TSTP Solution File: SWC025+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC025+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n022.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 20:22:41 EDT 2023
% Result : Theorem 31.84s 32.20s
% Output : Proof 31.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.16 % Problem : SWC025+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.17 % Command : do_cvc5 %s %d
% 0.14/0.37 % Computer : n022.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Aug 28 17:50:24 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.19/0.53 %----Proving TF0_NAR, FOF, or CNF
% 31.84/32.20 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.NBznbPBF2R/cvc5---1.0.5_10148.p...
% 31.84/32.20 ------- get file name : TPTP file name is SWC025+1
% 31.84/32.20 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10148.smt2...
% 31.84/32.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 31.84/32.20 --- Run --no-e-matching --full-saturate-quant at 5...
% 31.84/32.20 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 31.84/32.20 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 31.84/32.20 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 31.84/32.20 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.84/32.20 % SZS status Theorem for SWC025+1
% 31.84/32.20 % SZS output start Proof for SWC025+1
% 31.84/32.20 (
% 31.84/32.20 (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)) (let ((_let_1 (= tptp.nil V))) (let ((_let_2 (= tptp.nil U))) (=> (tptp.ssList X) (or (not (= V X)) (not (= U W)) (not (tptp.duplicatefreeP W)) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.memberP X Y))) (let ((_let_2 (tptp.memberP W Y))) (and (tptp.ssItem Y) (or (and (not _let_1) _let_2) (and (not _let_2) _let_1)))))) (and (or (not _let_1) _let_2) (or (not _let_2) _let_1)))))))))))))))) (let ((_let_2 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (not (tptp.memberP tptp.nil U)))))) (let ((_let_3 (forall ((U $$unsorted)) (=> (tptp.ssItem U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (forall ((W $$unsorted)) (=> (tptp.ssList W) (= (tptp.memberP (tptp.cons V W) U) (or (= U V) (tptp.memberP W U))))))))))) (let ((_let_4 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssItem V) (= (tptp.hd (tptp.cons V U)) V))))))) (let ((_let_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (=> (not (= tptp.nil U)) (tptp.ssItem (tptp.hd U))))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (or (= tptp.nil U) (exists ((V $$unsorted)) (and (tptp.ssList V) (exists ((W $$unsorted)) (and (tptp.ssItem W) (= (tptp.cons W V) U)))))))))) (let ((_let_7 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_7))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28 (tptp.hd _let_7)))) (let ((_let_10 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10))) (let ((_let_12 (tptp.memberP (tptp.cons _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27) _let_10))) (let ((_let_13 (not _let_8))) (let ((_let_14 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_28))) (let ((_let_15 (not _let_14))) (let ((_let_16 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_27))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_13))) (let ((_let_19 (forall ((V $$unsorted) (BOUND_VARIABLE_3443 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3443)) (not (= (tptp.cons BOUND_VARIABLE_3443 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_20 (not _let_18))) (let ((_let_21 (not _let_19))) (let ((_let_22 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22 _let_21))) (let ((_let_26 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (not (forall ((V $$unsorted) (BOUND_VARIABLE_3443 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3443)) (not (= U (tptp.cons BOUND_VARIABLE_3443 V)))))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((not (= (tptp.ssList U) false))))) (let ((_let_30 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_22))) (let ((_let_33 (not _let_22))) (let ((_let_34 (or _let_33 _let_30))) (let ((_let_35 (and _let_34 _let_32))) (let ((_let_36 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (forall ((V $$unsorted) (BOUND_VARIABLE_3443 $$unsorted)) (or (not (tptp.ssList V)) (not (tptp.ssItem BOUND_VARIABLE_3443)) (not (= (tptp.cons BOUND_VARIABLE_3443 V) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_38 (not _let_37))) (let ((_let_39 (not _let_36))) (let ((_let_40 (or _let_39 _let_30 _let_38))) (let ((_let_41 (tptp.hd SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_42 (tptp.ssItem _let_41))) (let ((_let_43 (or _let_39 _let_30 _let_42))) (let ((_let_44 (tptp.cons SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_45 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_44))) (let ((_let_46 (not _let_45))) (let ((_let_47 (tptp.ssItem SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_48 (not _let_47))) (let ((_let_49 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_50 (not _let_49))) (let ((_let_51 (or _let_50 _let_48 _let_46))) (let ((_let_52 (tptp.memberP tptp.nil _let_41))) (let ((_let_53 (not _let_52))) (let ((_let_54 (not _let_42))) (let ((_let_55 (or _let_54 _let_53))) (let ((_let_56 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_41))) (let ((_let_57 (not _let_56))) (let ((_let_58 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_41))) (let ((_let_59 (not _let_58))) (let ((_let_60 (or _let_56 _let_59))) (let ((_let_61 (and _let_60 (or _let_58 _let_57)))) (let ((_let_62 (or _let_54 _let_61))) (let ((_let_63 (tptp.memberP (tptp.cons _let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_41))) (let ((_let_64 (or _let_54 _let_54 _let_50 _let_63))) (let ((_let_65 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 (tptp.hd _let_44)))) (let ((_let_66 (or _let_50 _let_48 _let_65))) (let ((_let_67 (forall ((Y $$unsorted)) (let ((_let_1 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y))) (let ((_let_2 (tptp.memberP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 Y))) (or (not (tptp.ssItem Y)) (and (or _let_1 (not _let_2)) (or _let_2 (not _let_1))))))))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_39 (not (tptp.duplicatefreeP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) _let_24 _let_35 _let_68))) (let ((_let_70 (forall ((U $$unsorted) (BOUND_VARIABLE_5280 $$unsorted)) (let ((_let_1 (= tptp.nil BOUND_VARIABLE_5280))) (let ((_let_2 (= tptp.nil U))) (or (not (tptp.ssList U)) (not (tptp.duplicatefreeP U)) (not (tptp.ssList BOUND_VARIABLE_5280)) (and (or (not _let_1) _let_2) (or (not _let_2) _let_1)) (not (forall ((Y $$unsorted)) (let ((_let_1 (tptp.memberP BOUND_VARIABLE_5280 Y))) (let ((_let_2 (tptp.memberP U Y))) (or (not (tptp.ssItem Y)) (and (or _let_1 (not _let_2)) (or _let_2 (not _let_1)))))))))))))) (let ((_let_71 (not _let_69))) (let ((_let_72 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_73 (or))) (let ((_let_74 (not _let_70))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_72) :args (_let_74))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_70))) (REFL :args (_let_71)) :args _let_73)) _let_72 :args (_let_71 true _let_70)))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_69 3)) _let_75 :args ((not _let_35) true _let_69)))) (let ((_let_77 (CNF_AND_NEG :args (_let_35)))) (let ((_let_78 (REFL :args (_let_69)))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_36))) :args _let_73)) :args ((or _let_36 _let_69))) _let_75 :args (_let_36 true _let_69)))) (let ((_let_80 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= tptp.nil U) (tptp.ssItem (tptp.hd U)))))) (let ((_let_81 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_82 (_let_80))) (let ((_let_83 ((not (= (tptp.ssList U) false))))) (let ((_let_84 (_let_38))) (let ((_let_85 (forall ((U $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.memberP tptp.nil U)))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (_let_85))) (let ((_let_88 ((not (= (tptp.ssItem U) false))))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 4)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_73)) :args ((or _let_67 _let_69))) _let_75 :args (_let_67 true _let_69)))) (let ((_let_90 (_let_67))) (let ((_let_91 ((not (= (tptp.ssItem Y) false))))) (let ((_let_92 (ASSUME :args _let_90))) (let ((_let_93 (REFL :args (_let_51)))) (let ((_let_94 (and _let_22 _let_53))) (let ((_let_95 (ASSUME :args (_let_53)))) (let ((_let_96 (APPLY_UF tptp.memberP))) (let ((_let_97 (REFL :args (_let_41)))) (let ((_let_98 (ASSUME :args (_let_22)))) (let ((_let_99 (forall ((U $$unsorted) (BOUND_VARIABLE_3910 $$unsorted) (BOUND_VARIABLE_3908 $$unsorted)) (or (not (tptp.ssItem U)) (not (tptp.ssItem BOUND_VARIABLE_3908)) (not (tptp.ssList BOUND_VARIABLE_3910)) (= (tptp.memberP (tptp.cons BOUND_VARIABLE_3908 BOUND_VARIABLE_3910) U) (or (= U BOUND_VARIABLE_3908) (tptp.memberP BOUND_VARIABLE_3910 U))))))) (let ((_let_100 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_101 (_let_99))) (let ((_let_102 (forall ((U $$unsorted) (BOUND_VARIABLE_3502 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssItem BOUND_VARIABLE_3502)) (= BOUND_VARIABLE_3502 (tptp.hd (tptp.cons BOUND_VARIABLE_3502 U))))))) (let ((_let_103 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_104 (_let_102))) (let ((_let_105 (and _let_45 _let_65 _let_63))) (let ((_let_106 (ASSUME :args (_let_63)))) (let ((_let_107 (APPLY_UF tptp.cons))) (let ((_let_108 (APPLY_UF tptp.hd))) (let ((_let_109 (ASSUME :args (_let_45)))) (let ((_let_110 (ASSUME :args (_let_65)))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_105)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_106 _let_109 _let_110) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS _let_109 (CONG (TRANS (SYMM (SYMM _let_110)) (CONG (SYMM _let_109) :args _let_108)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) :args _let_107)) _let_97 :args _let_96) (TRUE_INTRO _let_106))) :args (_let_63 _let_45 _let_65))) :args (_let_45 _let_65 _let_63))) :args (true _let_105)) :args ((or _let_46 (not _let_65) _let_58 (not _let_63)))) (REORDERING (CNF_OR_POS :args (_let_60)) :args ((or _let_56 _let_59 (not _let_60)))) (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_50 _let_48 _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_CBQI_PROP)) :args _let_104)) _let_103 :args (_let_66 false _let_102)) (REORDERING (FACTORING (CNF_OR_POS :args (_let_64))) :args ((or _let_54 _let_50 _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_100 :args (_let_41 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_41 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_101))) _let_100 :args (_let_64 false _let_99)) (REORDERING (CNF_AND_POS :args (_let_61 0)) :args ((or _let_60 (not _let_61)))) (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_94)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_95 _let_98) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM _let_98) _let_97 :args _let_96) (FALSE_INTRO _let_95))) :args (_let_53 _let_22))) :args (_let_22 _let_53))) :args (true _let_94)) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) (REFL :args (_let_57)) :args _let_73)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 2)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_45))) :args _let_73)) :args ((or _let_45 _let_51))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 1)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_73)) :args ((or _let_47 _let_51))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_49))) :args _let_73)) :args ((or _let_49 _let_51))) (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_54 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (_let_41 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_91)) :args _let_90)) _let_89 :args (_let_62 false _let_67)) (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_54 _let_53 (not _let_55)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (_let_41 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_88)) :args _let_87)) _let_86 :args (_let_55 false _let_85)) (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84) (REWRITE :args ((=> _let_38 (not (or _let_50 _let_48 (not (= _let_44 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_37))) (REFL :args ((not _let_51))) :args _let_73)) (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_39 _let_30 _let_42 (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_83)) :args _let_82)) _let_81 :args (_let_43 false _let_80)) _let_79 (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_30 _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28))) _let_27 :args (_let_40 false _let_26)) _let_79 (CNF_OR_NEG :args (_let_34 1)) _let_77 _let_76 (REORDERING (CNF_OR_NEG :args (_let_32 1)) :args ((or _let_33 _let_32))) :args (_let_33 true _let_58 false _let_65 false _let_66 false _let_63 false _let_64 false _let_60 true _let_56 false _let_45 false _let_47 false _let_49 false _let_61 false _let_62 true _let_52 false _let_55 true _let_51 false _let_42 false _let_43 false _let_36 true _let_37 false _let_40 false _let_36 true _let_30 true _let_34 true _let_35 false _let_32)))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 2)) (CONG _let_78 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_23))) :args _let_73)) :args ((or _let_23 _let_69))) _let_75 :args (_let_23 true _let_69)))) (let ((_let_113 (_let_21))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE (ASSUME :args _let_113)) :args _let_113) (REWRITE :args ((=> _let_21 (not (or _let_17 _let_15 (not (= _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_19))) (REFL :args (_let_20)) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 _let_21 (not _let_25)))) _let_112 _let_111 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28))) _let_27 :args (_let_25 false _let_26)) :args (_let_21 false _let_23 true _let_22 false _let_25)) :args (_let_20 true _let_19)))) (let ((_let_115 (REFL :args (_let_18)))) (let ((_let_116 (or _let_17 _let_15 _let_9))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_18 0)) (CONG _let_115 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_73)) :args ((or _let_16 _let_18))) _let_114 :args (_let_16 true _let_18)))) (let ((_let_118 (not _let_11))) (let ((_let_119 (tptp.memberP 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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)))))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.84/32.21 )
% 31.84/32.21 % SZS output end Proof for SWC025+1
% 31.84/32.21 % cvc5---1.0.5 exiting
% 31.84/32.21 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------