TSTP Solution File: SWC075+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SWC075+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 20:23:03 EDT 2023
% Result : Theorem 11.25s 11.45s
% Output : Proof 11.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC075+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 14:52:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 11.25/11.45 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.EZO0kiMPDu/cvc5---1.0.5_3294.p...
% 11.25/11.45 ------- get file name : TPTP file name is SWC075+1
% 11.25/11.45 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3294.smt2...
% 11.25/11.45 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 11.25/11.45 --- Run --no-e-matching --full-saturate-quant at 5...
% 11.25/11.45 % SZS status Theorem for SWC075+1
% 11.25/11.45 % SZS output start Proof for SWC075+1
% 11.25/11.45 (
% 11.25/11.45 (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)) (exists ((Y $$unsorted)) (and (tptp.ssList Y) (tptp.neq Y tptp.nil) (tptp.segmentP V Y) (tptp.segmentP U Y))) (forall ((Z $$unsorted)) (=> (tptp.ssList Z) (forall ((X1 $$unsorted)) (or (not (tptp.ssList X1)) (not (= (tptp.app Z X1) X)) (not (= (tptp.app X1 Z) W)))))) (and (= tptp.nil V) (= tptp.nil U))))))))))))) (let ((_let_2 (forall ((U $$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.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_5 (forall ((U $$unsorted)) (=> (tptp.ssList U) (tptp.segmentP U U))))) (let ((_let_6 (forall ((U $$unsorted)) (=> (tptp.ssList U) (= (tptp.app tptp.nil U) U))))) (let ((_let_7 (tptp.ssList tptp.nil))) (let ((_let_8 (forall ((U $$unsorted)) (=> (tptp.ssList U) (forall ((V $$unsorted)) (=> (tptp.ssList V) (= (tptp.neq U V) (not (= U V))))))))) (let ((_let_9 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (= tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (and _let_10 _let_9))) (let ((_let_12 (tptp.neq SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil))) (let ((_let_13 (not _let_9))) (let ((_let_14 (= _let_13 _let_12))) (let ((_let_15 (not _let_7))) (let ((_let_16 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_15 _let_14))) (let ((_let_19 (forall ((U $$unsorted) (BOUND_VARIABLE_3280 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_3280)) (= (tptp.neq U BOUND_VARIABLE_3280) (not (= U BOUND_VARIABLE_3280))))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (_let_19))) (let ((_let_22 (tptp.ssList SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (= tptp.nil _let_24))) (let ((_let_26 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_27 (= tptp.nil _let_26))) (let ((_let_28 (and _let_27 _let_25))) (let ((_let_29 (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) Y)) (not (tptp.segmentP (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) Y)))))) (let ((_let_30 (not _let_29))) (let ((_let_31 (tptp.ssList _let_24))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 (not (tptp.ssList _let_26)) _let_30 _let_28 _let_17 _let_23))) (let ((_let_34 (forall ((BOUND_VARIABLE_5385 $$unsorted) (BOUND_VARIABLE_5383 $$unsorted)) (let ((_let_1 (tptp.app BOUND_VARIABLE_5383 BOUND_VARIABLE_5385))) (let ((_let_2 (tptp.app BOUND_VARIABLE_5385 BOUND_VARIABLE_5383))) (or (not (tptp.ssList _let_1)) (not (tptp.ssList _let_2)) (not (forall ((Y $$unsorted)) (or (not (tptp.ssList Y)) (not (tptp.neq Y tptp.nil)) (not (tptp.segmentP (tptp.app BOUND_VARIABLE_5385 BOUND_VARIABLE_5383) Y)) (not (tptp.segmentP (tptp.app BOUND_VARIABLE_5383 BOUND_VARIABLE_5385) Y))))) (and (= tptp.nil _let_2) (= tptp.nil _let_1)) (not (tptp.ssList BOUND_VARIABLE_5385)) (not (tptp.ssList BOUND_VARIABLE_5383)))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (or))) (let ((_let_38 (not _let_34))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_36) :args (_let_38))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_37)) _let_36 :args (_let_35 true _let_34)))) (let ((_let_40 (REFL :args (_let_33)))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 4)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_16))) :args _let_37)) :args ((or _let_16 _let_33))) _let_39 :args (_let_16 true _let_33)))) (let ((_let_42 (ASSUME :args (_let_7)))) (let ((_let_43 (tptp.segmentP _let_24 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_44 (not _let_43))) (let ((_let_45 (tptp.segmentP _let_26 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_46 (not _let_45))) (let ((_let_47 (not _let_12))) (let ((_let_48 (or _let_17 _let_47 _let_46 _let_44))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 2)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_29))) :args _let_37)) :args ((or _let_29 _let_33))) _let_39 :args (_let_29 true _let_33)))) (let ((_let_50 (_let_29))) (let ((_let_51 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM))) (let ((_let_52 (ASSUME :args _let_50))) (let ((_let_53 (tptp.app _let_24 tptp.nil))) (let ((_let_54 (tptp.segmentP _let_53 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_55 (= _let_24 _let_53))) (let ((_let_56 (tptp.segmentP SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_17 _let_17 _let_57 _let_23 _let_15 _let_54))) (let ((_let_59 (forall ((U $$unsorted) (BOUND_VARIABLE_4454 $$unsorted) (BOUND_VARIABLE_4452 $$unsorted) (BOUND_VARIABLE_4450 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4450)) (not (tptp.segmentP U BOUND_VARIABLE_4450)) (not (tptp.ssList BOUND_VARIABLE_4454)) (not (tptp.ssList BOUND_VARIABLE_4452)) (tptp.segmentP (tptp.app (tptp.app BOUND_VARIABLE_4454 U) BOUND_VARIABLE_4452) BOUND_VARIABLE_4450))))) (let ((_let_60 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_61 (_let_59))) (let ((_let_62 (or _let_17 _let_56))) (let ((_let_63 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (tptp.segmentP U U))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (_let_63))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_17 _let_56 (not _let_62)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args _let_51) :args _let_65)) _let_64 :args (_let_62 false _let_63)) :args (_let_56 false _let_16 false _let_62)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 5)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_37)) :args ((or _let_22 _let_33))) _let_39 :args (_let_22 true _let_33)))) (let ((_let_68 (or _let_32 _let_55))) (let ((_let_69 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app U tptp.nil)))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG _let_40 (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_37)) :args ((or _let_31 _let_33))) _let_39 :args (_let_31 true _let_33)))) (let ((_let_73 (and _let_55 _let_54))) (let ((_let_74 (ASSUME :args (_let_54)))) (let ((_let_75 (APPLY_UF tptp.segmentP))) (let ((_let_76 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_77 (ASSUME :args (_let_55)))) (let ((_let_78 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_79 (tptp.segmentP (tptp.app _let_78 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_80 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_78))) (let ((_let_81 (or _let_17 _let_17 _let_57 _let_15 _let_23 _let_79))) (let ((_let_82 (or _let_17 _let_80))) (let ((_let_83 (forall ((U $$unsorted)) (or (not (tptp.ssList U)) (= U (tptp.app tptp.nil U)))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 (and _let_80 _let_79))) (let ((_let_87 (ASSUME :args (_let_79)))) (let ((_let_88 (APPLY_UF tptp.app))) (let ((_let_89 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_90 (ASSUME :args (_let_80)))) (let ((_let_91 (not _let_14))) (let ((_let_92 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_14)) (CONG (REFL :args (_let_91)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_9))) (REFL :args (_let_12)) :args _let_37)) :args ((or _let_9 _let_12 _let_91))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or _let_17 _let_47 _let_46 _let_44 (not _let_48)))) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_86)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_87 _let_90) (SCOPE (TRUE_ELIM (TRANS (CONG (CONG (SYMM (SYMM _let_90)) _let_89 :args _let_88) _let_76 :args _let_75) (TRUE_INTRO _let_87))) :args (_let_79 _let_80))) :args (_let_80 _let_79))) :args (true _let_86)) :args ((or _let_45 (not _let_80) (not _let_79)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_17 _let_80 (not _let_82)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args _let_51) :args _let_85)) _let_84 :args (_let_82 false _let_83)) :args (_let_80 false _let_16 false _let_82)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_81))) :args ((or _let_15 _let_17 _let_23 _let_57 _let_79 (not _let_81)))) _let_42 _let_41 _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61)) _let_60 :args (_let_81 false _let_59)) :args (_let_79 false _let_7 false _let_16 false _let_22 false _let_56 false _let_81)) :args (_let_45 false _let_80 false _let_79)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_73)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_77) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_77)) _let_76 :args _let_75) (TRUE_INTRO _let_74))) :args (_let_54 _let_55))) :args (_let_55 _let_54))) :args (true _let_73)) :args ((or (not _let_55) _let_43 (not _let_54)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_32 _let_55 (not _let_68)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_24 QUANTIFIERS_INST_CBQI_PROP)) :args _let_71)) _let_70 :args (_let_68 false _let_69)) :args (_let_55 false _let_31 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_58))) :args ((or _let_15 _let_17 _let_23 _let_57 _let_54 (not _let_58)))) _let_42 _let_41 _let_67 _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_61)) _let_60 :args (_let_58 false _let_59)) :args (_let_54 false _let_7 false _let_16 false _let_22 false _let_56 false _let_58)) :args (_let_43 false _let_55 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args _let_51) :args _let_50)) _let_49 :args (_let_48 false _let_29)) :args (_let_47 false _let_16 false _let_45 false _let_43 false _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_15 _let_17 _let_14 (not _let_18)))) _let_42 _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 tptp.nil QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_21))) _let_20 :args (_let_18 false _let_19)) :args (_let_14 false _let_7 false _let_16 false _let_18)) :args (_let_9 true _let_12 false _let_14)))) (let ((_let_93 (= _let_27 _let_11))) (let ((_let_94 (not _let_11))) (let ((_let_95 (or _let_17 _let_23 _let_93))) (let ((_let_96 (forall ((U $$unsorted) (BOUND_VARIABLE_4861 $$unsorted)) (or (not (tptp.ssList U)) (not (tptp.ssList BOUND_VARIABLE_4861)) (= (= tptp.nil (tptp.app U BOUND_VARIABLE_4861)) (and (= tptp.nil BOUND_VARIABLE_4861) (= tptp.nil U))))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_96))) (let ((_let_99 (tptp.neq _let_24 tptp.nil))) (let ((_let_100 (not _let_25))) (let ((_let_101 (= _let_100 _let_99))) (let ((_let_102 (or _let_32 _let_15 _let_101))) (let ((_let_103 (tptp.segmentP _let_24 _let_24))) (let ((_let_104 (not _let_103))) (let ((_let_105 (tptp.segmentP _let_26 _let_24))) (let ((_let_106 (not _let_105))) (let ((_let_107 (not _let_99))) (let ((_let_108 (or _let_32 _let_107 _let_106 _let_104))) (let ((_let_109 (_let_24 QUANTIFIERS_INST_ENUM))) (let ((_let_110 (or _let_32 _let_103))) (let ((_let_111 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_110)) :args ((or _let_32 _let_103 (not _let_110)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args _let_109) :args _let_65)) _let_64 :args (_let_110 false _let_63)) :args (_let_103 false _let_31 false _let_110)))) (let ((_let_112 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.nil)))) (let ((_let_113 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 (tptp.app tptp.nil SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_114 (or _let_23 _let_112))) (let ((_let_115 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_PROP))) (let ((_let_116 (or _let_23 _let_113))) (let ((_let_117 (not _let_112))) (let ((_let_118 (not _let_113))) (let ((_let_119 (ASSUME :args (_let_106)))) (let ((_let_120 (ASSUME :args (_let_9)))) (let ((_let_121 (SYMM _let_120))) (let ((_let_122 (ASSUME :args (_let_113)))) (let ((_let_123 (ASSUME :args (_let_112)))) (let ((_let_124 (ASSUME :args (_let_103)))) (let ((_let_125 (not _let_101))) (let ((_let_126 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args (_let_101)) (CONG (REFL :args (_let_125)) (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_25))) (REFL :args (_let_99)) :args _let_37)) :args ((or _let_25 _let_99 _let_125))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_108)) :args ((or _let_32 _let_107 _let_106 _let_104 (not _let_108)))) _let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_119 _let_120 _let_122 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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))))))))) _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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 11.25/11.45 )
% 11.25/11.45 % SZS output end Proof for SWC075+1
% 11.29/11.45 % cvc5---1.0.5 exiting
% 11.29/11.45 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------