%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWC078+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 20:23:04 EDT 2023

% Result   : Theorem 31.82s 32.05s
% Output   : Proof 31.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : SWC078+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 18:25:43 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 31.82/32.05  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.i718PpPGrt/cvc5---1.0.5_16731.p...
% 31.82/32.05  ------- get file name : TPTP file name is SWC078+1
% 31.82/32.05  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16731.smt2...
% 31.82/32.05  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.82/32.05  --- Run --no-e-matching --full-saturate-quant at 5...
% 31.82/32.05  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.82/32.05  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.82/32.05  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.82/32.05  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.82/32.05  % SZS status Theorem for SWC078+1
% 31.82/32.05  % SZS output start Proof for SWC078+1
% 31.82/32.05  (
% 31.82/32.05  (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (and (= tptp.nil V) (= tptp.nil U)) (and (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (or (not (= (tptp.cons Z tptp.nil) W)) (not (tptp.memberP X Z))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))))))))))))))) (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 $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_8 (tptp.ssList tptp.nil))) (let ((_let_9 (forall ((U $$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) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.memberP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app W (tptp.cons V X)) U)))))))))))) (let ((_let_12 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (not _let_12))) (let ((_let_16 (not _let_13))) (let ((_let_17 (or _let_16 _let_15))) (let ((_let_18 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_19))) (let ((_let_26 (and _let_25 _let_17))) (let ((_let_27 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)) (not (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30 _let_28 _let_14 _let_26))) (let ((_let_34 (forall ((U $$unsorted) (BOUND_VARIABLE_5374 $$unsorted) (BOUND_VARIABLE_5372 $$unsorted)) (let ((_let_1 (= tptp.nil U))) (let ((_let_2 (= tptp.nil BOUND_VARIABLE_5372))) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5372)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP BOUND_VARIABLE_5372 Y)) (not (tptp.segmentP U Y))))) (and _let_2 _let_1) (and (or (not (tptp.ssItem BOUND_VARIABLE_5374)) (not (= U (tptp.cons BOUND_VARIABLE_5374 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5372 BOUND_VARIABLE_5374))) (or (not _let_2) (not _let_1))))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or))) (let ((_let_38 (not _let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_38))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_37)) _let_36 :args (_let_35 true _let_34)))) (let ((_let_40 (= tptp.nil _let_20))) (let ((_let_41 (not _let_40))) (let ((_let_42 (not _let_8))) (let ((_let_43 (or _let_42 _let_24 _let_41))) (let ((_let_44 (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_45 (not _let_44))) (let ((_let_46 (= _let_18 _let_45))) (let ((_let_47 (or _let_30 _let_24 _let_46))) (let ((_let_48 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_49 (= _let_15 _let_48))) (let ((_let_50 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_51 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_50))) (let ((_let_52 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_51))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_55 (not _let_54))) (let ((_let_56 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_55 _let_53))) (let ((_let_59 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_62 (not _let_61))) (let ((_let_63 (not _let_48))) (let ((_let_64 (or _let_32 _let_63 _let_62 _let_60))) (let ((_let_65 (= _let_50 (tptp.app _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_66 (or _let_55 _let_24 _let_65))) (let ((_let_67 (tptp.ssList _let_50))) (let ((_let_68 (or _let_55 _let_24 _let_67))) (let ((_let_69 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_70 (tptp.segmentP (tptp.app _let_69 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_71 (or _let_32 _let_32 _let_60 _let_42 _let_55 _let_70))) (let ((_let_72 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_73 (tptp.segmentP (tptp.app _let_51 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_69))) (let ((_let_75 (tptp.segmentP _let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_76 (not _let_75))) (let ((_let_77 (not _let_67))) (let ((_let_78 (or _let_77 _let_32 _let_76 _let_57 _let_42 _let_73))) (let ((_let_79 (REFL :args (_let_25)))) (let ((_let_80 (ASSUME :args (_let_8)))) (let ((_let_81 (forall ((U $$unsorted) (BOUND_VARIABLE_3328 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3328)) (not (= U (tptp.cons BOUND_VARIABLE_3328 U))))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (REFL :args (_let_33)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 1)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_37)) :args ((or _let_29 _let_33))) _let_39 :args (_let_29 true _let_33)))) (let ((_let_85 (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_86 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (and _let_21 _let_41))) (let ((_let_88 (ASSUME :args (_let_41)))) (let ((_let_89 (ASSUME :args (_let_21)))) (let ((_let_90 (SYMM _let_89))) (let ((_let_91 (REFL :args (tptp.nil)))) (let ((_let_92 (or _let_32 _let_42 _let_49))) (let ((_let_93 (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_94 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_37)) :args ((or _let_31 _let_33))) _let_39 :args (_let_31 true _let_33)))) (let ((_let_96 (not _let_49))) (let ((_let_97 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_12))))) (let ((_let_98 (_let_45))) (let ((_let_99 (_let_27))) (let ((_let_100 (or _let_32 _let_59))) (let ((_let_101 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_32 _let_59 (not _let_100)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_101))) _let_102 :args (_let_100 false _let_101)) :args (_let_59 false _let_31 false _let_100)))) (let ((_let_104 (REFL :args (_let_58)))) (let ((_let_105 (forall ((U $$unsorted) (BOUND_VARIABLE_4791 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4791)) (= (tptp.cons BOUND_VARIABLE_4791 U) (tptp.app (tptp.cons BOUND_VARIABLE_4791 tptp.nil) U)))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_107 (forall ((U $$unsorted) (BOUND_VARIABLE_3303 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3303)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3303 U)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (forall ((U $$unsorted) (BOUND_VARIABLE_4454 $$unsorted) (BOUND_VARIABLE_4452 $$unsorted) (BOUND_VARIABLE_4450 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4450)) (not (tptp.segmentP U BOUND_VARIABLE_4450)) (not (tptp.ssList BOUND_VARIABLE_4454)) (not (tptp.ssList BOUND_VARIABLE_4452)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4454 U) BOUND_VARIABLE_4452) BOUND_VARIABLE_4450))))) (let ((_let_110 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_111 (_let_109))) (let ((_let_112 (or _let_30 _let_72))) (let ((_let_113 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (not _let_73))) (let ((_let_116 (not _let_72))) (let ((_let_117 (and _let_72 _let_62 _let_52))) (let ((_let_118 (ASSUME :args (_let_62)))) (let ((_let_119 (APPLY_UF tptp.segmentP))) (let ((_let_120 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_121 (ASSUME :args (_let_72)))) (let ((_let_122 (APPLY_UF tptp.app))) (let ((_let_123 (ASSUME :args (_let_52)))) (let ((_let_124 (or _let_32 _let_74))) (let ((_let_125 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_126 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_127 (and _let_21 _let_74 _let_65 _let_70))) (let ((_let_128 (ASSUME :args (_let_70)))) (let ((_let_129 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12)))) (let ((_let_130 (ASSUME :args (_let_74)))) (let ((_let_131 (ASSUME :args (_let_65)))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_26)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 4)) _let_39 :args ((not _let_26) true _let_33)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_42 _let_32 _let_57 _let_77 _let_76 _let_73 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (_let_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4454 U) BOUND_VARIABLE_4452) BOUND_VARIABLE_4450) true))))) :args _let_111)) _let_110 :args (_let_78 false _let_109)) _let_95 _let_80 (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_127)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_128 _let_130 _let_89 _let_131) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_131)) (CONG _let_90 _let_129 :args _let_122) (CONG (SYMM (SYMM _let_130)) _let_129 :args _let_122)) _let_120 :args _let_119) (TRUE_INTRO _let_128))) :args (_let_70 _let_74 _let_21 _let_65))) :args (_let_21 _let_74 _let_65 _let_70))) :args (true _let_127)) :args ((or _let_22 (not _let_74) _let_75 (not _let_65) (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_32 _let_74 (not _let_124)))) _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_125))) _let_126 :args (_let_124 false _let_125)) :args (_let_74 false _let_31 false _let_124)) (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_117)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_118 _let_121 _let_123) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (CONG (SYMM _let_123) _let_91 :args _let_122) (SYMM _let_121)) _let_120 :args _let_119) (FALSE_INTRO _let_118))) :args (_let_62 _let_72 _let_52))) :args (_let_72 _let_62 _let_52))) :args (true _let_117)) (CONG (REFL :args (_let_116)) (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) (REFL :args (_let_53)) (REFL :args (_let_115)) :args _let_37)) :args ((or _let_61 _let_116 _let_53 _let_115))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_30 _let_72 (not _let_112)))) _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_113))) _let_114 :args (_let_112 false _let_113)) :args (_let_72 false _let_29 false _let_112)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_71))) :args ((or _let_42 _let_32 _let_60 _let_55 _let_70 (not _let_71)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_110 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_111)) _let_110 :args (_let_71 false _let_109)) _let_103 _let_95 _let_80 (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_24 _let_55 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_107))) _let_108 :args (_let_68 false _let_107)) (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_24 _let_55 _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_4791 U)))) :args (_let_105))) _let_106 :args (_let_66 false _let_105)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 2)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_37)) :args ((or _let_52 _let_58))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 1)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_37)) :args ((or _let_54 _let_58))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_58 0)) (CONG _let_104 (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_56))) :args _let_37)) :args ((or _let_56 _let_58))) (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_32 _let_60 _let_63 _let_62 (not _let_64)))) _let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_99) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList Y) false))))) :args _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_83 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_37)) :args ((or _let_27 _let_33))) _let_39 :args (_let_27 true _let_33)) :args (_let_64 false _let_27)) _let_95 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_98)) :args _let_98)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) (REFL :args ((not _let_58))) :args _let_37)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_49)) (CONG (REFL :args (_let_96)) _let_97 (REFL :args (_let_48)) :args _let_37)) :args ((or _let_12 _let_48 _let_96))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_42 _let_32 _let_49 (not _let_92)))) _let_80 _let_95 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_94 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_93)))) _let_94 :args (_let_92 false _let_93)) :args (_let_49 false _let_8 false _let_31 false _let_92)) (REORDERING (CNF_EQUIV_POS1 :args (_let_46)) :args ((or _let_19 _let_45 (not _let_46)))) (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_87)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_88 _let_89) (SCOPE (FALSE_ELIM (TRANS (CONG _let_91 (SYMM _let_90) :args (=)) (FALSE_INTRO _let_88))) :args (_let_41 _let_21))) :args (_let_21 _let_41))) :args (true _let_87)) (CONG (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) (REFL :args (_let_15)) :args _let_37)) :args ((or _let_22 _let_15 _let_40))) (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_30 _let_24 _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.memberP U BOUND_VARIABLE_2171)))) :args (_let_85))) _let_86 :args (_let_47 false _let_85)) _let_84 (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_24 _let_41 (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_81))) _let_82 :args (_let_43 false _let_81)) _let_80 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_18))) :args _let_37)) :args ((or _let_18 _let_25))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_37)) :args ((or _let_21 _let_25))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_79 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_37)) :args ((or _let_23 _let_25))) :args (_let_25 false _let_78 false _let_31 false _let_8 false _let_75 false _let_74 true _let_73 false _let_72 false _let_70 false _let_71 false _let_59 false _let_31 false _let_8 false _let_67 false _let_68 false _let_65 false _let_66 false _let_52 false _let_54 false _let_56 true _let_61 false _let_59 false _let_64 false _let_31 true _let_58 false _let_48 false _let_49 true _let_44 true _let_12 false _let_46 false _let_47 false _let_29 true _let_40 false _let_43 false _let_8 false _let_18 false _let_21 false _let_23)) :args ((not _let_17) true _let_26 false _let_25)))) (let ((_let_133 (REFL :args (_let_17)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 1)) (CONG _let_133 _let_97 :args _let_37)) :args ((or _let_12 _let_17))) _let_132 :args (_let_12 true _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 0)) (CONG _let_133 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_13))) :args _let_37)) :args ((or _let_13 _let_17))) _let_132 :args (_let_13 true _let_17)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 3)) _let_39 :args ((not _let_14) true _let_33)) :args (false false _let_12 false _let_13 true _let_14)) :args ((forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.neq U V) (not (= U V))))))) (exists ((U $$unsorted)) (and (tptp.ssItem U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) _let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.frontsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app V W) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.rearsegP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (= (tptp.app W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.segmentP U V) (exists ((W $$unsorted)) (and (tptp.ssList W) (exists ((X $$unsorted)) (and (tptp.ssList X) (= (tptp.app (tptp.app W V) X) U)))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.cyclefreeP 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (not (and (tptp.leq V W) (tptp.leq W V))))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderP 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.leq V W) (tptp.leq W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderP 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (or (tptp.lt V W) (tptp.lt W V)))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.totalorderedP 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.leq V W))))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.strictorderedP 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 $$unsorted)) (=> (tptp.ssList Z) (=> (= (tptp.app (tptp.app X (tptp.cons V Y)) (tptp.cons W Z)) U) (tptp.lt V W))))))))))))))) (forall ((U $$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_10 _let_9 _let_8 _let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) (not (tptp.singletonP tptp.nil)) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V W)) (tptp.frontsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.frontsegP U V) (tptp.frontsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (= (tptp.frontsegP (tptp.cons U W) (tptp.cons V X)) (and (= U V) (tptp.frontsegP W X))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.frontsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V W)) (tptp.rearsegP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.rearsegP U V) (tptp.rearsegP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (tptp.rearsegP U V) (tptp.rearsegP (tptp.app W U) V)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.rearsegP U tptp.nil))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.rearsegP tptp.nil U) (= tptp.nil U)))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (=> (and (tptp.segmentP U V) (tptp.segmentP V W)) (tptp.segmentP U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) _let_5 _let_4 (forall ((U $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.82/32.06  )
% 31.82/32.06  % SZS output end Proof for SWC078+1
% 31.82/32.06  % cvc5---1.0.5 exiting
% 31.82/32.06  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------