%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC390+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 20:25:16 EDT 2023

% Result   : Theorem 32.70s 32.95s
% Output   : Proof 32.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SWC390+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.12  % Command    : do_cvc5 %s %d
% 0.11/0.32  % Computer : n007.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Mon Aug 28 15:04:43 EDT 2023
% 0.11/0.33  % CPUTime    : 
% 0.17/0.43  %----Proving TF0_NAR, FOF, or CNF
% 32.70/32.95  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.OUL0KIAuDh/cvc5---1.0.5_28966.p...
% 32.70/32.95  ------- get file name : TPTP file name is SWC390+1
% 32.70/32.95  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28966.smt2...
% 32.70/32.95  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 32.70/32.95  --- Run --no-e-matching --full-saturate-quant at 5...
% 32.70/32.95  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 32.70/32.95  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 32.70/32.95  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 32.70/32.95  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 32.70/32.95  % SZS status Theorem for SWC390+1
% 32.70/32.95  % SZS output start Proof for SWC390+1
% 32.70/32.95  (
% 32.70/32.95  (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 (not (= tptp.nil W)) (= tptp.nil X)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y))))) (tptp.neq X tptp.nil)) (and (tptp.segmentP V U) (or (not (tptp.neq V tptp.nil)) (tptp.singletonP U))))))))))))))) (let ((_let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (=> (tptp.segmentP U V) (tptp.segmentP (tptp.app (tptp.app W U) X) V)))))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_13 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= (tptp.cons V tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_14 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_15 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16))) (let ((_let_20 (not _let_13))) (let ((_let_21 (tptp.singletonP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (= _let_21 _let_20))) (let ((_let_23 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (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_27 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_29 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_18 _let_16 _let_30))) (let ((_let_32 (and _let_31 _let_28))) (let ((_let_33 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (not _let_34))) (let ((_let_36 (and _let_35 _let_33))) (let ((_let_37 (not _let_28))) (let ((_let_38 (or _let_37 _let_21))) (let ((_let_39 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_40 (and _let_39 _let_38))) (let ((_let_41 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_24 _let_42 _let_40 _let_36 _let_32))) (let ((_let_44 (forall ((U $$unsorted) (BOUND_VARIABLE_5360 $$unsorted) (BOUND_VARIABLE_5358 $$unsorted)) (let ((_let_1 (tptp.neq BOUND_VARIABLE_5358 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5358)) (and (tptp.segmentP BOUND_VARIABLE_5358 U) (or (not _let_1) (tptp.singletonP U))) (and (not (= tptp.nil U)) (= tptp.nil BOUND_VARIABLE_5358)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5360)) (not (= U (tptp.cons BOUND_VARIABLE_5360 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5358 BOUND_VARIABLE_5360))) _let_1)))))) (let ((_let_45 (not _let_43))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (or))) (let ((_let_48 (not _let_44))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_46) :args (_let_48))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_44))) (REFL :args (_let_45)) :args _let_47)) _let_46 :args (_let_45 true _let_44)))) (let ((_let_50 (REFL :args (_let_43)))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 0)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_47)) :args ((or _let_23 _let_43))) _let_49 :args (_let_23 true _let_43)))) (let ((_let_52 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_53 (not _let_33))) (let ((_let_54 (= _let_28 _let_53))) (let ((_let_55 (forall ((W $$unsorted) (BOUND_VARIABLE_2140 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2140)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2140)))))))) (let ((_let_56 (not _let_55))) (let ((_let_57 (= _let_29 _let_56))) (let ((_let_58 (or _let_42 _let_18 _let_57))) (let ((_let_59 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_60 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_59))) (let ((_let_61 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_60))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_64 (not _let_63))) (let ((_let_65 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_62))) (let ((_let_68 (= _let_59 (tptp.app _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_69 (or _let_64 _let_18 _let_68))) (let ((_let_70 (tptp.ssList _let_59))) (let ((_let_71 (or _let_64 _let_18 _let_70))) (let ((_let_72 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_73 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_74 (tptp.segmentP (tptp.app _let_73 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_75 (not _let_8))) (let ((_let_76 (not _let_72))) (let ((_let_77 (or _let_24 _let_24 _let_76 _let_75 _let_64 _let_74))) (let ((_let_78 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_79 (tptp.segmentP (tptp.app _let_60 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_80 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_73))) (let ((_let_81 (tptp.segmentP _let_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_82 (not _let_81))) (let ((_let_83 (not _let_70))) (let ((_let_84 (or _let_83 _let_24 _let_82 _let_66 _let_75 _let_79))) (let ((_let_85 (or _let_42 _let_52))) (let ((_let_86 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG _let_50 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_47)) :args ((or _let_41 _let_43))) _let_49 :args (_let_41 true _let_43)))) (let ((_let_89 (not _let_52))) (let ((_let_90 (not _let_39))) (let ((_let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_90) _let_39))))) (let ((_let_92 (ASSUME :args (_let_52)))) (let ((_let_93 (APPLY_UF tptp.segmentP))) (let ((_let_94 (ASSUME :args (_let_34)))) (let ((_let_95 (ASSUME :args (_let_90)))) (let ((_let_96 (FALSE_INTRO _let_95))) (let ((_let_97 (_let_36))) (let ((_let_98 (or _let_42 _let_75 _let_54))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_3275 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3275)) (= (tptp.neq U BOUND_VARIABLE_3275) (not (= U BOUND_VARIABLE_3275))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (ASSUME :args (_let_8)))) (let ((_let_102 (not _let_54))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 4)) _let_49 :args ((not _let_32) true _let_43)))) (let ((_let_104 (not _let_31))) (let ((_let_105 (REORDERING (CNF_AND_NEG :args (_let_32)) :args ((or _let_37 _let_32 _let_104))))) (let ((_let_106 (REFL :args (_let_31)))) (let ((_let_107 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_47)) :args ((or _let_17 _let_31))))) (let ((_let_108 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_106 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_47)) :args ((or _let_15 _let_31))))) (let ((_let_109 (forall ((U $$unsorted) (BOUND_VARIABLE_2166 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2166)) (= (tptp.memberP U BOUND_VARIABLE_2166) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2140 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2140)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2166 BOUND_VARIABLE_2140)))))))))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_56))) (let ((_let_112 (REFL :args (_let_67)))) (let ((_let_113 (forall ((U $$unsorted) (BOUND_VARIABLE_4786 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4786)) (= (tptp.cons BOUND_VARIABLE_4786 U) (tptp.app (tptp.cons BOUND_VARIABLE_4786 tptp.nil) U)))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (forall ((U $$unsorted) (BOUND_VARIABLE_3298 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3298)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3298 U)))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (or _let_24 _let_72))) (let ((_let_118 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (forall ((U $$unsorted) (BOUND_VARIABLE_4449 $$unsorted) (BOUND_VARIABLE_4447 $$unsorted) (BOUND_VARIABLE_4445 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4445)) (not (tptp.segmentP U BOUND_VARIABLE_4445)) (not (tptp.ssList BOUND_VARIABLE_4449)) (not (tptp.ssList BOUND_VARIABLE_4447)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4449 U) BOUND_VARIABLE_4447) BOUND_VARIABLE_4445))))) (let ((_let_121 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_122 (_let_120))) (let ((_let_123 (or _let_42 _let_78))) (let ((_let_124 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_125 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_126 (and _let_90 _let_78 _let_61))) (let ((_let_127 (_let_90 _let_78 _let_61))) (let ((_let_128 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_129 (ASSUME :args (_let_78)))) (let ((_let_130 (APPLY_UF tptp.app))) (let ((_let_131 (ASSUME :args (_let_61)))) (let ((_let_132 (or _let_24 _let_80))) (let ((_let_133 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_134 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_135 (and _let_15 _let_80 _let_68 _let_74))) (let ((_let_136 (ASSUME :args (_let_74)))) (let ((_let_137 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)))) (let ((_let_138 (ASSUME :args (_let_80)))) (let ((_let_139 (ASSUME :args (_let_15)))) (let ((_let_140 (ASSUME :args (_let_68)))) (let ((_let_141 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_40)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_43 2)) _let_49 :args ((not _let_40) true _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_75 _let_24 _let_66 _let_83 _let_82 _let_79 (not _let_84)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (_let_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4449 U) BOUND_VARIABLE_4447) BOUND_VARIABLE_4445) true))))) :args _let_122)) _let_121 :args (_let_84 false _let_120)) _let_51 _let_101 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_135)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_136 _let_138 _let_139 _let_140) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_140)) (CONG (SYMM _let_139) _let_137 :args _let_130) (CONG (SYMM (SYMM _let_138)) _let_137 :args _let_130)) _let_128 :args _let_93) (TRUE_INTRO _let_136))) :args (_let_74 _let_80 _let_15 _let_68))) :args (_let_15 _let_80 _let_68 _let_74))) :args (true _let_135)) :args ((or _let_16 (not _let_80) _let_81 (not _let_68) (not _let_74)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_132)) :args ((or _let_24 _let_80 (not _let_132)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_134 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_133))) _let_134 :args (_let_132 false _let_133)) :args (_let_80 false _let_23 false _let_132)) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_126)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_95 _let_129 _let_131) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (SYMM _let_131) (REFL :args (tptp.nil)) :args _let_130) (SYMM _let_129)) _let_128 :args _let_93) _let_96)) :args _let_127)) :args _let_127)) :args (true _let_126)) (CONG _let_91 (REFL :args ((not _let_78))) (REFL :args (_let_62)) (REFL :args ((not _let_79))) :args _let_47)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_42 _let_78 (not _let_123)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_125 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_124))) _let_125 :args 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(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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_6 _let_5 _let_4 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 32.70/32.95  )
% 32.70/32.95  % SZS output end Proof for SWC390+1
% 32.70/32.95  % cvc5---1.0.5 exiting
% 32.70/32.95  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------