TSTP Solution File: SWC113+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC113+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 20:23:21 EDT 2023
% Result : Theorem 31.66s 31.89s
% Output : Proof 31.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC113+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n010.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 15:55:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 31.66/31.89 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.KsnbyG2eix/cvc5---1.0.5_558.p...
% 31.66/31.89 ------- get file name : TPTP file name is SWC113+1
% 31.66/31.89 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_558.smt2...
% 31.66/31.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.66/31.89 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.66/31.89 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.66/31.89 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.66/31.89 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.66/31.89 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.66/31.89 % SZS status Theorem for SWC113+1
% 31.66/31.89 % SZS output start Proof for SWC113+1
% 31.66/31.89 (
% 31.66/31.89 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (and (forall ((Y $$unsorted)) (or (not (tptp.ssItem Y)) (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y)))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (or (not (= tptp.nil V)) (= tptp.nil U)) (or (not (tptp.neq V tptp.nil)) (and (tptp.neq U tptp.nil) (tptp.segmentP V U))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_4 (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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_9 (tptp.ssList tptp.nil))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_12 (forall ((U $$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_13 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_14 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13))) (let ((_let_15 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15))) (let ((_let_17 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_18 (= _let_17 (tptp.app _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14)))) (let ((_let_19 (tptp.segmentP _let_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (tptp.segmentP (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_21 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (not _let_21))) (let ((_let_23 (not _let_14))) (let ((_let_24 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_22))) (let ((_let_27 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_28 (not _let_27))) (let ((_let_29 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28))) (let ((_let_32 (and _let_26 _let_31))) (let ((_let_33 (or _let_30 _let_27))) (let ((_let_34 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_36 (and _let_35 _let_34))) (let ((_let_37 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36))) (let ((_let_40 (and _let_33 _let_39))) (let ((_let_41 (tptp.neq tptp.nil tptp.nil))) (let ((_let_42 (tptp.memberP tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_25 _let_43))) (let ((_let_45 (or))) (let ((_let_46 (REFL :args (_let_26)))) (let ((_let_47 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_45)) :args ((or _let_24 _let_26))))) (let ((_let_48 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_45)) :args ((or _let_21 _let_26))))) (let ((_let_49 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.memberP tptp.nil U)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (and _let_29 _let_21))) (let ((_let_52 (ASSUME :args (_let_21)))) (let ((_let_53 (ASSUME :args (_let_29)))) (let ((_let_54 (SYMM _let_53))) (let ((_let_55 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (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 (or _let_58 _let_56 _let_40 _let_32))) (let ((_let_60 (forall ((U $$unsorted) (BOUND_VARIABLE_5355 $$unsorted) (BOUND_VARIABLE_5353 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (not (= tptp.nil BOUND_VARIABLE_5353)))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5353)) (and (or _let_2 _let_1) (or (not (tptp.neq BOUND_VARIABLE_5353 tptp.nil)) (and (tptp.neq U tptp.nil) (tptp.segmentP BOUND_VARIABLE_5353 U)))) (and (or (not (tptp.ssItem BOUND_VARIABLE_5355)) (not (= U (tptp.cons BOUND_VARIABLE_5355 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5353 BOUND_VARIABLE_5355))) (or _let_2 (not _let_1))))))))) (let ((_let_61 (not _let_59))) (let ((_let_62 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_63 (not _let_60))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_62) :args (_let_63))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_60))) (REFL :args (_let_61)) :args _let_45)) _let_62 :args (_let_61 true _let_60)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 3)) _let_64 :args ((not _let_32) true _let_59)))) (let ((_let_66 (CNF_AND_NEG :args (_let_32)))) (let ((_let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))))) (let ((_let_68 (REFL :args (_let_31)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_59 2)) _let_64 :args ((not _let_40) true _let_59)))) (let ((_let_70 (CNF_AND_NEG :args (_let_40)))) (let ((_let_71 (not _let_41))) (let ((_let_72 (not _let_9))) (let ((_let_73 (or _let_72 _let_72 _let_71))) (let ((_let_74 (forall ((U $$unsorted) (BOUND_VARIABLE_3280 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3280)) (= (tptp.neq U BOUND_VARIABLE_3280) (not (= U BOUND_VARIABLE_3280))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_74))) (let ((_let_77 (ASSUME :args (_let_9)))) (let ((_let_78 (and _let_29 _let_71))) (let ((_let_79 (ASSUME :args (_let_71)))) (let ((_let_80 (REFL :args (tptp.nil)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_53) (SCOPE (FALSE_ELIM (TRANS (CONG _let_54 _let_80 :args (APPLY_UF tptp.neq)) (FALSE_INTRO _let_79))) :args (_let_71 _let_29))) :args (_let_29 _let_71))) :args (true _let_78)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_41))) (REFL :args (_let_38)) :args _let_45)) :args ((or _let_30 _let_38 _let_41))) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_73))) :args ((or _let_72 _let_71 (not _let_73)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.nil tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_76))) _let_75 :args (_let_73 false _let_74)) :args (_let_71 false _let_9 false _let_73)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG (REFL :args (_let_39)) (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) :args _let_45)) :args ((or _let_37 _let_39))) _let_70 _let_69 (CNF_OR_NEG :args (_let_33 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_68 _let_67 :args _let_45)) :args ((or _let_27 _let_31))) _let_66 _let_65 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_51)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_53) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_54) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args (APPLY_UF tptp.memberP)) (TRUE_INTRO _let_52))) :args (_let_21 _let_29))) :args (_let_29 _let_21))) :args (true _let_51)) (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_25 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_49))) _let_50 :args (_let_44 false _let_49)) _let_48 _let_47 :args ((or _let_30 _let_26) true _let_42 false _let_44 false _let_21 false _let_24)) :args (_let_30 true _let_41 false _let_37 true _let_39 true _let_40 false _let_33 false _let_27 true _let_31 true _let_32 false _let_26)))) (let ((_let_82 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))))) (let ((_let_83 (MACRO_RESOLUTION_TRUST _let_66 _let_65 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_68 _let_82 :args _let_45)) :args ((or _let_29 _let_31))) _let_81 :args (_let_31 true _let_29)) :args ((not _let_26) true _let_32 false _let_31)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_14))) :args _let_45)) :args ((or _let_14 _let_26))) _let_83 :args (_let_14 true _let_26)))) (let ((_let_85 (or _let_58 _let_16))) (let ((_let_86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (REFL :args (_let_59)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 0)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_45)) :args ((or _let_57 _let_59))) _let_64 :args (_let_57 true _let_59)))) (let ((_let_90 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_25 _let_18))) (let ((_let_93 (forall ((U $$unsorted) (BOUND_VARIABLE_4791 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4791)) (= (tptp.cons BOUND_VARIABLE_4791 U) (tptp.app (tptp.cons BOUND_VARIABLE_4791 tptp.nil) U)))))) (let ((_let_94 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 _let_17))) (let ((_let_96 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_95))) (let ((_let_97 (not _let_96))) (let ((_let_98 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_99 (not _let_98))) (let ((_let_100 (or _let_99 _let_91 _let_97))) (let ((_let_101 (forall ((W $$unsorted) (BOUND_VARIABLE_2145 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2145)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2145)))))))) (let ((_let_102 (not _let_100))) (let ((_let_103 (not _let_101))) (let ((_let_104 (= _let_21 _let_103))) (let ((_let_105 (or _let_56 _let_25 _let_104))) (let ((_let_106 (forall ((U $$unsorted) (BOUND_VARIABLE_2171 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2171)) (= (tptp.memberP U BOUND_VARIABLE_2171) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2145 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2145)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2171 BOUND_VARIABLE_2145)))))))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST _let_47 _let_83 :args (_let_24 true _let_26)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_59 1)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_45)) :args ((or _let_55 _let_59))) _let_64 :args (_let_55 true _let_59)))) (let ((_let_110 (_let_103))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_110)) :args _let_110)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_103) _let_101))) (REFL :args (_let_102)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_104)) :args ((or _let_22 _let_103 (not _let_104)))) (MACRO_RESOLUTION_TRUST _let_48 _let_83 :args (_let_21 true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_56 _let_25 _let_104 (not _let_105)))) _let_109 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2171)))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_104 false _let_55 false _let_24 false _let_105)) :args (_let_103 false _let_21 false _let_104)) :args (_let_102 true _let_101)))) (let ((_let_112 (REFL :args (_let_100)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_100 1)) (CONG _let_112 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) :args _let_45)) :args ((or _let_90 _let_100))) _let_111 :args (_let_90 true _let_100)))) (let ((_let_114 (tptp.segmentP (tptp.app _let_95 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_115 (not _let_19))) (let ((_let_116 (tptp.ssList _let_17))) (let ((_let_117 (not _let_116))) (let ((_let_118 (or _let_117 _let_58 _let_115 _let_99 _let_72 _let_114))) (let ((_let_119 (forall ((U $$unsorted) (BOUND_VARIABLE_4454 $$unsorted) (BOUND_VARIABLE_4452 $$unsorted) (BOUND_VARIABLE_4450 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4450)) (not (tptp.segmentP U BOUND_VARIABLE_4450)) (not (tptp.ssList BOUND_VARIABLE_4454)) (not (tptp.ssList BOUND_VARIABLE_4452)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4454 U) BOUND_VARIABLE_4452) BOUND_VARIABLE_4450))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (_let_119))) (let ((_let_122 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_123 (not _let_114))) (let ((_let_124 (or _let_56 _let_122))) (let ((_let_125 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT 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(tptp.ssList U) (forall ((V $$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_7 (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 $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) _let_6 (not (tptp.singletonP tptp.nil)) (forall ((U $$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_5 _let_4 (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderP (tptp.cons U tptp.nil)))) (tptp.strictorderP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.totalorderedP (tptp.cons U tptp.nil)))) (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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.strictorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.strictorderedP V) (tptp.lt U (tptp.hd V)))))))))) (forall ((U $$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_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) _let_2 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.66/31.90 )
% 31.66/31.90 % SZS output end Proof for SWC113+1
% 31.66/31.90 % cvc5---1.0.5 exiting
% 31.66/31.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------