TSTP Solution File: SWC307+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC307+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:24:38 EDT 2023
% Result : Theorem 43.28s 43.59s
% Output : Proof 43.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SWC307+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 16:22:17 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 43.28/43.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.MqNMGBeYLk/cvc5---1.0.5_12102.p...
% 43.28/43.59 ------- get file name : TPTP file name is SWC307+1
% 43.28/43.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12102.smt2...
% 43.28/43.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 43.28/43.59 --- Run --no-e-matching --full-saturate-quant at 5...
% 43.28/43.59 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 43.28/43.59 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 43.28/43.59 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 43.28/43.59 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 43.28/43.59 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 43.28/43.59 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 43.28/43.59 % SZS status Theorem for SWC307+1
% 43.28/43.59 % SZS output start Proof for SWC307+1
% 43.28/43.59 (
% 43.28/43.59 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.segmentP X W)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (=> (tptp.ssList X2) (forall ((X3 $$unsorted)) (=> (tptp.ssList X3) (or (not (= (tptp.app (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) X2) (tptp.cons Z tptp.nil)) X3) U)) (not (tptp.lt Z Y))))))))))))) (and (not (tptp.singletonP W)) (tptp.neq X tptp.nil)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_18 (tptp.ssList tptp.nil))) (let ((_let_19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_20 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_21 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.equalelemsP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))))) (let ((_let_22 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.duplicatefreeP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (= V W)))))))))))))))))) (let ((_let_23 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (forall ((Y $$unsorted)) (=> (tptp.ssList Y) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))))) (let ((_let_24 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_25 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 tptp.nil))) (let ((_let_26 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_27 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_28 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_27))) (let ((_let_29 (tptp.app _let_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (tptp.app _let_29 _let_26))) (let ((_let_31 (tptp.app _let_30 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_32 (= _let_31 _let_25))) (let ((_let_33 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.hd _let_25)))) (let ((_let_34 (tptp.totalorderedP _let_31))) (let ((_let_35 (tptp.hd _let_31))) (let ((_let_36 (tptp.cons _let_35 tptp.nil))) (let ((_let_37 (tptp.totalorderedP _let_36))) (let ((_let_38 (not _let_32))) (let ((_let_39 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) (tptp.app (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))))))) (let ((_let_43 (not _let_41))) (let ((_let_44 (not _let_42))) (let ((_let_45 (tptp.singletonP _let_31))) (let ((_let_46 (= _let_45 _let_44))) (let ((_let_47 (tptp.ssList _let_31))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46))) (let ((_let_50 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_24)) (MACRO_SR_EQ_INTRO :args (_let_24 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_53 (not _let_45))) (let ((_let_54 (and _let_53 _let_52))) (let ((_let_55 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_31))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.lt SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_68 (not _let_67))) (let ((_let_69 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_70 (not _let_69))) (let ((_let_71 (or _let_48 _let_70 _let_68 _let_66 _let_64 _let_62 _let_60 _let_58 _let_56 _let_54))) (let ((_let_72 (forall ((BOUND_VARIABLE_5437 $$unsorted) (BOUND_VARIABLE_5414 $$unsorted) (BOUND_VARIABLE_5412 $$unsorted) (BOUND_VARIABLE_5410 $$unsorted) (BOUND_VARIABLE_5408 $$unsorted) (BOUND_VARIABLE_5406 $$unsorted)) (let ((_let_1 (tptp.app (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5408 (tptp.cons BOUND_VARIABLE_5406 tptp.nil)) BOUND_VARIABLE_5412) (tptp.cons BOUND_VARIABLE_5414 tptp.nil)) BOUND_VARIABLE_5410))) (or (not (tptp.ssList _let_1)) (not (tptp.ssItem BOUND_VARIABLE_5406)) (not (tptp.ssItem BOUND_VARIABLE_5414)) (not (tptp.lt BOUND_VARIABLE_5414 BOUND_VARIABLE_5406)) (not (tptp.ssList BOUND_VARIABLE_5408)) (not (tptp.ssList BOUND_VARIABLE_5412)) (not (tptp.ssList BOUND_VARIABLE_5410)) (not (tptp.ssList BOUND_VARIABLE_5437)) (not (tptp.segmentP BOUND_VARIABLE_5437 _let_1)) (and (not (tptp.singletonP _let_1)) (tptp.neq BOUND_VARIABLE_5437 tptp.nil))))))) (let ((_let_73 (not _let_71))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (or))) (let ((_let_76 (not _let_72))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_74) :args (_let_76))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_72))) (REFL :args (_let_73)) :args _let_75)) _let_74 :args (_let_73 true _let_72)))) (let ((_let_78 (REFL :args (_let_71)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_75)) :args ((or _let_47 _let_71))) _let_77 :args (_let_47 true _let_71)))) (let ((_let_80 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_81 (not _let_80))) (let ((_let_82 (= _let_52 _let_81))) (let ((_let_83 (not _let_18))) (let ((_let_84 (or _let_58 _let_83 _let_82))) (let ((_let_85 (forall ((U $$unsorted) (BOUND_VARIABLE_3294 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3294)) (= (tptp.neq U BOUND_VARIABLE_3294) (not (= U BOUND_VARIABLE_3294))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_20)) (MACRO_SR_EQ_INTRO :args (_let_20 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 7)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_75)) :args ((or _let_57 _let_71))) _let_77 :args (_let_57 true _let_71)))) (let ((_let_88 (ASSUME :args (_let_18)))) (let ((_let_89 (tptp.segmentP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_90 (= _let_80 _let_89))) (let ((_let_91 (or _let_58 _let_90))) (let ((_let_92 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (_let_92))) (let ((_let_95 ((not (= (tptp.ssList U) false))))) (let ((_let_96 (tptp.segmentP tptp.nil _let_31))) (let ((_let_97 (not _let_89))) (let ((_let_98 (or _let_83 _let_58 _let_97 _let_48 _let_56 _let_96))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_4357 $$unsorted) (BOUND_VARIABLE_4355 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4355)) (not (tptp.segmentP U BOUND_VARIABLE_4355)) (not (tptp.ssList BOUND_VARIABLE_4357)) (not (tptp.segmentP BOUND_VARIABLE_4355 BOUND_VARIABLE_4357)) (tptp.segmentP U BOUND_VARIABLE_4357))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (= tptp.nil _let_31))) (let ((_let_102 (= _let_101 _let_96))) (let ((_let_103 (not _let_96))) (let ((_let_104 (or _let_48 _let_102))) (let ((_let_105 (= tptp.nil _let_30))) (let ((_let_106 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_107 (and _let_106 _let_105))) (let ((_let_108 (= _let_101 _let_107))) (let ((_let_109 (not _let_101))) (let ((_let_110 (tptp.ssList _let_30))) (let ((_let_111 (not _let_110))) (let ((_let_112 (or _let_111 _let_60 _let_108))) (let ((_let_113 (forall ((U $$unsorted) (BOUND_VARIABLE_4875 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4875)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4875)) (and (= tptp.nil BOUND_VARIABLE_4875) (= tptp.nil U))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (_let_113))) (let ((_let_116 ((tptp.app U BOUND_VARIABLE_4875)))) (let ((_let_117 (tptp.ssList _let_26))) (let ((_let_118 (not _let_117))) (let ((_let_119 (tptp.ssList _let_29))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_118 _let_110))) (let ((_let_122 (forall ((U $$unsorted) (BOUND_VARIABLE_3575 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3575)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3575)))))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (_let_122))) (let ((_let_125 ((tptp.app U BOUND_VARIABLE_3575)))) (let ((_let_126 (or _let_83 _let_68 _let_117))) (let ((_let_127 (forall ((U $$unsorted) (BOUND_VARIABLE_3317 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3317)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3317 U)))))) (let ((_let_128 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_129 (_let_127))) (let ((_let_130 ((tptp.cons BOUND_VARIABLE_3317 U)))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 2)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_75)) :args ((or _let_67 _let_71))) _let_77 :args (_let_67 true _let_71)))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_83 _let_68 _let_117 (not _let_126)))) _let_88 _let_131 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_130)) :args _let_129)) _let_128 :args (_let_126 false _let_127)) :args (_let_117 false _let_18 false _let_67 false _let_126)))) (let ((_let_133 (tptp.ssList _let_28))) (let ((_let_134 (not _let_133))) (let ((_let_135 (or _let_134 _let_62 _let_119))) (let ((_let_136 (tptp.ssList _let_27))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_64 _let_137 _let_133))) (let ((_let_139 (or _let_83 _let_70 _let_136))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_71 1)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_69))) :args _let_75)) :args ((or _let_69 _let_71))) _let_77 :args (_let_69 true _let_71)))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_83 _let_70 _let_136 (not _let_139)))) _let_88 _let_140 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_128 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_130)) :args _let_129)) _let_128 :args (_let_139 false _let_127)) :args (_let_136 false _let_18 false _let_69 false _let_139)))) (let ((_let_142 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE 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(tptp.segmentP U tptp.nil))) _let_9 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.cyclefreeP (tptp.cons U tptp.nil)))) (tptp.cyclefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderP (tptp.cons U tptp.nil)))) (tptp.totalorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) _let_8 (tptp.totalorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))) (tptp.strictorderedP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) _let_7 (tptp.duplicatefreeP tptp.nil) _let_6 (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app W V) (tptp.app U V)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) _let_5 _let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) _let_3 _let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 43.28/43.60 )
% 43.28/43.60 % SZS output end Proof for SWC307+1
% 43.28/43.60 % cvc5---1.0.5 exiting
% 43.28/43.60 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------