TSTP Solution File: SWC123+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC123+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 20:23:25 EDT 2023
% Result : Theorem 80.58s 80.88s
% Output : Proof 80.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : SWC123+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.17 % Command : do_cvc5 %s %d
% 0.17/0.39 % Computer : n001.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Mon Aug 28 17:48:20 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.24/0.53 %----Proving TF0_NAR, FOF, or CNF
% 80.58/80.88 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mxqix6scfq/cvc5---1.0.5_15430.p...
% 80.58/80.88 ------- get file name : TPTP file name is SWC123+1
% 80.58/80.88 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15430.smt2...
% 80.58/80.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 80.58/80.88 --- Run --no-e-matching --full-saturate-quant at 5...
% 80.58/80.88 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 80.58/80.88 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 80.58/80.88 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 80.58/80.88 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 80.58/80.88 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 80.58/80.88 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 80.58/80.88 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 80.58/80.88 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 80.58/80.88 --- Run --relevant-triggers --full-saturate-quant at 5...
% 80.58/80.88 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 80.58/80.88 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 80.58/80.88 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 80.58/80.88 % SZS status Theorem for SWC123+1
% 80.58/80.88 % SZS output start Proof for SWC123+1
% 80.58/80.88 (
% 80.58/80.88 (let ((_let_1 (not (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (forall ((X $$unsorted)) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.neq V tptp.nil)) (not (tptp.frontsegP X W)) (not (tptp.equalelemsP W)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq W Y) (tptp.frontsegP X Y) (tptp.segmentP Y W) (tptp.equalelemsP Y))) (and (tptp.neq U tptp.nil) (tptp.segmentP V U)))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (= (tptp.cons (tptp.hd U) (tptp.tl U)) U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.equalelemsP (tptp.cons U tptp.nil)))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U tptp.nil))))) (let ((_let_5 (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_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_7 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.frontsegP U tptp.nil))))) (let ((_let_8 (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))))))))))))) (let ((_let_9 (tptp.singletonP tptp.nil))) (let ((_let_10 (not _let_9))) (let ((_let_11 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_12 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))))) (let ((_let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_15 (tptp.ssList tptp.nil))) (let ((_let_16 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_17 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_18 (forall ((U $$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)))))))))) (let ((_let_19 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.singletonP U) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.cons V tptp.nil) U)))))))) (let ((_let_20 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_21 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_22))) (let ((_let_24 (tptp.segmentP (tptp.app _let_22 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (not _let_20))) (let ((_let_26 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25))) (let ((_let_29 (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 W))))))) (let ((_let_30 (not _let_28))) (let ((_let_31 (not _let_29))) (let ((_let_32 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35 _let_33))) (let ((_let_39 (forall ((U $$unsorted) (BOUND_VARIABLE_2221 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_2221)) (= (tptp.frontsegP U BOUND_VARIABLE_2221) (not (forall ((W $$unsorted)) (or (not (tptp.ssList W)) (not (= U (tptp.app BOUND_VARIABLE_2221 W))))))))))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_18)) (MACRO_SR_EQ_INTRO :args (_let_18 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y)) (not (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)) (not (tptp.segmentP Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.equalelemsP Y)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not _let_32))) (let ((_let_44 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_45 (and _let_44 _let_21))) (let ((_let_46 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil))) (let ((_let_47 (not _let_46))) (let ((_let_48 (or _let_35 (not (tptp.equalelemsP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_37 _let_47 _let_45 _let_43 _let_42))) (let ((_let_49 (forall ((U $$unsorted) (BOUND_VARIABLE_5275 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.equalelemsP U)) (not (tptp.ssList BOUND_VARIABLE_5275)) (not (tptp.neq BOUND_VARIABLE_5275 tptp.nil)) (and (tptp.neq U tptp.nil) (tptp.segmentP BOUND_VARIABLE_5275 U)) (not (tptp.frontsegP BOUND_VARIABLE_5275 U)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq U Y)) (not (tptp.frontsegP BOUND_VARIABLE_5275 Y)) (not (tptp.segmentP Y U)) (not (tptp.equalelemsP Y))))))))) (let ((_let_50 (not _let_48))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (REFL :args (_let_48)))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 2)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_52)) :args ((or _let_36 _let_48))) _let_54 :args (_let_36 true _let_48)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 0)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_52)) :args ((or _let_34 _let_48))) _let_54 :args (_let_34 true _let_48)))) (let ((_let_58 (_let_31))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_58)) :args _let_58)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_29))) (REFL :args (_let_30)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_43 _let_31 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 5)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_32))) :args _let_52)) :args ((or _let_32 _let_48))) _let_54 :args (_let_32 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_35 _let_37 _let_33 (not _let_38)))) _let_57 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.frontsegP U BOUND_VARIABLE_2221)))) :args (_let_39))) _let_40 :args (_let_38 false _let_39)) :args (_let_33 false _let_34 false _let_36 false _let_38)) :args (_let_31 false _let_32 false _let_33)) :args (_let_30 true _let_29)))) (let ((_let_60 (REFL :args (_let_28)))) (let ((_let_61 (not _let_21))) (let ((_let_62 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_63 (not _let_62))) (let ((_let_64 (= _let_44 _let_63))) (let ((_let_65 (not _let_15))) (let ((_let_66 (or _let_35 _let_65 _let_64))) (let ((_let_67 (forall ((U $$unsorted) (BOUND_VARIABLE_3270 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3270)) (= (tptp.neq U BOUND_VARIABLE_3270) (not (= U BOUND_VARIABLE_3270))))))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (_let_67))) (let ((_let_70 (ASSUME :args (_let_15)))) (let ((_let_71 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_72 (tptp.cons _let_71 tptp.nil))) (let ((_let_73 (= tptp.nil _let_72))) (let ((_let_74 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_72))) (let ((_let_75 (tptp.segmentP _let_72 tptp.nil))) (let ((_let_76 (tptp.segmentP _let_72 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_77 (not _let_74))) (let ((_let_78 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_72))) (let ((_let_79 (= _let_78 _let_77))) (let ((_let_80 (tptp.equalelemsP _let_72))) (let ((_let_81 (not _let_80))) (let ((_let_82 (not _let_76))) (let ((_let_83 (tptp.frontsegP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_72))) (let ((_let_84 (not _let_83))) (let ((_let_85 (not _let_78))) (let ((_let_86 (tptp.ssList _let_72))) (let ((_let_87 (not _let_86))) (let ((_let_88 (or _let_87 _let_85 _let_84 _let_82 _let_81))) (let ((_let_89 (not _let_73))) (let ((_let_90 (tptp.ssItem _let_71))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_89))) (let ((_let_93 (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= tptp.nil (tptp.cons V tptp.nil))))))) (let ((_let_94 (not _let_93))) (let ((_let_95 (= _let_9 _let_94))) (let ((_let_96 (or _let_65 _let_95))) (let ((_let_97 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= (tptp.singletonP U) (not (forall ((V $$unsorted)) (or (not (tptp.ssItem V)) (not (= U (tptp.cons V tptp.nil))))))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_19)) (MACRO_SR_EQ_INTRO :args (_let_19 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (not _let_95))) (let ((_let_100 (_let_93))) (let ((_let_101 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_102 (or _let_37 _let_101 _let_90))) (let ((_let_103 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_104 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_105 (not _let_101))) (let ((_let_106 (= _let_46 _let_105))) (let ((_let_107 (or _let_37 _let_65 _let_106))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_106)) :args ((or _let_47 _let_105 (not _let_106)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_48 3)) (CONG _let_55 (MACRO_SR_PRED_INTRO :args ((= (not _let_47) _let_46))) :args _let_52)) :args ((or _let_46 _let_48))) _let_54 :args (_let_46 true _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_107)) :args ((or _let_65 _let_37 _let_106 (not _let_107)))) _let_70 _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_68 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil QUANTIFIERS_INST_CBQI_PROP)) :args _let_69))) _let_68 :args (_let_107 false _let_67)) :args (_let_106 false _let_15 false _let_36 false _let_107)) :args (_let_105 false _let_46 false _let_106)))) (let ((_let_109 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_37 _let_101 _let_90 (not _let_102)))) _let_56 _let_108 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_104 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssList U) false))))) :args (_let_103))) _let_104 :args (_let_102 false _let_103)) :args (_let_90 false _let_36 true _let_101 false _let_102)))) (let ((_let_110 (and _let_62 _let_89))) (let ((_let_111 (ASSUME :args (_let_89)))) (let ((_let_112 (REFL :args (_let_72)))) (let ((_let_113 (ASSUME :args (_let_62)))) (let ((_let_114 (SYMM _let_113))) (let ((_let_115 (or _let_87 _let_75))) (let ((_let_116 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U tptp.nil))))) (let ((_let_117 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_118 (or _let_65 _let_91 _let_86))) (let ((_let_119 (forall ((U $$unsorted) (BOUND_VARIABLE_3293 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3293)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3293 U)))))) (let ((_let_120 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_121 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_118)) :args ((or _let_65 _let_91 _let_86 (not _let_118)))) _let_70 _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_120 :args (tptp.nil _let_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cons BOUND_VARIABLE_3293 U)))) :args (_let_119))) _let_120 :args (_let_118 false _let_119)) :args (_let_86 false _let_15 false _let_90 false _let_118)))) (let ((_let_122 (and _let_62 _let_75))) (let ((_let_123 (ASSUME :args (_let_75)))) (let ((_let_124 (APPLY_UF tptp.segmentP))) (let ((_let_125 (or _let_35 _let_87 _let_79))) (let ((_let_126 (not _let_79))) (let ((_let_127 (or _let_91 _let_80))) (let ((_let_128 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (tptp.equalelemsP (tptp.cons U tptp.nil)))))) (let ((_let_129 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_130 (_let_41))) (let ((_let_131 (tptp.tl SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_132 (tptp.cons _let_71 _let_131))) (let ((_let_133 (tptp.frontsegP _let_132 _let_72))) (let ((_let_134 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_132))) (let ((_let_135 (tptp.frontsegP _let_131 tptp.nil))) (let ((_let_136 (= _let_135 _let_133))) (let ((_let_137 (tptp.ssList _let_131))) (let ((_let_138 (not _let_137))) (let ((_let_139 (or _let_91 _let_91 _let_138 _let_65 _let_136))) (let ((_let_140 (forall ((U $$unsorted) (BOUND_VARIABLE_4123 $$unsorted) (BOUND_VARIABLE_4121 $$unsorted) (BOUND_VARIABLE_4119 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_4119)) (not (tptp.ssList BOUND_VARIABLE_4123)) (not (tptp.ssList BOUND_VARIABLE_4121)) (= (tptp.frontsegP (tptp.cons U BOUND_VARIABLE_4123) (tptp.cons BOUND_VARIABLE_4119 BOUND_VARIABLE_4121)) (and (= U BOUND_VARIABLE_4119) (tptp.frontsegP BOUND_VARIABLE_4123 BOUND_VARIABLE_4121))))))) (let ((_let_141 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_142 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_143 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.tl _let_142)))) (let ((_let_144 (= 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(_let_110)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_111 _let_113) (SCOPE (FALSE_ELIM (TRANS (CONG _let_114 _let_112 :args (=)) (FALSE_INTRO _let_111))) :args (_let_89 _let_62))) :args (_let_62 _let_89))) :args (true _let_110)) (CONG (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_73))) (REFL :args (_let_77)) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_91 _let_89 (not _let_92)))) _let_109 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_100) :args (_let_71 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ssItem V) false))))) :args _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_95)) (CONG (REFL :args (_let_99)) (REFL :args (_let_9)) (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_93))) :args _let_52)) :args ((or _let_9 _let_93 _let_99))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) 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(_let_44 true _let_62 false _let_64)) :args (_let_61 true _let_45 false _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_28 1)) (CONG _let_60 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_20))) :args _let_52)) :args ((or _let_20 _let_28))) _let_59 :args (_let_20 true _let_28)) :args (false false _let_24 false _let_23 true _let_21 false _let_20)) :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)))))) (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_19 _let_18 (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_17 _let_16 _let_15 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= (tptp.cons V U) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (forall ((X $$unsorted)) (=> (tptp.ssItem X) (=> (= (tptp.cons W U) (tptp.cons X V)) (and (= W X) (= V U))))))))))) _let_14 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (not (= tptp.nil (tptp.cons V U))))))) _let_13 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssList (tptp.tl U))))) _let_12 (forall ((U $$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_11 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.leq U V) (tptp.leq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.leq V W)) (tptp.leq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.leq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.geq U V) (tptp.leq V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.lt U V) (not (tptp.lt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.lt U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.gt U V) (tptp.lt V U)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.app V W) U) (or (tptp.memberP V U) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))) _let_10 (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 $$unsorted)) (=> (tptp.ssList W) (=> (tptp.frontsegP U V) (tptp.frontsegP (tptp.app U W) V)))))))) _let_8 _let_7 (forall ((U $$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_6 _let_5 _let_4 (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 $$unsorted)) (=> (tptp.ssItem U) (tptp.duplicatefreeP (tptp.cons U tptp.nil)))) (tptp.duplicatefreeP tptp.nil) _let_3 (tptp.equalelemsP tptp.nil) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssItem V) (= (tptp.hd U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (exists ((V $$unsorted)) (and (tptp.ssList V) (= (tptp.tl U) V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (and (not (= tptp.nil V)) (not (= tptp.nil U)) (= (tptp.hd V) (tptp.hd U)) (= (tptp.tl V) (tptp.tl U))) (= V U)))))) _let_2 (forall ((U $$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 $$unsorted)) (=> (tptp.ssList W) (=> (= (tptp.app V W) (tptp.app V U)) (= W U)))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.cons V U) (tptp.app (tptp.cons V tptp.nil) U)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (= tptp.nil (tptp.app U V)) (and (= tptp.nil V) (= tptp.nil U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app U tptp.nil) U))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.hd (tptp.app U V)) (tptp.hd U))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (=> (not (= tptp.nil U)) (= (tptp.tl (tptp.app U V)) (tptp.app (tptp.tl U) V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (and (tptp.geq U V) (tptp.geq V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.geq U V) (tptp.geq V W)) (tptp.geq U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (tptp.geq U U))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.lt U U)))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.leq U V) (tptp.lt V W)) (tptp.lt U W)))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.leq U V) (or (= U V) (tptp.lt U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.lt U V) (and (not (= U V)) (tptp.leq U V))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (=> (tptp.gt U V) (not (tptp.gt V U))))))) (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (=> (and (tptp.gt U V) (tptp.gt V W)) (tptp.gt U W)))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 80.58/80.90 )
% 80.58/80.90 % SZS output end Proof for SWC123+1
% 80.58/80.90 % cvc5---1.0.5 exiting
% 80.58/80.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------