TSTP Solution File: SET768+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n024.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 14:40:15 EDT 2023
% Result : Theorem 0.23s 0.59s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET768+4 : TPTP v8.1.2. Released v2.2.0.
% 0.08/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 10:05:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.59 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.whGTUjSPLY/cvc5---1.0.5_31132.p...
% 0.23/0.59 ------- get file name : TPTP file name is SET768+4
% 0.23/0.59 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31132.smt2...
% 0.23/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.59 % SZS status Theorem for SET768+4
% 0.23/0.59 % SZS output start Proof for SET768+4
% 0.23/0.59 (
% 0.23/0.59 (let ((_let_1 (not (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.equivalence R E) (tptp.member A E) (tptp.member B E)) (= (tptp.equal_set (tptp.equivalence_class A E R) (tptp.equivalence_class B E R)) (tptp.apply R A B))))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.equivalence_class A E R)) (and (tptp.member X E) (tptp.apply R A X)))))) (let ((_let_3 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (tptp.apply R X Y) (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A) (tptp.member Z A)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_7 (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_7))) (let ((_let_9 (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_8))) (let ((_let_13 (tptp.subset _let_9 _let_7))) (let ((_let_14 (= _let_13 _let_6))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_16 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_17 (_let_15))) (let ((_let_18 ((tptp.subset A B)))) (let ((_let_19 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (_let_9 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_18)) :args _let_17)) _let_16 :args (_let_14 false _let_15)))) (let ((_let_20 (tptp.subset _let_7 _let_9))) (let ((_let_21 (and _let_20 _let_13))) (let ((_let_22 (tptp.equal_set _let_7 _let_9))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (_let_4))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_7 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_24)) _let_25 :args (_let_23 false _let_4)))) (let ((_let_27 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_28 (= _let_22 _let_27))) (let ((_let_29 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_7))) (let ((_let_30 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_9))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_29))) (let ((_let_33 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (and _let_34 _let_33))) (let ((_let_36 (= _let_30 _let_35))) (let ((_let_37 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_38 (and _let_34 _let_37))) (let ((_let_39 (= _let_29 _let_38))) (let ((_let_40 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (not _let_33))) (let ((_let_43 (not _let_27))) (let ((_let_44 (not _let_34))) (let ((_let_45 (not _let_41))) (let ((_let_46 (not _let_40))) (let ((_let_47 (or _let_46 _let_45 _let_44 _let_43 _let_42 _let_37))) (let ((_let_48 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (not _let_48))) (let ((_let_50 (or _let_49 _let_46 _let_45 _let_28))) (let ((_let_51 (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.equivalence R E)) (not (tptp.member A E)) (not (tptp.member B E)) (= (tptp.equal_set (tptp.equivalence_class A E R) (tptp.equivalence_class B E R)) (tptp.apply R A B)))))) (let ((_let_52 (not _let_50))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_50 3)) _let_56 :args ((not _let_28) true _let_50)))) (let ((_let_58 (_let_28))) (let ((_let_59 (REORDERING (CNF_EQUIV_NEG1 :args _let_58) :args ((or _let_22 _let_27 _let_28))))) (let ((_let_60 (not _let_23))) (let ((_let_61 (not _let_21))) (let ((_let_62 (_let_23))) (let ((_let_63 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_64 (= _let_20 _let_63))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (_let_7 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_18)) :args _let_17)) _let_16 :args (_let_64 false _let_15)))) (let ((_let_66 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_67 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_7))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_66))) (let ((_let_70 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_71 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_72 (and _let_71 _let_70))) (let ((_let_73 (= _let_67 _let_72))) (let ((_let_74 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_75 (and _let_71 _let_74))) (let ((_let_76 (= _let_66 _let_75))) (let ((_let_77 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_78 (not _let_70))) (let ((_let_79 (not _let_77))) (let ((_let_80 (not _let_71))) (let ((_let_81 (or _let_45 _let_46 _let_80 _let_79 _let_78 _let_74))) (let ((_let_82 (_let_2))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (tptp.equivalence_class A E R))) (let ((_let_85 ((tptp.member X _let_84)))) (let ((_let_86 (not _let_72))) (let ((_let_87 (REFL :args (_let_50)))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 1)) (CONG _let_87 (MACRO_SR_PRED_INTRO :args ((= (not _let_46) _let_40))) :args _let_54)) :args ((or _let_40 _let_50))) _let_56 :args (_let_40 true _let_50)))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 2)) (CONG _let_87 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) :args _let_54)) :args ((or _let_41 _let_50))) _let_56 :args (_let_41 true _let_50)))) (let ((_let_90 (and _let_40 _let_77))) (let ((_let_91 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_9))) (let ((_let_92 (= _let_91 _let_90))) (let ((_let_93 (_let_84 (tptp.apply R A X)))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_93)) :args _let_82)) _let_83 :args (_let_92 false _let_2)))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_7))) (let ((_let_96 (not _let_95))) (let ((_let_97 (or _let_96 _let_91))) (let ((_let_98 (or _let_46 _let_45 _let_43 _let_77))) (let ((_let_99 (not _let_92))) (let ((_let_100 (not _let_90))) (let ((_let_101 (_let_92))) (let ((_let_102 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_103 (and _let_40 _let_102))) (let ((_let_104 (= _let_95 _let_103))) (let ((_let_105 (or _let_46 _let_102))) (let ((_let_106 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))))) (let ((_let_107 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_108 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X))))) (let ((_let_109 (and _let_106 _let_108 _let_107))) (let ((_let_110 (= _let_48 _let_109))) (let ((_let_111 (forall ((A $$unsorted) (R $$unsorted)) (= (tptp.equivalence R A) (and (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.apply R X Y)) (tptp.apply R Y X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member Y A)) (not (tptp.member Z A)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_112 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_110)) :args ((or _let_49 _let_109 (not _let_110)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_50 0)) (CONG _let_87 (MACRO_SR_PRED_INTRO :args ((= (not _let_49) _let_48))) :args _let_54)) :args ((or _let_48 _let_50))) _let_56 :args (_let_48 true _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_112 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equivalence R A)))) :args (_let_111))) _let_112 :args (_let_110 false _let_111)) :args (_let_109 false _let_48 false _let_110)))) (let ((_let_114 (not _let_109))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_109 0)) :args ((or _let_106 _let_114))) _let_113 :args (_let_106 false _let_109)))) (let ((_let_116 (_let_106))) (let ((_let_117 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) (let ((_let_118 (ASSUME :args _let_116))) (let ((_let_119 (_let_63))) (let ((_let_120 (_let_108))) (let ((_let_121 (not _let_64))) (let ((_let_122 (_let_64))) (let ((_let_123 (REORDERING (CNF_EQUIV_POS1 :args _let_62) :args ((or (not _let_22) _let_21 _let_60))))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_109 2)) :args ((or _let_107 _let_114))) _let_113 :args (_let_107 false _let_109)))) (let ((_let_125 (_let_107))) (let ((_let_126 (ASSUME :args _let_125))) (let ((_let_127 (not _let_63))) (let ((_let_128 (_let_127))) (let ((_let_129 (not _let_14))) (let ((_let_130 (not _let_6))) (let ((_let_131 (_let_14))) (let ((_let_132 (_let_130))) (let ((_let_133 (not _let_35))) (let ((_let_134 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_45 _let_43 _let_37 _let_44 _let_42 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z) true)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) :args _let_125)) _let_124 :args (_let_47 false _let_107)) _let_89 _let_88 (CNF_AND_NEG :args (_let_38)) (REORDERING (CNF_AND_POS :args (_let_35 1)) :args ((or _let_33 _let_133))) (REORDERING (CNF_AND_POS :args (_let_35 0)) :args ((or _let_34 _let_133))) (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_29 (not _let_38) (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_82)) _let_83 :args (_let_39 false _let_2)) (REORDERING (CNF_EQUIV_POS1 :args (_let_36)) :args ((or _let_31 _let_35 (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_82)) _let_83 :args (_let_36 false _let_2)) (CNF_OR_NEG :args (_let_32 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_32 0)) (CONG (REFL :args (_let_32)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_54)) :args ((or _let_30 _let_32))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_132)) :args _let_132)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_130) _let_6))) (REFL :args ((not _let_32))) :args _let_54)) (REORDERING (CNF_EQUIV_POS2 :args _let_131) :args ((or _let_13 _let_130 _let_129))) _let_19 (CNF_AND_NEG :args (_let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_122) :args ((or _let_20 _let_127 _let_121))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_128)) :args _let_128)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_63))) (REFL :args ((not _let_69))) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_46 _let_45 _let_79 _let_74 _let_80 _let_78 (not _let_81)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_126 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false)) (not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false)) (not (= (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_125)) _let_124 :args (_let_81 false _let_107)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 1)) :args ((or _let_77 _let_100))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_101) :args ((or _let_90 (not _let_91) _let_99))) (MACRO_RESOLUTION_TRUST _let_123 _let_26 (REORDERING (CNF_AND_POS :args (_let_21 0)) :args ((or _let_20 _let_61))) _let_59 _let_57 (REORDERING (CNF_EQUIV_POS1 :args _let_122) :args ((or (not _let_20) _let_63 _let_121))) _let_65 (REORDERING (CNF_OR_POS :args (_let_98)) :args ((or _let_46 _let_45 _let_43 _let_77 (not _let_98)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_120) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) :args _let_120)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_109 1)) :args ((or _let_108 _let_114))) _let_113 :args (_let_108 false _let_109)) :args (_let_98 false _let_108)) _let_89 _let_88 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_119) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X _let_9) true))))) :args _let_119)) (REORDERING (CNF_AND_NEG :args (_let_90)) :args ((or _let_46 _let_79 _let_90))) _let_88 (REORDERING (CNF_OR_POS :args (_let_97)) :args ((or _let_91 _let_96 (not _let_97)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_104)) :args ((or _let_95 (not _let_103) (not _let_104)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_103)) :args ((or _let_46 (not _let_102) _let_103))) _let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_46 _let_102 (not _let_105)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_117)) :args _let_116)) _let_115 :args (_let_105 false _let_106)) :args (_let_102 false _let_40 false _let_105)) :args (_let_103 false _let_40 false _let_102)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_93)) :args _let_82)) _let_83 :args (_let_104 false _let_2)) :args (_let_95 false _let_103 false _let_104)) (REORDERING (CNF_EQUIV_POS2 :args _let_101) :args ((or _let_91 _let_100 _let_99))) _let_94 :args (_let_91 false _let_23 true _let_21 false _let_22 true _let_28 true _let_20 false _let_64 true _let_27 false _let_98 false _let_41 false _let_40 true _let_63 true _let_77 false _let_40 true _let_97 false _let_95 true _let_90 false _let_92)) _let_94 :args (_let_90 false _let_91 false _let_92)) :args (_let_77 false _let_90)) _let_89 _let_88 (CNF_AND_NEG :args (_let_75)) (REORDERING (CNF_AND_POS :args (_let_72 1)) :args ((or _let_70 _let_86))) (REORDERING (CNF_AND_POS :args (_let_72 0)) :args ((or _let_71 _let_86))) (REORDERING (CNF_EQUIV_POS2 :args (_let_76)) :args ((or _let_66 (not _let_75) (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_82)) _let_83 :args (_let_76 false _let_2)) (REORDERING (CNF_EQUIV_POS1 :args (_let_73)) :args ((or _let_68 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_82)) _let_83 :args (_let_73 false _let_2)) (CNF_OR_NEG :args (_let_69 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_69 0)) (CONG (REFL :args (_let_69)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_67))) :args _let_54)) :args ((or _let_67 _let_69))) :args (_let_69 false _let_81 false _let_77 false _let_41 false _let_40 true _let_74 false _let_70 false _let_71 true _let_75 false _let_76 false _let_72 false _let_73 true _let_66 false _let_67)) :args (_let_63 false _let_69)) _let_65 :args (_let_20 false _let_63 false _let_64)) (REORDERING (CNF_EQUIV_POS2 :args _let_62) :args ((or _let_22 _let_61 _let_60))) _let_26 _let_59 _let_57 :args (_let_22 false _let_47 false _let_41 false _let_40 true _let_37 false _let_33 false _let_34 true _let_38 false _let_39 false _let_35 false _let_36 true _let_29 false _let_30 true _let_32 true _let_6 false _let_14 true _let_13 false _let_20 true _let_21 false _let_23 false _let_27 true _let_28)))) (let ((_let_135 (not _let_12))) (let ((_let_136 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_137 (and _let_41 _let_136))) (let ((_let_138 (= _let_10 _let_137))) (let ((_let_139 (or _let_45 _let_136))) (let ((_let_140 (and _let_41 _let_27))) (let ((_let_141 (= _let_8 _let_140))) (let ((_let_142 (not _let_8))) (let ((_let_143 (not _let_140))) (let ((_let_144 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_144) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X _let_7) true))))) :args _let_144)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_8 _let_11 _let_135))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_141)) :args ((or _let_140 _let_142 (not _let_141)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_140 1)) :args ((or _let_27 _let_143))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_58) _let_57 _let_134 :args (_let_43 true _let_28 false _let_22)) :args (_let_143 true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_93)) :args _let_82)) _let_83 :args (_let_141 false _let_2)) :args (_let_142 true _let_140 false _let_141)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_138)) :args ((or _let_10 (not _let_137) (not _let_138)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_137)) :args ((or _let_45 (not _let_136) _let_137))) _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_45 _let_136 (not _let_139)))) _let_89 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_118 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_117)) :args _let_116)) _let_115 :args (_let_139 false _let_106)) :args (_let_136 false _let_41 false _let_139)) :args (_let_137 false _let_41 false _let_136)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_93)) :args _let_82)) _let_83 :args (_let_138 false _let_2)) :args (_let_10 false _let_137 false _let_138)) :args (_let_135 true _let_8 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_131) :args ((or (not _let_13) _let_6 _let_129))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_13 _let_61))) (MACRO_RESOLUTION_TRUST _let_123 _let_134 _let_26 :args (_let_21 false _let_22 false _let_23)) :args (_let_13 false _let_21)) _let_19 :args (_let_6 false _let_13 false _let_14)) :args (false true _let_12 false _let_6)) :args (_let_5 _let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))) (forall ((A $$unsorted) (E $$unsorted)) (= (tptp.partition A E) (and (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X E))) (forall ((X $$unsorted)) (=> (tptp.member X E) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X A) (tptp.member Y A)) (=> (exists ((Z $$unsorted)) (and (tptp.member Z X) (tptp.member Z Y))) (= X Y))))))) _let_3 _let_2 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.pre_order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.59 )
% 0.23/0.59 % SZS output end Proof for SET768+4
% 0.23/0.59 % cvc5---1.0.5 exiting
% 0.23/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------