110.t2.t1 (cl (= veriT_vr31 veriT_vr63)) :rule refl)
 (step t110.t2.t2 (cl (= @p_170 (! (rraise$ veriT_vr63) :named @p_349))) :rule cong :premises (t110.t2.t1))
 (step t110.t2.t3 (cl (= @p_350 (! (= x2$ @p_349) :named @p_351))) :rule cong :premises (t110.t2.t2))
 (step t110.t2.t4 (cl (= @p_352 (! (not @p_351) :named @p_353))) :rule cong :premises (t110.t2.t3))
 (step t110.t2 (cl (= @p_348 (! (forall ((veriT_vr63 V$)) @p_353) :named @p_361))) :rule bind)
-(anchor :step t110.t3 :args ((:= veriT_vr32 veriT_vr64)))
+(anchor :step t110.t3 :args ((:= (veriT_vr32 Abort$) veriT_vr64)))
 (step t110.t3.t1 (cl (= veriT_vr32 veriT_vr64)) :rule refl)
 (step t110.t3.t2 (cl (= @p_175 (! (rabort$ veriT_vr64) :named @p_355))) :rule cong :premises (t110.t3.t1))
 (step t110.t3.t3 (cl (= @p_356 (! (= x2$ @p_355) :named @p_357))) :rule cong :premises (t110.t3.t2))
@@ -7846,13 +8366,13 @@
 (step t110.t7 (cl (! (not @p_365) :named @p_394) @p_360) :rule not_not)
 (step t110.t8 (cl @p_367 @p_360 @p_366) :rule th_resolution :premises (t110.t7 t110.t6))
 (step t110.t9 (cl @p_366) :rule th_resolution :premises (t110.h1 t110.t5 t110.t8))
-(anchor :step t110.t10 :args ((:= veriT_vr63 veriT_vr65)))
+(anchor :step t110.t10 :args ((:= (veriT_vr63 V$) veriT_vr65)))
 (step t110.t10.t1 (cl (= veriT_vr63 veriT_vr65)) :rule refl)
 (step t110.t10.t2 (cl (= @p_349 @p_369)) :rule cong :premises (t110.t10.t1))
 (step t110.t10.t3 (cl (= @p_351 @p_370)) :rule cong :premises (t110.t10.t2))
 (step t110.t10.t4 (cl (= @p_353 @p_368)) :rule cong :premises (t110.t10.t3))
 (step t110.t10 (cl (= @p_361 (! (forall ((veriT_vr65 V$)) @p_368) :named @p_374))) :rule bind)
-(anchor :step t110.t11 :args ((:= veriT_vr64 veriT_vr66)))
+(anchor :step t110.t11 :args ((:= (veriT_vr64 Abort$) veriT_vr66)))
 (step t110.t11.t1 (cl (= veriT_vr64 veriT_vr66)) :rule refl)
 (step t110.t11.t2 (cl (= @p_355 @p_372)) :rule cong :premises (t110.t11.t1))
 (step t110.t11.t3 (cl (= @p_357 @p_373)) :rule cong :premises (t110.t11.t2))
@@ -7864,13 +8384,13 @@
 (step t110.t15 (cl (not @p_379) @p_363) :rule not_not)
 (step t110.t16 (cl @p_380 @p_363 @p_378) :rule th_resolution :premises (t110.t15 t110.t14))
 (step t110.t17 (cl @p_378) :rule th_resolution :premises (t110.t9 t110.t13 t110.t16))
-(anchor :step t110.t18 :args ((:= veriT_vr65 veriT_sk0)))
+(anchor :step t110.t18 :args ((:= (veriT_vr65 V$) veriT_sk0)))
 (step t110.t18.t1 (cl (= veriT_vr65 veriT_sk0)) :rule refl)
 (step t110.t18.t2 (cl (= @p_369 (! (rraise$ veriT_sk0) :named @p_383))) :rule cong :premises (t110.t18.t1))
 (step t110.t18.t3 (cl (= @p_370 (! (= x2$ @p_383) :named @p_384))) :rule cong :premises (t110.t18.t2))
 (step t110.t18.t4 (cl (= @p_368 (! (not @p_384) :named @p_381))) :rule cong :premises (t110.t18.t3))
 (step t110.t18 (cl (= @p_374 @p_381)) :rule sko_forall)
-(anchor :step t110.t19 :args ((:= veriT_vr66 veriT_sk1)))
+(anchor :step t110.t19 :args ((:= (veriT_vr66 Abort$) veriT_sk1)))
 (step t110.t19.t1 (cl (= veriT_vr66 veriT_sk1)) :rule refl)
 (step t110.t19.t2 (cl (= @p_372 (! (rabort$ veriT_sk1) :named @p_387))) :rule cong :premises (t110.t19.t1))
 (step t110.t19.t3 (cl (= @p_373 (! (= x2$ @p_387) :named @p_388))) :rule cong :premises (t110.t19.t2))
@@ -7897,13 +8417,13 @@
 (step t122 (cl (or @p_399 (! (and (! (=> (! (= @p_346 @p_346) :named @p_400) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_1 (! (pair$ @p_346 veriT_vr25) :named @p_403)) :named @p_405)) :named @p_402)) :named @p_407) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_1 (! (pair$ @p_346 veriT_vr26) :named @p_410)) :named @p_411)) :named @p_412)) :named @p_409)) :named @p_414) @p_400) :named @p_416)) :named @p_401))) :rule forall_inst :args ((:= veriT_vr23 @p_346) (:= veriT_vr24 @p_1)))
 (anchor :step t123)
 (assume t123.h1 @p_401)
-(anchor :step t123.t2 :args ((:= veriT_vr25 veriT_vr72)))
+(anchor :step t123.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr72)))
 (step t123.t2.t1 (cl (= veriT_vr25 veriT_vr72)) :rule refl)
 (step t123.t2.t2 (cl (= @p_403 (! (pair$ @p_346 veriT_vr72) :named @p_404))) :rule cong :premises (t123.t2.t1))
 (step t123.t2.t3 (cl (= @p_405 (! (= @p_1 @p_404) :named @p_406))) :rule cong :premises (t123.t2.t2))
 (step t123.t2 (cl (= @p_402 (! (exists ((veriT_vr72 V_list_v_result$)) @p_406) :named @p_408))) :rule bind)
 (step t123.t3 (cl (= @p_407 (! (=> @p_400 @p_408) :named @p_418))) :rule cong :premises (t123.t2))
-(anchor :step t123.t4 :args ((:= veriT_vr26 veriT_vr72)))
+(anchor :step t123.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr72)))
 (step t123.t4.t1 (cl (= veriT_vr26 veriT_vr72)) :rule refl)
 (step t123.t4.t2 (cl (= @p_410 @p_404)) :rule cong :premises (t123.t4.t1))
 (step t123.t4.t3 (cl (= @p_411 @p_406)) :rule cong :premises (t123.t4.t2))
@@ -7927,14 +8447,14 @@
 (step t123.t20 (cl (! (= @p_422 @p_408) :named @p_427)) :rule trans :premises (t123.t17 t123.t18 t123.t19))
 (step t123.t21 (cl (not @p_427) (not @p_422) @p_408) :rule equiv_pos2)
 (step t123.t22 (cl @p_408) :rule th_resolution :premises (t123.t9 t123.t20 t123.t21))
-(anchor :step t123.t23 :args ((:= veriT_vr72 veriT_vr73)))
+(anchor :step t123.t23 :args ((:= (veriT_vr72 V_list_v_result$) veriT_vr73)))
 (step t123.t23.t1 (cl (= veriT_vr72 veriT_vr73)) :rule refl)
 (step t123.t23.t2 (cl (= @p_404 @p_429)) :rule cong :premises (t123.t23.t1))
 (step t123.t23.t3 (cl (= @p_406 @p_428)) :rule cong :premises (t123.t23.t2))
 (step t123.t23 (cl (! (= @p_408 (! (exists ((veriT_vr73 V_list_v_result$)) @p_428) :named @p_431)) :named @p_430)) :rule bind)
 (step t123.t24 (cl (not @p_430) (not @p_408) @p_431) :rule equiv_pos2)
 (step t123.t25 (cl @p_431) :rule th_resolution :premises (t123.t22 t123.t23 t123.t24))
-(anchor :step t123.t26 :args ((:= veriT_vr73 veriT_sk3)))
+(anchor :step t123.t26 :args ((:= (veriT_vr73 V_list_v_result$) veriT_sk3)))
 (step t123.t26.t1 (cl (= veriT_vr73 veriT_sk3)) :rule refl)
 (step t123.t26.t2 (cl (= @p_429 (! (pair$ @p_346 veriT_sk3) :named @p_434))) :rule cong :premises (t123.t26.t1))
 (step t123.t26.t3 (cl (= @p_428 (! (= @p_1 @p_434) :named @p_432))) :rule cong :premises (t123.t26.t2))
@@ -7950,13 +8470,13 @@
 (step t129 (cl (or @p_399 (! (and (! (=> (! (= st$ (! (fst$ @p_438) :named @p_674)) :named @p_439) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_438 (! (pair$ st$ veriT_vr25) :named @p_442)) :named @p_444)) :named @p_441)) :named @p_446) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_438 (! (pair$ st$ veriT_vr26) :named @p_449)) :named @p_450)) :named @p_451)) :named @p_448)) :named @p_453) @p_439) :named @p_455)) :named @p_440))) :rule forall_inst :args ((:= veriT_vr23 st$) (:= veriT_vr24 @p_438)))
 (anchor :step t130)
 (assume t130.h1 @p_440)
-(anchor :step t130.t2 :args ((:= veriT_vr25 veriT_vr106)))
+(anchor :step t130.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr106)))
 (step t130.t2.t1 (cl (= veriT_vr25 veriT_vr106)) :rule refl)
 (step t130.t2.t2 (cl (= @p_442 (! (pair$ st$ veriT_vr106) :named @p_443))) :rule cong :premises (t130.t2.t1))
 (step t130.t2.t3 (cl (= @p_444 (! (= @p_438 @p_443) :named @p_445))) :rule cong :premises (t130.t2.t2))
 (step t130.t2 (cl (= @p_441 (! (exists ((veriT_vr106 V_list_v_result$)) @p_445) :named @p_447))) :rule bind)
 (step t130.t3 (cl (= @p_446 (! (=> @p_439 @p_447) :named @p_457))) :rule cong :premises (t130.t2))
-(anchor :step t130.t4 :args ((:= veriT_vr26 veriT_vr106)))
+(anchor :step t130.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr106)))
 (step t130.t4.t1 (cl (= veriT_vr26 veriT_vr106)) :rule refl)
 (step t130.t4.t2 (cl (= @p_449 @p_443)) :rule cong :premises (t130.t4.t1))
 (step t130.t4.t3 (cl (= @p_450 @p_445)) :rule cong :premises (t130.t4.t2))
@@ -7967,7 +8487,7 @@
 (step t130.t7 (cl (! (= @p_440 (! (and @p_457 @p_458) :named @p_461)) :named @p_459)) :rule cong :premises (t130.t3 t130.t6))
 (step t130.t8 (cl (not @p_459) (! (not @p_440) :named @p_460) @p_461) :rule equiv_pos2)
 (step t130.t9 (cl @p_461) :rule th_resolution :premises (t130.h1 t130.t7 t130.t8))
-(anchor :step t130.t10 :args ((:= veriT_vr106 veriT_vr107)))
+(anchor :step t130.t10 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr107)))
 (step t130.t10.t1 (cl (= veriT_vr106 veriT_vr107)) :rule refl)
 (step t130.t10.t2 (cl (= @p_443 (! (pair$ st$ veriT_vr107) :named @p_462))) :rule cong :premises (t130.t10.t1))
 (step t130.t10.t3 (cl (= @p_445 (! (= @p_438 @p_462) :named @p_463))) :rule cong :premises (t130.t10.t2))
@@ -7978,13 +8498,13 @@
 (step t130.t13 (cl (! (= @p_461 (! (and @p_457 @p_467) :named @p_469)) :named @p_468)) :rule cong :premises (t130.t12))
 (step t130.t14 (cl (not @p_468) (not @p_461) @p_469) :rule equiv_pos2)
 (step t130.t15 (cl @p_469) :rule th_resolution :premises (t130.t9 t130.t13 t130.t14))
-(anchor :step t130.t16 :args ((:= veriT_vr106 veriT_vr108)))
+(anchor :step t130.t16 :args ((:= (veriT_vr106 V_list_v_result$) veriT_vr108)))
 (step t130.t16.t1 (cl (= veriT_vr106 veriT_vr108)) :rule refl)
 (step t130.t16.t2 (cl (= @p_443 @p_471)) :rule cong :premises (t130.t16.t1))
 (step t130.t16.t3 (cl (= @p_445 @p_470)) :rule cong :premises (t130.t16.t2))
 (step t130.t16 (cl (= @p_447 (! (exists ((veriT_vr108 V_list_v_result$)) @p_470) :named @p_472))) :rule bind)
 (step t130.t17 (cl (= @p_457 (! (=> @p_439 @p_472) :named @p_478))) :rule cong :premises (t130.t16))
-(anchor :step t130.t18 :args ((:= veriT_vr107 veriT_vr109)))
+(anchor :step t130.t18 :args ((:= (veriT_vr107 V_list_v_result$) veriT_vr109)))
 (step t130.t18.t1 (cl (= veriT_vr107 veriT_vr109)) :rule refl)
 (step t130.t18.t2 (cl (= @p_462 (! (pair$ st$ veriT_vr109) :named @p_473))) :rule cong :premises (t130.t18.t1))
 (step t130.t18.t3 (cl (= @p_463 (! (= @p_438 @p_473) :named @p_474))) :rule cong :premises (t130.t18.t2))
@@ -7995,7 +8515,7 @@
 (step t130.t21 (cl (! (= @p_469 (! (and @p_478 @p_479) :named @p_481)) :named @p_480)) :rule cong :premises (t130.t17 t130.t20))
 (step t130.t22 (cl (not @p_480) (not @p_469) @p_481) :rule equiv_pos2)
 (step t130.t23 (cl @p_481) :rule th_resolution :premises (t130.t15 t130.t21 t130.t22))
-(anchor :step t130.t24 :args ((:= veriT_vr108 veriT_sk11)))
+(anchor :step t130.t24 :args ((:= (veriT_vr108 V_list_v_result$) veriT_sk11)))
 (step t130.t24.t1 (cl (= veriT_vr108 veriT_sk11)) :rule refl)
 (step t130.t24.t2 (cl (= @p_471 (! (pair$ st$ veriT_sk11) :named @p_484))) :rule cong :premises (t130.t24.t1))
 (step t130.t24.t3 (cl (= @p_470 (! (= @p_438 @p_484) :named @p_482))) :rule cong :premises (t130.t24.t2))
@@ -8004,7 +8524,7 @@
 (step t130.t26 (cl (! (= @p_481 (! (and @p_485 @p_479) :named @p_487)) :named @p_486)) :rule cong :premises (t130.t25))
 (step t130.t27 (cl (not @p_486) (not @p_481) @p_487) :rule equiv_pos2)
 (step t130.t28 (cl @p_487) :rule th_resolution :premises (t130.t23 t130.t26 t130.t27))
-(anchor :step t130.t29 :args ((:= veriT_vr109 veriT_vr110)))
+(anchor :step t130.t29 :args ((:= (veriT_vr109 V_list_v_result$) veriT_vr110)))
 (step t130.t29.t1 (cl (= veriT_vr109 veriT_vr110)) :rule refl)
 (step t130.t29.t2 (cl (= @p_473 (! (pair$ st$ veriT_vr110) :named @p_489))) :rule cong :premises (t130.t29.t1))
 (step t130.t29.t3 (cl (= @p_474 (! (= @p_438 @p_489) :named @p_490))) :rule cong :premises (t130.t29.t2))
@@ -8133,13 +8653,13 @@
 (step t245 (cl (or @p_399 (! (and (! (=> (! (= @p_565 @p_504) :named @p_585) (! (exists ((veriT_vr25 V_list_v_result$)) (! (= @p_547 (! (pair$ @p_504 veriT_vr25) :named @p_588)) :named @p_590)) :named @p_587)) :named @p_592) (! (=> (! (not (! (forall ((veriT_vr26 V_list_v_result$)) (! (not (! (= @p_547 (! (pair$ @p_504 veriT_vr26) :named @p_595)) :named @p_596)) :named @p_597)) :named @p_594)) :named @p_599) @p_585) :named @p_601)) :named @p_586))) :rule forall_inst :args ((:= veriT_vr23 @p_504) (:= veriT_vr24 @p_547)))
 (anchor :step t246)
 (assume t246.h1 @p_586)
-(anchor :step t246.t2 :args ((:= veriT_vr25 veriT_vr3120)))
+(anchor :step t246.t2 :args ((:= (veriT_vr25 V_list_v_result$) veriT_vr3120)))
 (step t246.t2.t1 (cl (= veriT_vr25 veriT_vr3120)) :rule refl)
 (step t246.t2.t2 (cl (= @p_588 (! (pair$ @p_504 veriT_vr3120) :named @p_589))) :rule cong :premises (t246.t2.t1))
 (step t246.t2.t3 (cl (= @p_590 (! (= @p_547 @p_589) :named @p_591))) :rule cong :premises (t246.t2.t2))
 (step t246.t2 (cl (= @p_587 (! (exists ((veriT_vr3120 V_list_v_result$)) @p_591) :named @p_593))) :rule bind)
 (step t246.t3 (cl (= @p_592 (! (=> @p_585 @p_593) :named @p_603))) :rule cong :premises (t246.t2))
-(anchor :step t246.t4 :args ((:= veriT_vr26 veriT_vr3120)))
+(anchor :step t246.t4 :args ((:= (veriT_vr26 V_list_v_result$) veriT_vr3120)))
 (step t246.t4.t1 (cl (= veriT_vr26 veriT_vr3120)) :rule refl)
 (step t246.t4.t2 (cl (= @p_595 @p_589)) :rule cong :premises (t246.t4.t1))
 (step t246.t4.t3 (cl (= @p_596 @p_591)) :rule cong :premises (t246.t4.t2))
@@ -8150,7 +8670,7 @@
 (step t246.t7 (cl (! (= @p_586 (! (and @p_603 @p_604) :named @p_607)) :named @p_605)) :rule cong :premises (t246.t3 t246.t6))
 (step t246.t8 (cl (not @p_605) (! (not @p_586) :named @p_606) @p_607) :rule equiv_pos2)
 (step t246.t9 (cl @p_607) :rule th_resolution :premises (t246.h1 t246.t7 t246.t8))
-(anchor :step t246.t10 :args ((:= veriT_vr3120 veriT_vr3121)))
+(anchor :step t246.t10 :args ((:= (veriT_vr3120 V_list_v_result$) veriT_vr3121)))
 (step t246.t10.t1 (cl (= veriT_vr3120 veriT_vr3121)) :rule refl)
 (step t246.t10.t2 (cl (= @p_589 (! (pair$ @p_504 veriT_vr3121) :named @p_608))) :rule cong :premises (t246.t10.t1))
 (step t246.t10.t3 (cl (= @p_591 (! (= @p_547 @p_608) :named @p_609))) :rule cong :premises (t246.t10.t2))
@@ -8161,13 +8681,13 @@
 (step t246.t13 (cl (! (= @p_607 (! (and @p_603 @p_613) :named @p_615)) :named @p_614)) :rule cong :premises (t246.t12))
 (step t246.t14 (cl (not @p_614) (not @p_607) @p_615) :rule equiv_pos2)
 (step t246.t15 (cl @p_615) :rule th_resolution :premises (t246.t9 t246.t13 t246.t14))
-(anchor :step t246.t16 :args ((:= veriT_vr3120 veriT_vr3122)))
+(anchor :step t246.t16 :args ((:= (veriT_vr3120 V_list_v_result$) veriT_vr3122)))
 (step t246.t16.t1 (cl (= veriT_vr3120 veriT_vr3122)) :rule refl)
 (step t246.t16.t2 (cl (= @p_589 @p_617)) :rule cong :premises (t246.t16.t1))
 (step t246.t16.t3 (cl (= @p_591 @p_616)) :rule cong :premises (t246.t16.t2))
 (step t246.t16 (cl (= @p_593 (! (exists ((veriT_vr3122 V_list_v_result$)) @p_616) :named @p_618))) :rule bind)
 (step t246.t17 (cl (= @p_603 (! (=> @p_585 @p_618) :named @p_624))) :rule cong :premises (t246.t16))
-(anchor :step t246.t18 :args ((:= veriT_vr3121 veriT_vr3123)))
+(anchor :step t246.t18 :args ((:= (veriT_vr3121 V_list_v_result$) veriT_vr3123)))
 (step t246.t18.t1 (cl (= veriT_vr3121 veriT_vr3123)) :rule refl)
 (step t246.t18.t2 (cl (= @p_608 (! (pair$ @p_504 veriT_vr3123) :named @p_619))) :rule cong :premises (t246.t18.t1))
 (step t246.t18.t3 (cl (= @p_609 (! (= @p_547 @p_619) :named @p_620))) :rule cong :premises (t246.t18.t2))
@@ -8178,7 +8698,7 @@
 (step t246.t21 (cl (! (= @p_615 (! (and @p_624 @p_625) :named @p_627)) :named @p_626)) :rule cong :premises (t246.t17 t246.t20))
 (step t246.t22 (cl (not @p_626) (not @p_615) @p_627) :rule equiv_pos2)
 (step t246.t23 (cl @p_627) :rule th_resolution :premises (t246.t15 t246.t21 t246.t22))
-(anchor :step t246.t24 :args ((:= veriT_vr3122 veriT_sk615)))
+(anchor :step t246.t24 :args ((:= (veriT_vr3122 V_list_v_result$) veriT_sk615)))
 (step t246.t24.t1 (cl (= veriT_vr3122 veriT_sk615)) :rule refl)
 (step t246.t24.t2 (cl (= @p_617 (! (pair$ @p_504 veriT_sk615) :named @p_630))) :rule cong :premises (t246.t24.t1))
 (step t246.t24.t3 (cl (= @p_616 (! (= @p_547 @p_630) :named @p_628))) :rule cong :premises (t246.t24.t2))
@@ -8187,7 +8707,7 @@
 (step t246.t26 (cl (! (= @p_627 (! (and @p_631 @p_625) :named @p_633)) :named @p_632)) :rule cong :premises (t246.t25))
 (step t246.t27 (cl (not @p_632) (not @p_627) @p_633) :rule equiv_pos2)
 (step t246.t28 (cl @p_633) :rule th_resolution :premises (t246.t23 t246.t26 t246.t27))
-(anchor :step t246.t29 :args ((:= veriT_vr3123 veriT_vr3124)))
+(anchor :step t246.t29 :args ((:= (veriT_vr3123 V_list_v_result$) veriT_vr3124)))
 (step t246.t29.t1 (cl (= veriT_vr3123 veriT_vr3124)) :rule refl)
 (step t246.t29.t2 (cl (= @p_619 (! (pair$ @p_504 veriT_vr3124) :named @p_635))) :rule cong :premises (t246.t29.t1))
 (step t246.t29.t3 (cl (= @p_620 (! (= @p_547 @p_635) :named @p_636))) :rule cong :premises (t246.t29.t2))
@@ -8270,523 +8790,3 @@
 (step t303 (cl @p_681 @p_682 @p_531 @p_573 @p_574 @p_381) :rule th_resolution :premises (t302 t230))
 (step t304 (cl @p_682 @p_531 @p_573 @p_574 @p_381 @p_678 @p_677 @p_666 @p_538) :rule th_resolution :premises (t303 t297))
 (step t305 (cl) :rule resolution :premises (t304 t299 t146 t235 t301 t164 t171 t196 t198 t282))
-ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0
-unsat
-(assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! (rec_join$ ?v0) :named @p_10) ?v1) :named @p_19) (! (and (! (=> (! (and (! (= nil$ ?v0) :named @p_11) (! (= uu$ ?v1) :named @p_20)) :named @p_22) false) :named @p_24) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= @p_8 ?v0) :named @p_17) (! (= @p_1 ?v1) :named @p_27)) :named @p_29) false) :named @p_31)) :named @p_25) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= @p_9 ?v0) :named @p_18) (! (= @p_7 ?v1) :named @p_35)) :named @p_37) false) :named @p_39)) :named @p_33)) :named @p_41)) :named @p_43)) :named @p_45) false) :named @p_47)) :named @p_14) (! (forall ((?v0 B_list$)) (! (=> (! (and (! (= @p_10 @p_10) :named @p_15) (! (and (! (=> (! (and @p_11 (! (= uu$ @p_10) :named @p_21)) :named @p_23) false) :named @p_16) (! (and (! (forall ((?v1 B$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 nil$) :named @p_162)) :named @p_163) (! (= @p_10 (! (coeff_cube_to_path$ ?v1) :named @p_12)) :named @p_165)) :named @p_166) false) :named @p_167)) :named @p_161) (! (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55))
-(anchor :step t2 :args (?v0 (:= ?v1 @p_10)))
-(step t2.t1 (cl @p_19) :rule refl)
-(step t2.t2 (cl (= @p_19 @p_15)) :rule cong :premises (t2.t1))
-(step t2.t3 (cl @p_19) :rule refl)
-(step t2.t4 (cl (= @p_20 @p_21)) :rule cong :premises (t2.t3))
-(step t2.t5 (cl (= @p_22 @p_23)) :rule cong :premises (t2.t4))
-(step t2.t6 (cl (= @p_24 @p_16)) :rule cong :premises (t2.t5))
-(anchor :step t2.t7 :args (?v2))
-(step t2.t7.t1 (cl @p_19) :rule refl)
-(step t2.t7.t2 (cl (= @p_27 (! (= @p_1 @p_10) :named @p_28))) :rule cong :premises (t2.t7.t1))
-(step t2.t7.t3 (cl (= @p_29 (! (and @p_17 @p_28) :named @p_30))) :rule cong :premises (t2.t7.t2))
-(step t2.t7.t4 (cl (= @p_31 (! (=> @p_30 false) :named @p_32))) :rule cong :premises (t2.t7.t3))
-(step t2.t7 (cl (= @p_25 (! (forall ((?v2 B$)) @p_32) :named @p_26))) :rule bind)
-(anchor :step t2.t8 :args (?v2 ?v3 ?v4))
-(step t2.t8.t1 (cl @p_19) :rule refl)
-(step t2.t8.t2 (cl (= @p_35 (! (= @p_7 @p_10) :named @p_36))) :rule cong :premises (t2.t8.t1))
-(step t2.t8.t3 (cl (= @p_37 (! (and @p_18 @p_36) :named @p_38))) :rule cong :premises (t2.t8.t2))
-(step t2.t8.t4 (cl (= @p_39 (! (=> @p_38 false) :named @p_40))) :rule cong :premises (t2.t8.t3))
-(step t2.t8 (cl (= @p_33 (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) @p_40) :named @p_34))) :rule bind)
-(step t2.t9 (cl (= @p_41 (! (and @p_26 @p_34) :named @p_42))) :rule cong :premises (t2.t7 t2.t8))
-(step t2.t10 (cl (= @p_43 (! (and @p_16 @p_42) :named @p_44))) :rule cong :premises (t2.t6 t2.t9))
-(step t2.t11 (cl (= @p_45 (! (and @p_15 @p_44) :named @p_46))) :rule cong :premises (t2.t2 t2.t10))
-(step t2.t12 (cl (= @p_47 (! (=> @p_46 false) :named @p_48))) :rule cong :premises (t2.t11))
-(step t2 (cl (= @p_14 (! (forall ((?v0 B_list$)) @p_48) :named @p_50))) :rule onepoint)
-(step t3 (cl (= @p_49 (! (= @p_50 @p_51) :named @p_54))) :rule cong :premises (t2))
-(step t4 (cl (= @p_52 (! (=> @p_53 @p_54) :named @p_56))) :rule cong :premises (t3))
-(step t5 (cl (! (= @p_55 (! (not @p_56) :named @p_58)) :named @p_57)) :rule cong :premises (t4))
-(step t6 (cl (! (not @p_57) :named @p_60) (! (not @p_55) :named @p_59) @p_58) :rule equiv_pos2)
-(step t7 (cl (not @p_59) @p_52) :rule not_not)
-(step t8 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t7 t6))
-(step t9 (cl @p_58) :rule th_resolution :premises (a1 t5 t8))
-(anchor :step t10 :args ((:= ?v0 veriT_vr2) (:= ?v1 veriT_vr3)))
-(step t10.t1 (cl (! (= ?v1 veriT_vr3) :named @p_70)) :rule refl)
-(step t10.t2 (cl (! (= @p_3 (! (rec_join$ veriT_vr3) :named @p_63)) :named @p_111)) :rule cong :premises (t10.t1))
-(step t10.t3 (cl (! (= ?v0 veriT_vr2) :named @p_71)) :rule refl)
-(step t10.t4 (cl (= @p_68 (! (= veriT_vr2 @p_63) :named @p_69))) :rule cong :premises (t10.t2 t10.t3))
-(step t10.t5 (cl @p_70) :rule refl)
-(step t10.t6 (cl (! (= @p_4 (! (= nil$ veriT_vr3) :named @p_64)) :named @p_114)) :rule cong :premises (t10.t5))
-(step t10.t7 (cl @p_71) :rule refl)
-(step t10.t8 (cl (= @p_72 (! (= uu$ veriT_vr2) :named @p_73))) :rule cong :premises (t10.t7))
-(step t10.t9 (cl (= @p_74 (! (and @p_64 @p_73) :named @p_75))) :rule cong :premises (t10.t6 t10.t8))
-(step t10.t10 (cl (= @p_76 (! (=> @p_75 false) :named @p_77))) :rule cong :premises (t10.t9))
-(anchor :step t10.t11 :args ((:= ?v2 veriT_vr4)))
-(step t10.t11.t1 (cl @p_70) :rule refl)
-(step t10.t11.t2 (cl (! (= ?v2 veriT_vr4) :named @p_81)) :rule refl)
-(step t10.t11.t3 (cl (! (= @p_8 (! (cons$ veriT_vr4 nil$) :named @p_80)) :named @p_123)) :rule cong :premises (t10.t11.t2))
-(step t10.t11.t4 (cl (! (= @p_5 (! (= veriT_vr3 @p_80) :named @p_65)) :named @p_124)) :rule cong :premises (t10.t11.t1 t10.t11.t3))
-(step t10.t11.t5 (cl @p_71) :rule refl)
-(step t10.t11.t6 (cl @p_81) :rule refl)
-(step t10.t11.t7 (cl (! (= @p_1 (! (coeff_cube_to_path$ veriT_vr4) :named @p_61)) :named @p_91)) :rule cong :premises (t10.t11.t6))
-(step t10.t11.t8 (cl (= @p_82 (! (= veriT_vr2 @p_61) :named @p_83))) :rule cong :premises (t10.t11.t5 t10.t11.t7))
-(step t10.t11.t9 (cl (= @p_84 (! (and @p_65 @p_83) :named @p_85))) :rule cong :premises (t10.t11.t4 t10.t11.t8))
-(step t10.t11.t10 (cl (= @p_86 (! (=> @p_85 false) :named @p_87))) :rule cong :premises (t10.t11.t9))
-(step t10.t11 (cl (= @p_78 (! (forall ((veriT_vr4 B$)) @p_87) :named @p_79))) :rule bind)
-(anchor :step t10.t12 :args ((:= ?v2 veriT_vr4) (:= ?v3 veriT_vr5) (:= ?v4 veriT_vr6)))
-(step t10.t12.t1 (cl @p_70) :rule refl)
-(step t10.t12.t2 (cl @p_81) :rule refl)
-(step t10.t12.t3 (cl (! (= ?v3 veriT_vr5) :named @p_92)) :rule refl)
-(step t10.t12.t4 (cl (! (= ?v4 veriT_vr6) :named @p_93)) :rule refl)
-(step t10.t12.t5 (cl (! (= @p_2 (! (cons$ veriT_vr5 veriT_vr6) :named @p_62)) :named @p_94)) :rule cong :premises (t10.t12.t3 t10.t12.t4))
-(step t10.t12.t6 (cl (! (= @p_9 (! (cons$ veriT_vr4 @p_62) :named @p_90)) :named @p_133)) :rule cong :premises (t10.t12.t2 t10.t12.t5))
-(step t10.t12.t7 (cl (! (= @p_6 (! (= veriT_vr3 @p_90) :named @p_66)) :named @p_134)) :rule cong :premises (t10.t12.t1 t10.t12.t6))
-(step t10.t12.t8 (cl @p_71) :rule refl)
-(step t10.t12.t9 (cl @p_81) :rule refl)
-(step t10.t12.t10 (cl @p_91) :rule cong :premises (t10.t12.t9))
-(step t10.t12.t11 (cl @p_92) :rule refl)
-(step t10.t12.t12 (cl @p_93) :rule refl)
-(step t10.t12.t13 (cl @p_94) :rule cong :premises (t10.t12.t11 t10.t12.t12))
-(step t10.t12.t14 (cl (! (= @p_95 (! (rec_join$ @p_62) :named @p_96)) :named @p_135)) :rule cong :premises (t10.t12.t13))
-(step t10.t12.t15 (cl (! (= @p_7 (! (joinpaths$ @p_61 @p_96) :named @p_67)) :named @p_136)) :rule cong :premises (t10.t12.t10 t10.t12.t14))
-(step t10.t12.t16 (cl (= @p_97 (! (= veriT_vr2 @p_67) :named @p_98))) :rule cong :premises (t10.t12.t8 t10.t12.t15))
-(step t10.t12.t17 (cl (= @p_99 (! (and @p_66 @p_98) :named @p_100))) :rule cong :premises (t10.t12.t7 t10.t12.t16))
-(step t10.t12.t18 (cl (= @p_101 (! (=> @p_100 false) :named @p_102))) :rule cong :premises (t10.t12.t17))
-(step t10.t12 (cl (= @p_88 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_102) :named @p_89))) :rule bind)
-(step t10.t13 (cl (= @p_103 (! (and @p_79 @p_89) :named @p_104))) :rule cong :premises (t10.t11 t10.t12))
-(step t10.t14 (cl (= @p_105 (! (and @p_77 @p_104) :named @p_106))) :rule cong :premises (t10.t10 t10.t13))
-(step t10.t15 (cl (= @p_107 (! (and @p_69 @p_106) :named @p_108))) :rule cong :premises (t10.t4 t10.t14))
-(step t10.t16 (cl (= @p_109 (! (=> @p_108 false) :named @p_110))) :rule cong :premises (t10.t15))
-(step t10.t17 (cl @p_70) :rule refl)
-(step t10.t18 (cl @p_111) :rule cong :premises (t10.t17))
-(step t10.t19 (cl @p_70) :rule refl)
-(step t10.t20 (cl @p_111) :rule cong :premises (t10.t19))
-(step t10.t21 (cl (= @p_112 (! (= @p_63 @p_63) :named @p_113))) :rule cong :premises (t10.t18 t10.t20))
-(step t10.t22 (cl @p_70) :rule refl)
-(step t10.t23 (cl @p_114) :rule cong :premises (t10.t22))
-(step t10.t24 (cl @p_70) :rule refl)
-(step t10.t25 (cl @p_111) :rule cong :premises (t10.t24))
-(step t10.t26 (cl (= @p_115 (! (= uu$ @p_63) :named @p_116))) :rule cong :premises (t10.t25))
-(step t10.t27 (cl (= @p_117 (! (and @p_64 @p_116) :named @p_118))) :rule cong :premises (t10.t23 t10.t26))
-(step t10.t28 (cl (= @p_119 (! (=> @p_118 false) :named @p_120))) :rule cong :premises (t10.t27))
-(anchor :step t10.t29 :args ((:= ?v2 veriT_vr4)))
-(step t10.t29.t1 (cl @p_70) :rule refl)
-(step t10.t29.t2 (cl @p_81) :rule refl)
-(step t10.t29.t3 (cl @p_123) :rule cong :premises (t10.t29.t2))
-(step t10.t29.t4 (cl @p_124) :rule cong :premises (t10.t29.t1 t10.t29.t3))
-(step t10.t29.t5 (cl @p_70) :rule refl)
-(step t10.t29.t6 (cl @p_111) :rule cong :premises (t10.t29.t5))
-(step t10.t29.t7 (cl @p_81) :rule refl)
-(step t10.t29.t8 (cl @p_91) :rule cong :premises (t10.t29.t7))
-(step t10.t29.t9 (cl (= @p_125 (! (= @p_63 @p_61) :named @p_126))) :rule cong :premises (t10.t29.t6 t10.t29.t8))
-(step t10.t29.t10 (cl (= @p_127 (! (and @p_65 @p_126) :named @p_128))) :rule cong :premises (t10.t29.t4 t10.t29.t9))
-(step t10.t29.t11 (cl (= @p_129 (! (=> @p_128 false) :named @p_130))) :rule cong :premises (t10.t29.t10))
-(step t10.t29 (cl (= @p_121 (! (forall ((veriT_vr4 B$)) @p_130) :named @p_122))) :rule bind)
-(anchor :step t10.t30 :args ((:= ?v2 veriT_vr4) (:= ?v3 veriT_vr5) (:= ?v4 veriT_vr6)))
-(step t10.t30.t1 (cl @p_70) :rule refl)
-(step t10.t30.t2 (cl @p_81) :rule refl)
-(step t10.t30.t3 (cl @p_92) :rule refl)
-(step t10.t30.t4 (cl @p_93) :rule refl)
-(step t10.t30.t5 (cl @p_94) :rule cong :premises (t10.t30.t3 t10.t30.t4))
-(step t10.t30.t6 (cl @p_133) :rule cong :premises (t10.t30.t2 t10.t30.t5))
-(step t10.t30.t7 (cl @p_134) :rule cong :premises (t10.t30.t1 t10.t30.t6))
-(step t10.t30.t8 (cl @p_70) :rule refl)
-(step t10.t30.t9 (cl @p_111) :rule cong :premises (t10.t30.t8))
-(step t10.t30.t10 (cl @p_81) :rule refl)
-(step t10.t30.t11 (cl @p_91) :rule cong :premises (t10.t30.t10))
-(step t10.t30.t12 (cl @p_92) :rule refl)
-(step t10.t30.t13 (cl @p_93) :rule refl)
-(step t10.t30.t14 (cl @p_94) :rule cong :premises (t10.t30.t12 t10.t30.t13))
-(step t10.t30.t15 (cl @p_135) :rule cong :premises (t10.t30.t14))
-(step t10.t30.t16 (cl @p_136) :rule cong :premises (t10.t30.t11 t10.t30.t15))
-(step t10.t30.t17 (cl (= @p_137 (! (= @p_63 @p_67) :named @p_138))) :rule cong :premises (t10.t30.t9 t10.t30.t16))
-(step t10.t30.t18 (cl (= @p_139 (! (and @p_66 @p_138) :named @p_140))) :rule cong :premises (t10.t30.t7 t10.t30.t17))
-(step t10.t30.t19 (cl (= @p_141 (! (=> @p_140 false) :named @p_142))) :rule cong :premises (t10.t30.t18))
-(step t10.t30 (cl (= @p_131 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_142) :named @p_132))) :rule bind)
-(step t10.t31 (cl (= @p_143 (! (and @p_122 @p_132) :named @p_144))) :rule cong :premises (t10.t29 t10.t30))
-(step t10.t32 (cl (= @p_145 (! (and @p_120 @p_144) :named @p_146))) :rule cong :premises (t10.t28 t10.t31))
-(step t10.t33 (cl (= @p_147 (! (and @p_113 @p_146) :named @p_148))) :rule cong :premises (t10.t21 t10.t32))
-(step t10.t34 (cl (= @p_149 (! (=> @p_148 false) :named @p_150))) :rule cong :premises (t10.t33))
-(step t10.t35 (cl (= @p_151 (! (= @p_110 @p_150) :named @p_152))) :rule cong :premises (t10.t16 t10.t34))
-(step t10 (cl (= @p_53 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_152) :named @p_184))) :rule bind)
-(anchor :step t11 :args ((:= ?v0 veriT_vr3)))
-(step t11.t1 (cl (! (= ?v0 veriT_vr3) :named @p_153)) :rule refl)
-(step t11.t2 (cl (! (= @p_10 @p_63) :named @p_154)) :rule cong :premises (t11.t1))
-(step t11.t3 (cl @p_153) :rule refl)
-(step t11.t4 (cl @p_154) :rule cong :premises (t11.t3))
-(step t11.t5 (cl (! (= @p_15 @p_113) :named @p_156)) :rule cong :premises (t11.t2 t11.t4))
-(step t11.t6 (cl @p_153) :rule refl)
-(step t11.t7 (cl (! (= @p_11 @p_64) :named @p_157)) :rule cong :premises (t11.t6))
-(step t11.t8 (cl @p_153) :rule refl)
-(step t11.t9 (cl @p_154) :rule cong :premises (t11.t8))
-(step t11.t10 (cl (! (= @p_21 @p_116) :named @p_158)) :rule cong :premises (t11.t9))
-(step t11.t11 (cl (! (= @p_23 @p_118) :named @p_159)) :rule cong :premises (t11.t7 t11.t10))
-(step t11.t12 (cl (! (= @p_16 @p_120) :named @p_160)) :rule cong :premises (t11.t11))
-(anchor :step t11.t13 :args ((:= ?v2 veriT_vr4)))
-(step t11.t13.t1 (cl @p_81) :rule refl)
-(step t11.t13.t2 (cl @p_123) :rule cong :premises (t11.t13.t1))
-(step t11.t13.t3 (cl @p_153) :rule refl)
-(step t11.t13.t4 (cl (= @p_17 @p_65)) :rule cong :premises (t11.t13.t2 t11.t13.t3))
-(step t11.t13.t5 (cl @p_81) :rule refl)
-(step t11.t13.t6 (cl @p_91) :rule cong :premises (t11.t13.t5))
-(step t11.t13.t7 (cl @p_153) :rule refl)
-(step t11.t13.t8 (cl @p_154) :rule cong :premises (t11.t13.t7))
-(step t11.t13.t9 (cl (= @p_28 @p_126)) :rule cong :premises (t11.t13.t6 t11.t13.t8))
-(step t11.t13.t10 (cl (= @p_30 @p_128)) :rule cong :premises (t11.t13.t4 t11.t13.t9))
-(step t11.t13.t11 (cl (= @p_32 @p_130)) :rule cong :premises (t11.t13.t10))
-(step t11.t13 (cl (= @p_26 @p_122)) :rule bind)
-(anchor :step t11.t14 :args ((:= ?v2 veriT_vr4) (:= ?v3 veriT_vr5) (:= ?v4 veriT_vr6)))
-(step t11.t14.t1 (cl @p_81) :rule refl)
-(step t11.t14.t2 (cl @p_92) :rule refl)
-(step t11.t14.t3 (cl @p_93) :rule refl)
-(step t11.t14.t4 (cl @p_94) :rule cong :premises (t11.t14.t2 t11.t14.t3))
-(step t11.t14.t5 (cl @p_133) :rule cong :premises (t11.t14.t1 t11.t14.t4))
-(step t11.t14.t6 (cl @p_153) :rule refl)
-(step t11.t14.t7 (cl (= @p_18 @p_66)) :rule cong :premises (t11.t14.t5 t11.t14.t6))
-(step t11.t14.t8 (cl @p_81) :rule refl)
-(step t11.t14.t9 (cl @p_91) :rule cong :premises (t11.t14.t8))
-(step t11.t14.t10 (cl @p_92) :rule refl)
-(step t11.t14.t11 (cl @p_93) :rule refl)
-(step t11.t14.t12 (cl @p_94) :rule cong :premises (t11.t14.t10 t11.t14.t11))
-(step t11.t14.t13 (cl @p_135) :rule cong :premises (t11.t14.t12))
-(step t11.t14.t14 (cl @p_136) :rule cong :premises (t11.t14.t9 t11.t14.t13))
-(step t11.t14.t15 (cl @p_153) :rule refl)
-(step t11.t14.t16 (cl @p_154) :rule cong :premises (t11.t14.t15))
-(step t11.t14.t17 (cl (= @p_36 @p_138)) :rule cong :premises (t11.t14.t14 t11.t14.t16))
-(step t11.t14.t18 (cl (= @p_38 @p_140)) :rule cong :premises (t11.t14.t7 t11.t14.t17))
-(step t11.t14.t19 (cl (= @p_40 @p_142)) :rule cong :premises (t11.t14.t18))
-(step t11.t14 (cl (= @p_34 @p_132)) :rule bind)
-(step t11.t15 (cl (= @p_42 @p_144)) :rule cong :premises (t11.t13 t11.t14))
-(step t11.t16 (cl (= @p_44 @p_146)) :rule cong :premises (t11.t12 t11.t15))
-(step t11.t17 (cl (= @p_46 @p_148)) :rule cong :premises (t11.t5 t11.t16))
-(step t11.t18 (cl (= @p_48 @p_150)) :rule cong :premises (t11.t17))
-(step t11 (cl (= @p_50 (! (forall ((veriT_vr3 B_list$)) @p_150) :named @p_155))) :rule bind)
-(anchor :step t12 :args ((:= ?v0 veriT_vr3)))
-(step t12.t1 (cl @p_153) :rule refl)
-(step t12.t2 (cl @p_154) :rule cong :premises (t12.t1))
-(step t12.t3 (cl @p_153) :rule refl)
-(step t12.t4 (cl @p_154) :rule cong :premises (t12.t3))
-(step t12.t5 (cl @p_156) :rule cong :premises (t12.t2 t12.t4))
-(step t12.t6 (cl @p_153) :rule refl)
-(step t12.t7 (cl @p_157) :rule cong :premises (t12.t6))
-(step t12.t8 (cl @p_153) :rule refl)
-(step t12.t9 (cl @p_154) :rule cong :premises (t12.t8))
-(step t12.t10 (cl @p_158) :rule cong :premises (t12.t9))
-(step t12.t11 (cl @p_159) :rule cong :premises (t12.t7 t12.t10))
-(step t12.t12 (cl @p_160) :rule cong :premises (t12.t11))
-(anchor :step t12.t13 :args ((:= ?v1 veriT_vr4)))
-(step t12.t13.t1 (cl @p_153) :rule refl)
-(step t12.t13.t2 (cl (! (= ?v1 veriT_vr4) :named @p_164)) :rule refl)
-(step t12.t13.t3 (cl (= @p_162 @p_80)) :rule cong :premises (t12.t13.t2))
-(step t12.t13.t4 (cl (= @p_163 @p_65)) :rule cong :premises (t12.t13.t1 t12.t13.t3))
-(step t12.t13.t5 (cl @p_153) :rule refl)
-(step t12.t13.t6 (cl @p_154) :rule cong :premises (t12.t13.t5))
-(step t12.t13.t7 (cl @p_164) :rule refl)
-(step t12.t13.t8 (cl (! (= @p_12 @p_61) :named @p_171)) :rule cong :premises (t12.t13.t7))
-(step t12.t13.t9 (cl (= @p_165 @p_126)) :rule cong :premises (t12.t13.t6 t12.t13.t8))
-(step t12.t13.t10 (cl (= @p_166 @p_128)) :rule cong :premises (t12.t13.t4 t12.t13.t9))
-(step t12.t13.t11 (cl (= @p_167 @p_130)) :rule cong :premises (t12.t13.t10))
-(step t12.t13 (cl (= @p_161 @p_122)) :rule bind)
-(anchor :step t12.t14 :args ((:= ?v1 veriT_vr4) (:= ?v2 veriT_vr5) (:= ?v3 veriT_vr6)))
-(step t12.t14.t1 (cl @p_153) :rule refl)
-(step t12.t14.t2 (cl @p_164) :rule refl)
-(step t12.t14.t3 (cl (! (= ?v2 veriT_vr5) :named @p_172)) :rule refl)
-(step t12.t14.t4 (cl (! (= ?v3 veriT_vr6) :named @p_173)) :rule refl)
-(step t12.t14.t5 (cl (! (= @p_13 @p_62) :named @p_174)) :rule cong :premises (t12.t14.t3 t12.t14.t4))
-(step t12.t14.t6 (cl (= @p_169 @p_90)) :rule cong :premises (t12.t14.t2 t12.t14.t5))
-(step t12.t14.t7 (cl (= @p_170 @p_66)) :rule cong :premises (t12.t14.t1 t12.t14.t6))
-(step t12.t14.t8 (cl @p_153) :rule refl)
-(step t12.t14.t9 (cl @p_154) :rule cong :premises (t12.t14.t8))
-(step t12.t14.t10 (cl @p_164) :rule refl)
-(step t12.t14.t11 (cl @p_171) :rule cong :premises (t12.t14.t10))
-(step t12.t14.t12 (cl @p_172) :rule refl)
-(step t12.t14.t13 (cl @p_173) :rule refl)
-(step t12.t14.t14 (cl @p_174) :rule cong :premises (t12.t14.t12 t12.t14.t13))
-(step t12.t14.t15 (cl (= @p_175 @p_96)) :rule cong :premises (t12.t14.t14))
-(step t12.t14.t16 (cl (= @p_176 @p_67)) :rule cong :premises (t12.t14.t11 t12.t14.t15))
-(step t12.t14.t17 (cl (= @p_177 @p_138)) :rule cong :premises (t12.t14.t9 t12.t14.t16))
-(step t12.t14.t18 (cl (= @p_178 @p_140)) :rule cong :premises (t12.t14.t7 t12.t14.t17))
-(step t12.t14.t19 (cl (= @p_179 @p_142)) :rule cong :premises (t12.t14.t18))
-(step t12.t14 (cl (= @p_168 @p_132)) :rule bind)
-(step t12.t15 (cl (= @p_180 @p_144)) :rule cong :premises (t12.t13 t12.t14))
-(step t12.t16 (cl (= @p_181 @p_146)) :rule cong :premises (t12.t12 t12.t15))
-(step t12.t17 (cl (= @p_182 @p_148)) :rule cong :premises (t12.t5 t12.t16))
-(step t12.t18 (cl (= @p_183 @p_150)) :rule cong :premises (t12.t17))
-(step t12 (cl (= @p_51 @p_155)) :rule bind)
-(step t13 (cl (= @p_54 (! (= @p_155 @p_155) :named @p_185))) :rule cong :premises (t11 t12))
-(step t14 (cl (= @p_56 (! (=> @p_184 @p_185) :named @p_186))) :rule cong :premises (t10 t13))
-(step t15 (cl (! (= @p_58 (! (not @p_186) :named @p_188)) :named @p_187)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_187) :named @p_190) (! (not @p_58) :named @p_189) @p_188) :rule equiv_pos2)
-(step t17 (cl (not @p_189) @p_56) :rule not_not)
-(step t18 (cl @p_190 @p_56 @p_188) :rule th_resolution :premises (t17 t16))
-(step t19 (cl @p_188) :rule th_resolution :premises (t9 t15 t18))
-(step t20 (cl (! (= @p_188 (! (and @p_184 (! (not @p_185) :named @p_203)) :named @p_192)) :named @p_191)) :rule bool_simplify)
-(step t21 (cl (! (not @p_191) :named @p_194) (! (not @p_188) :named @p_193) @p_192) :rule equiv_pos2)
-(step t22 (cl (not @p_193) @p_186) :rule not_not)
-(step t23 (cl @p_194 @p_186 @p_192) :rule th_resolution :premises (t22 t21))
-(step t24 (cl @p_192) :rule th_resolution :premises (t19 t20 t23))
-(anchor :step t25 :args (veriT_vr2 veriT_vr3))
-(step t25.t1 (cl (= @p_108 (! (and @p_69 @p_77 @p_79 @p_89) :named @p_195))) :rule ac_simp)
-(step t25.t2 (cl (= @p_110 (! (=> @p_195 false) :named @p_196))) :rule cong :premises (t25.t1))
-(step t25.t3 (cl (! (= @p_148 (! (and @p_113 @p_120 @p_122 @p_132) :named @p_197)) :named @p_200)) :rule ac_simp)
-(step t25.t4 (cl (! (= @p_150 (! (=> @p_197 false) :named @p_198)) :named @p_201)) :rule cong :premises (t25.t3))
-(step t25.t5 (cl (= @p_152 (! (= @p_196 @p_198) :named @p_199))) :rule cong :premises (t25.t2 t25.t4))
-(step t25 (cl (= @p_184 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_199) :named @p_205))) :rule bind)
-(anchor :step t26 :args (veriT_vr3))
-(step t26.t1 (cl @p_200) :rule ac_simp)
-(step t26.t2 (cl @p_201) :rule cong :premises (t26.t1))
-(step t26 (cl (= @p_155 (! (forall ((veriT_vr3 B_list$)) @p_198) :named @p_202))) :rule bind)
-(step t27 (cl (= @p_185 (! (= @p_202 @p_202) :named @p_204))) :rule cong :premises (t26 t26))
-(step t28 (cl (= @p_203 (! (not @p_204) :named @p_206))) :rule cong :premises (t27))
-(step t29 (cl (! (= @p_192 (! (and @p_205 @p_206) :named @p_208)) :named @p_207)) :rule ac_simp :premises (t25 t28))
-(step t30 (cl (not @p_207) (not @p_192) @p_208) :rule equiv_pos2)
-(step t31 (cl @p_208) :rule th_resolution :premises (t24 t29 t30))
-(anchor :step t32 :args (veriT_vr2 veriT_vr3))
-(step t32.t1 (cl (= @p_77 (! (not @p_75) :named @p_209))) :rule implies_simplify)
-(anchor :step t32.t2 :args (veriT_vr4))
-(step t32.t2.t1 (cl (= @p_87 (! (not @p_85) :named @p_211))) :rule implies_simplify)
-(step t32.t2 (cl (= @p_79 (! (forall ((veriT_vr4 B$)) @p_211) :named @p_210))) :rule bind)
-(anchor :step t32.t3 :args (veriT_vr4 veriT_vr5 veriT_vr6))
-(step t32.t3.t1 (cl (= @p_102 (! (not @p_100) :named @p_213))) :rule implies_simplify)
-(step t32.t3 (cl (= @p_89 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_213) :named @p_212))) :rule bind)
-(step t32.t4 (cl (= @p_195 (! (and @p_69 @p_209 @p_210 @p_212) :named @p_214))) :rule cong :premises (t32.t1 t32.t2 t32.t3))
-(step t32.t5 (cl (= @p_196 (! (=> @p_214 false) :named @p_215))) :rule cong :premises (t32.t4))
-(step t32.t6 (cl (= @p_215 (! (not @p_214) :named @p_216))) :rule implies_simplify)
-(step t32.t7 (cl (= @p_196 @p_216)) :rule trans :premises (t32.t5 t32.t6))
-(step t32.t8 (cl (! (= @p_113 true) :named @p_228)) :rule eq_simplify)
-(step t32.t9 (cl (! (= @p_120 (! (not @p_118) :named @p_217)) :named @p_229)) :rule implies_simplify)
-(anchor :step t32.t10 :args (veriT_vr4))
-(step t32.t10.t1 (cl (! (= @p_130 (! (not @p_128) :named @p_219)) :named @p_231)) :rule implies_simplify)
-(step t32.t10 (cl (! (= @p_122 (! (forall ((veriT_vr4 B$)) @p_219) :named @p_218)) :named @p_230)) :rule bind)
-(anchor :step t32.t11 :args (veriT_vr4 veriT_vr5 veriT_vr6))
-(step t32.t11.t1 (cl (! (= @p_142 (! (not @p_140) :named @p_221)) :named @p_233)) :rule implies_simplify)
-(step t32.t11 (cl (! (= @p_132 (! (forall ((veriT_vr4 B$) (veriT_vr5 B$) (veriT_vr6 B_list$)) @p_221) :named @p_220)) :named @p_232)) :rule bind)
-(step t32.t12 (cl (! (= @p_197 (! (and true @p_217 @p_218 @p_220) :named @p_222)) :named @p_234)) :rule cong :premises (t32.t8 t32.t9 t32.t10 t32.t11))
-(step t32.t13 (cl (! (= @p_222 (! (and @p_217 @p_218 @p_220) :named @p_223)) :named @p_235)) :rule and_simplify)
-(step t32.t14 (cl (! (= @p_197 @p_223) :named @p_236)) :rule trans :premises (t32.t12 t32.t13))
-(step t32.t15 (cl (! (= @p_198 (! (=> @p_223 false) :named @p_224)) :named @p_237)) :rule cong :premises (t32.t14))
-(step t32.t16 (cl (! (= @p_224 (! (not @p_223) :named @p_225)) :named @p_238)) :rule implies_simplify)
-(step t32.t17 (cl (! (= @p_198 @p_225) :named @p_239)) :rule trans :premises (t32.t15 t32.t16))
-(step t32.t18 (cl (= @p_199 (! (= @p_216 @p_225) :named @p_226))) :rule cong :premises (t32.t7 t32.t17))
-(step t32.t19 (cl (= @p_226 (! (= @p_214 @p_223) :named @p_227))) :rule equiv_simplify)
-(step t32.t20 (cl (= @p_199 @p_227)) :rule trans :premises (t32.t18 t32.t19))
-(step t32 (cl (= @p_205 (! (forall ((veriT_vr2 Real_a_fun$) (veriT_vr3 B_list$)) @p_227) :named @p_243))) :rule bind)
-(anchor :step t33 :args (veriT_vr3))
-(step t33.t1 (cl @p_228) :rule eq_simplify)
-(step t33.t2 (cl @p_229) :rule implies_simplify)
-(anchor :step t33.t3 :args (veriT_vr4))
-(step t33.t3.t1 (cl @p_231) :rule implies_simplify)
-(step t33.t3 (cl @p_230) :rule bind)
-(anchor :step t33.t4 :args (veriT_vr4 veriT_vr5 veriT_vr6))
-(step t33.t4.t1 (cl @p_233) :rule implies_simplify)
-(step t33.t4 (cl @p_232) :rule bind)
-(step t33.t5 (cl @p_234) :rule cong :premises (t33.t1 t33.t2 t33.t3 t33.t4))
-(step t33.t6 (cl @p_235) :rule and_simplify)
-(step t33.t7 (cl @p_236) :rule trans :premises (t33.t5 t33.t6))
-(step t33.t8 (cl @p_237) :rule cong :premises (t33.t7))
-(step t33.t9 (cl @p_238) :rule implies_simplify)
-(step t33.t10 (cl @p_239) :rule trans :premises (t33.t8 t33.t9))
-(step t33 (cl (= @p_202 (! (forall ((veriT_vr3 B_list$)) @p_225) :named @p_240))) :rule bind)
-(step t34 (cl (= @p_204 (! (= @p_240 @p_240) :named @p_241))) :rule cong :premises (t33 t33))
-(step t35 (cl (= @p_241 true)) :rule equiv_simplify)
-(step t36 (cl (= @p_204 true)) :rule trans :premises (t34 t35))
-(step t37 (cl (= @p_206 (! (not true) :named @p_242))) :rule cong :premises (t36))
-(step t38 (cl (= @p_242 false)) :rule not_simplify)
-(step t39 (cl (= @p_206 false)) :rule trans :premises (t37 t38))
-(step t40 (cl (= @p_208 (! (and @p_243 false) :named @p_244))) :rule cong :premises (t32 t39))
-(step t41 (cl (= @p_244 false)) :rule and_simplify)
-(step t42 (cl (! (= @p_208 false) :named @p_245)) :rule trans :premises (t40 t41))
-(step t43 (cl (not @p_245) (not @p_208) false) :rule equiv_pos2)
-(step t44 (cl false) :rule th_resolution :premises (t31 t42 t43))
-(step t45 (cl (not false)) :rule false)
-(step t46 (cl) :rule resolution :premises (t44 t45))
-2da165964e2359aec5a20e66969cc8494006e9ba 36 0
-unsat
-(assume a4 (! (forall ((?v0 Int)) (! (and (! (pred$e ?v0) :named @p_4) (! (or (! (pred$d (! (cons$d ?v0 nil$d) :named @p_7)) :named @p_1) (! (not @p_1) :named @p_11)) :named @p_13)) :named @p_15)) :named @p_2))
-(assume a5 (not (! (pred$e 1) :named @p_26)))
-(anchor :step t3 :args ((:= ?v0 veriT_vr8)))
-(step t3.t1 (cl (! (= ?v0 veriT_vr8) :named @p_6)) :rule refl)
-(step t3.t2 (cl (= @p_4 (! (pred$e veriT_vr8) :named @p_5))) :rule cong :premises (t3.t1))
-(step t3.t3 (cl @p_6) :rule refl)
-(step t3.t4 (cl (! (= @p_7 (! (cons$d veriT_vr8 nil$d) :named @p_8)) :named @p_9)) :rule cong :premises (t3.t3))
-(step t3.t5 (cl (! (= @p_1 (! (pred$d @p_8) :named @p_3)) :named @p_10)) :rule cong :premises (t3.t4))
-(step t3.t6 (cl @p_6) :rule refl)
-(step t3.t7 (cl @p_9) :rule cong :premises (t3.t6))
-(step t3.t8 (cl @p_10) :rule cong :premises (t3.t7))
-(step t3.t9 (cl (= @p_11 (! (not @p_3) :named @p_12))) :rule cong :premises (t3.t8))
-(step t3.t10 (cl (= @p_13 (! (or @p_3 @p_12) :named @p_14))) :rule cong :premises (t3.t5 t3.t9))
-(step t3.t11 (cl (= @p_15 (! (and @p_5 @p_14) :named @p_16))) :rule cong :premises (t3.t2 t3.t10))
-(step t3 (cl (! (= @p_2 (! (forall ((veriT_vr8 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind)
-(step t4 (cl (not @p_17) (not @p_2) @p_18) :rule equiv_pos2)
-(step t5 (cl @p_18) :rule th_resolution :premises (a4 t3 t4))
-(anchor :step t6 :args (veriT_vr8))
-(step t6.t1 (cl (= @p_14 true)) :rule or_simplify)
-(step t6.t2 (cl (= @p_16 (! (and @p_5 true) :named @p_19))) :rule cong :premises (t6.t1))
-(step t6.t3 (cl (= @p_19 (! (and @p_5) :named @p_20))) :rule and_simplify)
-(step t6.t4 (cl (= @p_20 @p_5)) :rule and_simplify)
-(step t6.t5 (cl (= @p_16 @p_5)) :rule trans :premises (t6.t2 t6.t3 t6.t4))
-(step t6 (cl (! (= @p_18 (! (forall ((veriT_vr8 Int)) @p_5) :named @p_22)) :named @p_21)) :rule bind)
-(step t7 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2)
-(step t8 (cl @p_22) :rule th_resolution :premises (t5 t6 t7))
-(anchor :step t9 :args ((:= veriT_vr8 veriT_vr9)))
-(step t9.t1 (cl (= veriT_vr8 veriT_vr9)) :rule refl)
-(step t9.t2 (cl (= @p_5 (! (pred$e veriT_vr9) :named @p_23))) :rule cong :premises (t9.t1))
-(step t9 (cl (! (= @p_22 (! (forall ((veriT_vr9 Int)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
-(step t10 (cl (not @p_24) (not @p_22) @p_25) :rule equiv_pos2)
-(step t11 (cl @p_25) :rule th_resolution :premises (t8 t9 t10))
-(step t12 (cl (or (! (not @p_25) :named @p_27) @p_26)) :rule forall_inst :args ((:= veriT_vr9 1)))
-(step t13 (cl @p_27 @p_26) :rule or :premises (t12))
-(step t14 (cl) :rule resolution :premises (t13 t11 a5))
-f9bb7f97f8819ceceaefe0cdf934d0eda3431a5b 158 0
-unsat
-(assume a0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (some$ ?v0) :named @p_5)) :named @p_7) (! (g$a (! (cons$ ?v0 nil$) :named @p_10)) :named @p_12)) :named @p_14)) :named @p_4))
-(assume a1 (forall ((?v0 Bool)) (= (g$b (some$a ?v0)) (g$c (cons$a ?v0 nil$a)))))
-(assume a6 (! (forall ((?v0 Bool_list$)) (! (= (! (g$c ?v0) :named @p_27) (! (size$ ?v0) :named @p_30)) :named @p_32)) :named @p_26))
-(assume a7 (! (forall ((?v0 Int_list$)) (! (= (! (g$a ?v0) :named @p_43) (! (size$a ?v0) :named @p_46)) :named @p_48)) :named @p_42))
-(assume a12 (! (= zero$ (! (size$ nil$a) :named @p_118)) :named @p_143))
-(assume a13 (! (= zero$ (! (size$a nil$) :named @p_133)) :named @p_144))
-(assume a14 (forall ((?v0 Bool) (?v1 Bool_list$)) (= (size$ (cons$a ?v0 ?v1)) (! (plus$ (! (size$ ?v1) :named @p_60) (! (suc$ zero$) :named @p_1)) :named @p_3))))
-(assume a15 (! (forall ((?v0 Int) (?v1 Int_list$)) (! (= (! (size$a (! (cons$ ?v0 ?v1) :named @p_96)) :named @p_98) (! (plus$ (! (size$a ?v1) :named @p_101) @p_1) :named @p_103)) :named @p_105)) :named @p_95))
-(assume a16 (not (! (= (! (g$ (some$ 3)) :named @p_124) (! (g$b (some$a true)) :named @p_2)) :named @p_141)))
-(step t10 (cl (and (= (g$b (some$a false)) (g$c (! (cons$a false nil$a) :named @p_119))) (! (= @p_2 (! (g$c (! (cons$a true nil$a) :named @p_121)) :named @p_122)) :named @p_117))) :rule bfun_elim :premises (a1))
-(step t11 (cl (! (forall ((?v1 Bool_list$)) (! (and (! (= @p_3 (! (size$ (! (cons$a false ?v1) :named @p_63)) :named @p_65)) :named @p_67) (! (= @p_3 (! (size$ (! (cons$a true ?v1) :named @p_71)) :named @p_73)) :named @p_75)) :named @p_77)) :named @p_58)) :rule bfun_elim :premises (a14))
-(anchor :step t12 :args ((:= ?v0 veriT_vr0)))
-(step t12.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl)
-(step t12.t2 (cl (= @p_5 (! (some$ veriT_vr0) :named @p_6))) :rule cong :premises (t12.t1))
-(step t12.t3 (cl (= @p_7 (! (g$ @p_6) :named @p_8))) :rule cong :premises (t12.t2))
-(step t12.t4 (cl @p_9) :rule refl)
-(step t12.t5 (cl (= @p_10 (! (cons$ veriT_vr0 nil$) :named @p_11))) :rule cong :premises (t12.t4))
-(step t12.t6 (cl (= @p_12 (! (g$a @p_11) :named @p_13))) :rule cong :premises (t12.t5))
-(step t12.t7 (cl (= @p_14 (! (= @p_8 @p_13) :named @p_15))) :rule cong :premises (t12.t3 t12.t6))
-(step t12 (cl (! (= @p_4 (! (forall ((veriT_vr0 Int)) @p_15) :named @p_17)) :named @p_16)) :rule bind)
-(step t13 (cl (not @p_16) (not @p_4) @p_17) :rule equiv_pos2)
-(step t14 (cl @p_17) :rule th_resolution :premises (a0 t12 t13))
-(anchor :step t15 :args ((:= veriT_vr0 veriT_vr1)))
-(step t15.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_20)) :rule refl)
-(step t15.t2 (cl (= @p_6 (! (some$ veriT_vr1) :named @p_18))) :rule cong :premises (t15.t1))
-(step t15.t3 (cl (= @p_8 (! (g$ @p_18) :named @p_19))) :rule cong :premises (t15.t2))
-(step t15.t4 (cl @p_20) :rule refl)
-(step t15.t5 (cl (= @p_11 (! (cons$ veriT_vr1 nil$) :named @p_21))) :rule cong :premises (t15.t4))
-(step t15.t6 (cl (= @p_13 (! (g$a @p_21) :named @p_22))) :rule cong :premises (t15.t5))
-(step t15.t7 (cl (= @p_15 (! (= @p_19 @p_22) :named @p_23))) :rule cong :premises (t15.t3 t15.t6))
-(step t15 (cl (! (= @p_17 (! (forall ((veriT_vr1 Int)) @p_23) :named @p_25)) :named @p_24)) :rule bind)
-(step t16 (cl (not @p_24) (not @p_17) @p_25) :rule equiv_pos2)
-(step t17 (cl @p_25) :rule th_resolution :premises (t14 t15 t16))
-(anchor :step t18 :args ((:= ?v0 veriT_vr2)))
-(step t18.t1 (cl (! (= ?v0 veriT_vr2) :named @p_29)) :rule refl)
-(step t18.t2 (cl (= @p_27 (! (g$c veriT_vr2) :named @p_28))) :rule cong :premises (t18.t1))
-(step t18.t3 (cl @p_29) :rule refl)
-(step t18.t4 (cl (= @p_30 (! (size$ veriT_vr2) :named @p_31))) :rule cong :premises (t18.t3))
-(step t18.t5 (cl (= @p_32 (! (= @p_28 @p_31) :named @p_33))) :rule cong :premises (t18.t2 t18.t4))
-(step t18 (cl (! (= @p_26 (! (forall ((veriT_vr2 Bool_list$)) @p_33) :named @p_35)) :named @p_34)) :rule bind)
-(step t19 (cl (not @p_34) (not @p_26) @p_35) :rule equiv_pos2)
-(step t20 (cl @p_35) :rule th_resolution :premises (a6 t18 t19))
-(anchor :step t21 :args ((:= veriT_vr2 veriT_vr3)))
-(step t21.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_37)) :rule refl)
-(step t21.t2 (cl (= @p_28 (! (g$c veriT_vr3) :named @p_36))) :rule cong :premises (t21.t1))
-(step t21.t3 (cl @p_37) :rule refl)
-(step t21.t4 (cl (= @p_31 (! (size$ veriT_vr3) :named @p_38))) :rule cong :premises (t21.t3))
-(step t21.t5 (cl (= @p_33 (! (= @p_36 @p_38) :named @p_39))) :rule cong :premises (t21.t2 t21.t4))
-(step t21 (cl (! (= @p_35 (! (forall ((veriT_vr3 Bool_list$)) @p_39) :named @p_41)) :named @p_40)) :rule bind)
-(step t22 (cl (not @p_40) (not @p_35) @p_41) :rule equiv_pos2)
-(step t23 (cl @p_41) :rule th_resolution :premises (t20 t21 t22))
-(anchor :step t24 :args ((:= ?v0 veriT_vr4)))
-(step t24.t1 (cl (! (= ?v0 veriT_vr4) :named @p_45)) :rule refl)
-(step t24.t2 (cl (= @p_43 (! (g$a veriT_vr4) :named @p_44))) :rule cong :premises (t24.t1))
-(step t24.t3 (cl @p_45) :rule refl)
-(step t24.t4 (cl (= @p_46 (! (size$a veriT_vr4) :named @p_47))) :rule cong :premises (t24.t3))
-(step t24.t5 (cl (= @p_48 (! (= @p_44 @p_47) :named @p_49))) :rule cong :premises (t24.t2 t24.t4))
-(step t24 (cl (! (= @p_42 (! (forall ((veriT_vr4 Int_list$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
-(step t25 (cl (not @p_50) (not @p_42) @p_51) :rule equiv_pos2)
-(step t26 (cl @p_51) :rule th_resolution :premises (a7 t24 t25))
-(anchor :step t27 :args ((:= veriT_vr4 veriT_vr5)))
-(step t27.t1 (cl (! (= veriT_vr4 veriT_vr5) :named @p_53)) :rule refl)
-(step t27.t2 (cl (= @p_44 (! (g$a veriT_vr5) :named @p_52))) :rule cong :premises (t27.t1))
-(step t27.t3 (cl @p_53) :rule refl)
-(step t27.t4 (cl (= @p_47 (! (size$a veriT_vr5) :named @p_54))) :rule cong :premises (t27.t3))
-(step t27.t5 (cl (= @p_49 (! (= @p_52 @p_54) :named @p_55))) :rule cong :premises (t27.t2 t27.t4))
-(step t27 (cl (! (= @p_51 (! (forall ((veriT_vr5 Int_list$)) @p_55) :named @p_57)) :named @p_56)) :rule bind)
-(step t28 (cl (not @p_56) (not @p_51) @p_57) :rule equiv_pos2)
-(step t29 (cl @p_57) :rule th_resolution :premises (t26 t27 t28))
-(anchor :step t30 :args ((:= ?v1 veriT_vr20)))
-(step t30.t1 (cl (! (= ?v1 veriT_vr20) :named @p_62)) :rule refl)
-(step t30.t2 (cl (! (= @p_60 (! (size$ veriT_vr20) :named @p_61)) :named @p_69)) :rule cong :premises (t30.t1))
-(step t30.t3 (cl (! (= @p_3 (! (plus$ @p_61 @p_1) :named @p_59)) :named @p_70)) :rule cong :premises (t30.t2))
-(step t30.t4 (cl @p_62) :rule refl)
-(step t30.t5 (cl (= @p_63 (! (cons$a false veriT_vr20) :named @p_64))) :rule cong :premises (t30.t4))
-(step t30.t6 (cl (= @p_65 (! (size$ @p_64) :named @p_66))) :rule cong :premises (t30.t5))
-(step t30.t7 (cl (= @p_67 (! (= @p_59 @p_66) :named @p_68))) :rule cong :premises (t30.t3 t30.t6))
-(step t30.t8 (cl @p_62) :rule refl)
-(step t30.t9 (cl @p_69) :rule cong :premises (t30.t8))
-(step t30.t10 (cl @p_70) :rule cong :premises (t30.t9))
-(step t30.t11 (cl @p_62) :rule refl)
-(step t30.t12 (cl (= @p_71 (! (cons$a true veriT_vr20) :named @p_72))) :rule cong :premises (t30.t11))
-(step t30.t13 (cl (= @p_73 (! (size$ @p_72) :named @p_74))) :rule cong :premises (t30.t12))
-(step t30.t14 (cl (= @p_75 (! (= @p_59 @p_74) :named @p_76))) :rule cong :premises (t30.t10 t30.t13))
-(step t30.t15 (cl (= @p_77 (! (and @p_68 @p_76) :named @p_78))) :rule cong :premises (t30.t7 t30.t14))
-(step t30 (cl (! (= @p_58 (! (forall ((veriT_vr20 Bool_list$)) @p_78) :named @p_80)) :named @p_79)) :rule bind)
-(step t31 (cl (not @p_79) (not @p_58) @p_80) :rule equiv_pos2)
-(step t32 (cl @p_80) :rule th_resolution :premises (t11 t30 t31))
-(anchor :step t33 :args ((:= veriT_vr20 veriT_vr21)))
-(step t33.t1 (cl (! (= veriT_vr20 veriT_vr21) :named @p_83)) :rule refl)
-(step t33.t2 (cl (! (= @p_61 (! (size$ veriT_vr21) :named @p_82)) :named @p_87)) :rule cong :premises (t33.t1))
-(step t33.t3 (cl (! (= @p_59 (! (plus$ @p_82 @p_1) :named @p_81)) :named @p_88)) :rule cong :premises (t33.t2))
-(step t33.t4 (cl @p_83) :rule refl)
-(step t33.t5 (cl (= @p_64 (! (cons$a false veriT_vr21) :named @p_84))) :rule cong :premises (t33.t4))
-(step t33.t6 (cl (= @p_66 (! (size$ @p_84) :named @p_85))) :rule cong :premises (t33.t5))
-(step t33.t7 (cl (= @p_68 (! (= @p_81 @p_85) :named @p_86))) :rule cong :premises (t33.t3 t33.t6))
-(step t33.t8 (cl @p_83) :rule refl)
-(step t33.t9 (cl @p_87) :rule cong :premises (t33.t8))
-(step t33.t10 (cl @p_88) :rule cong :premises (t33.t9))
-(step t33.t11 (cl @p_83) :rule refl)
-(step t33.t12 (cl (= @p_72 (! (cons$a true veriT_vr21) :named @p_89))) :rule cong :premises (t33.t11))
-(step t33.t13 (cl (= @p_74 (! (size$ @p_89) :named @p_90))) :rule cong :premises (t33.t12))
-(step t33.t14 (cl (= @p_76 (! (= @p_81 @p_90) :named @p_91))) :rule cong :premises (t33.t10 t33.t13))
-(step t33.t15 (cl (= @p_78 (! (and @p_86 @p_91) :named @p_92))) :rule cong :premises (t33.t7 t33.t14))
-(step t33 (cl (! (= @p_80 (! (forall ((veriT_vr21 Bool_list$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
-(step t34 (cl (not @p_93) (not @p_80) @p_94) :rule equiv_pos2)
-(step t35 (cl @p_94) :rule th_resolution :premises (t32 t33 t34))
-(anchor :step t36 :args ((:= ?v0 veriT_vr22) (:= ?v1 veriT_vr23)))
-(step t36.t1 (cl (= ?v0 veriT_vr22)) :rule refl)
-(step t36.t2 (cl (! (= ?v1 veriT_vr23) :named @p_100)) :rule refl)
-(step t36.t3 (cl (= @p_96 (! (cons$ veriT_vr22 veriT_vr23) :named @p_97))) :rule cong :premises (t36.t1 t36.t2))
-(step t36.t4 (cl (= @p_98 (! (size$a @p_97) :named @p_99))) :rule cong :premises (t36.t3))
-(step t36.t5 (cl @p_100) :rule refl)
-(step t36.t6 (cl (= @p_101 (! (size$a veriT_vr23) :named @p_102))) :rule cong :premises (t36.t5))
-(step t36.t7 (cl (= @p_103 (! (plus$ @p_102 @p_1) :named @p_104))) :rule cong :premises (t36.t6))
-(step t36.t8 (cl (= @p_105 (! (= @p_99 @p_104) :named @p_106))) :rule cong :premises (t36.t4 t36.t7))
-(step t36 (cl (! (= @p_95 (! (forall ((veriT_vr22 Int) (veriT_vr23 Int_list$)) @p_106) :named @p_108)) :named @p_107)) :rule bind)
-(step t37 (cl (not @p_107) (not @p_95) @p_108) :rule equiv_pos2)
-(step t38 (cl @p_108) :rule th_resolution :premises (a15 t36 t37))
-(anchor :step t39 :args ((:= veriT_vr22 veriT_vr24) (:= veriT_vr23 veriT_vr25)))
-(step t39.t1 (cl (= veriT_vr22 veriT_vr24)) :rule refl)
-(step t39.t2 (cl (! (= veriT_vr23 veriT_vr25) :named @p_111)) :rule refl)
-(step t39.t3 (cl (= @p_97 (! (cons$ veriT_vr24 veriT_vr25) :named @p_109))) :rule cong :premises (t39.t1 t39.t2))
-(step t39.t4 (cl (= @p_99 (! (size$a @p_109) :named @p_110))) :rule cong :premises (t39.t3))
-(step t39.t5 (cl @p_111) :rule refl)
-(step t39.t6 (cl (= @p_102 (! (size$a veriT_vr25) :named @p_112))) :rule cong :premises (t39.t5))
-(step t39.t7 (cl (= @p_104 (! (plus$ @p_112 @p_1) :named @p_113))) :rule cong :premises (t39.t6))
-(step t39.t8 (cl (= @p_106 (! (= @p_110 @p_113) :named @p_114))) :rule cong :premises (t39.t4 t39.t7))
-(step t39 (cl (! (= @p_108 (! (forall ((veriT_vr24 Int) (veriT_vr25 Int_list$)) @p_114) :named @p_116)) :named @p_115)) :rule bind)
-(step t40 (cl (not @p_115) (not @p_108) @p_116) :rule equiv_pos2)
-(step t41 (cl @p_116) :rule th_resolution :premises (t38 t39 t40))
-(step t42 (cl @p_117) :rule and :premises (t10))
-(step t43 (cl (or (! (not @p_94) :named @p_127) (! (and (= (! (plus$ @p_118 @p_1) :named @p_120) (size$ @p_119)) (! (= @p_120 (! (size$ @p_121) :named @p_123)) :named @p_126)) :named @p_125))) :rule forall_inst :args ((:= veriT_vr21 nil$a)))
-(step t44 (cl (or (! (not @p_41) :named @p_128) (! (= @p_122 @p_123) :named @p_129))) :rule forall_inst :args ((:= veriT_vr3 @p_121)))
-(step t45 (cl (or (! (not @p_25) :named @p_130) (! (= @p_124 (! (g$a (! (cons$ 3 nil$) :named @p_132)) :named @p_134)) :named @p_131))) :rule forall_inst :args ((:= veriT_vr1 3)))
-(step t46 (cl (not @p_125) @p_126) :rule and_pos)
-(step t47 (cl @p_127 @p_125) :rule or :premises (t43))
-(step t48 (cl @p_125) :rule resolution :premises (t47 t35))
-(step t49 (cl @p_126) :rule resolution :premises (t46 t48))
-(step t50 (cl @p_128 @p_129) :rule or :premises (t44))
-(step t51 (cl @p_129) :rule resolution :premises (t50 t23))
-(step t52 (cl @p_130 @p_131) :rule or :premises (t45))
-(step t53 (cl @p_131) :rule resolution :premises (t52 t17))
-(step t54 (cl (or (! (not @p_116) :named @p_136) (! (= (! (size$a @p_132) :named @p_135) (! (plus$ @p_133 @p_1) :named @p_140)) :named @p_137))) :rule forall_inst :args ((:= veriT_vr24 3) (:= veriT_vr25 nil$)))
-(step t55 (cl (or (! (not @p_57) :named @p_138) (! (= @p_134 @p_135) :named @p_139))) :rule forall_inst :args ((:= veriT_vr5 @p_132)))
-(step t56 (cl @p_136 @p_137) :rule or :premises (t54))
-(step t57 (cl @p_137) :rule resolution :premises (t56 t41))
-(step t58 (cl @p_138 @p_139) :rule or :premises (t55))
-(step t59 (cl @p_139) :rule resolution :premises (t58 t29))
-(step t60 (cl (! (not @p_131) :named @p_150) (! (not @p_139) :named @p_151) (! (not @p_137) :named @p_152) (not (! (= @p_120 @p_140) :named @p_142)) (! (not @p_126) :named @p_153) (! (not @p_129) :named @p_154) (! (not @p_117) :named @p_155) @p_141) :rule eq_transitive)
-(step t61 (cl (not (! (= @p_118 @p_133) :named @p_145)) (! (not (! (= @p_1 @p_1) :named @p_149)) :named @p_146) @p_142) :rule eq_congruent)
-(step t62 (cl (! (not @p_143) :named @p_147) (! (not @p_144) :named @p_148) @p_145) :rule eq_transitive)
-(step t63 (cl @p_146 @p_142 @p_147 @p_148) :rule th_resolution :premises (t61 t62))
-(step t64 (cl @p_149) :rule eq_reflexive)
-(step t65 (cl @p_142 @p_147 @p_148) :rule th_resolution :premises (t63 t64))
-(step t66 (cl @p_150 @p_151 @p_152 @p_153 @p_154 @p_155 @p_141 @p_147 @p_148) :rule th_resolution :premises (t60 t65))
-(step t67 (cl) :rule resolution :premises (t66 t42 a12 a13 a16 t49 t51 t53 t57 t59))