TSTP Solution File: SWC342+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC342+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:24:54 EDT 2023
% Result : Theorem 31.96s 32.23s
% Output : Proof 31.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWC342+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 18:13:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.51 %----Proving TF0_NAR, FOF, or CNF
% 31.96/32.23 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.FVXn0fwEey/cvc5---1.0.5_27310.p...
% 31.96/32.23 ------- get file name : TPTP file name is SWC342+1
% 31.96/32.23 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_27310.smt2...
% 31.96/32.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.96/32.23 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.96/32.23 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.96/32.23 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.96/32.23 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.96/32.23 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.96/32.23 % SZS status Theorem for SWC342+1
% 31.96/32.23 % SZS output start Proof for SWC342+1
% 31.96/32.23 (
% 31.96/32.23 (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)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.segmentP V U) (tptp.totalorderedP U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (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_4 (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 ((_let_5 (tptp.totalorderedP tptp.nil))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_15 (tptp.totalorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_18 (tptp.totalorderedP _let_16))) (let ((_let_19 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (and _let_19 _let_15))) (let ((_let_21 (not _let_15))) (let ((_let_22 (forall ((W $$unsorted) (BOUND_VARIABLE_2302 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2302)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2302))))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (= _let_19 _let_23))) (let ((_let_25 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_11))) (let ((_let_31 (or _let_30 _let_29 _let_27))) (let ((_let_32 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (not _let_32))) (let ((_let_34 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_17))) (let ((_let_40 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_38))) (let ((_let_43 (and _let_42 _let_36))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_29 _let_24))) (let ((_let_47 (forall ((U $$unsorted) (BOUND_VARIABLE_2327 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2327)) (= (tptp.segmentP U BOUND_VARIABLE_2327) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2302 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2302)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2327) BOUND_VARIABLE_2302))))))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or _let_29 _let_45 _let_20 _let_43))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_5358 $$unsorted) (BOUND_VARIABLE_5356 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5356)) (and (tptp.segmentP BOUND_VARIABLE_5356 U) (tptp.totalorderedP U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5358)) (not (= U (tptp.cons BOUND_VARIABLE_5358 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5356 BOUND_VARIABLE_5358))) (or (not (= tptp.nil BOUND_VARIABLE_5356)) (not (= tptp.nil U)))))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_52) :args (_let_54))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST _let_55 _let_52 :args (_let_51 true _let_50)))) (let ((_let_57 (REFL :args (_let_49)))) (let ((_let_58 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_53)) :args ((or _let_44 _let_49))))) (let ((_let_59 (MACRO_RESOLUTION_TRUST _let_58 _let_56 :args (_let_44 true _let_49)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_53)) :args ((or _let_28 _let_49))) _let_56 :args (_let_28 true _let_49)))) (let ((_let_61 (not _let_24))) (let ((_let_62 (_let_22))) (let ((_let_63 (ASSUME :args (_let_11)))) (let ((_let_64 (= tptp.nil (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_65 (= _let_32 _let_64))) (let ((_let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_25))) (let ((_let_67 (REFL :args (_let_36)))) (let ((_let_68 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_53)) :args ((or _let_34 _let_36))))) (let ((_let_69 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_53)) :args ((or _let_32 _let_36))))) (let ((_let_70 (or _let_29 _let_29 _let_65))) (let ((_let_71 (forall ((U $$unsorted) (BOUND_VARIABLE_4853 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4853)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4853)) (and (= tptp.nil BOUND_VARIABLE_4853) (= tptp.nil U))))))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or _let_29 _let_66))) (let ((_let_74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_29 _let_66 (not _let_73)))) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_74))) _let_75 :args (_let_73 false _let_74)) :args (_let_66 false _let_28 false _let_73)))) (let ((_let_77 (not _let_66))) (let ((_let_78 (REFL :args (_let_35)))) (let ((_let_79 (and _let_34 _let_66 _let_27))) (let ((_let_80 (ASSUME :args (_let_27)))) (let ((_let_81 (=))) (let ((_let_82 (APPLY_UF tptp.app))) (let ((_let_83 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_84 (ASSUME :args (_let_66)))) (let ((_let_85 (SYMM (SYMM _let_84)))) (let ((_let_86 (ASSUME :args (_let_34)))) (let ((_let_87 (SYMM _let_86))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_49 3)) _let_56 :args ((not _let_43) true _let_49)))) (let ((_let_89 (CNF_AND_NEG :args (_let_43)))) (let ((_let_90 (REFL :args (_let_42)))) (let ((_let_91 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_53)) :args ((or _let_40 _let_42))))) (let ((_let_92 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_90 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_17))) :args _let_53)) :args ((or _let_17 _let_42))))) (let ((_let_93 (forall ((U $$unsorted) (BOUND_VARIABLE_2163 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2163)) (= (tptp.memberP U BOUND_VARIABLE_2163) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2137 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2137)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2163 BOUND_VARIABLE_2137)))))))))))) (let ((_let_94 (forall ((W $$unsorted) (BOUND_VARIABLE_2137 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2137)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2137)))))))) (let ((_let_95 (not _let_94))) (let ((_let_96 (= _let_37 _let_95))) (let ((_let_97 (or _let_45 _let_41 _let_96))) (let ((_let_98 (forall ((U $$unsorted) (BOUND_VARIABLE_3320 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3320)) (not (= U (tptp.cons BOUND_VARIABLE_3320 U))))))) (let ((_let_99 (= tptp.nil _let_16))) (let ((_let_100 (not _let_99))) (let ((_let_101 (or _let_30 _let_41 _let_100))) (let ((_let_102 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_103 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_102))) (let ((_let_104 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_103))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_107 (not _let_106))) (let ((_let_108 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_109 (not _let_108))) (let ((_let_110 (or _let_109 _let_107 _let_105))) (let ((_let_111 (= _let_102 (tptp.app _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_112 (or _let_107 _let_41 _let_111))) (let ((_let_113 (tptp.ssList _let_102))) (let ((_let_114 (or _let_107 _let_41 _let_113))) (let ((_let_115 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_116 (tptp.segmentP (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_117 (not _let_115))) (let ((_let_118 (or _let_29 _let_29 _let_117 _let_30 _let_107 _let_116))) (let ((_let_119 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_120 (tptp.segmentP (tptp.app _let_103 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_121 (tptp.segmentP _let_102 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_122 (not _let_121))) (let ((_let_123 (not _let_113))) (let ((_let_124 (or _let_123 _let_29 _let_122 _let_109 _let_30 _let_120))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (REFL :args (_let_33)))) (let ((_let_128 (REFL :args (_let_39)))) (let ((_let_129 (and _let_17 _let_100))) (let ((_let_130 (ASSUME :args (_let_100)))) (let ((_let_131 (ASSUME :args (_let_17)))) (let ((_let_132 (SYMM _let_131))) (let ((_let_133 (REFL :args (tptp.nil)))) (let ((_let_134 (_let_95))) (let ((_let_135 (REFL :args (_let_110)))) (let ((_let_136 (forall ((U $$unsorted) (BOUND_VARIABLE_4783 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4783)) (= (tptp.cons BOUND_VARIABLE_4783 U) (tptp.app (tptp.cons BOUND_VARIABLE_4783 tptp.nil) U)))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (forall ((U $$unsorted) (BOUND_VARIABLE_3295 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3295)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3295 U)))))) (let ((_let_139 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT 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(EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_149 (not _let_19))) (let ((_let_150 (and _let_149 _let_119 _let_104))) (let ((_let_151 (_let_149 _let_119 _let_104))) (let ((_let_152 (ASSUME :args (_let_149)))) (let ((_let_153 (APPLY_UF tptp.segmentP))) (let ((_let_154 (ASSUME :args (_let_119)))) (let ((_let_155 (ASSUME :args (_let_104)))) (let ((_let_156 (and _let_17 _let_66 _let_111 _let_116))) (let ((_let_157 (ASSUME :args (_let_116)))) (let ((_let_158 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_159 (ASSUME :args (_let_111)))) (let ((_let_160 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_20)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_49 2)) _let_56 :args ((not _let_20) true _let_49)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_30 _let_29 _let_109 _let_123 _let_122 _let_120 (not _let_124)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM 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(= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_12 _let_11 _let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_9 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$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)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_8 _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.segmentP tptp.nil U) (= tptp.nil U)))) (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) _let_6 _let_5 (forall ((U $$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)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))) (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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_4 (forall ((U $$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_3 _let_2 (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))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$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)))))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.96/32.24 )
% 31.96/32.24 % SZS output end Proof for SWC342+1
% 31.96/32.24 % cvc5---1.0.5 exiting
% 31.96/32.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------