TSTP Solution File: SWC061-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC061-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 20:22:57 EDT 2023
% Result : Unsatisfiable 25.64s 26.02s
% Output : Proof 25.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWC061-1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n013.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 17:25:31 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.lmuCtvwrQ4/cvc5---1.0.5_27253.p...
% 0.21/0.53 ------- get file name : TPTP file name is SWC061-1
% 0.21/0.53 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27253.smt2...
% 0.21/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.48/10.71 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.55/15.74 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.58/20.77 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.58/25.82 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.64/26.02 % SZS status Unsatisfiable for SWC061-1
% 25.64/26.02 % SZS output start Proof for SWC061-1
% 25.64/26.03 (
% 25.64/26.03 (let ((_let_1 (tptp.neq tptp.sk2 tptp.nil))) (let ((_let_2 (or (not (= tptp.nil tptp.sk1)) _let_1))) (let ((_let_3 (forall ((A $$unsorted)) (or (= tptp.nil tptp.sk2) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A)))))) (let ((_let_4 (= tptp.nil tptp.sk2))) (let ((_let_5 (or _let_4 _let_1))) (let ((_let_6 (tptp.neq tptp.sk4 tptp.nil))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.cons tptp.sk5 tptp.nil))) (let ((_let_9 (tptp.app tptp.sk6 _let_8))) (let ((_let_10 (or (= _let_9 tptp.sk3) _let_7))) (let ((_let_11 (tptp.app _let_8 tptp.sk6))) (let ((_let_12 (or (= _let_11 tptp.sk4) _let_7))) (let ((_let_13 (tptp.ssList tptp.sk6))) (let ((_let_14 (or _let_13 _let_7))) (let ((_let_15 (tptp.ssItem tptp.sk5))) (let ((_let_16 (or _let_15 _let_7))) (let ((_let_17 (= tptp.nil tptp.sk4))) (let ((_let_18 (not _let_17))) (let ((_let_19 (= tptp.nil tptp.sk3))) (let ((_let_20 (or _let_19 _let_18))) (let ((_let_21 (= tptp.sk1 tptp.sk3))) (let ((_let_22 (= tptp.sk2 tptp.sk4))) (let ((_let_23 (tptp.ssList tptp.sk4))) (let ((_let_24 (tptp.ssList tptp.sk3))) (let ((_let_25 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app (tptp.app U V) W) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList X)) (tptp.segmentP X V))))) (let ((_let_26 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.ssList W)) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP (tptp.app (tptp.app X U) W) V))))) (let ((_let_27 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= (tptp.app (tptp.app W V) U) (tptp.app W (tptp.app V U))))))) (let ((_let_28 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (= (tptp.app (tptp.cons U tptp.nil) V) (tptp.cons U V)))))) (let ((_let_29 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))) (let ((_let_30 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= V U))))) (let ((_let_31 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.cons U V) tptp.nil)) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) (let ((_let_32 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (tptp.ssList (tptp.cons U V)))))) (let ((_let_33 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app tptp.nil U) U))))) (let ((_let_34 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.app U tptp.nil) U))))) (let ((_let_35 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_36 (tptp.ssList tptp.nil))) (let ((_let_37 (= tptp.sk4 _let_11))) (let ((_let_38 (= tptp.sk3 _let_9))) (let ((_let_39 (tptp.app _let_8 tptp.nil))) (let ((_let_40 (= _let_8 _let_39))) (let ((_let_41 (tptp.segmentP tptp.sk3 tptp.sk4))) (let ((_let_42 (tptp.app _let_9 tptp.nil))) (let ((_let_43 (= _let_42 (tptp.app tptp.sk6 _let_39)))) (let ((_let_44 (tptp.segmentP _let_42 _let_8))) (let ((_let_45 (= tptp.nil tptp.sk6))) (let ((_let_46 (tptp.ssList _let_8))) (let ((_let_47 (not _let_36))) (let ((_let_48 (not _let_15))) (let ((_let_49 (or _let_48 _let_47 _let_46))) (let ((_let_50 (= tptp.nil _let_8))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_48 _let_47))) (let ((_let_53 (not _let_13))) (let ((_let_54 (not _let_46))) (let ((_let_55 (= tptp.nil _let_9))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_54 _let_53 _let_50))) (let ((_let_58 (not _let_19))) (let ((_let_59 (AND_INTRO (ASSUME :args (_let_21)) (ASSUME :args (_let_22))))) (let ((_let_60 (ASSUME :args (_let_16)))) (let ((_let_61 (REORDERING (ASSUME :args (_let_14)) :args ((or _let_7 _let_13))))) (let ((_let_62 (REORDERING (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) :args ((or _let_7 _let_38))))) (let ((_let_63 (ASSUME :args (_let_36)))) (let ((_let_64 (_let_32))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.sk5 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons U V)))) :args _let_64)) _let_65 :args (_let_49 false _let_32)))) (let ((_let_67 (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_47 _let_48 _let_46 (not _let_49)))))) (let ((_let_68 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.cons U V))) (not (tptp.ssItem U)) (not (tptp.ssList V)))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_31)) (MACRO_SR_EQ_INTRO :args (_let_31 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil (tptp.app U V))) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil V))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_29)) (MACRO_SR_EQ_INTRO :args (_let_29 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (and _let_19 _let_38))) (let ((_let_73 (ASSUME :args (_let_38)))) (let ((_let_74 (SYMM _let_73))) (let ((_let_75 (SYMM _let_74))) (let ((_let_76 (ASSUME :args (_let_19)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (ASSUME :args (_let_20)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_73 _let_76) (SCOPE (TRANS (SYMM (SYMM _let_76)) _let_75) :args (_let_38 _let_19))) :args (_let_19 _let_38))) :args (true _let_72)) (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_53 _let_50 _let_54 _let_56 (not _let_57)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.sk6 _let_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.app U V)))) :args (_let_70))) _let_71 :args (_let_57 false _let_70)) (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_47 _let_48 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (tptp.sk5 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons U V)))) :args (_let_68))) _let_69 :args (_let_52 false _let_68)) _let_63 _let_67 _let_66 _let_63 _let_62 _let_61 _let_60 (REORDERING (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO _let_59 :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args ((or _let_6 _let_58))) :args (_let_58 true _let_55 false _let_57 true _let_50 false _let_52 false _let_36 false _let_46 false _let_49 false _let_36 false _let_38 false _let_13 false _let_15 false _let_6)) :args (_let_18 true _let_19)))) (let ((_let_78 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO _let_59 :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) _let_77 :args (_let_6 true _let_17)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))) :args ((or _let_7 _let_37))) _let_78 :args (_let_37 false _let_6)))) (let ((_let_80 (MACRO_RESOLUTION_TRUST _let_62 _let_78 :args (_let_38 false _let_6)))) (let ((_let_81 (or _let_48 _let_47 _let_40))) (let ((_let_82 (_let_28))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (MACRO_RESOLUTION_TRUST _let_60 _let_78 :args (_let_15 false _let_6)))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_47 _let_48 _let_40 (not _let_81)))) _let_63 _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (tptp.sk5 tptp.nil QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons U V)))) :args _let_82))) _let_83 :args (_let_81 false _let_28)) :args (_let_40 false _let_36 false _let_15 false _let_81)))) (let ((_let_86 (not _let_41))) (let ((_let_87 (tptp.segmentP tptp.sk4 tptp.sk4))) (let ((_let_88 (not _let_87))) (let ((_let_89 (not _let_23))) (let ((_let_90 (or _let_89 _let_7 _let_88 _let_86))) (let ((_let_91 (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk4 A)) (not (tptp.segmentP tptp.sk3 A)))))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_59 :args ((or _let_4 (forall ((A $$unsorted)) (or (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))))) SB_DEFAULT SBA_FIXPOINT)))) _let_77 :args (_let_91 true _let_17)))) (let ((_let_93 (_let_91))) (let ((_let_94 ((not (= (tptp.ssList A) false))))) (let ((_let_95 (ASSUME :args _let_93))) (let ((_let_96 (or _let_89 _let_87))) (let ((_let_97 (_let_35))) (let ((_let_98 (ASSUME :args _let_97))) (let ((_let_99 ((not (= (tptp.ssList U) false))))) (let ((_let_100 (ASSUME :args (_let_23)))) (let ((_let_101 (or _let_47 _let_54 _let_53 _let_43))) (let ((_let_102 (_let_27))) (let ((_let_103 (ASSUME :args _let_102))) (let ((_let_104 (MACRO_RESOLUTION_TRUST _let_67 _let_63 _let_84 _let_66 :args (_let_46 false _let_36 false _let_15 false _let_49)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST _let_61 _let_78 :args (_let_13 false _let_6)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_47 _let_53 _let_54 _let_43 (not _let_101)))) _let_63 _let_105 _let_104 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (tptp.nil _let_8 tptp.sk6 QUANTIFIERS_INST_E_MATCHING ((tptp.app (tptp.app W V) U)))) :args _let_102)) _let_103 :args (_let_101 false _let_27)) :args (_let_43 false _let_36 false _let_13 false _let_46 false _let_101)))) (let ((_let_107 (tptp.ssList _let_42))) (let ((_let_108 (not _let_107))) (let ((_let_109 (or _let_47 _let_53 _let_54 _let_108 _let_44))) (let ((_let_110 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.app (tptp.app U V) W))) (or (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList _let_1)) (tptp.segmentP _let_1 V)))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_25)) (MACRO_SR_EQ_INTRO :args (_let_25 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (ASSUME :args (_let_24)))) (let ((_let_113 (not _let_43))) (let ((_let_114 (not _let_40))) (let ((_let_115 (not _let_38))) (let ((_let_116 (and _let_24 _let_38 _let_40 _let_43))) (let ((_let_117 (_let_24 _let_38 _let_40 _let_43))) (let ((_let_118 (APPLY_UF tptp.app))) (let ((_let_119 (ASSUME :args (_let_40)))) (let ((_let_120 (SYMM _let_119))) (let ((_let_121 (SYMM _let_120))) (let ((_let_122 (REFL :args (tptp.sk6)))) (let ((_let_123 (ASSUME :args (_let_43)))) (let ((_let_124 (SYMM (SYMM _let_123)))) (let ((_let_125 (tptp.neq tptp.sk6 tptp.nil))) (let ((_let_126 (or _let_47 _let_53 _let_125 _let_45))) (let ((_let_127 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (tptp.neq V U) (= U V))))) (let ((_let_128 (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO :args (_let_30 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_129 (tptp.segmentP tptp.sk3 tptp.sk6))) (let ((_let_130 (not _let_129))) (let ((_let_131 (tptp.segmentP tptp.sk4 tptp.sk6))) (let ((_let_132 (not _let_131))) (let ((_let_133 (not _let_125))) (let ((_let_134 (or _let_53 _let_133 _let_132 _let_130))) (let ((_let_135 (tptp.app tptp.nil tptp.sk6))) (let ((_let_136 (tptp.segmentP (tptp.app _let_135 _let_8) tptp.sk6))) (let ((_let_137 (= tptp.sk6 _let_135))) (let ((_let_138 (tptp.segmentP tptp.sk6 tptp.sk6))) (let ((_let_139 (not _let_138))) (let ((_let_140 (or _let_139 _let_54 _let_47 _let_53 _let_53 _let_136))) (let ((_let_141 (_let_26))) (let ((_let_142 (ASSUME :args _let_141))) (let ((_let_143 (or _let_53 _let_138))) (let ((_let_144 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_143)) :args ((or _let_53 _let_138 (not _let_143)))) _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (tptp.sk6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_97)) _let_98 :args (_let_143 false _let_35)) :args (_let_138 false _let_13 false _let_143)))) (let ((_let_145 (or _let_53 _let_137))) (let ((_let_146 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_147 (EQ_RESOLVE (ASSUME :args (_let_33)) (MACRO_SR_EQ_INTRO :args (_let_33 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_148 (and _let_38 _let_137 _let_136))) (let ((_let_149 (ASSUME :args (_let_136)))) (let ((_let_150 (APPLY_UF tptp.segmentP))) (let ((_let_151 (REFL :args (_let_8)))) (let ((_let_152 (ASSUME :args (_let_137)))) (let ((_let_153 (tptp.segmentP (tptp.app _let_11 tptp.nil) tptp.sk6))) (let ((_let_154 (= tptp.sk4 (tptp.app tptp.sk4 tptp.nil)))) (let ((_let_155 (or _let_139 _let_47 _let_54 _let_53 _let_53 _let_153))) (let ((_let_156 (or _let_89 _let_154))) (let ((_let_157 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_158 (EQ_RESOLVE (ASSUME :args (_let_34)) (MACRO_SR_EQ_INTRO :args (_let_34 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_159 (not _let_37))) (let ((_let_160 (and _let_37 _let_154 _let_153))) (let ((_let_161 (ASSUME :args (_let_153)))) (let ((_let_162 (ASSUME :args (_let_37)))) (let ((_let_163 (SYMM _let_162))) (let ((_let_164 (ASSUME :args (_let_154)))) (let ((_let_165 (not _let_44))) (let ((_let_166 (not _let_45))) (let ((_let_167 (ASSUME :args (_let_86)))) (let ((_let_168 (ASSUME :args (_let_45)))) (let ((_let_169 (ASSUME :args (_let_44)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_167 _let_73 _let_119 _let_123 _let_162 _let_168 _let_169) :args (_let_37 _let_38 _let_45 _let_40 _let_43 _let_44 _let_86)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_169)) (CONG (TRANS _let_124 (CONG _let_122 _let_120 :args _let_118) _let_74) (TRANS _let_121 (CONG _let_151 (SYMM (SYMM _let_168)) :args _let_118) _let_163) :args _let_150) (FALSE_INTRO _let_167))) :args (_let_86 _let_38 _let_40 _let_43 _let_37 _let_45 _let_44)) :args ((not (and _let_37 _let_38 _let_45 _let_40 _let_43 _let_44 _let_86)) SB_LITERAL))) (CONG (REFL :args (_let_159)) (REFL :args (_let_115)) (REFL :args (_let_166)) (REFL :args (_let_114)) (REFL :args (_let_113)) (REFL :args (_let_165)) (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_41))) :args (or))) :args ((or _let_159 _let_115 _let_41 _let_166 _let_114 _let_113 _let_165))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_126)) :args ((or _let_47 _let_53 _let_45 _let_125 (not _let_126)))) _let_63 _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_53 _let_133 _let_132 _let_130 (not _let_134)))) _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_160)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_161 _let_162 _let_164) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_164 (CONG (SYMM _let_163) (REFL :args (tptp.nil)) :args _let_118)) _let_122 :args _let_150) (TRUE_INTRO _let_161))) :args (_let_153 _let_37 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$$unsorted) (V $$unsorted)) (or (not (= (tptp.app U V) tptp.nil)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= tptp.nil U))) _let_29 _let_28 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U V) (= U V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.hd (tptp.app V U)) (tptp.hd V)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP V) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP V) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V U)) (not (tptp.ssList U)) (not (tptp.ssList V)) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (tptp.ssItem U)) (not (tptp.ssItem V)) (= V U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf46 U V) V) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app V (tptp.skaf45 U V)) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= (tptp.tl (tptp.app V U)) (tptp.app (tptp.tl V) U)))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.strictorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.lt U (tptp.hd V)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.totalorderedP (tptp.cons U V))) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.leq U (tptp.hd V)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.rearsegP (tptp.app W U) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP (tptp.app U W) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= U V)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.memberP (tptp.cons V W) U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.cons W U) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app U W) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (tptp.memberP (tptp.app W U) V))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.equalelemsP U) (= (tptp.app (tptp.skaf80 U) (tptp.cons (tptp.skaf78 U) (tptp.cons (tptp.skaf79 U) (tptp.skaf81 U)))) U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (tptp.rearsegP W V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (tptp.frontsegP W U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= tptp.nil U)) (not (= tptp.nil V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app U V) tptp.nil))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.gt U V)) (not (tptp.gt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.gt U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.lt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.geq U V)) (not (tptp.geq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.geq U W))) _let_27 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app U W))) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssList W)) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (= (tptp.app U V) (tptp.app W V))) (not (tptp.ssList U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.segmentP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.segmentP U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.rearsegP U V)) (not (tptp.rearsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.rearsegP U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.frontsegP U V)) (not (tptp.frontsegP V W)) (not (tptp.ssList W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (tptp.frontsegP U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.lt U V)) (not (tptp.lt V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.lt U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V W)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (tptp.leq U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList V)) (not (tptp.ssList W)) (= (tptp.cons U (tptp.app V W)) (tptp.app (tptp.cons U V) W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.app U V) W)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (tptp.memberP V W) (tptp.memberP U W))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.leq U (tptp.hd V))) (not (tptp.totalorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.totalorderedP (tptp.cons U V)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.lt U (tptp.hd V))) (not (tptp.strictorderedP V)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (tptp.strictorderedP (tptp.cons U V)) (= tptp.nil V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.memberP (tptp.cons U V) W)) (not (tptp.ssList V)) (not (tptp.ssItem U)) (not (tptp.ssItem W)) (tptp.memberP V W) (= W U))) (forall ((U $$unsorted)) (let ((_let_1 (tptp.skaf74 U))) (or (not (tptp.ssList U)) (tptp.duplicatefreeP U) (= (tptp.app (tptp.app (tptp.skaf75 U) (tptp.cons _let_1 (tptp.skaf76 U))) (tptp.cons _let_1 (tptp.skaf77 U))) U)))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.strictorderedP U) (= (tptp.app (tptp.app (tptp.skaf71 U) (tptp.cons (tptp.skaf69 U) (tptp.skaf72 U))) (tptp.cons (tptp.skaf70 U) (tptp.skaf73 U))) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderedP U) (= (tptp.app (tptp.app (tptp.skaf66 U) (tptp.cons (tptp.skaf64 U) (tptp.skaf67 U))) (tptp.cons (tptp.skaf65 U) (tptp.skaf68 U))) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.strictorderP U) (= (tptp.app (tptp.app (tptp.skaf61 U) (tptp.cons (tptp.skaf59 U) (tptp.skaf62 U))) (tptp.cons (tptp.skaf60 U) (tptp.skaf63 U))) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.totalorderP U) (= (tptp.app (tptp.app (tptp.skaf56 U) (tptp.cons (tptp.skaf54 U) (tptp.skaf57 U))) (tptp.cons (tptp.skaf55 U) (tptp.skaf58 U))) U))) (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.cyclefreeP U) (= (tptp.app (tptp.app (tptp.skaf51 U) (tptp.cons (tptp.skaf49 U) (tptp.skaf52 U))) (tptp.cons (tptp.skaf50 U) (tptp.skaf53 U))) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.segmentP U V)) (not (tptp.ssList V)) (not (tptp.ssList U)) (= (tptp.app (tptp.app (tptp.skaf47 U V) V) (tptp.skaf48 V U)) U))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.memberP U V)) (not (tptp.ssItem V)) (not (tptp.ssList U)) (= (tptp.app (tptp.skaf42 U V) (tptp.cons V (tptp.skaf43 V U))) U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (not (tptp.ssList X)) (not (tptp.ssList V)) (= U W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (not (tptp.ssList X)) (not (tptp.ssList V)) (= X V))) _let_26 _let_25 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (tptp.frontsegP V X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (= (tptp.app U (tptp.cons V W)) X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.ssList X)) (tptp.memberP X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP (tptp.cons U V) (tptp.cons W X))) (not (tptp.ssList X)) (not (tptp.ssList V)) (not (tptp.ssItem W)) (not (tptp.ssItem U)) (= U W))) (forall ((U $$unsorted) (V $$unsorted)) (or (not (= (tptp.tl U) (tptp.tl V))) (not (= (tptp.hd U) (tptp.hd V))) (not (tptp.ssList U)) (not (tptp.ssList V)) (= tptp.nil V) (= U V) (= tptp.nil U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.frontsegP U V)) (not (= W X)) (not (tptp.ssList V)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem W)) (tptp.frontsegP (tptp.cons W U) (tptp.cons X V)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons V X)) Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem V)) (not (tptp.duplicatefreeP Y)) (not (tptp.ssList Y)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.app U (tptp.cons V (tptp.cons W X))) Y)) (not (tptp.ssList X)) (not (tptp.ssList U)) (not (tptp.ssItem W)) (not (tptp.ssItem V)) (not (tptp.equalelemsP Y)) (not (tptp.ssList Y)) (= V W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.strictorderedP Z)) (not (tptp.ssList Z)) (tptp.lt V X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.totalorderedP Z)) (not (tptp.ssList Z)) (tptp.leq V X))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.strictorderP Z)) (not (tptp.ssList Z)) (tptp.lt V X) (tptp.lt X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.app (tptp.app U (tptp.cons V W)) (tptp.cons X Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList W)) (not (tptp.ssList U)) (not (tptp.ssItem X)) (not (tptp.ssItem V)) (not (tptp.totalorderP Z)) (not (tptp.ssList Z)) (tptp.leq V X) (tptp.leq X V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.leq U V)) (not (tptp.leq V U)) (not (= (tptp.app (tptp.app W (tptp.cons U X)) (tptp.cons V Y)) Z)) (not (tptp.ssList Y)) (not (tptp.ssList X)) (not (tptp.ssList W)) (not (tptp.ssItem V)) (not (tptp.ssItem U)) (not (tptp.cyclefreeP Z)) (not (tptp.ssList Z)))) (tptp.ssList tptp.sk1) (tptp.ssList tptp.sk2) _let_24 _let_23 _let_22 _let_21 _let_20 _let_16 _let_14 _let_12 _let_10 _let_5 _let_3 _let_2 (forall ((A $$unsorted)) (or (not (= tptp.nil tptp.sk1)) (not (tptp.ssList A)) (not (tptp.neq A tptp.nil)) (not (tptp.segmentP tptp.sk2 A)) (not (tptp.segmentP tptp.sk1 A))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.64/26.03 )
% 25.64/26.03 % SZS output end Proof for SWC061-1
% 25.64/26.03 % cvc5---1.0.5 exiting
% 25.64/26.04 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------