%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET358+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 14:38:37 EDT 2023

% Result   : Theorem 0.21s 0.55s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET358+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.34  % Computer : n029.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Sat Aug 26 10:13:55 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.gIazwNfXKT/cvc5---1.0.5_1275.p...
% 0.21/0.55  ------- get file name : TPTP file name is SET358+4
% 0.21/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1275.smt2...
% 0.21/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.55  % SZS status Theorem for SET358+4
% 0.21/0.55  % SZS output start Proof for SET358+4
% 0.21/0.55  (
% 0.21/0.55  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.equal_set (tptp.union (tptp.sum A) (tptp.sum B)) (tptp.sum (tptp.union A B)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (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 $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Y)))))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_9))) (let ((_let_13 (not _let_7))) (let ((_let_14 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_14))) (let ((_let_16 (= _let_15 _let_13))) (let ((_let_17 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.member X Y))))))))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (_let_17))) (let ((_let_20 ((tptp.member X (tptp.sum A))))) (let ((_let_21 (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21))) (let ((_let_23 (or _let_15 _let_22))) (let ((_let_24 (tptp.union _let_14 _let_21))) (let ((_let_25 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_24))) (let ((_let_26 (= _let_25 _let_23))) (let ((_let_27 (not _let_23))) (let ((_let_28 (_let_4))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 ((tptp.member X (tptp.union A B))))) (let ((_let_31 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (tptp.sum _let_31))) (let ((_let_33 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_32))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_25))) (let ((_let_36 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.sum (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.union (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (tptp.subset _let_32 _let_24))) (let ((_let_39 (= _let_38 _let_36))) (let ((_let_40 (not _let_36))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((tptp.subset A B)))) (let ((_let_45 (tptp.subset _let_24 _let_32))) (let ((_let_46 (and _let_45 _let_38))) (let ((_let_47 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.sum SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.sum (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_48 (= _let_45 _let_47))) (let ((_let_49 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_32))) (let ((_let_50 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_24))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_21))) (let ((_let_54 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14))) (let ((_let_55 (or _let_54 _let_53))) (let ((_let_56 (= _let_50 _let_55))) (let ((_let_57 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)))))) (let ((_let_58 (not _let_57))) (let ((_let_59 (= _let_49 _let_58))) (let ((_let_60 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9))) (let ((_let_61 (not _let_60))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_31))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_61))) (let ((_let_65 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_31))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_66))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_61))) (let ((_let_73 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)))))) (let ((_let_74 (not _let_73))) (let ((_let_75 (= _let_54 _let_74))) (let ((_let_76 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)))))) (let ((_let_77 (not _let_76))) (let ((_let_78 (= _let_53 _let_77))) (let ((_let_79 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_80 _let_66))) (let ((_let_82 (or (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_79))) (let ((_let_83 (= _let_67 _let_82))) (let ((_let_84 (or))) (let ((_let_85 (not _let_59))) (let ((_let_86 (_let_57))) (let ((_let_87 ((not (= (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y) false))))) (let ((_let_88 (ASSUME :args _let_86))) (let ((_let_89 (or _let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_90 (= _let_62 _let_89))) (let ((_let_91 (not _let_64))) (let ((_let_92 (REFL :args (_let_72)))) (let ((_let_93 (_let_74))) (let ((_let_94 (_let_77))) (let ((_let_95 (REFL :args (_let_81)))) (let ((_let_96 (not _let_47))) (let ((_let_97 (_let_96))) (let ((_let_98 (tptp.equal_set _let_24 _let_32))) (let ((_let_99 (= _let_98 _let_46))) (let ((_let_100 (not _let_46))) (let ((_let_101 (_let_5))) (let ((_let_102 (ASSUME :args _let_101))) (let ((_let_103 (not _let_98))) (let ((_let_104 (_let_2))) (let ((_let_105 (ASSUME :args _let_104))) (let ((_let_106 (_let_40))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_106)) :args _let_106)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_36))) (REFL :args (_let_37)) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_39)) :args ((or _let_38 _let_40 (not _let_39)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_99)) :args ((or _let_98 _let_100 (not _let_99)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_105) :args _let_104)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_103)) :args _let_84)) _let_105 :args (_let_103 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (_let_24 _let_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_101)) _let_102 :args (_let_99 false _let_5)) :args (_let_100 true _let_98 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_48)) :args ((or _let_45 _let_96 (not _let_48)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_96) _let_47))) (REFL :args ((not _let_52))) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_83)) :args ((or _let_67 (not _let_82) (not _let_83)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_28)) _let_29 :args (_let_83 false _let_4)) (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_66 _let_68 (not _let_69)))) (REORDERING (CNF_OR_NEG :args (_let_82 1)) :args ((or _let_80 _let_82))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 1)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_65))) :args _let_84)) :args ((or _let_65 _let_81))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_81 0)) (CONG _let_95 (MACRO_SR_PRED_INTRO :args ((= (not _let_80) _let_79))) :args _let_84)) :args ((or _let_79 _let_81))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) (REFL :args ((not _let_81))) :args _let_84)) (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or (not _let_53) _let_77 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_78 false _let_17)) (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_54 _let_53 (not _let_55)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_75)) :args ((or (not _let_54) _let_74 (not _let_75)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_75 false _let_17)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_93)) :args _let_93)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_73))) (REFL :args ((not _let_72))) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_90)) :args ((or _let_62 (not _let_89) (not _let_90)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_28)) _let_29 :args (_let_90 false _let_4)) (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_61 _let_63 _let_91))) (REORDERING (CNF_OR_NEG :args (_let_89 0)) :args ((or _let_71 _let_89))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_84)) :args ((or _let_60 _let_72))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_92 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_84)) :args ((or _let_70 _let_72))) :args ((or _let_72 _let_91) false _let_90 true _let_62 false _let_89 false _let_60 false _let_70)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_87)) :args _let_86)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_87)) :args _let_86)) (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_59)) (CONG (REFL :args (_let_85)) (REFL :args (_let_49)) (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_84)) :args ((or _let_49 _let_57 _let_85))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_31 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_59 false _let_17)) (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or _let_51 _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14 _let_21 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_28)) _let_29 :args (_let_56 false _let_4)) (CNF_OR_NEG :args (_let_52 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_50))) :args _let_84)) :args ((or _let_50 _let_52))) :args (_let_52 false _let_83 true _let_67 false _let_82 false _let_65 false _let_79 true _let_81 true _let_76 false _let_78 false _let_53 true _let_54 false _let_75 false _let_73 false _let_72 false _let_69 false _let_64 false _let_57 false _let_59 false _let_55 false _let_56 true _let_49 false _let_50)) :args (_let_47 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_24 _let_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_48 false _let_41)) :args (_let_45 false _let_47 false _let_48)) :args ((not _let_38) true _let_46 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_32 _let_24 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_39 false _let_41)) :args (_let_40 true _let_38 false _let_39)) :args (_let_37 true _let_36)))) (let ((_let_108 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_26)) :args ((or _let_25 _let_27 (not _let_26)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 1)) _let_107 :args ((not _let_25) true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_14 _let_21 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_28)) _let_29 :args (_let_26 false _let_4)) :args (_let_27 true _let_25 false _let_26)))) (let ((_let_109 (not _let_16))) (let ((_let_110 (not _let_12))) (let ((_let_111 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_112 (or _let_10 _let_111))) (let ((_let_113 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_31))) (let ((_let_114 (= _let_113 _let_112))) (let ((_let_115 (not _let_113))) (let ((_let_116 (or _let_115 _let_9))) (let ((_let_117 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Y)))))) (let ((_let_118 (not _let_116))) (let ((_let_119 (not _let_117))) (let ((_let_120 (= _let_33 _let_119))) (let ((_let_121 (_let_119))) (let ((_let_122 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_121)) :args _let_121)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_119) _let_117))) (REFL :args (_let_118)) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_120)) :args ((or _let_34 _let_119 (not _let_120)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_84)) :args ((or _let_33 _let_35))) _let_107 :args (_let_33 true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_31 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_120 false _let_17)) :args (_let_119 false _let_33 false _let_120)) :args (_let_118 true _let_117)))) (let ((_let_123 (REFL :args (_let_116)))) (let ((_let_124 (not _let_111))) (let ((_let_125 (or _let_124 _let_9))) (let ((_let_126 (forall ((Y $$unsorted)) (or (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 Y)))))) (let ((_let_127 (not _let_126))) (let ((_let_128 (= _let_22 _let_127))) (let ((_let_129 (not _let_128))) (let ((_let_130 (_let_126))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_116 1)) (CONG _let_123 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_84)) :args ((or _let_8 _let_116))) _let_122 :args (_let_8 true _let_116)))) (let ((_let_132 (_let_7))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_132) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_132)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_9 _let_11 _let_110))) _let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_112)) :args ((or _let_10 _let_111 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_9 _let_124 (not _let_125)))) _let_131 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_130) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_130)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_128)) (CONG (REFL :args (_let_129)) (REFL :args (_let_22)) (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_126))) :args _let_84)) :args ((or _let_22 _let_126 _let_129))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 1)) _let_108 :args ((not _let_22) true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_128 false _let_17)) :args (_let_126 true _let_22 false _let_128)) :args (_let_125 false _let_126)) :args (_let_124 false _let_8 false _let_125)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_114)) :args ((or _let_115 _let_112 (not _let_114)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_116 0)) (CONG _let_123 (MACRO_SR_PRED_INTRO :args ((= (not _let_115) _let_113))) :args _let_84)) :args ((or _let_113 _let_116))) _let_122 :args (_let_113 true _let_116)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_30)) :args _let_28)) _let_29 :args (_let_114 false _let_4)) :args (_let_112 false _let_113 false _let_114)) :args (_let_10 true _let_111 false _let_112)) :args (_let_110 false _let_8 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_16)) (CONG (REFL :args (_let_109)) (REFL :args (_let_15)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_7))) :args _let_84)) :args ((or _let_15 _let_7 _let_109))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 0)) _let_108 :args ((not _let_15) true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_18 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_19)) _let_18 :args (_let_16 false _let_17)) :args (_let_7 true _let_15 false _let_16)) :args (false true _let_12 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)))) _let_4 (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 $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) _let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for SET358+4
% 0.21/0.55  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------