TSTP Solution File: SWC190+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC190+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n009.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 20:23:54 EDT 2023
% Result : Theorem 77.29s 77.51s
% Output : Proof 77.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC190+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n009.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 16:52:35 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 77.29/77.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.aNnK85WoZx/cvc5---1.0.5_21403.p...
% 77.29/77.51 ------- get file name : TPTP file name is SWC190+1
% 77.29/77.51 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_21403.smt2...
% 77.29/77.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 77.29/77.51 --- Run --no-e-matching --full-saturate-quant at 5...
% 77.29/77.51 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 77.29/77.51 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 77.29/77.51 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 77.29/77.51 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 77.29/77.51 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 77.29/77.51 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 77.29/77.51 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 77.29/77.51 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 77.29/77.51 --- Run --relevant-triggers --full-saturate-quant at 5...
% 77.29/77.51 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 77.29/77.51 --- Run --pre-skolem-quant=on --full-saturate-quant at 10...
% 77.29/77.51 --- Run --cbqi-vo-exp --full-saturate-quant at 10...
% 77.29/77.51 % SZS status Theorem for SWC190+1
% 77.29/77.51 % SZS output start Proof for SWC190+1
% 77.29/77.51 (
% 77.29/77.51 (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)) (or (not (tptp.ssList X)) (not (= V X)) (not (= U W)) (forall ((Y $$unsorted)) (=> (tptp.ssItem Y) (forall ((Z $$unsorted)) (=> (tptp.ssItem Z) (forall ((X1 $$unsorted)) (=> (tptp.ssList X1) (forall ((X2 $$unsorted)) (or (not (tptp.ssList X2)) (not (= (tptp.app (tptp.app (tptp.app X1 (tptp.cons Y tptp.nil)) (tptp.cons Z tptp.nil)) X2) U)) (= Y Z))))))))) (forall ((X3 $$unsorted)) (=> (tptp.ssItem X3) (exists ((X4 $$unsorted)) (and (tptp.ssItem X4) (not (= X3 X4)) (tptp.memberP W X4)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.app (tptp.app U V) W) (tptp.app U (tptp.app V W))))))))))) (let ((_let_3 (forall ((U $$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))))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (forall ((W $$unsorted)) (=> (tptp.ssItem W) (= (tptp.cons W (tptp.app V U)) (tptp.app (tptp.cons W V) U)))))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (tptp.ssList (tptp.app U V)))))))) (let ((_let_7 (tptp.ssList tptp.nil))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (tptp.ssList (tptp.cons V U)))))))) (let ((_let_9 (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_10 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (let ((_let_11 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil))) (let ((_let_12 (tptp.app _let_11 _let_10))) (let ((_let_13 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_12))) (let ((_let_14 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11))) (let ((_let_15 (tptp.app _let_14 _let_10))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (tptp.app tptp.nil _let_10))) (let ((_let_18 (= _let_12 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_17)))) (let ((_let_19 (= _let_10 _let_17))) (let ((_let_20 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_10)))) (let ((_let_21 (= _let_13 _let_20))) (let ((_let_22 (tptp.ssList _let_10))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.ssList _let_11))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_16))) (let ((_let_29 (forall ((U $$unsorted) (BOUND_VARIABLE_4849 $$unsorted) (BOUND_VARIABLE_4847 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4847)) (not (tptp.ssList BOUND_VARIABLE_4849)) (= (tptp.app (tptp.app U BOUND_VARIABLE_4847) BOUND_VARIABLE_4849) (tptp.app U (tptp.app BOUND_VARIABLE_4847 BOUND_VARIABLE_4849))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (_let_29))) (let ((_let_32 ((tptp.app (tptp.app U BOUND_VARIABLE_4847) BOUND_VARIABLE_4849)))) (let ((_let_33 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_34 (not _let_33))) (let ((_let_35 (not _let_7))) (let ((_let_36 (or _let_35 _let_34 _let_22))) (let ((_let_37 (forall ((U $$unsorted) (BOUND_VARIABLE_3317 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3317)) (tptp.ssList (tptp.cons BOUND_VARIABLE_3317 U)))))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (_let_37))) (let ((_let_40 ((tptp.cons BOUND_VARIABLE_3317 U)))) (let ((_let_41 (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.memberP (tptp.app (tptp.app (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil)) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil)) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) X4)))))) (let ((_let_42 (not _let_41))) (let ((_let_43 (not (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_44 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_45 (not _let_44))) (let ((_let_46 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_47 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.app _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_50 (tptp.ssList _let_49))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_48 _let_34 _let_46 _let_27 _let_45 _let_43 _let_42))) (let ((_let_53 (forall ((BOUND_VARIABLE_5418 $$unsorted) (BOUND_VARIABLE_5399 $$unsorted) (BOUND_VARIABLE_5397 $$unsorted) (BOUND_VARIABLE_5395 $$unsorted) (BOUND_VARIABLE_5393 $$unsorted)) (or (not (tptp.ssList (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5395 (tptp.cons BOUND_VARIABLE_5393 tptp.nil)) (tptp.cons BOUND_VARIABLE_5399 tptp.nil)) BOUND_VARIABLE_5397))) (not (tptp.ssItem BOUND_VARIABLE_5393)) (not (tptp.ssItem BOUND_VARIABLE_5399)) (= BOUND_VARIABLE_5393 BOUND_VARIABLE_5399) (not (tptp.ssList BOUND_VARIABLE_5395)) (not (tptp.ssList BOUND_VARIABLE_5397)) (not (tptp.ssItem BOUND_VARIABLE_5418)) (not (forall ((X4 $$unsorted)) (or (not (tptp.ssItem X4)) (= X4 BOUND_VARIABLE_5418) (not (tptp.memberP (tptp.app (tptp.app (tptp.app BOUND_VARIABLE_5395 (tptp.cons BOUND_VARIABLE_5393 tptp.nil)) (tptp.cons BOUND_VARIABLE_5399 tptp.nil)) BOUND_VARIABLE_5397) X4))))))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (or))) (let ((_let_56 (not _let_53))) (let ((_let_57 (_let_56))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57) (REWRITE :args ((=> _let_56 (not (or _let_51 _let_48 _let_34 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) _let_27 _let_45 _let_43 _let_42))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_53))) (REFL :args (_let_54)) :args _let_55)) (NOT_OR_ELIM (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) :args (1)) :args (_let_54 true _let_53)))) (let ((_let_59 (REFL :args (_let_52)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 2)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_55)) :args ((or _let_33 _let_52))) _let_58 :args (_let_33 true _let_52)))) (let ((_let_61 (ASSUME :args (_let_7)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_34 _let_22 (not _let_36)))) _let_61 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_36 false _let_37)) :args (_let_22 false _let_7 false _let_33 false _let_36)))) (let ((_let_63 (or _let_35 _let_48 _let_24))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 1)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_55)) :args ((or _let_47 _let_52))) _let_58 :args (_let_47 true _let_52)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_35 _let_48 _let_24 (not _let_63)))) _let_61 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_40)) :args _let_39)) _let_38 :args (_let_63 false _let_37)) :args (_let_24 false _let_7 false _let_47 false _let_63)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 4)) (CONG _let_59 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_26))) :args _let_55)) :args ((or _let_26 _let_52))) _let_58 :args (_let_26 true _let_52)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_25 _let_23 _let_16 (not _let_28)))) _let_66 _let_65 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_10 _let_11 QUANTIFIERS_INST_E_MATCHING _let_32)) :args _let_31)) _let_30 :args (_let_28 false _let_29)) :args (_let_16 false _let_26 false _let_24 false _let_22 false _let_28)))) (let ((_let_68 (or _let_23 _let_35 _let_48 _let_18))) (let ((_let_69 (forall ((U $$unsorted) (BOUND_VARIABLE_3617 $$unsorted) (BOUND_VARIABLE_3615 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3615)) (not (tptp.ssItem BOUND_VARIABLE_3617)) (= (tptp.cons BOUND_VARIABLE_3617 (tptp.app BOUND_VARIABLE_3615 U)) (tptp.app (tptp.cons BOUND_VARIABLE_3617 BOUND_VARIABLE_3615) U)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 ((tptp.app (tptp.cons BOUND_VARIABLE_3617 BOUND_VARIABLE_3615) U)))) (let ((_let_73 (or _let_23 _let_19))) (let ((_let_74 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (_let_74))) (let ((_let_77 ((not (= (tptp.ssList U) false))))) (let ((_let_78 (not _let_21))) (let ((_let_79 (or _let_27 _let_23 _let_78))) (let ((_let_80 (forall ((W $$unsorted) (BOUND_VARIABLE_2159 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2159)) (not (= (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 (tptp.app (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil) (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 tptp.nil))) (tptp.app W (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 BOUND_VARIABLE_2159)))))))) (let ((_let_81 (not _let_80))) (let ((_let_82 (tptp.memberP _let_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_83 (= _let_82 _let_81))) (let ((_let_84 (tptp.ssList _let_13))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_48 _let_83))) (let ((_let_87 (forall ((U $$unsorted) (BOUND_VARIABLE_2185 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_2185)) (= (tptp.memberP U BOUND_VARIABLE_2185) (not (forall ((W $$unsorted) (BOUND_VARIABLE_2159 $$unsorted)) (or (not (tptp.ssList W)) (not (tptp.ssList BOUND_VARIABLE_2159)) (not (= U (tptp.app W (tptp.cons BOUND_VARIABLE_2185 BOUND_VARIABLE_2159)))))))))))) (let ((_let_88 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_89 (_let_87))) (let ((_let_90 (tptp.ssList _let_15))) (let ((_let_91 (tptp.ssList _let_14))) (let ((_let_92 (not _let_91))) (let ((_let_93 (or _let_92 _let_23 _let_90))) (let ((_let_94 (forall ((U $$unsorted) (BOUND_VARIABLE_3575 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3575)) (tptp.ssList (tptp.app U BOUND_VARIABLE_3575)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (_let_94))) (let ((_let_97 ((tptp.app U BOUND_VARIABLE_3575)))) (let ((_let_98 (or _let_27 _let_25 _let_91))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_27 _let_25 _let_91 (not _let_98)))) _let_66 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_98 false _let_94)) :args (_let_91 false _let_26 false _let_24 false _let_98)))) (let ((_let_100 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_92 _let_23 _let_90 (not _let_93)))) _let_99 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (_let_14 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_93 false _let_94)) :args (_let_90 false _let_91 false _let_22 false _let_93)))) (let ((_let_101 (and _let_90 _let_16))) (let ((_let_102 (_let_90 _let_16))) (let ((_let_103 (ASSUME :args (_let_90)))) (let ((_let_104 (APPLY_UF tptp.ssList))) (let ((_let_105 (ASSUME :args (_let_16)))) (let ((_let_106 (SYMM _let_105))) (let ((_let_107 (SYMM _let_106))) (let ((_let_108 (SYMM _let_107))) (let ((_let_109 (tptp.memberP _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_110 (not _let_82))) (let ((_let_111 (or _let_109 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9)))) (let ((_let_112 (not _let_109))) (let ((_let_113 (tptp.memberP _let_49 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_114 (= _let_113 _let_111))) (let ((_let_115 (not _let_111))) (let ((_let_116 (not _let_90))) (let ((_let_117 (or _let_48 _let_116 _let_45 _let_114))) (let ((_let_118 (forall ((U $$unsorted) (BOUND_VARIABLE_3882 $$unsorted) (BOUND_VARIABLE_3880 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssList BOUND_VARIABLE_3880)) (not (tptp.ssList BOUND_VARIABLE_3882)) (= (tptp.memberP (tptp.app BOUND_VARIABLE_3880 BOUND_VARIABLE_3882) U) (or (tptp.memberP BOUND_VARIABLE_3880 U) (tptp.memberP BOUND_VARIABLE_3882 U))))))) (let ((_let_119 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_120 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 5)) (CONG _let_59 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QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_77)) :args _let_76)) _let_75 :args (_let_73 false _let_74)) :args (_let_19 false _let_22 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_35 _let_48 _let_23 _let_18 (not _let_68)))) _let_61 _let_64 _let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 tptp.nil QUANTIFIERS_INST_E_MATCHING _let_72)) :args _let_71))) _let_70 :args (_let_68 false _let_69)) :args (_let_18 false _let_7 false _let_47 false _let_22 false _let_68)) _let_67 :args (false true _let_21 false _let_19 false _let_18 false _let_16)) :args ((forall ((U $$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 $$unsorted)) (and (tptp.ssItem V) (not (= U V)))))) _let_9 (forall ((U $$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))))))))))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))) _let_8 _let_7 (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))))))))))) (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 $$unsorted)) (=> (tptp.ssItem V) (= (tptp.tl (tptp.cons V U)) U))))) _let_6 _let_5 _let_4 (forall ((U $$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)))))) _let_3 (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 $$unsorted)) (=> (tptp.ssList V) (=> (and (tptp.segmentP U V) (tptp.segmentP V U)) (= U V)))))) (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))) (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)))))))))) (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)))))))) (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_2 (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 77.29/77.51 )
% 77.29/77.51 % SZS output end Proof for SWC190+1
% 77.29/77.51 % cvc5---1.0.5 exiting
% 77.29/77.51 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------