%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC354+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 20:24:59 EDT 2023

% Result   : Theorem 26.70s 26.96s
% Output   : Proof 26.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SWC354+1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon Aug 28 18:30:58 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 26.70/26.96  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.KyzOB9i5kM/cvc5---1.0.5_19209.p...
% 26.70/26.96  ------- get file name : TPTP file name is SWC354+1
% 26.70/26.96  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_19209.smt2...
% 26.70/26.96  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.70/26.96  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.70/26.96  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.70/26.96  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.70/26.96  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.70/26.96  % SZS status Theorem for SWC354+1
% 26.70/26.96  % SZS output start Proof for SWC354+1
% 26.70/26.96  (
% 26.70/26.96  (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)) (let ((_let_1 (not (tptp.neq V tptp.nil)))) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (and (or _let_1 (exists ((Y $$unsorted)) (and (tptp.ssList Y) (not (= W Y)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (= (tptp.cons Z tptp.nil) Y) (= (tptp.hd X) Z) (tptp.neq tptp.nil X))))) (tptp.segmentP V U)) (or _let_1 (tptp.neq X tptp.nil)))))))))))))))) (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.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_7 (forall ((U $$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_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 $$unsorted)) (=> (tptp.ssList U) (forall ((V $$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_12 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_13 (tptp.ssItem _let_12))) (let ((_let_14 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_15 (tptp.cons _let_12 tptp.nil))) (let ((_let_16 (tptp.cons _let_12 _let_14))) (let ((_let_17 (= _let_16 (tptp.app _let_15 _let_14)))) (let ((_let_18 (not _let_13))) (let ((_let_19 (tptp.ssList _let_14))) (let ((_let_20 (not _let_19))) (let ((_let_21 (or _let_20 _let_18 _let_17))) (let ((_let_22 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_13))) (let ((_let_26 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (not _let_22))) (let ((_let_29 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_30 (= _let_29 _let_28))) (let ((_let_31 (not _let_8))) (let ((_let_32 (or _let_24 _let_31 _let_30))) (let ((_let_33 (forall ((U $$unsorted) (BOUND_VARIABLE_3276 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3276)) (= (tptp.neq U BOUND_VARIABLE_3276) (not (= U BOUND_VARIABLE_3276))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_15))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.ssList _let_15))) (let ((_let_39 (tptp.neq tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_40 (and _let_39 _let_13 _let_38 _let_37))) (let ((_let_41 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_42 (not _let_29))) (let ((_let_43 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_24 _let_42 _let_41 _let_40))) (let ((_let_46 (forall ((U $$unsorted) (BOUND_VARIABLE_5328 $$unsorted)) (let ((_let_1 (tptp.hd BOUND_VARIABLE_5328))) (let ((_let_2 (tptp.cons _let_1 tptp.nil))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5328)) (not (tptp.neq BOUND_VARIABLE_5328 tptp.nil)) (tptp.segmentP BOUND_VARIABLE_5328 U) (and (tptp.neq tptp.nil BOUND_VARIABLE_5328) (tptp.ssItem _let_1) (tptp.ssList _let_2) (not (= U _let_2))))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or))) (let ((_let_50 (not _let_46))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_48) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_49)) _let_48 :args (_let_47 true _let_46)))) (let ((_let_52 (REFL :args (_let_45)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_49)) :args ((or _let_23 _let_45))) _let_51 :args (_let_23 true _let_45)))) (let ((_let_54 (ASSUME :args (_let_8)))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or _let_42 _let_28 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 2)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_29))) :args _let_49)) :args ((or _let_29 _let_45))) _let_51 :args (_let_29 true _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_24 _let_30 (not _let_32)))) _let_54 _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_35))) _let_34 :args (_let_32 false _let_33)) :args (_let_30 false _let_8 false _let_23 false _let_32)) :args (_let_28 false _let_29 false _let_30)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_13 _let_22 (not _let_25)))) _let_53 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_26))) _let_27 :args (_let_25 false _let_26)) :args (_let_13 false _let_23 true _let_22 false _let_25)))) (let ((_let_57 (forall ((U $$unsorted) (BOUND_VARIABLE_4787 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4787)) (= (tptp.cons BOUND_VARIABLE_4787 U) (tptp.app (tptp.cons BOUND_VARIABLE_4787 tptp.nil) U)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_60 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.tl _let_59)))) (let ((_let_61 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_59))) (let ((_let_62 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_63 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_64 (not _let_63))) (let ((_let_65 (not _let_62))) (let ((_let_66 (or _let_65 _let_64 _let_60))) (let ((_let_67 (forall ((U $$unsorted) (BOUND_VARIABLE_3535 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3535)) (= U (tptp.tl (tptp.cons BOUND_VARIABLE_3535 U))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (not _let_61))) (let ((_let_70 (or _let_65 _let_64 _let_69))) (let ((_let_71 (forall ((V $$unsorted) (BOUND_VARIABLE_3446 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3446)) (not (= (tptp.cons BOUND_VARIABLE_3446 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_72 (not _let_70))) (let ((_let_73 (not _let_71))) (let ((_let_74 (or _let_24 _let_22 _let_73))) (let ((_let_75 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3446 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3446)) (not (= U (tptp.cons BOUND_VARIABLE_3446 V)))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_73))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_77)) :args _let_77) (REWRITE :args ((=> _let_73 (not (or _let_65 _let_64 (not (= _let_59 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_71))) (REFL :args (_let_72)) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_24 _let_22 _let_73 (not _let_74)))) _let_53 _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_75)))) _let_76 :args (_let_74 false _let_75)) :args (_let_73 false _let_23 true _let_22 false _let_74)) :args (_let_72 true _let_71)))) (let ((_let_79 (REFL :args (_let_70)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_62))) :args _let_49)) :args ((or _let_62 _let_70))) _let_78 :args (_let_62 true _let_70)))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_65 _let_64 _let_60 (not _let_66)))) _let_80 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_49)) :args ((or _let_63 _let_70))) _let_78 :args (_let_63 true _let_70)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_67))) _let_68 :args (_let_66 false _let_67)) :args (_let_60 false _let_62 false _let_63 false _let_66)))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_70 2)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_61))) :args _let_49)) :args ((or _let_61 _let_70))) _let_78 :args (_let_61 true _let_70)))) (let ((_let_83 (and _let_62 _let_61 _let_60))) (let ((_let_84 (ASSUME :args (_let_62)))) (let ((_let_85 (ASSUME :args (_let_60)))) (let ((_let_86 (ASSUME :args (_let_61)))) (let ((_let_87 (TRANS (CONG (SYMM (SYMM _let_86)) :args (APPLY_UF tptp.tl)) (SYMM _let_85)))) (let ((_let_88 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_89 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app _let_88 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_90 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_16))) (let ((_let_91 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_88))) (let ((_let_92 (not _let_17))) (let ((_let_93 (not _let_89))) (let ((_let_94 (or _let_31 _let_65 _let_93))) (let ((_let_95 (forall ((W $$unsorted) (BOUND_VARIABLE_2306 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2306)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2306))))))) (let ((_let_96 (not _let_95))) (let ((_let_97 (= _let_41 _let_96))) (let ((_let_98 (or _let_24 _let_44 _let_97))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_2331 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2331)) (= (tptp.segmentP U BOUND_VARIABLE_2331) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2306 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2306)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2331) BOUND_VARIABLE_2306))))))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_52 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_49)) :args ((or _let_43 _let_45))) _let_51 :args (_let_43 true _let_45)))) (let ((_let_102 (not _let_97))) (let ((_let_103 (_let_95))) (let ((_let_104 (or _let_24 _let_22 _let_90))) (let ((_let_105 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (= U (tptp.cons (tptp.hd U) (tptp.tl U))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (or _let_44 _let_91))) (let ((_let_108 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_109 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_110 (or _let_31 _let_18 _let_38))) (let ((_let_111 (forall ((U $$unsorted) (BOUND_VARIABLE_3299 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3299)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3299 U)))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (= _let_39 _let_28))) (let ((_let_114 (or _let_31 _let_24 _let_113))) (let ((_let_115 (not _let_113))) (let ((_let_116 (not _let_38))) (let ((_let_117 (not _let_39))) (let ((_let_118 (_let_40))) (let ((_let_119 (and _let_36 _let_91 _let_90 _let_61 _let_60 _let_93))) (let ((_let_120 (ASSUME :args (_let_93)))) (let ((_let_121 (APPLY_UF tptp.app))) (let ((_let_122 (ASSUME :args (_let_91)))) (let ((_let_123 (ASSUME :args (_let_36)))) (let ((_let_124 (ASSUME :args (_let_90)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_18 _let_20 _let_17 (not _let_21)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_119)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_120 _let_124 _let_122 _let_123 _let_85 _let_86) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_124) (TRANS (CONG (SYMM _let_123) _let_87 :args _let_121) (CONG (SYMM (SYMM _let_122)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)) :args _let_121)) :args (=)) (FALSE_INTRO _let_120))) :args (_let_93 _let_90 _let_91 _let_36 _let_60 _let_61))) :args (_let_36 _let_91 _let_90 _let_61 _let_60 _let_93))) :args (true _let_119)) (CONG (REFL :args (_let_37)) (REFL :args ((not _let_91))) (REFL :args ((not _let_90))) (REFL :args (_let_69)) (REFL :args ((not _let_60))) (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_89))) (REFL :args (_let_92)) :args _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_118) (CONG (REFL :args _let_118) (REFL :args (_let_117)) (REFL :args (_let_18)) (REFL :args (_let_116)) (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_49)) :args ((or _let_36 _let_40 _let_117 _let_18 _let_116))) 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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 $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_3 (forall ((U $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.70/26.97  )
% 26.70/26.97  % SZS output end Proof for SWC354+1
% 26.70/26.97  % cvc5---1.0.5 exiting
% 26.80/26.97  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------