%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n029.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 14:40:16 EDT 2023

% Result   : Theorem 0.24s 0.58s
% Output   : Proof 0.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16  % Problem    : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.16  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n029.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Sat Aug 26 13:55:40 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.24/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.58  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.XTfK63Wkn4/cvc5---1.0.5_18289.p...
% 0.24/0.58  ------- get file name : TPTP file name is SET770+4
% 0.24/0.58  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_18289.smt2...
% 0.24/0.58  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.24/0.58  % SZS status Theorem for SET770+4
% 0.24/0.58  % SZS output start Proof for SET770+4
% 0.24/0.58  (
% 0.24/0.58  (let ((_let_1 (not (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.equivalence_class B E R))) (let ((_let_2 (tptp.equivalence_class A E R))) (=> (and (tptp.equivalence R E) (tptp.member A E) (tptp.member B E)) (or (tptp.equal_set _let_2 _let_1) (tptp.disjoint _let_2 _let_1))))))))) (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.disjoint A B) (not (exists ((X $$unsorted)) (and (tptp.member X A) (tptp.member X B)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z))))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_9 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_12 (not _let_11))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (not _let_15))) (let ((_let_17 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (not _let_17))) (let ((_let_19 (or _let_18 _let_16 _let_14 _let_12 _let_10 _let_8))) (let ((_let_20 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 Y X))))) (let ((_let_21 (and (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X X))) _let_20 _let_7))) (let ((_let_22 (tptp.equivalence SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (= _let_22 _let_21))) (let ((_let_24 (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_25 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_26 (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_27 (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (tptp.disjoint _let_27 _let_26))) (let ((_let_29 (tptp.equal_set _let_27 _let_26))) (let ((_let_30 (not _let_22))) (let ((_let_31 (or _let_30 _let_16 _let_18 _let_29 _let_28))) (let ((_let_32 (forall ((E $$unsorted) (R $$unsorted) (A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.equivalence_class B E R))) (let ((_let_2 (tptp.equivalence_class A E R))) (or (not (tptp.equivalence R E)) (not (tptp.member A E)) (not (tptp.member B E)) (tptp.equal_set _let_2 _let_1) (tptp.disjoint _let_2 _let_1))))))) (let ((_let_33 (not _let_31))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (or))) (let ((_let_36 (not _let_32))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_34) :args (_let_36))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_32))) (REFL :args (_let_33)) :args _let_35)) _let_34 :args (_let_33 true _let_32)))) (let ((_let_38 (REFL :args (_let_31)))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_23)) :args ((or _let_30 _let_21 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 0)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_22))) :args _let_35)) :args ((or _let_22 _let_31))) _let_37 :args (_let_22 true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equivalence R A)))) :args (_let_24))) _let_25 :args (_let_23 false _let_24)) :args (_let_21 false _let_22 false _let_23)))) (let ((_let_40 (not _let_21))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 2)) :args ((or _let_7 _let_40))) _let_39 :args (_let_7 false _let_21)))) (let ((_let_42 (not _let_19))) (let ((_let_43 (and _let_13 _let_9))) (let ((_let_44 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_27))) (let ((_let_45 (= _let_44 _let_43))) (let ((_let_46 (_let_2))) (let ((_let_47 (ASSUME :args _let_46))) (let ((_let_48 ((tptp.member X (tptp.equivalence_class A E R))))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_26))) (let ((_let_50 (not _let_44))) (let ((_let_51 (or _let_50 _let_49))) (let ((_let_52 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_53 (not _let_51))) (let ((_let_54 (tptp.subset _let_27 _let_26))) (let ((_let_55 (= _let_54 _let_52))) (let ((_let_56 (not _let_52))) (let ((_let_57 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_57))) (let ((_let_60 ((tptp.subset A B)))) (let ((_let_61 (tptp.subset _let_26 _let_27))) (let ((_let_62 (and _let_54 _let_61))) (let ((_let_63 (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_64 (= _let_61 _let_63))) (let ((_let_65 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_27))) (let ((_let_66 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_26))) (let ((_let_67 (not _let_66))) (let ((_let_68 (or _let_67 _let_65))) (let ((_let_69 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (and _let_70 _let_69))) (let ((_let_72 (= _let_66 _let_71))) (let ((_let_73 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_74 (and _let_70 _let_73))) (let ((_let_75 (= _let_65 _let_74))) (let ((_let_76 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_77 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_78 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_79 (not _let_69))) (let ((_let_80 (not _let_77))) (let ((_let_81 (not _let_70))) (let ((_let_82 (not _let_76))) (let ((_let_83 (or _let_82 _let_18 _let_81 _let_80 _let_79 _let_78))) (let ((_let_84 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_85 (not _let_78))) (let ((_let_86 (not _let_84))) (let ((_let_87 (or _let_16 _let_82 _let_81 _let_86 _let_85 _let_73))) (let ((_let_88 (not _let_71))) (let ((_let_89 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 2)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_17))) :args _let_35)) :args ((or _let_17 _let_31))) _let_37 :args (_let_17 true _let_31)))) (let ((_let_90 (and _let_76 _let_84))) (let ((_let_91 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_27))) (let ((_let_92 (= _let_91 _let_90))) (let ((_let_93 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_26))) (let ((_let_94 (not _let_93))) (let ((_let_95 (not _let_91))) (let ((_let_96 (or _let_95 _let_94))) (let ((_let_97 (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))) (not (tptp.member X (tptp.equivalence_class SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_98 (not _let_96))) (let ((_let_99 (= _let_28 _let_97))) (let ((_let_100 (not _let_97))) (let ((_let_101 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (not (tptp.member X B)))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_100))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_103)) :args _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_100) _let_97))) (REFL :args (_let_98)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_99)) :args ((or _let_28 _let_100 (not _let_99)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 4)) _let_37 :args ((not _let_28) true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (_let_27 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.disjoint A B)))) :args (_let_101))) _let_102 :args (_let_99 false _let_101)) :args (_let_100 true _let_28 false _let_99)) :args (_let_98 true _let_97)))) (let ((_let_105 (REFL :args (_let_96)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_92)) :args ((or _let_95 _let_90 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_95) _let_91))) :args _let_35)) :args ((or _let_91 _let_96))) _let_104 :args (_let_91 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :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_48)) :args _let_46)) _let_47 :args (_let_92 false _let_2)) :args (_let_90 false _let_91 false _let_92)))) (let ((_let_107 (not _let_90))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 0)) :args ((or _let_76 _let_107))) _let_106 :args (_let_76 false _let_90)))) (let ((_let_109 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_110 (not _let_109))) (let ((_let_111 (or _let_18 _let_82 _let_110 _let_77))) (let ((_let_112 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_20 _let_40))) _let_39 :args (_let_20 false _let_21)))) (let ((_let_113 (_let_20))) (let ((_let_114 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) (let ((_let_115 (ASSUME :args _let_113))) (let ((_let_116 (and _let_76 _let_109))) (let ((_let_117 (= _let_93 _let_116))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_111)) :args ((or _let_18 _let_82 _let_110 _let_77 (not _let_111)))) _let_89 _let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_116 1)) :args ((or _let_109 (not _let_116)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_117)) :args ((or _let_94 _let_116 (not _let_117)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_96 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_93))) :args _let_35)) :args ((or _let_93 _let_96))) _let_104 :args (_let_93 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :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_48)) :args _let_46)) _let_47 :args (_let_117 false _let_2)) :args (_let_116 false _let_93 false _let_117)) :args (_let_109 false _let_116)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113)) _let_112 :args (_let_111 false _let_20)) :args (_let_77 false _let_17 false _let_76 false _let_109 false _let_111)))) (let ((_let_119 (_let_7))) (let ((_let_120 ((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))))) (let ((_let_121 (ASSUME :args _let_119))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_31 1)) (CONG _let_38 (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_15))) :args _let_35)) :args ((or _let_15 _let_31))) _let_37 :args (_let_15 true _let_31)))) (let ((_let_123 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_90 1)) :args ((or _let_84 _let_107))) _let_106 :args (_let_84 false _let_90)))) (let ((_let_124 ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Z) true)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 X Y) false))))) (let ((_let_125 (not _let_63))) (let ((_let_126 (_let_125))) (let ((_let_127 (= _let_29 _let_62))) (let ((_let_128 (not _let_62))) (let ((_let_129 (_let_5))) (let ((_let_130 (ASSUME :args _let_129))) (let ((_let_131 (_let_56))) (let ((_let_132 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_131)) :args _let_131)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_52))) (REFL :args (_let_53)) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_55)) :args ((or _let_54 _let_56 (not _let_55)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_127)) :args ((or _let_29 _let_128 (not _let_127)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_31 3)) _let_37 :args ((not _let_29) true _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_130 :args (_let_27 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_129)) _let_130 :args (_let_127 false _let_5)) :args (_let_128 true _let_29 false _let_127)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_64)) :args ((or _let_61 _let_125 (not _let_64)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_126)) :args _let_126)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_125) _let_63))) (REFL :args ((not _let_68))) :args _let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_16 _let_82 _let_86 _let_73 _let_81 _let_85 (not _let_87)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_124)) :args _let_119)) _let_41 :args (_let_87 false _let_7)) _let_123 _let_108 _let_122 (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_18 _let_82 _let_81 _let_79 _let_80 _let_78 (not _let_83)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_119)) _let_41 :args (_let_83 false _let_7)) _let_118 _let_108 _let_89 (CNF_AND_NEG :args (_let_74)) (REORDERING (CNF_AND_POS :args (_let_71 1)) :args ((or _let_69 _let_88))) (REORDERING (CNF_AND_POS :args (_let_71 0)) :args ((or _let_70 _let_88))) (REORDERING (CNF_EQUIV_POS2 :args (_let_75)) :args ((or _let_65 (not _let_74) (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_48)) :args _let_46)) _let_47 :args (_let_75 false _let_2)) (REORDERING (CNF_EQUIV_POS1 :args (_let_72)) :args ((or _let_67 _let_71 (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_48)) :args _let_46)) _let_47 :args (_let_72 false _let_2)) (CNF_OR_NEG :args (_let_68 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_68 0)) (CONG (REFL :args (_let_68)) (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_35)) :args ((or _let_66 _let_68))) :args (_let_68 false _let_87 false _let_84 false _let_76 false _let_15 false _let_78 false _let_83 false _let_77 false _let_76 false _let_17 true _let_73 false _let_69 false _let_70 true _let_74 false _let_75 false _let_71 false _let_72 true _let_65 false _let_66)) :args (_let_63 false _let_68)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_26 _let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_64 false _let_57)) :args (_let_61 false _let_63 false _let_64)) :args ((not _let_54) true _let_62 false _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (_let_27 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_60)) :args _let_59)) _let_58 :args (_let_55 false _let_57)) :args (_let_56 true _let_54 false _let_55)) :args (_let_53 true _let_52)))) (let ((_let_133 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_50 _let_43 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_51 0)) (CONG (REFL :args (_let_51)) (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_44))) :args _let_35)) :args ((or _let_44 _let_51))) _let_132 :args (_let_44 true _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :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_48)) :args _let_46)) _let_47 :args (_let_45 false _let_2)) :args (_let_43 false _let_44 false _let_45)))) (let ((_let_134 (not _let_43))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_43 0)) :args ((or _let_13 _let_134))) _let_133 :args (_let_13 false _let_43)))) (let ((_let_136 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_16 _let_18 _let_137 _let_11))) (let ((_let_139 (or _let_16 _let_82 _let_18 _let_86 _let_80 _let_136))) (let ((_let_140 (and _let_13 _let_8))) (let ((_let_141 (= _let_49 _let_140))) (let ((_let_142 (not _let_140))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING _let_124)) :args _let_119)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_19)) :args ((or _let_16 _let_18 _let_8 _let_12 _let_14 _let_10 _let_42))) _let_122 _let_89 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_140)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_141)) :args ((or _let_49 _let_142 (not _let_141)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_51 1)) _let_132 :args ((not _let_49) true _let_51)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :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_48)) :args _let_46)) _let_47 :args (_let_141 false _let_2)) :args (_let_142 true _let_49 false _let_141)) _let_135 :args ((not _let_8) true _let_140 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_138)) :args ((or _let_16 _let_18 _let_137 _let_11 (not _let_138)))) _let_122 _let_89 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_16 _let_18 _let_82 _let_86 _let_136 _let_80 (not _let_139)))) _let_122 _let_89 _let_108 _let_123 _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_120)) :args _let_119)) _let_41 :args (_let_139 false _let_7)) :args (_let_136 false _let_15 false _let_17 false _let_76 false _let_84 false _let_77 false _let_139)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_115 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_114)) :args _let_113)) _let_112 :args (_let_138 false _let_20)) :args (_let_11 false _let_15 false _let_17 false _let_136 false _let_138)) _let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_43 1)) :args ((or _let_9 _let_134))) _let_133 :args (_let_9 false _let_43)) :args (_let_42 false _let_15 false _let_17 true _let_8 false _let_11 false _let_13 false _let_9)) _let_41 :args (false true _let_19 false _let_7)) :args (_let_6 _let_5 (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))))) _let_4 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.24/0.59  )
% 0.24/0.59  % SZS output end Proof for SET770+4
% 0.24/0.59  % cvc5---1.0.5 exiting
% 0.24/0.59  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------