%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC125+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 20:23:26 EDT 2023

% Result   : Theorem 77.40s 77.68s
% Output   : Proof 77.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SWC125+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.34  % Computer : n009.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 28 15:25:50 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.48  %----Proving TF0_NAR, FOF, or CNF
% 77.40/77.68  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.oXwH129CyW/cvc5---1.0.5_15409.p...
% 77.40/77.68  ------- get file name : TPTP file name is SWC125+1
% 77.40/77.68  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15409.smt2...
% 77.40/77.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 77.40/77.68  --- Run --no-e-matching --full-saturate-quant at 5...
% 77.40/77.68  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 77.40/77.68  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 77.40/77.68  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 77.40/77.68  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 77.40/77.68  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 77.40/77.68  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 77.40/77.68  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 77.40/77.68  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 77.40/77.68  --- Run --relevant-triggers --full-saturate-quant at 5...
% 77.40/77.68  --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 77.40/77.68  --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.40/77.68  --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 77.40/77.68  % SZS status Theorem for SWC125+1
% 77.40/77.68  % SZS output start Proof for SWC125+1
% 77.40/77.68  (
% 77.40/77.68  (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.neq V tptp.nil)) (not (tptp.segmentP X W)) (not (tptp.strictorderedP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.segmentP X Y) (tptp.segmentP Y W) (tptp.strictorderedP Y))) (and (tptp.neq U tptp.nil) (tptp.segmentP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.strictorderedP (tptp.cons U tptp.nil)))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_6 (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_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_8 (tptp.singletonP tptp.nil))) (let ((_let_9 (not _let_8))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_13 (forall ((U $$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_14 (tptp.ssList tptp.nil))) (let ((_let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_18 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_20 (tptp.cons _let_19 _let_18))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_22 (tptp.cons _let_19 tptp.nil))) (let ((_let_23 (= _let_20 (tptp.app _let_22 _let_18)))) (let ((_let_24 (tptp.app tptp.nil _let_22))) (let ((_let_25 (= _let_22 _let_24))) (let ((_let_26 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_22))) (let ((_let_27 (tptp.segmentP (tptp.app _let_24 _let_18) _let_22))) (let ((_let_28 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or _let_30 _let_28 _let_21))) (let ((_let_32 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (not _let_28))) (let ((_let_35 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_36 (= _let_35 _let_34))) (let ((_let_37 (not _let_14))) (let ((_let_38 (or _let_30 _let_37 _let_36))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_3270 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3270)) (= (tptp.neq U BOUND_VARIABLE_3270) (not (= U BOUND_VARIABLE_3270))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (_let_39))) (let ((_let_42 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.strictorderedP Y)))))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_45 (not _let_44))) (let ((_let_46 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_47 (and _let_46 _let_44))) (let ((_let_48 (not _let_35))) (let ((_let_49 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 (not (tptp.strictorderedP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_30 _let_48 _let_47 _let_45 _let_43))) (let ((_let_52 (forall ((U $$unsorted) (BOUND_VARIABLE_5274 $$unsorted)) (let ((_let_1 (tptp.segmentP BOUND_VARIABLE_5274 U))) (or (not (tptp.ssList U)) (not (tptp.strictorderedP U)) (not (tptp.ssList BOUND_VARIABLE_5274)) (not (tptp.neq BOUND_VARIABLE_5274 tptp.nil)) (and (tptp.neq U tptp.nil) _let_1) (not _let_1) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.segmentP BOUND_VARIABLE_5274 Y)) (not (tptp.segmentP Y U)) (not (tptp.strictorderedP Y)))))))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (or))) (let ((_let_56 (not _let_52))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_54) :args (_let_56))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_52))) (REFL :args (_let_53)) :args _let_55)) _let_54 :args (_let_53 true _let_52)))) (let ((_let_58 (REFL :args (_let_51)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 2)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_55)) :args ((or _let_29 _let_51))) _let_57 :args (_let_29 true _let_51)))) (let ((_let_60 (ASSUME :args (_let_14)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_48 _let_34 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 3)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_35))) :args _let_55)) :args ((or _let_35 _let_51))) _let_57 :args (_let_35 true _let_51)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_30 _let_36 (not _let_38)))) _let_60 _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_41))) _let_40 :args (_let_38 false _let_39)) :args (_let_36 false _let_14 false _let_29 false _let_38)) :args (_let_34 false _let_35 false _let_36)))) (let ((_let_62 (tptp.ssItem _let_19))) (let ((_let_63 (not _let_62))) (let ((_let_64 (tptp.ssList _let_18))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63 _let_23))) (let ((_let_67 (forall ((U $$unsorted) (BOUND_VARIABLE_4781 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4781)) (= (tptp.cons BOUND_VARIABLE_4781 U) (tptp.app (tptp.cons BOUND_VARIABLE_4781 tptp.nil) U)))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_70 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_69)))) (let ((_let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_69))) (let ((_let_72 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_73 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_74 (not _let_73))) (let ((_let_75 (not _let_72))) (let ((_let_76 (or _let_75 _let_74 _let_70))) (let ((_let_77 (forall ((U $$unsorted) (BOUND_VARIABLE_3529 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3529)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3529 U))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (not _let_71))) (let ((_let_80 (or _let_75 _let_74 _let_79))) (let ((_let_81 (forall ((V $$unsorted) (BOUND_VARIABLE_3440 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3440)) (not (= (tptp.cons BOUND_VARIABLE_3440 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_82 (not _let_80))) (let ((_let_83 (not _let_81))) (let ((_let_84 (or _let_30 _let_28 _let_83))) (let ((_let_85 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3440 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3440)) (not (= U (tptp.cons BOUND_VARIABLE_3440 V)))))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_83))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_87)) :args _let_87) (REWRITE :args ((=> _let_83 (not (or _let_75 _let_74 (not (= _let_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_81))) (REFL :args (_let_82)) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_30 _let_28 _let_83 (not _let_84)))) _let_59 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_85)))) _let_86 :args (_let_84 false _let_85)) :args (_let_83 false _let_29 true _let_28 false _let_84)) :args (_let_82 true _let_81)))) (let ((_let_89 (REFL :args (_let_80)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 0)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_72))) :args _let_55)) :args ((or _let_72 _let_80))) _let_88 :args (_let_72 true _let_80)))) (let ((_let_91 (and _let_72 _let_71 _let_70))) (let ((_let_92 (ASSUME :args (_let_72)))) (let ((_let_93 (ASSUME :args (_let_70)))) (let ((_let_94 (ASSUME :args (_let_71)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_91)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_92 _let_93 _let_94) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (CONG (SYMM (SYMM _let_94)) :args (APPLY_UF tptp.tl)) (SYMM _let_93)) :args (APPLY_UF tptp.ssList)) (TRUE_INTRO _let_92))) :args (_let_72 _let_70 _let_71))) :args (_let_72 _let_71 _let_70))) :args (true _let_91)) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 2)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_79) _let_71))) :args _let_55)) :args ((or _let_71 _let_80))) _let_88 :args (_let_71 true _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_74 _let_70 (not _let_76)))) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_80 1)) (CONG _let_89 (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) :args _let_55)) :args ((or _let_73 _let_80))) _let_88 :args (_let_73 true _let_80)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_70 false _let_72 false _let_73 false _let_76)) :args (_let_64 false _let_72 false _let_71 false _let_70)))) (let ((_let_96 (or _let_30 _let_28 _let_62))) (let ((_let_97 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_30 _let_28 _let_62 (not _let_96)))) _let_59 _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_97))) _let_98 :args (_let_96 false _let_97)) :args (_let_62 false _let_29 true _let_28 false _let_96)))) (let ((_let_100 (tptp.ssList _let_22))) (let ((_let_101 (not _let_100))) (let ((_let_102 (or _let_101 _let_25))) (let ((_let_103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (or _let_37 _let_63 _let_100))) (let ((_let_106 (forall ((U $$unsorted) (BOUND_VARIABLE_3293 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3293)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3293 U)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_15)) (MACRO_SR_EQ_INTRO :args (_let_15 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_37 _let_63 _let_100 (not _let_105)))) _let_60 _let_99 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (tptp.nil _let_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_100 false _let_14 false _let_62 false _let_105)))) (let ((_let_109 (tptp.strictorderedP _let_22))) (let ((_let_110 (not _let_109))) (let ((_let_111 (tptp.segmentP _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_112 (not _let_111))) (let ((_let_113 (not _let_26))) (let ((_let_114 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_115 (not _let_114))) (let ((_let_116 (or _let_101 _let_115 _let_113 _let_112 _let_110))) (let ((_let_117 (_let_42))) (let ((_let_118 (tptp.segmentP _let_22 tptp.nil))) (let ((_let_119 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_120 (or _let_101 _let_118))) (let ((_let_121 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_123 (not _let_119))) (let ((_let_124 (= _let_46 _let_123))) (let ((_let_125 (or _let_50 _let_37 _let_124))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_58 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_55)) :args ((or _let_49 _let_51))) _let_57 :args (_let_49 true _let_51)))) (let ((_let_127 (not _let_46))) (let ((_let_128 (not _let_124))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_124)) (CONG (REFL :args (_let_128)) (REFL :args (_let_46)) 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(tptp.ssItem W) (forall ((X $$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.lt V W))))))))))))))) (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)))))))))))))))) (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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) _let_16 _let_15 _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_12 (forall ((U $$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))))) _let_11 (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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_10 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_9 (forall ((U $$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_7 _let_6 _let_5 (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 $$unsorted)) (let ((_let_1 (= tptp.nil V))) (=> (tptp.ssList V) (= (tptp.totalorderedP (tptp.cons U V)) (or _let_1 (and (not _let_1) (tptp.totalorderedP V) (tptp.leq U (tptp.hd V)))))))))) _let_4 (tptp.strictorderedP tptp.nil) (forall ((U $$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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_3 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_2 (forall ((U $$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))))))) (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 77.40/77.69  )
% 77.40/77.69  % SZS output end Proof for SWC125+1
% 77.50/77.69  % cvc5---1.0.5 exiting
% 77.50/77.69  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------