TSTP Solution File: SWC329+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC329+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.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 20:24:48 EDT 2023
% Result : Theorem 39.43s 39.67s
% Output : Proof 39.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC329+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n001.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 18:30:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 %----Proving TF0_NAR, FOF, or CNF
% 39.43/39.67 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.MbhIoyquhH/cvc5---1.0.5_10011.p...
% 39.43/39.67 ------- get file name : TPTP file name is SWC329+1
% 39.43/39.67 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10011.smt2...
% 39.43/39.67 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 39.43/39.67 --- Run --no-e-matching --full-saturate-quant at 5...
% 39.43/39.67 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 39.43/39.67 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 39.43/39.67 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 39.43/39.67 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 39.43/39.67 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 39.43/39.67 % SZS status Theorem for SWC329+1
% 39.43/39.67 % SZS output start Proof for SWC329+1
% 39.43/39.67 (
% 39.43/39.67 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (and (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (or (not (= (tptp.cons Y tptp.nil) W)) (not (tptp.memberP X Y)) (exists ((Z $$unsorted)) (and (tptp.ssItem Z) (not (= Y Z)) (tptp.memberP X Z) (tptp.leq Y Z)))))) (or (not (= tptp.nil X)) (not (= tptp.nil W)))) (and (tptp.segmentP V U) (tptp.equalelemsP U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))))) (let ((_let_5 (tptp.equalelemsP tptp.nil))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))))) (let ((_let_7 (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_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_9 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_10 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))))) (let ((_let_11 (tptp.ssList tptp.nil))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_13 (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_14 (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_15 (tptp.equalelemsP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_16 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_18 (tptp.equalelemsP _let_16))) (let ((_let_19 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (and _let_19 _let_15))) (let ((_let_21 (not _let_15))) (let ((_let_22 (forall ((W $$unsorted) (BOUND_VARIABLE_2311 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2311)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app (tptp.app W SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) BOUND_VARIABLE_2311))))))) (let ((_let_23 (not _let_22))) (let ((_let_24 (= _let_19 _let_23))) (let ((_let_25 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_26 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_27 (not _let_26))) (let ((_let_28 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_29 (not _let_28))) (let ((_let_30 (not _let_11))) (let ((_let_31 (or _let_30 _let_29 _let_27))) (let ((_let_32 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (not _let_32))) (let ((_let_34 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_33))) (let ((_let_37 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_17))) (let ((_let_40 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_39 _let_38 (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Z)) (not (tptp.leq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Z)))))))) (let ((_let_43 (and _let_42 _let_36))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_29 _let_24))) (let ((_let_47 (forall ((U $$unsorted) (BOUND_VARIABLE_2336 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2336)) (= (tptp.segmentP U BOUND_VARIABLE_2336) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2311 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2311)) (not (= U (tptp.app (tptp.app W BOUND_VARIABLE_2336) BOUND_VARIABLE_2311))))))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or _let_29 _let_45 _let_20 _let_43))) (let ((_let_50 (forall ((U $$unsorted) (BOUND_VARIABLE_5419 $$unsorted) (BOUND_VARIABLE_5417 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_5417)) (and (tptp.segmentP BOUND_VARIABLE_5417 U) (tptp.equalelemsP U)) (and (or (not (tptp.ssItem BOUND_VARIABLE_5419)) (not (= U (tptp.cons BOUND_VARIABLE_5419 tptp.nil))) (not (tptp.memberP BOUND_VARIABLE_5417 BOUND_VARIABLE_5419)) (not (forall ((Z $$unsorted)) (or (not (tptp.ssItem Z)) (= Z BOUND_VARIABLE_5419) (not (tptp.memberP BOUND_VARIABLE_5417 Z)) (not (tptp.leq BOUND_VARIABLE_5419 Z)))))) (or (not (= tptp.nil BOUND_VARIABLE_5417)) (not (= tptp.nil U)))))))) (let ((_let_51 (not _let_49))) (let ((_let_52 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_53 (or))) (let ((_let_54 (not _let_50))) (let ((_let_55 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_52) :args (_let_54))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_50))) (REFL :args (_let_51)) :args _let_53)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST _let_55 _let_52 :args (_let_51 true _let_50)))) (let ((_let_57 (REFL :args (_let_49)))) (let ((_let_58 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 1)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_53)) :args ((or _let_44 _let_49))))) (let ((_let_59 (MACRO_RESOLUTION_TRUST _let_58 _let_56 :args (_let_44 true _let_49)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_49 0)) (CONG _let_57 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_53)) :args ((or _let_28 _let_49))) _let_56 :args (_let_28 true _let_49)))) (let ((_let_61 (not _let_24))) (let ((_let_62 (_let_22))) (let ((_let_63 (ASSUME :args (_let_11)))) (let ((_let_64 (= tptp.nil (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_65 (= _let_32 _let_64))) (let ((_let_66 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_25))) (let ((_let_67 (REFL :args (_let_36)))) (let ((_let_68 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 1)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_53)) :args ((or _let_32 _let_36))))) (let ((_let_69 (or _let_29 _let_29 _let_65))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_4862 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4862)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4862)) (and (= tptp.nil BOUND_VARIABLE_4862) (= tptp.nil U))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (or _let_29 _let_66))) (let ((_let_73 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_74 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_72)) :args ((or _let_29 _let_66 (not _let_72)))) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_74 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_73))) _let_74 :args (_let_72 false _let_73)) :args (_let_66 false _let_28 false _let_72)))) (let ((_let_76 (not _let_64))) (let ((_let_77 (not _let_66))) (let ((_let_78 (and _let_34 _let_66 _let_27))) (let ((_let_79 (ASSUME :args (_let_27)))) (let ((_let_80 (=))) (let ((_let_81 (APPLY_UF tptp.app))) (let ((_let_82 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_83 (ASSUME :args (_let_66)))) (let ((_let_84 (SYMM (SYMM _let_83)))) (let ((_let_85 (ASSUME :args (_let_34)))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_49 3)) _let_56 :args ((not _let_43) true _let_49)))) (let ((_let_87 (CNF_AND_NEG :args (_let_43)))) (let ((_let_88 (REFL :args (_let_42)))) (let ((_let_89 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_53)) :args ((or _let_40 _let_42))))) (let ((_let_90 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 1)) (CONG _let_88 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_17))) :args _let_53)) :args ((or _let_17 _let_42))))) (let ((_let_91 (forall ((U $$unsorted) (BOUND_VARIABLE_2172 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2172)) (= (tptp.memberP U BOUND_VARIABLE_2172) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2146)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2172 BOUND_VARIABLE_2146)))))))))))) (let ((_let_92 (forall ((W $$unsorted) (BOUND_VARIABLE_2146 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2146)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 BOUND_VARIABLE_2146)))))))) (let ((_let_93 (not _let_92))) (let ((_let_94 (= _let_37 _let_93))) (let ((_let_95 (or _let_45 _let_41 _let_94))) (let ((_let_96 (forall ((U $$unsorted) (BOUND_VARIABLE_3329 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3329)) (not (= U (tptp.cons BOUND_VARIABLE_3329 U))))))) (let ((_let_97 (= tptp.nil _let_16))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_30 _let_41 _let_98))) (let ((_let_100 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_101 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23 _let_100))) (let ((_let_102 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_101))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_23))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_105 _let_103))) (let ((_let_109 (= _let_100 (tptp.app _let_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)))) (let ((_let_110 (or _let_105 _let_41 _let_109))) (let ((_let_111 (tptp.ssList _let_100))) (let ((_let_112 (or _let_105 _let_41 _let_111))) (let ((_let_113 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_114 (tptp.segmentP (tptp.app _let_25 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_115 (not _let_113))) (let ((_let_116 (or _let_29 _let_29 _let_115 _let_30 _let_105 _let_114))) (let ((_let_117 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)))) (let ((_let_118 (tptp.segmentP (tptp.app _let_101 tptp.nil) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_119 (tptp.segmentP _let_100 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_120 (not _let_119))) (let ((_let_121 (not _let_111))) (let ((_let_122 (or _let_121 _let_29 _let_120 _let_107 _let_30 _let_118))) (let ((_let_123 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_124 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_125 (REFL :args (_let_33)))) (let ((_let_126 (REFL :args (_let_39)))) (let ((_let_127 (and _let_17 _let_98))) (let ((_let_128 (ASSUME :args (_let_98)))) (let ((_let_129 (ASSUME :args (_let_17)))) (let ((_let_130 (SYMM _let_129))) (let ((_let_131 (REFL :args (tptp.nil)))) (let ((_let_132 (_let_93))) (let ((_let_133 (REFL :args (_let_108)))) (let ((_let_134 (forall ((U $$unsorted) (BOUND_VARIABLE_4792 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_4792)) (= (tptp.cons BOUND_VARIABLE_4792 U) (tptp.app (tptp.cons BOUND_VARIABLE_4792 tptp.nil) U)))))) (let ((_let_135 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_136 (forall ((U $$unsorted) (BOUND_VARIABLE_3304 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3304)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3304 U)))))) (let ((_let_137 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_138 (or _let_29 _let_113))) (let ((_let_139 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_140 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_141 (forall ((U $$unsorted) (BOUND_VARIABLE_4455 $$unsorted) (BOUND_VARIABLE_4453 $$unsorted) (BOUND_VARIABLE_4451 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4451)) (not (tptp.segmentP U BOUND_VARIABLE_4451)) (not (tptp.ssList BOUND_VARIABLE_4455)) (not (tptp.ssList BOUND_VARIABLE_4453)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4455 U) BOUND_VARIABLE_4453) BOUND_VARIABLE_4451))))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (_let_141))) (let ((_let_144 (or _let_45 _let_117))) (let ((_let_145 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_146 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_147 (not _let_19))) (let ((_let_148 (and _let_147 _let_117 _let_102))) (let ((_let_149 (_let_147 _let_117 _let_102))) (let ((_let_150 (ASSUME :args (_let_147)))) (let ((_let_151 (APPLY_UF tptp.segmentP))) (let ((_let_152 (ASSUME :args (_let_117)))) (let ((_let_153 (ASSUME :args (_let_102)))) (let ((_let_154 (and _let_17 _let_66 _let_109 _let_114))) (let ((_let_155 (ASSUME :args (_let_114)))) (let ((_let_156 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_24)))) (let ((_let_157 (ASSUME :args (_let_109)))) (let ((_let_158 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_20)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_49 2)) _let_56 :args ((not _let_20) 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(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 $$unsorted)) (=> (tptp.ssList Y) (=> (= (tptp.app X (tptp.cons V (tptp.cons W Y))) U) (= V W))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_12 _let_11 _let_10 (forall ((U $$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 $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))) _let_9 (forall ((U $$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_8 _let_7 (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) _let_6 _let_5 (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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) _let_4 (forall ((U $$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))))))))) _let_3 _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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 39.43/39.68 )
% 39.43/39.68 % SZS output end Proof for SWC329+1
% 39.43/39.68 % cvc5---1.0.5 exiting
% 39.43/39.68 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------