# HG changeset patch # User Mathias Fleury # Date 1705668986 -3600 # Node ID 157de27b0863cc8c6fac2564ce2f0b38573d36cf # Parent b21d8401f0ca26cda14d5dfc45613fa722fe8a60 fix reconstruction of Alethe's and_pos rule diff -r b21d8401f0ca -r 157de27b0863 src/HOL/SMT.thy --- a/src/HOL/SMT.thy Mon Feb 05 10:06:34 2024 +0100 +++ b/src/HOL/SMT.thy Fri Jan 19 13:56:26 2024 +0100 @@ -252,6 +252,9 @@ lemma verit_and_pos: \(a \ \(b \ c) \ A) \ \(a \ b \ c) \ A\ \(a \ b \ A) \ \(a \ b) \ A\ + by blast+ + +lemma verit_farkas: \(a \ A) \ \a \ A\ \(\a \ A) \ a \ A\ by blast+ diff -r b21d8401f0ca -r 157de27b0863 src/HOL/SMT_Examples/SMT_Examples_Verit.certs --- a/src/HOL/SMT_Examples/SMT_Examples_Verit.certs Mon Feb 05 10:06:34 2024 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.certs Fri Jan 19 13:56:26 2024 +0100 @@ -210,661 +210,6 @@ (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)) -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$) :named @p_405)) :named @p_463)) :named @p_410))) -(anchor :step t21 :args ((:= (?v0 Int) veriT_vr0))) -(step t21.t1 (cl (= ?v0 veriT_vr0)) :rule refl) -(step t21.t2 (cl (= @p_13 (! (fun_app$ uua$ veriT_vr0) :named @p_14))) :rule cong :premises (t21.t1)) -(step t21.t3 (cl (= @p_15 (! (= @p_12 @p_14) :named @p_16))) :rule cong :premises (t21.t2)) -(step t21 (cl (! (= @p_11 (! (forall ((veriT_vr0 Int)) @p_16) :named @p_18)) :named @p_17)) :rule bind) -(step t22 (cl (not @p_17) (not @p_11) @p_18) :rule equiv_pos2) -(step t23 (cl @p_18) :rule th_resolution :premises (a0 t21 t22)) -(anchor :step t24 :args ((:= (veriT_vr0 Int) veriT_vr1))) -(step t24.t1 (cl (= veriT_vr0 veriT_vr1)) :rule refl) -(step t24.t2 (cl (= @p_14 (! (fun_app$ uua$ veriT_vr1) :named @p_19))) :rule cong :premises (t24.t1)) -(step t24.t3 (cl (= @p_16 (! (= @p_12 @p_19) :named @p_20))) :rule cong :premises (t24.t2)) -(step t24 (cl (! (= @p_18 (! (forall ((veriT_vr1 Int)) @p_20) :named @p_22)) :named @p_21)) :rule bind) -(step t25 (cl (not @p_21) (not @p_18) @p_22) :rule equiv_pos2) -(step t26 (cl @p_22) :rule th_resolution :premises (t23 t24 t25)) -(anchor :step t27 :args ((:= (?v0 Int) veriT_vr2))) -(step t27.t1 (cl (= ?v0 veriT_vr2)) :rule refl) -(step t27.t2 (cl (= @p_25 (! (fun_app$ uu$ veriT_vr2) :named @p_26))) :rule cong :premises (t27.t1)) -(step t27.t3 (cl (= @p_27 (! (= @p_24 @p_26) :named @p_28))) :rule cong :premises (t27.t2)) -(step t27 (cl (! (= @p_23 (! (forall ((veriT_vr2 Int)) @p_28) :named @p_30)) :named @p_29)) :rule bind) -(step t28 (cl (not @p_29) (not @p_23) @p_30) :rule equiv_pos2) -(step t29 (cl @p_30) :rule th_resolution :premises (a1 t27 t28)) -(anchor :step t30 :args ((:= (veriT_vr2 Int) veriT_vr3))) -(step t30.t1 (cl (= veriT_vr2 veriT_vr3)) :rule refl) -(step t30.t2 (cl (= @p_26 (! (fun_app$ uu$ veriT_vr3) :named @p_31))) :rule cong :premises (t30.t1)) -(step t30.t3 (cl (= @p_28 (! (= @p_24 @p_31) :named @p_32))) :rule cong :premises (t30.t2)) -(step t30 (cl (! (= @p_30 (! (forall ((veriT_vr3 Int)) @p_32) :named @p_34)) :named @p_33)) :rule bind) -(step t31 (cl (not @p_33) (not @p_30) @p_34) :rule equiv_pos2) -(step t32 (cl @p_34) :rule th_resolution :premises (t29 t30 t31)) -(anchor :step t33 :args ((:= (?v0 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr4) (:= (?v1 Int_real_real_real_prod_fun_prod$) veriT_vr5))) -(step t33.t1 (cl (! (= ?v0 veriT_vr4) :named @p_38)) :rule refl) -(step t33.t2 (cl (! (= ?v1 veriT_vr5) :named @p_39)) :rule refl) -(step t33.t3 (cl (= @p_36 (! (case_prod$ veriT_vr4 veriT_vr5) :named @p_37))) :rule cong :premises (t33.t1 t33.t2)) -(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$)) @p_49) :named @p_51)) :named @p_50)) :rule bind) -(step t34 (cl (not @p_50) (not @p_35) @p_51) :rule equiv_pos2) -(step t35 (cl @p_51) :rule th_resolution :premises (a2 t33 t34)) -(anchor :step t36 :args ((:= (veriT_vr4 Int_real_real_real_prod_fun_bool_fun_fun$) veriT_vr6) (:= (veriT_vr5 Int_real_real_real_prod_fun_prod$) veriT_vr7))) -(step t36.t1 (cl (! (= veriT_vr4 veriT_vr6) :named @p_53)) :rule refl) -(step t36.t2 (cl (! (= veriT_vr5 veriT_vr7) :named @p_54)) :rule refl) -(step t36.t3 (cl (= @p_37 (! (case_prod$ veriT_vr6 veriT_vr7) :named @p_52))) :rule cong :premises (t36.t1 t36.t2)) -(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 (! 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(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 Real) veriT_vr18) (:= (veriT_vr17 Real) veriT_vr19))) -(step t54.t1 (cl (! (= veriT_vr17 veriT_vr19) :named @p_114)) :rule refl) -(step t54.t2 (cl (= veriT_vr16 veriT_vr18)) :rule refl) -(step t54.t3 (cl (= @p_103 (! (pair$a veriT_vr18) :named @p_113))) :rule cong :premises (t54.t2)) -(step t54.t4 (cl @p_114) :rule refl) -(step t54.t5 (cl (= @p_106 (! (fun_app$b @p_113 veriT_vr19) :named @p_115))) :rule cong :premises (t54.t3 t54.t4)) -(step t54.t6 (cl (= @p_108 (! (snd$a @p_115) :named @p_116))) :rule cong :premises (t54.t5)) -(step t54.t7 (cl (= @p_110 (! (= veriT_vr19 @p_116) :named @p_117))) :rule cong :premises (t54.t1 t54.t6)) -(step t54 (cl (! (= @p_112 (! (forall ((veriT_vr18 Real) (veriT_vr19 Real)) @p_117) :named @p_119)) :named @p_118)) :rule bind) -(step t55 (cl (not @p_118) (not @p_112) @p_119) :rule equiv_pos2) -(step t56 (cl @p_119) :rule th_resolution :premises (t53 t54 t55)) -(anchor :step t57 :args ((:= (?v0 Real_real_prod_set$) veriT_vr20) (:= (?v1 Real_real_prod$) veriT_vr21) (:= (?v2 Real_real_prod_set$) veriT_vr22))) -(step t57.t1 (cl (! (= ?v0 veriT_vr20) :named @p_127)) :rule refl) -(step t57.t2 (cl (! (= ?v1 veriT_vr21) :named @p_126)) :rule refl) -(step t57.t3 (cl (! (= ?v2 veriT_vr22) :named @p_132)) :rule refl) -(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 (! 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(forall ((veriT_vr20 Real_real_prod_set$) (veriT_vr21 Real_real_prod$) (veriT_vr22 Real_real_prod_set$)) @p_140) :named @p_142)) :named @p_141)) :rule bind) -(step t58 (cl (not @p_141) (not @p_120) @p_142) :rule equiv_pos2) -(step t59 (cl @p_142) :rule th_resolution :premises (a7 t57 t58)) -(anchor :step t60 :args ((:= (veriT_vr20 Real_real_prod_set$) veriT_vr23) (:= (veriT_vr21 Real_real_prod$) veriT_vr24) (:= (veriT_vr22 Real_real_prod_set$) veriT_vr25))) -(step t60.t1 (cl (! (= veriT_vr20 veriT_vr23) :named @p_147)) :rule refl) -(step t60.t2 (cl (! (= veriT_vr21 veriT_vr24) :named @p_146)) :rule refl) -(step t60.t3 (cl (! (= veriT_vr22 veriT_vr25) :named @p_150)) :rule refl) -(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$)) @p_154) :named @p_156)) :named @p_155)) :rule bind) -(step t61 (cl (not @p_155) (not @p_142) @p_156) :rule equiv_pos2) -(step t62 (cl @p_156) :rule th_resolution :premises (t59 t60 t61)) -(anchor :step t63 :args ((:= (?v0 Real_real_prod_set$) veriT_vr26) (:= (?v1 Real_real_prod$) veriT_vr27))) -(step t63.t1 (cl (! (= ?v0 veriT_vr26) :named @p_159)) :rule refl) -(step t63.t2 (cl (= @p_4 (! (finite$ veriT_vr26) :named @p_158))) :rule cong :premises (t63.t1)) -(step t63.t3 (cl (= ?v1 veriT_vr27)) :rule refl) -(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 Real_real_prod_set$) veriT_vr28) (:= (veriT_vr27 Real_real_prod$) veriT_vr29))) -(step t66.t1 (cl (! (= veriT_vr26 veriT_vr28) :named @p_169)) :rule refl) -(step t66.t2 (cl (= @p_158 (! (finite$ veriT_vr28) :named @p_168))) :rule cong :premises (t66.t1)) -(step t66.t3 (cl (= veriT_vr27 veriT_vr29)) :rule refl) -(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 Real_real_prod$) veriT_vr30) (:= (?v1 Real_real_prod_set$) veriT_vr31))) -(step t69.t1 (cl (! (= ?v0 veriT_vr30) :named @p_179)) :rule refl) -(step t69.t2 (cl (! (= ?v1 veriT_vr31) :named @p_178)) :rule refl) -(step t69.t3 (cl (= @p_176 (! (member$a veriT_vr30 veriT_vr31) :named @p_177))) :rule cong :premises (t69.t1 t69.t2)) -(step t69.t4 (cl @p_178) :rule refl) -(step t69.t5 (cl @p_179) :rule refl) -(step t69.t6 (cl @p_178) :rule refl) -(step t69.t7 (cl (= @p_2 (! (insert$ veriT_vr30 veriT_vr31) :named @p_180))) :rule cong :premises (t69.t5 t69.t6)) -(step t69.t8 (cl (= @p_181 (! 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(forall ((veriT_vr35 Real_real_prod_set$)) @p_203) :named @p_205)) :named @p_204)) :rule bind) -(step t79 (cl (not @p_204) (not @p_201) @p_205) :rule equiv_pos2) -(step t80 (cl @p_205) :rule th_resolution :premises (t77 t78 t79)) -(anchor :step t81 :args ((:= (?v0 Real_real_prod$) veriT_vr36) (:= (?v1 Real_real_prod$) veriT_vr37) (:= (?v2 Real_real_prod_set$) veriT_vr38))) -(step t81.t1 (cl (! (= ?v0 veriT_vr36) :named @p_211)) :rule refl) -(step t81.t2 (cl (! (= ?v1 veriT_vr37) :named @p_210)) :rule refl) -(step t81.t3 (cl (! (= ?v2 veriT_vr38) :named @p_212)) :rule refl) -(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 (! 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(=> @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$)) @p_393) :named @p_398))) :rule bind) -(anchor :step t134 :args ((:= (veriT_vr61 Int_real_real_real_prod_fun_prod$) veriT_vr63))) -(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl) -(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1)) -(step t134.t3 (cl @p_395) :rule refl) -(step t134.t4 (cl (= @p_385 (! (case_prod$ 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$)) @@ -2545,74 +1890,6 @@ (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)) -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)) -(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0))) -(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl) -(step t2.t2 (cl (= @p_2 (! (< 0 veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1)) -(step t2.t3 (cl @p_4) :rule refl) -(step t2.t4 (cl (= @p_5 (! (+ veriT_vr0 1) :named @p_6))) :rule cong :premises (t2.t3)) -(step t2.t5 (cl (= @p_7 (! (< 0 @p_6) :named @p_8))) :rule cong :premises (t2.t4)) -(step t2.t6 (cl @p_4) :rule refl) -(step t2.t7 (cl (= @p_9 (! (< veriT_vr0 1) :named @p_10))) :rule cong :premises (t2.t6)) -(step t2.t8 (cl (= @p_11 (! (ite @p_3 @p_8 @p_10) :named @p_12))) :rule cong :premises (t2.t2 t2.t5 t2.t7)) -(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int)) @p_12) :named @p_14))) :rule bind) -(step t3 (cl (! (= @p_13 (! (not @p_14) :named @p_16)) :named @p_15)) :rule cong :premises (t2)) -(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_13) :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)) -(anchor :step t8 :args ((veriT_vr0 Int))) -(step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_19))) :rule sum_simplify) -(step t8.t2 (cl (= @p_8 (! (< 0 @p_19) :named @p_20))) :rule cong :premises (t8.t1)) -(step t8.t3 (cl (= @p_12 (! (ite @p_3 @p_20 @p_10) :named @p_21))) :rule cong :premises (t8.t2)) -(step t8 (cl (= @p_14 (! (forall ((veriT_vr0 Int)) @p_21) :named @p_22))) :rule bind) -(step t9 (cl (! (= @p_16 (! (not @p_22) :named @p_24)) :named @p_23)) :rule cong :premises (t8)) -(step t10 (cl (! (not @p_23) :named @p_26) (! (not @p_16) :named @p_25) @p_24) :rule equiv_pos2) -(step t11 (cl (not @p_25) @p_14) :rule not_not) -(step t12 (cl @p_26 @p_14 @p_24) :rule th_resolution :premises (t11 t10)) -(step t13 (cl @p_24) :rule th_resolution :premises (t7 t9 t12)) -(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr1))) -(step t14.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_28)) :rule refl) -(step t14.t2 (cl (= @p_3 @p_27)) :rule cong :premises (t14.t1)) -(step t14.t3 (cl @p_28) :rule refl) -(step t14.t4 (cl (= @p_19 @p_29)) :rule cong :premises (t14.t3)) -(step t14.t5 (cl (= @p_20 @p_30)) :rule cong :premises (t14.t4)) -(step t14.t6 (cl @p_28) :rule refl) -(step t14.t7 (cl (= @p_10 @p_31)) :rule cong :premises (t14.t6)) -(step t14.t8 (cl (= @p_21 @p_32)) :rule cong :premises (t14.t2 t14.t5 t14.t7)) -(step t14 (cl (= @p_22 (! (forall ((veriT_vr1 Int)) @p_32) :named @p_33))) :rule bind) -(step t15 (cl (! (= @p_24 (! (not @p_33) :named @p_35)) :named @p_34)) :rule cong :premises (t14)) -(step t16 (cl (! (not @p_34) :named @p_37) (! (not @p_24) :named @p_36) @p_35) :rule equiv_pos2) -(step t17 (cl (not @p_36) @p_22) :rule not_not) -(step t18 (cl @p_37 @p_22 @p_35) :rule th_resolution :premises (t17 t16)) -(step t19 (cl @p_35) :rule th_resolution :premises (t13 t15 t18)) -(anchor :step t20 :args ((:= (veriT_vr1 Int) veriT_sk0))) -(step t20.t1 (cl (! (= veriT_vr1 veriT_sk0) :named @p_40)) :rule refl) -(step t20.t2 (cl (= @p_27 (! (< 0 veriT_sk0) :named @p_39))) :rule cong :premises (t20.t1)) -(step t20.t3 (cl @p_40) :rule refl) -(step t20.t4 (cl (= @p_29 (! (+ 1 veriT_sk0) :named @p_41))) :rule cong :premises (t20.t3)) -(step t20.t5 (cl (= @p_30 (! (< 0 @p_41) :named @p_42))) :rule cong :premises (t20.t4)) -(step t20.t6 (cl @p_40) :rule refl) -(step t20.t7 (cl (= @p_31 (! (< veriT_sk0 1) :named @p_43))) :rule cong :premises (t20.t6)) -(step t20.t8 (cl (= @p_32 (! (ite @p_39 @p_42 @p_43) :named @p_44))) :rule cong :premises (t20.t2 t20.t5 t20.t7)) -(step t20 (cl (= @p_33 @p_44)) :rule sko_forall) -(step t21 (cl (! (= @p_35 (! (not @p_44) :named @p_46)) :named @p_45)) :rule cong :premises (t20)) -(step t22 (cl (! (not @p_45) :named @p_48) (! (not @p_35) :named @p_47) @p_46) :rule equiv_pos2) -(step t23 (cl (not @p_47) @p_33) :rule not_not) -(step t24 (cl @p_48 @p_33 @p_46) :rule th_resolution :premises (t23 t22)) -(step t25 (cl @p_46) :rule th_resolution :premises (t19 t21 t24)) -(step t26 (cl @p_39 (! (not @p_43) :named @p_50)) :rule not_ite1 :premises (t25)) -(step t27 (cl (! (not @p_39) :named @p_49) (not @p_42)) :rule not_ite2 :premises (t25)) -(step t28 (cl @p_43 @p_42) :rule la_generic :args (1 1)) -(step t29 (cl @p_49 @p_42) :rule la_generic :args (1 1)) -(step t30 (cl @p_42) :rule resolution :premises (t29 t26 t28)) -(step t31 (cl @p_49) :rule resolution :premises (t27 t30)) -(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)) 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)) @@ -2721,6 +1998,74 @@ (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)) +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)) +(anchor :step t2 :args ((:= (?v0 Int) veriT_vr0))) +(step t2.t1 (cl (! (= ?v0 veriT_vr0) :named @p_4)) :rule refl) +(step t2.t2 (cl (= @p_2 (! (< 0 veriT_vr0) :named @p_3))) :rule cong :premises (t2.t1)) +(step t2.t3 (cl @p_4) :rule refl) +(step t2.t4 (cl (= @p_5 (! (+ veriT_vr0 1) :named @p_6))) :rule cong :premises (t2.t3)) +(step t2.t5 (cl (= @p_7 (! (< 0 @p_6) :named @p_8))) :rule cong :premises (t2.t4)) +(step t2.t6 (cl @p_4) :rule refl) +(step t2.t7 (cl (= @p_9 (! (< veriT_vr0 1) :named @p_10))) :rule cong :premises (t2.t6)) +(step t2.t8 (cl (= @p_11 (! (ite @p_3 @p_8 @p_10) :named @p_12))) :rule cong :premises (t2.t2 t2.t5 t2.t7)) +(step t2 (cl (= @p_1 (! (forall ((veriT_vr0 Int)) @p_12) :named @p_14))) :rule bind) +(step t3 (cl (! (= @p_13 (! (not @p_14) :named @p_16)) :named @p_15)) :rule cong :premises (t2)) +(step t4 (cl (! (not @p_15) :named @p_18) (! (not @p_13) :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)) +(anchor :step t8 :args ((veriT_vr0 Int))) +(step t8.t1 (cl (= @p_6 (! (+ 1 veriT_vr0) :named @p_19))) :rule sum_simplify) +(step t8.t2 (cl (= @p_8 (! (< 0 @p_19) :named @p_20))) :rule cong :premises (t8.t1)) +(step t8.t3 (cl (= @p_12 (! (ite @p_3 @p_20 @p_10) :named @p_21))) :rule cong :premises (t8.t2)) +(step t8 (cl (= @p_14 (! (forall ((veriT_vr0 Int)) @p_21) :named @p_22))) :rule bind) +(step t9 (cl (! (= @p_16 (! (not @p_22) :named @p_24)) :named @p_23)) :rule cong :premises (t8)) +(step t10 (cl (! (not @p_23) :named @p_26) (! (not @p_16) :named @p_25) @p_24) :rule equiv_pos2) +(step t11 (cl (not @p_25) @p_14) :rule not_not) +(step t12 (cl @p_26 @p_14 @p_24) :rule th_resolution :premises (t11 t10)) +(step t13 (cl @p_24) :rule th_resolution :premises (t7 t9 t12)) +(anchor :step t14 :args ((:= (veriT_vr0 Int) veriT_vr1))) +(step t14.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_28)) :rule refl) +(step t14.t2 (cl (= @p_3 @p_27)) :rule cong :premises (t14.t1)) +(step t14.t3 (cl @p_28) :rule refl) +(step t14.t4 (cl (= @p_19 @p_29)) :rule cong :premises (t14.t3)) +(step t14.t5 (cl (= @p_20 @p_30)) :rule cong :premises (t14.t4)) +(step t14.t6 (cl @p_28) :rule refl) +(step t14.t7 (cl (= @p_10 @p_31)) :rule cong :premises (t14.t6)) +(step t14.t8 (cl (= @p_21 @p_32)) :rule cong :premises (t14.t2 t14.t5 t14.t7)) +(step t14 (cl (= @p_22 (! (forall ((veriT_vr1 Int)) @p_32) :named @p_33))) :rule bind) +(step t15 (cl (! (= @p_24 (! (not @p_33) :named @p_35)) :named @p_34)) :rule cong :premises (t14)) +(step t16 (cl (! (not @p_34) :named @p_37) (! (not @p_24) :named @p_36) @p_35) :rule equiv_pos2) +(step t17 (cl (not @p_36) @p_22) :rule not_not) +(step t18 (cl @p_37 @p_22 @p_35) :rule th_resolution :premises (t17 t16)) +(step t19 (cl @p_35) :rule th_resolution :premises (t13 t15 t18)) +(anchor :step t20 :args ((:= (veriT_vr1 Int) veriT_sk0))) +(step t20.t1 (cl (! (= veriT_vr1 veriT_sk0) :named @p_40)) :rule refl) +(step t20.t2 (cl (= @p_27 (! (< 0 veriT_sk0) :named @p_39))) :rule cong :premises (t20.t1)) +(step t20.t3 (cl @p_40) :rule refl) +(step t20.t4 (cl (= @p_29 (! (+ 1 veriT_sk0) :named @p_41))) :rule cong :premises (t20.t3)) +(step t20.t5 (cl (= @p_30 (! (< 0 @p_41) :named @p_42))) :rule cong :premises (t20.t4)) +(step t20.t6 (cl @p_40) :rule refl) +(step t20.t7 (cl (= @p_31 (! (< veriT_sk0 1) :named @p_43))) :rule cong :premises (t20.t6)) +(step t20.t8 (cl (= @p_32 (! (ite @p_39 @p_42 @p_43) :named @p_44))) :rule cong :premises (t20.t2 t20.t5 t20.t7)) +(step t20 (cl (= @p_33 @p_44)) :rule sko_forall) +(step t21 (cl (! (= @p_35 (! (not @p_44) :named @p_46)) :named @p_45)) :rule cong :premises (t20)) +(step t22 (cl (! (not @p_45) :named @p_48) (! (not @p_35) :named @p_47) @p_46) :rule equiv_pos2) +(step t23 (cl (not @p_47) @p_33) :rule not_not) +(step t24 (cl @p_48 @p_33 @p_46) :rule th_resolution :premises (t23 t22)) +(step t25 (cl @p_46) :rule th_resolution :premises (t19 t21 t24)) +(step t26 (cl @p_39 (! (not @p_43) :named @p_50)) :rule not_ite1 :premises (t25)) +(step t27 (cl (! (not @p_39) :named @p_49) (not @p_42)) :rule not_ite2 :premises (t25)) +(step t28 (cl @p_43 @p_42) :rule la_generic :args (1 1)) +(step t29 (cl @p_49 @p_42) :rule la_generic :args (1 1)) +(step t30 (cl @p_42) :rule resolution :premises (t29 t26 t28)) +(step t31 (cl @p_49) :rule resolution :premises (t27 t30)) +(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)) 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)) @@ -3718,34 +3063,6 @@ (step t21 (cl false) :rule th_resolution :premises (t15 t19 t20)) (step t22 (cl (not false)) :rule false) (step t23 (cl) :rule resolution :premises (t21 t22)) -c16c43a541a3283a006315d4b74b5196ee73be5b 27 0 -unsat -(assume a0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true))) -(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0)) -(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0))) -(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl) -(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1)) -(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind) -(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3)) -(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4)) -(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5)) -(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2) -(step t8 (cl (not @p_14) @p_8) :rule not_not) -(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7)) -(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9)) -(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify) -(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2) -(step t13 (cl (not @p_18) @p_11) :rule not_not) -(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12)) -(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14)) -(step t16 (cl (= @p_20 false)) :rule not_simplify) -(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16)) -(step t18 (cl (= @p_21 false)) :rule and_simplify) -(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18)) -(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2) -(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20)) -(step t22 (cl (not false)) :rule false) -(step t23 (cl) :rule resolution :premises (t21 t22)) bfe8d775ab64ce32fa8986be49dfdcae57d75099 60 0 unsat (assume a0 (! (forall ((?v0 Int) (?v1 Int)) (! (= (! (fun_app$ (! (fun_app$a uu$ ?v0) :named @p_2) ?v1) :named @p_4) (! (<= ?v0 ?v1) :named @p_8)) :named @p_10)) :named @p_1)) @@ -3957,6 +3274,34 @@ (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)) +c16c43a541a3283a006315d4b74b5196ee73be5b 27 0 +unsat +(assume a0 (not (=> (f$ (! (forall ((?v0 A$)) (! (g$ ?v0) :named @p_2)) :named @p_1)) true))) +(step t2 (cl (! (not (! (=> (! (ite @p_1 (! (f$ true) :named @p_6) (! (f$ false) :named @p_7)) :named @p_4) true) :named @p_8)) :named @p_10)) :rule bfun_elim :premises (a0)) +(anchor :step t3 :args ((:= (?v0 A$) veriT_vr0))) +(step t3.t1 (cl (= ?v0 veriT_vr0)) :rule refl) +(step t3.t2 (cl (= @p_2 (! (g$ veriT_vr0) :named @p_3))) :rule cong :premises (t3.t1)) +(step t3 (cl (= @p_1 (! (forall ((veriT_vr0 A$)) @p_3) :named @p_5))) :rule bind) +(step t4 (cl (= @p_4 (! (ite @p_5 @p_6 @p_7) :named @p_9))) :rule cong :premises (t3)) +(step t5 (cl (= @p_8 (! (=> @p_9 true) :named @p_11))) :rule cong :premises (t4)) +(step t6 (cl (! (= @p_10 (! (not @p_11) :named @p_13)) :named @p_12)) :rule cong :premises (t5)) +(step t7 (cl (! (not @p_12) :named @p_15) (! (not @p_10) :named @p_14) @p_13) :rule equiv_pos2) +(step t8 (cl (not @p_14) @p_8) :rule not_not) +(step t9 (cl @p_15 @p_8 @p_13) :rule th_resolution :premises (t8 t7)) +(step t10 (cl @p_13) :rule th_resolution :premises (t2 t6 t9)) +(step t11 (cl (! (= @p_13 (! (and @p_9 (! (not true) :named @p_20)) :named @p_17)) :named @p_16)) :rule bool_simplify) +(step t12 (cl (! (not @p_16) :named @p_19) (! (not @p_13) :named @p_18) @p_17) :rule equiv_pos2) +(step t13 (cl (not @p_18) @p_11) :rule not_not) +(step t14 (cl @p_19 @p_11 @p_17) :rule th_resolution :premises (t13 t12)) +(step t15 (cl @p_17) :rule th_resolution :premises (t10 t11 t14)) +(step t16 (cl (= @p_20 false)) :rule not_simplify) +(step t17 (cl (= @p_17 (! (and @p_9 false) :named @p_21))) :rule cong :premises (t16)) +(step t18 (cl (= @p_21 false)) :rule and_simplify) +(step t19 (cl (! (= @p_17 false) :named @p_22)) :rule trans :premises (t17 t18)) +(step t20 (cl (not @p_22) (not @p_17) false) :rule equiv_pos2) +(step t21 (cl false) :rule th_resolution :premises (t15 t19 t20)) +(step t22 (cl (not false)) :rule false) +(step t23 (cl) :rule resolution :premises (t21 t22)) 3fb3269903eddb271bcd0f8b72a806a38020c0d1 107 0 unsat (assume a0 (! (forall ((?v0 Int)) (! (= (! (dec_10$ ?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)) @@ -5549,6 +4894,661 @@ (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)) +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 (! 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(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 Int_real_real_real_prod_fun_prod$) veriT_vr61))) +(step t129.t1 (cl (! (= veriT_vr60 veriT_vr61) :named @p_384)) :rule refl) +(step t129.t2 (cl (= @p_369 (! (member$ veriT_vr61 one_chain_typeI$) :named @p_383))) :rule cong :premises (t129.t1)) +(step t129.t3 (cl @p_384) :rule refl) +(step t129.t4 (cl (= @p_365 (! (case_prod$ 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$)) @p_386) :named @p_387))) :rule bind) +(step t130 (cl (! (= @p_382 (! (and @p_377 @p_374 @p_387) :named @p_389)) :named @p_388)) :rule cong :premises (t129)) +(step t131 (cl (not @p_388) (not @p_382) @p_389) :rule equiv_pos2) +(step t132 (cl @p_389) :rule th_resolution :premises (t128 t130 t131)) +(anchor :step t133 :args ((:= (veriT_vr60 Int_real_real_real_prod_fun_prod$) veriT_vr62))) +(step t133.t1 (cl (! (= veriT_vr60 veriT_vr62) :named @p_391)) :rule refl) +(step t133.t2 (cl (= @p_363 (! (member$ veriT_vr62 one_chain_typeII$) :named @p_390))) :rule cong :premises (t133.t1)) +(step t133.t3 (cl @p_391) :rule refl) +(step t133.t4 (cl (= @p_365 (! (case_prod$ uua$ veriT_vr62) :named @p_392))) :rule cong :premises (t133.t3)) +(step t133.t5 (cl (= @p_367 (! (=> @p_390 @p_392) :named @p_393))) :rule cong :premises (t133.t2 t133.t4)) +(step t133 (cl (= @p_374 (! (forall ((veriT_vr62 Int_real_real_real_prod_fun_prod$)) @p_393) :named @p_398))) :rule bind) +(anchor :step t134 :args ((:= (veriT_vr61 Int_real_real_real_prod_fun_prod$) veriT_vr63))) +(step t134.t1 (cl (! (= veriT_vr61 veriT_vr63) :named @p_395)) :rule refl) +(step t134.t2 (cl (= @p_383 (! (member$ veriT_vr63 one_chain_typeI$) :named @p_394))) :rule cong :premises (t134.t1)) +(step t134.t3 (cl @p_395) :rule refl) +(step t134.t4 (cl (= @p_385 (! (case_prod$ 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)) 7d1d28af77b48e47cf45f7abbbccb64bffffc3f9 6 0 unsat (assume a0 (! (< 0.0 (+ x$ (! (* 2.0 y$) :named @p_1))) :named @p_2)) @@ -6075,6 +6075,574 @@ (step t201 (cl @p_378 @p_381 @p_376 @p_344 @p_342 @p_378 @p_380) :rule th_resolution :premises (t197 t200)) (step t202 (cl @p_378 @p_381 @p_376 @p_344 @p_342 @p_380) :rule contraction :premises (t201)) (step t203 (cl) :rule resolution :premises (t202 t156 t165 t149 t173 t180 t196)) +f79704028180f39e90d9e958e4416fd1e60a60df 567 0 +unsat +(define-fun veriT_sk0 () A$ (! (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)) +(assume a31 (! (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (! (=> (! (and @p_1 (! (and @p_2 (! (member$ ?v1 ?v0) :named @p_38)) :named @p_40)) :named @p_42) (! (less_eq$ (! (fun_app$ ?v2 (! (arg_min_on$ ?v2 ?v0) :named @p_45)) :named @p_47) (! (fun_app$ ?v2 ?v1) :named @p_50)) :named @p_52)) :named @p_54)) :named @p_33)) +(assume a33 (! (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (! (= (! (fun_app$a (! (comp$ ?v0 ?v1) :named @p_78) ?v2) :named @p_80) (! (fun_app$ ?v0 (! (fun_app$b ?v1 ?v2) :named @p_3)) :named @p_86)) :named @p_88)) :named @p_77)) +(assume a36 (! (forall ((?v0 A_set$) (?v1 A_b_fun$)) (! (=> (! (finite$a ?v0) :named @p_103) (! (finite$ (! (image$b ?v1 ?v0) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_102)) +(assume a40 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (! (=> (! (and (! (member$ ?v0 (! (image$b ?v1 ?v2) :named @p_122)) :named @p_124) (! (forall ((?v3 A$)) (! (=> (! (and (! (= ?v0 (! (fun_app$b ?v1 ?v3) :named @p_130)) :named @p_132) (! (member$a ?v3 ?v2) :named @p_136)) :named @p_138) false) :named @p_140)) :named @p_126)) :named @p_142) false) :named @p_144)) :named @p_121)) +(assume a44 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (! (=> (! (and (! (= @p_3 ?v0) :named @p_173) (! (member$a ?v2 ?v3) :named @p_176)) :named @p_178) (! (member$ ?v0 (! (image$b ?v1 ?v3) :named @p_183)) :named @p_185)) :named @p_187)) :named @p_171)) +(assume a48 (! (forall ((?v0 A_b_fun$) (?v1 A_set$)) (! (= (! (= bot$ (! (image$b ?v0 ?v1) :named @p_205)) :named @p_207) (! (= bot$a ?v1) :named @p_210)) :named @p_212)) :named @p_204)) +(assume a50 (! (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (! (=> (! (and (! (inj_on$ ?v0 ?v1) :named @p_224) (! (and (! (= (! (fun_app$ ?v0 ?v2) :named @p_227) (! (fun_app$ ?v0 ?v3) :named @p_229)) :named @p_231) (! (and (! (member$ ?v2 ?v1) :named @p_235) (! (member$ ?v3 ?v1) :named @p_238)) :named @p_240)) :named @p_242)) :named @p_244) (! (= ?v3 ?v2) :named @p_246)) :named @p_248)) :named @p_223)) +(assume a51 (! (forall ((?v0 C$) (?v1 C$)) (! (= (! (less$ ?v0 ?v1) :named @p_272) (! (and (! (less_eq$ ?v0 ?v1) :named @p_276) (! (not (! (= ?v0 ?v1) :named @p_278)) :named @p_280)) :named @p_282)) :named @p_284)) :named @p_271)) +(assume a23 (! (inj_on$ f$ @p_6) :named @p_353)) +(assume a24 (! (finite$a b$) :named @p_332)) +(assume a25 (not (! (= bot$a b$) :named @p_331))) +(assume a26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_4) b$) :named @p_5) b$) :named @p_423)) +(assume a27 (! (not (! (exists ((?v0 A$)) (! (and (! (member$a ?v0 b$) :named @p_300) (! (less$ (! (fun_app$a @p_4 ?v0) :named @p_303) (! (fun_app$a @p_4 @p_5) :named @p_299)) :named @p_305)) :named @p_307)) :named @p_298)) :named @p_309)) +(assume a52 (not (! (= @p_336 (! (fun_app$b g$ @p_5) :named @p_333)) :named @p_355))) +(anchor :step t16 :args ((:= (?v0 B_set$) veriT_vr0) (:= (?v1 B_c_fun$) veriT_vr1))) +(step t16.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl) +(step t16.t2 (cl (= @p_1 (! (finite$ veriT_vr0) :named @p_8))) :rule cong :premises (t16.t1)) +(step t16.t3 (cl @p_9) :rule refl) +(step t16.t4 (cl (= @p_10 (! (= bot$ veriT_vr0) :named @p_11))) :rule cong :premises (t16.t3)) +(step t16.t5 (cl (= @p_2 (! (not @p_11) :named @p_12))) :rule cong :premises (t16.t4)) +(step t16.t6 (cl (= @p_13 (! (and @p_8 @p_12) :named @p_14))) :rule cong :premises (t16.t2 t16.t5)) +(step t16.t7 (cl (= ?v1 veriT_vr1)) :rule refl) +(step t16.t8 (cl @p_9) :rule refl) +(step t16.t9 (cl (= @p_15 (! (arg_min_on$ veriT_vr1 veriT_vr0) :named @p_16))) :rule cong :premises (t16.t7 t16.t8)) +(step t16.t10 (cl @p_9) :rule refl) +(step t16.t11 (cl (= @p_17 (! (member$ @p_16 veriT_vr0) :named @p_18))) :rule cong :premises (t16.t9 t16.t10)) +(step t16.t12 (cl (= @p_19 (! (=> @p_14 @p_18) :named @p_20))) :rule cong :premises (t16.t6 t16.t11)) +(step t16 (cl (! (= @p_7 (! (forall ((veriT_vr0 B_set$) (veriT_vr1 B_c_fun$)) @p_20) :named @p_22)) :named @p_21)) :rule bind) +(step t17 (cl (not @p_21) (not @p_7) @p_22) :rule equiv_pos2) +(step t18 (cl @p_22) :rule th_resolution :premises (a29 t16 t17)) +(anchor :step t19 :args ((:= (veriT_vr0 B_set$) veriT_vr2) (:= (veriT_vr1 B_c_fun$) veriT_vr3))) +(step t19.t1 (cl (! (= veriT_vr0 veriT_vr2) :named @p_24)) :rule refl) +(step t19.t2 (cl (= @p_8 (! (finite$ veriT_vr2) :named @p_23))) :rule cong :premises (t19.t1)) +(step t19.t3 (cl @p_24) :rule refl) +(step t19.t4 (cl (= @p_11 (! (= bot$ veriT_vr2) :named @p_25))) :rule cong :premises (t19.t3)) +(step t19.t5 (cl (= @p_12 (! (not @p_25) :named @p_26))) :rule cong :premises (t19.t4)) +(step t19.t6 (cl (= @p_14 (! (and @p_23 @p_26) :named @p_27))) :rule cong :premises (t19.t2 t19.t5)) +(step t19.t7 (cl (= veriT_vr1 veriT_vr3)) :rule refl) +(step t19.t8 (cl @p_24) :rule refl) +(step t19.t9 (cl (= @p_16 (! (arg_min_on$ veriT_vr3 veriT_vr2) :named @p_28))) :rule cong :premises (t19.t7 t19.t8)) +(step t19.t10 (cl @p_24) :rule refl) +(step t19.t11 (cl (= @p_18 (! (member$ @p_28 veriT_vr2) :named @p_29))) :rule cong :premises (t19.t9 t19.t10)) +(step t19.t12 (cl (= @p_20 (! (=> @p_27 @p_29) :named @p_30))) :rule cong :premises (t19.t6 t19.t11)) +(step t19 (cl (! (= @p_22 (! (forall ((veriT_vr2 B_set$) (veriT_vr3 B_c_fun$)) @p_30) :named @p_32)) :named @p_31)) :rule bind) +(step t20 (cl (not @p_31) (not @p_22) @p_32) :rule equiv_pos2) +(step t21 (cl @p_32) :rule th_resolution :premises (t18 t19 t20)) +(anchor :step t22 :args ((:= (?v0 B_set$) veriT_vr8) (:= (?v1 B$) veriT_vr9) (:= (?v2 B_c_fun$) veriT_vr10))) +(step t22.t1 (cl (! (= ?v0 veriT_vr8) :named @p_35)) :rule refl) +(step t22.t2 (cl (= @p_1 (! (finite$ veriT_vr8) :named @p_34))) :rule cong :premises (t22.t1)) +(step t22.t3 (cl @p_35) :rule refl) +(step t22.t4 (cl (= @p_10 (! (= bot$ veriT_vr8) :named @p_36))) :rule cong :premises (t22.t3)) +(step t22.t5 (cl (= @p_2 (! (not @p_36) :named @p_37))) :rule cong :premises (t22.t4)) +(step t22.t6 (cl (! (= ?v1 veriT_vr9) :named @p_49)) :rule refl) +(step t22.t7 (cl @p_35) :rule refl) +(step t22.t8 (cl (= @p_38 (! (member$ veriT_vr9 veriT_vr8) :named @p_39))) :rule cong :premises (t22.t6 t22.t7)) +(step t22.t9 (cl (= @p_40 (! (and @p_37 @p_39) :named @p_41))) :rule cong :premises (t22.t5 t22.t8)) +(step t22.t10 (cl (= @p_42 (! (and @p_34 @p_41) :named @p_43))) :rule cong :premises (t22.t2 t22.t9)) +(step t22.t11 (cl (! (= ?v2 veriT_vr10) :named @p_44)) :rule refl) +(step t22.t12 (cl @p_44) :rule refl) +(step t22.t13 (cl @p_35) :rule refl) +(step t22.t14 (cl (= @p_45 (! (arg_min_on$ veriT_vr10 veriT_vr8) :named @p_46))) :rule cong :premises (t22.t12 t22.t13)) +(step t22.t15 (cl (= @p_47 (! (fun_app$ veriT_vr10 @p_46) :named @p_48))) :rule cong :premises (t22.t11 t22.t14)) +(step t22.t16 (cl @p_44) :rule refl) +(step t22.t17 (cl @p_49) :rule refl) +(step t22.t18 (cl (= @p_50 (! (fun_app$ veriT_vr10 veriT_vr9) :named @p_51))) :rule cong :premises (t22.t16 t22.t17)) +(step t22.t19 (cl (= @p_52 (! (less_eq$ @p_48 @p_51) :named @p_53))) :rule cong :premises (t22.t15 t22.t18)) +(step t22.t20 (cl (= @p_54 (! (=> @p_43 @p_53) :named @p_55))) :rule cong :premises (t22.t10 t22.t19)) +(step t22 (cl (! (= @p_33 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_55) :named @p_57)) :named @p_56)) :rule bind) +(step t23 (cl (not @p_56) (not @p_33) @p_57) :rule equiv_pos2) +(step t24 (cl @p_57) :rule th_resolution :premises (a31 t22 t23)) +(anchor :step t25 :args ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$))) +(step t25.t1 (cl (= @p_43 (! (and @p_34 @p_37 @p_39) :named @p_58))) :rule ac_simp) +(step t25.t2 (cl (= @p_55 (! (=> @p_58 @p_53) :named @p_59))) :rule cong :premises (t25.t1)) +(step t25 (cl (! (= @p_57 (! (forall ((veriT_vr8 B_set$) (veriT_vr9 B$) (veriT_vr10 B_c_fun$)) @p_59) :named @p_61)) :named @p_60)) :rule bind) +(step t26 (cl (not @p_60) (not @p_57) @p_61) :rule equiv_pos2) +(step t27 (cl @p_61) :rule th_resolution :premises (t24 t25 t26)) +(anchor :step t28 :args ((:= (veriT_vr8 B_set$) veriT_vr11) (:= (veriT_vr9 B$) veriT_vr12) (:= (veriT_vr10 B_c_fun$) veriT_vr13))) +(step t28.t1 (cl (! (= veriT_vr8 veriT_vr11) :named @p_63)) :rule refl) +(step t28.t2 (cl (= @p_34 (! (finite$ veriT_vr11) :named @p_62))) :rule cong :premises (t28.t1)) +(step t28.t3 (cl @p_63) :rule refl) +(step t28.t4 (cl (= @p_36 (! (= bot$ veriT_vr11) :named @p_64))) :rule cong :premises (t28.t3)) +(step t28.t5 (cl (= @p_37 (! (not @p_64) :named @p_65))) :rule cong :premises (t28.t4)) +(step t28.t6 (cl (! (= veriT_vr9 veriT_vr12) :named @p_71)) :rule refl) +(step t28.t7 (cl @p_63) :rule refl) +(step t28.t8 (cl (= @p_39 (! (member$ veriT_vr12 veriT_vr11) :named @p_66))) :rule cong :premises (t28.t6 t28.t7)) +(step t28.t9 (cl (= @p_58 (! (and @p_62 @p_65 @p_66) :named @p_67))) :rule cong :premises (t28.t2 t28.t5 t28.t8)) +(step t28.t10 (cl (! (= veriT_vr10 veriT_vr13) :named @p_68)) :rule refl) +(step t28.t11 (cl @p_68) :rule refl) +(step t28.t12 (cl @p_63) :rule refl) +(step t28.t13 (cl (= @p_46 (! (arg_min_on$ veriT_vr13 veriT_vr11) :named @p_69))) :rule cong :premises (t28.t11 t28.t12)) +(step t28.t14 (cl (= @p_48 (! (fun_app$ veriT_vr13 @p_69) :named @p_70))) :rule cong :premises (t28.t10 t28.t13)) +(step t28.t15 (cl @p_68) :rule refl) +(step t28.t16 (cl @p_71) :rule refl) +(step t28.t17 (cl (= @p_51 (! (fun_app$ veriT_vr13 veriT_vr12) :named @p_72))) :rule cong :premises (t28.t15 t28.t16)) +(step t28.t18 (cl (= @p_53 (! 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(= ?v3 veriT_vr125) :named @p_237)) :rule refl) +(step t64.t9 (cl (= @p_229 (! (fun_app$ veriT_vr122 veriT_vr125) :named @p_230))) :rule cong :premises (t64.t7 t64.t8)) +(step t64.t10 (cl (= @p_231 (! (= @p_228 @p_230) :named @p_232))) :rule cong :premises (t64.t6 t64.t9)) +(step t64.t11 (cl @p_233) :rule refl) +(step t64.t12 (cl @p_234) :rule refl) +(step t64.t13 (cl (= @p_235 (! (member$ veriT_vr124 veriT_vr123) :named @p_236))) :rule cong :premises (t64.t11 t64.t12)) +(step t64.t14 (cl @p_237) :rule refl) +(step t64.t15 (cl @p_234) :rule refl) +(step t64.t16 (cl (= @p_238 (! (member$ veriT_vr125 veriT_vr123) :named @p_239))) :rule cong :premises (t64.t14 t64.t15)) +(step t64.t17 (cl (= @p_240 (! (and @p_236 @p_239) :named @p_241))) :rule cong :premises (t64.t13 t64.t16)) +(step t64.t18 (cl (= @p_242 (! (and @p_232 @p_241) :named @p_243))) :rule cong :premises (t64.t10 t64.t17)) +(step t64.t19 (cl (= @p_244 (! (and @p_225 @p_243) :named @p_245))) :rule cong :premises (t64.t3 t64.t18)) +(step t64.t20 (cl @p_237) :rule refl) +(step t64.t21 (cl @p_233) :rule refl) +(step t64.t22 (cl (= @p_246 (! (= veriT_vr124 veriT_vr125) :named @p_247))) :rule cong :premises (t64.t20 t64.t21)) +(step t64.t23 (cl (= @p_248 (! (=> @p_245 @p_247) :named @p_249))) :rule cong :premises (t64.t19 t64.t22)) +(step t64 (cl (! (= @p_223 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_249) :named @p_251)) :named @p_250)) :rule bind) +(step t65 (cl (not @p_250) (not @p_223) @p_251) :rule equiv_pos2) +(step t66 (cl @p_251) :rule th_resolution :premises (a50 t64 t65)) +(anchor :step t67 :args ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$))) +(step t67.t1 (cl (= @p_245 (! (and @p_225 @p_232 @p_236 @p_239) :named @p_252))) :rule ac_simp) +(step t67.t2 (cl (= @p_249 (! (=> @p_252 @p_247) :named @p_253))) :rule cong :premises (t67.t1)) +(step t67 (cl (! (= @p_251 (! (forall ((veriT_vr122 B_c_fun$) (veriT_vr123 B_set$) (veriT_vr124 B$) (veriT_vr125 B$)) @p_253) :named @p_255)) :named @p_254)) :rule bind) +(step t68 (cl (not @p_254) (not @p_251) @p_255) :rule equiv_pos2) +(step t69 (cl @p_255) :rule th_resolution :premises (t66 t67 t68)) +(anchor :step t70 :args ((:= (veriT_vr122 B_c_fun$) veriT_vr126) (:= (veriT_vr123 B_set$) veriT_vr127) (:= (veriT_vr124 B$) veriT_vr128) (:= (veriT_vr125 B$) veriT_vr129))) +(step t70.t1 (cl (! (= veriT_vr122 veriT_vr126) :named @p_257)) :rule refl) +(step t70.t2 (cl (! (= veriT_vr123 veriT_vr127) :named @p_262)) :rule refl) +(step t70.t3 (cl (= @p_225 (! (inj_on$ veriT_vr126 veriT_vr127) :named @p_256))) :rule cong :premises (t70.t1 t70.t2)) +(step t70.t4 (cl @p_257) :rule refl) +(step t70.t5 (cl (! (= veriT_vr124 veriT_vr128) :named @p_261)) :rule refl) +(step t70.t6 (cl (= @p_228 (! (fun_app$ veriT_vr126 veriT_vr128) :named @p_258))) :rule cong :premises (t70.t4 t70.t5)) +(step t70.t7 (cl @p_257) :rule refl) +(step t70.t8 (cl (! (= veriT_vr125 veriT_vr129) :named @p_264)) :rule refl) +(step t70.t9 (cl (= @p_230 (! (fun_app$ veriT_vr126 veriT_vr129) :named @p_259))) :rule cong :premises (t70.t7 t70.t8)) +(step t70.t10 (cl (= @p_232 (! (= @p_258 @p_259) :named @p_260))) :rule cong :premises (t70.t6 t70.t9)) +(step t70.t11 (cl @p_261) :rule refl) +(step t70.t12 (cl @p_262) :rule refl) +(step t70.t13 (cl (= @p_236 (! (member$ veriT_vr128 veriT_vr127) :named @p_263))) :rule cong :premises (t70.t11 t70.t12)) +(step t70.t14 (cl @p_264) :rule refl) +(step t70.t15 (cl @p_262) :rule refl) +(step t70.t16 (cl (= @p_239 (! (member$ veriT_vr129 veriT_vr127) :named @p_265))) :rule cong :premises (t70.t14 t70.t15)) +(step t70.t17 (cl (= @p_252 (! (and @p_256 @p_260 @p_263 @p_265) :named @p_266))) :rule cong :premises (t70.t3 t70.t10 t70.t13 t70.t16)) +(step t70.t18 (cl @p_261) :rule refl) +(step t70.t19 (cl @p_264) :rule refl) +(step t70.t20 (cl (= @p_247 (! (= veriT_vr128 veriT_vr129) :named @p_267))) :rule cong :premises (t70.t18 t70.t19)) +(step t70.t21 (cl (= @p_253 (! (=> @p_266 @p_267) :named @p_268))) :rule cong :premises (t70.t17 t70.t20)) +(step t70 (cl (! (= @p_255 (! (forall ((veriT_vr126 B_c_fun$) (veriT_vr127 B_set$) (veriT_vr128 B$) (veriT_vr129 B$)) @p_268) :named @p_270)) :named @p_269)) :rule bind) +(step t71 (cl (not @p_269) (not @p_255) @p_270) :rule equiv_pos2) +(step t72 (cl @p_270) :rule th_resolution :premises (t69 t70 t71)) +(anchor :step t73 :args ((:= (?v0 C$) veriT_vr130) (:= (?v1 C$) veriT_vr131))) +(step t73.t1 (cl (! (= ?v0 veriT_vr130) :named @p_274)) :rule refl) +(step t73.t2 (cl (! (= ?v1 veriT_vr131) :named @p_275)) :rule refl) +(step t73.t3 (cl (= @p_272 (! (less$ veriT_vr130 veriT_vr131) :named @p_273))) :rule cong :premises (t73.t1 t73.t2)) +(step t73.t4 (cl @p_274) :rule refl) +(step t73.t5 (cl @p_275) :rule refl) +(step t73.t6 (cl (= @p_276 (! (less_eq$ veriT_vr130 veriT_vr131) :named @p_277))) :rule cong :premises (t73.t4 t73.t5)) +(step t73.t7 (cl @p_274) :rule refl) +(step t73.t8 (cl @p_275) :rule refl) +(step t73.t9 (cl (= @p_278 (! (= veriT_vr130 veriT_vr131) :named @p_279))) :rule cong :premises (t73.t7 t73.t8)) +(step t73.t10 (cl (= @p_280 (! (not @p_279) :named @p_281))) :rule cong :premises (t73.t9)) +(step t73.t11 (cl (= @p_282 (! (and @p_277 @p_281) :named @p_283))) :rule cong :premises (t73.t6 t73.t10)) +(step t73.t12 (cl (= @p_284 (! (= @p_273 @p_283) :named @p_285))) :rule cong :premises (t73.t3 t73.t11)) +(step t73 (cl (! (= @p_271 (! (forall ((veriT_vr130 C$) (veriT_vr131 C$)) @p_285) :named @p_287)) :named @p_286)) :rule bind) +(step t74 (cl (not @p_286) (not @p_271) @p_287) :rule equiv_pos2) +(step t75 (cl @p_287) :rule th_resolution :premises (a51 t73 t74)) +(anchor :step t76 :args ((:= (veriT_vr130 C$) veriT_vr132) (:= (veriT_vr131 C$) veriT_vr133))) +(step t76.t1 (cl (! (= veriT_vr130 veriT_vr132) :named @p_289)) :rule refl) +(step t76.t2 (cl (! (= veriT_vr131 veriT_vr133) :named @p_290)) :rule refl) +(step t76.t3 (cl (= @p_273 (! (less$ veriT_vr132 veriT_vr133) :named @p_288))) :rule cong :premises (t76.t1 t76.t2)) +(step t76.t4 (cl @p_289) :rule refl) +(step t76.t5 (cl @p_290) :rule refl) +(step t76.t6 (cl (= @p_277 (! (less_eq$ veriT_vr132 veriT_vr133) :named @p_291))) :rule cong :premises (t76.t4 t76.t5)) +(step t76.t7 (cl @p_289) :rule refl) +(step t76.t8 (cl @p_290) :rule refl) +(step t76.t9 (cl (= @p_279 (! (= veriT_vr132 veriT_vr133) :named @p_292))) :rule cong :premises (t76.t7 t76.t8)) +(step t76.t10 (cl (= @p_281 (! (not @p_292) :named @p_293))) :rule cong :premises (t76.t9)) +(step t76.t11 (cl (= @p_283 (! (and @p_291 @p_293) :named @p_294))) :rule cong :premises (t76.t6 t76.t10)) +(step t76.t12 (cl (= @p_285 (! (= @p_288 @p_294) :named @p_295))) :rule cong :premises (t76.t3 t76.t11)) +(step t76 (cl (! (= @p_287 (! (forall ((veriT_vr132 C$) (veriT_vr133 C$)) @p_295) :named @p_297)) :named @p_296)) :rule bind) +(step t77 (cl (not @p_296) (not @p_287) @p_297) :rule equiv_pos2) +(step t78 (cl @p_297) :rule th_resolution :premises (t75 t76 t77)) +(anchor :step t79 :args ((:= (?v0 A$) veriT_vr134))) +(step t79.t1 (cl (! (= ?v0 veriT_vr134) :named @p_302)) :rule refl) +(step t79.t2 (cl (= @p_300 (! (member$a veriT_vr134 b$) :named @p_301))) :rule cong :premises (t79.t1)) +(step t79.t3 (cl @p_302) :rule refl) +(step t79.t4 (cl (= @p_303 (! (fun_app$a @p_4 veriT_vr134) :named @p_304))) :rule cong :premises (t79.t3)) +(step t79.t5 (cl (= @p_305 (! (less$ @p_304 @p_299) :named @p_306))) :rule cong :premises (t79.t4)) +(step t79.t6 (cl (= @p_307 (! (and @p_301 @p_306) :named @p_308))) :rule cong :premises (t79.t2 t79.t5)) +(step t79 (cl (= @p_298 (! (exists ((veriT_vr134 A$)) @p_308) :named @p_310))) :rule bind) +(step t80 (cl (! (= @p_309 (! (not @p_310) :named @p_312)) :named @p_311)) :rule cong :premises (t79)) +(step t81 (cl (! (not @p_311) :named @p_314) (! (not @p_309) :named @p_313) @p_312) :rule equiv_pos2) +(step t82 (cl (not @p_313) @p_298) :rule not_not) +(step t83 (cl @p_314 @p_298 @p_312) :rule th_resolution :premises (t82 t81)) +(step t84 (cl @p_312) :rule th_resolution :premises (a27 t80 t83)) +(anchor :step t85 :args ((:= (veriT_vr134 A$) veriT_vr135))) +(step t85.t1 (cl (! (= veriT_vr134 veriT_vr135) :named @p_316)) :rule refl) +(step t85.t2 (cl (= @p_301 (! (member$a veriT_vr135 b$) :named @p_315))) :rule cong :premises (t85.t1)) +(step t85.t3 (cl @p_316) :rule refl) +(step t85.t4 (cl (= @p_304 (! (fun_app$a @p_4 veriT_vr135) :named @p_317))) :rule cong :premises (t85.t3)) +(step t85.t5 (cl (= @p_306 (! (less$ @p_317 @p_299) :named @p_318))) :rule cong :premises (t85.t4)) +(step t85.t6 (cl (= @p_308 (! (and @p_315 @p_318) :named @p_319))) :rule cong :premises (t85.t2 t85.t5)) +(step t85 (cl (= @p_310 (! (exists ((veriT_vr135 A$)) @p_319) :named @p_320))) :rule bind) +(step t86 (cl (! (= @p_312 (! (not @p_320) :named @p_322)) :named @p_321)) :rule cong :premises (t85)) +(step t87 (cl (! (not @p_321) :named @p_324) (! (not @p_312) :named @p_323) @p_322) :rule equiv_pos2) +(step t88 (cl (not @p_323) @p_310) :rule not_not) +(step t89 (cl @p_324 @p_310 @p_322) :rule th_resolution :premises (t88 t87)) +(step t90 (cl @p_322) :rule th_resolution :premises (t84 t86 t89)) +(step t91 (cl (= @p_320 (! (not (! (forall ((veriT_vr135 A$)) (not @p_319)) :named @p_330)) :named @p_325))) :rule connective_def) +(step t92 (cl (! (= @p_322 (! (not @p_325) :named @p_327)) :named @p_326)) :rule cong :premises (t91)) +(step t93 (cl (! (not @p_326) :named @p_329) (! (not @p_322) :named @p_328) @p_327) :rule equiv_pos2) +(step t94 (cl (not @p_328) @p_320) :rule not_not) +(step t95 (cl @p_329 @p_320 @p_327) :rule th_resolution :premises (t94 t93)) +(step t96 (cl (not @p_327) @p_330) :rule not_not) +(step t97 (cl @p_329 @p_320 @p_330) :rule th_resolution :premises (t96 t95)) +(step t98 (cl @p_327) :rule th_resolution :premises (t90 t92 t97)) +(step t99 (cl @p_330) :rule th_resolution :premises (t96 t98)) +(step t100 (cl (or (! (not @p_203) :named @p_421) (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) (or (not @p_192) (not @p_194) @p_200)) :named @p_422))) :rule qnt_cnf) +(step t101 (cl (or (! (not @p_222) :named @p_339) (! (= (! (= bot$ @p_6) :named @p_335) @p_331) :named @p_337))) :rule forall_inst :args ((:= veriT_vr116 g$) (:= veriT_vr117 b$))) +(step t102 (cl (or (! (not @p_120) :named @p_342) (! (=> @p_332 (! (finite$ @p_6) :named @p_334)) :named @p_341))) :rule forall_inst :args ((:= veriT_vr36 b$) (:= veriT_vr37 g$))) +(step t103 (cl (or (! (not @p_101) :named @p_344) (! (= @p_299 (! (fun_app$ f$ @p_333) :named @p_354)) :named @p_345))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 @p_5))) +(step t104 (cl (or (! (not @p_32) :named @p_351) (! (=> (! (and @p_334 (! (not @p_335) :named @p_338)) :named @p_346) (! (member$ @p_336 @p_6) :named @p_350)) :named @p_349))) :rule forall_inst :args ((:= veriT_vr2 @p_6) (:= veriT_vr3 f$))) +(step t105 (cl (! (not @p_337) :named @p_340) @p_338 @p_331) :rule equiv_pos2) +(step t106 (cl @p_339 @p_337) :rule or :premises (t101)) +(step t107 (cl @p_340 @p_338) :rule resolution :premises (t105 a25)) +(step t108 (cl @p_337) :rule resolution :premises (t106 t63)) +(step t109 (cl @p_338) :rule resolution :premises (t107 t108)) +(step t110 (cl (! (not @p_341) :named @p_343) (not @p_332) @p_334) :rule implies_pos) +(step t111 (cl @p_342 @p_341) :rule or :premises (t102)) +(step t112 (cl @p_343 @p_334) :rule resolution :premises (t110 a24)) +(step t113 (cl @p_341) :rule resolution :premises (t111 t42)) +(step t114 (cl @p_334) :rule resolution :premises (t112 t113)) +(step t115 (cl @p_344 @p_345) :rule or :premises (t103)) +(step t116 (cl @p_345) :rule resolution :premises (t115 t36)) +(step t117 (cl @p_346 (! (not @p_334) :named @p_348) (! (not @p_338) :named @p_347)) :rule and_neg) +(step t118 (cl (not @p_347) @p_335) :rule not_not) +(step t119 (cl @p_346 @p_348 @p_335) :rule th_resolution :premises (t118 t117)) +(step t120 (cl (! (not @p_349) :named @p_352) (not @p_346) @p_350) :rule implies_pos) +(step t121 (cl @p_351 @p_349) :rule or :premises (t104)) +(step t122 (cl @p_346) :rule resolution :premises (t119 t109 t114)) +(step t123 (cl @p_352 @p_350) :rule resolution :premises (t120 t122)) +(step t124 (cl @p_349) :rule resolution :premises (t121 t21)) +(step t125 (cl @p_350) :rule resolution :premises (t123 t124)) +(step t126 (cl (or (! (not @p_270) :named @p_410) (! (=> (! (and @p_353 (! (= @p_354 (! (fun_app$ f$ @p_336) :named @p_406)) :named @p_408) @p_350 (! (member$ @p_333 @p_6) :named @p_405)) :named @p_407) @p_355) :named @p_409))) :rule forall_inst :args ((:= veriT_vr126 f$) (:= veriT_vr127 @p_6) (:= veriT_vr128 @p_336) (:= veriT_vr129 @p_333))) +(step t127 (cl (or (! (not @p_170) :named @p_401) (! (not (! (and @p_350 (! (forall ((veriT_vr65 A$)) (! (not (! (and (! (= @p_336 (! (fun_app$b g$ veriT_vr65) :named @p_359)) :named @p_361) (! (member$a veriT_vr65 b$) :named @p_364)) :named @p_366)) :named @p_368)) :named @p_358)) :named @p_370)) :named @p_356))) :rule forall_inst :args ((:= veriT_vr62 @p_336) (:= veriT_vr63 g$) (:= veriT_vr64 b$))) +(anchor :step t128) +(assume t128.h1 @p_356) +(anchor :step t128.t2 :args ((:= (veriT_vr65 A$) veriT_vr144))) +(step t128.t2.t1 (cl (! (= veriT_vr65 veriT_vr144) :named @p_363)) :rule refl) +(step t128.t2.t2 (cl (= @p_359 (! (fun_app$b g$ veriT_vr144) :named @p_360))) :rule cong :premises (t128.t2.t1)) +(step t128.t2.t3 (cl (= @p_361 (! (= @p_336 @p_360) :named @p_362))) :rule cong :premises (t128.t2.t2)) +(step t128.t2.t4 (cl @p_363) :rule refl) +(step t128.t2.t5 (cl (= @p_364 (! (member$a veriT_vr144 b$) :named @p_365))) :rule cong :premises (t128.t2.t4)) +(step t128.t2.t6 (cl (= @p_366 (! (and @p_362 @p_365) :named @p_367))) :rule cong :premises (t128.t2.t3 t128.t2.t5)) +(step t128.t2.t7 (cl (= @p_368 (! (not @p_367) :named @p_369))) :rule cong :premises (t128.t2.t6)) +(step t128.t2 (cl (= @p_358 (! (forall ((veriT_vr144 A$)) @p_369) :named @p_371))) :rule bind) +(step t128.t3 (cl (= @p_370 (! (and @p_350 @p_371) :named @p_372))) :rule cong :premises (t128.t2)) +(step t128.t4 (cl (! (= @p_356 (! (not @p_372) :named @p_375)) :named @p_373)) :rule cong :premises (t128.t3)) +(step t128.t5 (cl (! (not @p_373) :named @p_376) (! (not @p_356) :named @p_374) @p_375) :rule equiv_pos2) +(step t128.t6 (cl (! (not @p_374) :named @p_400) @p_370) :rule not_not) +(step t128.t7 (cl @p_376 @p_370 @p_375) :rule th_resolution :premises (t128.t6 t128.t5)) +(step t128.t8 (cl @p_375) :rule th_resolution :premises (t128.h1 t128.t4 t128.t7)) +(anchor :step t128.t9 :args ((:= (veriT_vr144 A$) veriT_vr145))) +(step t128.t9.t1 (cl (! (= veriT_vr144 veriT_vr145) :named @p_380)) :rule refl) +(step t128.t9.t2 (cl (= @p_360 @p_378)) :rule cong :premises (t128.t9.t1)) +(step t128.t9.t3 (cl (= @p_362 @p_379)) :rule cong :premises (t128.t9.t2)) +(step t128.t9.t4 (cl @p_380) :rule refl) +(step t128.t9.t5 (cl (= @p_365 @p_381)) :rule cong :premises (t128.t9.t4)) +(step t128.t9.t6 (cl (= @p_367 @p_382)) :rule cong :premises (t128.t9.t3 t128.t9.t5)) +(step t128.t9.t7 (cl (= @p_369 @p_377)) :rule cong :premises (t128.t9.t6)) +(step t128.t9 (cl (= @p_371 (! (forall ((veriT_vr145 A$)) @p_377) :named @p_383))) :rule bind) +(step t128.t10 (cl (= @p_372 (! (and @p_350 @p_383) :named @p_384))) :rule cong :premises (t128.t9)) +(step t128.t11 (cl (! (= @p_375 (! (not @p_384) :named @p_386)) :named @p_385)) :rule cong :premises (t128.t10)) +(step t128.t12 (cl (! (not @p_385) :named @p_388) (! (not @p_375) :named @p_387) @p_386) :rule equiv_pos2) +(step t128.t13 (cl (not @p_387) @p_372) :rule not_not) +(step t128.t14 (cl @p_388 @p_372 @p_386) :rule th_resolution :premises (t128.t13 t128.t12)) +(step t128.t15 (cl @p_386) :rule th_resolution :premises (t128.t8 t128.t11 t128.t14)) +(anchor :step t128.t16 :args ((:= (veriT_vr145 A$) veriT_sk0))) +(step t128.t16.t1 (cl (! (= veriT_vr145 veriT_sk0) :named @p_392)) :rule refl) +(step t128.t16.t2 (cl (= @p_378 (! (fun_app$b g$ veriT_sk0) :named @p_390))) :rule cong :premises (t128.t16.t1)) +(step t128.t16.t3 (cl (= @p_379 (! (= @p_336 @p_390) :named @p_391))) :rule cong :premises (t128.t16.t2)) +(step t128.t16.t4 (cl @p_392) :rule refl) +(step t128.t16.t5 (cl (= @p_381 (! (member$a veriT_sk0 b$) :named @p_393))) :rule cong :premises (t128.t16.t4)) +(step t128.t16.t6 (cl (= @p_382 (! (and @p_391 @p_393) :named @p_394))) :rule cong :premises (t128.t16.t3 t128.t16.t5)) +(step t128.t16.t7 (cl (= @p_377 (! (not @p_394) :named @p_389))) :rule cong :premises (t128.t16.t6)) +(step t128.t16 (cl (= @p_383 @p_389)) :rule sko_forall) +(step t128.t17 (cl (= @p_384 (! (and @p_350 @p_389) :named @p_395))) :rule cong :premises (t128.t16)) +(step t128.t18 (cl (! (= @p_386 (! (not @p_395) :named @p_396)) :named @p_397)) :rule cong :premises (t128.t17)) +(step t128.t19 (cl (! (not @p_397) :named @p_399) (! (not @p_386) :named @p_398) @p_396) :rule equiv_pos2) +(step t128.t20 (cl (not @p_398) @p_384) :rule not_not) +(step t128.t21 (cl @p_399 @p_384 @p_396) :rule th_resolution :premises (t128.t20 t128.t19)) +(step t128.t22 (cl @p_396) :rule th_resolution :premises (t128.t15 t128.t18 t128.t21)) +(step t128 (cl @p_374 @p_396) :rule subproof :discharge (h1)) +(step t129 (cl @p_400 @p_370) :rule not_not) +(step t130 (cl @p_370 @p_396) :rule th_resolution :premises (t129 t128)) +(step t131 (cl @p_401 @p_356) :rule or :premises (t127)) +(step t132 (cl (! (or @p_401 @p_396) :named @p_403) (! (not @p_401) :named @p_402)) :rule or_neg) +(step t133 (cl (not @p_402) @p_170) :rule not_not) +(step t134 (cl @p_403 @p_170) :rule th_resolution :premises (t133 t132)) +(step t135 (cl @p_403 (! (not @p_396) :named @p_404)) :rule or_neg) +(step t136 (cl (not @p_404) @p_395) :rule not_not) +(step t137 (cl @p_403 @p_395) :rule th_resolution :premises (t136 t135)) +(step t138 (cl @p_403) :rule th_resolution :premises (t131 t130 t134 t137)) +(step t139 (cl (or (! (not @p_76) :named @p_420) (! (=> (! (and @p_334 @p_338 @p_405) :named @p_417) (! (less_eq$ @p_406 @p_354) :named @p_419)) :named @p_418))) :rule forall_inst :args ((:= veriT_vr11 @p_6) (:= veriT_vr12 @p_333) (:= veriT_vr13 f$))) +(step t140 (cl @p_407 (not @p_353) (! (not @p_408) :named @p_411) (! (not @p_350) :named @p_415) (! (not @p_405) :named @p_412)) :rule and_neg) +(step t141 (cl (! (not @p_409) :named @p_413) (! (not @p_407) :named @p_414) @p_355) :rule implies_pos) +(step t142 (cl @p_410 @p_409) :rule or :premises (t126)) +(step t143 (cl @p_407 @p_411 @p_412) :rule resolution :premises (t140 a23 t125)) +(step t144 (cl @p_413 @p_414) :rule resolution :premises (t141 a52)) +(step t145 (cl @p_409) :rule resolution :premises (t142 t72)) +(step t146 (cl @p_414) :rule resolution :premises (t144 t145)) +(step t147 (cl @p_389 @p_391) :rule and_pos) +(step t148 (cl @p_389 @p_393) :rule and_pos) +(step t149 (cl @p_395 @p_415 (! (not @p_389) :named @p_416)) :rule and_neg) +(step t150 (cl (not @p_416) @p_394) :rule not_not) +(step t151 (cl @p_395 @p_415 @p_394) :rule th_resolution :premises (t150 t149)) +(step t152 (cl @p_401 @p_396) :rule or :premises (t138)) +(step t153 (cl @p_395 @p_394) :rule resolution :premises (t151 t125)) +(step t154 (cl @p_396) :rule resolution :premises (t152 t51)) +(step t155 (cl @p_394) :rule resolution :premises (t153 t154)) +(step t156 (cl @p_391) :rule resolution :premises (t147 t155)) +(step t157 (cl @p_393) :rule resolution :premises (t148 t155)) +(step t158 (cl @p_417 @p_348 @p_347 @p_412) :rule and_neg) +(step t159 (cl @p_417 @p_348 @p_335 @p_412) :rule th_resolution :premises (t118 t158)) +(step t160 (cl (not @p_418) (not @p_417) @p_419) :rule implies_pos) +(step t161 (cl @p_420 @p_418) :rule or :premises (t139)) +(step t162 (cl @p_417 @p_412) :rule resolution :premises (t159 t109 t114)) +(step t163 (cl @p_418) :rule resolution :premises (t161 t30)) +(step t164 (cl @p_421 @p_422) :rule or :premises (t100)) +(step t165 (cl (or (! (not @p_422) :named @p_424) (! (or (! (not (! (= @p_333 @p_333) :named @p_430)) :named @p_431) (! (not @p_423) :named @p_429) @p_405) :named @p_425))) :rule forall_inst :args ((:= veriT_vr94 @p_333) (:= veriT_vr95 g$) (:= veriT_vr96 @p_5) (:= veriT_vr97 b$))) +(step t166 (cl @p_424 @p_425) :rule or :premises (t165)) +(step t167 (cl (! (or @p_421 @p_425) :named @p_427) (! (not @p_421) :named @p_426)) :rule or_neg) +(step t168 (cl (not @p_426) @p_203) :rule not_not) +(step t169 (cl @p_427 @p_203) :rule th_resolution :premises (t168 t167)) +(step t170 (cl @p_427 (! (not @p_425) :named @p_428)) :rule or_neg) +(step t171 (cl @p_427) :rule th_resolution :premises (t164 t166 t169 t170)) +(anchor :step t172) +(assume t172.h1 @p_425) +(step t172.t2 (cl (= @p_430 true)) :rule eq_simplify) +(step t172.t3 (cl (= @p_431 (! (not true) :named @p_432))) :rule cong :premises (t172.t2)) +(step t172.t4 (cl (= @p_432 false)) :rule not_simplify) +(step t172.t5 (cl (= @p_431 false)) :rule trans :premises (t172.t3 t172.t4)) +(step t172.t6 (cl (= @p_425 (! (or false @p_429 @p_405) :named @p_433))) :rule cong :premises (t172.t5)) +(step t172.t7 (cl (= @p_433 (! (or @p_429 @p_405) :named @p_434))) :rule or_simplify) +(step t172.t8 (cl (! (= @p_425 @p_434) :named @p_435)) :rule trans :premises (t172.t6 t172.t7)) +(step t172.t9 (cl (not @p_435) @p_428 @p_434) :rule equiv_pos2) +(step t172.t10 (cl @p_434) :rule th_resolution :premises (t172.h1 t172.t8 t172.t9)) +(step t172 (cl @p_428 @p_434) :rule subproof :discharge (h1)) +(step t173 (cl @p_421 @p_425) :rule or :premises (t171)) +(step t174 (cl (! (or @p_421 @p_434) :named @p_436) @p_426) :rule or_neg) +(step t175 (cl @p_436 @p_203) :rule th_resolution :premises (t168 t174)) +(step t176 (cl @p_436 (! (not @p_434) :named @p_437)) :rule or_neg) +(step t177 (cl @p_436) :rule th_resolution :premises (t173 t172 t175 t176)) +(step t178 (cl @p_437 @p_429 @p_405) :rule or_pos) +(step t179 (cl @p_421 @p_434) :rule or :premises (t177)) +(step t180 (cl @p_437 @p_405) :rule resolution :premises (t178 a26)) +(step t181 (cl @p_434) :rule resolution :premises (t179 t57)) +(step t182 (cl @p_405) :rule resolution :premises (t180 t181)) +(step t183 (cl @p_411) :rule resolution :premises (t143 t182 t146)) +(step t184 (cl @p_417) :rule resolution :premises (t162 t182)) +(step t185 (cl @p_419) :rule resolution :premises (t160 t184 t163)) +(step t186 (cl (or @p_325 (! (not (! (and @p_393 (! (less$ (! (fun_app$a @p_4 veriT_sk0) :named @p_438) @p_299) :named @p_440)) :named @p_439)) :named @p_441))) :rule forall_inst :args ((:= veriT_vr135 veriT_sk0))) +(step t187 (cl (or (! (not @p_297) :named @p_448) (! (= (! (less$ @p_406 @p_354) :named @p_447) (! (and @p_419 @p_411) :named @p_443)) :named @p_446))) :rule forall_inst :args ((:= veriT_vr132 @p_406) (:= veriT_vr133 @p_354))) +(step t188 (cl (or @p_344 (! (= @p_438 (! (fun_app$ f$ @p_390) :named @p_451)) :named @p_450))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 veriT_sk0))) +(step t189 (cl @p_439 (not @p_393) (! (not @p_440) :named @p_442)) :rule and_neg) +(step t190 (cl @p_325 @p_441) :rule or :premises (t186)) +(step t191 (cl @p_439 @p_442) :rule resolution :premises (t189 t157)) +(step t192 (cl @p_441) :rule resolution :premises (t190 t99)) +(step t193 (cl @p_442) :rule resolution :premises (t191 t192)) +(step t194 (cl @p_443 (! (not @p_419) :named @p_445) (! (not @p_411) :named @p_444)) :rule and_neg) +(step t195 (cl (not @p_444) @p_408) :rule not_not) +(step t196 (cl @p_443 @p_445 @p_408) :rule th_resolution :premises (t195 t194)) +(step t197 (cl (! (not @p_446) :named @p_449) @p_447 (not @p_443)) :rule equiv_pos1) +(step t198 (cl @p_448 @p_446) :rule or :premises (t187)) +(step t199 (cl @p_443) :rule resolution :premises (t196 t183 t185)) +(step t200 (cl @p_449 @p_447) :rule resolution :premises (t197 t199)) +(step t201 (cl @p_446) :rule resolution :premises (t198 t78)) +(step t202 (cl @p_447) :rule resolution :premises (t200 t201)) +(step t203 (cl @p_344 @p_450) :rule or :premises (t188)) +(step t204 (cl @p_450) :rule resolution :premises (t203 t36)) +(step t205 (cl (not (! (= @p_406 @p_438) :named @p_452)) (! (not @p_345) :named @p_457) (! (not @p_447) :named @p_458) @p_440) :rule eq_congruent_pred) +(step t206 (cl (not (! (= @p_406 @p_451) :named @p_453)) (! (not @p_450) :named @p_456) @p_452) :rule eq_transitive) +(step t207 (cl (not (! (= f$ f$) :named @p_454)) (! (not @p_391) :named @p_455) @p_453) :rule eq_congruent) +(step t208 (cl @p_454) :rule eq_reflexive) +(step t209 (cl @p_455 @p_453) :rule th_resolution :premises (t207 t208)) +(step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209)) +(step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210)) +(step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204)) 268d7e42d22bc05b4bcc195eddbced079a39fedf 791 0 unsat (assume a0 (! (forall ((?v0 Real)) (! (= (! (fun_app$ 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)) @@ -6867,574 +7435,6 @@ (step t332 (cl @p_568 @p_563 @p_564 @p_555 @p_556 @p_557 @p_527) :rule contraction :premises (t331)) (step t333 (cl @p_561 @p_403 @p_288 @p_568 @p_563 @p_555 @p_556 @p_557 @p_527) :rule th_resolution :premises (t325 t332)) (step t334 (cl) :rule resolution :premises (t333 t81 t217 t221 t277 t270 t286 t295 t300 t316)) -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)) -(assume a31 (! (forall ((?v0 B_set$) (?v1 B$) (?v2 B_c_fun$)) (! (=> (! (and @p_1 (! (and @p_2 (! (member$ ?v1 ?v0) :named @p_38)) :named @p_40)) :named @p_42) (! (less_eq$ (! (fun_app$ ?v2 (! (arg_min_on$ ?v2 ?v0) :named @p_45)) :named @p_47) (! (fun_app$ ?v2 ?v1) :named @p_50)) :named @p_52)) :named @p_54)) :named @p_33)) -(assume a33 (! (forall ((?v0 B_c_fun$) (?v1 A_b_fun$) (?v2 A$)) (! (= (! (fun_app$a (! (comp$ ?v0 ?v1) :named @p_78) ?v2) :named @p_80) (! (fun_app$ ?v0 (! (fun_app$b ?v1 ?v2) :named @p_3)) :named @p_86)) :named @p_88)) :named @p_77)) -(assume a36 (! (forall ((?v0 A_set$) (?v1 A_b_fun$)) (! (=> (! (finite$a ?v0) :named @p_103) (! (finite$ (! (image$b ?v1 ?v0) :named @p_106)) :named @p_108)) :named @p_110)) :named @p_102)) -(assume a40 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A_set$)) (! (=> (! (and (! (member$ ?v0 (! (image$b ?v1 ?v2) :named @p_122)) :named @p_124) (! (forall ((?v3 A$)) (! (=> (! (and (! (= ?v0 (! (fun_app$b ?v1 ?v3) :named @p_130)) :named @p_132) (! (member$a ?v3 ?v2) :named @p_136)) :named @p_138) false) :named @p_140)) :named @p_126)) :named @p_142) false) :named @p_144)) :named @p_121)) -(assume a44 (! (forall ((?v0 B$) (?v1 A_b_fun$) (?v2 A$) (?v3 A_set$)) (! (=> (! (and (! (= @p_3 ?v0) :named @p_173) (! (member$a ?v2 ?v3) :named @p_176)) :named @p_178) (! (member$ ?v0 (! (image$b ?v1 ?v3) :named @p_183)) :named @p_185)) :named @p_187)) :named @p_171)) -(assume a48 (! (forall ((?v0 A_b_fun$) (?v1 A_set$)) (! (= (! (= bot$ (! (image$b ?v0 ?v1) :named @p_205)) :named @p_207) (! (= bot$a ?v1) :named @p_210)) :named @p_212)) :named @p_204)) -(assume a50 (! (forall ((?v0 B_c_fun$) (?v1 B_set$) (?v2 B$) (?v3 B$)) (! (=> (! (and (! (inj_on$ ?v0 ?v1) :named @p_224) (! (and (! (= (! (fun_app$ ?v0 ?v2) :named @p_227) (! (fun_app$ ?v0 ?v3) :named @p_229)) :named @p_231) (! (and (! (member$ ?v2 ?v1) :named @p_235) (! (member$ ?v3 ?v1) :named @p_238)) :named @p_240)) :named @p_242)) :named @p_244) (! (= ?v3 ?v2) :named @p_246)) :named @p_248)) :named @p_223)) -(assume a51 (! (forall ((?v0 C$) (?v1 C$)) (! (= (! (less$ ?v0 ?v1) :named @p_272) (! (and (! (less_eq$ ?v0 ?v1) :named @p_276) (! (not (! (= ?v0 ?v1) :named @p_278)) :named @p_280)) :named @p_282)) :named @p_284)) :named @p_271)) -(assume a23 (! (inj_on$ f$ @p_6) :named @p_353)) -(assume a24 (! (finite$a b$) :named @p_332)) -(assume a25 (not (! (= bot$a b$) :named @p_331))) -(assume a26 (! (member$a (! (arg_min_on$a (! (comp$ f$ g$) :named @p_4) b$) :named @p_5) b$) :named @p_423)) -(assume a27 (! (not (! (exists ((?v0 A$)) (! (and (! (member$a ?v0 b$) :named @p_300) (! (less$ (! (fun_app$a @p_4 ?v0) :named @p_303) (! (fun_app$a @p_4 @p_5) :named @p_299)) :named @p_305)) :named @p_307)) :named @p_298)) :named @p_309)) -(assume a52 (not (! (= @p_336 (! (fun_app$b g$ @p_5) :named @p_333)) :named @p_355))) -(anchor :step t16 :args ((:= (?v0 B_set$) veriT_vr0) (:= (?v1 B_c_fun$) veriT_vr1))) -(step t16.t1 (cl (! (= ?v0 veriT_vr0) :named @p_9)) :rule refl) -(step t16.t2 (cl (= @p_1 (! (finite$ veriT_vr0) :named @p_8))) :rule cong :premises (t16.t1)) -(step t16.t3 (cl @p_9) :rule refl) -(step t16.t4 (cl (= @p_10 (! (= bot$ veriT_vr0) :named @p_11))) :rule cong :premises (t16.t3)) -(step t16.t5 (cl (= @p_2 (! (not @p_11) :named @p_12))) :rule cong :premises (t16.t4)) -(step t16.t6 (cl (= @p_13 (! (and @p_8 @p_12) :named @p_14))) :rule cong :premises (t16.t2 t16.t5)) -(step t16.t7 (cl (= ?v1 veriT_vr1)) :rule refl) -(step t16.t8 (cl @p_9) :rule refl) -(step t16.t9 (cl (= @p_15 (! (arg_min_on$ veriT_vr1 veriT_vr0) :named @p_16))) :rule cong :premises (t16.t7 t16.t8)) -(step t16.t10 (cl @p_9) :rule refl) -(step t16.t11 (cl (= @p_17 (! 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(fun_app$b veriT_vr91 veriT_vr92) :named @p_172))) :rule cong :premises (t52.t1 t52.t2)) -(step t52.t4 (cl (! (= ?v0 veriT_vr90) :named @p_180)) :rule refl) -(step t52.t5 (cl (= @p_173 (! (= veriT_vr90 @p_172) :named @p_174))) :rule cong :premises (t52.t3 t52.t4)) -(step t52.t6 (cl @p_175) :rule refl) -(step t52.t7 (cl (! (= ?v3 veriT_vr93) :named @p_182)) :rule refl) -(step t52.t8 (cl (= @p_176 (! (member$a veriT_vr92 veriT_vr93) :named @p_177))) :rule cong :premises (t52.t6 t52.t7)) -(step t52.t9 (cl (= @p_178 (! (and @p_174 @p_177) :named @p_179))) :rule cong :premises (t52.t5 t52.t8)) -(step t52.t10 (cl @p_180) :rule refl) -(step t52.t11 (cl @p_181) :rule refl) -(step t52.t12 (cl @p_182) :rule refl) -(step t52.t13 (cl (= @p_183 (! (image$b veriT_vr91 veriT_vr93) :named @p_184))) :rule cong :premises (t52.t11 t52.t12)) -(step t52.t14 (cl (= @p_185 (! (member$ veriT_vr90 @p_184) :named @p_186))) :rule cong :premises (t52.t10 t52.t13)) -(step t52.t15 (cl (= @p_187 (! (=> @p_179 @p_186) :named @p_188))) :rule cong :premises (t52.t9 t52.t14)) -(step t52 (cl (! (= @p_171 (! (forall ((veriT_vr90 B$) (veriT_vr91 A_b_fun$) (veriT_vr92 A$) (veriT_vr93 A_set$)) @p_188) :named @p_190)) :named @p_189)) :rule bind) -(step t53 (cl (not @p_189) (not @p_171) @p_190) :rule equiv_pos2) -(step t54 (cl @p_190) :rule th_resolution :premises (a44 t52 t53)) -(anchor :step t55 :args ((:= (veriT_vr90 B$) veriT_vr94) (:= (veriT_vr91 A_b_fun$) veriT_vr95) (:= (veriT_vr92 A$) veriT_vr96) (:= (veriT_vr93 A_set$) veriT_vr97))) -(step t55.t1 (cl (! (= veriT_vr90 veriT_vr94) :named @p_196)) :rule refl) -(step t55.t2 (cl (! (= veriT_vr91 veriT_vr95) :named @p_197)) :rule refl) -(step t55.t3 (cl (! (= veriT_vr92 veriT_vr96) :named @p_193)) :rule refl) -(step t55.t4 (cl (= @p_172 (! (fun_app$b veriT_vr95 veriT_vr96) :named @p_191))) :rule cong :premises (t55.t2 t55.t3)) -(step t55.t5 (cl (= @p_174 (! (= veriT_vr94 @p_191) :named @p_192))) :rule cong :premises (t55.t1 t55.t4)) -(step t55.t6 (cl @p_193) :rule refl) -(step t55.t7 (cl (! (= veriT_vr93 veriT_vr97) :named @p_198)) :rule refl) -(step t55.t8 (cl (= @p_177 (! (member$a veriT_vr96 veriT_vr97) :named @p_194))) :rule cong :premises (t55.t6 t55.t7)) -(step t55.t9 (cl (= @p_179 (! (and @p_192 @p_194) :named @p_195))) :rule cong :premises (t55.t5 t55.t8)) -(step t55.t10 (cl @p_196) :rule refl) -(step t55.t11 (cl @p_197) :rule refl) -(step t55.t12 (cl @p_198) :rule refl) -(step t55.t13 (cl (= @p_184 (! (image$b veriT_vr95 veriT_vr97) :named @p_199))) :rule cong :premises (t55.t11 t55.t12)) -(step t55.t14 (cl (= @p_186 (! (member$ veriT_vr94 @p_199) :named @p_200))) :rule cong :premises (t55.t10 t55.t13)) -(step t55.t15 (cl (= @p_188 (! (=> @p_195 @p_200) :named @p_201))) :rule cong :premises (t55.t9 t55.t14)) -(step t55 (cl (! (= @p_190 (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) @p_201) :named @p_203)) :named @p_202)) :rule bind) -(step t56 (cl (not @p_202) (not @p_190) @p_203) :rule equiv_pos2) -(step t57 (cl @p_203) :rule th_resolution :premises (t54 t55 t56)) -(anchor :step t58 :args ((:= (?v0 A_b_fun$) veriT_vr114) (:= (?v1 A_set$) veriT_vr115))) -(step t58.t1 (cl (= ?v0 veriT_vr114)) :rule refl) -(step t58.t2 (cl (! (= ?v1 veriT_vr115) :named @p_209)) :rule refl) -(step t58.t3 (cl (= @p_205 (! (image$b veriT_vr114 veriT_vr115) :named @p_206))) :rule cong :premises (t58.t1 t58.t2)) -(step t58.t4 (cl (= @p_207 (! (= bot$ @p_206) :named @p_208))) :rule cong :premises (t58.t3)) -(step t58.t5 (cl @p_209) :rule refl) -(step t58.t6 (cl (= @p_210 (! (= bot$a veriT_vr115) :named @p_211))) :rule cong :premises (t58.t5)) -(step t58.t7 (cl (= @p_212 (! (= @p_208 @p_211) :named @p_213))) :rule cong :premises (t58.t4 t58.t6)) -(step t58 (cl (! (= @p_204 (! (forall ((veriT_vr114 A_b_fun$) (veriT_vr115 A_set$)) @p_213) :named @p_215)) :named @p_214)) :rule bind) -(step t59 (cl (not @p_214) (not @p_204) @p_215) :rule equiv_pos2) -(step t60 (cl @p_215) :rule th_resolution :premises (a48 t58 t59)) -(anchor :step t61 :args ((:= (veriT_vr114 A_b_fun$) veriT_vr116) (:= (veriT_vr115 A_set$) veriT_vr117))) -(step t61.t1 (cl (= veriT_vr114 veriT_vr116)) :rule refl) -(step t61.t2 (cl (! (= veriT_vr115 veriT_vr117) :named @p_218)) :rule refl) -(step t61.t3 (cl (= @p_206 (! (image$b veriT_vr116 veriT_vr117) :named @p_216))) :rule cong :premises (t61.t1 t61.t2)) -(step t61.t4 (cl (= @p_208 (! (= bot$ @p_216) :named @p_217))) :rule cong :premises (t61.t3)) -(step t61.t5 (cl @p_218) :rule refl) -(step t61.t6 (cl (= @p_211 (! (= bot$a veriT_vr117) :named @p_219))) :rule cong :premises (t61.t5)) -(step t61.t7 (cl (= @p_213 (! (= @p_217 @p_219) :named @p_220))) :rule cong :premises (t61.t4 t61.t6)) -(step t61 (cl (! (= @p_215 (! (forall ((veriT_vr116 A_b_fun$) (veriT_vr117 A_set$)) @p_220) :named @p_222)) :named @p_221)) :rule bind) -(step t62 (cl (not @p_221) (not @p_215) @p_222) :rule equiv_pos2) -(step t63 (cl @p_222) :rule th_resolution :premises (t60 t61 t62)) -(anchor :step t64 :args ((:= (?v0 B_c_fun$) veriT_vr122) (:= (?v1 B_set$) veriT_vr123) (:= (?v2 B$) veriT_vr124) (:= (?v3 B$) veriT_vr125))) -(step t64.t1 (cl (! (= ?v0 veriT_vr122) :named @p_226)) :rule refl) -(step t64.t2 (cl (! (= ?v1 veriT_vr123) :named @p_234)) :rule refl) -(step t64.t3 (cl (= @p_224 (! (inj_on$ veriT_vr122 veriT_vr123) :named @p_225))) :rule cong :premises (t64.t1 t64.t2)) -(step t64.t4 (cl @p_226) :rule refl) -(step t64.t5 (cl (! (= ?v2 veriT_vr124) :named @p_233)) :rule refl) -(step t64.t6 (cl (= @p_227 (! (fun_app$ veriT_vr122 veriT_vr124) :named @p_228))) :rule cong :premises (t64.t4 t64.t5)) -(step t64.t7 (cl @p_226) :rule refl) -(step t64.t8 (cl (! 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(forall ((veriT_vr130 C$) (veriT_vr131 C$)) @p_285) :named @p_287)) :named @p_286)) :rule bind) -(step t74 (cl (not @p_286) (not @p_271) @p_287) :rule equiv_pos2) -(step t75 (cl @p_287) :rule th_resolution :premises (a51 t73 t74)) -(anchor :step t76 :args ((:= (veriT_vr130 C$) veriT_vr132) (:= (veriT_vr131 C$) veriT_vr133))) -(step t76.t1 (cl (! (= veriT_vr130 veriT_vr132) :named @p_289)) :rule refl) -(step t76.t2 (cl (! (= veriT_vr131 veriT_vr133) :named @p_290)) :rule refl) -(step t76.t3 (cl (= @p_273 (! (less$ veriT_vr132 veriT_vr133) :named @p_288))) :rule cong :premises (t76.t1 t76.t2)) -(step t76.t4 (cl @p_289) :rule refl) -(step t76.t5 (cl @p_290) :rule refl) -(step t76.t6 (cl (= @p_277 (! (less_eq$ veriT_vr132 veriT_vr133) :named @p_291))) :rule cong :premises (t76.t4 t76.t5)) -(step t76.t7 (cl @p_289) :rule refl) -(step t76.t8 (cl @p_290) :rule refl) -(step t76.t9 (cl (= @p_279 (! (= veriT_vr132 veriT_vr133) :named @p_292))) :rule cong :premises (t76.t7 t76.t8)) -(step t76.t10 (cl (= @p_281 (! (not @p_292) :named @p_293))) :rule cong :premises (t76.t9)) -(step t76.t11 (cl (= @p_283 (! (and @p_291 @p_293) :named @p_294))) :rule cong :premises (t76.t6 t76.t10)) -(step t76.t12 (cl (= @p_285 (! (= @p_288 @p_294) :named @p_295))) :rule cong :premises (t76.t3 t76.t11)) -(step t76 (cl (! (= @p_287 (! (forall ((veriT_vr132 C$) (veriT_vr133 C$)) @p_295) :named @p_297)) :named @p_296)) :rule bind) -(step t77 (cl (not @p_296) (not @p_287) @p_297) :rule equiv_pos2) -(step t78 (cl @p_297) :rule th_resolution :premises (t75 t76 t77)) -(anchor :step t79 :args ((:= (?v0 A$) veriT_vr134))) -(step t79.t1 (cl (! (= ?v0 veriT_vr134) :named @p_302)) :rule refl) -(step t79.t2 (cl (= @p_300 (! (member$a veriT_vr134 b$) :named @p_301))) :rule cong :premises (t79.t1)) -(step t79.t3 (cl @p_302) :rule refl) -(step t79.t4 (cl (= @p_303 (! (fun_app$a @p_4 veriT_vr134) :named @p_304))) :rule cong :premises (t79.t3)) -(step t79.t5 (cl (= @p_305 (! (less$ @p_304 @p_299) :named @p_306))) :rule cong :premises (t79.t4)) -(step t79.t6 (cl (= @p_307 (! (and @p_301 @p_306) :named @p_308))) :rule cong :premises (t79.t2 t79.t5)) -(step t79 (cl (= @p_298 (! (exists ((veriT_vr134 A$)) @p_308) :named @p_310))) :rule bind) -(step t80 (cl (! (= @p_309 (! (not @p_310) :named @p_312)) :named @p_311)) :rule cong :premises (t79)) -(step t81 (cl (! (not @p_311) :named @p_314) (! (not @p_309) :named @p_313) @p_312) :rule equiv_pos2) -(step t82 (cl (not @p_313) @p_298) :rule not_not) -(step t83 (cl @p_314 @p_298 @p_312) :rule th_resolution :premises (t82 t81)) -(step t84 (cl @p_312) :rule th_resolution :premises (a27 t80 t83)) -(anchor :step t85 :args ((:= (veriT_vr134 A$) veriT_vr135))) -(step t85.t1 (cl (! (= veriT_vr134 veriT_vr135) :named @p_316)) :rule refl) -(step t85.t2 (cl (= @p_301 (! (member$a veriT_vr135 b$) :named @p_315))) :rule cong :premises (t85.t1)) -(step t85.t3 (cl @p_316) :rule refl) -(step t85.t4 (cl (= @p_304 (! (fun_app$a @p_4 veriT_vr135) :named @p_317))) :rule cong :premises (t85.t3)) -(step t85.t5 (cl (= @p_306 (! (less$ @p_317 @p_299) :named @p_318))) :rule cong :premises (t85.t4)) -(step t85.t6 (cl (= @p_308 (! (and @p_315 @p_318) :named @p_319))) :rule cong :premises (t85.t2 t85.t5)) -(step t85 (cl (= @p_310 (! (exists ((veriT_vr135 A$)) @p_319) :named @p_320))) :rule bind) -(step t86 (cl (! (= @p_312 (! (not @p_320) :named @p_322)) :named @p_321)) :rule cong :premises (t85)) -(step t87 (cl (! (not @p_321) :named @p_324) (! (not @p_312) :named @p_323) @p_322) :rule equiv_pos2) -(step t88 (cl (not @p_323) @p_310) :rule not_not) -(step t89 (cl @p_324 @p_310 @p_322) :rule th_resolution :premises (t88 t87)) -(step t90 (cl @p_322) :rule th_resolution :premises (t84 t86 t89)) -(step t91 (cl (= @p_320 (! (not (! (forall ((veriT_vr135 A$)) (not @p_319)) :named @p_330)) :named @p_325))) :rule connective_def) -(step t92 (cl (! (= @p_322 (! (not @p_325) :named @p_327)) :named @p_326)) :rule cong :premises (t91)) -(step t93 (cl (! (not @p_326) :named @p_329) (! (not @p_322) :named @p_328) @p_327) :rule equiv_pos2) -(step t94 (cl (not @p_328) @p_320) :rule not_not) -(step t95 (cl @p_329 @p_320 @p_327) :rule th_resolution :premises (t94 t93)) -(step t96 (cl (not @p_327) @p_330) :rule not_not) -(step t97 (cl @p_329 @p_320 @p_330) :rule th_resolution :premises (t96 t95)) -(step t98 (cl @p_327) :rule th_resolution :premises (t90 t92 t97)) -(step t99 (cl @p_330) :rule th_resolution :premises (t96 t98)) -(step t100 (cl (or (! (not @p_203) :named @p_421) (! (forall ((veriT_vr94 B$) (veriT_vr95 A_b_fun$) (veriT_vr96 A$) (veriT_vr97 A_set$)) (or (not @p_192) (not @p_194) @p_200)) :named @p_422))) :rule qnt_cnf) -(step t101 (cl (or (! (not @p_222) :named @p_339) (! (= (! (= bot$ @p_6) :named @p_335) @p_331) :named @p_337))) :rule forall_inst :args ((:= veriT_vr116 g$) (:= veriT_vr117 b$))) -(step t102 (cl (or (! (not @p_120) :named @p_342) (! (=> @p_332 (! (finite$ @p_6) :named @p_334)) :named @p_341))) :rule forall_inst :args ((:= veriT_vr36 b$) (:= veriT_vr37 g$))) -(step t103 (cl (or (! (not @p_101) :named @p_344) (! (= @p_299 (! (fun_app$ f$ @p_333) :named @p_354)) :named @p_345))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 @p_5))) -(step t104 (cl (or (! (not @p_32) :named @p_351) (! (=> (! (and @p_334 (! (not @p_335) :named @p_338)) :named @p_346) (! (member$ @p_336 @p_6) :named @p_350)) :named @p_349))) :rule forall_inst :args ((:= veriT_vr2 @p_6) (:= veriT_vr3 f$))) -(step t105 (cl (! (not @p_337) :named @p_340) @p_338 @p_331) :rule equiv_pos2) -(step t106 (cl @p_339 @p_337) :rule or :premises (t101)) -(step t107 (cl @p_340 @p_338) :rule resolution :premises (t105 a25)) -(step t108 (cl @p_337) :rule resolution :premises (t106 t63)) -(step t109 (cl @p_338) :rule resolution :premises (t107 t108)) -(step t110 (cl (! (not @p_341) :named @p_343) (not @p_332) @p_334) :rule implies_pos) -(step t111 (cl @p_342 @p_341) :rule or :premises (t102)) -(step t112 (cl @p_343 @p_334) :rule resolution :premises (t110 a24)) -(step t113 (cl @p_341) :rule resolution :premises (t111 t42)) -(step t114 (cl @p_334) :rule resolution :premises (t112 t113)) -(step t115 (cl @p_344 @p_345) :rule or :premises (t103)) -(step t116 (cl @p_345) :rule resolution :premises (t115 t36)) -(step t117 (cl @p_346 (! (not @p_334) :named @p_348) (! (not @p_338) :named @p_347)) :rule and_neg) -(step t118 (cl (not @p_347) @p_335) :rule not_not) -(step t119 (cl @p_346 @p_348 @p_335) :rule th_resolution :premises (t118 t117)) -(step t120 (cl (! (not @p_349) :named @p_352) (not @p_346) @p_350) :rule implies_pos) -(step t121 (cl @p_351 @p_349) :rule or :premises (t104)) -(step t122 (cl @p_346) :rule resolution :premises (t119 t109 t114)) -(step t123 (cl @p_352 @p_350) :rule resolution :premises (t120 t122)) -(step t124 (cl @p_349) :rule resolution :premises (t121 t21)) -(step t125 (cl @p_350) :rule resolution :premises (t123 t124)) -(step t126 (cl (or (! (not @p_270) :named @p_410) (! (=> (! (and @p_353 (! (= @p_354 (! (fun_app$ f$ @p_336) :named @p_406)) :named @p_408) @p_350 (! (member$ @p_333 @p_6) :named @p_405)) :named @p_407) @p_355) :named @p_409))) :rule forall_inst :args ((:= veriT_vr126 f$) (:= veriT_vr127 @p_6) (:= veriT_vr128 @p_336) (:= veriT_vr129 @p_333))) -(step t127 (cl (or (! (not @p_170) :named @p_401) (! (not (! (and @p_350 (! (forall ((veriT_vr65 A$)) (! (not (! (and (! (= @p_336 (! (fun_app$b g$ veriT_vr65) :named @p_359)) :named @p_361) (! (member$a veriT_vr65 b$) :named @p_364)) :named @p_366)) :named @p_368)) :named @p_358)) :named @p_370)) :named @p_356))) :rule forall_inst :args ((:= veriT_vr62 @p_336) (:= veriT_vr63 g$) (:= veriT_vr64 b$))) -(anchor :step t128) -(assume t128.h1 @p_356) -(anchor :step t128.t2 :args ((:= (veriT_vr65 A$) veriT_vr144))) -(step t128.t2.t1 (cl (! (= veriT_vr65 veriT_vr144) :named @p_363)) :rule refl) -(step t128.t2.t2 (cl (= @p_359 (! (fun_app$b g$ veriT_vr144) :named @p_360))) :rule cong :premises (t128.t2.t1)) -(step t128.t2.t3 (cl (= @p_361 (! (= @p_336 @p_360) :named @p_362))) :rule cong :premises (t128.t2.t2)) -(step t128.t2.t4 (cl @p_363) :rule refl) -(step t128.t2.t5 (cl (= @p_364 (! (member$a veriT_vr144 b$) :named @p_365))) :rule cong :premises (t128.t2.t4)) -(step t128.t2.t6 (cl (= @p_366 (! (and @p_362 @p_365) :named @p_367))) :rule cong :premises (t128.t2.t3 t128.t2.t5)) -(step t128.t2.t7 (cl (= @p_368 (! (not @p_367) :named @p_369))) :rule cong :premises (t128.t2.t6)) -(step t128.t2 (cl (= @p_358 (! (forall ((veriT_vr144 A$)) @p_369) :named @p_371))) :rule bind) -(step t128.t3 (cl (= @p_370 (! (and @p_350 @p_371) :named @p_372))) :rule cong :premises (t128.t2)) -(step t128.t4 (cl (! (= @p_356 (! (not @p_372) :named @p_375)) :named @p_373)) :rule cong :premises (t128.t3)) -(step t128.t5 (cl (! (not @p_373) :named @p_376) (! (not @p_356) :named @p_374) @p_375) :rule equiv_pos2) -(step t128.t6 (cl (! (not @p_374) :named @p_400) @p_370) :rule not_not) -(step t128.t7 (cl @p_376 @p_370 @p_375) :rule th_resolution :premises (t128.t6 t128.t5)) -(step t128.t8 (cl @p_375) :rule th_resolution :premises (t128.h1 t128.t4 t128.t7)) -(anchor :step t128.t9 :args ((:= (veriT_vr144 A$) veriT_vr145))) -(step t128.t9.t1 (cl (! (= veriT_vr144 veriT_vr145) :named @p_380)) :rule refl) -(step t128.t9.t2 (cl (= @p_360 @p_378)) :rule cong :premises (t128.t9.t1)) -(step t128.t9.t3 (cl (= @p_362 @p_379)) :rule cong :premises (t128.t9.t2)) -(step t128.t9.t4 (cl @p_380) :rule refl) -(step t128.t9.t5 (cl (= @p_365 @p_381)) :rule cong :premises (t128.t9.t4)) -(step t128.t9.t6 (cl (= @p_367 @p_382)) :rule cong :premises (t128.t9.t3 t128.t9.t5)) -(step t128.t9.t7 (cl (= @p_369 @p_377)) :rule cong :premises (t128.t9.t6)) -(step t128.t9 (cl (= @p_371 (! (forall ((veriT_vr145 A$)) @p_377) :named @p_383))) :rule bind) -(step t128.t10 (cl (= @p_372 (! (and @p_350 @p_383) :named @p_384))) :rule cong :premises (t128.t9)) -(step t128.t11 (cl (! (= @p_375 (! (not @p_384) :named @p_386)) :named @p_385)) :rule cong :premises (t128.t10)) -(step t128.t12 (cl (! (not @p_385) :named @p_388) (! (not @p_375) :named @p_387) @p_386) :rule equiv_pos2) -(step t128.t13 (cl (not @p_387) @p_372) :rule not_not) -(step t128.t14 (cl @p_388 @p_372 @p_386) :rule th_resolution :premises (t128.t13 t128.t12)) -(step t128.t15 (cl @p_386) :rule th_resolution :premises (t128.t8 t128.t11 t128.t14)) -(anchor :step t128.t16 :args ((:= (veriT_vr145 A$) veriT_sk0))) -(step t128.t16.t1 (cl (! (= veriT_vr145 veriT_sk0) :named @p_392)) :rule refl) -(step t128.t16.t2 (cl (= @p_378 (! (fun_app$b g$ veriT_sk0) :named @p_390))) :rule cong :premises (t128.t16.t1)) -(step t128.t16.t3 (cl (= @p_379 (! (= @p_336 @p_390) :named @p_391))) :rule cong :premises (t128.t16.t2)) -(step t128.t16.t4 (cl @p_392) :rule refl) -(step t128.t16.t5 (cl (= @p_381 (! (member$a veriT_sk0 b$) :named @p_393))) :rule cong :premises (t128.t16.t4)) -(step t128.t16.t6 (cl (= @p_382 (! (and @p_391 @p_393) :named @p_394))) :rule cong :premises (t128.t16.t3 t128.t16.t5)) -(step t128.t16.t7 (cl (= @p_377 (! (not @p_394) :named @p_389))) :rule cong :premises (t128.t16.t6)) -(step t128.t16 (cl (= @p_383 @p_389)) :rule sko_forall) -(step t128.t17 (cl (= @p_384 (! (and @p_350 @p_389) :named @p_395))) :rule cong :premises (t128.t16)) -(step t128.t18 (cl (! (= @p_386 (! (not @p_395) :named @p_396)) :named @p_397)) :rule cong :premises (t128.t17)) -(step t128.t19 (cl (! (not @p_397) :named @p_399) (! (not @p_386) :named @p_398) @p_396) :rule equiv_pos2) -(step t128.t20 (cl (not @p_398) @p_384) :rule not_not) -(step t128.t21 (cl @p_399 @p_384 @p_396) :rule th_resolution :premises (t128.t20 t128.t19)) -(step t128.t22 (cl @p_396) :rule th_resolution :premises (t128.t15 t128.t18 t128.t21)) -(step t128 (cl @p_374 @p_396) :rule subproof :discharge (h1)) -(step t129 (cl @p_400 @p_370) :rule not_not) -(step t130 (cl @p_370 @p_396) :rule th_resolution :premises (t129 t128)) -(step t131 (cl @p_401 @p_356) :rule or :premises (t127)) -(step t132 (cl (! (or @p_401 @p_396) :named @p_403) (! (not @p_401) :named @p_402)) :rule or_neg) -(step t133 (cl (not @p_402) @p_170) :rule not_not) -(step t134 (cl @p_403 @p_170) :rule th_resolution :premises (t133 t132)) -(step t135 (cl @p_403 (! (not @p_396) :named @p_404)) :rule or_neg) -(step t136 (cl (not @p_404) @p_395) :rule not_not) -(step t137 (cl @p_403 @p_395) :rule th_resolution :premises (t136 t135)) -(step t138 (cl @p_403) :rule th_resolution :premises (t131 t130 t134 t137)) -(step t139 (cl (or (! (not @p_76) :named @p_420) (! (=> (! (and @p_334 @p_338 @p_405) :named @p_417) (! (less_eq$ @p_406 @p_354) :named @p_419)) :named @p_418))) :rule forall_inst :args ((:= veriT_vr11 @p_6) (:= veriT_vr12 @p_333) (:= veriT_vr13 f$))) -(step t140 (cl @p_407 (not @p_353) (! (not @p_408) :named @p_411) (! (not @p_350) :named @p_415) (! (not @p_405) :named @p_412)) :rule and_neg) -(step t141 (cl (! (not @p_409) :named @p_413) (! (not @p_407) :named @p_414) @p_355) :rule implies_pos) -(step t142 (cl @p_410 @p_409) :rule or :premises (t126)) -(step t143 (cl @p_407 @p_411 @p_412) :rule resolution :premises (t140 a23 t125)) -(step t144 (cl @p_413 @p_414) :rule resolution :premises (t141 a52)) -(step t145 (cl @p_409) :rule resolution :premises (t142 t72)) -(step t146 (cl @p_414) :rule resolution :premises (t144 t145)) -(step t147 (cl @p_389 @p_391) :rule and_pos) -(step t148 (cl @p_389 @p_393) :rule and_pos) -(step t149 (cl @p_395 @p_415 (! (not @p_389) :named @p_416)) :rule and_neg) -(step t150 (cl (not @p_416) @p_394) :rule not_not) -(step t151 (cl @p_395 @p_415 @p_394) :rule th_resolution :premises (t150 t149)) -(step t152 (cl @p_401 @p_396) :rule or :premises (t138)) -(step t153 (cl @p_395 @p_394) :rule resolution :premises (t151 t125)) -(step t154 (cl @p_396) :rule resolution :premises (t152 t51)) -(step t155 (cl @p_394) :rule resolution :premises (t153 t154)) -(step t156 (cl @p_391) :rule resolution :premises (t147 t155)) -(step t157 (cl @p_393) :rule resolution :premises (t148 t155)) -(step t158 (cl @p_417 @p_348 @p_347 @p_412) :rule and_neg) -(step t159 (cl @p_417 @p_348 @p_335 @p_412) :rule th_resolution :premises (t118 t158)) -(step t160 (cl (not @p_418) (not @p_417) @p_419) :rule implies_pos) -(step t161 (cl @p_420 @p_418) :rule or :premises (t139)) -(step t162 (cl @p_417 @p_412) :rule resolution :premises (t159 t109 t114)) -(step t163 (cl @p_418) :rule resolution :premises (t161 t30)) -(step t164 (cl @p_421 @p_422) :rule or :premises (t100)) -(step t165 (cl (or (! (not @p_422) :named @p_424) (! (or (! (not (! (= @p_333 @p_333) :named @p_430)) :named @p_431) (! (not @p_423) :named @p_429) @p_405) :named @p_425))) :rule forall_inst :args ((:= veriT_vr94 @p_333) (:= veriT_vr95 g$) (:= veriT_vr96 @p_5) (:= veriT_vr97 b$))) -(step t166 (cl @p_424 @p_425) :rule or :premises (t165)) -(step t167 (cl (! (or @p_421 @p_425) :named @p_427) (! (not @p_421) :named @p_426)) :rule or_neg) -(step t168 (cl (not @p_426) @p_203) :rule not_not) -(step t169 (cl @p_427 @p_203) :rule th_resolution :premises (t168 t167)) -(step t170 (cl @p_427 (! (not @p_425) :named @p_428)) :rule or_neg) -(step t171 (cl @p_427) :rule th_resolution :premises (t164 t166 t169 t170)) -(anchor :step t172) -(assume t172.h1 @p_425) -(step t172.t2 (cl (= @p_430 true)) :rule eq_simplify) -(step t172.t3 (cl (= @p_431 (! (not true) :named @p_432))) :rule cong :premises (t172.t2)) -(step t172.t4 (cl (= @p_432 false)) :rule not_simplify) -(step t172.t5 (cl (= @p_431 false)) :rule trans :premises (t172.t3 t172.t4)) -(step t172.t6 (cl (= @p_425 (! (or false @p_429 @p_405) :named @p_433))) :rule cong :premises (t172.t5)) -(step t172.t7 (cl (= @p_433 (! (or @p_429 @p_405) :named @p_434))) :rule or_simplify) -(step t172.t8 (cl (! (= @p_425 @p_434) :named @p_435)) :rule trans :premises (t172.t6 t172.t7)) -(step t172.t9 (cl (not @p_435) @p_428 @p_434) :rule equiv_pos2) -(step t172.t10 (cl @p_434) :rule th_resolution :premises (t172.h1 t172.t8 t172.t9)) -(step t172 (cl @p_428 @p_434) :rule subproof :discharge (h1)) -(step t173 (cl @p_421 @p_425) :rule or :premises (t171)) -(step t174 (cl (! (or @p_421 @p_434) :named @p_436) @p_426) :rule or_neg) -(step t175 (cl @p_436 @p_203) :rule th_resolution :premises (t168 t174)) -(step t176 (cl @p_436 (! (not @p_434) :named @p_437)) :rule or_neg) -(step t177 (cl @p_436) :rule th_resolution :premises (t173 t172 t175 t176)) -(step t178 (cl @p_437 @p_429 @p_405) :rule or_pos) -(step t179 (cl @p_421 @p_434) :rule or :premises (t177)) -(step t180 (cl @p_437 @p_405) :rule resolution :premises (t178 a26)) -(step t181 (cl @p_434) :rule resolution :premises (t179 t57)) -(step t182 (cl @p_405) :rule resolution :premises (t180 t181)) -(step t183 (cl @p_411) :rule resolution :premises (t143 t182 t146)) -(step t184 (cl @p_417) :rule resolution :premises (t162 t182)) -(step t185 (cl @p_419) :rule resolution :premises (t160 t184 t163)) -(step t186 (cl (or @p_325 (! (not (! (and @p_393 (! (less$ (! (fun_app$a @p_4 veriT_sk0) :named @p_438) @p_299) :named @p_440)) :named @p_439)) :named @p_441))) :rule forall_inst :args ((:= veriT_vr135 veriT_sk0))) -(step t187 (cl (or (! (not @p_297) :named @p_448) (! (= (! (less$ @p_406 @p_354) :named @p_447) (! (and @p_419 @p_411) :named @p_443)) :named @p_446))) :rule forall_inst :args ((:= veriT_vr132 @p_406) (:= veriT_vr133 @p_354))) -(step t188 (cl (or @p_344 (! (= @p_438 (! (fun_app$ f$ @p_390) :named @p_451)) :named @p_450))) :rule forall_inst :args ((:= veriT_vr23 f$) (:= veriT_vr24 g$) (:= veriT_vr25 veriT_sk0))) -(step t189 (cl @p_439 (not @p_393) (! (not @p_440) :named @p_442)) :rule and_neg) -(step t190 (cl @p_325 @p_441) :rule or :premises (t186)) -(step t191 (cl @p_439 @p_442) :rule resolution :premises (t189 t157)) -(step t192 (cl @p_441) :rule resolution :premises (t190 t99)) -(step t193 (cl @p_442) :rule resolution :premises (t191 t192)) -(step t194 (cl @p_443 (! (not @p_419) :named @p_445) (! (not @p_411) :named @p_444)) :rule and_neg) -(step t195 (cl (not @p_444) @p_408) :rule not_not) -(step t196 (cl @p_443 @p_445 @p_408) :rule th_resolution :premises (t195 t194)) -(step t197 (cl (! (not @p_446) :named @p_449) @p_447 (not @p_443)) :rule equiv_pos1) -(step t198 (cl @p_448 @p_446) :rule or :premises (t187)) -(step t199 (cl @p_443) :rule resolution :premises (t196 t183 t185)) -(step t200 (cl @p_449 @p_447) :rule resolution :premises (t197 t199)) -(step t201 (cl @p_446) :rule resolution :premises (t198 t78)) -(step t202 (cl @p_447) :rule resolution :premises (t200 t201)) -(step t203 (cl @p_344 @p_450) :rule or :premises (t188)) -(step t204 (cl @p_450) :rule resolution :premises (t203 t36)) -(step t205 (cl (not (! (= @p_406 @p_438) :named @p_452)) (! (not @p_345) :named @p_457) (! (not @p_447) :named @p_458) @p_440) :rule eq_congruent_pred) -(step t206 (cl (not (! (= @p_406 @p_451) :named @p_453)) (! (not @p_450) :named @p_456) @p_452) :rule eq_transitive) -(step t207 (cl (not (! (= f$ f$) :named @p_454)) (! (not @p_391) :named @p_455) @p_453) :rule eq_congruent) -(step t208 (cl @p_454) :rule eq_reflexive) -(step t209 (cl @p_455 @p_453) :rule th_resolution :premises (t207 t208)) -(step t210 (cl @p_456 @p_452 @p_455) :rule th_resolution :premises (t206 t209)) -(step t211 (cl @p_457 @p_458 @p_440 @p_456 @p_455) :rule th_resolution :premises (t205 t210)) -(step t212 (cl) :rule resolution :premises (t211 t116 t156 t193 t202 t204)) ba9da4ba7350e0a8fc453119da89963e8ee28018 323 0 unsat (assume a1 (! (not (! (=> (! (forall ((?v0 Real_a_fun$) (?v1 B_list$)) (! (= (! (=> (! (and (! (= (! (rec_join$ ?v1) :named @p_3) ?v0) :named @p_68) (! (and (! (=> (! (and (! (= ?v1 nil$) :named @p_4) (! (= uu$ ?v0) :named @p_72)) :named @p_74) false) :named @p_76) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 nil$) :named @p_8)) :named @p_5) (! (= ?v0 (! (coeff_cube_to_path$ ?v2) :named @p_1)) :named @p_82)) :named @p_84) false) :named @p_86)) :named @p_78) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= ?v1 (! (cons$ ?v2 (! (cons$ ?v3 ?v4) :named @p_2)) :named @p_9)) :named @p_6) (! (= ?v0 (! (joinpaths$ @p_1 (! (rec_join$ @p_2) :named @p_95)) :named @p_7)) :named @p_97)) :named @p_99) false) :named @p_101)) :named @p_88)) :named @p_103)) :named @p_105)) :named @p_107) false) :named @p_109) (! (=> (! (and (! (= @p_3 @p_3) :named @p_112) (! (and (! (=> (! (and @p_4 (! (= uu$ @p_3) :named @p_115)) :named @p_117) false) :named @p_119) (! (and (! (forall ((?v2 B$)) (! (=> (! (and @p_5 (! (= @p_3 @p_1) :named @p_125)) :named @p_127) false) :named @p_129)) :named @p_121) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and @p_6 (! (= @p_3 @p_7) :named @p_137)) :named @p_139) false) :named @p_141)) :named @p_131)) :named @p_143)) :named @p_145)) :named @p_147) false) :named @p_149)) :named @p_151)) :named @p_53) (! (= (! (forall ((?v0 B_list$) (?v1 Real_a_fun$)) (! (=> (! (and (! (= (! (rec_join$ ?v0) :named @p_10) ?v1) :named @p_19) (! (and (! (=> (! (and (! (= nil$ ?v0) :named @p_11) (! (= uu$ ?v1) :named @p_20)) :named @p_22) false) :named @p_24) (! (and (! (forall ((?v2 B$)) (! (=> (! (and (! (= @p_8 ?v0) :named @p_17) (! (= @p_1 ?v1) :named @p_27)) :named @p_29) false) :named @p_31)) :named @p_25) (! (forall ((?v2 B$) (?v3 B$) (?v4 B_list$)) (! (=> (! (and (! (= @p_9 ?v0) :named @p_18) (! (= @p_7 ?v1) :named @p_35)) :named @p_37) false) :named @p_39)) :named @p_33)) :named @p_41)) :named @p_43)) :named @p_45) false) :named @p_47)) :named @p_14) (! (forall ((?v0 B_list$)) (! (=> (! (and (! (= @p_10 @p_10) :named @p_15) (! (and (! (=> (! (and @p_11 (! (= uu$ @p_10) :named @p_21)) :named @p_23) false) :named @p_16) (! (and (! (forall ((?v1 B$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 nil$) :named @p_162)) :named @p_163) (! (= @p_10 (! (coeff_cube_to_path$ ?v1) :named @p_12)) :named @p_165)) :named @p_166) false) :named @p_167)) :named @p_161) (! (forall ((?v1 B$) (?v2 B$) (?v3 B_list$)) (! (=> (! (and (! (= ?v0 (! (cons$ ?v1 (! (cons$ ?v2 ?v3) :named @p_13)) :named @p_169)) :named @p_170) (! (= @p_10 (! (joinpaths$ @p_12 (! (rec_join$ @p_13) :named @p_175)) :named @p_176)) :named @p_177)) :named @p_178) false) :named @p_179)) :named @p_168)) :named @p_180)) :named @p_181)) :named @p_182) false) :named @p_183)) :named @p_51)) :named @p_49)) :named @p_52)) :named @p_55)) @@ -7955,550 +7955,6 @@ (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)) -79bb70ff288db1936aaccee9c58bb4c098292b28 543 0 -unsat -(define-fun veriT_sk0 () Exp$ (! (choice ((veriT_vr40 Exp$)) (not (! (=> (! (member$ veriT_vr40 (! (myset$ z$) :named @p_199)) :named @p_278) (! (not (! (forall ((veriT_vr41 FreeExp$)) (! (not (! (= veriT_vr40 (! (fun_app$ uu$ veriT_vr41) :named @p_281)) :named @p_282)) :named @p_283)) :named @p_279)) :named @p_284)) :named @p_277))) :named @p_201)) -(define-fun veriT_sk1 () FreeExp_list$ (! (choice ((veriT_vr42 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr42) :named @p_286)) :named @p_285)) :named @p_301)) -(define-fun veriT_sk2 () FreeExp$ (! (choice ((veriT_vr48 FreeExp$)) (not (! (not (! (= veriT_sk0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ veriT_vr48 bot$) :named @p_356)) :named @p_357)) :named @p_358)) :named @p_359)) :named @p_355))) :named @p_366)) -(assume a0 (! (forall ((?v0 FreeExp$)) (! (= (! (fun_app$ uu$ ?v0) :named @p_3) (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v0 bot$) :named @p_6)) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_2)) -(assume a1 (! (forall ((?v0 FreeExp_list$)) (! (= (! (abs_ExpList$ ?v0) :named @p_1) (! (map2$ uu$ ?v0) :named @p_27)) :named @p_29)) :named @p_24)) -(assume a2 (! (forall ((?v0 Exp$)) (! (=> (! (forall ((?v1 FreeExp$)) (! (=> (! (= ?v0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v1 bot$) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_48) false) :named @p_50)) :named @p_40) false) :named @p_52)) :named @p_39)) -(assume a3 (! (forall ((?v0 Exp_list$) (?v1 FreeExp_exp_fun$)) (! (= (! (exists ((?v2 FreeExp_list$)) (! (= ?v0 (! (map2$ ?v1 ?v2) :named @p_74)) :named @p_76)) :named @p_72) (! (forall ((?v2 Exp$)) (! (=> (! (member$ ?v2 (! (myset$ ?v0) :named @p_81)) :named @p_83) (! (exists ((?v3 FreeExp$)) (! (= ?v2 (! (fun_app$ ?v1 ?v3) :named @p_89)) :named @p_91)) :named @p_85)) :named @p_93)) :named @p_78)) :named @p_95)) :named @p_71)) -(assume a4 (! (not (! (exists ((?v0 FreeExp_list$)) (! (= @p_1 z$) :named @p_178)) :named @p_176)) :named @p_180)) -(anchor :step t6 :args ((:= (?v0 FreeExp$) veriT_vr0))) -(step t6.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl) -(step t6.t2 (cl (= @p_3 (! (fun_app$ uu$ veriT_vr0) :named @p_4))) :rule cong :premises (t6.t1)) -(step t6.t3 (cl @p_5) :rule refl) -(step t6.t4 (cl (= @p_6 (! (insert$ veriT_vr0 bot$) :named @p_7))) :rule cong :premises (t6.t3)) -(step t6.t5 (cl (= @p_8 (! (myImage$ exprel$ @p_7) :named @p_9))) :rule cong :premises (t6.t4)) -(step t6.t6 (cl (= @p_10 (! (abs_Exp$ @p_9) :named @p_11))) :rule cong :premises (t6.t5)) -(step t6.t7 (cl (= @p_12 (! (= @p_4 @p_11) :named @p_13))) :rule cong :premises (t6.t2 t6.t6)) -(step t6 (cl (! (= @p_2 (! (forall ((veriT_vr0 FreeExp$)) @p_13) :named @p_15)) :named @p_14)) :rule bind) -(step t7 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2) -(step t8 (cl @p_15) :rule th_resolution :premises (a0 t6 t7)) -(anchor :step t9 :args ((:= (veriT_vr0 FreeExp$) veriT_vr1))) -(step t9.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_17)) :rule refl) -(step t9.t2 (cl (= @p_4 (! (fun_app$ uu$ veriT_vr1) :named @p_16))) :rule cong :premises (t9.t1)) -(step t9.t3 (cl @p_17) :rule refl) -(step t9.t4 (cl (= @p_7 (! (insert$ veriT_vr1 bot$) :named @p_18))) :rule cong :premises (t9.t3)) -(step t9.t5 (cl (= @p_9 (! (myImage$ exprel$ @p_18) :named @p_19))) :rule cong :premises (t9.t4)) -(step t9.t6 (cl (= @p_11 (! (abs_Exp$ @p_19) :named @p_20))) :rule cong :premises (t9.t5)) -(step t9.t7 (cl (= @p_13 (! (= @p_16 @p_20) :named @p_21))) :rule cong :premises (t9.t2 t9.t6)) -(step t9 (cl (! (= @p_15 (! (forall ((veriT_vr1 FreeExp$)) @p_21) :named @p_23)) :named @p_22)) :rule bind) -(step t10 (cl (not @p_22) (not @p_15) @p_23) :rule equiv_pos2) -(step t11 (cl @p_23) :rule th_resolution :premises (t8 t9 t10)) -(anchor :step t12 :args ((:= (?v0 FreeExp_list$) veriT_vr2))) -(step t12.t1 (cl (! (= ?v0 veriT_vr2) :named @p_26)) :rule refl) -(step t12.t2 (cl (= @p_1 (! (abs_ExpList$ veriT_vr2) :named @p_25))) :rule cong :premises (t12.t1)) -(step t12.t3 (cl @p_26) :rule refl) -(step t12.t4 (cl (= @p_27 (! (map2$ uu$ veriT_vr2) :named @p_28))) :rule cong :premises (t12.t3)) -(step t12.t5 (cl (= @p_29 (! (= @p_25 @p_28) :named @p_30))) :rule cong :premises (t12.t2 t12.t4)) -(step t12 (cl (! (= @p_24 (! (forall ((veriT_vr2 FreeExp_list$)) @p_30) :named @p_32)) :named @p_31)) :rule bind) -(step t13 (cl (not @p_31) (not @p_24) @p_32) :rule equiv_pos2) -(step t14 (cl @p_32) :rule th_resolution :premises (a1 t12 t13)) -(anchor :step t15 :args ((:= (veriT_vr2 FreeExp_list$) veriT_vr3))) -(step t15.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_34)) :rule refl) -(step t15.t2 (cl (= @p_25 (! (abs_ExpList$ veriT_vr3) :named @p_33))) :rule cong :premises (t15.t1)) -(step t15.t3 (cl @p_34) :rule refl) -(step t15.t4 (cl (= @p_28 (! (map2$ uu$ veriT_vr3) :named @p_35))) :rule cong :premises (t15.t3)) -(step t15.t5 (cl (= @p_30 (! (= @p_33 @p_35) :named @p_36))) :rule cong :premises (t15.t2 t15.t4)) -(step t15 (cl (! (= @p_32 (! (forall ((veriT_vr3 FreeExp_list$)) @p_36) :named @p_38)) :named @p_37)) :rule bind) -(step t16 (cl (not @p_37) (not @p_32) @p_38) :rule equiv_pos2) -(step t17 (cl @p_38) :rule th_resolution :premises (t14 t15 t16)) -(anchor :step t18 :args ((:= (?v0 Exp$) veriT_vr4))) -(anchor :step t18.t1 :args ((:= (?v1 FreeExp$) veriT_vr5))) -(step t18.t1.t1 (cl (= ?v0 veriT_vr4)) :rule refl) -(step t18.t1.t2 (cl (= ?v1 veriT_vr5)) :rule refl) -(step t18.t1.t3 (cl (= @p_42 (! (insert$ veriT_vr5 bot$) :named @p_43))) :rule cong :premises (t18.t1.t2)) -(step t18.t1.t4 (cl (= @p_44 (! (myImage$ exprel$ @p_43) :named @p_45))) :rule cong :premises (t18.t1.t3)) -(step t18.t1.t5 (cl (= @p_46 (! (abs_Exp$ @p_45) :named @p_47))) :rule cong :premises (t18.t1.t4)) -(step t18.t1.t6 (cl (= @p_48 (! (= veriT_vr4 @p_47) :named @p_49))) :rule cong :premises (t18.t1.t1 t18.t1.t5)) -(step t18.t1.t7 (cl (= @p_50 (! (=> @p_49 false) :named @p_51))) :rule cong :premises (t18.t1.t6)) -(step t18.t1 (cl (= @p_40 (! (forall ((veriT_vr5 FreeExp$)) @p_51) :named @p_41))) :rule bind) -(step t18.t2 (cl (= @p_52 (! (=> @p_41 false) :named @p_53))) :rule cong :premises (t18.t1)) -(step t18 (cl (! (= @p_39 (! (forall ((veriT_vr4 Exp$)) @p_53) :named @p_55)) :named @p_54)) :rule bind) -(step t19 (cl (not @p_54) (not @p_39) @p_55) :rule equiv_pos2) -(step t20 (cl @p_55) :rule th_resolution :premises (a2 t18 t19)) -(anchor :step t21 :args ((veriT_vr4 Exp$))) -(anchor :step t21.t1 :args ((veriT_vr5 FreeExp$))) -(step t21.t1.t1 (cl (= @p_51 (! (not @p_49) :named @p_57))) :rule implies_simplify) -(step t21.t1 (cl (= @p_41 (! (forall ((veriT_vr5 FreeExp$)) @p_57) :named @p_56))) :rule bind) -(step t21.t2 (cl (= @p_53 (! (=> @p_56 false) :named @p_58))) :rule cong :premises (t21.t1)) -(step t21.t3 (cl (= @p_58 (! (not @p_56) :named @p_59))) :rule implies_simplify) -(step t21.t4 (cl (= @p_53 @p_59)) :rule trans :premises (t21.t2 t21.t3)) -(step t21 (cl (! (= @p_55 (! (forall ((veriT_vr4 Exp$)) @p_59) :named @p_61)) :named @p_60)) :rule bind) -(step t22 (cl (not @p_60) (not @p_55) @p_61) :rule equiv_pos2) -(step t23 (cl @p_61) :rule th_resolution :premises (t20 t21 t22)) -(anchor :step t24 :args ((:= (veriT_vr4 Exp$) veriT_vr6))) -(anchor :step t24.t1 :args ((:= (veriT_vr5 FreeExp$) veriT_vr7))) -(step t24.t1.t1 (cl (= veriT_vr4 veriT_vr6)) :rule refl) -(step t24.t1.t2 (cl (= veriT_vr5 veriT_vr7)) :rule refl) -(step t24.t1.t3 (cl (= @p_43 (! (insert$ veriT_vr7 bot$) :named @p_63))) :rule cong :premises (t24.t1.t2)) -(step t24.t1.t4 (cl (= @p_45 (! (myImage$ exprel$ @p_63) :named @p_64))) :rule cong :premises (t24.t1.t3)) -(step t24.t1.t5 (cl (= @p_47 (! (abs_Exp$ @p_64) :named @p_65))) :rule cong :premises (t24.t1.t4)) -(step t24.t1.t6 (cl (= @p_49 (! (= veriT_vr6 @p_65) :named @p_66))) :rule cong :premises (t24.t1.t1 t24.t1.t5)) -(step t24.t1.t7 (cl (= @p_57 (! (not @p_66) :named @p_67))) :rule cong :premises (t24.t1.t6)) -(step t24.t1 (cl (= @p_56 (! (forall ((veriT_vr7 FreeExp$)) @p_67) :named @p_62))) :rule bind) -(step t24.t2 (cl (= @p_59 (! (not @p_62) :named @p_68))) :rule cong :premises (t24.t1)) -(step t24 (cl (! (= @p_61 (! (forall ((veriT_vr6 Exp$)) @p_68) :named @p_70)) :named @p_69)) :rule bind) -(step t25 (cl (not @p_69) (not @p_61) @p_70) :rule equiv_pos2) -(step t26 (cl @p_70) :rule th_resolution :premises (t23 t24 t25)) -(anchor :step t27 :args ((:= (?v0 Exp_list$) veriT_vr8) (:= (?v1 FreeExp_exp_fun$) veriT_vr9))) -(anchor :step t27.t1 :args ((:= (?v2 FreeExp_list$) veriT_vr10))) -(step t27.t1.t1 (cl (! (= ?v0 veriT_vr8) :named @p_80)) :rule refl) -(step t27.t1.t2 (cl (! (= ?v1 veriT_vr9) :named @p_88)) :rule refl) -(step t27.t1.t3 (cl (= ?v2 veriT_vr10)) :rule refl) -(step t27.t1.t4 (cl (= @p_74 (! (map2$ veriT_vr9 veriT_vr10) :named @p_75))) :rule cong :premises (t27.t1.t2 t27.t1.t3)) -(step t27.t1.t5 (cl (= @p_76 (! (= veriT_vr8 @p_75) :named @p_77))) :rule cong :premises (t27.t1.t1 t27.t1.t4)) -(step t27.t1 (cl (= @p_72 (! (exists ((veriT_vr10 FreeExp_list$)) @p_77) :named @p_73))) :rule bind) -(anchor :step t27.t2 :args ((:= (?v2 Exp$) veriT_vr11))) -(step t27.t2.t1 (cl (! (= ?v2 veriT_vr11) :named @p_87)) :rule refl) -(step t27.t2.t2 (cl @p_80) :rule refl) -(step t27.t2.t3 (cl (= @p_81 (! (myset$ veriT_vr8) :named @p_82))) :rule cong :premises (t27.t2.t2)) -(step t27.t2.t4 (cl (= @p_83 (! (member$ veriT_vr11 @p_82) :named @p_84))) :rule cong :premises (t27.t2.t1 t27.t2.t3)) -(anchor :step t27.t2.t5 :args ((:= (?v3 FreeExp$) veriT_vr12))) -(step t27.t2.t5.t1 (cl @p_87) :rule refl) -(step t27.t2.t5.t2 (cl @p_88) :rule refl) -(step t27.t2.t5.t3 (cl (= ?v3 veriT_vr12)) :rule refl) -(step t27.t2.t5.t4 (cl (= @p_89 (! (fun_app$ veriT_vr9 veriT_vr12) :named @p_90))) :rule cong :premises (t27.t2.t5.t2 t27.t2.t5.t3)) -(step t27.t2.t5.t5 (cl (= @p_91 (! (= veriT_vr11 @p_90) :named @p_92))) :rule cong :premises (t27.t2.t5.t1 t27.t2.t5.t4)) -(step t27.t2.t5 (cl (= @p_85 (! (exists ((veriT_vr12 FreeExp$)) @p_92) :named @p_86))) :rule bind) -(step t27.t2.t6 (cl (= @p_93 (! (=> @p_84 @p_86) :named @p_94))) :rule cong :premises (t27.t2.t4 t27.t2.t5)) -(step t27.t2 (cl (= @p_78 (! (forall ((veriT_vr11 Exp$)) @p_94) :named @p_79))) :rule bind) -(step t27.t3 (cl (= @p_95 (! (= @p_73 @p_79) :named @p_96))) :rule cong :premises (t27.t1 t27.t2)) -(step t27 (cl (! (= @p_71 (! 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(not @p_183) :named @p_191) @p_190) :rule equiv_pos2) -(step t54 (cl (not @p_191) @p_181) :rule not_not) -(step t55 (cl @p_192 @p_181 @p_190) :rule th_resolution :premises (t54 t53)) -(step t56 (cl @p_190) :rule th_resolution :premises (t50 t52 t55)) -(step t57 (cl (= @p_188 (! (not (! (forall ((veriT_vr30 FreeExp_list$)) (not @p_187)) :named @p_198)) :named @p_193))) :rule connective_def) -(step t58 (cl (! (= @p_190 (! (not @p_193) :named @p_195)) :named @p_194)) :rule cong :premises (t57)) -(step t59 (cl (! (not @p_194) :named @p_197) (! (not @p_190) :named @p_196) @p_195) :rule equiv_pos2) -(step t60 (cl (not @p_196) @p_188) :rule not_not) -(step t61 (cl @p_197 @p_188 @p_195) :rule th_resolution :premises (t60 t59)) -(step t62 (cl (not @p_195) @p_198) :rule not_not) -(step t63 (cl @p_197 @p_188 @p_198) :rule th_resolution :premises (t62 t61)) -(step t64 (cl @p_195) :rule th_resolution :premises (t56 t58 t63)) -(step t65 (cl @p_198) :rule th_resolution :premises (t62 t64)) -(step t66 (cl (or (! (not @p_175) :named @p_336) (! (and (! (=> (! (not (! (forall ((veriT_vr23 FreeExp_list$)) (! (not (! (= z$ (! (map2$ uu$ veriT_vr23) :named @p_203)) :named @p_205)) :named @p_207)) :named @p_202)) :named @p_209) (! (forall ((veriT_vr24 Exp$)) (! (=> (! (member$ veriT_vr24 @p_199) :named @p_212) (! (exists ((veriT_vr25 FreeExp$)) (! (= veriT_vr24 (! (fun_app$ uu$ veriT_vr25) :named @p_217)) :named @p_219)) :named @p_214)) :named @p_221)) :named @p_211)) :named @p_223) (! (=> (! (forall ((veriT_vr26 Exp$)) (! (=> (! (member$ veriT_vr26 @p_199) :named @p_227) (! (not (! (forall ((veriT_vr27 FreeExp$)) (! (not (! (= veriT_vr26 (! (fun_app$ uu$ veriT_vr27) :named @p_231)) :named @p_232)) :named @p_233)) :named @p_228)) :named @p_235)) :named @p_237)) :named @p_226) (! (exists ((veriT_vr28 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr28) :named @p_240)) :named @p_241)) :named @p_239)) :named @p_242)) :named @p_200))) :rule forall_inst :args ((:= veriT_vr21 z$) (:= veriT_vr22 uu$))) -(anchor :step t67) -(assume t67.h1 @p_200) -(anchor :step t67.t2 :args ((:= (veriT_vr23 FreeExp_list$) veriT_vr31))) -(step t67.t2.t1 (cl (= veriT_vr23 veriT_vr31)) :rule refl) -(step t67.t2.t2 (cl (= @p_203 (! (map2$ uu$ veriT_vr31) :named @p_204))) :rule cong :premises (t67.t2.t1)) -(step t67.t2.t3 (cl (= @p_205 (! (= z$ @p_204) :named @p_206))) :rule cong :premises (t67.t2.t2)) -(step t67.t2.t4 (cl (= @p_207 (! (not @p_206) :named @p_208))) :rule cong :premises (t67.t2.t3)) -(step t67.t2 (cl (= @p_202 (! (forall ((veriT_vr31 FreeExp_list$)) @p_208) :named @p_210))) :rule bind) -(step t67.t3 (cl (= @p_209 (! (not @p_210) :named @p_224))) :rule cong :premises (t67.t2)) -(anchor :step t67.t4 :args ((:= (veriT_vr24 Exp$) veriT_vr32))) -(step t67.t4.t1 (cl (! (= veriT_vr24 veriT_vr32) :named @p_216)) :rule refl) -(step t67.t4.t2 (cl (= @p_212 (! (member$ veriT_vr32 @p_199) :named @p_213))) :rule cong :premises (t67.t4.t1)) -(anchor :step t67.t4.t3 :args ((:= (veriT_vr25 FreeExp$) veriT_vr33))) -(step t67.t4.t3.t1 (cl @p_216) :rule refl) -(step t67.t4.t3.t2 (cl (= veriT_vr25 veriT_vr33)) :rule refl) -(step t67.t4.t3.t3 (cl (= @p_217 (! (fun_app$ uu$ veriT_vr33) :named @p_218))) :rule cong :premises (t67.t4.t3.t2)) -(step t67.t4.t3.t4 (cl (= @p_219 (! (= veriT_vr32 @p_218) :named @p_220))) :rule cong :premises (t67.t4.t3.t1 t67.t4.t3.t3)) -(step t67.t4.t3 (cl (= @p_214 (! (exists ((veriT_vr33 FreeExp$)) @p_220) :named @p_215))) :rule bind) -(step t67.t4.t4 (cl (= @p_221 (! (=> @p_213 @p_215) :named @p_222))) :rule cong :premises (t67.t4.t2 t67.t4.t3)) -(step t67.t4 (cl (= @p_211 (! (forall ((veriT_vr32 Exp$)) @p_222) :named @p_225))) :rule bind) -(step t67.t5 (cl (= @p_223 (! (=> @p_224 @p_225) :named @p_245))) :rule cong :premises (t67.t3 t67.t4)) -(anchor :step t67.t6 :args ((:= (veriT_vr26 Exp$) veriT_vr32))) -(step t67.t6.t1 (cl (! (= veriT_vr26 veriT_vr32) :named @p_230)) :rule refl) -(step t67.t6.t2 (cl (= @p_227 @p_213)) :rule cong :premises (t67.t6.t1)) -(anchor :step t67.t6.t3 :args ((:= (veriT_vr27 FreeExp$) veriT_vr33))) -(step t67.t6.t3.t1 (cl @p_230) :rule refl) -(step t67.t6.t3.t2 (cl (= veriT_vr27 veriT_vr33)) :rule refl) -(step t67.t6.t3.t3 (cl (= @p_231 @p_218)) :rule cong :premises (t67.t6.t3.t2)) -(step t67.t6.t3.t4 (cl (= @p_232 @p_220)) :rule cong :premises (t67.t6.t3.t1 t67.t6.t3.t3)) -(step t67.t6.t3.t5 (cl (= @p_233 (! (not @p_220) :named @p_234))) :rule cong :premises (t67.t6.t3.t4)) -(step t67.t6.t3 (cl (= @p_228 (! (forall ((veriT_vr33 FreeExp$)) @p_234) :named @p_229))) :rule bind) -(step t67.t6.t4 (cl (= @p_235 (! (not @p_229) :named @p_236))) :rule cong :premises (t67.t6.t3)) -(step t67.t6.t5 (cl (= @p_237 (! (=> @p_213 @p_236) :named @p_238))) :rule cong :premises (t67.t6.t2 t67.t6.t4)) -(step t67.t6 (cl (= @p_226 (! (forall ((veriT_vr32 Exp$)) @p_238) :named @p_243))) :rule bind) -(anchor :step t67.t7 :args ((:= (veriT_vr28 FreeExp_list$) veriT_vr31))) -(step t67.t7.t1 (cl (= veriT_vr28 veriT_vr31)) :rule refl) -(step t67.t7.t2 (cl (= @p_240 @p_204)) :rule cong :premises (t67.t7.t1)) -(step t67.t7.t3 (cl (= @p_241 @p_206)) :rule cong :premises (t67.t7.t2)) -(step t67.t7 (cl (= @p_239 (! (exists ((veriT_vr31 FreeExp_list$)) @p_206) :named @p_244))) :rule bind) -(step t67.t8 (cl (= @p_242 (! (=> @p_243 @p_244) :named @p_246))) :rule cong :premises (t67.t6 t67.t7)) -(step t67.t9 (cl (! (= @p_200 (! (and @p_245 @p_246) :named @p_249)) :named @p_247)) :rule cong :premises (t67.t5 t67.t8)) -(step t67.t10 (cl (not @p_247) (! (not @p_200) :named @p_248) @p_249) :rule equiv_pos2) -(step t67.t11 (cl @p_249) :rule th_resolution :premises (t67.h1 t67.t9 t67.t10)) -(anchor :step t67.t12 :args ((:= (veriT_vr32 Exp$) veriT_vr34))) -(step t67.t12.t1 (cl (! (= veriT_vr32 veriT_vr34) :named @p_252)) :rule refl) -(step t67.t12.t2 (cl (= @p_213 (! (member$ veriT_vr34 @p_199) :named @p_250))) :rule cong :premises (t67.t12.t1)) -(anchor :step t67.t12.t3 :args ((:= (veriT_vr33 FreeExp$) veriT_vr35))) -(step t67.t12.t3.t1 (cl @p_252) :rule refl) -(step t67.t12.t3.t2 (cl (= veriT_vr33 veriT_vr35)) :rule refl) -(step t67.t12.t3.t3 (cl (= @p_218 (! (fun_app$ uu$ veriT_vr35) :named @p_253))) :rule cong :premises (t67.t12.t3.t2)) -(step t67.t12.t3.t4 (cl (= @p_220 (! (= veriT_vr34 @p_253) :named @p_254))) :rule cong :premises (t67.t12.t3.t1 t67.t12.t3.t3)) -(step t67.t12.t3.t5 (cl (= @p_234 (! (not @p_254) :named @p_255))) :rule cong :premises (t67.t12.t3.t4)) -(step t67.t12.t3 (cl (= @p_229 (! (forall ((veriT_vr35 FreeExp$)) @p_255) :named @p_251))) :rule bind) -(step t67.t12.t4 (cl (= @p_236 (! (not @p_251) :named @p_256))) :rule cong :premises (t67.t12.t3)) -(step t67.t12.t5 (cl (= @p_238 (! (=> @p_250 @p_256) :named @p_257))) :rule cong :premises (t67.t12.t2 t67.t12.t4)) -(step t67.t12 (cl (= @p_243 (! (forall ((veriT_vr34 Exp$)) @p_257) :named @p_260))) :rule bind) -(anchor :step t67.t13 :args ((:= (veriT_vr31 FreeExp_list$) veriT_vr36))) -(step t67.t13.t1 (cl (= veriT_vr31 veriT_vr36)) :rule refl) -(step t67.t13.t2 (cl (= @p_204 (! (map2$ uu$ veriT_vr36) :named @p_258))) :rule cong :premises (t67.t13.t1)) -(step t67.t13.t3 (cl (= @p_206 (! (= z$ @p_258) :named @p_259))) :rule cong :premises (t67.t13.t2)) -(step t67.t13 (cl (= @p_244 (! (exists ((veriT_vr36 FreeExp_list$)) @p_259) :named @p_261))) :rule bind) -(step t67.t14 (cl (= @p_246 (! (=> @p_260 @p_261) :named @p_262))) :rule cong :premises (t67.t12 t67.t13)) -(step t67.t15 (cl (! (= @p_249 (! (and @p_245 @p_262) :named @p_264)) :named @p_263)) :rule cong :premises (t67.t14)) -(step t67.t16 (cl (not @p_263) (not @p_249) @p_264) :rule equiv_pos2) -(step t67.t17 (cl @p_264) :rule th_resolution :premises (t67.t11 t67.t15 t67.t16)) -(anchor :step t67.t18 :args ((:= (veriT_vr31 FreeExp_list$) veriT_vr37))) -(step t67.t18.t1 (cl (= veriT_vr31 veriT_vr37)) :rule refl) -(step t67.t18.t2 (cl (= @p_204 (! (map2$ uu$ veriT_vr37) :named @p_265))) :rule cong :premises (t67.t18.t1)) -(step t67.t18.t3 (cl (= @p_206 (! (= z$ @p_265) :named @p_266))) :rule cong :premises (t67.t18.t2)) -(step t67.t18.t4 (cl (= @p_208 (! (not @p_266) :named @p_267))) :rule cong :premises (t67.t18.t3)) -(step t67.t18 (cl (= @p_210 (! (forall ((veriT_vr37 FreeExp_list$)) @p_267) :named @p_268))) :rule bind) -(step t67.t19 (cl (= @p_224 (! (not @p_268) :named @p_275))) :rule cong :premises (t67.t18)) -(anchor :step t67.t20 :args ((:= (veriT_vr32 Exp$) veriT_vr38))) -(step t67.t20.t1 (cl (! (= veriT_vr32 veriT_vr38) :named @p_271)) :rule refl) -(step t67.t20.t2 (cl (= @p_213 (! (member$ veriT_vr38 @p_199) :named @p_269))) :rule cong :premises (t67.t20.t1)) -(anchor :step t67.t20.t3 :args ((:= (veriT_vr33 FreeExp$) veriT_vr39))) -(step t67.t20.t3.t1 (cl @p_271) :rule refl) -(step t67.t20.t3.t2 (cl (= veriT_vr33 veriT_vr39)) :rule refl) -(step t67.t20.t3.t3 (cl (= @p_218 (! (fun_app$ uu$ veriT_vr39) :named @p_272))) :rule cong :premises (t67.t20.t3.t2)) -(step t67.t20.t3.t4 (cl (= @p_220 (! (= veriT_vr38 @p_272) :named @p_273))) :rule cong :premises (t67.t20.t3.t1 t67.t20.t3.t3)) -(step t67.t20.t3 (cl (= @p_215 (! (exists ((veriT_vr39 FreeExp$)) @p_273) :named @p_270))) :rule bind) -(step t67.t20.t4 (cl (= @p_222 (! 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(= veriT_vr34 veriT_vr40) :named @p_280)) :rule refl) -(step t67.t22.t2 (cl (= @p_250 @p_278)) :rule cong :premises (t67.t22.t1)) -(anchor :step t67.t22.t3 :args ((:= (veriT_vr35 FreeExp$) veriT_vr41))) -(step t67.t22.t3.t1 (cl @p_280) :rule refl) -(step t67.t22.t3.t2 (cl (= veriT_vr35 veriT_vr41)) :rule refl) -(step t67.t22.t3.t3 (cl (= @p_253 @p_281)) :rule cong :premises (t67.t22.t3.t2)) -(step t67.t22.t3.t4 (cl (= @p_254 @p_282)) :rule cong :premises (t67.t22.t3.t1 t67.t22.t3.t3)) -(step t67.t22.t3.t5 (cl (= @p_255 @p_283)) :rule cong :premises (t67.t22.t3.t4)) -(step t67.t22.t3 (cl (= @p_251 @p_279)) :rule bind) -(step t67.t22.t4 (cl (= @p_256 @p_284)) :rule cong :premises (t67.t22.t3)) -(step t67.t22.t5 (cl (= @p_257 @p_277)) :rule cong :premises (t67.t22.t2 t67.t22.t4)) -(step t67.t22 (cl (= @p_260 (! (forall ((veriT_vr40 Exp$)) @p_277) :named @p_287))) :rule bind) -(anchor :step t67.t23 :args ((:= (veriT_vr36 FreeExp_list$) veriT_vr42))) -(step t67.t23.t1 (cl (= veriT_vr36 veriT_vr42)) :rule refl) -(step t67.t23.t2 (cl (= @p_258 @p_286)) :rule cong :premises (t67.t23.t1)) -(step t67.t23.t3 (cl (= @p_259 @p_285)) :rule cong :premises (t67.t23.t2)) -(step t67.t23 (cl (= @p_261 (! (exists ((veriT_vr42 FreeExp_list$)) @p_285) :named @p_288))) :rule bind) -(step t67.t24 (cl (= @p_262 (! (=> @p_287 @p_288) :named @p_290))) :rule cong :premises (t67.t22 t67.t23)) -(step t67.t25 (cl (! (= @p_264 (! (and @p_289 @p_290) :named @p_292)) :named @p_291)) :rule cong :premises (t67.t21 t67.t24)) -(step t67.t26 (cl (not @p_291) (not @p_264) @p_292) :rule equiv_pos2) -(step t67.t27 (cl @p_292) :rule th_resolution :premises (t67.t17 t67.t25 t67.t26)) -(anchor :step t67.t28 :args ((:= (veriT_vr40 Exp$) veriT_sk0))) -(step t67.t28.t1 (cl (! (= veriT_vr40 veriT_sk0) :named @p_295)) :rule refl) -(step t67.t28.t2 (cl (= @p_278 (! (member$ veriT_sk0 @p_199) :named @p_293))) :rule cong :premises (t67.t28.t1)) -(anchor :step t67.t28.t3 :args ((veriT_vr41 FreeExp$))) -(step t67.t28.t3.t1 (cl @p_295) :rule refl) -(step t67.t28.t3.t2 (cl (= @p_282 (! (= @p_281 veriT_sk0) :named @p_296))) :rule cong :premises (t67.t28.t3.t1)) -(step t67.t28.t3.t3 (cl (= @p_283 (! (not @p_296) :named @p_297))) :rule cong :premises (t67.t28.t3.t2)) -(step t67.t28.t3 (cl (= @p_279 (! (forall ((veriT_vr41 FreeExp$)) @p_297) :named @p_294))) :rule bind) -(step t67.t28.t4 (cl (= @p_284 (! (not @p_294) :named @p_298))) :rule cong :premises (t67.t28.t3)) -(step t67.t28.t5 (cl (= @p_277 (! 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(= veriT_vr38 veriT_vr44) :named @p_314)) :rule refl) -(step t67.t36.t2 (cl (= @p_269 (! (member$ veriT_vr44 @p_199) :named @p_312))) :rule cong :premises (t67.t36.t1)) -(anchor :step t67.t36.t3 :args ((:= (veriT_vr39 FreeExp$) veriT_vr45))) -(step t67.t36.t3.t1 (cl @p_314) :rule refl) -(step t67.t36.t3.t2 (cl (= veriT_vr39 veriT_vr45)) :rule refl) -(step t67.t36.t3.t3 (cl (= @p_272 (! (fun_app$ uu$ veriT_vr45) :named @p_315))) :rule cong :premises (t67.t36.t3.t2)) -(step t67.t36.t3.t4 (cl (= @p_273 (! (= veriT_vr44 @p_315) :named @p_316))) :rule cong :premises (t67.t36.t3.t1 t67.t36.t3.t3)) -(step t67.t36.t3 (cl (= @p_270 (! (exists ((veriT_vr45 FreeExp$)) @p_316) :named @p_313))) :rule bind) -(step t67.t36.t4 (cl (= @p_274 (! (=> @p_312 @p_313) :named @p_317))) :rule cong :premises (t67.t36.t2 t67.t36.t3)) -(step t67.t36 (cl (= @p_276 (! (forall ((veriT_vr44 Exp$)) @p_317) :named @p_311))) :rule bind) -(step t67.t37 (cl (= @p_289 (! (=> @p_310 @p_311) :named @p_318))) :rule cong :premises (t67.t35 t67.t36)) -(anchor :step t67.t38 :args ((:= (veriT_vr41 FreeExp$) veriT_vr45))) -(step t67.t38.t1 (cl (= veriT_vr41 veriT_vr45)) :rule refl) -(step t67.t38.t2 (cl (= @p_281 @p_315)) :rule cong :premises (t67.t38.t1)) -(step t67.t38.t3 (cl (= @p_296 (! (= veriT_sk0 @p_315) :named @p_319))) :rule cong :premises (t67.t38.t2)) -(step t67.t38.t4 (cl (= @p_297 (! (not @p_319) :named @p_320))) :rule cong :premises (t67.t38.t3)) -(step t67.t38 (cl (= @p_294 (! (forall ((veriT_vr45 FreeExp$)) @p_320) :named @p_321))) :rule bind) -(step t67.t39 (cl (= @p_298 (! (not @p_321) :named @p_322))) :rule cong :premises (t67.t38)) -(step t67.t40 (cl (= @p_299 (! (=> @p_293 @p_322) :named @p_323))) :rule cong :premises (t67.t39)) -(step t67.t41 (cl (= @p_303 (! (=> @p_323 @p_300) :named @p_324))) :rule cong :premises (t67.t40)) -(step t67.t42 (cl (! (= @p_305 (! (and @p_318 @p_324) :named @p_326)) :named @p_325)) :rule cong :premises (t67.t37 t67.t41)) -(step t67.t43 (cl (not @p_325) (not @p_305) @p_326) :rule equiv_pos2) -(step t67.t44 (cl @p_326) :rule th_resolution :premises (t67.t33 t67.t42 t67.t43)) -(anchor :step t67.t45 :args ((:= (veriT_vr45 FreeExp$) veriT_vr46))) -(step t67.t45.t1 (cl (= veriT_vr45 veriT_vr46)) :rule refl) -(step t67.t45.t2 (cl (= @p_315 (! (fun_app$ uu$ veriT_vr46) :named @p_328))) :rule cong :premises (t67.t45.t1)) -(step t67.t45.t3 (cl (= @p_319 (! (= veriT_sk0 @p_328) :named @p_329))) :rule cong :premises (t67.t45.t2)) -(step t67.t45.t4 (cl (= @p_320 (! (not @p_329) :named @p_330))) :rule cong :premises (t67.t45.t3)) -(step t67.t45 (cl (= @p_321 (! (forall ((veriT_vr46 FreeExp$)) @p_330) :named @p_327))) :rule bind) -(step t67.t46 (cl (= @p_322 (! (not @p_327) :named @p_331))) :rule cong :premises (t67.t45)) -(step t67.t47 (cl (= @p_323 (! (=> @p_293 @p_331) :named @p_332))) :rule cong :premises (t67.t46)) -(step t67.t48 (cl (= @p_324 (! (=> @p_332 @p_300) :named @p_333))) :rule cong :premises (t67.t47)) -(step t67.t49 (cl (! (= @p_326 (! (and @p_318 @p_333) :named @p_334)) :named @p_335)) :rule cong :premises (t67.t48)) -(step t67.t50 (cl (not @p_335) (not @p_326) @p_334) :rule equiv_pos2) -(step t67.t51 (cl @p_334) :rule th_resolution :premises (t67.t44 t67.t49 t67.t50)) -(step t67 (cl @p_248 @p_334) :rule subproof :discharge (h1)) -(step t68 (cl @p_336 @p_200) :rule or :premises (t66)) -(step t69 (cl (! (or @p_336 @p_334) :named @p_338) (! (not @p_336) :named @p_337)) :rule or_neg) -(step t70 (cl (not @p_337) @p_175) :rule not_not) -(step t71 (cl @p_338 @p_175) :rule th_resolution :premises (t70 t69)) -(step t72 (cl @p_338 (! (not @p_334) :named @p_340)) :rule or_neg) -(step t73 (cl @p_338) :rule th_resolution :premises (t68 t67 t71 t72)) -(step t74 (cl @p_332 (! (not @p_331) :named @p_339)) :rule implies_neg2) -(step t75 (cl (not @p_339) @p_327) :rule not_not) -(step t76 (cl @p_332 @p_327) :rule th_resolution :premises (t75 t74)) -(step t77 (cl (not @p_333) (! (not @p_332) :named @p_393) @p_300) :rule implies_pos) -(step t78 (cl @p_340 @p_333) :rule and_pos) -(step t79 (cl @p_336 @p_334) :rule or :premises (t73)) -(step t80 (cl @p_334) :rule resolution :premises (t79 t44)) -(step t81 (cl @p_333) :rule resolution :premises (t78 t80)) -(step t82 (cl (or (! (not @p_70) :named @p_377) (! (not (! (forall ((veriT_vr7 FreeExp$)) (! (not (! (= @p_65 veriT_sk0) :named @p_346)) :named @p_348)) :named @p_342)) :named @p_341))) :rule forall_inst :args ((:= veriT_vr6 veriT_sk0))) -(anchor :step t83) -(assume t83.h1 @p_341) -(anchor :step t83.t2 :args ((:= (veriT_vr7 FreeExp$) veriT_vr47))) -(step t83.t2.t1 (cl (= veriT_vr7 veriT_vr47)) :rule refl) -(step t83.t2.t2 (cl (= @p_63 (! (insert$ veriT_vr47 bot$) :named @p_343))) :rule cong :premises (t83.t2.t1)) -(step t83.t2.t3 (cl (= @p_64 (! (myImage$ exprel$ @p_343) :named @p_344))) :rule cong :premises (t83.t2.t2)) -(step t83.t2.t4 (cl (= @p_65 (! (abs_Exp$ @p_344) :named @p_345))) :rule cong :premises (t83.t2.t3)) -(step t83.t2.t5 (cl (= @p_346 (! (= veriT_sk0 @p_345) :named @p_347))) :rule cong :premises (t83.t2.t4)) -(step t83.t2.t6 (cl (= @p_348 (! (not @p_347) :named @p_349))) :rule cong :premises (t83.t2.t5)) -(step t83.t2 (cl (= @p_342 (! (forall ((veriT_vr47 FreeExp$)) @p_349) :named @p_350))) :rule bind) -(step t83.t3 (cl (! (= @p_341 (! (not @p_350) :named @p_353)) :named @p_351)) :rule cong :premises (t83.t2)) -(step t83.t4 (cl (! (not @p_351) :named @p_354) (! (not @p_341) :named @p_352) @p_353) :rule equiv_pos2) -(step t83.t5 (cl (! (not @p_352) :named @p_376) @p_342) :rule not_not) -(step t83.t6 (cl @p_354 @p_342 @p_353) :rule th_resolution :premises (t83.t5 t83.t4)) -(step t83.t7 (cl @p_353) :rule th_resolution :premises (t83.h1 t83.t3 t83.t6)) -(anchor :step t83.t8 :args ((:= (veriT_vr47 FreeExp$) veriT_vr48))) -(step t83.t8.t1 (cl (= veriT_vr47 veriT_vr48)) :rule refl) -(step t83.t8.t2 (cl (= @p_343 @p_356)) :rule cong :premises (t83.t8.t1)) -(step t83.t8.t3 (cl (= @p_344 @p_357)) :rule cong :premises (t83.t8.t2)) -(step t83.t8.t4 (cl (= @p_345 @p_358)) :rule cong :premises (t83.t8.t3)) -(step t83.t8.t5 (cl (= @p_347 @p_359)) :rule cong :premises (t83.t8.t4)) -(step t83.t8.t6 (cl (= @p_349 @p_355)) :rule cong :premises (t83.t8.t5)) -(step t83.t8 (cl (= @p_350 (! (forall ((veriT_vr48 FreeExp$)) @p_355) :named @p_360))) :rule bind) -(step t83.t9 (cl (! (= @p_353 (! (not @p_360) :named @p_362)) :named @p_361)) :rule cong :premises (t83.t8)) -(step t83.t10 (cl (! (not @p_361) :named @p_364) (! (not @p_353) :named @p_363) @p_362) :rule equiv_pos2) -(step t83.t11 (cl (not @p_363) @p_350) :rule not_not) -(step t83.t12 (cl @p_364 @p_350 @p_362) :rule th_resolution :premises (t83.t11 t83.t10)) -(step t83.t13 (cl @p_362) :rule th_resolution :premises (t83.t7 t83.t9 t83.t12)) -(anchor :step t83.t14 :args ((:= (veriT_vr48 FreeExp$) veriT_sk2))) -(step t83.t14.t1 (cl (= veriT_vr48 veriT_sk2)) :rule refl) -(step t83.t14.t2 (cl (= @p_356 (! (insert$ veriT_sk2 bot$) :named @p_367))) :rule cong :premises (t83.t14.t1)) -(step t83.t14.t3 (cl (= @p_357 (! (myImage$ exprel$ @p_367) :named @p_368))) :rule cong :premises (t83.t14.t2)) -(step t83.t14.t4 (cl (= @p_358 (! (abs_Exp$ @p_368) :named @p_369))) :rule cong :premises (t83.t14.t3)) -(step t83.t14.t5 (cl (= @p_359 (! (= veriT_sk0 @p_369) :named @p_365))) :rule cong :premises (t83.t14.t4)) -(step t83.t14.t6 (cl (= @p_355 (! (not @p_365) :named @p_370))) :rule cong :premises (t83.t14.t5)) -(step t83.t14 (cl (= @p_360 @p_370)) :rule sko_forall) -(step t83.t15 (cl (! (= @p_362 (! (not @p_370) :named @p_372)) :named @p_371)) :rule cong :premises (t83.t14)) -(step t83.t16 (cl (! (not @p_371) :named @p_374) (! (not @p_362) :named @p_373) @p_372) :rule equiv_pos2) -(step t83.t17 (cl (not @p_373) @p_360) :rule not_not) -(step t83.t18 (cl @p_374 @p_360 @p_372) :rule th_resolution :premises (t83.t17 t83.t16)) -(step t83.t19 (cl (! (not @p_372) :named @p_375) @p_365) :rule not_not) -(step t83.t20 (cl @p_374 @p_360 @p_365) :rule th_resolution :premises (t83.t19 t83.t18)) -(step t83.t21 (cl @p_372) :rule th_resolution :premises (t83.t13 t83.t15 t83.t20)) -(step t83.t22 (cl @p_375 @p_365) :rule not_not) -(step t83.t23 (cl @p_365) :rule th_resolution :premises (t83.t22 t83.t21)) -(step t83.t24 (cl (= @p_372 @p_365)) :rule not_simplify) -(step t83.t25 (cl @p_365) :rule th_resolution :premises (t83.t23 t83.t24)) -(step t83 (cl @p_352 @p_365) :rule subproof :discharge (h1)) -(step t84 (cl @p_376 @p_342) :rule not_not) -(step t85 (cl @p_342 @p_365) :rule th_resolution :premises (t84 t83)) -(step t86 (cl @p_377 @p_341) :rule or :premises (t82)) -(step t87 (cl (! (or @p_377 @p_365) :named @p_379) (! (not @p_377) :named @p_378)) :rule or_neg) -(step t88 (cl (not @p_378) @p_70) :rule not_not) -(step t89 (cl @p_379 @p_70) :rule th_resolution :premises (t88 t87)) -(step t90 (cl @p_379 @p_370) :rule or_neg) -(step t91 (cl @p_379) :rule th_resolution :premises (t86 t85 t89 t90)) -(step t92 (cl @p_377 @p_365) :rule or :premises (t91)) -(step t93 (cl @p_365) :rule resolution :premises (t92 t26)) -(step t94 (cl (or @p_331 (! (not (! (= veriT_sk0 (! (fun_app$ uu$ veriT_sk2) :named @p_381)) :named @p_392)) :named @p_382))) :rule forall_inst :args ((:= veriT_vr46 veriT_sk2))) -(step t95 (cl (or @p_193 (! (not (! (= z$ (! (abs_ExpList$ veriT_sk1) :named @p_380)) :named @p_389)) :named @p_383))) :rule forall_inst :args ((:= veriT_vr30 veriT_sk1))) -(step t96 (cl (or (! (not @p_38) :named @p_384) (! (= @p_302 @p_380) :named @p_385))) :rule forall_inst :args ((:= veriT_vr3 veriT_sk1))) -(step t97 (cl (or (! (not @p_23) :named @p_386) (! (= @p_369 @p_381) :named @p_387))) :rule forall_inst :args ((:= veriT_vr1 veriT_sk2))) -(step t98 (cl @p_331 @p_382) :rule or :premises (t94)) -(step t99 (cl @p_193 @p_383) :rule or :premises (t95)) -(step t100 (cl @p_383) :rule resolution :premises (t99 t65)) -(step t101 (cl @p_384 @p_385) :rule or :premises (t96)) -(step t102 (cl @p_385) :rule resolution :premises (t101 t17)) -(step t103 (cl @p_386 @p_387) :rule or :premises (t97)) -(step t104 (cl @p_387) :rule resolution :premises (t103 t11)) -(step t105 (cl (! (= z$ z$) :named @p_388)) :rule eq_reflexive) -(step t106 (cl (not @p_388) (! (not @p_300) :named @p_390) (! (not @p_385) :named @p_391) @p_389) :rule eq_transitive) -(step t107 (cl @p_390 @p_391 @p_389) :rule th_resolution :premises (t106 t105)) -(step t108 (cl @p_390) :rule resolution :premises (t107 t100 t102)) -(step t109 (cl @p_370 (not @p_387) @p_392) :rule eq_transitive) -(step t110 (cl @p_392) :rule resolution :premises (t109 t93 t104)) -(step t111 (cl @p_393) :rule resolution :premises (t77 t108 t81)) -(step t112 (cl @p_331) :rule resolution :premises (t98 t110)) -(step t113 (cl) :rule resolution :premises (t76 t111 t112)) 40b27e0a4a8779ad293f698e9d6f54d1b11a66ce 3015 0 unsat (define-fun veriT_sk0 () A_b_c_M_state_fun$ (! (choice ((veriT_vr57 A_b_c_M_state_fun$)) (not (forall ((veriT_vr58 A_b_c_M_state_fun$)) (! (=> (! (forall ((veriT_vr59 A$) (veriT_vr60 C$)) (! (or (! (is_fail$ (! (run$ (! (fun_app$ veriT_vr57 veriT_vr59) :named @p_552) veriT_vr60) :named @p_544)) :named @p_542) (! (and (! (= (! (is_fail$ (! (run$ (! (fun_app$ veriT_vr58 veriT_vr59) :named @p_554) veriT_vr60) :named @p_543)) :named @p_556) @p_542) :named @p_561) (! (forall ((veriT_vr61 B$) (veriT_vr62 C$)) (! (= (! (is_res$ @p_543 (! (pair$ veriT_vr61 veriT_vr62) :named @p_545)) :named @p_566) (! (is_res$ @p_544 @p_545) :named @p_570)) :named @p_571)) :named @p_562)) :named @p_572)) :named @p_573)) :named @p_551) (! (forall ((veriT_vr63 D$)) (! (or (! (is_fail$a (! (run$a (! (b$ veriT_vr57) :named @p_575) veriT_vr63) :named @p_546)) :named @p_548) (! (exists ((veriT_vr64 E$) (veriT_vr65 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr64 veriT_vr65) :named @p_580)) :named @p_581) (! (is_fail$b (! (run$b (! (c$ veriT_vr64 veriT_vr57) :named @p_583) veriT_vr65) :named @p_585)) :named @p_586)) :named @p_587)) :named @p_576) (! (and (! (and (! (=> (! (or (! (is_fail$a (! (run$a (! (b$ veriT_vr58) :named @p_588) veriT_vr63) :named @p_547)) :named @p_549) (! (exists ((veriT_vr66 E$) (veriT_vr67 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr66 veriT_vr67) :named @p_592)) :named @p_593) (! (is_fail$b (! (run$b (! (c$ veriT_vr66 veriT_vr58) :named @p_595) veriT_vr67) :named @p_597)) :named @p_598)) :named @p_599)) :named @p_589)) :named @p_600) (! (or @p_548 (! (exists ((veriT_vr68 E$) (veriT_vr69 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr68 veriT_vr69) :named @p_603)) :named @p_604) (! (is_fail$b (! (run$b (! (c$ veriT_vr68 veriT_vr57) :named @p_606) veriT_vr69) :named @p_608)) :named @p_609)) :named @p_610)) :named @p_602)) :named @p_611)) :named @p_613) (! (=> (! (or @p_548 (! (exists ((veriT_vr70 E$) (veriT_vr71 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr70 veriT_vr71) :named @p_615)) :named @p_616) (! (is_fail$b (! (run$b (! (c$ veriT_vr70 veriT_vr57) :named @p_618) veriT_vr71) :named @p_620)) :named @p_621)) :named @p_622)) :named @p_614)) :named @p_623) (! (or @p_549 (! (exists ((veriT_vr72 E$) (veriT_vr73 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr72 veriT_vr73) :named @p_626)) :named @p_627) (! (is_fail$b (! (run$b (! (c$ veriT_vr72 veriT_vr58) :named @p_629) veriT_vr73) :named @p_631)) :named @p_632)) :named @p_633)) :named @p_625)) :named @p_634)) :named @p_636)) :named @p_637) (! (forall ((veriT_vr74 F$) (veriT_vr75 D$)) (! (and (! (=> (! (or @p_549 (! (exists ((veriT_vr76 E$) (veriT_vr77 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr76 veriT_vr77) :named @p_640)) :named @p_641) (! (is_res$b (! (run$b (! (c$ veriT_vr76 veriT_vr58) :named @p_643) veriT_vr77) :named @p_645) (! (pair$b veriT_vr74 veriT_vr75) :named @p_550)) :named @p_646)) :named @p_647)) :named @p_639)) :named @p_648) (! (or @p_548 (! (exists ((veriT_vr78 E$) (veriT_vr79 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr78 veriT_vr79) :named @p_650)) :named @p_651) (! (is_res$b (! (run$b (! (c$ veriT_vr78 veriT_vr57) :named @p_653) veriT_vr79) :named @p_655) @p_550) :named @p_659)) :named @p_660)) :named @p_649)) :named @p_661)) :named @p_663) (! (=> (! (or @p_548 (! (exists ((veriT_vr80 E$) (veriT_vr81 D$)) (! (and (! (is_res$a @p_546 (! (pair$a veriT_vr80 veriT_vr81) :named @p_665)) :named @p_666) (! (is_res$b (! (run$b (! (c$ veriT_vr80 veriT_vr57) :named @p_668) veriT_vr81) :named @p_670) @p_550) :named @p_671)) :named @p_672)) :named @p_664)) :named @p_673) (! (or @p_549 (! (exists ((veriT_vr82 E$) (veriT_vr83 D$)) (! (and (! (is_res$a @p_547 (! (pair$a veriT_vr82 veriT_vr83) :named @p_675)) :named @p_676) (! (is_res$b (! (run$b (! (c$ veriT_vr82 veriT_vr58) :named @p_678) veriT_vr83) :named @p_680) @p_550) :named @p_681)) :named @p_682)) :named @p_674)) :named @p_683)) :named @p_685)) :named @p_686)) :named @p_638)) :named @p_687)) :named @p_688)) :named @p_574)) :named @p_689)))) :named @p_696)) @@ -11515,6 +10971,1852 @@ (step t468 (cl @p_1652) :rule resolution :premises (t321 t467 t463)) (step t469 (cl @p_1700) :rule resolution :premises (t264 t468 t467)) (step t470 (cl) :rule resolution :premises (t328 t468 t463 t330 t469)) +79bb70ff288db1936aaccee9c58bb4c098292b28 543 0 +unsat +(define-fun veriT_sk0 () Exp$ (! (choice ((veriT_vr40 Exp$)) (not (! (=> (! (member$ veriT_vr40 (! (myset$ z$) :named @p_199)) :named @p_278) (! (not (! (forall ((veriT_vr41 FreeExp$)) (! (not (! (= veriT_vr40 (! (fun_app$ uu$ veriT_vr41) :named @p_281)) :named @p_282)) :named @p_283)) :named @p_279)) :named @p_284)) :named @p_277))) :named @p_201)) +(define-fun veriT_sk1 () FreeExp_list$ (! (choice ((veriT_vr42 FreeExp_list$)) (! (= z$ (! (map2$ uu$ veriT_vr42) :named @p_286)) :named @p_285)) :named @p_301)) +(define-fun veriT_sk2 () FreeExp$ (! (choice ((veriT_vr48 FreeExp$)) (not (! (not (! (= veriT_sk0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ veriT_vr48 bot$) :named @p_356)) :named @p_357)) :named @p_358)) :named @p_359)) :named @p_355))) :named @p_366)) +(assume a0 (! (forall ((?v0 FreeExp$)) (! (= (! (fun_app$ uu$ ?v0) :named @p_3) (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v0 bot$) :named @p_6)) :named @p_8)) :named @p_10)) :named @p_12)) :named @p_2)) +(assume a1 (! (forall ((?v0 FreeExp_list$)) (! (= (! (abs_ExpList$ ?v0) :named @p_1) (! (map2$ uu$ ?v0) :named @p_27)) :named @p_29)) :named @p_24)) +(assume a2 (! (forall ((?v0 Exp$)) (! (=> (! (forall ((?v1 FreeExp$)) (! (=> (! (= ?v0 (! (abs_Exp$ (! (myImage$ exprel$ (! (insert$ ?v1 bot$) :named @p_42)) :named @p_44)) :named @p_46)) :named @p_48) false) :named @p_50)) :named @p_40) false) :named @p_52)) :named @p_39)) +(assume a3 (! (forall ((?v0 Exp_list$) (?v1 FreeExp_exp_fun$)) (! (= (! (exists ((?v2 FreeExp_list$)) (! (= ?v0 (! (map2$ ?v1 ?v2) :named @p_74)) :named @p_76)) :named @p_72) (! (forall ((?v2 Exp$)) (! (=> (! (member$ ?v2 (! (myset$ ?v0) :named @p_81)) :named @p_83) (! (exists ((?v3 FreeExp$)) (! (= ?v2 (! (fun_app$ ?v1 ?v3) :named @p_89)) :named @p_91)) :named @p_85)) :named @p_93)) :named @p_78)) :named @p_95)) :named @p_71)) +(assume a4 (! (not (! (exists ((?v0 FreeExp_list$)) (! (= @p_1 z$) :named @p_178)) :named @p_176)) :named @p_180)) +(anchor :step t6 :args ((:= (?v0 FreeExp$) veriT_vr0))) +(step t6.t1 (cl (! (= ?v0 veriT_vr0) :named @p_5)) :rule refl) +(step t6.t2 (cl (= @p_3 (! (fun_app$ uu$ veriT_vr0) :named @p_4))) :rule cong :premises (t6.t1)) +(step t6.t3 (cl @p_5) :rule refl) +(step t6.t4 (cl (= @p_6 (! (insert$ veriT_vr0 bot$) :named @p_7))) :rule cong :premises (t6.t3)) +(step t6.t5 (cl (= @p_8 (! (myImage$ exprel$ @p_7) :named @p_9))) :rule cong :premises (t6.t4)) +(step t6.t6 (cl (= @p_10 (! (abs_Exp$ @p_9) :named @p_11))) :rule cong :premises (t6.t5)) +(step t6.t7 (cl (= @p_12 (! (= @p_4 @p_11) :named @p_13))) :rule cong :premises (t6.t2 t6.t6)) +(step t6 (cl (! (= @p_2 (! (forall ((veriT_vr0 FreeExp$)) @p_13) :named @p_15)) :named @p_14)) :rule bind) +(step t7 (cl (not @p_14) (not @p_2) @p_15) :rule equiv_pos2) +(step t8 (cl @p_15) :rule th_resolution :premises (a0 t6 t7)) +(anchor :step t9 :args ((:= (veriT_vr0 FreeExp$) veriT_vr1))) +(step t9.t1 (cl (! (= veriT_vr0 veriT_vr1) :named @p_17)) :rule refl) +(step t9.t2 (cl (= @p_4 (! (fun_app$ uu$ veriT_vr1) :named @p_16))) :rule cong :premises (t9.t1)) +(step t9.t3 (cl @p_17) :rule refl) +(step t9.t4 (cl (= @p_7 (! (insert$ veriT_vr1 bot$) :named @p_18))) :rule cong :premises (t9.t3)) +(step t9.t5 (cl (= @p_9 (! (myImage$ exprel$ @p_18) :named @p_19))) :rule cong :premises (t9.t4)) +(step t9.t6 (cl (= @p_11 (! (abs_Exp$ @p_19) :named @p_20))) :rule cong :premises (t9.t5)) +(step t9.t7 (cl (= @p_13 (! (= @p_16 @p_20) :named @p_21))) :rule cong :premises (t9.t2 t9.t6)) +(step t9 (cl (! (= @p_15 (! (forall ((veriT_vr1 FreeExp$)) @p_21) :named @p_23)) :named @p_22)) :rule bind) +(step t10 (cl (not @p_22) (not @p_15) @p_23) :rule equiv_pos2) +(step t11 (cl @p_23) :rule th_resolution :premises (t8 t9 t10)) +(anchor :step t12 :args ((:= (?v0 FreeExp_list$) veriT_vr2))) +(step t12.t1 (cl (! (= ?v0 veriT_vr2) :named @p_26)) :rule refl) +(step t12.t2 (cl (= @p_1 (! (abs_ExpList$ veriT_vr2) :named @p_25))) :rule cong :premises (t12.t1)) +(step t12.t3 (cl @p_26) :rule refl) +(step t12.t4 (cl (= @p_27 (! (map2$ uu$ veriT_vr2) :named @p_28))) :rule cong :premises (t12.t3)) +(step t12.t5 (cl (= @p_29 (! (= @p_25 @p_28) :named @p_30))) :rule cong :premises (t12.t2 t12.t4)) +(step t12 (cl (! (= @p_24 (! (forall ((veriT_vr2 FreeExp_list$)) @p_30) :named @p_32)) :named @p_31)) :rule bind) +(step t13 (cl (not @p_31) (not @p_24) @p_32) :rule equiv_pos2) +(step t14 (cl @p_32) :rule th_resolution :premises (a1 t12 t13)) +(anchor :step t15 :args ((:= (veriT_vr2 FreeExp_list$) veriT_vr3))) +(step t15.t1 (cl (! (= veriT_vr2 veriT_vr3) :named @p_34)) :rule refl) +(step t15.t2 (cl (= @p_25 (! (abs_ExpList$ veriT_vr3) :named @p_33))) :rule cong :premises (t15.t1)) +(step t15.t3 (cl @p_34) :rule refl) +(step t15.t4 (cl (= @p_28 (! (map2$ uu$ veriT_vr3) :named @p_35))) :rule cong :premises (t15.t3)) +(step t15.t5 (cl (= @p_30 (! (= @p_33 @p_35) :named @p_36))) :rule cong :premises (t15.t2 t15.t4)) +(step t15 (cl (! (= @p_32 (! (forall ((veriT_vr3 FreeExp_list$)) @p_36) :named @p_38)) :named @p_37)) :rule bind) +(step t16 (cl (not @p_37) (not @p_32) @p_38) :rule equiv_pos2) +(step t17 (cl @p_38) :rule th_resolution :premises (t14 t15 t16)) +(anchor :step t18 :args ((:= (?v0 Exp$) veriT_vr4))) +(anchor :step t18.t1 :args ((:= (?v1 FreeExp$) veriT_vr5))) +(step t18.t1.t1 (cl (= ?v0 veriT_vr4)) :rule refl) +(step t18.t1.t2 (cl (= ?v1 veriT_vr5)) :rule refl) +(step t18.t1.t3 (cl (= @p_42 (! (insert$ veriT_vr5 bot$) :named @p_43))) :rule cong :premises (t18.t1.t2)) +(step t18.t1.t4 (cl (= @p_44 (! (myImage$ exprel$ @p_43) :named @p_45))) :rule cong :premises (t18.t1.t3)) +(step t18.t1.t5 (cl (= @p_46 (! (abs_Exp$ @p_45) :named @p_47))) :rule cong :premises (t18.t1.t4)) +(step t18.t1.t6 (cl (= @p_48 (! (= veriT_vr4 @p_47) :named @p_49))) :rule cong :premises (t18.t1.t1 t18.t1.t5)) +(step t18.t1.t7 (cl (= @p_50 (! (=> @p_49 false) :named @p_51))) :rule cong :premises (t18.t1.t6)) +(step t18.t1 (cl (= @p_40 (! (forall ((veriT_vr5 FreeExp$)) @p_51) :named @p_41))) :rule bind) +(step t18.t2 (cl (= @p_52 (! (=> @p_41 false) :named @p_53))) :rule cong :premises (t18.t1)) +(step t18 (cl (! (= @p_39 (! (forall ((veriT_vr4 Exp$)) @p_53) :named @p_55)) :named @p_54)) :rule bind) +(step t19 (cl (not @p_54) (not @p_39) @p_55) :rule equiv_pos2) +(step t20 (cl @p_55) :rule th_resolution :premises (a2 t18 t19)) +(anchor :step t21 :args ((veriT_vr4 Exp$))) +(anchor :step t21.t1 :args ((veriT_vr5 FreeExp$))) +(step t21.t1.t1 (cl (= @p_51 (! (not @p_49) :named @p_57))) :rule implies_simplify) +(step t21.t1 (cl (= @p_41 (! (forall ((veriT_vr5 FreeExp$)) @p_57) :named @p_56))) :rule bind) +(step t21.t2 (cl (= @p_53 (! (=> @p_56 false) :named @p_58))) :rule cong :premises (t21.t1)) +(step t21.t3 (cl (= @p_58 (! (not @p_56) :named @p_59))) :rule implies_simplify) +(step t21.t4 (cl (= @p_53 @p_59)) :rule trans :premises (t21.t2 t21.t3)) +(step t21 (cl (! (= @p_55 (! (forall ((veriT_vr4 Exp$)) @p_59) :named @p_61)) :named @p_60)) :rule bind) +(step t22 (cl (not @p_60) (not @p_55) @p_61) :rule equiv_pos2) +(step t23 (cl @p_61) :rule th_resolution :premises (t20 t21 t22)) +(anchor :step t24 :args ((:= (veriT_vr4 Exp$) veriT_vr6))) +(anchor :step t24.t1 :args ((:= (veriT_vr5 FreeExp$) veriT_vr7))) +(step t24.t1.t1 (cl (= veriT_vr4 veriT_vr6)) :rule refl) +(step t24.t1.t2 (cl (= veriT_vr5 veriT_vr7)) :rule refl) +(step t24.t1.t3 (cl (= @p_43 (! (insert$ veriT_vr7 bot$) :named @p_63))) :rule cong :premises (t24.t1.t2)) +(step t24.t1.t4 (cl (= @p_45 (! (myImage$ exprel$ @p_63) :named @p_64))) :rule cong :premises (t24.t1.t3)) +(step t24.t1.t5 (cl (= @p_47 (! (abs_Exp$ @p_64) :named @p_65))) :rule cong :premises (t24.t1.t4)) +(step t24.t1.t6 (cl (= @p_49 (! (= veriT_vr6 @p_65) :named @p_66))) :rule cong :premises (t24.t1.t1 t24.t1.t5)) +(step t24.t1.t7 (cl (= @p_57 (! (not @p_66) :named @p_67))) :rule cong :premises (t24.t1.t6)) +(step t24.t1 (cl (= @p_56 (! (forall ((veriT_vr7 FreeExp$)) @p_67) :named @p_62))) :rule bind) +(step t24.t2 (cl (= @p_59 (! (not @p_62) :named @p_68))) :rule cong :premises (t24.t1)) +(step t24 (cl (! (= @p_61 (! (forall ((veriT_vr6 Exp$)) @p_68) :named @p_70)) :named @p_69)) :rule bind) +(step t25 (cl (not @p_69) (not @p_61) @p_70) :rule equiv_pos2) +(step t26 (cl @p_70) :rule th_resolution :premises (t23 t24 t25)) +(anchor :step t27 :args ((:= (?v0 Exp_list$) veriT_vr8) (:= (?v1 FreeExp_exp_fun$) veriT_vr9))) +(anchor :step t27.t1 :args ((:= (?v2 FreeExp_list$) veriT_vr10))) +(step t27.t1.t1 (cl (! (= ?v0 veriT_vr8) :named @p_80)) :rule refl) +(step t27.t1.t2 (cl (! (= ?v1 veriT_vr9) :named @p_88)) :rule refl) +(step t27.t1.t3 (cl (= ?v2 veriT_vr10)) :rule refl) +(step t27.t1.t4 (cl (= @p_74 (! (map2$ veriT_vr9 veriT_vr10) :named @p_75))) :rule cong :premises (t27.t1.t2 t27.t1.t3)) +(step t27.t1.t5 (cl (= @p_76 (! (= veriT_vr8 @p_75) :named @p_77))) :rule cong :premises (t27.t1.t1 t27.t1.t4)) +(step t27.t1 (cl (= @p_72 (! (exists ((veriT_vr10 FreeExp_list$)) @p_77) :named @p_73))) :rule bind) +(anchor :step t27.t2 :args ((:= (?v2 Exp$) veriT_vr11))) +(step t27.t2.t1 (cl (! (= ?v2 veriT_vr11) :named @p_87)) :rule refl) +(step t27.t2.t2 (cl @p_80) :rule refl) +(step t27.t2.t3 (cl (= @p_81 (! (myset$ veriT_vr8) :named @p_82))) :rule cong :premises (t27.t2.t2)) +(step t27.t2.t4 (cl (= @p_83 (! (member$ veriT_vr11 @p_82) :named @p_84))) :rule cong :premises (t27.t2.t1 t27.t2.t3)) +(anchor :step t27.t2.t5 :args ((:= (?v3 FreeExp$) veriT_vr12))) +(step t27.t2.t5.t1 (cl @p_87) :rule refl) +(step t27.t2.t5.t2 (cl @p_88) :rule refl) +(step t27.t2.t5.t3 (cl (= ?v3 veriT_vr12)) :rule refl) +(step t27.t2.t5.t4 (cl (= @p_89 (! (fun_app$ veriT_vr9 veriT_vr12) :named @p_90))) :rule cong :premises (t27.t2.t5.t2 t27.t2.t5.t3)) +(step t27.t2.t5.t5 (cl (= @p_91 (! (= veriT_vr11 @p_90) :named @p_92))) :rule cong :premises (t27.t2.t5.t1 t27.t2.t5.t4)) +(step t27.t2.t5 (cl (= @p_85 (! (exists ((veriT_vr12 FreeExp$)) @p_92) :named @p_86))) :rule bind) +(step t27.t2.t6 (cl (= @p_93 (! (=> @p_84 @p_86) :named @p_94))) :rule cong :premises (t27.t2.t4 t27.t2.t5)) +(step t27.t2 (cl (= @p_78 (! (forall ((veriT_vr11 Exp$)) @p_94) :named @p_79))) :rule bind) +(step t27.t3 (cl (= @p_95 (! (= @p_73 @p_79) :named @p_96))) :rule cong :premises (t27.t1 t27.t2)) +(step t27 (cl (! (= @p_71 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_96) :named @p_98)) :named @p_97)) :rule bind) +(step t28 (cl (not @p_97) (not @p_71) @p_98) :rule equiv_pos2) +(step t29 (cl @p_98) :rule th_resolution :premises (a3 t27 t28)) +(anchor :step t30 :args ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$))) +(step t30.t1 (cl (= @p_96 (! (and (! (=> @p_73 @p_79) :named @p_115) (! (=> @p_79 @p_73) :named @p_128)) :named @p_99))) :rule connective_def) +(step t30 (cl (! (= @p_98 (! (forall ((veriT_vr8 Exp_list$) (veriT_vr9 FreeExp_exp_fun$)) @p_99) :named @p_101)) :named @p_100)) :rule bind) +(step t31 (cl (not @p_100) (not @p_98) @p_101) :rule equiv_pos2) +(step t32 (cl @p_101) :rule th_resolution :premises (t29 t30 t31)) +(anchor :step t33 :args ((:= (veriT_vr8 Exp_list$) veriT_vr13) (:= (veriT_vr9 FreeExp_exp_fun$) veriT_vr14))) +(anchor :step t33.t1 :args ((:= (veriT_vr10 FreeExp_list$) veriT_vr15))) +(step t33.t1.t1 (cl (! (= veriT_vr8 veriT_vr13) :named @p_107)) :rule refl) +(step t33.t1.t2 (cl (! (= veriT_vr9 veriT_vr14) :named @p_111)) :rule refl) +(step t33.t1.t3 (cl (= veriT_vr10 veriT_vr15)) :rule refl) +(step t33.t1.t4 (cl (= @p_75 (! (map2$ veriT_vr14 veriT_vr15) :named @p_104))) :rule cong :premises (t33.t1.t2 t33.t1.t3)) +(step t33.t1.t5 (cl (= @p_77 (! (= veriT_vr13 @p_104) :named @p_105))) :rule cong :premises (t33.t1.t1 t33.t1.t4)) +(step t33.t1 (cl (= @p_73 (! (exists ((veriT_vr15 FreeExp_list$)) @p_105) :named @p_103))) :rule bind) +(anchor :step t33.t2 :args ((:= (veriT_vr11 Exp$) veriT_vr16))) +(step t33.t2.t1 (cl (! (= veriT_vr11 veriT_vr16) :named @p_110)) :rule refl) +(step t33.t2.t2 (cl @p_107) :rule refl) +(step t33.t2.t3 (cl (! (= @p_82 (! (myset$ veriT_vr13) :named @p_102)) :named @p_118)) :rule cong :premises (t33.t2.t2)) +(step t33.t2.t4 (cl (= @p_84 (! (member$ veriT_vr16 @p_102) :named @p_108))) :rule cong :premises (t33.t2.t1 t33.t2.t3)) +(anchor :step t33.t2.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr17))) +(step t33.t2.t5.t1 (cl @p_110) :rule refl) +(step t33.t2.t5.t2 (cl @p_111) :rule refl) +(step t33.t2.t5.t3 (cl (= veriT_vr12 veriT_vr17)) :rule refl) +(step t33.t2.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr17) :named @p_112))) :rule cong :premises (t33.t2.t5.t2 t33.t2.t5.t3)) +(step t33.t2.t5.t5 (cl (= @p_92 (! (= veriT_vr16 @p_112) :named @p_113))) :rule cong :premises (t33.t2.t5.t1 t33.t2.t5.t4)) +(step t33.t2.t5 (cl (= @p_86 (! (exists ((veriT_vr17 FreeExp$)) @p_113) :named @p_109))) :rule bind) +(step t33.t2.t6 (cl (= @p_94 (! (=> @p_108 @p_109) :named @p_114))) :rule cong :premises (t33.t2.t4 t33.t2.t5)) +(step t33.t2 (cl (= @p_79 (! (forall ((veriT_vr16 Exp$)) @p_114) :named @p_106))) :rule bind) +(step t33.t3 (cl (= @p_115 (! (=> @p_103 @p_106) :named @p_116))) :rule cong :premises (t33.t1 t33.t2)) +(anchor :step t33.t4 :args ((:= (veriT_vr11 Exp$) veriT_vr18))) +(step t33.t4.t1 (cl (! (= veriT_vr11 veriT_vr18) :named @p_121)) :rule refl) +(step t33.t4.t2 (cl @p_107) :rule refl) +(step t33.t4.t3 (cl @p_118) :rule cong :premises (t33.t4.t2)) +(step t33.t4.t4 (cl (= @p_84 (! (member$ veriT_vr18 @p_102) :named @p_119))) :rule cong :premises (t33.t4.t1 t33.t4.t3)) +(anchor :step t33.t4.t5 :args ((:= (veriT_vr12 FreeExp$) veriT_vr19))) +(step t33.t4.t5.t1 (cl @p_121) :rule refl) +(step t33.t4.t5.t2 (cl @p_111) :rule refl) +(step t33.t4.t5.t3 (cl (= veriT_vr12 veriT_vr19)) :rule refl) +(step t33.t4.t5.t4 (cl (= @p_90 (! (fun_app$ veriT_vr14 veriT_vr19) :named @p_122))) :rule cong :premises (t33.t4.t5.t2 t33.t4.t5.t3)) +(step t33.t4.t5.t5 (cl (= @p_92 (! (= veriT_vr18 @p_122) :named @p_123))) :rule cong :premises (t33.t4.t5.t1 t33.t4.t5.t4)) +(step t33.t4.t5 (cl (= @p_86 (! (exists ((veriT_vr19 FreeExp$)) @p_123) :named @p_120))) :rule bind) +(step t33.t4.t6 (cl (= @p_94 (! (=> @p_119 @p_120) :named @p_124))) :rule cong :premises (t33.t4.t4 t33.t4.t5)) +(step t33.t4 (cl (= @p_79 (! 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(forall ((veriT_vr13 Exp_list$) (veriT_vr14 FreeExp_exp_fun$)) @p_130) :named @p_132)) :named @p_131)) :rule bind) +(step t34 (cl (not @p_131) (not @p_101) @p_132) :rule equiv_pos2) +(step t35 (cl @p_132) :rule th_resolution :premises (t32 t33 t34)) +(anchor :step t36 :args ((:= (veriT_vr13 Exp_list$) veriT_vr21) (:= (veriT_vr14 FreeExp_exp_fun$) veriT_vr22))) +(anchor :step t36.t1 :args ((:= (veriT_vr15 FreeExp_list$) veriT_vr23))) +(step t36.t1.t1 (cl (! (= veriT_vr13 veriT_vr21) :named @p_137)) :rule refl) +(step t36.t1.t2 (cl (! (= veriT_vr14 veriT_vr22) :named @p_142)) :rule refl) +(step t36.t1.t3 (cl (= veriT_vr15 veriT_vr23)) :rule refl) +(step t36.t1.t4 (cl (= @p_104 (! (map2$ veriT_vr22 veriT_vr23) :named @p_135))) :rule cong :premises (t36.t1.t2 t36.t1.t3)) +(step t36.t1.t5 (cl (= @p_105 (! (= veriT_vr21 @p_135) :named @p_136))) :rule cong :premises (t36.t1.t1 t36.t1.t4)) +(step t36.t1 (cl (= @p_103 (! 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(not @p_180) :named @p_184) @p_183) :rule equiv_pos2) +(step t48 (cl (not @p_184) @p_176) :rule not_not) +(step t49 (cl @p_185 @p_176 @p_183) :rule th_resolution :premises (t48 t47)) +(step t50 (cl @p_183) :rule th_resolution :premises (a4 t46 t49)) +(anchor :step t51 :args ((:= (veriT_vr29 FreeExp_list$) veriT_vr30))) +(step t51.t1 (cl (= veriT_vr29 veriT_vr30)) :rule refl) +(step t51.t2 (cl (= @p_177 (! (abs_ExpList$ veriT_vr30) :named @p_186))) :rule cong :premises (t51.t1)) +(step t51.t3 (cl (= @p_179 (! (= z$ @p_186) :named @p_187))) :rule cong :premises (t51.t2)) +(step t51 (cl (= @p_181 (! (exists ((veriT_vr30 FreeExp_list$)) @p_187) :named @p_188))) :rule bind) +(step t52 (cl (! (= @p_183 (! (not @p_188) :named @p_190)) :named @p_189)) :rule cong :premises (t51)) +(step t53 (cl (! (not @p_189) :named @p_192) (! (not @p_183) :named @p_191) @p_190) :rule equiv_pos2) +(step t54 (cl (not @p_191) @p_181) :rule not_not) +(step t55 (cl @p_192 @p_181 @p_190) :rule th_resolution :premises (t54 t53)) +(step t56 (cl @p_190) :rule th_resolution :premises (t50 t52 t55)) +(step t57 (cl (= @p_188 (! (not (! (forall ((veriT_vr30 FreeExp_list$)) (not @p_187)) :named @p_198)) :named @p_193))) :rule connective_def) +(step t58 (cl (! (= @p_190 (! (not @p_193) :named @p_195)) :named @p_194)) :rule cong :premises (t57)) +(step t59 (cl (! (not @p_194) :named @p_197) (! (not @p_190) :named @p_196) @p_195) :rule equiv_pos2) +(step t60 (cl (not @p_196) @p_188) :rule not_not) +(step t61 (cl @p_197 @p_188 @p_195) :rule th_resolution :premises (t60 t59)) +(step t62 (cl (not @p_195) @p_198) :rule not_not) +(step t63 (cl @p_197 @p_188 @p_198) :rule th_resolution :premises (t62 t61)) +(step t64 (cl @p_195) :rule th_resolution :premises (t56 t58 t63)) +(step t65 (cl @p_198) :rule th_resolution :premises (t62 t64)) +(step t66 (cl (or (! (not @p_175) :named @p_336) (! (and (! (=> (! (not (! (forall ((veriT_vr23 FreeExp_list$)) (! (not (! (= z$ (! (map2$ uu$ veriT_vr23) :named @p_203)) :named @p_205)) :named @p_207)) :named @p_202)) :named @p_209) (! (forall ((veriT_vr24 Exp$)) (! (=> (! (member$ veriT_vr24 @p_199) :named @p_212) (! (exists ((veriT_vr25 FreeExp$)) (! (= veriT_vr24 (! (fun_app$ uu$ veriT_vr25) :named @p_217)) :named @p_219)) :named @p_214)) :named @p_221)) :named @p_211)) :named @p_223) (! (=> (! (forall ((veriT_vr26 Exp$)) (! (=> (! 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(= @p_369 @p_381) :named @p_387))) :rule forall_inst :args ((:= veriT_vr1 veriT_sk2))) +(step t98 (cl @p_331 @p_382) :rule or :premises (t94)) +(step t99 (cl @p_193 @p_383) :rule or :premises (t95)) +(step t100 (cl @p_383) :rule resolution :premises (t99 t65)) +(step t101 (cl @p_384 @p_385) :rule or :premises (t96)) +(step t102 (cl @p_385) :rule resolution :premises (t101 t17)) +(step t103 (cl @p_386 @p_387) :rule or :premises (t97)) +(step t104 (cl @p_387) :rule resolution :premises (t103 t11)) +(step t105 (cl (! (= z$ z$) :named @p_388)) :rule eq_reflexive) +(step t106 (cl (not @p_388) (! (not @p_300) :named @p_390) (! (not @p_385) :named @p_391) @p_389) :rule eq_transitive) +(step t107 (cl @p_390 @p_391 @p_389) :rule th_resolution :premises (t106 t105)) +(step t108 (cl @p_390) :rule resolution :premises (t107 t100 t102)) +(step t109 (cl @p_370 (not @p_387) @p_392) :rule eq_transitive) +(step t110 (cl @p_392) :rule resolution :premises (t109 t93 t104)) +(step t111 (cl @p_393) :rule resolution :premises (t77 t108 t81)) +(step t112 (cl @p_331) :rule resolution :premises (t98 t110)) +(step t113 (cl) :rule resolution :premises (t76 t111 t112)) +2536758f543bcfd0058986403f6d9a8774a2224b 1301 0 +unsat +(define-fun veriT_sk0 () Afset$ (! (choice ((veriT_vr43 Afset$)) (not (forall ((veriT_vr44 Afset$) (veriT_vr45 Afset$)) (! (not (! (and (! (= s2$ (! (pair$ veriT_vr43 veriT_vr44) :named @p_535)) :named @p_536) (! (= s3$ (! (pair$ veriT_vr45 veriT_vr44) :named @p_538)) :named @p_451) (! (= const2$ const3$) :named @p_249) (! (forall ((veriT_vr46 A$)) (! (=> (! (member$ veriT_vr46 (! (fun_app$ fset$ veriT_vr43) :named @p_541)) :named @p_542) (! (exists ((veriT_vr47 A$)) (! (and (! (member$ veriT_vr47 (! (fun_app$ fset$ (! (fun_app$a (! (fun_app$b union_fset$ const3$) :named @p_447) (! (fun_app$a (! (fun_app$b union_fset$ veriT_vr45) :named @p_457) veriT_vr44) :named @p_545)) :named @p_546)) :named @p_448)) :named @p_452) (! (exists ((veriT_vr48 A$)) (! (and (! (member$ veriT_vr48 @p_448) :named @p_453) (! (or (! (and (! (tranclp$ (! (fun_app$c ground_resolution$ veriT_vr48) :named @p_449) veriT_vr47 veriT_vr46) :named @p_555) (! (exists ((veriT_vr49 A$)) (! (and (! (member$ veriT_vr49 (! (fun_app$ fset$ veriT_vr45) :named @p_557)) :named @p_558) (! (rtranclp$ @p_449 veriT_vr46 veriT_vr49) :named @p_561)) :named @p_562)) :named @p_556)) :named @p_454) (! (fun_app$d (! (fun_app$e is_least_false_clause$ (! (fun_app$a (! (fun_app$b union_fset$ const2$) :named @p_244) (! (fun_app$a (! (fun_app$b union_fset$ veriT_vr43) :named @p_563) veriT_vr44) :named @p_564)) :named @p_565)) :named @p_566) veriT_vr46) :named @p_567)) :named @p_568)) :named @p_569)) :named @p_547)) :named @p_570)) :named @p_543)) :named @p_571)) :named @p_539)) :named @p_572)) :named @p_534)))) :named @p_450)) +(define-fun veriT_sk1 () Afset$ (! (choice ((veriT_vr44 Afset$)) (not (forall ((veriT_vr45 Afset$)) (not (and (= s2$ (pair$ @p_450 veriT_vr44)) @p_451 @p_249 (forall ((veriT_vr46 A$)) (=> (! (member$ veriT_vr46 (fun_app$ fset$ @p_450)) :named @p_456) (exists ((veriT_vr47 A$)) (and @p_452 (exists ((veriT_vr48 A$)) (and @p_453 (or @p_454 (fun_app$d (fun_app$e is_least_false_clause$ (fun_app$a @p_244 (fun_app$a (! (fun_app$b union_fset$ @p_450) :named @p_459) veriT_vr44))) veriT_vr46))))))))))))) :named @p_455)) +(define-fun veriT_sk2 () Afset$ (! (choice ((veriT_vr45 Afset$)) (not (not (and (= s2$ (pair$ @p_450 @p_455)) (= s3$ (pair$ veriT_vr45 @p_455)) @p_249 (forall ((veriT_vr46 A$)) (=> @p_456 (exists ((veriT_vr47 A$)) (and (member$ veriT_vr47 (! (fun_app$ fset$ (fun_app$a @p_447 (fun_app$a @p_457 @p_455))) :named @p_458)) (exists ((veriT_vr48 A$)) (and (member$ veriT_vr48 @p_458) (or @p_454 (fun_app$d (fun_app$e is_least_false_clause$ (fun_app$a @p_244 (fun_app$a @p_459 @p_455))) veriT_vr46)))))))))))) :named @p_460)) +(define-fun veriT_sk6 () A$ (! (choice ((veriT_vr91 A$)) (not (! (=> (! (member$ veriT_vr91 (! (fun_app$ fset$ veriT_sk0) :named @p_581)) :named @p_719) (! (not (! (forall ((veriT_vr92 A$)) (! (not (! (and (! (member$ veriT_vr92 (! (fun_app$ fset$ (! (fun_app$a @p_244 (! (fun_app$a (! (fun_app$b union_fset$ veriT_sk2) :named @p_592) veriT_sk1) :named @p_593)) :named @p_1010)) :named @p_658)) :named @p_721) (! (not (! (forall ((veriT_vr93 A$)) (! (not (! (and (! (member$ veriT_vr93 @p_658) :named @p_723) (! (or (! (and (! (tranclp$ (! (fun_app$c ground_resolution$ veriT_vr93) :named @p_660) veriT_vr92 veriT_vr91) :named @p_727) (! (not (! (forall ((veriT_vr94 A$)) (! (not (! (and (! (member$ veriT_vr94 (! (fun_app$ fset$ veriT_sk2) :named @p_582)) :named @p_729) (! (rtranclp$ @p_660 veriT_vr91 veriT_vr94) :named @p_732)) :named @p_733)) :named @p_734)) :named @p_728)) :named @p_735)) :named @p_736) (! (fun_app$d (! (fun_app$e is_least_false_clause$ (! (fun_app$a @p_244 (! (fun_app$a (! (fun_app$b union_fset$ veriT_sk0) :named @p_606) veriT_sk1) :named @p_607)) :named @p_608)) :named @p_583) veriT_vr91) :named @p_737)) :named @p_738)) :named @p_739)) :named @p_740)) :named @p_722)) :named @p_741)) :named @p_742)) :named @p_743)) :named @p_720)) :named @p_744)) :named @p_718))) :named @p_661)) +(define-fun veriT_sk10 () A$ (! (choice ((veriT_vr107 A$)) (! (and (! (member$ veriT_vr107 (! (fun_app$ fset$ (! (fun_app$a @p_447 @p_593) :named @p_594)) :named @p_461)) :named @p_847) (! (exists ((veriT_vr108 A$)) (! (and (! (member$ veriT_vr108 @p_461) :named @p_808) (! (or (! (and (! (tranclp$ (! (fun_app$c ground_resolution$ veriT_vr108) :named @p_807) veriT_vr107 veriT_sk6) :named @p_851) (! (exists ((veriT_vr109 A$)) (! (and (! (member$ veriT_vr109 @p_582) :named @p_812) (! (rtranclp$ @p_807 veriT_sk6 veriT_vr109) :named @p_854)) :named @p_855)) :named @p_810)) :named @p_856) (! (fun_app$d @p_583 veriT_sk6) :named @p_750)) :named @p_857)) :named @p_858)) :named @p_848)) :named @p_846)) :named @p_809)) +(define-fun veriT_sk11 () A$ (! (choice ((veriT_vr108 A$)) (and @p_808 (or (and (tranclp$ @p_807 @p_809 veriT_sk6) @p_810) @p_750))) :named @p_811)) +(define-fun veriT_sk12 () A$ (! (choice ((veriT_vr109 A$)) (and @p_812 (rtranclp$ (fun_app$c ground_resolution$ @p_811) veriT_sk6 veriT_vr109))) :named @p_814)) +(assume a0 (! (forall ((?v0 Afset$) (?v1 Afset_afset_prod$) (?v2 Afset$) (?v3 Afset_afset_prod$)) (! (=> (! (and (! (l2_matches_L3$ ground_resolution$ is_least_false_clause$ fset$ union_fset$ ?v0 ?v1 ?v2 ?v3) :named @p_7) (! (forall ((?v4 Afset$) (?v5 Afset$) (?v6 Afset$) (?v7 Afset$) (?v8 Afset$) (?v9 Afset$)) (! (=> (! (and (! (= ?v0 ?v4) :named @p_16) (! (and (! (= ?v1 (! (pair$ ?v5 ?v6) :named @p_90)) :named @p_8) (! (and (! (= ?v2 ?v7) :named @p_18) (! (and (! (= ?v3 (! (pair$ ?v8 ?v9) :named @p_21)) :named @p_23) (! (and (! (= ?v4 ?v7) :named @p_25) (! (and (! (= ?v6 ?v9) :named @p_20) (! (forall ((?v10 A$)) (! (=> (! (member$ ?v10 (! (fun_app$ fset$ ?v5) :named @p_103)) :named @p_9) (! (exists ((?v11 A$)) (! (and (! (member$ ?v11 (! (fun_app$ fset$ (! (fun_app$a (! (fun_app$b union_fset$ ?v7) :named @p_32) (! (fun_app$a (! (fun_app$b union_fset$ ?v8) :named @p_10) ?v9) :named @p_34)) :named @p_36)) :named @p_1)) :named @p_38) (! (exists ((?v12 A$)) (! (and (! (member$ ?v12 @p_1) :named @p_46) (! (or (! (and (! (tranclp$ (! 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(forall ((?v0 Afset$) (?v1 Afset$) (?v2 Afset$) (?v3 Afset$)) (! (=> (! (and (! (= ?v0 const2$) :named @p_246) (! (and (! (= ?v0 const3$) :named @p_248) (! (and (! (= s2$ (! (pair$ ?v1 ?v2) :named @p_299)) :named @p_238) (! (and (! (= s3$ (! (pair$ ?v3 ?v2) :named @p_303)) :named @p_239) (! (forall ((?v4 A$)) (! (=> (! (member$ ?v4 (! (fun_app$ fset$ ?v1) :named @p_308)) :named @p_240) (! (exists ((?v5 A$)) (! (and (! (member$ ?v5 (! (fun_app$ fset$ (! (fun_app$a (! (fun_app$b union_fset$ ?v0) :named @p_5) (! (fun_app$a (! (fun_app$b union_fset$ ?v3) :named @p_313) ?v2) :named @p_241)) :named @p_254)) :named @p_3)) :named @p_256) (! (exists ((?v6 A$)) (! (and (! (member$ ?v6 @p_3) :named @p_263) (! (or (! (and (! (tranclp$ (! (fun_app$c ground_resolution$ ?v6) :named @p_4) ?v5 ?v4) :named @p_327) (! (exists ((?v7 A$)) (! (and (! (member$ ?v7 (! (fun_app$ fset$ ?v3) :named @p_331)) :named @p_333) (! 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(and @p_376 @p_370) :named @p_378)) :named @p_377)) :rule cong :premises (t42)) +(step t44 (cl (not @p_377) (not @p_372) @p_378) :rule equiv_pos2) +(step t45 (cl @p_378) :rule th_resolution :premises (t41 t43 t44)) +(anchor :step t46 :args ((:= (veriT_vr22 Afset$) veriT_vr29) (:= (veriT_vr23 Afset$) veriT_vr30) (:= (veriT_vr24 Afset$) veriT_vr31))) +(step t46.t1 (cl (! (= veriT_vr22 veriT_vr29) :named @p_387)) :rule refl) +(step t46.t2 (cl (! (= veriT_vr23 veriT_vr30) :named @p_383)) :rule refl) +(step t46.t3 (cl (= @p_300 (! (pair$ veriT_vr29 veriT_vr30) :named @p_381))) :rule cong :premises (t46.t1 t46.t2)) +(step t46.t4 (cl (= @p_301 (! (= s2$ @p_381) :named @p_382))) :rule cong :premises (t46.t3)) +(step t46.t5 (cl (! (= veriT_vr24 veriT_vr31) :named @p_391)) :rule refl) +(step t46.t6 (cl @p_383) :rule refl) +(step t46.t7 (cl (= @p_304 (! (pair$ veriT_vr31 veriT_vr30) :named @p_384))) :rule cong :premises (t46.t5 t46.t6)) +(step t46.t8 (cl (= @p_305 (! (= s3$ @p_384) :named @p_385))) :rule cong :premises (t46.t7)) +(anchor :step t46.t9 :args ((:= (veriT_vr25 A$) veriT_vr32))) +(step t46.t9.t1 (cl (! (= veriT_vr25 veriT_vr32) :named @p_404)) :rule refl) +(step t46.t9.t2 (cl @p_387) :rule refl) +(step t46.t9.t3 (cl (= @p_309 (! (fun_app$ fset$ veriT_vr29) :named @p_388))) :rule cong :premises (t46.t9.t2)) +(step t46.t9.t4 (cl (= @p_310 (! (member$ veriT_vr32 @p_388) :named @p_389))) :rule cong :premises (t46.t9.t1 t46.t9.t3)) +(anchor :step t46.t9.t5 :args ((:= (veriT_vr26 A$) veriT_vr33))) +(step t46.t9.t5.t1 (cl (! (= veriT_vr26 veriT_vr33) :named @p_403)) :rule refl) +(step t46.t9.t5.t2 (cl @p_391) :rule refl) +(step t46.t9.t5.t3 (cl (! (= @p_314 (! (fun_app$b union_fset$ veriT_vr31) :named @p_392)) :named @p_397)) :rule cong :premises (t46.t9.t5.t2)) +(step t46.t9.t5.t4 (cl @p_383) :rule refl) +(step t46.t9.t5.t5 (cl (! (= @p_315 (! (fun_app$a @p_392 veriT_vr30) :named @p_393)) :named @p_398)) :rule cong :premises (t46.t9.t5.t3 t46.t9.t5.t4)) +(step t46.t9.t5.t6 (cl (! (= @p_316 (! (fun_app$a @p_244 @p_393) :named @p_394)) :named @p_399)) :rule cong :premises (t46.t9.t5.t5)) +(step t46.t9.t5.t7 (cl (! (= @p_297 (! (fun_app$ fset$ @p_394) :named @p_379)) :named @p_400)) :rule cong :premises (t46.t9.t5.t6)) +(step t46.t9.t5.t8 (cl (= @p_317 (! (member$ veriT_vr33 @p_379) :named @p_395))) :rule cong :premises (t46.t9.t5.t1 t46.t9.t5.t7)) +(anchor :step t46.t9.t5.t9 :args ((:= (veriT_vr27 A$) veriT_vr34))) +(step t46.t9.t5.t9.t1 (cl (! (= veriT_vr27 veriT_vr34) :named @p_402)) :rule refl) +(step t46.t9.t5.t9.t2 (cl @p_391) :rule refl) +(step t46.t9.t5.t9.t3 (cl @p_397) :rule cong :premises (t46.t9.t5.t9.t2)) +(step t46.t9.t5.t9.t4 (cl @p_383) :rule refl) +(step t46.t9.t5.t9.t5 (cl @p_398) :rule cong :premises (t46.t9.t5.t9.t3 t46.t9.t5.t9.t4)) +(step t46.t9.t5.t9.t6 (cl @p_399) :rule cong :premises (t46.t9.t5.t9.t5)) +(step t46.t9.t5.t9.t7 (cl @p_400) :rule cong :premises (t46.t9.t5.t9.t6)) +(step t46.t9.t5.t9.t8 (cl (= @p_323 (! (member$ veriT_vr34 @p_379) :named @p_401))) :rule cong :premises (t46.t9.t5.t9.t1 t46.t9.t5.t9.t7)) +(step t46.t9.t5.t9.t9 (cl @p_402) :rule refl) +(step t46.t9.t5.t9.t10 (cl (! (= @p_298 (! (fun_app$c ground_resolution$ veriT_vr34) :named @p_380)) :named @p_409)) :rule cong :premises (t46.t9.t5.t9.t9)) +(step t46.t9.t5.t9.t11 (cl @p_403) :rule refl) +(step t46.t9.t5.t9.t12 (cl @p_404) :rule refl) +(step t46.t9.t5.t9.t13 (cl (= @p_328 (! (tranclp$ @p_380 veriT_vr33 veriT_vr32) :named @p_405))) :rule cong :premises (t46.t9.t5.t9.t10 t46.t9.t5.t9.t11 t46.t9.t5.t9.t12)) +(anchor :step t46.t9.t5.t9.t14 :args ((:= (veriT_vr28 A$) veriT_vr35))) +(step t46.t9.t5.t9.t14.t1 (cl (! (= veriT_vr28 veriT_vr35) :named @p_410)) :rule refl) +(step t46.t9.t5.t9.t14.t2 (cl @p_391) :rule refl) +(step t46.t9.t5.t9.t14.t3 (cl (= @p_332 (! (fun_app$ fset$ veriT_vr31) :named @p_407))) :rule cong :premises (t46.t9.t5.t9.t14.t2)) +(step t46.t9.t5.t9.t14.t4 (cl (= @p_334 (! (member$ veriT_vr35 @p_407) :named @p_408))) :rule cong :premises (t46.t9.t5.t9.t14.t1 t46.t9.t5.t9.t14.t3)) +(step t46.t9.t5.t9.t14.t5 (cl @p_402) :rule refl) +(step t46.t9.t5.t9.t14.t6 (cl @p_409) :rule cong :premises (t46.t9.t5.t9.t14.t5)) +(step t46.t9.t5.t9.t14.t7 (cl @p_404) :rule refl) +(step t46.t9.t5.t9.t14.t8 (cl @p_410) :rule refl) +(step t46.t9.t5.t9.t14.t9 (cl (= @p_338 (! 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(fun_app$a @p_244 @p_415) :named @p_416))) :rule cong :premises (t46.t9.t5.t9.t19)) +(step t46.t9.t5.t9.t21 (cl (= @p_346 (! (fun_app$e is_least_false_clause$ @p_416) :named @p_417))) :rule cong :premises (t46.t9.t5.t9.t20)) +(step t46.t9.t5.t9.t22 (cl @p_404) :rule refl) +(step t46.t9.t5.t9.t23 (cl (= @p_347 (! (fun_app$d @p_417 veriT_vr32) :named @p_418))) :rule cong :premises (t46.t9.t5.t9.t21 t46.t9.t5.t9.t22)) +(step t46.t9.t5.t9.t24 (cl (= @p_348 (! (or @p_413 @p_418) :named @p_419))) :rule cong :premises (t46.t9.t5.t9.t15 t46.t9.t5.t9.t23)) +(step t46.t9.t5.t9.t25 (cl (= @p_349 (! (and @p_401 @p_419) :named @p_420))) :rule cong :premises (t46.t9.t5.t9.t8 t46.t9.t5.t9.t24)) +(step t46.t9.t5.t9 (cl (= @p_318 (! (exists ((veriT_vr34 A$)) @p_420) :named @p_396))) :rule bind) +(step t46.t9.t5.t10 (cl (= @p_350 (! (and @p_395 @p_396) :named @p_421))) :rule cong :premises (t46.t9.t5.t8 t46.t9.t5.t9)) +(step t46.t9.t5 (cl (= @p_311 (! (exists ((veriT_vr33 A$)) @p_421) :named @p_390))) :rule bind) +(step t46.t9.t6 (cl (= @p_351 (! (=> @p_389 @p_390) :named @p_422))) :rule cong :premises (t46.t9.t4 t46.t9.t5)) +(step t46.t9 (cl (= @p_306 (! (forall ((veriT_vr32 A$)) @p_422) :named @p_386))) :rule bind) +(step t46.t10 (cl (= @p_374 (! (and @p_249 @p_382 @p_385 @p_386) :named @p_423))) :rule cong :premises (t46.t4 t46.t8 t46.t9)) +(step t46.t11 (cl (= @p_375 (! (=> @p_423 thesis$) :named @p_424))) :rule cong :premises (t46.t10)) +(step t46 (cl (= @p_376 (! (forall ((veriT_vr29 Afset$) (veriT_vr30 Afset$) (veriT_vr31 Afset$)) @p_424) :named @p_425))) :rule bind) +(step t47 (cl (! (= @p_378 (! (and @p_425 @p_370) :named @p_427)) :named @p_426)) :rule cong :premises (t46)) +(step t48 (cl (not @p_426) (not @p_378) @p_427) :rule equiv_pos2) +(step t49 (cl @p_427) :rule th_resolution :premises (t45 t47 t48)) +(anchor :step t50 :args ((veriT_vr29 Afset$) (veriT_vr30 Afset$) (veriT_vr31 Afset$))) +(anchor :step t50.t1 :args ((veriT_vr32 A$))) +(anchor :step t50.t1.t1 :args ((veriT_vr33 A$))) +(anchor :step t50.t1.t1.t1 :args ((veriT_vr34 A$))) +(step t50.t1.t1.t1.t1 (cl (= @p_406 (! (not (forall ((veriT_vr35 A$)) (not @p_412))) :named @p_431))) :rule connective_def) +(step t50.t1.t1.t1.t2 (cl (= @p_413 (! (and @p_405 @p_431) :named @p_432))) :rule cong :premises (t50.t1.t1.t1.t1)) +(step t50.t1.t1.t1.t3 (cl (= @p_419 (! (or @p_432 @p_418) :named @p_433))) :rule cong :premises (t50.t1.t1.t1.t2)) +(step t50.t1.t1.t1.t4 (cl (= @p_420 (! (and @p_401 @p_433) :named @p_430))) :rule cong :premises (t50.t1.t1.t1.t3)) +(step t50.t1.t1.t1 (cl (= @p_396 (! (exists ((veriT_vr34 A$)) @p_430) :named @p_434))) :rule bind) +(step t50.t1.t1.t2 (cl (= @p_434 (! (not (forall ((veriT_vr34 A$)) (not @p_430))) :named @p_435))) :rule connective_def) +(step t50.t1.t1.t3 (cl (= @p_396 @p_435)) :rule trans :premises (t50.t1.t1.t1 t50.t1.t1.t2)) +(step t50.t1.t1.t4 (cl (= @p_421 (! (and @p_395 @p_435) :named @p_429))) :rule cong :premises (t50.t1.t1.t3)) +(step t50.t1.t1 (cl (= @p_390 (! (exists ((veriT_vr33 A$)) @p_429) :named @p_436))) :rule bind) +(step t50.t1.t2 (cl (= @p_436 (! (not (forall ((veriT_vr33 A$)) (not @p_429))) :named @p_437))) :rule connective_def) +(step t50.t1.t3 (cl (= @p_390 @p_437)) :rule trans :premises (t50.t1.t1 t50.t1.t2)) +(step t50.t1.t4 (cl (= @p_422 (! (=> @p_389 @p_437) :named @p_438))) :rule cong :premises (t50.t1.t3)) +(step t50.t1 (cl (= @p_386 (! (forall ((veriT_vr32 A$)) @p_438) :named @p_428))) :rule bind) +(step t50.t2 (cl (= @p_423 (! (and @p_249 @p_382 @p_385 @p_428) :named @p_439))) :rule cong :premises (t50.t1)) +(step t50.t3 (cl (= @p_424 (! (=> @p_439 thesis$) :named @p_440))) :rule cong :premises (t50.t2)) +(step t50 (cl (= @p_425 (! (forall ((veriT_vr29 Afset$) (veriT_vr30 Afset$) (veriT_vr31 Afset$)) @p_440) :named @p_441))) :rule bind) +(step t51 (cl (! (= @p_427 (! (and @p_441 @p_370) :named @p_443)) :named @p_442)) :rule cong :premises (t50)) +(step t52 (cl (not @p_442) (not @p_427) @p_443) :rule equiv_pos2) +(step t53 (cl @p_443) :rule th_resolution :premises (t49 t51 t52)) +(step t54 (cl @p_441) :rule and :premises (t53)) +(step t55 (cl @p_370) :rule and :premises (t53)) +(step t56 (cl (or (! (not @p_236) :named @p_651) (! (not (! (and @p_444 (! (forall ((veriT_vr15 Afset$) (veriT_vr16 Afset$) (veriT_vr17 Afset$)) (! (not (! (and (! (= s2$ @p_182) :named @p_467) (! (= s3$ @p_186) :named @p_471) @p_249 (! (forall ((veriT_vr18 A$)) (! (=> @p_194 (! (exists ((veriT_vr19 A$)) (! (and (! (member$ veriT_vr19 (! (fun_app$ fset$ (! (fun_app$a @p_447 @p_199) :named @p_483)) :named @p_445)) :named @p_485) (! (exists ((veriT_vr20 A$)) (! (and (! (member$ veriT_vr20 @p_445) :named @p_493) (! (or @p_220 (! (fun_app$d (! (fun_app$e is_least_false_clause$ (! (fun_app$a @p_244 @p_223) :named @p_509)) :named @p_511) veriT_vr18) :named @p_513)) :named @p_515)) :named @p_517)) :named @p_487)) :named @p_519)) :named @p_478)) :named @p_521)) :named @p_473)) :named @p_523)) :named @p_525)) :named @p_463)) :named @p_527)) :named @p_446))) :rule forall_inst :args ((:= veriT_vr11 const2$) (:= veriT_vr12 s2$) (:= veriT_vr13 const3$) (:= veriT_vr14 s3$))) +(anchor :step t57) +(assume t57.h1 @p_446) +(anchor :step t57.t2 :args ((:= (veriT_vr15 Afset$) veriT_vr36) (:= (veriT_vr16 Afset$) veriT_vr37) (:= (veriT_vr17 Afset$) veriT_vr38))) +(step t57.t2.t1 (cl (! (= veriT_vr15 veriT_vr36) :named @p_475)) :rule refl) +(step t57.t2.t2 (cl (! (= veriT_vr16 veriT_vr37) :named @p_469)) :rule refl) +(step t57.t2.t3 (cl (= @p_182 (! (pair$ veriT_vr36 veriT_vr37) :named @p_466))) :rule cong :premises (t57.t2.t1 t57.t2.t2)) +(step t57.t2.t4 (cl (= @p_467 (! (= s2$ @p_466) :named @p_468))) :rule cong :premises (t57.t2.t3)) +(step t57.t2.t5 (cl (! (= veriT_vr17 veriT_vr38) :named @p_480)) :rule refl) +(step t57.t2.t6 (cl @p_469) :rule refl) +(step t57.t2.t7 (cl (= @p_186 (! (pair$ veriT_vr38 veriT_vr37) :named @p_470))) :rule cong :premises (t57.t2.t5 t57.t2.t6)) +(step t57.t2.t8 (cl (= @p_471 (! (= s3$ @p_470) :named @p_472))) :rule cong :premises (t57.t2.t7)) +(anchor :step t57.t2.t9 :args ((:= (veriT_vr18 A$) veriT_vr39))) +(step t57.t2.t9.t1 (cl (! (= veriT_vr18 veriT_vr39) :named @p_497)) :rule refl) +(step t57.t2.t9.t2 (cl @p_475) :rule refl) +(step t57.t2.t9.t3 (cl (= @p_193 (! (fun_app$ fset$ veriT_vr36) :named @p_476))) :rule cong :premises (t57.t2.t9.t2)) +(step t57.t2.t9.t4 (cl (= @p_194 (! 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(and @p_601 @p_610) :named @p_611))) :rule cong :premises (t57.t16.t9.t4.t8.t7 t57.t16.t9.t4.t8.t17)) +(step t57.t16.t9.t4.t8 (cl (= @p_547 (! (exists ((veriT_vr48 A$)) @p_611) :named @p_596))) :rule bind) +(step t57.t16.t9.t4.t9 (cl (= @p_570 (! (and @p_595 @p_596) :named @p_612))) :rule cong :premises (t57.t16.t9.t4.t7 t57.t16.t9.t4.t8)) +(step t57.t16.t9.t4 (cl (= @p_543 (! (exists ((veriT_vr47 A$)) @p_612) :named @p_590))) :rule bind) +(step t57.t16.t9.t5 (cl (= @p_571 (! (=> @p_589 @p_590) :named @p_613))) :rule cong :premises (t57.t16.t9.t3 t57.t16.t9.t4)) +(step t57.t16.t9 (cl (= @p_539 (! (forall ((veriT_vr46 A$)) @p_613) :named @p_587))) :rule bind) +(step t57.t16.t10 (cl (= @p_572 (! (and @p_579 @p_580 @p_249 @p_587) :named @p_614))) :rule cong :premises (t57.t16.t4 t57.t16.t8 t57.t16.t9)) +(step t57.t16.t11 (cl (= @p_534 (! (not @p_614) :named @p_615))) :rule cong :premises (t57.t16.t10)) +(step t57.t16 (cl (= @p_573 @p_615)) :rule sko_forall) +(step t57.t17 (cl (= @p_574 (! (and @p_444 @p_615) :named @p_616))) :rule cong :premises (t57.t16)) +(step t57.t18 (cl (! (= @p_576 (! (not @p_616) :named @p_618)) :named @p_617)) :rule cong :premises (t57.t17)) +(step t57.t19 (cl (! (not @p_617) :named @p_620) (! (not @p_576) :named @p_619) @p_618) :rule equiv_pos2) +(step t57.t20 (cl (not @p_619) @p_574) :rule not_not) +(step t57.t21 (cl @p_620 @p_574 @p_618) :rule th_resolution :premises (t57.t20 t57.t19)) +(step t57.t22 (cl @p_618) :rule th_resolution :premises (t57.t15 t57.t18 t57.t21)) +(anchor :step t57.t23 :args ((:= (veriT_vr46 A$) veriT_vr50))) +(step t57.t23.t1 (cl (! (= veriT_vr46 veriT_vr50) :named @p_629)) :rule refl) +(step t57.t23.t2 (cl (= @p_589 (! (member$ veriT_vr50 @p_581) :named @p_622))) :rule cong :premises (t57.t23.t1)) +(anchor :step t57.t23.t3 :args ((:= (veriT_vr47 A$) veriT_vr51))) +(step t57.t23.t3.t1 (cl (! (= veriT_vr47 veriT_vr51) :named @p_628)) :rule refl) +(step t57.t23.t3.t2 (cl (= @p_595 (! (member$ veriT_vr51 @p_461) :named @p_624))) :rule cong :premises (t57.t23.t3.t1)) +(anchor :step t57.t23.t3.t3 :args ((:= (veriT_vr48 A$) veriT_vr52))) +(step t57.t23.t3.t3.t1 (cl (! (= veriT_vr48 veriT_vr52) :named @p_627)) :rule refl) +(step t57.t23.t3.t3.t2 (cl (= @p_601 (! (member$ veriT_vr52 @p_461) :named @p_626))) :rule cong :premises (t57.t23.t3.t3.t1)) +(step t57.t23.t3.t3.t3 (cl @p_627) :rule refl) +(step t57.t23.t3.t3.t4 (cl (! (= @p_449 (! (fun_app$c ground_resolution$ veriT_vr52) :named @p_462)) :named @p_633)) :rule cong :premises (t57.t23.t3.t3.t3)) +(step t57.t23.t3.t3.t5 (cl @p_628) :rule refl) +(step t57.t23.t3.t3.t6 (cl @p_629) :rule refl) +(step t57.t23.t3.t3.t7 (cl (= @p_555 (! (tranclp$ @p_462 veriT_vr51 veriT_vr50) :named @p_630))) :rule cong :premises (t57.t23.t3.t3.t4 t57.t23.t3.t3.t5 t57.t23.t3.t3.t6)) +(anchor :step t57.t23.t3.t3.t8 :args ((:= (veriT_vr49 A$) veriT_vr53))) +(step t57.t23.t3.t3.t8.t1 (cl (! (= veriT_vr49 veriT_vr53) :named @p_634)) :rule refl) +(step t57.t23.t3.t3.t8.t2 (cl (= @p_603 (! (member$ veriT_vr53 @p_582) :named @p_632))) :rule cong :premises (t57.t23.t3.t3.t8.t1)) +(step t57.t23.t3.t3.t8.t3 (cl @p_627) :rule refl) +(step t57.t23.t3.t3.t8.t4 (cl @p_633) :rule cong :premises (t57.t23.t3.t3.t8.t3)) +(step t57.t23.t3.t3.t8.t5 (cl @p_629) :rule refl) +(step t57.t23.t3.t3.t8.t6 (cl @p_634) :rule refl) +(step t57.t23.t3.t3.t8.t7 (cl (= @p_561 (! (rtranclp$ @p_462 veriT_vr50 veriT_vr53) :named @p_635))) :rule cong :premises (t57.t23.t3.t3.t8.t4 t57.t23.t3.t3.t8.t5 t57.t23.t3.t3.t8.t6)) +(step t57.t23.t3.t3.t8.t8 (cl (= @p_604 (! 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(and @p_624 @p_625) :named @p_641))) :rule cong :premises (t57.t23.t3.t2 t57.t23.t3.t3)) +(step t57.t23.t3 (cl (= @p_590 (! (exists ((veriT_vr51 A$)) @p_641) :named @p_623))) :rule bind) +(step t57.t23.t4 (cl (= @p_613 (! (=> @p_622 @p_623) :named @p_642))) :rule cong :premises (t57.t23.t2 t57.t23.t3)) +(step t57.t23 (cl (= @p_587 (! (forall ((veriT_vr50 A$)) @p_642) :named @p_621))) :rule bind) +(step t57.t24 (cl (= @p_614 (! (and @p_579 @p_580 @p_249 @p_621) :named @p_643))) :rule cong :premises (t57.t23)) +(step t57.t25 (cl (= @p_615 (! (not @p_643) :named @p_644))) :rule cong :premises (t57.t24)) +(step t57.t26 (cl (= @p_616 (! (and @p_444 @p_644) :named @p_645))) :rule cong :premises (t57.t25)) +(step t57.t27 (cl (! (= @p_618 (! (not @p_645) :named @p_646)) :named @p_647)) :rule cong :premises (t57.t26)) +(step t57.t28 (cl (! (not @p_647) :named @p_649) (! (not @p_618) :named @p_648) @p_646) :rule equiv_pos2) +(step t57.t29 (cl (not @p_648) @p_616) :rule not_not) +(step t57.t30 (cl @p_649 @p_616 @p_646) :rule th_resolution :premises (t57.t29 t57.t28)) +(step t57.t31 (cl @p_646) :rule th_resolution :premises (t57.t22 t57.t27 t57.t30)) +(step t57 (cl @p_531 @p_646) :rule subproof :discharge (h1)) +(step t58 (cl @p_650 @p_527) :rule not_not) +(step t59 (cl @p_527 @p_646) :rule th_resolution :premises (t58 t57)) +(step t60 (cl @p_651 @p_446) :rule or :premises (t56)) +(step t61 (cl (! (or @p_651 @p_646) :named @p_653) (! (not @p_651) :named @p_652)) :rule or_neg) +(step t62 (cl (not @p_652) @p_236) :rule not_not) +(step t63 (cl @p_653 @p_236) :rule th_resolution :premises (t62 t61)) +(step t64 (cl @p_653 (! (not @p_646) :named @p_654)) :rule or_neg) +(step t65 (cl (not @p_654) @p_645) :rule not_not) +(step t66 (cl @p_653 @p_645) :rule th_resolution :premises (t65 t64)) +(step t67 (cl @p_653) :rule th_resolution :premises (t60 t59 t63 t66)) +(step t68 (cl @p_644 @p_579) :rule and_pos) +(step t69 (cl @p_644 @p_580) :rule and_pos) +(step t70 (cl @p_644 @p_249) :rule and_pos) +(step t71 (cl @p_644 @p_621) :rule and_pos) +(step t72 (cl @p_645 (! (not @p_444) :named @p_656) (! (not @p_644) :named @p_655)) :rule and_neg) +(step t73 (cl (not @p_655) @p_643) :rule not_not) +(step t74 (cl @p_645 @p_656 @p_643) :rule th_resolution :premises (t73 t72)) +(step t75 (cl @p_651 @p_646) :rule or :premises (t67)) +(step t76 (cl @p_645 @p_643) :rule resolution :premises (t74 a1)) +(step t77 (cl @p_646) :rule resolution :premises (t75 t18)) +(step t78 (cl @p_643) :rule resolution :premises (t76 t77)) +(step t79 (cl @p_579) :rule resolution :premises (t68 t78)) +(step t80 (cl @p_580) :rule resolution :premises (t69 t78)) +(step t81 (cl @p_249) :rule resolution :premises (t70 t78)) +(step t82 (cl @p_621) :rule resolution :premises (t71 t78)) +(step t83 (cl (not (! (not (! (not @p_441) :named @p_657)) :named @p_799)) @p_441) :rule not_not) +(step t84 (cl (or @p_657 (! (=> (! (and @p_249 @p_579 @p_580 (! (forall ((veriT_vr32 A$)) (! (=> (! (member$ veriT_vr32 @p_581) :named @p_665) (! (not (! (forall ((veriT_vr33 A$)) (! (not (! (and (! (member$ veriT_vr33 @p_658) :named @p_669) (! (not (! (forall ((veriT_vr34 A$)) (! (not (! (and (! (member$ veriT_vr34 @p_658) :named @p_673) (! (or (! (and @p_405 (! (not (! (forall ((veriT_vr35 A$)) (! (not (! (and (! (member$ veriT_vr35 @p_582) :named @p_681) @p_411) :named @p_686)) :named @p_688)) :named @p_679)) :named @p_690)) :named @p_692) (! (fun_app$d @p_583 veriT_vr32) :named @p_694)) :named @p_696)) :named @p_698)) :named @p_700)) :named @p_671)) :named @p_702)) :named @p_704)) :named @p_706)) :named @p_667)) :named @p_708)) :named @p_710)) :named @p_663)) :named @p_712) thesis$) :named @p_659))) :rule forall_inst :args ((:= veriT_vr29 veriT_sk0) (:= veriT_vr30 veriT_sk1) (:= veriT_vr31 veriT_sk2))) +(anchor :step t85) +(assume t85.h1 @p_659) +(anchor :step t85.t2 :args ((:= (veriT_vr32 A$) veriT_vr87))) +(step t85.t2.t1 (cl (! (= veriT_vr32 veriT_vr87) :named @p_677)) :rule refl) +(step t85.t2.t2 (cl (= @p_665 (! 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(and @p_896 @p_904) :named @p_906))) :rule cong :premises (t129.t2.t5 t129.t2.t7)) +(step t129.t2.t9 (cl (= @p_907 (! (or @p_906 @p_750) :named @p_908))) :rule cong :premises (t129.t2.t8)) +(step t129.t2.t10 (cl (= @p_909 (! (and @p_893 @p_908) :named @p_910))) :rule cong :premises (t129.t2.t2 t129.t2.t9)) +(step t129.t2.t11 (cl (= @p_911 (! (not @p_910) :named @p_912))) :rule cong :premises (t129.t2.t10)) +(step t129.t2 (cl (= @p_891 (! (forall ((veriT_vr118 A$)) @p_912) :named @p_914))) :rule bind) +(step t129.t3 (cl (= @p_913 (! (not @p_914) :named @p_916))) :rule cong :premises (t129.t2)) +(step t129.t4 (cl (= @p_915 (! (and @p_889 @p_916) :named @p_917))) :rule cong :premises (t129.t3)) +(step t129.t5 (cl (! (= @p_888 (! (not @p_917) :named @p_920)) :named @p_918)) :rule cong :premises (t129.t4)) +(step t129.t6 (cl (! (not @p_918) :named @p_921) (! (not @p_888) :named @p_919) @p_920) :rule equiv_pos2) +(step t129.t7 (cl (! (not @p_919) :named @p_944) @p_915) :rule not_not) +(step t129.t8 (cl @p_921 @p_915 @p_920) :rule th_resolution :premises (t129.t7 t129.t6)) +(step t129.t9 (cl @p_920) :rule th_resolution :premises (t129.h1 t129.t5 t129.t8)) +(anchor :step t129.t10 :args ((:= (veriT_vr118 A$) veriT_vr120))) +(step t129.t10.t1 (cl (! (= veriT_vr118 veriT_vr120) :named @p_924)) :rule refl) +(step t129.t10.t2 (cl (= @p_893 (! (member$ veriT_vr120 @p_658) :named @p_923))) :rule cong :premises (t129.t10.t1)) +(step t129.t10.t3 (cl @p_924) :rule refl) +(step t129.t10.t4 (cl (! (= @p_892 (! (fun_app$c ground_resolution$ veriT_vr120) :named @p_890)) :named @p_928)) :rule cong :premises (t129.t10.t3)) +(step t129.t10.t5 (cl (= @p_896 (! (tranclp$ @p_890 veriT_sk11 veriT_sk6) :named @p_925))) :rule cong :premises (t129.t10.t4)) +(anchor :step t129.t10.t6 :args ((:= (veriT_vr119 A$) veriT_vr121))) +(step t129.t10.t6.t1 (cl (! (= veriT_vr119 veriT_vr121) :named @p_929)) :rule refl) +(step t129.t10.t6.t2 (cl (= @p_898 (! (member$ veriT_vr121 @p_582) :named @p_927))) :rule cong :premises (t129.t10.t6.t1)) +(step t129.t10.t6.t3 (cl @p_924) :rule refl) +(step t129.t10.t6.t4 (cl @p_928) :rule cong :premises (t129.t10.t6.t3)) +(step t129.t10.t6.t5 (cl @p_929) :rule refl) +(step t129.t10.t6.t6 (cl (= @p_901 (! (rtranclp$ @p_890 veriT_sk6 veriT_vr121) :named @p_930))) :rule cong :premises (t129.t10.t6.t4 t129.t10.t6.t5)) +(step t129.t10.t6.t7 (cl (= @p_902 (! (and @p_927 @p_930) :named @p_931))) :rule cong :premises (t129.t10.t6.t2 t129.t10.t6.t6)) +(step t129.t10.t6.t8 (cl (= @p_903 (! (not @p_931) :named @p_932))) :rule cong :premises (t129.t10.t6.t7)) +(step t129.t10.t6 (cl (= @p_897 (! (forall ((veriT_vr121 A$)) @p_932) :named @p_926))) :rule bind) +(step t129.t10.t7 (cl (= @p_904 (! (not @p_926) :named @p_933))) :rule cong :premises (t129.t10.t6)) +(step t129.t10.t8 (cl (= @p_906 (! (and @p_925 @p_933) :named @p_934))) :rule cong :premises (t129.t10.t5 t129.t10.t7)) +(step t129.t10.t9 (cl (= @p_908 (! (or @p_934 @p_750) :named @p_935))) :rule cong :premises (t129.t10.t8)) +(step t129.t10.t10 (cl (= @p_910 (! (and @p_923 @p_935) :named @p_936))) :rule cong :premises (t129.t10.t2 t129.t10.t9)) +(step t129.t10.t11 (cl (= @p_912 (! (not @p_936) :named @p_937))) :rule cong :premises (t129.t10.t10)) +(step t129.t10 (cl (= @p_914 (! (forall ((veriT_vr120 A$)) @p_937) :named @p_922))) :rule bind) +(step t129.t11 (cl (= @p_916 (! (not @p_922) :named @p_938))) :rule cong :premises (t129.t10)) +(step t129.t12 (cl (= @p_917 (! (and @p_889 @p_938) :named @p_939))) :rule cong :premises (t129.t11)) +(step t129.t13 (cl (! (= @p_920 (! (not @p_939) :named @p_940)) :named @p_941)) :rule cong :premises (t129.t12)) +(step t129.t14 (cl (! (not @p_941) :named @p_943) (! (not @p_920) :named @p_942) @p_940) :rule equiv_pos2) +(step t129.t15 (cl (not @p_942) @p_917) :rule not_not) +(step t129.t16 (cl @p_943 @p_917 @p_940) :rule th_resolution :premises (t129.t15 t129.t14)) +(step t129.t17 (cl @p_940) :rule th_resolution :premises (t129.t9 t129.t13 t129.t16)) +(step t129 (cl @p_919 @p_940) :rule subproof :discharge (h1)) +(step t130 (cl @p_944 @p_915) :rule not_not) +(step t131 (cl @p_915 @p_940) :rule th_resolution :premises (t130 t129)) +(step t132 (cl @p_794 @p_888) :rule or :premises (t128)) +(step t133 (cl (! (or @p_794 @p_940) :named @p_945) @p_801) :rule or_neg) +(step t134 (cl @p_945 @p_772) :rule th_resolution :premises (t93 t133)) +(step t135 (cl @p_945 (! (not @p_940) :named @p_946)) :rule or_neg) +(step t136 (cl (not @p_946) @p_939) :rule not_not) +(step t137 (cl @p_945 @p_939) :rule th_resolution :premises (t136 t135)) +(step t138 (cl @p_945) :rule th_resolution :premises (t132 t131 t134 t137)) +(step t139 (cl (or @p_794 (! (not (! (and (! (member$ veriT_sk10 @p_658) :named @p_948) (! (not (! (forall ((veriT_vr96 A$)) (! (not (! (and @p_775 (! (or (! (and (! (tranclp$ @p_662 veriT_sk10 veriT_sk6) :named @p_954) @p_786) :named @p_964) @p_750) :named @p_966)) :named @p_968)) :named @p_970)) :named @p_950)) :named @p_972)) :named @p_974)) :named @p_947))) :rule forall_inst :args ((:= veriT_vr95 veriT_sk10))) +(anchor :step t140) +(assume t140.h1 @p_947) +(anchor :step t140.t2 :args ((:= (veriT_vr96 A$) veriT_vr122))) +(step t140.t2.t1 (cl (! (= veriT_vr96 veriT_vr122) :named @p_953)) :rule refl) +(step t140.t2.t2 (cl (= @p_775 (! (member$ veriT_vr122 @p_658) :named @p_952))) :rule cong :premises (t140.t2.t1)) +(step t140.t2.t3 (cl @p_953) :rule refl) +(step t140.t2.t4 (cl (! (= @p_662 (! (fun_app$c ground_resolution$ veriT_vr122) :named @p_951)) :named @p_958)) :rule cong :premises (t140.t2.t3)) +(step t140.t2.t5 (cl (= @p_954 (! (tranclp$ @p_951 veriT_sk10 veriT_sk6) :named @p_955))) :rule cong :premises (t140.t2.t4)) +(anchor :step t140.t2.t6 :args ((:= (veriT_vr97 A$) veriT_vr123))) +(step t140.t2.t6.t1 (cl (! (= veriT_vr97 veriT_vr123) :named @p_959)) :rule refl) +(step t140.t2.t6.t2 (cl (= @p_780 (! (member$ veriT_vr123 @p_582) :named @p_957))) :rule cong :premises (t140.t2.t6.t1)) +(step t140.t2.t6.t3 (cl @p_953) :rule refl) +(step t140.t2.t6.t4 (cl @p_958) :rule cong :premises (t140.t2.t6.t3)) +(step t140.t2.t6.t5 (cl @p_959) :rule refl) +(step t140.t2.t6.t6 (cl (= @p_783 (! (rtranclp$ @p_951 veriT_sk6 veriT_vr123) :named @p_960))) :rule cong :premises (t140.t2.t6.t4 t140.t2.t6.t5)) +(step t140.t2.t6.t7 (cl (= @p_784 (! (and @p_957 @p_960) :named @p_961))) :rule cong :premises (t140.t2.t6.t2 t140.t2.t6.t6)) +(step t140.t2.t6.t8 (cl (= @p_785 (! (not @p_961) :named @p_962))) :rule cong :premises (t140.t2.t6.t7)) +(step t140.t2.t6 (cl (= @p_779 (! (forall ((veriT_vr123 A$)) @p_962) :named @p_956))) :rule bind) +(step t140.t2.t7 (cl (= @p_786 (! (not @p_956) :named @p_963))) :rule cong :premises (t140.t2.t6)) +(step t140.t2.t8 (cl (= @p_964 (! (and @p_955 @p_963) :named @p_965))) :rule cong :premises (t140.t2.t5 t140.t2.t7)) +(step t140.t2.t9 (cl (= @p_966 (! (or @p_965 @p_750) :named @p_967))) :rule cong :premises (t140.t2.t8)) +(step t140.t2.t10 (cl (= @p_968 (! (and @p_952 @p_967) :named @p_969))) :rule cong :premises (t140.t2.t2 t140.t2.t9)) +(step t140.t2.t11 (cl (= @p_970 (! (not @p_969) :named @p_971))) :rule cong :premises (t140.t2.t10)) +(step t140.t2 (cl (= @p_950 (! (forall ((veriT_vr122 A$)) @p_971) :named @p_973))) :rule bind) +(step t140.t3 (cl (= @p_972 (! (not @p_973) :named @p_975))) :rule cong :premises (t140.t2)) +(step t140.t4 (cl (= @p_974 (! (and @p_948 @p_975) :named @p_976))) :rule cong :premises (t140.t3)) +(step t140.t5 (cl (! (= @p_947 (! (not @p_976) :named @p_979)) :named @p_977)) :rule cong :premises (t140.t4)) +(step t140.t6 (cl (! (not @p_977) :named @p_980) (! (not @p_947) :named @p_978) @p_979) :rule equiv_pos2) +(step t140.t7 (cl (! (not @p_978) :named @p_1003) @p_974) :rule not_not) +(step t140.t8 (cl @p_980 @p_974 @p_979) :rule th_resolution :premises (t140.t7 t140.t6)) +(step t140.t9 (cl @p_979) :rule th_resolution :premises (t140.h1 t140.t5 t140.t8)) +(anchor :step t140.t10 :args ((:= (veriT_vr122 A$) veriT_vr124))) +(step t140.t10.t1 (cl (! (= veriT_vr122 veriT_vr124) :named @p_983)) :rule refl) +(step t140.t10.t2 (cl (= @p_952 (! (member$ veriT_vr124 @p_658) :named @p_982))) :rule cong :premises (t140.t10.t1)) +(step t140.t10.t3 (cl @p_983) :rule refl) +(step t140.t10.t4 (cl (! (= @p_951 (! (fun_app$c ground_resolution$ veriT_vr124) :named @p_949)) :named @p_987)) :rule cong :premises (t140.t10.t3)) +(step t140.t10.t5 (cl (= @p_955 (! (tranclp$ @p_949 veriT_sk10 veriT_sk6) :named @p_984))) :rule cong :premises (t140.t10.t4)) +(anchor :step t140.t10.t6 :args ((:= (veriT_vr123 A$) veriT_vr125))) +(step t140.t10.t6.t1 (cl (! (= veriT_vr123 veriT_vr125) :named @p_988)) :rule refl) +(step t140.t10.t6.t2 (cl (= @p_957 (! (member$ veriT_vr125 @p_582) :named @p_986))) :rule cong :premises (t140.t10.t6.t1)) +(step t140.t10.t6.t3 (cl @p_983) :rule refl) +(step t140.t10.t6.t4 (cl @p_987) :rule cong :premises (t140.t10.t6.t3)) +(step t140.t10.t6.t5 (cl @p_988) :rule refl) +(step t140.t10.t6.t6 (cl (= @p_960 (! (rtranclp$ @p_949 veriT_sk6 veriT_vr125) :named @p_989))) :rule cong :premises (t140.t10.t6.t4 t140.t10.t6.t5)) +(step t140.t10.t6.t7 (cl (= @p_961 (! (and @p_986 @p_989) :named @p_990))) :rule cong :premises (t140.t10.t6.t2 t140.t10.t6.t6)) +(step t140.t10.t6.t8 (cl (= @p_962 (! (not @p_990) :named @p_991))) :rule cong :premises (t140.t10.t6.t7)) +(step t140.t10.t6 (cl (= @p_956 (! 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(not @p_998) :named @p_999)) :named @p_1000)) :rule cong :premises (t140.t12)) +(step t140.t14 (cl (! (not @p_1000) :named @p_1002) (! (not @p_979) :named @p_1001) @p_999) :rule equiv_pos2) +(step t140.t15 (cl (not @p_1001) @p_976) :rule not_not) +(step t140.t16 (cl @p_1002 @p_976 @p_999) :rule th_resolution :premises (t140.t15 t140.t14)) +(step t140.t17 (cl @p_999) :rule th_resolution :premises (t140.t9 t140.t13 t140.t16)) +(step t140 (cl @p_978 @p_999) :rule subproof :discharge (h1)) +(step t141 (cl @p_1003 @p_974) :rule not_not) +(step t142 (cl @p_974 @p_999) :rule th_resolution :premises (t141 t140)) +(step t143 (cl @p_794 @p_947) :rule or :premises (t139)) +(step t144 (cl (! (or @p_794 @p_999) :named @p_1004) @p_801) :rule or_neg) +(step t145 (cl @p_1004 @p_772) :rule th_resolution :premises (t93 t144)) +(step t146 (cl @p_1004 (! (not @p_999) :named @p_1005)) :rule or_neg) +(step t147 (cl (not @p_1005) @p_998) :rule not_not) +(step t148 (cl @p_1004 @p_998) :rule th_resolution :premises (t147 t146)) +(step t149 (cl @p_1004) :rule th_resolution :premises (t143 t142 t145 t148)) +(step t150 (cl @p_939 (! (not @p_889) :named @p_1007) (! (not @p_938) :named @p_1006)) :rule and_neg) +(step t151 (cl (not @p_1006) @p_922) :rule not_not) +(step t152 (cl @p_939 @p_1007 @p_922) :rule th_resolution :premises (t151 t150)) +(step t153 (cl @p_794 @p_940) :rule or :premises (t138)) +(step t154 (cl @p_940) :rule resolution :premises (t153 t104)) +(step t155 (cl @p_998 (! (not @p_948) :named @p_1009) (! (not @p_997) :named @p_1008)) :rule and_neg) +(step t156 (cl (not @p_1008) @p_981) :rule not_not) +(step t157 (cl @p_998 @p_1009 @p_981) :rule th_resolution :premises (t156 t155)) +(step t158 (cl @p_794 @p_999) :rule or :premises (t149)) +(step t159 (cl @p_999) :rule resolution :premises (t158 t104)) +(step t160 (cl (! (= fset$ fset$) :named @p_1020)) :rule eq_reflexive) +(step t161 (cl (! (= union_fset$ union_fset$) :named @p_1011)) :rule eq_reflexive) +(step t162 (cl (not (! (= @p_244 @p_447) :named @p_1013)) (! (not (! (= @p_593 @p_593) :named @p_1016)) :named @p_1014) (! (= @p_594 @p_1010) :named @p_1015)) :rule eq_congruent) +(step t163 (cl (not @p_1011) @p_1012 @p_1013) :rule eq_congruent) +(step t164 (cl @p_1012 @p_1013) :rule th_resolution :premises (t163 t161)) +(step t165 (cl @p_1014 @p_1015 @p_1012) :rule th_resolution :premises (t162 t164)) +(step t166 (cl @p_1016) :rule eq_reflexive) +(step t167 (cl @p_1015 @p_1012) :rule th_resolution :premises (t165 t166)) +(step t168 (cl (not (! (= veriT_sk10 veriT_sk10) :named @p_1017)) (! (not (! (= @p_461 @p_658) :named @p_1021)) :named @p_1018) @p_948 (! (not @p_862) :named @p_1019)) :rule eq_congruent_pred) +(step t169 (cl @p_1017) :rule eq_reflexive) +(step t170 (cl @p_1018 @p_948 @p_1019) :rule th_resolution :premises (t168 t169)) +(step t171 (cl (not @p_1020) (! (not @p_1015) :named @p_1022) @p_1021) :rule eq_congruent) +(step t172 (cl @p_1022 @p_1021) :rule th_resolution :premises (t171 t160)) +(step t173 (cl @p_1021 @p_1012) :rule th_resolution :premises (t172 t167)) +(step t174 (cl @p_948 @p_1019 @p_1012) :rule th_resolution :premises (t170 t173)) +(step t175 (cl @p_948) :rule resolution :premises (t174 t81 t125)) +(step t176 (cl (! (not (! (= veriT_sk11 veriT_sk11) :named @p_1025)) :named @p_1023) @p_1018 @p_889 (! (not @p_863) :named @p_1024)) :rule eq_congruent_pred) +(step t177 (cl @p_1023 @p_889 @p_1024 @p_1012) :rule th_resolution :premises (t176 t173)) +(step t178 (cl @p_1025) :rule eq_reflexive) +(step t179 (cl @p_889 @p_1024 @p_1012) :rule th_resolution :premises (t177 t178)) +(step t180 (cl @p_889) :rule resolution :premises (t179 t81 t126)) +(step t181 (cl @p_981) :rule resolution :premises (t157 t175 t159)) +(step t182 (cl @p_922) :rule resolution :premises (t152 t180 t154)) +(step t183 (cl (or @p_997 (! (forall ((veriT_vr124 A$) (veriT_vr125 A$)) (or (not @p_982) (not @p_984) (not @p_986) (not @p_989))) :named @p_1026))) :rule qnt_cnf) +(step t184 (cl (or @p_938 (! (forall ((veriT_vr120 A$)) (or (not @p_923) (! (not @p_750) :named @p_1035))) :named @p_1034))) :rule qnt_cnf) +(step t185 (cl @p_997 @p_1026) :rule or :premises (t183)) +(step t186 (cl (or (! (not @p_1026) :named @p_1027) (! (or @p_1007 (! (not @p_864) :named @p_1031) (! (not @p_865) :named @p_1032) (! (not @p_866) :named @p_1033)) :named @p_1028))) :rule forall_inst :args ((:= veriT_vr124 veriT_sk11) (:= veriT_vr125 veriT_sk12))) +(step t187 (cl @p_1027 @p_1028) :rule or :premises (t186)) +(step t188 (cl (! (or @p_997 @p_1028) :named @p_1029) @p_1008) :rule or_neg) +(step t189 (cl @p_1029 @p_981) :rule th_resolution :premises (t156 t188)) +(step t190 (cl @p_1029 (! (not @p_1028) :named @p_1030)) :rule or_neg) +(step t191 (cl @p_1029) :rule th_resolution :premises (t185 t187 t189 t190)) +(step t192 (cl @p_1030 @p_1007 @p_1031 @p_1032 @p_1033) :rule or_pos) +(step t193 (cl @p_997 @p_1028) :rule or :premises (t191)) +(step t194 (cl @p_1030 @p_1031 @p_1032 @p_1033) :rule resolution :premises (t192 t180)) +(step t195 (cl @p_1028) :rule resolution :premises (t193 t181)) +(step t196 (cl @p_886) :rule resolution :premises (t194 t117 t116 t115 t195)) +(step t197 (cl @p_750) :rule resolution :premises (t118 t196 t127)) +(step t198 (cl @p_938 @p_1034) :rule or :premises (t184)) +(step t199 (cl (or (! (not @p_1034) :named @p_1036) (! (or @p_1007 @p_1035) :named @p_1037))) :rule forall_inst :args ((:= veriT_vr120 veriT_sk11))) +(step t200 (cl @p_1036 @p_1037) :rule or :premises (t199)) +(step t201 (cl (! (or @p_938 @p_1037) :named @p_1038) @p_1006) :rule or_neg) +(step t202 (cl @p_1038 @p_922) :rule th_resolution :premises (t151 t201)) +(step t203 (cl @p_1038 (! (not @p_1037) :named @p_1039)) :rule or_neg) +(step t204 (cl @p_1038) :rule th_resolution :premises (t198 t200 t202 t203)) +(step t205 (cl @p_1039 @p_1007 @p_1035) :rule or_pos) +(step t206 (cl @p_938 @p_1037) :rule or :premises (t204)) +(step t207 (cl @p_1039) :rule resolution :premises (t205 t197 t180)) +(step t208 (cl) :rule resolution :premises (t206 t182 t207)) 672f5a048dc0215d5adebfbf2f0a3a36f69e286e 910 0 unsat (define-fun veriT_sk0 () V$ (! (choice ((veriT_vr65 V$)) (not (! (not (! (= x2$ (! (rraise$ veriT_vr65) :named @p_401)) :named @p_402)) :named @p_400))) :named @p_414)) diff -r b21d8401f0ca -r 157de27b0863 src/HOL/SMT_Examples/SMT_Examples_Verit.thy --- a/src/HOL/SMT_Examples/SMT_Examples_Verit.thy Mon Feb 05 10:06:34 2024 +0100 +++ b/src/HOL/SMT_Examples/SMT_Examples_Verit.thy Fri Jan 19 13:56:26 2024 +0100 @@ -15,7 +15,7 @@ external_file \SMT_Examples_Verit.certs\ declare [[smt_certificates = "SMT_Examples_Verit.certs"]] -declare [[smt_read_only_certificates = false]] +declare [[smt_read_only_certificates = true]] section \Propositional and first-order logic\ @@ -815,4 +815,44 @@ done end + +context + fixes + L2_final :: "'afset \ 'afset \ 'afset \ bool" and + L3_final :: "'afset \ 'afset \ 'afset \ bool" and + ground_resolution :: "'a \ 'a \ 'a \ bool" and + is_least_false_clause :: "'afset \ 'a \ bool" and + fset :: "'afset \ 'a set" and + union_fset :: "'afset \ 'afset \ 'afset" (infixr "|\|" 50) +begin +term "a |\| b" + +fun L2_matches_L3 where + "L2_matches_L3 N2 (Ur2, Uff2) N3 (Urr3, Uff3) \ + N2 = N3 \ Uff2 = Uff3 \ + (\Cr \ fset Ur2. \C \ fset (N3 |\| Urr3 |\| Uff3). \D \ fset (N3 |\| Urr3 |\| Uff3). + (ground_resolution D)\<^sup>+\<^sup>+ C Cr \ + (\Crr \ fset Urr3. (ground_resolution D)\<^sup>*\<^sup>* Cr Crr) \ (is_least_false_clause (N2 |\| Ur2 |\| Uff2) Cr))" + +lemma + assumes match: "L2_matches_L3 Const2 S2 Const3 S3" + shows "L2_final Const2 S2 \ L2_final Const3 S3" +proof - + from match obtain N Ur Uff Urr where + state_simps: + "Const2 = N" + "Const3 = N" + "S2 = (Ur, Uff)" + "S3 = (Urr, Uff)" and + Ur_spec: " + \Cr \ fset Ur. + \C \ fset (N |\| Urr |\| Uff). + \D \ fset (N |\| Urr |\| Uff). + (ground_resolution D)\<^sup>+\<^sup>+ C Cr \ + (\Crr \ fset Urr. (ground_resolution D)\<^sup>*\<^sup>* Cr Crr) \ + (is_least_false_clause (N |\| Ur |\| Uff) Cr)" + by (smt (verit) L2_matches_L3.elims(2)) + oops +end + end \ No newline at end of file diff -r b21d8401f0ca -r 157de27b0863 src/HOL/Tools/SMT/lethe_replay_methods.ML --- a/src/HOL/Tools/SMT/lethe_replay_methods.ML Mon Feb 05 10:06:34 2024 +0100 +++ b/src/HOL/Tools/SMT/lethe_replay_methods.ML Fri Jan 19 13:56:26 2024 +0100 @@ -793,7 +793,7 @@ fun or_pos_prove ctxt _ = K (unfold_tac ctxt @{thms de_Morgan_disj not_not}) - THEN' match_tac ctxt @{thms verit_and_pos} + THEN' match_tac ctxt @{thms verit_and_pos verit_farkas} THEN' K (unfold_tac ctxt @{thms de_Morgan_conj de_Morgan_disj not_not}) THEN' TRY' (assume_tac ctxt) diff -r b21d8401f0ca -r 157de27b0863 src/HOL/Tools/SMT/smt_replay_arith.ML --- a/src/HOL/Tools/SMT/smt_replay_arith.ML Mon Feb 05 10:06:34 2024 +0100 +++ b/src/HOL/Tools/SMT/smt_replay_arith.ML Fri Jan 19 13:56:26 2024 +0100 @@ -109,7 +109,7 @@ |> Simplifier.full_simp_tac fun la_farkas args ctxt = - REPEAT' (resolve_tac ctxt @{thms verit_and_pos(3,4)}) + REPEAT' (resolve_tac ctxt @{thms verit_farkas}) THEN' TRY' (resolve_tac ctxt @{thms ccontr}) THEN' TRY' (rewrite_only_thms ctxt @{thms linorder_class.not_less linorder_class.not_le not_not}) THEN' (Subgoal.FOCUS (fn focus => la_farkas_tac focus args) ctxt)