src/HOL/SMT_Examples/SMT_Examples_Verit.certs

--- a/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Thu Oct 15 14:42:05 2020 +0200
+++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.certs	Thu Oct 15 18:17:57 2020 +0200
@@ -1,33 +1,4 @@
-c055bd110ab5330ffea7ea071d4ae520b8d8969f 12 0
-unsat
-(assume a0 (! (not (! (or p$ (not p$)) :named @p_1)) :named @p_2))
-(step t2 (cl (= @p_1 true)) :rule or_simplify)
-(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
-(step t4 (cl (= @p_3 false)) :rule not_simplify)
-(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
-(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
-(step t7 (cl (not @p_5) @p_1) :rule not_not)
-(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
-(step t10 (cl (not false)) :rule false)
-(step t11 (cl) :rule resolution :premises (t9 t10))
-22855940eecd8c13f695c6c889897cf3ad4802c6 15 0
-unsat
-(assume a0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1))
-(step t2 (cl (! (= @p_1 (! (and @p_2 (! (not q$) :named @p_10)) :named @p_4)) :named @p_3)) :rule bool_simplify)
-(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_1) :named @p_5) @p_4) :rule equiv_pos2)
-(step t4 (cl (not @p_5) @p_6) :rule not_not)
-(step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5))
-(step t7 (cl (! (= @p_4 (! (and @p_8 @p_9 @p_10) :named @p_12)) :named @p_11)) :rule ac_simp)
-(step t8 (cl (not @p_11) (not @p_4) @p_12) :rule equiv_pos2)
-(step t9 (cl @p_12) :rule th_resolution :premises (t6 t7 t8))
-(step t10 (cl @p_8) :rule and :premises (t9))
-(step t11 (cl p$ q$) :rule or :premises (t10))
-(step t12 (cl @p_9) :rule and :premises (t9))
-(step t13 (cl @p_10) :rule and :premises (t9))
-(step t14 (cl) :rule resolution :premises (t11 t12 t13))
-5151c0ef6f1906845c0fb5bdaf2e74bf1b74e293 17 0
+d4888d8ad473d347e6ab6d509244a7583a7babd4 17 0
 unsat
 (assume a0 (! (not (! (= (! (and p$ true) :named @p_1) p$) :named @p_3)) :named @p_5))
 (step t2 (cl (= @p_1 (! (and p$) :named @p_2))) :rule and_simplify)
@@ -45,37 +16,43 @@
 (step t14 (cl false) :rule th_resolution :premises (a0 t10 t13))
 (step t15 (cl (not false)) :rule false)
 (step t16 (cl) :rule resolution :premises (t14 t15))
-203f8541d7252e23e071560483b681b0d332320d 29 0
+95a654bfff554e647800fe77ff2ba30347402e24 9 0
+unsat
+(assume a0 (! (not true) :named @p_1))
+(step t2 (cl (! (= @p_1 false) :named @p_2)) :rule not_simplify)
+(step t3 (cl (! (not @p_2) :named @p_4) (! (not @p_1) :named @p_3) false) :rule equiv_pos2)
+(step t4 (cl (not @p_3) true) :rule not_not)
+(step t5 (cl @p_4 true false) :rule th_resolution :premises (t4 t3))
+(step t6 (cl false) :rule th_resolution :premises (a0 t2 t5))
+(step t7 (cl (not false)) :rule false)
+(step t8 (cl) :rule resolution :premises (t6 t7))
+064ce4a7bbfaa11e79501270fc838c420c703181 12 0
 unsat
-(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11))
-(step t2 (cl (= @p_1 true)) :rule equiv_simplify)
-(step t3 (cl (= @p_2 (! (= true p$) :named @p_3))) :rule cong :premises (t2))
-(step t4 (cl (= @p_3 p$)) :rule equiv_simplify)
-(step t5 (cl @p_4) :rule trans :premises (t3 t4))
-(step t6 (cl (= @p_4 @p_1)) :rule cong :premises (t5))
-(step t7 (cl (= @p_4 true)) :rule trans :premises (t6 t2))
-(step t8 (cl (= @p_5 @p_3)) :rule cong :premises (t7))
-(step t9 (cl @p_6) :rule trans :premises (t8 t4))
-(step t10 (cl (= @p_6 @p_1)) :rule cong :premises (t9))
-(step t11 (cl (= @p_6 true)) :rule trans :premises (t10 t2))
-(step t12 (cl (= @p_7 @p_3)) :rule cong :premises (t11))
-(step t13 (cl @p_8) :rule trans :premises (t12 t4))
-(step t14 (cl (= @p_8 @p_1)) :rule cong :premises (t13))
-(step t15 (cl (= @p_8 true)) :rule trans :premises (t14 t2))
-(step t16 (cl (= @p_9 @p_3)) :rule cong :premises (t15))
-(step t17 (cl @p_10) :rule trans :premises (t16 t4))
-(step t18 (cl (= @p_10 @p_1)) :rule cong :premises (t17))
-(step t19 (cl (= @p_10 true)) :rule trans :premises (t18 t2))
-(step t20 (cl (= @p_11 (! (not true) :named @p_12))) :rule cong :premises (t19))
-(step t21 (cl (= @p_12 false)) :rule not_simplify)
-(step t22 (cl (! (= @p_11 false) :named @p_13)) :rule trans :premises (t20 t21))
-(step t23 (cl (! (not @p_13) :named @p_15) (! (not @p_11) :named @p_14) false) :rule equiv_pos2)
-(step t24 (cl (not @p_14) @p_10) :rule not_not)
-(step t25 (cl @p_15 @p_10 false) :rule th_resolution :premises (t24 t23))
-(step t26 (cl false) :rule th_resolution :premises (a0 t22 t25))
-(step t27 (cl (not false)) :rule false)
-(step t28 (cl) :rule resolution :premises (t26 t27))
-f08b7e9d00093c5579cef71fa922f4b1ea326f1a 12 0
+(assume a0 (! (not (! (or p$ (not p$)) :named @p_1)) :named @p_2))
+(step t2 (cl (= @p_1 true)) :rule or_simplify)
+(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
+(step t4 (cl (= @p_3 false)) :rule not_simplify)
+(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
+(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
+(step t7 (cl (not @p_5) @p_1) :rule not_not)
+(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
+(step t10 (cl (not false)) :rule false)
+(step t11 (cl) :rule resolution :premises (t9 t10))
+10d84ea161ad298d0be18624997ac708a1f26ba1 12 0
+unsat
+(assume a0 (! (not (! (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1) :named @p_6)) :named @p_2))
+(step t2 (cl (! (= @p_2 (! (and @p_1 (not @p_1)) :named @p_4)) :named @p_3)) :rule bool_simplify)
+(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_2) :named @p_5) @p_4) :rule equiv_pos2)
+(step t4 (cl (not @p_5) @p_6) :rule not_not)
+(step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3))
+(step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5))
+(step t7 (cl (! (= @p_4 false) :named @p_8)) :rule and_simplify)
+(step t8 (cl (not @p_8) (not @p_4) false) :rule equiv_pos2)
+(step t9 (cl false) :rule th_resolution :premises (t6 t7 t8))
+(step t10 (cl (not false)) :rule false)
+(step t11 (cl) :rule resolution :premises (t9 t10))
+9edc95cdafbdeeaebc87884ea4bcc53a0e812967 12 0
 unsat
 (assume a0 (! (not (! (=> (! (or (and p1$ p2$) p3$) :named @p_2) (! (or (! (=> p1$ (or (and p3$ p2$) (and p1$ p3$))) :named @p_10) p1$) :named @p_3)) :named @p_7)) :named @p_1))
 (step t2 (cl (! (= @p_1 (! (and @p_2 (! (not @p_3) :named @p_9)) :named @p_5)) :named @p_4)) :rule bool_simplify)
@@ -88,30 +65,23 @@
 (step t9 (cl p1$) :rule not_implies1 :premises (t8))
 (step t10 (cl (not p1$)) :rule not_or :premises (t7))
 (step t11 (cl) :rule resolution :premises (t10 t9))
-0a3e14bc8f00b5bf07f38962ea996d3c2d20ffc8 12 0
+337e2bffaa7ce02e1ab772f593ffdbb243d5e449 15 0
 unsat
-(assume a0 (! (not (! (=> (! (or (and a$ b$) (and c$ d$)) :named @p_1) @p_1) :named @p_6)) :named @p_2))
-(step t2 (cl (! (= @p_2 (! (and @p_1 (not @p_1)) :named @p_4)) :named @p_3)) :rule bool_simplify)
-(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_2) :named @p_5) @p_4) :rule equiv_pos2)
+(assume a0 (! (not (! (=> (! (and (! (or p$ q$) :named @p_8) (! (not p$) :named @p_9)) :named @p_2) q$) :named @p_6)) :named @p_1))
+(step t2 (cl (! (= @p_1 (! (and @p_2 (! (not q$) :named @p_10)) :named @p_4)) :named @p_3)) :rule bool_simplify)
+(step t3 (cl (! (not @p_3) :named @p_7) (! (not @p_1) :named @p_5) @p_4) :rule equiv_pos2)
 (step t4 (cl (not @p_5) @p_6) :rule not_not)
 (step t5 (cl @p_7 @p_6 @p_4) :rule th_resolution :premises (t4 t3))
 (step t6 (cl @p_4) :rule th_resolution :premises (a0 t2 t5))
-(step t7 (cl (! (= @p_4 false) :named @p_8)) :rule and_simplify)
-(step t8 (cl (not @p_8) (not @p_4) false) :rule equiv_pos2)
-(step t9 (cl false) :rule th_resolution :premises (t6 t7 t8))
-(step t10 (cl (not false)) :rule false)
-(step t11 (cl) :rule resolution :premises (t9 t10))
-9f6c7e127b3fe4f4c06297dd72a18082c9f01f8a 9 0
-unsat
-(assume a0 (! (not true) :named @p_1))
-(step t2 (cl (! (= @p_1 false) :named @p_2)) :rule not_simplify)
-(step t3 (cl (! (not @p_2) :named @p_4) (! (not @p_1) :named @p_3) false) :rule equiv_pos2)
-(step t4 (cl (not @p_3) true) :rule not_not)
-(step t5 (cl @p_4 true false) :rule th_resolution :premises (t4 t3))
-(step t6 (cl false) :rule th_resolution :premises (a0 t2 t5))
-(step t7 (cl (not false)) :rule false)
-(step t8 (cl) :rule resolution :premises (t6 t7))
-b2829fdf215ad44dbeaf94aa26094427083ac2a9 59 0
+(step t7 (cl (! (= @p_4 (! (and @p_8 @p_9 @p_10) :named @p_12)) :named @p_11)) :rule ac_simp)
+(step t8 (cl (not @p_11) (not @p_4) @p_12) :rule equiv_pos2)
+(step t9 (cl @p_12) :rule th_resolution :premises (t6 t7 t8))
+(step t10 (cl @p_8) :rule and :premises (t9))
+(step t11 (cl p$ q$) :rule or :premises (t10))
+(step t12 (cl @p_9) :rule and :premises (t9))
+(step t13 (cl @p_10) :rule and :premises (t9))
+(step t14 (cl) :rule resolution :premises (t11 t12 t13))
+ef250e7a4e9499952e8416cff69ed029a37c7aa3 59 0
 unsat
 (assume a0 (! (or a$ (or b$ (or c$ d$))) :named @p_1))
 (assume a2 (! (or (! (not (! (or a$ (! (and c$ (! (not c$) :named @p_40)) :named @p_4)) :named @p_5)) :named @p_8) b$) :named @p_9))
@@ -171,7 +141,37 @@
 (step t56 (cl @p_26) :rule resolution :premises (t54 t50))
 (step t57 (cl a$) :rule resolution :premises (t51 t55 t50 t56))
 (step t58 (cl) :rule resolution :premises (t52 t55 t57))
-e3b0f8bc56ad2ce76e39c6e618b58c09ec3f7474 38 0
+f8dcc171fd9ab79494da2e1c5e4771e075fd9d51 29 0
+unsat
+(assume a0 (! (not (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= (! (= p$ p$) :named @p_1) p$) :named @p_2) p$) :named @p_4) p$) :named @p_5) p$) :named @p_6) p$) :named @p_7) p$) :named @p_8) p$) :named @p_9) p$) :named @p_10)) :named @p_11))
+(step t2 (cl (= @p_1 true)) :rule equiv_simplify)
+(step t3 (cl (= @p_2 (! (= true p$) :named @p_3))) :rule cong :premises (t2))
+(step t4 (cl (= @p_3 p$)) :rule equiv_simplify)
+(step t5 (cl @p_4) :rule trans :premises (t3 t4))
+(step t6 (cl (= @p_4 @p_1)) :rule cong :premises (t5))
+(step t7 (cl (= @p_4 true)) :rule trans :premises (t6 t2))
+(step t8 (cl (= @p_5 @p_3)) :rule cong :premises (t7))
+(step t9 (cl @p_6) :rule trans :premises (t8 t4))
+(step t10 (cl (= @p_6 @p_1)) :rule cong :premises (t9))
+(step t11 (cl (= @p_6 true)) :rule trans :premises (t10 t2))
+(step t12 (cl (= @p_7 @p_3)) :rule cong :premises (t11))
+(step t13 (cl @p_8) :rule trans :premises (t12 t4))
+(step t14 (cl (= @p_8 @p_1)) :rule cong :premises (t13))
+(step t15 (cl (= @p_8 true)) :rule trans :premises (t14 t2))
+(step t16 (cl (= @p_9 @p_3)) :rule cong :premises (t15))
+(step t17 (cl @p_10) :rule trans :premises (t16 t4))
+(step t18 (cl (= @p_10 @p_1)) :rule cong :premises (t17))
+(step t19 (cl (= @p_10 true)) :rule trans :premises (t18 t2))
+(step t20 (cl (= @p_11 (! (not true) :named @p_12))) :rule cong :premises (t19))
+(step t21 (cl (= @p_12 false)) :rule not_simplify)
+(step t22 (cl (! (= @p_11 false) :named @p_13)) :rule trans :premises (t20 t21))
+(step t23 (cl (! (not @p_13) :named @p_15) (! (not @p_11) :named @p_14) false) :rule equiv_pos2)
+(step t24 (cl (not @p_14) @p_10) :rule not_not)
+(step t25 (cl @p_15 @p_10 false) :rule th_resolution :premises (t24 t23))
+(step t26 (cl false) :rule th_resolution :premises (a0 t22 t25))
+(step t27 (cl (not false)) :rule false)
+(step t28 (cl) :rule resolution :premises (t26 t27))
+a331481eed4f18a666baadda4e1010ca7a295ccf 38 0
 unsat
 (assume a0 (! (forall ((?v0 A$) (?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$)) :named @p_21)) :named @p_20)) :named @p_24))
@@ -210,7 +210,662 @@
 (step t19 (cl (or (! (not @p_18) :named @p_29) @p_21)) :rule forall_inst :args ((:= veriT_vr2 a$) (:= veriT_vr3 b$)))
 (step t20 (cl @p_29 @p_21) :rule or :premises (t19))
 (step t21 (cl) :rule resolution :premises (t20 t8 t18))
-2b7ca9ab80d78db50690054e655456fb60950de8 333 0
+8616c6debd3ebae49adf8409b8c1ecb6665bc881 654 0
+unsat
+(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11))
+(assume a1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23))
+(assume a2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
+(assume a3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62))
+(assume a4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85))
+(assume a5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101))
+(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402))
+(assume a7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120))
+(assume a8 (! (finite$ bot$) :named @p_414))
+(assume a9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157))
+(assume a10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499))
+(assume a11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175))
+(assume a12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500))
+(assume a13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195))
+(assume a14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206))
+(assume a15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231))
+(assume a16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250))
+(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$) :named @p_405)) :named @p_463)) :named @p_410)))
+(anchor :step t21 :args ((:= ?v0 veriT_vr0)))
+(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t21.t2 (cl (= @p_13 (! (fun_app$ 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)))
+(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)))
+(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)))
+(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)))
+(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))
+(step t33.t4 (cl @p_38) :rule refl)
+(step t33.t5 (cl @p_39) :rule refl)
+(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5))
+(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6))
+(step t33.t8 (cl @p_39) :rule refl)
+(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8))
+(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9))
+(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10))
+(step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
+(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
+(step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34))
+(anchor :step t36 :args ((:= veriT_vr4 veriT_vr6) (:= veriT_vr5 veriT_vr7)))
+(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl)
+(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl)
+(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2))
+(step t36.t4 (cl @p_53) :rule refl)
+(step t36.t5 (cl @p_54) :rule refl)
+(step t36.t6 (cl (= @p_41 (! (fst$ veriT_vr7) :named @p_55))) :rule cong :premises (t36.t5))
+(step t36.t7 (cl (= @p_43 (! (fun_app$ veriT_vr6 @p_55) :named @p_56))) :rule cong :premises (t36.t4 t36.t6))
+(step t36.t8 (cl @p_54) :rule refl)
+(step t36.t9 (cl (= @p_45 (! (snd$ veriT_vr7) :named @p_57))) :rule cong :premises (t36.t8))
+(step t36.t10 (cl (= @p_47 (! (fun_app$a @p_56 @p_57) :named @p_58))) :rule cong :premises (t36.t7 t36.t9))
+(step t36.t11 (cl (= @p_49 (! (= @p_52 @p_58) :named @p_59))) :rule cong :premises (t36.t3 t36.t10))
+(step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
+(step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2)
+(step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37))
+(anchor :step t39 :args ((:= ?v0 veriT_vr8) (:= ?v1 veriT_vr9)))
+(step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl)
+(step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1))
+(step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl)
+(step t39.t4 (cl (= @p_64 (! (insert$ veriT_vr9 bot$) :named @p_65))) :rule cong :premises (t39.t3))
+(step t39.t5 (cl (= @p_66 (! (= @p_63 @p_65) :named @p_67))) :rule cong :premises (t39.t2 t39.t4))
+(step t39.t6 (cl @p_68) :rule refl)
+(step t39.t7 (cl @p_69) :rule refl)
+(step t39.t8 (cl (= @p_70 (! (= veriT_vr8 veriT_vr9) :named @p_71))) :rule cong :premises (t39.t6 t39.t7))
+(step t39.t9 (cl (= @p_72 (! (=> @p_67 @p_71) :named @p_73))) :rule cong :premises (t39.t5 t39.t8))
+(step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
+(step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2)
+(step t41 (cl @p_75) :rule th_resolution :premises (a3 t39 t40))
+(anchor :step t42 :args ((:= veriT_vr8 veriT_vr10) (:= veriT_vr9 veriT_vr11)))
+(step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl)
+(step t42.t2 (cl (= @p_63 (! (insert$ veriT_vr10 bot$) :named @p_76))) :rule cong :premises (t42.t1))
+(step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl)
+(step t42.t4 (cl (= @p_65 (! (insert$ veriT_vr11 bot$) :named @p_77))) :rule cong :premises (t42.t3))
+(step t42.t5 (cl (= @p_67 (! (= @p_76 @p_77) :named @p_78))) :rule cong :premises (t42.t2 t42.t4))
+(step t42.t6 (cl @p_79) :rule refl)
+(step t42.t7 (cl @p_80) :rule refl)
+(step t42.t8 (cl (= @p_71 (! (= veriT_vr10 veriT_vr11) :named @p_81))) :rule cong :premises (t42.t6 t42.t7))
+(step t42.t9 (cl (= @p_73 (! (=> @p_78 @p_81) :named @p_82))) :rule cong :premises (t42.t5 t42.t8))
+(step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
+(step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
+(step t44 (cl @p_84) :rule th_resolution :premises (t41 t42 t43))
+(anchor :step t45 :args ((:= ?v0 veriT_vr12) (:= ?v1 veriT_vr13)))
+(step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl)
+(step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
+(step t45.t3 (cl @p_86) :rule refl)
+(step t45.t4 (cl (= @p_87 (! (pair$ veriT_vr12 veriT_vr13) :named @p_88))) :rule cong :premises (t45.t2 t45.t3))
+(step t45.t5 (cl (= @p_89 (! (snd$ @p_88) :named @p_90))) :rule cong :premises (t45.t4))
+(step t45.t6 (cl (= @p_91 (! (= veriT_vr13 @p_90) :named @p_92))) :rule cong :premises (t45.t1 t45.t5))
+(step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
+(step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2)
+(step t47 (cl @p_94) :rule th_resolution :premises (a4 t45 t46))
+(anchor :step t48 :args ((:= veriT_vr12 veriT_vr14) (:= veriT_vr13 veriT_vr15)))
+(step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl)
+(step t48.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
+(step t48.t3 (cl @p_95) :rule refl)
+(step t48.t4 (cl (= @p_88 (! (pair$ veriT_vr14 veriT_vr15) :named @p_96))) :rule cong :premises (t48.t2 t48.t3))
+(step t48.t5 (cl (= @p_90 (! (snd$ @p_96) :named @p_97))) :rule cong :premises (t48.t4))
+(step t48.t6 (cl (= @p_92 (! (= veriT_vr15 @p_97) :named @p_98))) :rule cong :premises (t48.t1 t48.t5))
+(step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind)
+(step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2)
+(step t50 (cl @p_100) :rule th_resolution :premises (t47 t48 t49))
+(anchor :step t51 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
+(step t51.t1 (cl (! (= ?v1 veriT_vr17) :named @p_104)) :rule refl)
+(step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl)
+(step t51.t3 (cl (= @p_102 (! (pair$a veriT_vr16) :named @p_103))) :rule cong :premises (t51.t2))
+(step t51.t4 (cl @p_104) :rule refl)
+(step t51.t5 (cl (= @p_105 (! (fun_app$b @p_103 veriT_vr17) :named @p_106))) :rule cong :premises (t51.t3 t51.t4))
+(step t51.t6 (cl (= @p_107 (! (snd$a @p_106) :named @p_108))) :rule cong :premises (t51.t5))
+(step t51.t7 (cl (= @p_109 (! (= veriT_vr17 @p_108) :named @p_110))) :rule cong :premises (t51.t1 t51.t6))
+(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)))
+(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$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2))
+(step t54.t4 (cl @p_114) :rule refl)
+(step t54.t5 (cl (= @p_106 (! (fun_app$b @p_113 veriT_vr19) :named @p_115))) :rule cong :premises (t54.t3 t54.t4))
+(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5))
+(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6))
+(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind)
+(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2)
+(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55))
+(anchor :step t57 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21) (:= ?v2 veriT_vr22)))
+(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl)
+(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl)
+(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl)
+(step t57.t4 (cl (= @p_1 (! (insert$ veriT_vr21 veriT_vr22) :named @p_121))) :rule cong :premises (t57.t2 t57.t3))
+(step t57.t5 (cl (= @p_122 (! (inf$ veriT_vr20 @p_121) :named @p_123))) :rule cong :premises (t57.t1 t57.t4))
+(step t57.t6 (cl (= @p_124 (! (= bot$ @p_123) :named @p_125))) :rule cong :premises (t57.t5))
+(step t57.t7 (cl @p_126) :rule refl)
+(step t57.t8 (cl @p_127) :rule refl)
+(step t57.t9 (cl (= @p_128 (! (member$a veriT_vr21 veriT_vr20) :named @p_129))) :rule cong :premises (t57.t7 t57.t8))
+(step t57.t10 (cl (= @p_130 (! (not @p_129) :named @p_131))) :rule cong :premises (t57.t9))
+(step t57.t11 (cl @p_127) :rule refl)
+(step t57.t12 (cl @p_132) :rule refl)
+(step t57.t13 (cl (= @p_133 (! (inf$ veriT_vr20 veriT_vr22) :named @p_134))) :rule cong :premises (t57.t11 t57.t12))
+(step t57.t14 (cl (= @p_135 (! (= bot$ @p_134) :named @p_136))) :rule cong :premises (t57.t13))
+(step t57.t15 (cl (= @p_137 (! (and @p_131 @p_136) :named @p_138))) :rule cong :premises (t57.t10 t57.t14))
+(step t57.t16 (cl (= @p_139 (! (= @p_125 @p_138) :named @p_140))) :rule cong :premises (t57.t6 t57.t15))
+(step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind)
+(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2)
+(step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58))
+(anchor :step t60 :args ((:= veriT_vr20 veriT_vr23) (:= veriT_vr21 veriT_vr24) (:= veriT_vr22 veriT_vr25)))
+(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl)
+(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl)
+(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl)
+(step t60.t4 (cl (= @p_121 (! (insert$ veriT_vr24 veriT_vr25) :named @p_143))) :rule cong :premises (t60.t2 t60.t3))
+(step t60.t5 (cl (= @p_123 (! (inf$ veriT_vr23 @p_143) :named @p_144))) :rule cong :premises (t60.t1 t60.t4))
+(step t60.t6 (cl (= @p_125 (! (= bot$ @p_144) :named @p_145))) :rule cong :premises (t60.t5))
+(step t60.t7 (cl @p_146) :rule refl)
+(step t60.t8 (cl @p_147) :rule refl)
+(step t60.t9 (cl (= @p_129 (! (member$a veriT_vr24 veriT_vr23) :named @p_148))) :rule cong :premises (t60.t7 t60.t8))
+(step t60.t10 (cl (= @p_131 (! (not @p_148) :named @p_149))) :rule cong :premises (t60.t9))
+(step t60.t11 (cl @p_147) :rule refl)
+(step t60.t12 (cl @p_150) :rule refl)
+(step t60.t13 (cl (= @p_134 (! (inf$ veriT_vr23 veriT_vr25) :named @p_151))) :rule cong :premises (t60.t11 t60.t12))
+(step t60.t14 (cl (= @p_136 (! (= bot$ @p_151) :named @p_152))) :rule cong :premises (t60.t13))
+(step t60.t15 (cl (= @p_138 (! (and @p_149 @p_152) :named @p_153))) :rule cong :premises (t60.t10 t60.t14))
+(step t60.t16 (cl (= @p_140 (! (= @p_145 @p_153) :named @p_154))) :rule cong :premises (t60.t6 t60.t15))
+(step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
+(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2)
+(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61))
+(anchor :step t63 :args ((:= ?v0 veriT_vr26) (:= ?v1 veriT_vr27)))
+(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl)
+(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1))
+(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl)
+(step t63.t4 (cl @p_159) :rule refl)
+(step t63.t5 (cl (= @p_160 (! (insert$ veriT_vr27 veriT_vr26) :named @p_161))) :rule cong :premises (t63.t3 t63.t4))
+(step t63.t6 (cl (= @p_162 (! (finite$ @p_161) :named @p_163))) :rule cong :premises (t63.t5))
+(step t63.t7 (cl (= @p_164 (! (=> @p_158 @p_163) :named @p_165))) :rule cong :premises (t63.t2 t63.t6))
+(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)))
+(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)
+(step t66.t4 (cl @p_169) :rule refl)
+(step t66.t5 (cl (= @p_161 (! (insert$ veriT_vr29 veriT_vr28) :named @p_170))) :rule cong :premises (t66.t3 t66.t4))
+(step t66.t6 (cl (= @p_163 (! (finite$ @p_170) :named @p_171))) :rule cong :premises (t66.t5))
+(step t66.t7 (cl (= @p_165 (! (=> @p_168 @p_171) :named @p_172))) :rule cong :premises (t66.t2 t66.t6))
+(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)))
+(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$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2))
+(step t69.t4 (cl @p_178) :rule refl)
+(step t69.t5 (cl @p_179) :rule refl)
+(step t69.t6 (cl @p_178) :rule refl)
+(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6))
+(step t69.t8 (cl (= @p_181 (! (= veriT_vr31 @p_180) :named @p_182))) :rule cong :premises (t69.t4 t69.t7))
+(step t69.t9 (cl (= @p_183 (! (=> @p_177 @p_182) :named @p_184))) :rule cong :premises (t69.t3 t69.t8))
+(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)))
+(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$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2))
+(step t72.t4 (cl @p_188) :rule refl)
+(step t72.t5 (cl @p_189) :rule refl)
+(step t72.t6 (cl @p_188) :rule refl)
+(step t72.t7 (cl (= @p_180 (! (insert$ veriT_vr32 veriT_vr33) :named @p_190))) :rule cong :premises (t72.t5 t72.t6))
+(step t72.t8 (cl (= @p_182 (! (= veriT_vr33 @p_190) :named @p_191))) :rule cong :premises (t72.t4 t72.t7))
+(step t72.t9 (cl (= @p_184 (! (=> @p_187 @p_191) :named @p_192))) :rule cong :premises (t72.t3 t72.t8))
+(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)))
+(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$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
+(step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2)
+(step t77 (cl @p_201) :rule th_resolution :premises (a13 t75 t76))
+(anchor :step t78 :args ((:= veriT_vr34 veriT_vr35)))
+(step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl)
+(step t78.t2 (cl (= @p_197 (! (inf$ 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$)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
+(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2)
+(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79))
+(anchor :step t81 :args ((:= ?v0 veriT_vr36) (:= ?v1 veriT_vr37) (:= ?v2 veriT_vr38)))
+(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl)
+(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl)
+(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl)
+(step t81.t4 (cl (= @p_1 (! (insert$ veriT_vr37 veriT_vr38) :named @p_207))) :rule cong :premises (t81.t2 t81.t3))
+(step t81.t5 (cl (= @p_208 (! (insert$ veriT_vr36 @p_207) :named @p_209))) :rule cong :premises (t81.t1 t81.t4))
+(step t81.t6 (cl @p_210) :rule refl)
+(step t81.t7 (cl @p_211) :rule refl)
+(step t81.t8 (cl @p_212) :rule refl)
+(step t81.t9 (cl (= @p_213 (! (insert$ veriT_vr36 veriT_vr38) :named @p_214))) :rule cong :premises (t81.t7 t81.t8))
+(step t81.t10 (cl (= @p_215 (! (insert$ veriT_vr37 @p_214) :named @p_216))) :rule cong :premises (t81.t6 t81.t9))
+(step t81.t11 (cl (= @p_217 (! (= @p_209 @p_216) :named @p_218))) :rule cong :premises (t81.t5 t81.t10))
+(step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind)
+(step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2)
+(step t83 (cl @p_220) :rule th_resolution :premises (a14 t81 t82))
+(anchor :step t84 :args ((:= veriT_vr36 veriT_vr39) (:= veriT_vr37 veriT_vr40) (:= veriT_vr38 veriT_vr41)))
+(step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl)
+(step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl)
+(step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl)
+(step t84.t4 (cl (= @p_207 (! (insert$ veriT_vr40 veriT_vr41) :named @p_221))) :rule cong :premises (t84.t2 t84.t3))
+(step t84.t5 (cl (= @p_209 (! (insert$ veriT_vr39 @p_221) :named @p_222))) :rule cong :premises (t84.t1 t84.t4))
+(step t84.t6 (cl @p_223) :rule refl)
+(step t84.t7 (cl @p_224) :rule refl)
+(step t84.t8 (cl @p_225) :rule refl)
+(step t84.t9 (cl (= @p_214 (! (insert$ veriT_vr39 veriT_vr41) :named @p_226))) :rule cong :premises (t84.t7 t84.t8))
+(step t84.t10 (cl (= @p_216 (! (insert$ veriT_vr40 @p_226) :named @p_227))) :rule cong :premises (t84.t6 t84.t9))
+(step t84.t11 (cl (= @p_218 (! (= @p_222 @p_227) :named @p_228))) :rule cong :premises (t84.t5 t84.t10))
+(step t84 (cl (! (= @p_220 (! (forall ((veriT_vr39 Real_real_prod$) (veriT_vr40 Real_real_prod$) (veriT_vr41 Real_real_prod_set$)) @p_228) :named @p_230)) :named @p_229)) :rule bind)
+(step t85 (cl (not @p_229) (not @p_220) @p_230) :rule equiv_pos2)
+(step t86 (cl @p_230) :rule th_resolution :premises (t83 t84 t85))
+(anchor :step t87 :args ((:= ?v0 veriT_vr42) (:= ?v1 veriT_vr43)))
+(step t87.t1 (cl (! (= ?v0 veriT_vr42) :named @p_233)) :rule refl)
+(step t87.t2 (cl (! (= ?v1 veriT_vr43) :named @p_235)) :rule refl)
+(step t87.t3 (cl (= @p_2 (! (insert$ veriT_vr42 veriT_vr43) :named @p_232))) :rule cong :premises (t87.t1 t87.t2))
+(step t87.t4 (cl @p_233) :rule refl)
+(step t87.t5 (cl (= @p_3 (! (insert$ veriT_vr42 bot$) :named @p_234))) :rule cong :premises (t87.t4))
+(step t87.t6 (cl @p_235) :rule refl)
+(step t87.t7 (cl (= @p_236 (! (sup$ @p_234 veriT_vr43) :named @p_237))) :rule cong :premises (t87.t5 t87.t6))
+(step t87.t8 (cl (= @p_238 (! (= @p_232 @p_237) :named @p_239))) :rule cong :premises (t87.t3 t87.t7))
+(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)))
+(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))
+(step t90.t4 (cl @p_243) :rule refl)
+(step t90.t5 (cl (= @p_234 (! (insert$ veriT_vr44 bot$) :named @p_244))) :rule cong :premises (t90.t4))
+(step t90.t6 (cl @p_245) :rule refl)
+(step t90.t7 (cl (= @p_237 (! (sup$ @p_244 veriT_vr45) :named @p_246))) :rule cong :premises (t90.t5 t90.t6))
+(step t90.t8 (cl (= @p_239 (! (= @p_242 @p_246) :named @p_247))) :rule cong :premises (t90.t3 t90.t7))
+(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)))
+(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)
+(step t93.t4 (cl (! (= ?v2 veriT_vr48) :named @p_263)) :rule refl)
+(step t93.t5 (cl (= @p_252 (! (line_integral_exists$ veriT_vr47 veriT_vr48) :named @p_253))) :rule cong :premises (t93.t3 t93.t4))
+(step t93.t6 (cl (! (= ?v3 veriT_vr49) :named @p_259)) :rule refl)
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+(step t93.t8 (cl @p_256) :rule refl)
+(step t93.t9 (cl (! (= ?v4 veriT_vr50) :named @p_264)) :rule refl)
+(step t93.t10 (cl (= @p_257 (! (line_integral_exists$ veriT_vr47 veriT_vr50) :named @p_258))) :rule cong :premises (t93.t8 t93.t9))
+(step t93.t11 (cl @p_259) :rule refl)
+(step t93.t12 (cl (= @p_260 (! (fun_app$a @p_258 veriT_vr49) :named @p_261))) :rule cong :premises (t93.t10 t93.t11))
+(step t93.t13 (cl @p_262) :rule refl)
+(step t93.t14 (cl @p_263) :rule refl)
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+(step t93.t17 (cl (= @p_267 (! (= veriT_vr46 @p_266) :named @p_268))) :rule cong :premises (t93.t13 t93.t16))
+(step t93.t18 (cl @p_263) :rule refl)
+(step t93.t19 (cl @p_264) :rule refl)
+(step t93.t20 (cl (= @p_269 (! (inf$ veriT_vr48 veriT_vr50) :named @p_270))) :rule cong :premises (t93.t18 t93.t19))
+(step t93.t21 (cl (= @p_271 (! (= bot$ @p_270) :named @p_272))) :rule cong :premises (t93.t20))
+(step t93.t22 (cl (= @p_273 (! (and @p_268 @p_272) :named @p_274))) :rule cong :premises (t93.t17 t93.t21))
+(step t93.t23 (cl (= @p_275 (! (and @p_261 @p_274) :named @p_276))) :rule cong :premises (t93.t12 t93.t22))
+(step t93.t24 (cl (= @p_277 (! (and @p_255 @p_276) :named @p_278))) :rule cong :premises (t93.t7 t93.t23))
+(step t93.t25 (cl (= @p_279 (! (and @p_251 @p_278) :named @p_280))) :rule cong :premises (t93.t2 t93.t24))
+(step t93.t26 (cl @p_256) :rule refl)
+(step t93.t27 (cl @p_262) :rule refl)
+(step t93.t28 (cl @p_259) :rule refl)
+(step t93.t29 (cl (= @p_281 (! (line_integral$ veriT_vr47 veriT_vr46 veriT_vr49) :named @p_282))) :rule cong :premises (t93.t26 t93.t27 t93.t28))
+(step t93.t30 (cl @p_256) :rule refl)
+(step t93.t31 (cl @p_263) :rule refl)
+(step t93.t32 (cl @p_259) :rule refl)
+(step t93.t33 (cl (= @p_283 (! (line_integral$ veriT_vr47 veriT_vr48 veriT_vr49) :named @p_284))) :rule cong :premises (t93.t30 t93.t31 t93.t32))
+(step t93.t34 (cl @p_256) :rule refl)
+(step t93.t35 (cl @p_264) :rule refl)
+(step t93.t36 (cl @p_259) :rule refl)
+(step t93.t37 (cl (= @p_285 (! (line_integral$ veriT_vr47 veriT_vr50 veriT_vr49) :named @p_286))) :rule cong :premises (t93.t34 t93.t35 t93.t36))
+(step t93.t38 (cl (= @p_287 (! (+ @p_284 @p_286) :named @p_288))) :rule cong :premises (t93.t33 t93.t37))
+(step t93.t39 (cl (= @p_289 (! (= @p_282 @p_288) :named @p_290))) :rule cong :premises (t93.t29 t93.t38))
+(step t93.t40 (cl (= @p_291 (! (=> @p_280 @p_290) :named @p_292))) :rule cong :premises (t93.t25 t93.t39))
+(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$)) @p_292) :named @p_294)) :named @p_293)) :rule bind)
+(step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2)
+(step t95 (cl @p_294) :rule th_resolution :premises (a16 t93 t94))
+(anchor :step t96 :args (veriT_vr46 veriT_vr47 veriT_vr48 veriT_vr49 veriT_vr50))
+(step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp)
+(step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1))
+(step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (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)))
+(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)
+(step t99.t4 (cl (! (= veriT_vr48 veriT_vr53) :named @p_307)) :rule refl)
+(step t99.t5 (cl (= @p_253 (! (line_integral_exists$ veriT_vr52 veriT_vr53) :named @p_300))) :rule cong :premises (t99.t3 t99.t4))
+(step t99.t6 (cl (! (= veriT_vr49 veriT_vr54) :named @p_304)) :rule refl)
+(step t99.t7 (cl (= @p_255 (! (fun_app$a @p_300 veriT_vr54) :named @p_301))) :rule cong :premises (t99.t5 t99.t6))
+(step t99.t8 (cl @p_302) :rule refl)
+(step t99.t9 (cl (! (= veriT_vr50 veriT_vr55) :named @p_308)) :rule refl)
+(step t99.t10 (cl (= @p_258 (! (line_integral_exists$ veriT_vr52 veriT_vr55) :named @p_303))) :rule cong :premises (t99.t8 t99.t9))
+(step t99.t11 (cl @p_304) :rule refl)
+(step t99.t12 (cl (= @p_261 (! (fun_app$a @p_303 veriT_vr54) :named @p_305))) :rule cong :premises (t99.t10 t99.t11))
+(step t99.t13 (cl @p_306) :rule refl)
+(step t99.t14 (cl @p_307) :rule refl)
+(step t99.t15 (cl @p_308) :rule refl)
+(step t99.t16 (cl (= @p_266 (! (sup$ veriT_vr53 veriT_vr55) :named @p_309))) :rule cong :premises (t99.t14 t99.t15))
+(step t99.t17 (cl (= @p_268 (! (= veriT_vr51 @p_309) :named @p_310))) :rule cong :premises (t99.t13 t99.t16))
+(step t99.t18 (cl @p_307) :rule refl)
+(step t99.t19 (cl @p_308) :rule refl)
+(step t99.t20 (cl (= @p_270 (! (inf$ veriT_vr53 veriT_vr55) :named @p_311))) :rule cong :premises (t99.t18 t99.t19))
+(step t99.t21 (cl (= @p_272 (! (= bot$ @p_311) :named @p_312))) :rule cong :premises (t99.t20))
+(step t99.t22 (cl (= @p_295 (! (and @p_299 @p_301 @p_305 @p_310 @p_312) :named @p_313))) :rule cong :premises (t99.t2 t99.t7 t99.t12 t99.t17 t99.t21))
+(step t99.t23 (cl @p_302) :rule refl)
+(step t99.t24 (cl @p_306) :rule refl)
+(step t99.t25 (cl @p_304) :rule refl)
+(step t99.t26 (cl (= @p_282 (! (line_integral$ veriT_vr52 veriT_vr51 veriT_vr54) :named @p_314))) :rule cong :premises (t99.t23 t99.t24 t99.t25))
+(step t99.t27 (cl @p_302) :rule refl)
+(step t99.t28 (cl @p_307) :rule refl)
+(step t99.t29 (cl @p_304) :rule refl)
+(step t99.t30 (cl (= @p_284 (! (line_integral$ veriT_vr52 veriT_vr53 veriT_vr54) :named @p_315))) :rule cong :premises (t99.t27 t99.t28 t99.t29))
+(step t99.t31 (cl @p_302) :rule refl)
+(step t99.t32 (cl @p_308) :rule refl)
+(step t99.t33 (cl @p_304) :rule refl)
+(step t99.t34 (cl (= @p_286 (! (line_integral$ veriT_vr52 veriT_vr55 veriT_vr54) :named @p_316))) :rule cong :premises (t99.t31 t99.t32 t99.t33))
+(step t99.t35 (cl (= @p_288 (! (+ @p_315 @p_316) :named @p_317))) :rule cong :premises (t99.t30 t99.t34))
+(step t99.t36 (cl (= @p_290 (! (= @p_314 @p_317) :named @p_318))) :rule cong :premises (t99.t26 t99.t35))
+(step t99.t37 (cl (= @p_296 (! (=> @p_313 @p_318) :named @p_319))) :rule cong :premises (t99.t22 t99.t36))
+(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$)) @p_319) :named @p_321)) :named @p_320)) :rule bind)
+(step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2)
+(step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100))
+(anchor :step t102 :args ((:= ?v0 veriT_vr56)))
+(step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl)
+(step t102.t2 (cl (= @p_9 (! (member$ 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$)) @p_327) :named @p_334))) :rule bind)
+(anchor :step t103 :args ((:= ?v0 veriT_vr56)))
+(step t103.t1 (cl @p_324) :rule refl)
+(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1))
+(step t103.t3 (cl @p_324) :rule refl)
+(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3))
+(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4))
+(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind)
+(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103))
+(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104))
+(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2)
+(step t107 (cl @p_340) :rule th_resolution :premises (a17 t105 t106))
+(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)))
+(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$) :named @p_343))) :rule cong :premises (t111.t1))
+(step t111.t3 (cl @p_344) :rule refl)
+(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3))
+(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4))
+(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind)
+(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111))
+(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2)
+(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113))
+(anchor :step t115 :args ((:= veriT_vr56 veriT_vr58)))
+(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl)
+(step t115.t2 (cl (= @p_323 (! (member$ 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$)) @p_353) :named @p_358))) :rule bind)
+(anchor :step t116 :args ((:= veriT_vr57 veriT_vr59)))
+(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl)
+(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1))
+(step t116.t3 (cl @p_355) :rule refl)
+(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3))
+(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4))
+(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind)
+(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116))
+(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2)
+(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118))
+(anchor :step t120 :args ((:= ?v0 veriT_vr60)))
+(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl)
+(step t120.t2 (cl (= @p_8 (! (member$ 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$)) @p_367) :named @p_374))) :rule bind)
+(anchor :step t121 :args ((:= ?v0 veriT_vr60)))
+(step t121.t1 (cl @p_364) :rule refl)
+(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1))
+(step t121.t3 (cl @p_364) :rule refl)
+(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3))
+(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4))
+(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind)
+(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121))
+(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122))
+(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2)
+(step t125 (cl @p_380) :rule th_resolution :premises (a18 t123 t124))
+(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)))
+(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$) :named @p_383))) :rule cong :premises (t129.t1))
+(step t129.t3 (cl @p_384) :rule refl)
+(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3))
+(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4))
+(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind)
+(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129))
+(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2)
+(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131))
+(anchor :step t133 :args ((:= veriT_vr60 veriT_vr62)))
+(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl)
+(step t133.t2 (cl (= @p_363 (! (member$ 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$)) @p_393) :named @p_398))) :rule bind)
+(anchor :step t134 :args ((:= veriT_vr61 veriT_vr63)))
+(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl)
+(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1))
+(step t134.t3 (cl @p_395) :rule refl)
+(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3))
+(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4))
+(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind)
+(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134))
+(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2)
+(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136))
+(step t138 (cl @p_358) :rule and :premises (t119))
+(step t139 (cl @p_399) :rule and :premises (t137))
+(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403)))
+(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403)))
+(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5)))
+(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7)))
+(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7)))
+(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$)))
+(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7)))
+(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$)))
+(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$)))
+(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$)))
+(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0)))
+(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0)))
+(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$)))
+(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$)))
+(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos)
+(step t155 (cl @p_422 @p_420) :rule or :premises (t140))
+(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 a6))
+(step t157 (cl @p_420) :rule resolution :premises (t155 t139))
+(step t158 (cl @p_421) :rule resolution :premises (t156 t157))
+(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos)
+(step t160 (cl @p_427 @p_424) :rule or :premises (t141))
+(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 a6))
+(step t162 (cl @p_424) :rule resolution :premises (t160 t138))
+(step t163 (cl @p_426) :rule resolution :premises (t161 t162))
+(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg)
+(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos)
+(step t166 (cl @p_406 @p_432) :rule or :premises (t142))
+(step t167 (cl @p_432) :rule resolution :premises (t166 t101))
+(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg)
+(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos)
+(step t170 (cl @p_406 @p_438) :rule or :premises (t143))
+(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 a19))
+(step t172 (cl @p_438) :rule resolution :premises (t170 t101))
+(step t173 (cl @p_440) :rule resolution :premises (t171 t172))
+(step t174 (cl @p_441 @p_411) :rule or :premises (t144))
+(step t175 (cl @p_411) :rule resolution :premises (t174 t92))
+(step t176 (cl @p_442 @p_443) :rule or :premises (t145))
+(step t177 (cl @p_443) :rule resolution :premises (t176 t86))
+(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos)
+(step t179 (cl @p_447 @p_444) :rule or :premises (t146))
+(step t180 (cl @p_444) :rule resolution :premises (t179 t74))
+(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos)
+(step t182 (cl @p_413 @p_448) :rule or :premises (t147))
+(step t183 (cl @p_448) :rule resolution :premises (t182 t68))
+(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos)
+(step t185 (cl @p_413 @p_449) :rule or :premises (t148))
+(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 a8))
+(step t187 (cl @p_449) :rule resolution :premises (t185 t68))
+(step t188 (cl @p_415) :rule resolution :premises (t186 t187))
+(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos)
+(step t190 (cl @p_413 @p_451) :rule or :premises (t149))
+(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 a8))
+(step t192 (cl @p_451) :rule resolution :premises (t190 t68))
+(step t193 (cl @p_416) :rule resolution :premises (t191 t192))
+(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183))
+(step t195 (cl @p_418 @p_454) :rule or :premises (t150))
+(step t196 (cl @p_454) :rule resolution :premises (t195 t56))
+(step t197 (cl @p_418 @p_455) :rule or :premises (t151))
+(step t198 (cl @p_455) :rule resolution :premises (t197 t56))
+(step t199 (cl @p_456 @p_457) :rule or :premises (t152))
+(step t200 (cl @p_457) :rule resolution :premises (t199 t50))
+(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos)
+(step t202 (cl @p_461 @p_458) :rule or :premises (t153))
+(step t203 (cl @p_458) :rule resolution :premises (t202 t44))
+(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality)
+(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204))
+(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 a19))
+(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5)))
+(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5)))
+(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$)))
+(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$)))
+(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403)))
+(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403)))
+(step t213 (cl @p_441 @p_474) :rule or :premises (t207))
+(step t214 (cl @p_474) :rule resolution :premises (t213 t92))
+(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos)
+(step t216 (cl @p_447 @p_475) :rule or :premises (t208))
+(step t217 (cl @p_475) :rule resolution :premises (t216 t74))
+(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not)
+(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg)
+(step t220 (cl (not @p_480) @p_468) :rule not_not)
+(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219))
+(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1)
+(step t223 (cl @p_469 @p_482) :rule or :premises (t209))
+(step t224 (cl @p_482) :rule resolution :premises (t223 t62))
+(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg)
+(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225))
+(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1)
+(step t228 (cl @p_469 @p_487) :rule or :premises (t210))
+(step t229 (cl @p_487) :rule resolution :premises (t228 t62))
+(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2)
+(step t231 (cl @p_472 @p_488) :rule or :premises (t211))
+(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163))
+(step t233 (cl @p_488) :rule resolution :premises (t231 t38))
+(step t234 (cl @p_489) :rule resolution :premises (t232 t233))
+(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2)
+(step t236 (cl @p_472 @p_491) :rule or :premises (t212))
+(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158))
+(step t238 (cl @p_491) :rule resolution :premises (t236 t38))
+(step t239 (cl @p_492) :rule resolution :premises (t237 t238))
+(step t240 (cl (or (! (not @p_205) :named @p_494) @p_479)) :rule forall_inst :args ((:= veriT_vr35 @p_5)))
+(step t241 (cl (or @p_494 @p_485)) :rule forall_inst :args ((:= veriT_vr35 @p_7)))
+(step t242 (cl @p_494 @p_479) :rule or :premises (t240))
+(step t243 (cl @p_479) :rule resolution :premises (t242 t80))
+(step t244 (cl @p_494 @p_485) :rule or :premises (t241))
+(step t245 (cl @p_485) :rule resolution :premises (t244 t80))
+(step t246 (cl (! (= @p_7 @p_7) :named @p_520)) :rule eq_reflexive)
+(step t247 (cl (not (! (= 1.0 0.0) :named @p_497))) :rule la_generic :args ((- 1)))
+(step t248 (cl (! (not @p_455) :named @p_505) (not (! (= @p_495 @p_496) :named @p_498)) (! (not @p_454) :named @p_506) @p_497) :rule eq_transitive)
+(step t249 (cl (not (! (= @p_417 @p_419) :named @p_501)) @p_498) :rule eq_congruent)
+(step t250 (cl (! (not @p_499) :named @p_502) (! (not @p_460) :named @p_503) (! (not @p_500) :named @p_504) @p_501) :rule eq_transitive)
+(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250))
+(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251))
+(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252))
+(step t254 (cl @p_503) :rule resolution :premises (t253 a10 a12 t196 t198))
+(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203))
+(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive)
+(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive)
+(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive)
+(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473)))
+(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473)))
+(step t261 (cl @p_510 @p_511) :rule or :premises (t259))
+(step t262 (cl @p_511) :rule resolution :premises (t261 t32))
+(step t263 (cl @p_512 @p_513) :rule or :premises (t260))
+(step t264 (cl @p_513) :rule resolution :premises (t263 t26))
+(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred)
+(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262))
+(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred)
+(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264))
+(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266))
+(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224))
+(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243))
+(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217))
+(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive)
+(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272))
+(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive)
+(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive)
+(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive)
+(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246))
+(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276))
+(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272))
+(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent)
+(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256))
+(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257))
+(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275))
+(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180))
+(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245))
+(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229))
+(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274))
+(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167))
+(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent)
+(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258))
+(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284))
+(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive)
+(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292))
+(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1)))
+(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294))
+(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272))
+(step t298 (cl @p_465) :rule resolution :premises (t206 t297))
+(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1))
+(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294))
+(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272))
+a5b152c08be1e0a4da353f094af8f11f36a16f52 333 0
 unsat
 (assume a0 (not x0$))
 (assume a1 (not x30$))
@@ -544,7 +1199,7 @@
 (step t330 (cl x36$) :rule resolution :premises (t159 t328))
 (step t331 (cl x42$) :rule resolution :premises (t287 t329))
 (step t332 (cl) :rule resolution :premises (t201 t330 t331))
-3f50b6bc75bba3bc427e4cc7f64b27bbceb4d4e3 64 0
+a73b15b00e6e103b31fc48e963d878be9038a417 64 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (! (=> (! (p$ 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))
@@ -609,7 +1264,7 @@
 (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))
-90ffc0572f49cac01988fa0e245f0987edde82e3 155 0
+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))
 (assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
@@ -765,7 +1420,7 @@
 (step t108 (cl (or @p_84 @p_92)) :rule forall_inst :args ((:= veriT_vr4 c$)))
 (step t109 (cl @p_84 @p_92) :rule or :premises (t108))
 (step t110 (cl) :rule resolution :premises (t109 t104 t107))
-2745032ad717e20a36605714726c17c0f3260db8 143 0
+6388f32213a8f0cba4b8bfe24dbcf79d47d5c156 143 0
 unsat
 (define-fun veriT_sk2 () A$ (! (choice ((veriT_vr9 A$)) (! (ite x$ (! (p$ true veriT_vr9) :named @p_48) (! (p$ false veriT_vr9) :named @p_50)) :named @p_51)) :named @p_62))
 (assume a0 (forall ((?v0 Bool) (?v1 A$)) (= (p$ ?v0 ?v1) ?v0)))
@@ -909,33 +1564,7 @@
 (step t96 (cl (or @p_84 @p_106)) :rule forall_inst :args ((:= veriT_vr10 c$)))
 (step t97 (cl @p_84 @p_106) :rule or :premises (t96))
 (step t98 (cl) :rule resolution :premises (t97 t94 t95))
-9c015c55d0136140309760a09ce754c95d1d3faa 12 0
-unsat
-(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2))
-(step t2 (cl (= @p_1 true)) :rule eq_simplify)
-(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
-(step t4 (cl (= @p_3 false)) :rule not_simplify)
-(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
-(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
-(step t7 (cl (not @p_5) @p_1) :rule not_not)
-(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
-(step t10 (cl (not false)) :rule false)
-(step t11 (cl) :rule resolution :premises (t9 t10))
-08eb77f45478246ccd84e33e8e66f49351a834c5 12 0
-unsat
-(assume a0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2))
-(step t2 (cl (= @p_1 true)) :rule eq_simplify)
-(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
-(step t4 (cl (= @p_3 false)) :rule not_simplify)
-(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
-(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
-(step t7 (cl (not @p_5) @p_1) :rule not_not)
-(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
-(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
-(step t10 (cl (not false)) :rule false)
-(step t11 (cl) :rule resolution :premises (t9 t10))
-d2da4c1f8287a8ebd2829df6fb08f0a8e938fa66 57 0
+8a6f5819f9bec363751118815580748c0df0e998 57 0
 unsat
 (assume a0 (! (ite (! (p$ 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$) :named @p_35)) :named @p_39)) :named @p_34))
@@ -993,7 +1622,33 @@
 (step t36 (cl (or @p_30 @p_44)) :rule forall_inst :args ((:= veriT_vr2 x$)))
 (step t37 (cl @p_30 @p_44) :rule or :premises (t36))
 (step t38 (cl) :rule resolution :premises (t37 t34 t35))
-413fc207ba9e12ba020fc37967fff3270d5abb5e 15 0
+fa126f313953bee2fb2b0380ecf176cbb28700f5 12 0
+unsat
+(assume a0 (! (not (! (= 3.0 3.0) :named @p_1)) :named @p_2))
+(step t2 (cl (= @p_1 true)) :rule eq_simplify)
+(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
+(step t4 (cl (= @p_3 false)) :rule not_simplify)
+(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
+(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
+(step t7 (cl (not @p_5) @p_1) :rule not_not)
+(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
+(step t10 (cl (not false)) :rule false)
+(step t11 (cl) :rule resolution :premises (t9 t10))
+ccb9d5509f5273cf85143c83133df9d0fe59cf61 12 0
+unsat
+(assume a0 (! (not (! (= 3 3) :named @p_1)) :named @p_2))
+(step t2 (cl (= @p_1 true)) :rule eq_simplify)
+(step t3 (cl (= @p_2 (! (not true) :named @p_3))) :rule cong :premises (t2))
+(step t4 (cl (= @p_3 false)) :rule not_simplify)
+(step t5 (cl (! (= @p_2 false) :named @p_4)) :rule trans :premises (t3 t4))
+(step t6 (cl (! (not @p_4) :named @p_6) (! (not @p_2) :named @p_5) false) :rule equiv_pos2)
+(step t7 (cl (not @p_5) @p_1) :rule not_not)
+(step t8 (cl @p_6 @p_1 false) :rule th_resolution :premises (t7 t6))
+(step t9 (cl false) :rule th_resolution :premises (a0 t5 t8))
+(step t10 (cl (not false)) :rule false)
+(step t11 (cl) :rule resolution :premises (t9 t10))
+2b1aff746608c673784b02123c7a44746cecbe40 15 0
 unsat
 (assume a0 (! (not (! (= (+ 3 1) 4) :named @p_1)) :named @p_3))
 (step t2 (cl @p_1) :rule sum_simplify)
@@ -1009,7 +1664,7 @@
 (step t12 (cl false) :rule th_resolution :premises (a0 t8 t11))
 (step t13 (cl (not false)) :rule false)
 (step t14 (cl) :rule resolution :premises (t12 t13))
-845b74b5125cd3ba120ea66952b9f97a5c6ab1c3 9 0
+c6b09353a7be5ebe2570119db169d6f24068d0d9 9 0
 unsat
 (assume a0 (not (! (= (! (+ x$ (+ y$ z$)) :named @p_2) (! (+ y$ (+ z$ x$)) :named @p_3)) :named @p_1)))
 (step t2 (cl (or @p_1 (! (not (! (<= @p_2 @p_3) :named @p_6)) :named @p_4) (! (not (! (<= @p_3 @p_2) :named @p_7)) :named @p_5))) :rule la_disequality)
@@ -1019,7 +1674,7 @@
 (step t6 (cl @p_5) :rule resolution :premises (t4 t5))
 (step t7 (cl @p_7) :rule la_generic :args (1))
 (step t8 (cl) :rule resolution :premises (t7 t6))
-d8dbfe74fd522039391998d9bbfb9e867f02f283 18 0
+91dfb7793d7cbf20aa8e7b00578ee445d34e2640 18 0
 unsat
 (assume a0 (! (not (! (< 5 (! (ite (! (<= 3 8) :named @p_1) 8 3) :named @p_2)) :named @p_4)) :named @p_6))
 (step t2 (cl (= @p_1 true)) :rule comp_simplify)
@@ -1038,7 +1693,7 @@
 (step t15 (cl false) :rule th_resolution :premises (a0 t11 t14))
 (step t16 (cl (not false)) :rule false)
 (step t17 (cl) :rule resolution :premises (t15 t16))
-aa08521b4449c3ee379b738c697dd0a12da6c519 52 0
+97cec8dc2da703d81d93c4024dc370fb1ecba1f5 52 0
 unsat
 (assume a0 (! (not (! (<= (! (ite (! (< (! (+ x$ y$) :named @p_1) 0.0) :named @p_6) (! (- @p_1) :named @p_7) @p_1) :named @p_3) (+ (! (ite (! (< x$ 0.0) :named @p_8) (! (- x$) :named @p_9) x$) :named @p_4) (! (ite (! (< y$ 0.0) :named @p_10) (! (- y$) :named @p_11) y$) :named @p_5))) :named @p_15)) :named @p_2))
 (step t2 (cl (! (= @p_2 (! (and (! (not (! (<= @p_3 (+ @p_4 @p_5)) :named @p_28)) :named @p_17) (! (ite @p_6 (! (= @p_7 @p_3) :named @p_20) (! (= @p_1 @p_3) :named @p_19)) :named @p_18) (! (ite @p_8 (! (= @p_9 @p_4) :named @p_23) (! (= x$ @p_4) :named @p_22)) :named @p_21) (! (ite @p_10 (! (= @p_11 @p_5) :named @p_26) (! (= y$ @p_5) :named @p_25)) :named @p_24)) :named @p_13)) :named @p_12)) :rule ite_intro)
@@ -1091,7 +1746,7 @@
 (step t49 (cl @p_19) :rule resolution :premises (t9 t48))
 (step t50 (cl @p_28 @p_36 @p_31 @p_29 @p_34) :rule la_generic :args (1.0 2.0 1 (- 1) (- 1)))
 (step t51 (cl) :rule resolution :premises (t50 t7 t49 t45 t46 t43))
-1a8db76be6f6a2bddea4084033566e745253b622 19 0
+7769e70c7b5fc90175ef68eb5528034a2de273a9 19 0
 unsat
 (assume a0 (not (= (p$ (! (< 2 3) :named @p_2)) (! (p$ true) :named @p_1))))
 (step t2 (cl (! (not (! (= @p_1 (! (ite @p_2 @p_1 (! (p$ false) :named @p_4)) :named @p_3)) :named @p_6)) :named @p_8)) :rule bfun_elim :premises (a0))
@@ -1111,7 +1766,7 @@
 (step t16 (cl false) :rule th_resolution :premises (t2 t12 t15))
 (step t17 (cl (not false)) :rule false)
 (step t18 (cl) :rule resolution :premises (t16 t17))
-229e9450bd215085107290b86bc3fa4754765364 14 0
+8efe160efd738ec7872179ed94f190d410e1ef4b 14 0
 unsat
 (assume a0 (! (not (! (or (! (<= 4 (! (+ x$ 3) :named @p_1)) :named @p_2) (! (< x$ 1) :named @p_6)) :named @p_4)) :named @p_7))
 (step t2 (cl (= @p_1 (! (+ 3 x$) :named @p_3))) :rule sum_simplify)
@@ -1126,7 +1781,7 @@
 (step t11 (cl (not @p_6)) :rule not_or :premises (t9))
 (step t12 (cl @p_6 @p_5) :rule la_generic :args (1 1))
 (step t13 (cl) :rule resolution :premises (t12 t10 t11))
-b1115b3662d14722175185e9377414ecb2b1046b 9 0
+2644c68299be3dd9fabbbba4920be4f3ffe3485b 9 0
 unsat
 (assume a1 (! (= y$ (! (+ x$ 4) :named @p_1)) :named @p_2))
 (assume a2 (not (! (< 0 (- y$ x$)) :named @p_6)))
@@ -1136,14 +1791,7 @@
 (step t6 (cl @p_5) :rule th_resolution :premises (a1 t4 t5))
 (step t7 (cl @p_6 (not @p_5)) :rule la_generic :args (1 1))
 (step t8 (cl) :rule resolution :premises (t7 t6 a2))
-dfc587dec547748e78f3739a9819c7922a81f17f 6 0
-unsat
-(assume a0 (! (< (+ (* 3 x$) (* 7 a$)) 4) :named @p_3))
-(assume a1 (! (< 3 (* 2 x$)) :named @p_1))
-(assume a2 (not (! (< a$ 0) :named @p_2)))
-(step t4 (cl (not @p_1) @p_2 (not @p_3)) :rule la_generic :args ((div 3 2) 7 1))
-(step t5 (cl) :rule resolution :premises (t4 a0 a1 a2))
-dedf92567622c8873796e3213079c20d4c0be727 20 0
+478778f1172d1db195bd4eb0883b9dd6613297c3 20 0
 unsat
 (assume a0 (! (not (! (not (! (= (! (+ 2 2) :named @p_3) 5) :named @p_2)) :named @p_5)) :named @p_1))
 (step t2 (cl (! (not @p_1) :named @p_9) @p_2) :rule not_not)
@@ -1164,7 +1812,14 @@
 (step t17 (cl false) :rule th_resolution :premises (t3 t13 t16))
 (step t18 (cl @p_6) :rule false)
 (step t19 (cl) :rule resolution :premises (t17 t18))
-282e1f4ae1fe9c95cfac6cd19305613aa9bb9fdc 29 0
+04820c02101d5d6a8a322ddf869652416ac9ae19 6 0
+unsat
+(assume a0 (! (< (+ (* 3 x$) (* 7 a$)) 4) :named @p_3))
+(assume a1 (! (< 3 (* 2 x$)) :named @p_1))
+(assume a2 (not (! (< a$ 0) :named @p_2)))
+(step t4 (cl (not @p_1) @p_2 (not @p_3)) :rule la_generic :args ((div 3 2) 7 1))
+(step t5 (cl) :rule resolution :premises (t4 a0 a1 a2))
+699e547ad956b6867c5f571d9e08d46038579011 29 0
 unsat
 (assume a0 (! (not (! (= (! (or (! (<= 0 (! (+ y$ (! (* (! (- 1) :named @p_14) x$) :named @p_15)) :named @p_16)) :named @p_3) (or (! (not (! (<= 0 x$) :named @p_1)) :named @p_4) @p_1)) :named @p_2) (! (not false) :named @p_7)) :named @p_5)) :named @p_8))
 (step t2 (cl (= @p_2 (! (or @p_3 @p_4 @p_1) :named @p_6))) :rule ac_simp)
@@ -1194,7 +1849,7 @@
 (step t26 (cl false) :rule th_resolution :premises (t8 t22 t25))
 (step t27 (cl @p_7) :rule false)
 (step t28 (cl) :rule resolution :premises (t26 t27))
-db4fd717bbfc4454488919af499429897e517aaf 62 0
+bf46578ff4814695a5afd6f19836b2d606a6b97c 62 0
 unsat
 (assume a0 (! (not (! (or (! (and (! (< n$ m$) :named @p_1) (! (< m$ n$a) :named @p_3)) :named @p_11) (or (! (and @p_1 (! (= m$ n$a) :named @p_6)) :named @p_12) (or (! (and (! (< n$ n$a) :named @p_8) (! (< n$a m$) :named @p_2)) :named @p_13) (or (! (and (! (= n$ n$a) :named @p_5) @p_2) :named @p_14) (or (! (and (! (= n$ m$) :named @p_4) @p_3) :named @p_15) (or (! (and @p_2 (! (< m$ n$) :named @p_7)) :named @p_16) (or (! (and @p_2 @p_4) :named @p_17) (or (! (and (! (< n$a n$) :named @p_9) @p_1) :named @p_18) (or (! (and @p_5 @p_1) :named @p_19) (or (! (and @p_6 @p_7) :named @p_20) (or (! (and @p_7 @p_8) :named @p_21) (or (! (and @p_7 @p_5) :named @p_22) (or (! (and @p_3 @p_9) :named @p_23) (or (! (and @p_4 @p_8) :named @p_24) (or (! (and @p_6 @p_9) :named @p_25) (! (and @p_6 @p_4) :named @p_26)))))))))))))))) :named @p_10)) :named @p_27))
 (step t2 (cl (= @p_10 (! (or @p_11 @p_12 @p_13 @p_14 @p_15 @p_16 @p_17 @p_18 @p_19 @p_20 @p_21 @p_22 @p_23 @p_24 @p_25 @p_26) :named @p_28))) :rule ac_simp)
@@ -1257,183 +1912,7 @@
 (step t59 (cl @p_40) :rule resolution :premises (t17 t57))
 (step t60 (cl @p_50) :rule resolution :premises (t42 t58))
 (step t61 (cl) :rule resolution :premises (t35 t59 t54 t60))
-930494d7814037632f0f2cf405656cd7e35a6de4 21 0
-unsat
-(assume a0 (! (not (! (or (! (< (! (+ x$ x$) :named @p_11) (! (+ (! (* 2.0 x$) :named @p_10) 1.0) :named @p_9)) :named @p_1) (or false @p_1)) :named @p_2)) :named @p_3))
-(step t2 (cl (= @p_2 (! (or @p_1 false) :named @p_4))) :rule ac_simp)
-(step t3 (cl (! (= @p_3 (! (not @p_4) :named @p_6)) :named @p_5)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_5) :named @p_8) (! (not @p_3) :named @p_7) @p_6) :rule equiv_pos2)
-(step t5 (cl (not @p_7) @p_2) :rule not_not)
-(step t6 (cl @p_8 @p_2 @p_6) :rule th_resolution :premises (t5 t4))
-(step t7 (cl @p_6) :rule th_resolution :premises (a0 t3 t6))
-(step t8 (cl (= @p_9 (! (+ 1.0 @p_10) :named @p_12))) :rule sum_simplify)
-(step t9 (cl (= @p_1 (! (< @p_11 @p_12) :named @p_13))) :rule cong :premises (t8))
-(step t10 (cl (= @p_4 (! (or @p_13 false) :named @p_14))) :rule cong :premises (t9))
-(step t11 (cl (= @p_14 (! (or @p_13) :named @p_15))) :rule or_simplify)
-(step t12 (cl (= @p_15 @p_13)) :rule or_simplify)
-(step t13 (cl (= @p_4 @p_13)) :rule trans :premises (t10 t11 t12))
-(step t14 (cl (! (= @p_6 (! (not @p_13) :named @p_17)) :named @p_16)) :rule cong :premises (t13))
-(step t15 (cl (! (not @p_16) :named @p_19) (! (not @p_6) :named @p_18) @p_17) :rule equiv_pos2)
-(step t16 (cl (not @p_18) @p_4) :rule not_not)
-(step t17 (cl @p_19 @p_4 @p_17) :rule th_resolution :premises (t16 t15))
-(step t18 (cl @p_17) :rule th_resolution :premises (t7 t14 t17))
-(step t19 (cl @p_13) :rule la_tautology)
-(step t20 (cl) :rule resolution :premises (t19 t18))
-af075a1bc11466b86b2e32272fabf79492e0766f 16 0
-unsat
-(assume a0 (! (not (! (not (! (exists ((?v0 Int)) false) :named @p_2)) :named @p_3)) :named @p_1))
-(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
-(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
-(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
-(step t8 (cl (not @p_6) @p_3) :rule not_not)
-(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
-(step t10 (cl (not @p_7) false) :rule not_not)
-(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
-(step t13 (cl false) :rule th_resolution :premises (t10 t12))
-(step t14 (cl @p_4) :rule false)
-(step t15 (cl) :rule resolution :premises (t13 t14))
-feb8f580c0ed1105dae26acee8e38d20f9cad1e9 16 0
-unsat
-(assume a0 (! (not (! (not (! (exists ((?v0 Real)) false) :named @p_2)) :named @p_3)) :named @p_1))
-(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
-(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
-(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
-(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
-(step t8 (cl (not @p_6) @p_3) :rule not_not)
-(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
-(step t10 (cl (not @p_7) false) :rule not_not)
-(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
-(step t13 (cl false) :rule th_resolution :premises (t10 t12))
-(step t14 (cl @p_4) :rule false)
-(step t15 (cl) :rule resolution :premises (t13 t14))
-91440d65260ff516e2ae884704f5e854d05caa5d 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)))
-(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)
-(step t2.t4 (cl (= @p_4 (! (= 1 1) :named @p_5))) :rule cong :premises (t2.t3))
-(step t2.t5 (cl (= @p_6 (! (and @p_3 @p_5) :named @p_7))) :rule cong :premises (t2.t2 t2.t4))
-(step t2.t6 (cl @p_2) :rule refl)
-(step t2.t7 (cl @p_4) :rule refl)
-(step t2.t8 (cl (= @p_8 (! (= 0 1) :named @p_9))) :rule cong :premises (t2.t6 t2.t7))
-(step t2.t9 (cl (= @p_10 (! (not @p_9) :named @p_11))) :rule cong :premises (t2.t8))
-(step t2.t10 (cl (= @p_12 (! (=> @p_7 @p_11) :named @p_13))) :rule cong :premises (t2.t5 t2.t9))
-(step t2 (cl (= @p_1 @p_13)) :rule onepoint)
-(step t3 (cl (! (= @p_14 (! (not @p_13) :named @p_16)) :named @p_15)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_14) :named @p_17) @p_16) :rule equiv_pos2)
-(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))
-(step t8 (cl (! (= @p_16 (! (and @p_7 (! (not @p_11) :named @p_23)) :named @p_20)) :named @p_19)) :rule bool_simplify)
-(step t9 (cl (! (not @p_19) :named @p_22) (! (not @p_16) :named @p_21) @p_20) :rule equiv_pos2)
-(step t10 (cl (not @p_21) @p_13) :rule not_not)
-(step t11 (cl @p_22 @p_13 @p_20) :rule th_resolution :premises (t10 t9))
-(step t12 (cl @p_20) :rule th_resolution :premises (t7 t8 t11))
-(step t13 (cl (! (= @p_20 (! (and @p_3 @p_5 @p_23) :named @p_25)) :named @p_24)) :rule ac_simp)
-(step t14 (cl (not @p_24) (not @p_20) @p_25) :rule equiv_pos2)
-(step t15 (cl @p_25) :rule th_resolution :premises (t12 t13 t14))
-(step t16 (cl (= @p_3 true)) :rule eq_simplify)
-(step t17 (cl (= @p_5 true)) :rule eq_simplify)
-(step t18 (cl (= @p_9 false)) :rule eq_simplify)
-(step t19 (cl (= @p_11 (! (not false) :named @p_26))) :rule cong :premises (t18))
-(step t20 (cl (= @p_26 true)) :rule not_simplify)
-(step t21 (cl (= @p_11 true)) :rule trans :premises (t19 t20))
-(step t22 (cl (= @p_23 (! (not true) :named @p_27))) :rule cong :premises (t21))
-(step t23 (cl (= @p_27 false)) :rule not_simplify)
-(step t24 (cl (= @p_23 false)) :rule trans :premises (t22 t23))
-(step t25 (cl (= @p_25 (! (and true true false) :named @p_28))) :rule cong :premises (t16 t17 t24))
-(step t26 (cl (= @p_28 (! (and false) :named @p_29))) :rule and_simplify)
-(step t27 (cl (= @p_29 false)) :rule and_simplify)
-(step t28 (cl (! (= @p_25 false) :named @p_30)) :rule trans :premises (t25 t26 t27))
-(step t29 (cl (not @p_30) (not @p_25) false) :rule equiv_pos2)
-(step t30 (cl false) :rule th_resolution :premises (t15 t28 t29))
-(step t31 (cl @p_26) :rule false)
-(step t32 (cl) :rule resolution :premises (t30 t31))
-10c5b784e1c17a8b9f972e3ab359ad726230a233 74 0
-unsat
-(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)))
-(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))
-(step t2.t4 (cl @p_4) :rule refl)
-(step t2.t5 (cl (= @p_5 (! (* 2 veriT_vr0) :named @p_6))) :rule cong :premises (t2.t4))
-(step t2.t6 (cl (= @p_7 (! (+ @p_6 1) :named @p_8))) :rule cong :premises (t2.t5))
-(step t2.t7 (cl @p_9) :rule refl)
-(step t2.t8 (cl (= @p_10 (! (* 2 veriT_vr1) :named @p_11))) :rule cong :premises (t2.t7))
-(step t2.t9 (cl (= @p_12 (! (< @p_8 @p_11) :named @p_13))) :rule cong :premises (t2.t6 t2.t8))
-(step t2.t10 (cl (= @p_14 (! (=> @p_3 @p_13) :named @p_15))) :rule cong :premises (t2.t3 t2.t9))
-(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_15) :named @p_17))) :rule bind)
-(step t3 (cl (! (= @p_16 (! (not @p_17) :named @p_19)) :named @p_18)) :rule cong :premises (t2))
-(step t4 (cl (! (not @p_18) :named @p_21) (! (not @p_16) :named @p_20) @p_19) :rule equiv_pos2)
-(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))
-(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))
-(step t8 (cl (= @p_17 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_24) :named @p_25))) :rule bind)
-(step t9 (cl (! (= @p_19 (! (not @p_25) :named @p_27)) :named @p_26)) :rule cong :premises (t8))
-(step t10 (cl (! (not @p_26) :named @p_29) (! (not @p_19) :named @p_28) @p_27) :rule equiv_pos2)
-(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)))
-(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))
-(step t14.t4 (cl @p_31) :rule refl)
-(step t14.t5 (cl (= @p_6 @p_32)) :rule cong :premises (t14.t4))
-(step t14.t6 (cl (= @p_22 @p_33)) :rule cong :premises (t14.t5))
-(step t14.t7 (cl @p_34) :rule refl)
-(step t14.t8 (cl (= @p_11 @p_35)) :rule cong :premises (t14.t7))
-(step t14.t9 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t6 t14.t8))
-(step t14.t10 (cl (= @p_24 @p_37)) :rule cong :premises (t14.t3 t14.t9))
-(step t14 (cl (= @p_25 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_37) :named @p_38))) :rule bind)
-(step t15 (cl (! (= @p_27 (! (not @p_38) :named @p_40)) :named @p_39)) :rule cong :premises (t14))
-(step t16 (cl (! (not @p_39) :named @p_42) (! (not @p_27) :named @p_41) @p_40) :rule equiv_pos2)
-(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)))
-(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))
-(step t20.t4 (cl @p_46) :rule refl)
-(step t20.t5 (cl (= @p_32 (! (* 2 veriT_sk0) :named @p_47))) :rule cong :premises (t20.t4))
-(step t20.t6 (cl (= @p_33 (! (+ 1 @p_47) :named @p_48))) :rule cong :premises (t20.t5))
-(step t20.t7 (cl @p_49) :rule refl)
-(step t20.t8 (cl (= @p_35 (! (* 2 veriT_sk1) :named @p_50))) :rule cong :premises (t20.t7))
-(step t20.t9 (cl (= @p_36 (! (< @p_48 @p_50) :named @p_51))) :rule cong :premises (t20.t6 t20.t8))
-(step t20.t10 (cl (= @p_37 (! (=> @p_45 @p_51) :named @p_52))) :rule cong :premises (t20.t3 t20.t9))
-(step t20 (cl (= @p_38 @p_52)) :rule sko_forall)
-(step t21 (cl (! (= @p_40 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
-(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_40) :named @p_55) @p_54) :rule equiv_pos2)
-(step t23 (cl (not @p_55) @p_38) :rule not_not)
-(step t24 (cl @p_56 @p_38 @p_54) :rule th_resolution :premises (t23 t22))
-(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
-(step t26 (cl (! (= @p_54 (! (and @p_45 (! (not @p_51) :named @p_61)) :named @p_58)) :named @p_57)) :rule bool_simplify)
-(step t27 (cl (! (not @p_57) :named @p_60) (! (not @p_54) :named @p_59) @p_58) :rule equiv_pos2)
-(step t28 (cl (not @p_59) @p_52) :rule not_not)
-(step t29 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t28 t27))
-(step t30 (cl @p_58) :rule th_resolution :premises (t25 t26 t29))
-(step t31 (cl @p_45) :rule and :premises (t30))
-(step t32 (cl @p_61) :rule and :premises (t30))
-(step t33 (cl @p_51 (not @p_45)) :rule la_generic :args ((div 1 2) 1))
-(step t34 (cl) :rule resolution :premises (t33 t31 t32))
-37c31d8c4e1a148b5be59fa2fa31b2125c42764a 371 0
+4aba1ea4675669f505d0a9484fd751da13811782 371 0
 unsat
 (assume a0 (! (not (! (=> (! (and (! (= x3$ (- (! (ite (! (< x2$ 0) :named @p_30) (! (- x2$) :named @p_31) x2$) :named @p_21) x1$)) :named @p_9) (and (! (= x4$ (- (! (ite (! (< x3$ 0) :named @p_32) (! (- x3$) :named @p_33) x3$) :named @p_22) x2$)) :named @p_10) (and (! (= x5$ (- (! (ite (! (< x4$ 0) :named @p_34) (! (- x4$) :named @p_35) x4$) :named @p_23) x3$)) :named @p_11) (and (! (= x6$ (- (! (ite (! (< x5$ 0) :named @p_36) (! (- x5$) :named @p_37) x5$) :named @p_24) x4$)) :named @p_12) (and (! (= x7$ (- (! (ite (! (< x6$ 0) :named @p_38) (! (- x6$) :named @p_39) x6$) :named @p_25) x5$)) :named @p_13) (and (! (= x8$ (- (! (ite (! (< x7$ 0) :named @p_40) (! (- x7$) :named @p_41) x7$) :named @p_26) x6$)) :named @p_14) (and (! (= x9$ (- (! (ite (! (< x8$ 0) :named @p_42) (! (- x8$) :named @p_43) x8$) :named @p_27) x7$)) :named @p_15) (and (! (= x10$ (- (! (ite (! (< x9$ 0) :named @p_44) (! (- x9$) :named @p_45) x9$) :named @p_28) x8$)) :named @p_16) (! (= x11$ (- (! (ite (! (< x10$ 0) :named @p_46) (! (- x10$) :named @p_47) x10$) :named @p_29) x9$)) :named @p_17))))))))) :named @p_2) (! (and (! (= x1$ x10$) :named @p_70) (! (= x2$ x11$) :named @p_71)) :named @p_3)) :named @p_7)) :named @p_1))
 (step t2 (cl (! (= @p_1 (! (and @p_2 (! (not @p_3) :named @p_18)) :named @p_5)) :named @p_4)) :rule bool_simplify)
@@ -1805,7 +2284,183 @@
 (step t368 (cl @p_74) :rule resolution :premises (t31 t367))
 (step t369 (cl @p_140) :rule resolution :premises (t107 t367 t368 t365))
 (step t370 (cl) :rule resolution :premises (t243 t368 t327 t326 t366 t308 t369))
-2bf1326b4ee67b65a19f29be926aaada4159282d 84 0
+8bfcf7a37e6d407d5cd3eb931a35cdc0c65c7e57 21 0
+unsat
+(assume a0 (! (not (! (or (! (< (! (+ x$ x$) :named @p_11) (! (+ (! (* 2.0 x$) :named @p_10) 1.0) :named @p_9)) :named @p_1) (or false @p_1)) :named @p_2)) :named @p_3))
+(step t2 (cl (= @p_2 (! (or @p_1 false) :named @p_4))) :rule ac_simp)
+(step t3 (cl (! (= @p_3 (! (not @p_4) :named @p_6)) :named @p_5)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_5) :named @p_8) (! (not @p_3) :named @p_7) @p_6) :rule equiv_pos2)
+(step t5 (cl (not @p_7) @p_2) :rule not_not)
+(step t6 (cl @p_8 @p_2 @p_6) :rule th_resolution :premises (t5 t4))
+(step t7 (cl @p_6) :rule th_resolution :premises (a0 t3 t6))
+(step t8 (cl (= @p_9 (! (+ 1.0 @p_10) :named @p_12))) :rule sum_simplify)
+(step t9 (cl (= @p_1 (! (< @p_11 @p_12) :named @p_13))) :rule cong :premises (t8))
+(step t10 (cl (= @p_4 (! (or @p_13 false) :named @p_14))) :rule cong :premises (t9))
+(step t11 (cl (= @p_14 (! (or @p_13) :named @p_15))) :rule or_simplify)
+(step t12 (cl (= @p_15 @p_13)) :rule or_simplify)
+(step t13 (cl (= @p_4 @p_13)) :rule trans :premises (t10 t11 t12))
+(step t14 (cl (! (= @p_6 (! (not @p_13) :named @p_17)) :named @p_16)) :rule cong :premises (t13))
+(step t15 (cl (! (not @p_16) :named @p_19) (! (not @p_6) :named @p_18) @p_17) :rule equiv_pos2)
+(step t16 (cl (not @p_18) @p_4) :rule not_not)
+(step t17 (cl @p_19 @p_4 @p_17) :rule th_resolution :premises (t16 t15))
+(step t18 (cl @p_17) :rule th_resolution :premises (t7 t14 t17))
+(step t19 (cl @p_13) :rule la_tautology)
+(step t20 (cl) :rule resolution :premises (t19 t18))
+3982a32a09aa6c7a103906438cf1f4eedfd441ab 16 0
+unsat
+(assume a0 (! (not (! (not (! (exists ((?v0 Int)) false) :named @p_2)) :named @p_3)) :named @p_1))
+(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
+(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
+(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
+(step t8 (cl (not @p_6) @p_3) :rule not_not)
+(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
+(step t10 (cl (not @p_7) false) :rule not_not)
+(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
+(step t13 (cl false) :rule th_resolution :premises (t10 t12))
+(step t14 (cl @p_4) :rule false)
+(step t15 (cl) :rule resolution :premises (t13 t14))
+74d9e4df0e27627f80a8b0c06331b33d5f261c17 16 0
+unsat
+(assume a0 (! (not (! (not (! (exists ((?v0 Real)) false) :named @p_2)) :named @p_3)) :named @p_1))
+(step t2 (cl (! (not @p_1) :named @p_6) @p_2) :rule not_not)
+(step t3 (cl @p_2) :rule th_resolution :premises (t2 a0))
+(step t4 (cl (= @p_2 false)) :rule qnt_rm_unused)
+(step t5 (cl (= @p_3 (! (not false) :named @p_4))) :rule cong :premises (t4))
+(step t6 (cl (! (= @p_1 (! (not @p_4) :named @p_7)) :named @p_5)) :rule cong :premises (t5))
+(step t7 (cl (! (not @p_5) :named @p_8) @p_6 @p_7) :rule equiv_pos2)
+(step t8 (cl (not @p_6) @p_3) :rule not_not)
+(step t9 (cl @p_8 @p_3 @p_7) :rule th_resolution :premises (t8 t7))
+(step t10 (cl (not @p_7) false) :rule not_not)
+(step t11 (cl @p_8 @p_3 false) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_7) :rule th_resolution :premises (t3 t6 t11))
+(step t13 (cl false) :rule th_resolution :premises (t10 t12))
+(step t14 (cl @p_4) :rule false)
+(step t15 (cl) :rule resolution :premises (t13 t14))
+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)))
+(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)
+(step t2.t4 (cl (= @p_4 (! (= 1 1) :named @p_5))) :rule cong :premises (t2.t3))
+(step t2.t5 (cl (= @p_6 (! (and @p_3 @p_5) :named @p_7))) :rule cong :premises (t2.t2 t2.t4))
+(step t2.t6 (cl @p_2) :rule refl)
+(step t2.t7 (cl @p_4) :rule refl)
+(step t2.t8 (cl (= @p_8 (! (= 0 1) :named @p_9))) :rule cong :premises (t2.t6 t2.t7))
+(step t2.t9 (cl (= @p_10 (! (not @p_9) :named @p_11))) :rule cong :premises (t2.t8))
+(step t2.t10 (cl (= @p_12 (! (=> @p_7 @p_11) :named @p_13))) :rule cong :premises (t2.t5 t2.t9))
+(step t2 (cl (= @p_1 @p_13)) :rule onepoint)
+(step t3 (cl (! (= @p_14 (! (not @p_13) :named @p_16)) :named @p_15)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_14) :named @p_17) @p_16) :rule equiv_pos2)
+(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))
+(step t8 (cl (! (= @p_16 (! (and @p_7 (! (not @p_11) :named @p_23)) :named @p_20)) :named @p_19)) :rule bool_simplify)
+(step t9 (cl (! (not @p_19) :named @p_22) (! (not @p_16) :named @p_21) @p_20) :rule equiv_pos2)
+(step t10 (cl (not @p_21) @p_13) :rule not_not)
+(step t11 (cl @p_22 @p_13 @p_20) :rule th_resolution :premises (t10 t9))
+(step t12 (cl @p_20) :rule th_resolution :premises (t7 t8 t11))
+(step t13 (cl (! (= @p_20 (! (and @p_3 @p_5 @p_23) :named @p_25)) :named @p_24)) :rule ac_simp)
+(step t14 (cl (not @p_24) (not @p_20) @p_25) :rule equiv_pos2)
+(step t15 (cl @p_25) :rule th_resolution :premises (t12 t13 t14))
+(step t16 (cl (= @p_3 true)) :rule eq_simplify)
+(step t17 (cl (= @p_5 true)) :rule eq_simplify)
+(step t18 (cl (= @p_9 false)) :rule eq_simplify)
+(step t19 (cl (= @p_11 (! (not false) :named @p_26))) :rule cong :premises (t18))
+(step t20 (cl (= @p_26 true)) :rule not_simplify)
+(step t21 (cl (= @p_11 true)) :rule trans :premises (t19 t20))
+(step t22 (cl (= @p_23 (! (not true) :named @p_27))) :rule cong :premises (t21))
+(step t23 (cl (= @p_27 false)) :rule not_simplify)
+(step t24 (cl (= @p_23 false)) :rule trans :premises (t22 t23))
+(step t25 (cl (= @p_25 (! (and true true false) :named @p_28))) :rule cong :premises (t16 t17 t24))
+(step t26 (cl (= @p_28 (! (and false) :named @p_29))) :rule and_simplify)
+(step t27 (cl (= @p_29 false)) :rule and_simplify)
+(step t28 (cl (! (= @p_25 false) :named @p_30)) :rule trans :premises (t25 t26 t27))
+(step t29 (cl (not @p_30) (not @p_25) false) :rule equiv_pos2)
+(step t30 (cl false) :rule th_resolution :premises (t15 t28 t29))
+(step t31 (cl @p_26) :rule false)
+(step t32 (cl) :rule resolution :premises (t30 t31))
+126e26a1f138f1b616eeae4aad01c11068cd71e0 74 0
+unsat
+(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)))
+(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))
+(step t2.t4 (cl @p_4) :rule refl)
+(step t2.t5 (cl (= @p_5 (! (* 2 veriT_vr0) :named @p_6))) :rule cong :premises (t2.t4))
+(step t2.t6 (cl (= @p_7 (! (+ @p_6 1) :named @p_8))) :rule cong :premises (t2.t5))
+(step t2.t7 (cl @p_9) :rule refl)
+(step t2.t8 (cl (= @p_10 (! (* 2 veriT_vr1) :named @p_11))) :rule cong :premises (t2.t7))
+(step t2.t9 (cl (= @p_12 (! (< @p_8 @p_11) :named @p_13))) :rule cong :premises (t2.t6 t2.t8))
+(step t2.t10 (cl (= @p_14 (! (=> @p_3 @p_13) :named @p_15))) :rule cong :premises (t2.t3 t2.t9))
+(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_15) :named @p_17))) :rule bind)
+(step t3 (cl (! (= @p_16 (! (not @p_17) :named @p_19)) :named @p_18)) :rule cong :premises (t2))
+(step t4 (cl (! (not @p_18) :named @p_21) (! (not @p_16) :named @p_20) @p_19) :rule equiv_pos2)
+(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))
+(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))
+(step t8 (cl (= @p_17 (! (forall ((veriT_vr0 Int) (veriT_vr1 Int)) @p_24) :named @p_25))) :rule bind)
+(step t9 (cl (! (= @p_19 (! (not @p_25) :named @p_27)) :named @p_26)) :rule cong :premises (t8))
+(step t10 (cl (! (not @p_26) :named @p_29) (! (not @p_19) :named @p_28) @p_27) :rule equiv_pos2)
+(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)))
+(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))
+(step t14.t4 (cl @p_31) :rule refl)
+(step t14.t5 (cl (= @p_6 @p_32)) :rule cong :premises (t14.t4))
+(step t14.t6 (cl (= @p_22 @p_33)) :rule cong :premises (t14.t5))
+(step t14.t7 (cl @p_34) :rule refl)
+(step t14.t8 (cl (= @p_11 @p_35)) :rule cong :premises (t14.t7))
+(step t14.t9 (cl (= @p_23 @p_36)) :rule cong :premises (t14.t6 t14.t8))
+(step t14.t10 (cl (= @p_24 @p_37)) :rule cong :premises (t14.t3 t14.t9))
+(step t14 (cl (= @p_25 (! (forall ((veriT_vr2 Int) (veriT_vr3 Int)) @p_37) :named @p_38))) :rule bind)
+(step t15 (cl (! (= @p_27 (! (not @p_38) :named @p_40)) :named @p_39)) :rule cong :premises (t14))
+(step t16 (cl (! (not @p_39) :named @p_42) (! (not @p_27) :named @p_41) @p_40) :rule equiv_pos2)
+(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)))
+(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))
+(step t20.t4 (cl @p_46) :rule refl)
+(step t20.t5 (cl (= @p_32 (! (* 2 veriT_sk0) :named @p_47))) :rule cong :premises (t20.t4))
+(step t20.t6 (cl (= @p_33 (! (+ 1 @p_47) :named @p_48))) :rule cong :premises (t20.t5))
+(step t20.t7 (cl @p_49) :rule refl)
+(step t20.t8 (cl (= @p_35 (! (* 2 veriT_sk1) :named @p_50))) :rule cong :premises (t20.t7))
+(step t20.t9 (cl (= @p_36 (! (< @p_48 @p_50) :named @p_51))) :rule cong :premises (t20.t6 t20.t8))
+(step t20.t10 (cl (= @p_37 (! (=> @p_45 @p_51) :named @p_52))) :rule cong :premises (t20.t3 t20.t9))
+(step t20 (cl (= @p_38 @p_52)) :rule sko_forall)
+(step t21 (cl (! (= @p_40 (! (not @p_52) :named @p_54)) :named @p_53)) :rule cong :premises (t20))
+(step t22 (cl (! (not @p_53) :named @p_56) (! (not @p_40) :named @p_55) @p_54) :rule equiv_pos2)
+(step t23 (cl (not @p_55) @p_38) :rule not_not)
+(step t24 (cl @p_56 @p_38 @p_54) :rule th_resolution :premises (t23 t22))
+(step t25 (cl @p_54) :rule th_resolution :premises (t19 t21 t24))
+(step t26 (cl (! (= @p_54 (! (and @p_45 (! (not @p_51) :named @p_61)) :named @p_58)) :named @p_57)) :rule bool_simplify)
+(step t27 (cl (! (not @p_57) :named @p_60) (! (not @p_54) :named @p_59) @p_58) :rule equiv_pos2)
+(step t28 (cl (not @p_59) @p_52) :rule not_not)
+(step t29 (cl @p_60 @p_52 @p_58) :rule th_resolution :premises (t28 t27))
+(step t30 (cl @p_58) :rule th_resolution :premises (t25 t26 t29))
+(step t31 (cl @p_45) :rule and :premises (t30))
+(step t32 (cl @p_61) :rule and :premises (t30))
+(step t33 (cl @p_51 (not @p_45)) :rule la_generic :args ((div 1 2) 1))
+(step t34 (cl) :rule resolution :premises (t33 t31 t32))
+8ef63c3af9accda70a9adb945698c9dc83c299cb 84 0
 unsat
 (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))
@@ -1890,7 +2545,7 @@
 (step t34 (cl @p_58) :rule resolution :premises (t31 t33))
 (step t35 (cl @p_60 @p_46) :rule la_generic :args (1 1))
 (step t36 (cl) :rule resolution :premises (t35 t26 t34))
-99600e9e235b6ce7e9b8a3d2c559c08161c6c86d 67 0
+009068a6f752b63c0ec5b63adbd0474d11cb4745 67 0
 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))
@@ -1958,7 +2613,7 @@
 (step t32 (cl @p_50) :rule resolution :premises (t26 t31))
 (step t33 (cl @p_43 @p_39) :rule la_generic :args (1 1))
 (step t34 (cl) :rule resolution :premises (t33 t31 t32))
-78fb89c5958debfdc5cd4bf36e64314b72b330d7 107 0
+72ef753af86f7012e75f73f9bc2d3adda07e800b 107 0
 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))
@@ -2066,7 +2721,7 @@
 (step t71 (cl @p_85) :rule false)
 (step t72 (cl @p_65 false) :rule or :premises (t70))
 (step t73 (cl) :rule resolution :premises (t72 t63 t71))
-3d6f96b90383a5a25927e677a0f1a6c0d59e14ee 74 0
+79c36cccfa675d72431ed7e3c2f6afc45f85907a 74 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Int)) (! (=> (! (and (! (< 0 veriT_vr2) :named @p_27) (! (< 0 veriT_vr3) :named @p_28)) :named @p_29) (! (< 0 (! (+ veriT_vr2 veriT_vr3) :named @p_32)) :named @p_33)) :named @p_34)))) :named @p_40))
 (define-fun veriT_sk1 () Int (! (choice ((veriT_vr3 Int)) (not (=> (and (< 0 @p_40) @p_28) (< 0 (+ @p_40 veriT_vr3))))) :named @p_41))
@@ -2141,7 +2796,7 @@
 (step t36 (cl @p_58) :rule and :premises (t33))
 (step t37 (cl (not @p_43) @p_48 (not @p_42)) :rule la_generic :args (1 1 1))
 (step t38 (cl) :rule resolution :premises (t37 t34 t35 t36))
-55b72bfb066df27d9fdbc3ae3e0d5919e30bcc28 77 0
+967b369bde4b5569be04c05ebef7c7c11a7dd949 77 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr2 Int)) (not (forall ((veriT_vr3 Real)) (! (=> (! (and (! (< 0 veriT_vr2) :named @p_32) (! (< 0.0 veriT_vr3) :named @p_33)) :named @p_34) (! (< (- 1) veriT_vr2) :named @p_36)) :named @p_37)))) :named @p_43))
 (define-fun veriT_sk1 () Real (! (choice ((veriT_vr3 Real)) (not (=> (and (< 0 @p_43) @p_33) (< (- 1) @p_43)))) :named @p_45))
@@ -2219,7 +2874,7 @@
 (step t41 (cl @p_59) :rule and :premises (t39))
 (step t42 (cl @p_49 (not @p_44)) :rule la_generic :args (1.0 1.0))
 (step t43 (cl) :rule resolution :premises (t42 t40 t41))
-6a29c7940c898207fc3ec2e9201980e49631f59c 49 0
+ad30a685f8670d5c182050b2758f164c00fa02de 49 0
 unsat
 (define-fun veriT_sk0 () Int (! (choice ((veriT_vr1 Int)) (not (! (or (! (< 0 veriT_vr1) :named @p_20) (! (< veriT_vr1 1) :named @p_22)) :named @p_23))) :named @p_29))
 (assume a0 (! (not (! (forall ((?v0 Int) (?v1 Int)) (! (or (! (< 0 ?v1) :named @p_9) (! (< ?v1 1) :named @p_12)) :named @p_2)) :named @p_1)) :named @p_3))
@@ -2269,7 +2924,7 @@
 (step t27 (cl (not @p_32)) :rule not_or :premises (t25))
 (step t28 (cl @p_32 @p_30) :rule la_generic :args (1 1))
 (step t29 (cl) :rule resolution :premises (t28 t26 t27))
-0dca9cb26a065d9037b253edeea7dfd938c4d74a 7 0
+c9141d00ebba589372c1920648d35b166a7ea6d0 7 0
 unsat
 (assume a0 (! (not (! (not (! (= 1 (* 2 (of_nat$ x$))) :named @p_2)) :named @p_3)) :named @p_1))
 (step t2 (cl (not @p_1) @p_2) :rule not_not)
@@ -2277,7 +2932,7 @@
 (step t4 (cl @p_3 @p_3) :rule lia_generic)
 (step t5 (cl @p_3) :rule contraction :premises (t4))
 (step t6 (cl) :rule resolution :premises (t5 t3))
-00f0e6a8fcdecc425e1f539e94cddf8d2f165175 11 0
+5c421c4131db57d719eecccd76e666bae936fa11 11 0
 unsat
 (assume a0 (! (not (! (=> (! (< (! (of_nat$ a$) :named @p_1) 3) :named @p_3) (! (< (* 2 @p_1) 7) :named @p_4)) :named @p_8)) :named @p_2))
 (step t2 (cl (! (= @p_2 (! (and @p_3 (! (not @p_4) :named @p_10)) :named @p_6)) :named @p_5)) :rule bool_simplify)
@@ -2289,7 +2944,7 @@
 (step t8 (cl @p_10) :rule and :premises (t6))
 (step t9 (cl @p_4 (not @p_3)) :rule la_generic :args ((div 1 2) 1))
 (step t10 (cl) :rule resolution :premises (t9 t7 t8))
-c564c917673f8ddcc3c8e83b6c17c836ab96aabf 21 0
+92da6e97ba29a34a876c0fa16d5e6d53b05316de 21 0
 unsat
 (assume a0 (! (not (! (< (! (* 0 (! (+ 1 (! (of_nat$ y$) :named @p_2)) :named @p_1)) :named @p_3) (! (ite (! (< @p_1 @p_2) :named @p_12) 0 (! (- @p_1 @p_2) :named @p_13)) :named @p_5)) :named @p_4)) :named @p_6))
 (step t2 (cl (= 0 @p_3)) :rule prod_simplify)
@@ -2311,7 +2966,7 @@
 (step t18 (cl @p_20) :rule resolution :premises (t16 t17))
 (step t19 (cl @p_21 (not @p_20)) :rule la_generic :args (1 (- 1)))
 (step t20 (cl) :rule resolution :premises (t19 t14 t18))
-faa000b2df6428276051b48e21683f2504617d26 33 0
+d2911e8674cbcffa4830ead7c6ef3c57cef2d6fa 33 0
 unsat
 (assume a0 (! (not (! (or false (or (! (= (! (ite (! (< 0 (! (+ 1 (! (of_nat$ y$) :named @p_1)) :named @p_2)) :named @p_13) true false) :named @p_3) (! (= @p_1 (! (ite (! (< @p_2 1) :named @p_27) 0 (! (- @p_2 1) :named @p_28)) :named @p_26)) :named @p_14)) :named @p_5) (! (=> (! (not @p_3) :named @p_15) false) :named @p_6))) :named @p_4)) :named @p_7))
 (assume a1 (! (<= 0 @p_1) :named @p_34))
@@ -2345,7 +3000,7 @@
 (step t30 (cl @p_16) :rule not_or :premises (t29))
 (step t31 (cl @p_13 (not @p_34)) :rule la_generic :args (1 1))
 (step t32 (cl) :rule resolution :premises (t31 t30 a1))
-0e67342ae09b659ec99568f03952d769c3c5f476 76 0
+1b01a203f415236790472915120aeba1d69e507b 76 0
 unsat
 (assume a4 (! (forall ((?v0 Int)) (! (= (! (of_nat$ (! (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))
@@ -2422,7 +3077,7 @@
 (step t50 (cl @p_62 @p_64 @p_58 (! (not @p_35) :named @p_65)) :rule la_generic :args (1 1 1 (- 1)))
 (step t51 (cl @p_62 @p_64 @p_65 @p_61 @p_55) :rule th_resolution :premises (t50 t42))
 (step t52 (cl) :rule resolution :premises (t51 t48 t49 t32 t39 t44))
-473e52f76301e5561016da909d7bb09254857479 337 0
+59999ffb5d66c5ffe3c4bd998e52a95d515ab9b4 337 0
 unsat
 (define-fun veriT_sk1 () Nat$ (! (choice ((veriT_vr18 Nat$)) (not (! (=> (! (dvd$ veriT_vr18 (! (nat$ (! (+ 1 (! (* 4 (! (of_nat$ m$) :named @p_3)) :named @p_117)) :named @p_119)) :named @p_120)) :named @p_206) (! (or (! (= 1 (! (of_nat$ veriT_vr18) :named @p_171)) :named @p_208) (! (= (! (of_nat$ @p_120) :named @p_158) @p_171) :named @p_210)) :named @p_211)) :named @p_205))) :named @p_172))
 (assume a0 (! (forall ((?v0 Nat$)) (! (= (! (prime_nat$ ?v0) :named @p_7) (! (and (! (< 1 (! (of_nat$ ?v0) :named @p_1)) :named @p_10) (! (forall ((?v1 Nat$)) (! (=> (! (dvd$ ?v1 ?v0) :named @p_14) (! (or (! (= 1 (! (of_nat$ ?v1) :named @p_2)) :named @p_17) (! (= @p_1 @p_2) :named @p_21)) :named @p_23)) :named @p_25)) :named @p_12)) :named @p_27)) :named @p_29)) :named @p_4))
@@ -2760,7 +3415,7 @@
 (step t84 (cl (! (not @p_246) :named @p_253) (! (not @p_244) :named @p_254) @p_251) :rule eq_transitive)
 (step t85 (cl @p_252 @p_110 @p_253 @p_254) :rule th_resolution :premises (t83 t84))
 (step t86 (cl) :rule resolution :premises (t85 t44 t67 t82 t79))
-7b70726cf72a0c74489606bae1ad61426f0b0ab9 7 0
+195c5f4e7eb20baa5a32cf916824c8152dd91637 7 0
 unsat
 (assume a0 (! (not (! (not (! (= 1 (* 2 x$)) :named @p_2)) :named @p_3)) :named @p_1))
 (step t2 (cl (not @p_1) @p_2) :rule not_not)
@@ -2768,7 +3423,7 @@
 (step t4 (cl @p_3 @p_3) :rule lia_generic)
 (step t5 (cl @p_3) :rule contraction :premises (t4))
 (step t6 (cl) :rule resolution :premises (t5 t3))
-bf831287a0298d285882760b346e495880eb16d1 35 0
+f45af256a4bceda428e7fbee4e1e3dbdf14a491e 35 0
 unsat
 (assume a0 (! (forall ((?v0 A$) (?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$) :named @p_19)) :named @p_23)) :named @p_17))
@@ -2804,7 +3459,7 @@
 (step t18 (cl @p_28) :rule resolution :premises (t17 t8))
 (step t19 (cl (not @p_28) (not @p_18) @p_19) :rule eq_transitive)
 (step t20 (cl) :rule resolution :premises (t19 t14 t15 t18))
-998e9357ccbe8a5d4cb8c349e083e5fd9d181b25 67 0
+22e3ad7a3ba163eb9b2786d30a493e2c63cf8f81 67 0
 unsat
 (assume a1 (! (forall ((?v0 A$) (?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))
@@ -2872,7 +3527,7 @@
 (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))
-fc4647afe32c480bbb8b8a4c6dcf695e2b726323 97 0
+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$) :named @p_63)) :named @p_34)) :named @p_38)) :named @p_32))
@@ -2970,7 +3625,7 @@
 (step t52 (cl @p_73) :rule resolution :premises (t48 t51))
 (step t53 (cl (not @p_58) (not @p_60) (not @p_71) (not @p_73) @p_34) :rule eq_transitive)
 (step t54 (cl) :rule resolution :premises (t53 t19 t34 t36 t50 t52))
-e0b4b05e5f6d1b962b2a9456c742aa35d01413a7 25 0
+5c8ad736381ed7e2bc55bcefd8a06994784b278f 25 0
 unsat
 (assume a0 (! (not (! (or (! (= (! (f$ g$ x$) :named @p_1) (! (and (! (fun_app$ g$ x$) :named @p_2) true) :named @p_13)) :named @p_4) (or (! (= @p_1 true) :named @p_5) (! (= @p_2 true) :named @p_6))) :named @p_3)) :named @p_7))
 (step t2 (cl (= @p_3 (! (or @p_4 @p_5 @p_6) :named @p_8))) :rule ac_simp)
@@ -2996,7 +3651,7 @@
 (step t22 (cl (not @p_1)) :rule not_or :premises (t19))
 (step t23 (cl (not @p_2)) :rule not_or :premises (t19))
 (step t24 (cl) :rule resolution :premises (t21 t22 t23))
-12292726bb00f25b0aea5ab0221cdea71601b8fd 38 0
+866c42407f20d04dcdd5beace79be280ba36c916 38 0
 unsat
 (assume a0 (! (forall ((?v0 A$)) (! (= ?v0 (! (id$ ?v0) :named @p_4)) :named @p_6)) :named @p_2))
 (assume a1 (forall ((?v0 Bool)) (= (id$a ?v0) ?v0)))
@@ -3035,7 +3690,7 @@
 (step t25 (cl (or (! (not @p_14) :named @p_31) @p_23)) :rule forall_inst :args ((:= veriT_vr1 x$)))
 (step t26 (cl @p_31 @p_23) :rule or :premises (t25))
 (step t27 (cl) :rule resolution :premises (t26 t10 t24))
-fab16bc820af74a6055b3e7aedc3c727e6f5f6af 27 0
+75683ef8683272f0e70a656b2aaeeba1b535ac8d 27 0
 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))
@@ -3063,7 +3718,35 @@
 (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))
-8f7e19d83778dca8772549964febf837f10fc07f 60 0
+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))
@@ -3124,35 +3807,7 @@
 (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))
-4e293cd43d036c71e0f6573a40238cbbbdfc63d9 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$)) @p_3) :named @p_5))) :rule bind)
-(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3))
-(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4))
-(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5))
-(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2)
-(step t8 (cl (not @p_14) @p_8) :rule not_not)
-(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7))
-(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9))
-(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify)
-(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2)
-(step t13 (cl (not @p_18) @p_11) :rule not_not)
-(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12))
-(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14))
-(step t16 (cl (= @p_20 false)) :rule not_simplify)
-(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16))
-(step t18 (cl (= @p_21 false)) :rule and_simplify)
-(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18))
-(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2)
-(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20))
-(step t22 (cl (not false)) :rule false)
-(step t23 (cl) :rule resolution :premises (t21 t22))
-0466d7eca133f7c37fadd223e6ede987a03df89f 125 0
+2224e31ba45ff13284551d05730c64492fbe999c 125 0
 unsat
 (assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ 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$) :named @p_22)) :named @p_24)) :named @p_21))
@@ -3278,7 +3933,7 @@
 (step t59 (cl @p_89 @p_91 @p_96 @p_94 @p_97) :rule th_resolution :premises (t55 t58))
 (step t60 (cl @p_98 @p_88 @p_89 @p_96 @p_94 @p_97) :rule th_resolution :premises (t54 t59))
 (step t61 (cl) :rule resolution :premises (t60 a3 t28 t39 t41 t51 t53))
-fea4fb556b09fdb802b089e39cc40016c69868f5 23 0
+9bfeafd531163b7b5dc1f3e29f35b01c7ed668dc 23 0
 unsat
 (assume a0 (! (not (! (or (! (forall ((?v0 A$)) (! (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)))
@@ -3302,7 +3957,7 @@
 (step t17 (cl false) :rule th_resolution :premises (t9 t13 t16))
 (step t18 (cl (not false)) :rule false)
 (step t19 (cl) :rule resolution :premises (t17 t18))
-b6f9f8108480d266f9742c4ac46381a03c300fd2 107 0
+3fb3269903eddb271bcd0f8b72a806a38020c0d1 107 0
 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)))
@@ -3410,7 +4065,7 @@
 (step t61 (cl @p_30) :rule resolution :premises (t25 t60 t30))
 (step t62 (cl (not @p_30) @p_67) :rule la_generic :args (1 (- 4)))
 (step t63 (cl) :rule resolution :premises (t62 t61 t32))
-a9a0192e0312157bc10296025518980a110117e0 48 0
+21ed8993747dbe3d7fd900d61cf02456b0a38afa 48 0
 unsat
 (assume a2 (! (forall ((?v0 A$) (?v1 A$) (?v2 A$)) (! (=> (! (and (! (less_eq$ ?v0 ?v1) :named @p_4) (! (less_eq$ ?v1 ?v2) :named @p_7)) :named @p_9) (! (less_eq$ ?v0 ?v2) :named @p_13)) :named @p_15)) :named @p_3))
 (assume a3 (! (less_eq$ (! (sup$ (collect$ uu$)) :named @p_2) (! (sup$ (collect$ uua$)) :named @p_1)) :named @p_31))
@@ -3459,7 +4114,7 @@
 (step t21 (cl @p_29 @p_35) :rule or :premises (t19))
 (step t22 (cl @p_38) :rule resolution :premises (t20 a3 a4 a5))
 (step t23 (cl) :rule resolution :premises (t21 t10 t22))
-33354ae90736acf767a389a3432693e110da91cb 1434 0
+c14292db1124938af032dfdc907662d28ea67e96 1434 0
 unsat
 (define-fun veriT_sk0 () A$ (! (choice ((veriT_vr57 A$)) (not (! (=> (! (member$ veriT_vr57 (! (set$ (! (remdups$ xs$) :named @p_9)) :named @p_380)) :named @p_429) (! (not (! (member$ veriT_vr57 (! (set$ (! (remdups$ ys$) :named @p_10)) :named @p_381)) :named @p_431)) :named @p_432)) :named @p_433))) :named @p_449))
 (define-fun veriT_sk1 () A$ (! (choice ((veriT_vr58 A$)) (not (! (=> (! (member$ veriT_vr58 @p_381) :named @p_434) (! (not (! (member$ veriT_vr58 @p_380) :named @p_436)) :named @p_437)) :named @p_438))) :named @p_455))
@@ -4894,669 +5549,14 @@
 (step t591 (cl @p_1136) :rule eq_reflexive)
 (step t592 (cl @p_1135 @p_790 @p_1092) :rule th_resolution :premises (t590 t591))
 (step t593 (cl) :rule resolution :premises (t592 a24 t588 t586))
-042a030a3ede99a1c051b4a3202d4371c64c6c35 654 0
-unsat
-(assume a0 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uua$ ?v0) :named @p_13) (! (line_integral_exists$ f$ (! (insert$ j$ bot$) :named @p_7)) :named @p_12)) :named @p_15)) :named @p_11))
-(assume a1 (! (forall ((?v0 Int)) (! (= (! (fun_app$ uu$ ?v0) :named @p_25) (! (line_integral_exists$ f$ (! (insert$ i$ bot$) :named @p_5)) :named @p_24)) :named @p_27)) :named @p_23))
-(assume a2 (! (forall ((?v0 Int_real_real_real_prod_fun_bool_fun_fun$) (?v1 Int_real_real_real_prod_fun_prod$)) (! (= (! (case_prod$ ?v0 ?v1) :named @p_36) (! (fun_app$a (! (fun_app$ ?v0 (! (fst$ ?v1) :named @p_40)) :named @p_42) (! (snd$ ?v1) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
-(assume a3 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$)) (! (=> (! (= (! (insert$ ?v0 bot$) :named @p_3) (! (insert$ ?v1 bot$) :named @p_64)) :named @p_66) (! (= ?v0 ?v1) :named @p_70)) :named @p_72)) :named @p_62))
-(assume a4 (! (forall ((?v0 Int) (?v1 Real_real_real_prod_fun$)) (! (= ?v1 (! (snd$ (! (pair$ ?v0 ?v1) :named @p_87)) :named @p_89)) :named @p_91)) :named @p_85))
-(assume a5 (! (forall ((?v0 Real) (?v1 Real)) (! (= ?v1 (! (snd$a (! (fun_app$b (! (pair$a ?v0) :named @p_102) ?v1) :named @p_105)) :named @p_107)) :named @p_109)) :named @p_101))
-(assume a6 (! (member$ (! (pair$ k$ g$) :named @p_403) one_chain_typeI$) :named @p_402))
-(assume a7 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (= bot$ (! (inf$ ?v0 (! (insert$ ?v1 ?v2) :named @p_1)) :named @p_122)) :named @p_124) (! (and (! (not (! (member$a ?v1 ?v0) :named @p_128)) :named @p_130) (! (= bot$ (! (inf$ ?v0 ?v2) :named @p_133)) :named @p_135)) :named @p_137)) :named @p_139)) :named @p_120))
-(assume a8 (! (finite$ bot$) :named @p_414))
-(assume a9 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod$)) (! (=> (! (finite$ ?v0) :named @p_4) (! (finite$ (! (insert$ ?v1 ?v0) :named @p_160)) :named @p_162)) :named @p_164)) :named @p_157))
-(assume a10 (! (= i$ (! (fun_app$b (pair$a 1.0) 0.0) :named @p_417)) :named @p_499))
-(assume a11 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (=> (! (member$a ?v0 ?v1) :named @p_176) (! (= ?v1 (! (insert$ ?v0 ?v1) :named @p_2)) :named @p_181)) :named @p_183)) :named @p_175))
-(assume a12 (! (= j$ (! (fun_app$b (pair$a 0.0) 1.0) :named @p_419)) :named @p_500))
-(assume a13 (! (forall ((?v0 Real_real_prod_set$)) (! (= bot$ (! (inf$ ?v0 bot$) :named @p_196)) :named @p_198)) :named @p_195))
-(assume a14 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod$) (?v2 Real_real_prod_set$)) (! (= (! (insert$ ?v0 @p_1) :named @p_208) (! (insert$ ?v1 (! (insert$ ?v0 ?v2) :named @p_213)) :named @p_215)) :named @p_217)) :named @p_206))
-(assume a15 (! (forall ((?v0 Real_real_prod$) (?v1 Real_real_prod_set$)) (! (= @p_2 (! (sup$ @p_3 ?v1) :named @p_236)) :named @p_238)) :named @p_231))
-(assume a16 (! (forall ((?v0 Real_real_prod_set$) (?v1 Real_real_prod_real_real_prod_fun$) (?v2 Real_real_prod_set$) (?v3 Real_real_real_prod_fun$) (?v4 Real_real_prod_set$)) (! (=> (! (and @p_4 (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v2) :named @p_252) ?v3) :named @p_254) (! (and (! (fun_app$a (! (line_integral_exists$ ?v1 ?v4) :named @p_257) ?v3) :named @p_260) (! (and (! (= ?v0 (! (sup$ ?v2 ?v4) :named @p_265)) :named @p_267) (! (= bot$ (! (inf$ ?v2 ?v4) :named @p_269)) :named @p_271)) :named @p_273)) :named @p_275)) :named @p_277)) :named @p_279) (! (= (! (line_integral$ ?v1 ?v0 ?v3) :named @p_281) (! (+ (! (line_integral$ ?v1 ?v2 ?v3) :named @p_283) (! (line_integral$ ?v1 ?v4 ?v3) :named @p_285)) :named @p_287)) :named @p_289)) :named @p_291)) :named @p_250))
-(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$) :named @p_405)) :named @p_463)) :named @p_410)))
-(anchor :step t21 :args ((:= ?v0 veriT_vr0)))
-(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t21.t2 (cl (= @p_13 (! (fun_app$ 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)))
-(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)))
-(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)))
-(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)))
-(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))
-(step t33.t4 (cl @p_38) :rule refl)
-(step t33.t5 (cl @p_39) :rule refl)
-(step t33.t6 (cl (= @p_40 (! (fst$ veriT_vr5) :named @p_41))) :rule cong :premises (t33.t5))
-(step t33.t7 (cl (= @p_42 (! (fun_app$ veriT_vr4 @p_41) :named @p_43))) :rule cong :premises (t33.t4 t33.t6))
-(step t33.t8 (cl @p_39) :rule refl)
-(step t33.t9 (cl (= @p_44 (! (snd$ veriT_vr5) :named @p_45))) :rule cong :premises (t33.t8))
-(step t33.t10 (cl (= @p_46 (! (fun_app$a @p_43 @p_45) :named @p_47))) :rule cong :premises (t33.t7 t33.t9))
-(step t33.t11 (cl (= @p_48 (! (= @p_37 @p_47) :named @p_49))) :rule cong :premises (t33.t3 t33.t10))
-(step t33 (cl (! (= @p_35 (! (forall ((veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr5 Int_real_real_real_prod_fun_prod$)) @p_49) :named @p_51)) :named @p_50)) :rule bind)
-(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2)
-(step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34))
-(anchor :step t36 :args ((:= veriT_vr4 veriT_vr6) (:= veriT_vr5 veriT_vr7)))
-(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl)
-(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl)
-(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2))
-(step t36.t4 (cl @p_53) :rule refl)
-(step t36.t5 (cl @p_54) :rule refl)
-(step t36.t6 (cl (= @p_41 (! (fst$ veriT_vr7) :named @p_55))) :rule cong :premises (t36.t5))
-(step t36.t7 (cl (= @p_43 (! (fun_app$ veriT_vr6 @p_55) :named @p_56))) :rule cong :premises (t36.t4 t36.t6))
-(step t36.t8 (cl @p_54) :rule refl)
-(step t36.t9 (cl (= @p_45 (! (snd$ veriT_vr7) :named @p_57))) :rule cong :premises (t36.t8))
-(step t36.t10 (cl (= @p_47 (! (fun_app$a @p_56 @p_57) :named @p_58))) :rule cong :premises (t36.t7 t36.t9))
-(step t36.t11 (cl (= @p_49 (! (= @p_52 @p_58) :named @p_59))) :rule cong :premises (t36.t3 t36.t10))
-(step t36 (cl (! (= @p_51 (! (forall ((veriT_vr6 Int_real_real_real_prod_fun_bool_fun_fun$) (veriT_vr7 Int_real_real_real_prod_fun_prod$)) @p_59) :named @p_61)) :named @p_60)) :rule bind)
-(step t37 (cl (not @p_60) (not @p_51) @p_61) :rule equiv_pos2)
-(step t38 (cl @p_61) :rule th_resolution :premises (t35 t36 t37))
-(anchor :step t39 :args ((:= ?v0 veriT_vr8) (:= ?v1 veriT_vr9)))
-(step t39.t1 (cl (! (= ?v0 veriT_vr8) :named @p_68)) :rule refl)
-(step t39.t2 (cl (= @p_3 (! (insert$ veriT_vr8 bot$) :named @p_63))) :rule cong :premises (t39.t1))
-(step t39.t3 (cl (! (= ?v1 veriT_vr9) :named @p_69)) :rule refl)
-(step t39.t4 (cl (= @p_64 (! (insert$ veriT_vr9 bot$) :named @p_65))) :rule cong :premises (t39.t3))
-(step t39.t5 (cl (= @p_66 (! (= @p_63 @p_65) :named @p_67))) :rule cong :premises (t39.t2 t39.t4))
-(step t39.t6 (cl @p_68) :rule refl)
-(step t39.t7 (cl @p_69) :rule refl)
-(step t39.t8 (cl (= @p_70 (! (= veriT_vr8 veriT_vr9) :named @p_71))) :rule cong :premises (t39.t6 t39.t7))
-(step t39.t9 (cl (= @p_72 (! (=> @p_67 @p_71) :named @p_73))) :rule cong :premises (t39.t5 t39.t8))
-(step t39 (cl (! (= @p_62 (! (forall ((veriT_vr8 Real_real_prod$) (veriT_vr9 Real_real_prod$)) @p_73) :named @p_75)) :named @p_74)) :rule bind)
-(step t40 (cl (not @p_74) (not @p_62) @p_75) :rule equiv_pos2)
-(step t41 (cl @p_75) :rule th_resolution :premises (a3 t39 t40))
-(anchor :step t42 :args ((:= veriT_vr8 veriT_vr10) (:= veriT_vr9 veriT_vr11)))
-(step t42.t1 (cl (! (= veriT_vr8 veriT_vr10) :named @p_79)) :rule refl)
-(step t42.t2 (cl (= @p_63 (! (insert$ veriT_vr10 bot$) :named @p_76))) :rule cong :premises (t42.t1))
-(step t42.t3 (cl (! (= veriT_vr9 veriT_vr11) :named @p_80)) :rule refl)
-(step t42.t4 (cl (= @p_65 (! (insert$ veriT_vr11 bot$) :named @p_77))) :rule cong :premises (t42.t3))
-(step t42.t5 (cl (= @p_67 (! (= @p_76 @p_77) :named @p_78))) :rule cong :premises (t42.t2 t42.t4))
-(step t42.t6 (cl @p_79) :rule refl)
-(step t42.t7 (cl @p_80) :rule refl)
-(step t42.t8 (cl (= @p_71 (! (= veriT_vr10 veriT_vr11) :named @p_81))) :rule cong :premises (t42.t6 t42.t7))
-(step t42.t9 (cl (= @p_73 (! (=> @p_78 @p_81) :named @p_82))) :rule cong :premises (t42.t5 t42.t8))
-(step t42 (cl (! (= @p_75 (! (forall ((veriT_vr10 Real_real_prod$) (veriT_vr11 Real_real_prod$)) @p_82) :named @p_84)) :named @p_83)) :rule bind)
-(step t43 (cl (not @p_83) (not @p_75) @p_84) :rule equiv_pos2)
-(step t44 (cl @p_84) :rule th_resolution :premises (t41 t42 t43))
-(anchor :step t45 :args ((:= ?v0 veriT_vr12) (:= ?v1 veriT_vr13)))
-(step t45.t1 (cl (! (= ?v1 veriT_vr13) :named @p_86)) :rule refl)
-(step t45.t2 (cl (= ?v0 veriT_vr12)) :rule refl)
-(step t45.t3 (cl @p_86) :rule refl)
-(step t45.t4 (cl (= @p_87 (! (pair$ veriT_vr12 veriT_vr13) :named @p_88))) :rule cong :premises (t45.t2 t45.t3))
-(step t45.t5 (cl (= @p_89 (! (snd$ @p_88) :named @p_90))) :rule cong :premises (t45.t4))
-(step t45.t6 (cl (= @p_91 (! (= veriT_vr13 @p_90) :named @p_92))) :rule cong :premises (t45.t1 t45.t5))
-(step t45 (cl (! (= @p_85 (! (forall ((veriT_vr12 Int) (veriT_vr13 Real_real_real_prod_fun$)) @p_92) :named @p_94)) :named @p_93)) :rule bind)
-(step t46 (cl (not @p_93) (not @p_85) @p_94) :rule equiv_pos2)
-(step t47 (cl @p_94) :rule th_resolution :premises (a4 t45 t46))
-(anchor :step t48 :args ((:= veriT_vr12 veriT_vr14) (:= veriT_vr13 veriT_vr15)))
-(step t48.t1 (cl (! (= veriT_vr13 veriT_vr15) :named @p_95)) :rule refl)
-(step t48.t2 (cl (= veriT_vr12 veriT_vr14)) :rule refl)
-(step t48.t3 (cl @p_95) :rule refl)
-(step t48.t4 (cl (= @p_88 (! (pair$ veriT_vr14 veriT_vr15) :named @p_96))) :rule cong :premises (t48.t2 t48.t3))
-(step t48.t5 (cl (= @p_90 (! (snd$ @p_96) :named @p_97))) :rule cong :premises (t48.t4))
-(step t48.t6 (cl (= @p_92 (! (= veriT_vr15 @p_97) :named @p_98))) :rule cong :premises (t48.t1 t48.t5))
-(step t48 (cl (! (= @p_94 (! (forall ((veriT_vr14 Int) (veriT_vr15 Real_real_real_prod_fun$)) @p_98) :named @p_100)) :named @p_99)) :rule bind)
-(step t49 (cl (not @p_99) (not @p_94) @p_100) :rule equiv_pos2)
-(step t50 (cl @p_100) :rule th_resolution :premises (t47 t48 t49))
-(anchor :step t51 :args ((:= ?v0 veriT_vr16) (:= ?v1 veriT_vr17)))
-(step t51.t1 (cl (! (= ?v1 veriT_vr17) :named @p_104)) :rule refl)
-(step t51.t2 (cl (= ?v0 veriT_vr16)) :rule refl)
-(step t51.t3 (cl (= @p_102 (! (pair$a veriT_vr16) :named @p_103))) :rule cong :premises (t51.t2))
-(step t51.t4 (cl @p_104) :rule refl)
-(step t51.t5 (cl (= @p_105 (! (fun_app$b @p_103 veriT_vr17) :named @p_106))) :rule cong :premises (t51.t3 t51.t4))
-(step t51.t6 (cl (= @p_107 (! (snd$a @p_106) :named @p_108))) :rule cong :premises (t51.t5))
-(step t51.t7 (cl (= @p_109 (! (= veriT_vr17 @p_108) :named @p_110))) :rule cong :premises (t51.t1 t51.t6))
-(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)))
-(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$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2))
-(step t54.t4 (cl @p_114) :rule refl)
-(step t54.t5 (cl (= @p_106 (! (fun_app$b @p_113 veriT_vr19) :named @p_115))) :rule cong :premises (t54.t3 t54.t4))
-(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5))
-(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6))
-(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind)
-(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2)
-(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55))
-(anchor :step t57 :args ((:= ?v0 veriT_vr20) (:= ?v1 veriT_vr21) (:= ?v2 veriT_vr22)))
-(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl)
-(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl)
-(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl)
-(step t57.t4 (cl (= @p_1 (! (insert$ veriT_vr21 veriT_vr22) :named @p_121))) :rule cong :premises (t57.t2 t57.t3))
-(step t57.t5 (cl (= @p_122 (! (inf$ veriT_vr20 @p_121) :named @p_123))) :rule cong :premises (t57.t1 t57.t4))
-(step t57.t6 (cl (= @p_124 (! (= bot$ @p_123) :named @p_125))) :rule cong :premises (t57.t5))
-(step t57.t7 (cl @p_126) :rule refl)
-(step t57.t8 (cl @p_127) :rule refl)
-(step t57.t9 (cl (= @p_128 (! (member$a veriT_vr21 veriT_vr20) :named @p_129))) :rule cong :premises (t57.t7 t57.t8))
-(step t57.t10 (cl (= @p_130 (! (not @p_129) :named @p_131))) :rule cong :premises (t57.t9))
-(step t57.t11 (cl @p_127) :rule refl)
-(step t57.t12 (cl @p_132) :rule refl)
-(step t57.t13 (cl (= @p_133 (! (inf$ veriT_vr20 veriT_vr22) :named @p_134))) :rule cong :premises (t57.t11 t57.t12))
-(step t57.t14 (cl (= @p_135 (! (= bot$ @p_134) :named @p_136))) :rule cong :premises (t57.t13))
-(step t57.t15 (cl (= @p_137 (! (and @p_131 @p_136) :named @p_138))) :rule cong :premises (t57.t10 t57.t14))
-(step t57.t16 (cl (= @p_139 (! (= @p_125 @p_138) :named @p_140))) :rule cong :premises (t57.t6 t57.t15))
-(step t57 (cl (! (= @p_120 (! (forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind)
-(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2)
-(step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58))
-(anchor :step t60 :args ((:= veriT_vr20 veriT_vr23) (:= veriT_vr21 veriT_vr24) (:= veriT_vr22 veriT_vr25)))
-(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl)
-(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl)
-(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl)
-(step t60.t4 (cl (= @p_121 (! (insert$ veriT_vr24 veriT_vr25) :named @p_143))) :rule cong :premises (t60.t2 t60.t3))
-(step t60.t5 (cl (= @p_123 (! (inf$ veriT_vr23 @p_143) :named @p_144))) :rule cong :premises (t60.t1 t60.t4))
-(step t60.t6 (cl (= @p_125 (! (= bot$ @p_144) :named @p_145))) :rule cong :premises (t60.t5))
-(step t60.t7 (cl @p_146) :rule refl)
-(step t60.t8 (cl @p_147) :rule refl)
-(step t60.t9 (cl (= @p_129 (! (member$a veriT_vr24 veriT_vr23) :named @p_148))) :rule cong :premises (t60.t7 t60.t8))
-(step t60.t10 (cl (= @p_131 (! (not @p_148) :named @p_149))) :rule cong :premises (t60.t9))
-(step t60.t11 (cl @p_147) :rule refl)
-(step t60.t12 (cl @p_150) :rule refl)
-(step t60.t13 (cl (= @p_134 (! (inf$ veriT_vr23 veriT_vr25) :named @p_151))) :rule cong :premises (t60.t11 t60.t12))
-(step t60.t14 (cl (= @p_136 (! (= bot$ @p_151) :named @p_152))) :rule cong :premises (t60.t13))
-(step t60.t15 (cl (= @p_138 (! (and @p_149 @p_152) :named @p_153))) :rule cong :premises (t60.t10 t60.t14))
-(step t60.t16 (cl (= @p_140 (! (= @p_145 @p_153) :named @p_154))) :rule cong :premises (t60.t6 t60.t15))
-(step t60 (cl (! (= @p_142 (! (forall ((veriT_vr23 Real_real_prod_set$) (veriT_vr24 Real_real_prod$) (veriT_vr25 Real_real_prod_set$)) @p_154) :named @p_156)) :named @p_155)) :rule bind)
-(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2)
-(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61))
-(anchor :step t63 :args ((:= ?v0 veriT_vr26) (:= ?v1 veriT_vr27)))
-(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl)
-(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1))
-(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl)
-(step t63.t4 (cl @p_159) :rule refl)
-(step t63.t5 (cl (= @p_160 (! (insert$ veriT_vr27 veriT_vr26) :named @p_161))) :rule cong :premises (t63.t3 t63.t4))
-(step t63.t6 (cl (= @p_162 (! (finite$ @p_161) :named @p_163))) :rule cong :premises (t63.t5))
-(step t63.t7 (cl (= @p_164 (! (=> @p_158 @p_163) :named @p_165))) :rule cong :premises (t63.t2 t63.t6))
-(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)))
-(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)
-(step t66.t4 (cl @p_169) :rule refl)
-(step t66.t5 (cl (= @p_161 (! (insert$ veriT_vr29 veriT_vr28) :named @p_170))) :rule cong :premises (t66.t3 t66.t4))
-(step t66.t6 (cl (= @p_163 (! (finite$ @p_170) :named @p_171))) :rule cong :premises (t66.t5))
-(step t66.t7 (cl (= @p_165 (! (=> @p_168 @p_171) :named @p_172))) :rule cong :premises (t66.t2 t66.t6))
-(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)))
-(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$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2))
-(step t69.t4 (cl @p_178) :rule refl)
-(step t69.t5 (cl @p_179) :rule refl)
-(step t69.t6 (cl @p_178) :rule refl)
-(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6))
-(step t69.t8 (cl (= @p_181 (! (= veriT_vr31 @p_180) :named @p_182))) :rule cong :premises (t69.t4 t69.t7))
-(step t69.t9 (cl (= @p_183 (! (=> @p_177 @p_182) :named @p_184))) :rule cong :premises (t69.t3 t69.t8))
-(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)))
-(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$a veriT_vr32 veriT_vr33) :named @p_187))) :rule cong :premises (t72.t1 t72.t2))
-(step t72.t4 (cl @p_188) :rule refl)
-(step t72.t5 (cl @p_189) :rule refl)
-(step t72.t6 (cl @p_188) :rule refl)
-(step t72.t7 (cl (= @p_180 (! (insert$ veriT_vr32 veriT_vr33) :named @p_190))) :rule cong :premises (t72.t5 t72.t6))
-(step t72.t8 (cl (= @p_182 (! (= veriT_vr33 @p_190) :named @p_191))) :rule cong :premises (t72.t4 t72.t7))
-(step t72.t9 (cl (= @p_184 (! (=> @p_187 @p_191) :named @p_192))) :rule cong :premises (t72.t3 t72.t8))
-(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)))
-(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$)) @p_199) :named @p_201)) :named @p_200)) :rule bind)
-(step t76 (cl (not @p_200) (not @p_195) @p_201) :rule equiv_pos2)
-(step t77 (cl @p_201) :rule th_resolution :premises (a13 t75 t76))
-(anchor :step t78 :args ((:= veriT_vr34 veriT_vr35)))
-(step t78.t1 (cl (= veriT_vr34 veriT_vr35)) :rule refl)
-(step t78.t2 (cl (= @p_197 (! (inf$ 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$)) @p_203) :named @p_205)) :named @p_204)) :rule bind)
-(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2)
-(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79))
-(anchor :step t81 :args ((:= ?v0 veriT_vr36) (:= ?v1 veriT_vr37) (:= ?v2 veriT_vr38)))
-(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl)
-(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl)
-(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl)
-(step t81.t4 (cl (= @p_1 (! (insert$ veriT_vr37 veriT_vr38) :named @p_207))) :rule cong :premises (t81.t2 t81.t3))
-(step t81.t5 (cl (= @p_208 (! (insert$ veriT_vr36 @p_207) :named @p_209))) :rule cong :premises (t81.t1 t81.t4))
-(step t81.t6 (cl @p_210) :rule refl)
-(step t81.t7 (cl @p_211) :rule refl)
-(step t81.t8 (cl @p_212) :rule refl)
-(step t81.t9 (cl (= @p_213 (! (insert$ veriT_vr36 veriT_vr38) :named @p_214))) :rule cong :premises (t81.t7 t81.t8))
-(step t81.t10 (cl (= @p_215 (! (insert$ veriT_vr37 @p_214) :named @p_216))) :rule cong :premises (t81.t6 t81.t9))
-(step t81.t11 (cl (= @p_217 (! (= @p_209 @p_216) :named @p_218))) :rule cong :premises (t81.t5 t81.t10))
-(step t81 (cl (! (= @p_206 (! (forall ((veriT_vr36 Real_real_prod$) (veriT_vr37 Real_real_prod$) (veriT_vr38 Real_real_prod_set$)) @p_218) :named @p_220)) :named @p_219)) :rule bind)
-(step t82 (cl (not @p_219) (not @p_206) @p_220) :rule equiv_pos2)
-(step t83 (cl @p_220) :rule th_resolution :premises (a14 t81 t82))
-(anchor :step t84 :args ((:= veriT_vr36 veriT_vr39) (:= veriT_vr37 veriT_vr40) (:= veriT_vr38 veriT_vr41)))
-(step t84.t1 (cl (! (= veriT_vr36 veriT_vr39) :named @p_224)) :rule refl)
-(step t84.t2 (cl (! (= veriT_vr37 veriT_vr40) :named @p_223)) :rule refl)
-(step t84.t3 (cl (! (= veriT_vr38 veriT_vr41) :named @p_225)) :rule refl)
-(step t84.t4 (cl (= @p_207 (! (insert$ veriT_vr40 veriT_vr41) :named @p_221))) :rule cong :premises (t84.t2 t84.t3))
-(step t84.t5 (cl (= @p_209 (! (insert$ veriT_vr39 @p_221) :named @p_222))) :rule cong :premises (t84.t1 t84.t4))
-(step t84.t6 (cl @p_223) :rule refl)
-(step t84.t7 (cl @p_224) :rule refl)
-(step t84.t8 (cl @p_225) :rule refl)
-(step t84.t9 (cl (= @p_214 (! (insert$ veriT_vr39 veriT_vr41) :named @p_226))) :rule cong :premises (t84.t7 t84.t8))
-(step t84.t10 (cl (= @p_216 (! (insert$ veriT_vr40 @p_226) :named @p_227))) :rule cong :premises (t84.t6 t84.t9))
-(step t84.t11 (cl (= @p_218 (! (= @p_222 @p_227) :named @p_228))) :rule cong :premises (t84.t5 t84.t10))
-(step t84 (cl (! (= @p_220 (! (forall ((veriT_vr39 Real_real_prod$) (veriT_vr40 Real_real_prod$) (veriT_vr41 Real_real_prod_set$)) @p_228) :named @p_230)) :named @p_229)) :rule bind)
-(step t85 (cl (not @p_229) (not @p_220) @p_230) :rule equiv_pos2)
-(step t86 (cl @p_230) :rule th_resolution :premises (t83 t84 t85))
-(anchor :step t87 :args ((:= ?v0 veriT_vr42) (:= ?v1 veriT_vr43)))
-(step t87.t1 (cl (! (= ?v0 veriT_vr42) :named @p_233)) :rule refl)
-(step t87.t2 (cl (! (= ?v1 veriT_vr43) :named @p_235)) :rule refl)
-(step t87.t3 (cl (= @p_2 (! (insert$ veriT_vr42 veriT_vr43) :named @p_232))) :rule cong :premises (t87.t1 t87.t2))
-(step t87.t4 (cl @p_233) :rule refl)
-(step t87.t5 (cl (= @p_3 (! (insert$ veriT_vr42 bot$) :named @p_234))) :rule cong :premises (t87.t4))
-(step t87.t6 (cl @p_235) :rule refl)
-(step t87.t7 (cl (= @p_236 (! (sup$ @p_234 veriT_vr43) :named @p_237))) :rule cong :premises (t87.t5 t87.t6))
-(step t87.t8 (cl (= @p_238 (! (= @p_232 @p_237) :named @p_239))) :rule cong :premises (t87.t3 t87.t7))
-(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)))
-(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))
-(step t90.t4 (cl @p_243) :rule refl)
-(step t90.t5 (cl (= @p_234 (! (insert$ veriT_vr44 bot$) :named @p_244))) :rule cong :premises (t90.t4))
-(step t90.t6 (cl @p_245) :rule refl)
-(step t90.t7 (cl (= @p_237 (! (sup$ @p_244 veriT_vr45) :named @p_246))) :rule cong :premises (t90.t5 t90.t6))
-(step t90.t8 (cl (= @p_239 (! (= @p_242 @p_246) :named @p_247))) :rule cong :premises (t90.t3 t90.t7))
-(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)))
-(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)
-(step t93.t4 (cl (! (= ?v2 veriT_vr48) :named @p_263)) :rule refl)
-(step t93.t5 (cl (= @p_252 (! (line_integral_exists$ veriT_vr47 veriT_vr48) :named @p_253))) :rule cong :premises (t93.t3 t93.t4))
-(step t93.t6 (cl (! (= ?v3 veriT_vr49) :named @p_259)) :rule refl)
-(step t93.t7 (cl (= @p_254 (! (fun_app$a @p_253 veriT_vr49) :named @p_255))) :rule cong :premises (t93.t5 t93.t6))
-(step t93.t8 (cl @p_256) :rule refl)
-(step t93.t9 (cl (! (= ?v4 veriT_vr50) :named @p_264)) :rule refl)
-(step t93.t10 (cl (= @p_257 (! (line_integral_exists$ veriT_vr47 veriT_vr50) :named @p_258))) :rule cong :premises (t93.t8 t93.t9))
-(step t93.t11 (cl @p_259) :rule refl)
-(step t93.t12 (cl (= @p_260 (! (fun_app$a @p_258 veriT_vr49) :named @p_261))) :rule cong :premises (t93.t10 t93.t11))
-(step t93.t13 (cl @p_262) :rule refl)
-(step t93.t14 (cl @p_263) :rule refl)
-(step t93.t15 (cl @p_264) :rule refl)
-(step t93.t16 (cl (= @p_265 (! (sup$ veriT_vr48 veriT_vr50) :named @p_266))) :rule cong :premises (t93.t14 t93.t15))
-(step t93.t17 (cl (= @p_267 (! (= veriT_vr46 @p_266) :named @p_268))) :rule cong :premises (t93.t13 t93.t16))
-(step t93.t18 (cl @p_263) :rule refl)
-(step t93.t19 (cl @p_264) :rule refl)
-(step t93.t20 (cl (= @p_269 (! (inf$ veriT_vr48 veriT_vr50) :named @p_270))) :rule cong :premises (t93.t18 t93.t19))
-(step t93.t21 (cl (= @p_271 (! (= bot$ @p_270) :named @p_272))) :rule cong :premises (t93.t20))
-(step t93.t22 (cl (= @p_273 (! (and @p_268 @p_272) :named @p_274))) :rule cong :premises (t93.t17 t93.t21))
-(step t93.t23 (cl (= @p_275 (! (and @p_261 @p_274) :named @p_276))) :rule cong :premises (t93.t12 t93.t22))
-(step t93.t24 (cl (= @p_277 (! (and @p_255 @p_276) :named @p_278))) :rule cong :premises (t93.t7 t93.t23))
-(step t93.t25 (cl (= @p_279 (! (and @p_251 @p_278) :named @p_280))) :rule cong :premises (t93.t2 t93.t24))
-(step t93.t26 (cl @p_256) :rule refl)
-(step t93.t27 (cl @p_262) :rule refl)
-(step t93.t28 (cl @p_259) :rule refl)
-(step t93.t29 (cl (= @p_281 (! (line_integral$ veriT_vr47 veriT_vr46 veriT_vr49) :named @p_282))) :rule cong :premises (t93.t26 t93.t27 t93.t28))
-(step t93.t30 (cl @p_256) :rule refl)
-(step t93.t31 (cl @p_263) :rule refl)
-(step t93.t32 (cl @p_259) :rule refl)
-(step t93.t33 (cl (= @p_283 (! (line_integral$ veriT_vr47 veriT_vr48 veriT_vr49) :named @p_284))) :rule cong :premises (t93.t30 t93.t31 t93.t32))
-(step t93.t34 (cl @p_256) :rule refl)
-(step t93.t35 (cl @p_264) :rule refl)
-(step t93.t36 (cl @p_259) :rule refl)
-(step t93.t37 (cl (= @p_285 (! (line_integral$ veriT_vr47 veriT_vr50 veriT_vr49) :named @p_286))) :rule cong :premises (t93.t34 t93.t35 t93.t36))
-(step t93.t38 (cl (= @p_287 (! (+ @p_284 @p_286) :named @p_288))) :rule cong :premises (t93.t33 t93.t37))
-(step t93.t39 (cl (= @p_289 (! (= @p_282 @p_288) :named @p_290))) :rule cong :premises (t93.t29 t93.t38))
-(step t93.t40 (cl (= @p_291 (! (=> @p_280 @p_290) :named @p_292))) :rule cong :premises (t93.t25 t93.t39))
-(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$)) @p_292) :named @p_294)) :named @p_293)) :rule bind)
-(step t94 (cl (not @p_293) (not @p_250) @p_294) :rule equiv_pos2)
-(step t95 (cl @p_294) :rule th_resolution :premises (a16 t93 t94))
-(anchor :step t96 :args (veriT_vr46 veriT_vr47 veriT_vr48 veriT_vr49 veriT_vr50))
-(step t96.t1 (cl (= @p_280 (! (and @p_251 @p_255 @p_261 @p_268 @p_272) :named @p_295))) :rule ac_simp)
-(step t96.t2 (cl (= @p_292 (! (=> @p_295 @p_290) :named @p_296))) :rule cong :premises (t96.t1))
-(step t96 (cl (! (= @p_294 (! (forall ((veriT_vr46 Real_real_prod_set$) (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)))
-(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)
-(step t99.t4 (cl (! (= veriT_vr48 veriT_vr53) :named @p_307)) :rule refl)
-(step t99.t5 (cl (= @p_253 (! (line_integral_exists$ veriT_vr52 veriT_vr53) :named @p_300))) :rule cong :premises (t99.t3 t99.t4))
-(step t99.t6 (cl (! (= veriT_vr49 veriT_vr54) :named @p_304)) :rule refl)
-(step t99.t7 (cl (= @p_255 (! (fun_app$a @p_300 veriT_vr54) :named @p_301))) :rule cong :premises (t99.t5 t99.t6))
-(step t99.t8 (cl @p_302) :rule refl)
-(step t99.t9 (cl (! (= veriT_vr50 veriT_vr55) :named @p_308)) :rule refl)
-(step t99.t10 (cl (= @p_258 (! (line_integral_exists$ veriT_vr52 veriT_vr55) :named @p_303))) :rule cong :premises (t99.t8 t99.t9))
-(step t99.t11 (cl @p_304) :rule refl)
-(step t99.t12 (cl (= @p_261 (! (fun_app$a @p_303 veriT_vr54) :named @p_305))) :rule cong :premises (t99.t10 t99.t11))
-(step t99.t13 (cl @p_306) :rule refl)
-(step t99.t14 (cl @p_307) :rule refl)
-(step t99.t15 (cl @p_308) :rule refl)
-(step t99.t16 (cl (= @p_266 (! (sup$ veriT_vr53 veriT_vr55) :named @p_309))) :rule cong :premises (t99.t14 t99.t15))
-(step t99.t17 (cl (= @p_268 (! (= veriT_vr51 @p_309) :named @p_310))) :rule cong :premises (t99.t13 t99.t16))
-(step t99.t18 (cl @p_307) :rule refl)
-(step t99.t19 (cl @p_308) :rule refl)
-(step t99.t20 (cl (= @p_270 (! (inf$ veriT_vr53 veriT_vr55) :named @p_311))) :rule cong :premises (t99.t18 t99.t19))
-(step t99.t21 (cl (= @p_272 (! (= bot$ @p_311) :named @p_312))) :rule cong :premises (t99.t20))
-(step t99.t22 (cl (= @p_295 (! (and @p_299 @p_301 @p_305 @p_310 @p_312) :named @p_313))) :rule cong :premises (t99.t2 t99.t7 t99.t12 t99.t17 t99.t21))
-(step t99.t23 (cl @p_302) :rule refl)
-(step t99.t24 (cl @p_306) :rule refl)
-(step t99.t25 (cl @p_304) :rule refl)
-(step t99.t26 (cl (= @p_282 (! (line_integral$ veriT_vr52 veriT_vr51 veriT_vr54) :named @p_314))) :rule cong :premises (t99.t23 t99.t24 t99.t25))
-(step t99.t27 (cl @p_302) :rule refl)
-(step t99.t28 (cl @p_307) :rule refl)
-(step t99.t29 (cl @p_304) :rule refl)
-(step t99.t30 (cl (= @p_284 (! (line_integral$ veriT_vr52 veriT_vr53 veriT_vr54) :named @p_315))) :rule cong :premises (t99.t27 t99.t28 t99.t29))
-(step t99.t31 (cl @p_302) :rule refl)
-(step t99.t32 (cl @p_308) :rule refl)
-(step t99.t33 (cl @p_304) :rule refl)
-(step t99.t34 (cl (= @p_286 (! (line_integral$ veriT_vr52 veriT_vr55 veriT_vr54) :named @p_316))) :rule cong :premises (t99.t31 t99.t32 t99.t33))
-(step t99.t35 (cl (= @p_288 (! (+ @p_315 @p_316) :named @p_317))) :rule cong :premises (t99.t30 t99.t34))
-(step t99.t36 (cl (= @p_290 (! (= @p_314 @p_317) :named @p_318))) :rule cong :premises (t99.t26 t99.t35))
-(step t99.t37 (cl (= @p_296 (! (=> @p_313 @p_318) :named @p_319))) :rule cong :premises (t99.t22 t99.t36))
-(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$)) @p_319) :named @p_321)) :named @p_320)) :rule bind)
-(step t100 (cl (not @p_320) (not @p_298) @p_321) :rule equiv_pos2)
-(step t101 (cl @p_321) :rule th_resolution :premises (t98 t99 t100))
-(anchor :step t102 :args ((:= ?v0 veriT_vr56)))
-(step t102.t1 (cl (! (= ?v0 veriT_vr56) :named @p_324)) :rule refl)
-(step t102.t2 (cl (= @p_9 (! (member$ 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$)) @p_327) :named @p_334))) :rule bind)
-(anchor :step t103 :args ((:= ?v0 veriT_vr56)))
-(step t103.t1 (cl @p_324) :rule refl)
-(step t103.t2 (cl (= @p_8 (! (member$ veriT_vr56 one_chain_typeII$) :named @p_329))) :rule cong :premises (t103.t1))
-(step t103.t3 (cl @p_324) :rule refl)
-(step t103.t4 (cl @p_330) :rule cong :premises (t103.t3))
-(step t103.t5 (cl (= @p_331 (! (=> @p_329 @p_325) :named @p_332))) :rule cong :premises (t103.t2 t103.t4))
-(step t103 (cl (= @p_328 (! (forall ((veriT_vr56 Int_real_real_real_prod_fun_prod$)) @p_332) :named @p_335))) :rule bind)
-(step t104 (cl (= @p_333 (! (and @p_334 @p_335) :named @p_338))) :rule cong :premises (t102 t103))
-(step t105 (cl (! (= @p_336 (! (and @p_337 @p_338) :named @p_340)) :named @p_339)) :rule cong :premises (t104))
-(step t106 (cl (not @p_339) (not @p_336) @p_340) :rule equiv_pos2)
-(step t107 (cl @p_340) :rule th_resolution :premises (a17 t105 t106))
-(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)))
-(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$) :named @p_343))) :rule cong :premises (t111.t1))
-(step t111.t3 (cl @p_344) :rule refl)
-(step t111.t4 (cl (= @p_325 (! (case_prod$ uu$ veriT_vr57) :named @p_345))) :rule cong :premises (t111.t3))
-(step t111.t5 (cl (= @p_332 (! (=> @p_343 @p_345) :named @p_346))) :rule cong :premises (t111.t2 t111.t4))
-(step t111 (cl (= @p_335 (! (forall ((veriT_vr57 Int_real_real_real_prod_fun_prod$)) @p_346) :named @p_347))) :rule bind)
-(step t112 (cl (! (= @p_342 (! (and @p_337 @p_334 @p_347) :named @p_349)) :named @p_348)) :rule cong :premises (t111))
-(step t113 (cl (not @p_348) (not @p_342) @p_349) :rule equiv_pos2)
-(step t114 (cl @p_349) :rule th_resolution :premises (t110 t112 t113))
-(anchor :step t115 :args ((:= veriT_vr56 veriT_vr58)))
-(step t115.t1 (cl (! (= veriT_vr56 veriT_vr58) :named @p_351)) :rule refl)
-(step t115.t2 (cl (= @p_323 (! (member$ 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$)) @p_353) :named @p_358))) :rule bind)
-(anchor :step t116 :args ((:= veriT_vr57 veriT_vr59)))
-(step t116.t1 (cl (! (= veriT_vr57 veriT_vr59) :named @p_355)) :rule refl)
-(step t116.t2 (cl (= @p_343 (! (member$ veriT_vr59 one_chain_typeII$) :named @p_354))) :rule cong :premises (t116.t1))
-(step t116.t3 (cl @p_355) :rule refl)
-(step t116.t4 (cl (= @p_345 (! (case_prod$ uu$ veriT_vr59) :named @p_356))) :rule cong :premises (t116.t3))
-(step t116.t5 (cl (= @p_346 (! (=> @p_354 @p_356) :named @p_357))) :rule cong :premises (t116.t2 t116.t4))
-(step t116 (cl (= @p_347 (! (forall ((veriT_vr59 Int_real_real_real_prod_fun_prod$)) @p_357) :named @p_359))) :rule bind)
-(step t117 (cl (! (= @p_349 (! (and @p_337 @p_358 @p_359) :named @p_361)) :named @p_360)) :rule cong :premises (t115 t116))
-(step t118 (cl (not @p_360) (not @p_349) @p_361) :rule equiv_pos2)
-(step t119 (cl @p_361) :rule th_resolution :premises (t114 t117 t118))
-(anchor :step t120 :args ((:= ?v0 veriT_vr60)))
-(step t120.t1 (cl (! (= ?v0 veriT_vr60) :named @p_364)) :rule refl)
-(step t120.t2 (cl (= @p_8 (! (member$ 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$)) @p_367) :named @p_374))) :rule bind)
-(anchor :step t121 :args ((:= ?v0 veriT_vr60)))
-(step t121.t1 (cl @p_364) :rule refl)
-(step t121.t2 (cl (= @p_9 (! (member$ veriT_vr60 one_chain_typeI$) :named @p_369))) :rule cong :premises (t121.t1))
-(step t121.t3 (cl @p_364) :rule refl)
-(step t121.t4 (cl @p_370) :rule cong :premises (t121.t3))
-(step t121.t5 (cl (= @p_371 (! (=> @p_369 @p_365) :named @p_372))) :rule cong :premises (t121.t2 t121.t4))
-(step t121 (cl (= @p_368 (! (forall ((veriT_vr60 Int_real_real_real_prod_fun_prod$)) @p_372) :named @p_375))) :rule bind)
-(step t122 (cl (= @p_373 (! (and @p_374 @p_375) :named @p_378))) :rule cong :premises (t120 t121))
-(step t123 (cl (! (= @p_376 (! (and @p_377 @p_378) :named @p_380)) :named @p_379)) :rule cong :premises (t122))
-(step t124 (cl (not @p_379) (not @p_376) @p_380) :rule equiv_pos2)
-(step t125 (cl @p_380) :rule th_resolution :premises (a18 t123 t124))
-(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)))
-(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$) :named @p_383))) :rule cong :premises (t129.t1))
-(step t129.t3 (cl @p_384) :rule refl)
-(step t129.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr61) :named @p_385))) :rule cong :premises (t129.t3))
-(step t129.t5 (cl (= @p_372 (! (=> @p_383 @p_385) :named @p_386))) :rule cong :premises (t129.t2 t129.t4))
-(step t129 (cl (= @p_375 (! (forall ((veriT_vr61 Int_real_real_real_prod_fun_prod$)) @p_386) :named @p_387))) :rule bind)
-(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129))
-(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2)
-(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131))
-(anchor :step t133 :args ((:= veriT_vr60 veriT_vr62)))
-(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl)
-(step t133.t2 (cl (= @p_363 (! (member$ 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$)) @p_393) :named @p_398))) :rule bind)
-(anchor :step t134 :args ((:= veriT_vr61 veriT_vr63)))
-(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl)
-(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1))
-(step t134.t3 (cl @p_395) :rule refl)
-(step t134.t4 (cl (= @p_385 (! (case_prod$ uua$ veriT_vr63) :named @p_396))) :rule cong :premises (t134.t3))
-(step t134.t5 (cl (= @p_386 (! (=> @p_394 @p_396) :named @p_397))) :rule cong :premises (t134.t2 t134.t4))
-(step t134 (cl (= @p_387 (! (forall ((veriT_vr63 Int_real_real_real_prod_fun_prod$)) @p_397) :named @p_399))) :rule bind)
-(step t135 (cl (! (= @p_389 (! (and @p_377 @p_398 @p_399) :named @p_401)) :named @p_400)) :rule cong :premises (t133 t134))
-(step t136 (cl (not @p_400) (not @p_389) @p_401) :rule equiv_pos2)
-(step t137 (cl @p_401) :rule th_resolution :premises (t132 t135 t136))
-(step t138 (cl @p_358) :rule and :premises (t119))
-(step t139 (cl @p_399) :rule and :premises (t137))
-(step t140 (cl (or (! (not @p_399) :named @p_422) (! (=> @p_402 (! (case_prod$ uua$ @p_403) :named @p_421)) :named @p_420))) :rule forall_inst :args ((:= veriT_vr63 @p_403)))
-(step t141 (cl (or (! (not @p_358) :named @p_427) (! (=> @p_402 (! (case_prod$ uu$ @p_403) :named @p_426)) :named @p_424))) :rule forall_inst :args ((:= veriT_vr58 @p_403)))
-(step t142 (cl (or (! (not @p_321) :named @p_406) (! (=> (! (and (! (finite$ @p_5) :named @p_415) (! (fun_app$a @p_12 g$) :named @p_409) (! (fun_app$a @p_24 g$) :named @p_408) (! (= @p_5 (! (sup$ @p_7 @p_5) :named @p_466)) :named @p_430) (! (= bot$ (inf$ @p_7 @p_5)) :named @p_431)) :named @p_429) (! (= @p_404 (! (+ @p_405 @p_404) :named @p_528)) :named @p_433)) :named @p_432))) :rule forall_inst :args ((:= veriT_vr51 @p_5) (:= veriT_vr52 f$) (:= veriT_vr53 @p_7) (:= veriT_vr54 g$) (:= veriT_vr55 @p_5)))
-(step t143 (cl (or @p_406 (! (=> (! (and (! (finite$ @p_407) :named @p_412) @p_408 @p_409 (! (= @p_407 (sup$ @p_5 @p_7)) :named @p_411) (! (= bot$ (inf$ @p_5 @p_7)) :named @p_437)) :named @p_434) @p_410) :named @p_438))) :rule forall_inst :args ((:= veriT_vr51 @p_407) (:= veriT_vr52 f$) (:= veriT_vr53 @p_5) (:= veriT_vr54 g$) (:= veriT_vr55 @p_7)))
-(step t144 (cl (or (! (not @p_249) :named @p_441) @p_411)) :rule forall_inst :args ((:= veriT_vr44 i$) (:= veriT_vr45 @p_7)))
-(step t145 (cl (or (! (not @p_230) :named @p_442) (! (= @p_407 (! (insert$ j$ @p_5) :named @p_467)) :named @p_443))) :rule forall_inst :args ((:= veriT_vr39 j$) (:= veriT_vr40 i$) (:= veriT_vr41 bot$)))
-(step t146 (cl (or (! (not @p_194) :named @p_447) (! (=> (! (member$a i$ @p_7) :named @p_445) (! (= @p_7 @p_407) :named @p_446)) :named @p_444))) :rule forall_inst :args ((:= veriT_vr32 i$) (:= veriT_vr33 @p_7)))
-(step t147 (cl (or (! (not @p_174) :named @p_413) (! (=> (! (finite$ @p_7) :named @p_416) @p_412) :named @p_448))) :rule forall_inst :args ((:= veriT_vr28 @p_7) (:= veriT_vr29 i$)))
-(step t148 (cl (or @p_413 (! (=> @p_414 @p_415) :named @p_449))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 i$)))
-(step t149 (cl (or @p_413 (! (=> @p_414 @p_416) :named @p_451))) :rule forall_inst :args ((:= veriT_vr28 bot$) (:= veriT_vr29 j$)))
-(step t150 (cl (or (! (not @p_119) :named @p_418) (! (= 0.0 (! (snd$a @p_417) :named @p_495)) :named @p_454))) :rule forall_inst :args ((:= veriT_vr18 1.0) (:= veriT_vr19 0.0)))
-(step t151 (cl (or @p_418 (! (= 1.0 (! (snd$a @p_419) :named @p_496)) :named @p_455))) :rule forall_inst :args ((:= veriT_vr18 0.0) (:= veriT_vr19 1.0)))
-(step t152 (cl (or (! (not @p_100) :named @p_456) (! (= g$ (! (snd$ @p_403) :named @p_471)) :named @p_457))) :rule forall_inst :args ((:= veriT_vr14 k$) (:= veriT_vr15 g$)))
-(step t153 (cl (or (! (not @p_84) :named @p_461) (! (=> (! (= @p_7 @p_5) :named @p_459) (! (= j$ i$) :named @p_460)) :named @p_458))) :rule forall_inst :args ((:= veriT_vr10 i$) (:= veriT_vr11 j$)))
-(step t154 (cl (! (not @p_420) :named @p_423) (! (not @p_402) :named @p_425) @p_421) :rule implies_pos)
-(step t155 (cl @p_422 @p_420) :rule or :premises (t140))
-(step t156 (cl @p_423 @p_421) :rule resolution :premises (t154 a6))
-(step t157 (cl @p_420) :rule resolution :premises (t155 t139))
-(step t158 (cl @p_421) :rule resolution :premises (t156 t157))
-(step t159 (cl (! (not @p_424) :named @p_428) @p_425 @p_426) :rule implies_pos)
-(step t160 (cl @p_427 @p_424) :rule or :premises (t141))
-(step t161 (cl @p_428 @p_426) :rule resolution :premises (t159 a6))
-(step t162 (cl @p_424) :rule resolution :premises (t160 t138))
-(step t163 (cl @p_426) :rule resolution :premises (t161 t162))
-(step t164 (cl @p_429 (not @p_415) (! (not @p_409) :named @p_436) (! (not @p_408) :named @p_435) (not @p_430) (not @p_431)) :rule and_neg)
-(step t165 (cl (not @p_432) (not @p_429) @p_433) :rule implies_pos)
-(step t166 (cl @p_406 @p_432) :rule or :premises (t142))
-(step t167 (cl @p_432) :rule resolution :premises (t166 t101))
-(step t168 (cl @p_434 (not @p_412) @p_435 @p_436 (not @p_411) (! (not @p_437) :named @p_515)) :rule and_neg)
-(step t169 (cl (! (not @p_438) :named @p_439) (! (not @p_434) :named @p_440) @p_410) :rule implies_pos)
-(step t170 (cl @p_406 @p_438) :rule or :premises (t143))
-(step t171 (cl @p_439 @p_440) :rule resolution :premises (t169 a19))
-(step t172 (cl @p_438) :rule resolution :premises (t170 t101))
-(step t173 (cl @p_440) :rule resolution :premises (t171 t172))
-(step t174 (cl @p_441 @p_411) :rule or :premises (t144))
-(step t175 (cl @p_411) :rule resolution :premises (t174 t92))
-(step t176 (cl @p_442 @p_443) :rule or :premises (t145))
-(step t177 (cl @p_443) :rule resolution :premises (t176 t86))
-(step t178 (cl (not @p_444) (! (not @p_445) :named @p_470) @p_446) :rule implies_pos)
-(step t179 (cl @p_447 @p_444) :rule or :premises (t146))
-(step t180 (cl @p_444) :rule resolution :premises (t179 t74))
-(step t181 (cl (not @p_448) (not @p_416) @p_412) :rule implies_pos)
-(step t182 (cl @p_413 @p_448) :rule or :premises (t147))
-(step t183 (cl @p_448) :rule resolution :premises (t182 t68))
-(step t184 (cl (! (not @p_449) :named @p_450) (! (not @p_414) :named @p_452) @p_415) :rule implies_pos)
-(step t185 (cl @p_413 @p_449) :rule or :premises (t148))
-(step t186 (cl @p_450 @p_415) :rule resolution :premises (t184 a8))
-(step t187 (cl @p_449) :rule resolution :premises (t185 t68))
-(step t188 (cl @p_415) :rule resolution :premises (t186 t187))
-(step t189 (cl (! (not @p_451) :named @p_453) @p_452 @p_416) :rule implies_pos)
-(step t190 (cl @p_413 @p_451) :rule or :premises (t149))
-(step t191 (cl @p_453 @p_416) :rule resolution :premises (t189 a8))
-(step t192 (cl @p_451) :rule resolution :premises (t190 t68))
-(step t193 (cl @p_416) :rule resolution :premises (t191 t192))
-(step t194 (cl @p_412) :rule resolution :premises (t181 t193 t183))
-(step t195 (cl @p_418 @p_454) :rule or :premises (t150))
-(step t196 (cl @p_454) :rule resolution :premises (t195 t56))
-(step t197 (cl @p_418 @p_455) :rule or :premises (t151))
-(step t198 (cl @p_455) :rule resolution :premises (t197 t56))
-(step t199 (cl @p_456 @p_457) :rule or :premises (t152))
-(step t200 (cl @p_457) :rule resolution :premises (t199 t50))
-(step t201 (cl (not @p_458) (! (not @p_459) :named @p_507) @p_460) :rule implies_pos)
-(step t202 (cl @p_461 @p_458) :rule or :premises (t153))
-(step t203 (cl @p_458) :rule resolution :premises (t202 t44))
-(step t204 (cl (or @p_410 (! (not (! (<= @p_462 @p_463) :named @p_534)) :named @p_464) (! (not (! (<= @p_463 @p_462) :named @p_535)) :named @p_465))) :rule la_disequality)
-(step t205 (cl @p_410 @p_464 @p_465) :rule or :premises (t204))
-(step t206 (cl @p_464 @p_465) :rule resolution :premises (t205 a19))
-(step t207 (cl (or @p_441 (! (= @p_466 @p_467) :named @p_474))) :rule forall_inst :args ((:= veriT_vr44 j$) (:= veriT_vr45 @p_5)))
-(step t208 (cl (or @p_447 (! (=> (! (member$a j$ @p_5) :named @p_468) (! (= @p_5 @p_467) :named @p_477)) :named @p_475))) :rule forall_inst :args ((:= veriT_vr32 j$) (:= veriT_vr33 @p_5)))
-(step t209 (cl (or (! (not @p_156) :named @p_469) (! (= @p_437 (! (and (! (not @p_468) :named @p_476) (! (= bot$ (inf$ @p_5 bot$)) :named @p_479)) :named @p_478)) :named @p_482))) :rule forall_inst :args ((:= veriT_vr23 @p_5) (:= veriT_vr24 j$) (:= veriT_vr25 bot$)))
-(step t210 (cl (or @p_469 (! (= @p_431 (! (and @p_470 (! (= bot$ (inf$ @p_7 bot$)) :named @p_485)) :named @p_483)) :named @p_487))) :rule forall_inst :args ((:= veriT_vr23 @p_7) (:= veriT_vr24 i$) (:= veriT_vr25 bot$)))
-(step t211 (cl (or (! (not @p_61) :named @p_472) (! (= @p_426 (! (fun_app$a (! (fun_app$ uu$ (! (fst$ @p_403) :named @p_473)) :named @p_508) @p_471) :named @p_489)) :named @p_488))) :rule forall_inst :args ((:= veriT_vr6 uu$) (:= veriT_vr7 @p_403)))
-(step t212 (cl (or @p_472 (! (= @p_421 (! (fun_app$a (! (fun_app$ uua$ @p_473) :named @p_509) @p_471) :named @p_492)) :named @p_491))) :rule forall_inst :args ((:= veriT_vr6 uua$) (:= veriT_vr7 @p_403)))
-(step t213 (cl @p_441 @p_474) :rule or :premises (t207))
-(step t214 (cl @p_474) :rule resolution :premises (t213 t92))
-(step t215 (cl (not @p_475) @p_476 @p_477) :rule implies_pos)
-(step t216 (cl @p_447 @p_475) :rule or :premises (t208))
-(step t217 (cl @p_475) :rule resolution :premises (t216 t74))
-(step t218 (cl (not (! (not @p_470) :named @p_484)) @p_445) :rule not_not)
-(step t219 (cl @p_478 (! (not @p_476) :named @p_480) (! (not @p_479) :named @p_481)) :rule and_neg)
-(step t220 (cl (not @p_480) @p_468) :rule not_not)
-(step t221 (cl @p_478 @p_468 @p_481) :rule th_resolution :premises (t220 t219))
-(step t222 (cl (not @p_482) @p_437 (! (not @p_478) :named @p_516)) :rule equiv_pos1)
-(step t223 (cl @p_469 @p_482) :rule or :premises (t209))
-(step t224 (cl @p_482) :rule resolution :premises (t223 t62))
-(step t225 (cl @p_483 @p_484 (! (not @p_485) :named @p_486)) :rule and_neg)
-(step t226 (cl @p_483 @p_445 @p_486) :rule th_resolution :premises (t218 t225))
-(step t227 (cl (not @p_487) @p_431 (not @p_483)) :rule equiv_pos1)
-(step t228 (cl @p_469 @p_487) :rule or :premises (t210))
-(step t229 (cl @p_487) :rule resolution :premises (t228 t62))
-(step t230 (cl (! (not @p_488) :named @p_490) (not @p_426) @p_489) :rule equiv_pos2)
-(step t231 (cl @p_472 @p_488) :rule or :premises (t211))
-(step t232 (cl @p_490 @p_489) :rule resolution :premises (t230 t163))
-(step t233 (cl @p_488) :rule resolution :premises (t231 t38))
-(step t234 (cl @p_489) :rule resolution :premises (t232 t233))
-(step t235 (cl (! (not @p_491) :named @p_493) (not @p_421) @p_492) :rule equiv_pos2)
-(step t236 (cl @p_472 @p_491) :rule or :premises (t212))
-(step t237 (cl @p_493 @p_492) :rule resolution :premises (t235 t158))
-(step t238 (cl @p_491) :rule resolution :premises (t236 t38))
-(step t239 (cl @p_492) :rule resolution :premises (t237 t238))
-(step t240 (cl (or (! (not @p_205) :named @p_494) @p_479)) :rule forall_inst :args ((:= veriT_vr35 @p_5)))
-(step t241 (cl (or @p_494 @p_485)) :rule forall_inst :args ((:= veriT_vr35 @p_7)))
-(step t242 (cl @p_494 @p_479) :rule or :premises (t240))
-(step t243 (cl @p_479) :rule resolution :premises (t242 t80))
-(step t244 (cl @p_494 @p_485) :rule or :premises (t241))
-(step t245 (cl @p_485) :rule resolution :premises (t244 t80))
-(step t246 (cl (! (= @p_7 @p_7) :named @p_520)) :rule eq_reflexive)
-(step t247 (cl (not (! (= 1.0 0.0) :named @p_497))) :rule la_generic :args ((- 1)))
-(step t248 (cl (! (not @p_455) :named @p_505) (not (! (= @p_495 @p_496) :named @p_498)) (! (not @p_454) :named @p_506) @p_497) :rule eq_transitive)
-(step t249 (cl (not (! (= @p_417 @p_419) :named @p_501)) @p_498) :rule eq_congruent)
-(step t250 (cl (! (not @p_499) :named @p_502) (! (not @p_460) :named @p_503) (! (not @p_500) :named @p_504) @p_501) :rule eq_transitive)
-(step t251 (cl @p_498 @p_502 @p_503 @p_504) :rule th_resolution :premises (t249 t250))
-(step t252 (cl @p_505 @p_506 @p_497 @p_502 @p_503 @p_504) :rule th_resolution :premises (t248 t251))
-(step t253 (cl @p_505 @p_506 @p_502 @p_503 @p_504) :rule th_resolution :premises (t247 t252))
-(step t254 (cl @p_503) :rule resolution :premises (t253 a10 a12 t196 t198))
-(step t255 (cl @p_507) :rule resolution :premises (t201 t254 t203))
-(step t256 (cl (! (= f$ f$) :named @p_523)) :rule eq_reflexive)
-(step t257 (cl (! (= g$ g$) :named @p_524)) :rule eq_reflexive)
-(step t258 (cl (! (= @p_405 @p_405) :named @p_527)) :rule eq_reflexive)
-(step t259 (cl (or (! (not @p_34) :named @p_510) (! (= @p_24 @p_508) :named @p_511))) :rule forall_inst :args ((:= veriT_vr3 @p_473)))
-(step t260 (cl (or (! (not @p_22) :named @p_512) (! (= @p_12 @p_509) :named @p_513))) :rule forall_inst :args ((:= veriT_vr1 @p_473)))
-(step t261 (cl @p_510 @p_511) :rule or :premises (t259))
-(step t262 (cl @p_511) :rule resolution :premises (t261 t32))
-(step t263 (cl @p_512 @p_513) :rule or :premises (t260))
-(step t264 (cl @p_513) :rule resolution :premises (t263 t26))
-(step t265 (cl (not @p_511) (! (not @p_457) :named @p_514) @p_408 (not @p_489)) :rule eq_congruent_pred)
-(step t266 (cl @p_408) :rule resolution :premises (t265 t200 t234 t262))
-(step t267 (cl (not @p_513) @p_514 @p_409 (not @p_492)) :rule eq_congruent_pred)
-(step t268 (cl @p_409) :rule resolution :premises (t267 t200 t239 t264))
-(step t269 (cl @p_515) :rule resolution :premises (t168 t268 t194 t173 t175 t266))
-(step t270 (cl @p_516) :rule resolution :premises (t222 t269 t224))
-(step t271 (cl @p_468) :rule resolution :premises (t221 t270 t243))
-(step t272 (cl @p_477) :rule resolution :premises (t215 t271 t217))
-(step t273 (cl (! (not @p_477) :named @p_517) (not @p_474) @p_430) :rule eq_transitive)
-(step t274 (cl @p_430) :rule resolution :premises (t273 t214 t272))
-(step t275 (cl @p_517 (! (not @p_443) :named @p_518) (! (= @p_5 @p_407) :named @p_519)) :rule eq_transitive)
-(step t276 (cl @p_518 @p_517 @p_519) :rule eq_transitive)
-(step t277 (cl (not @p_520) (! (not @p_446) :named @p_521) (! (not @p_519) :named @p_522) @p_459) :rule eq_transitive)
-(step t278 (cl @p_521 @p_522 @p_459) :rule th_resolution :premises (t277 t246))
-(step t279 (cl @p_521 @p_459 @p_518 @p_517) :rule th_resolution :premises (t278 t276))
-(step t280 (cl @p_521) :rule resolution :premises (t279 t177 t255 t272))
-(step t281 (cl (not @p_523) @p_522 (! (not @p_524) :named @p_525) (! (= @p_462 @p_404) :named @p_526)) :rule eq_congruent)
-(step t282 (cl @p_522 @p_525 @p_526) :rule th_resolution :premises (t281 t256))
-(step t283 (cl @p_522 @p_526) :rule th_resolution :premises (t282 t257))
-(step t284 (cl @p_526 @p_517 @p_518) :rule th_resolution :premises (t283 t275))
-(step t285 (cl @p_470) :rule resolution :premises (t178 t280 t180))
-(step t286 (cl @p_483) :rule resolution :premises (t226 t285 t245))
-(step t287 (cl @p_431) :rule resolution :premises (t227 t286 t229))
-(step t288 (cl @p_429) :rule resolution :premises (t164 t287 t188 t266 t268 t274))
-(step t289 (cl @p_433) :rule resolution :premises (t165 t288 t167))
-(step t290 (cl (not @p_527) (! (not @p_526) :named @p_529) (! (= (! (+ @p_405 @p_462) :named @p_531) @p_528) :named @p_530)) :rule eq_congruent)
-(step t291 (cl @p_529 @p_530) :rule th_resolution :premises (t290 t258))
-(step t292 (cl @p_530 @p_517 @p_518) :rule th_resolution :premises (t291 t284))
-(step t293 (cl (! (not @p_433) :named @p_532) (not @p_530) (! (= @p_404 @p_531) :named @p_533)) :rule eq_transitive)
-(step t294 (cl @p_532 @p_533 @p_517 @p_518) :rule th_resolution :premises (t293 t292))
-(step t295 (cl @p_534 @p_529 (! (not @p_533) :named @p_536)) :rule la_generic :args (1.0 (- 2) (- 1)))
-(step t296 (cl @p_534 @p_517 @p_518 @p_532) :rule th_resolution :premises (t295 t284 t294))
-(step t297 (cl @p_534) :rule resolution :premises (t296 t289 t177 t272))
-(step t298 (cl @p_465) :rule resolution :premises (t206 t297))
-(step t299 (cl @p_535 @p_529 @p_536) :rule la_generic :args (1.0 2 1))
-(step t300 (cl @p_535 @p_517 @p_518 @p_532) :rule th_resolution :premises (t299 t284 t294))
-(step t301 (cl) :rule resolution :premises (t300 t289 t177 t298 t272))
-1b1ef677d2a459ea9bcbad2db18e951f812782ca 6 0
+7d1d28af77b48e47cf45f7abbbccb64bffffc3f9 6 0
 unsat
 (assume a0 (! (< 0.0 (+ x$ (! (* 2.0 y$) :named @p_1))) :named @p_2))
 (assume a1 (! (< 0.0 (- x$ @p_1)) :named @p_3))
 (assume a2 (! (< x$ 0.0) :named @p_4))
 (step t4 (cl (not @p_2) (not @p_3) (not @p_4)) :rule la_generic :args (1.0 1.0 2.0))
 (step t5 (cl) :rule resolution :premises (t4 a0 a1 a2))
-8983b40ecc1de094c5b355c5a66dc3ff3a0c8509 735 0
+f17b9d0590c7cefc8013c1518981dc710a40e813 735 0
 unsat
 (assume a0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
 (assume a3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
@@ -6292,58 +6292,7 @@
 (step t426 (cl @p_571 @p_485 @p_572 @p_484 @p_574 @p_415 @p_413 @p_483 @p_557 @p_554 @p_558 @p_562 @p_563 @p_483 @p_484 @p_557 @p_554 @p_558 @p_562 @p_563) :rule th_resolution :premises (t425 t419))
 (step t427 (cl @p_571 @p_485 @p_572 @p_484 @p_574 @p_415 @p_413 @p_483 @p_557 @p_554 @p_558 @p_562 @p_563) :rule contraction :premises (t426))
 (step t428 (cl) :rule resolution :premises (t427 t172 t176 t232 t226 t204 t408 t410 t413 t385 t387 t386 t384 t383))
-76e04d808f9049c53498efd03433d66318b777cb 26 0
-unsat
-(assume a0 (! (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (! (p$ ?v0 ?v1) :named @p_2)) :named @p_1))
-(assume a1 (! (=> (! (p$ z$ y$) :named @p_12) false) :named @p_11))
-(step t3 (cl (! (= @p_1 (! (forall ((?v0 A$) (?v1 B$)) @p_2) :named @p_4)) :named @p_3)) :rule qnt_rm_unused)
-(step t4 (cl (not @p_3) (not @p_1) @p_4) :rule equiv_pos2)
-(step t5 (cl @p_4) :rule th_resolution :premises (a0 t3 t4))
-(anchor :step t6 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
-(step t6.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
-(step t6.t2 (cl (= ?v1 veriT_vr1)) :rule refl)
-(step t6.t3 (cl (= @p_2 (! (p$ 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)))
-(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))
-(step t9 (cl (! (= @p_7 (! (forall ((veriT_vr2 A$) (veriT_vr3 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
-(step t10 (cl (not @p_9) (not @p_7) @p_10) :rule equiv_pos2)
-(step t11 (cl @p_10) :rule th_resolution :premises (t8 t9 t10))
-(step t12 (cl (! (= @p_11 (! (not @p_12) :named @p_14)) :named @p_13)) :rule implies_simplify)
-(step t13 (cl (not @p_13) (not @p_11) @p_14) :rule equiv_pos2)
-(step t14 (cl @p_14) :rule th_resolution :premises (a1 t12 t13))
-(step t15 (cl (or (! (not @p_10) :named @p_15) @p_12)) :rule forall_inst :args ((:= veriT_vr2 z$) (:= veriT_vr3 y$)))
-(step t16 (cl @p_15 @p_12) :rule or :premises (t15))
-(step t17 (cl) :rule resolution :premises (t16 t11 t14))
-1fd041856d406153ff429b6c1d40eb368a3738f2 23 0
-unsat
-(assume a0 (! (not (! (<= y$ (! (ite (! (<= x$ y$) :named @p_3) y$ x$) :named @p_2)) :named @p_7)) :named @p_1))
-(step t2 (cl (! (= @p_1 (! (and (! (not (! (<= y$ @p_2) :named @p_13)) :named @p_9) (! (ite @p_3 (! (= y$ @p_2) :named @p_12) (! (= x$ @p_2) :named @p_11)) :named @p_10)) :named @p_5)) :named @p_4)) :rule ite_intro)
-(step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
-(step t4 (cl (not @p_6) @p_7) :rule not_not)
-(step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
-(step t6 (cl @p_5) :rule th_resolution :premises (a0 t2 t5))
-(step t7 (cl @p_9) :rule and :premises (t6))
-(step t8 (cl @p_10) :rule and :premises (t6))
-(step t9 (cl @p_3 @p_11) :rule ite1 :premises (t8))
-(step t10 (cl (! (not @p_3) :named @p_15) @p_12) :rule ite2 :premises (t8))
-(step t11 (cl @p_13 @p_3 (! (not @p_11) :named @p_14)) :rule la_generic :args (1 1 (- 1)))
-(step t12 (cl @p_3 @p_14) :rule resolution :premises (t11 t7))
-(step t13 (cl (not (! (= y$ x$) :named @p_17)) (! (not @p_12) :named @p_16) @p_15 @p_13) :rule eq_congruent_pred)
-(step t14 (cl @p_16 @p_14 @p_17) :rule eq_transitive)
-(step t15 (cl @p_16 @p_15 @p_13 @p_16 @p_14) :rule th_resolution :premises (t13 t14))
-(step t16 (cl @p_16 @p_15 @p_13 @p_14) :rule contraction :premises (t15))
-(step t17 (cl @p_16 @p_15 @p_14) :rule resolution :premises (t16 t7))
-(step t18 (cl @p_14) :rule resolution :premises (t17 t10 t12))
-(step t19 (cl @p_3) :rule resolution :premises (t9 t18))
-(step t20 (cl @p_12) :rule resolution :premises (t10 t19))
-(step t21 (cl @p_13 @p_16) :rule la_generic :args (1 (- 1)))
-(step t22 (cl) :rule resolution :premises (t21 t7 t20))
-e6caa829a170f55dd7b52a2f7910337007b8ab18 484 0
+268d7e42d22bc05b4bcc195eddbced079a39fedf 484 0
 unsat
 (assume a0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uuc$ ?v0) :named @p_9) (! (pair$ (! (times$ (! (- ?v0 (! (divide$ 1.0 2.0) :named @p_7)) :named @p_12) d$) :named @p_1) (! (diamond_y$ @p_1) :named @p_16)) :named @p_18)) :named @p_20)) :named @p_6))
 (assume a3 (! (forall ((?v0 Real)) (! (= (! (fun_app$ uub$ ?v0) :named @p_37) (! (pair$ (! (- (! (divide$ d$ 2.0) :named @p_3)) :named @p_2) (! (times$ (! (- (! (* 2.0 ?v0) :named @p_40) 1.0) :named @p_42) (! (diamond_y$ @p_2) :named @p_36)) :named @p_44)) :named @p_46)) :named @p_48)) :named @p_35))
@@ -6828,7 +6777,58 @@
 (step t207 (cl @p_389 @p_388 @p_391 @p_262) :rule th_resolution :premises (t206 t189))
 (step t208 (cl @p_389) :rule resolution :premises (t207 t175 t181 t188))
 (step t209 (cl) :rule resolution :premises (t197 t204 t199 t208))
-a2ae6f83b2ea3d3da88443f025d092ee4567250b 567 0
[phone]c370281d48d21e99833e7ceba6103960 26 0
+unsat
+(assume a0 (! (forall ((?v0 A$) (?v1 B$) (?v2 C$)) (! (p$ ?v0 ?v1) :named @p_2)) :named @p_1))
+(assume a1 (! (=> (! (p$ z$ y$) :named @p_12) false) :named @p_11))
+(step t3 (cl (! (= @p_1 (! (forall ((?v0 A$) (?v1 B$)) @p_2) :named @p_4)) :named @p_3)) :rule qnt_rm_unused)
+(step t4 (cl (not @p_3) (not @p_1) @p_4) :rule equiv_pos2)
+(step t5 (cl @p_4) :rule th_resolution :premises (a0 t3 t4))
+(anchor :step t6 :args ((:= ?v0 veriT_vr0) (:= ?v1 veriT_vr1)))
+(step t6.t1 (cl (= ?v0 veriT_vr0)) :rule refl)
+(step t6.t2 (cl (= ?v1 veriT_vr1)) :rule refl)
+(step t6.t3 (cl (= @p_2 (! (p$ 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)))
+(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))
+(step t9 (cl (! (= @p_7 (! (forall ((veriT_vr2 A$) (veriT_vr3 B$)) @p_8) :named @p_10)) :named @p_9)) :rule bind)
+(step t10 (cl (not @p_9) (not @p_7) @p_10) :rule equiv_pos2)
+(step t11 (cl @p_10) :rule th_resolution :premises (t8 t9 t10))
+(step t12 (cl (! (= @p_11 (! (not @p_12) :named @p_14)) :named @p_13)) :rule implies_simplify)
+(step t13 (cl (not @p_13) (not @p_11) @p_14) :rule equiv_pos2)
+(step t14 (cl @p_14) :rule th_resolution :premises (a1 t12 t13))
+(step t15 (cl (or (! (not @p_10) :named @p_15) @p_12)) :rule forall_inst :args ((:= veriT_vr2 z$) (:= veriT_vr3 y$)))
+(step t16 (cl @p_15 @p_12) :rule or :premises (t15))
+(step t17 (cl) :rule resolution :premises (t16 t11 t14))
+732d0d825854417fe8b0c85959caf9624dd11670 23 0
+unsat
+(assume a0 (! (not (! (<= y$ (! (ite (! (<= x$ y$) :named @p_3) y$ x$) :named @p_2)) :named @p_7)) :named @p_1))
+(step t2 (cl (! (= @p_1 (! (and (! (not (! (<= y$ @p_2) :named @p_13)) :named @p_9) (! (ite @p_3 (! (= y$ @p_2) :named @p_12) (! (= x$ @p_2) :named @p_11)) :named @p_10)) :named @p_5)) :named @p_4)) :rule ite_intro)
+(step t3 (cl (! (not @p_4) :named @p_8) (! (not @p_1) :named @p_6) @p_5) :rule equiv_pos2)
+(step t4 (cl (not @p_6) @p_7) :rule not_not)
+(step t5 (cl @p_8 @p_7 @p_5) :rule th_resolution :premises (t4 t3))
+(step t6 (cl @p_5) :rule th_resolution :premises (a0 t2 t5))
+(step t7 (cl @p_9) :rule and :premises (t6))
+(step t8 (cl @p_10) :rule and :premises (t6))
+(step t9 (cl @p_3 @p_11) :rule ite1 :premises (t8))
+(step t10 (cl (! (not @p_3) :named @p_15) @p_12) :rule ite2 :premises (t8))
+(step t11 (cl @p_13 @p_3 (! (not @p_11) :named @p_14)) :rule la_generic :args (1 1 (- 1)))
+(step t12 (cl @p_3 @p_14) :rule resolution :premises (t11 t7))
+(step t13 (cl (not (! (= y$ x$) :named @p_17)) (! (not @p_12) :named @p_16) @p_15 @p_13) :rule eq_congruent_pred)
+(step t14 (cl @p_16 @p_14 @p_17) :rule eq_transitive)
+(step t15 (cl @p_16 @p_15 @p_13 @p_16 @p_14) :rule th_resolution :premises (t13 t14))
+(step t16 (cl @p_16 @p_15 @p_13 @p_14) :rule contraction :premises (t15))
+(step t17 (cl @p_16 @p_15 @p_14) :rule resolution :premises (t16 t7))
+(step t18 (cl @p_14) :rule resolution :premises (t17 t10 t12))
+(step t19 (cl @p_3) :rule resolution :premises (t9 t18))
+(step t20 (cl @p_12) :rule resolution :premises (t10 t19))
+(step t21 (cl @p_13 @p_16) :rule la_generic :args (1 (- 1)))
+(step t22 (cl) :rule resolution :premises (t21 t7 t20))
+f79704028180f39e90d9e958e4416fd1e60a60df 567 0
 unsat
 (define-fun veriT_sk0 () A$ (! (choice ((veriT_vr145 A$)) (not (! (not (! (and (! (= (! (arg_min_on$ f$ (! (image$b g$ b$) :named @p_6)) :named @p_336) (! (fun_app$b g$ veriT_vr145) :named @p_378)) :named @p_379) (! (member$a veriT_vr145 b$) :named @p_381)) :named @p_382)) :named @p_377))) :named @p_357))
 (assume a29 (! (forall ((?v0 B_set$) (?v1 B_c_fun$)) (! (=> (! (and (! (finite$ ?v0) :named @p_1) (! (not (! (= ?v0 bot$) :named @p_10)) :named @p_2)) :named @p_13) (! (member$ (! (arg_min_on$ ?v1 ?v0) :named @p_15) ?v0) :named @p_17)) :named @p_19)) :named @p_7))
@@ -7396,7 +7396,7 @@
 (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))
-3e665c1d341eae599d476b91a009646c76f6e530 323 0
+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)))
@@ -7720,7 +7720,7 @@
 (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))
-dcd554acdbd4961913628ae6c525018e8ccd853b 36 0
+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$e 1) :named @p_26)))
@@ -7757,7 +7757,7 @@
 (step t12 (cl (or (! (not @p_25) :named @p_27) @p_26)) :rule forall_inst :args ((:= veriT_vr9 1)))
 (step t13 (cl @p_27 @p_26) :rule or :premises (t12))
 (step t14 (cl) :rule resolution :premises (t13 t11 a5))
-cec5afc0b0ddc7f0bb72ad78466b1f47a6cdaa4d 158 0
+f9bb7f97f8819ceceaefe0cdf934d0eda3431a5b 158 0
 unsat
 (assume a0 (! (forall ((?v0 Int)) (! (= (! (g$ (! (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)))))
@@ -7916,7 +7916,7 @@
 (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))
-339ffce021197fcaff7dca24e8371a4573b5ea1c 873 0
+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))
 (define-fun veriT_sk1 () Abort$ (! (choice ((veriT_vr66 Abort$)) (not (! (not (! (= x2$ (! (rabort$ veriT_vr66) :named @p_372)) :named @p_373)) :named @p_371))) :named @p_386))