%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n005.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 16:29:28 EDT 2023

% Result   : Theorem 25.71s 26.47s
% Output   : Proof 25.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU135+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n005.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   : Wed Aug 23 19:28:24 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 25.71/26.47  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VhFKZMHFlL/cvc5---1.0.5_14813.p...
% 25.71/26.47  ------- get file name : TPTP file name is SEU135+2
% 25.71/26.47  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_14813.smt2...
% 25.71/26.47  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.71/26.47  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.71/26.47  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.71/26.47  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.71/26.47  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.71/26.47  % SZS status Theorem for SEU135+2
% 25.71/26.47  % SZS output start Proof for SEU135+2
% 25.71/26.47  (
% 25.71/26.47  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))) (let ((_let_3 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))))) (let ((_let_5 (not _let_4))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_12 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (tptp.set_union2 _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_14 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12))) (let ((_let_15 (= _let_14 _let_13))) (let ((_let_16 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 _let_14))) (let ((_let_17 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 _let_13))) (let ((_let_18 (_let_11))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 ((tptp.set_union2 A B)))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_18)) _let_19 :args (_let_15 false _let_11)))) (let ((_let_22 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_16))) (let ((_let_25 (not _let_16))) (let ((_let_26 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.in C (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_27 (not _let_24))) (let ((_let_28 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14))) (let ((_let_29 (= _let_28 _let_26))) (let ((_let_30 (not _let_26))) (let ((_let_31 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_31))) (let ((_let_34 ((tptp.subset A B)))) (let ((_let_35 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_36 (tptp.subset _let_35 _let_14))) (let ((_let_37 (not _let_28))) (let ((_let_38 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_36))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 (tptp.set_difference _let_13 tptp.empty_set))) (let ((_let_45 (tptp.set_difference _let_35 tptp.empty_set))) (let ((_let_46 (tptp.subset _let_45 _let_44))) (let ((_let_47 (= _let_13 _let_44))) (let ((_let_48 (= _let_35 _let_45))) (let ((_let_49 (not _let_36))) (let ((_let_50 (tptp.subset _let_44 _let_45))) (let ((_let_51 (and _let_50 _let_46))) (let ((_let_52 (not _let_46))) (let ((_let_53 (= _let_45 _let_44))) (let ((_let_54 (= _let_51 _let_53))) (let ((_let_55 (not _let_51))) (let ((_let_56 (_let_10))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (= _let_14 _let_35))) (let ((_let_59 (not _let_53))) (let ((_let_60 (forall ((A $$unsorted)) (= A (tptp.set_difference A tptp.empty_set))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_13 QUANTIFIERS_INST_CBQI_PROP)) :args _let_62)) _let_61 :args (_let_47 false _let_60)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_35 QUANTIFIERS_INST_CBQI_PROP)) :args _let_62)) _let_61 :args (_let_48 false _let_60)))) (let ((_let_65 (not _let_58))) (let ((_let_66 (_let_5))) (let ((_let_67 (ASSUME :args _let_66))) (let ((_let_68 (or))) (let ((_let_69 (_let_65))) (let ((_let_70 (not _let_47))) (let ((_let_71 (REFL :args (_let_70)))) (let ((_let_72 (not _let_48))) (let ((_let_73 (REFL :args (_let_72)))) (let ((_let_74 (not _let_15))) (let ((_let_75 (REFL :args (_let_74)))) (let ((_let_76 (and _let_65 _let_15 _let_48 _let_47))) (let ((_let_77 (ASSUME :args _let_69))) (let ((_let_78 (ASSUME :args (_let_48)))) (let ((_let_79 (SYMM (SYMM _let_78)))) (let ((_let_80 (SYMM _let_79))) (let ((_let_81 (ASSUME :args (_let_15)))) (let ((_let_82 (SYMM (SYMM _let_81)))) (let ((_let_83 (ASSUME :args (_let_47)))) (let ((_let_84 (SYMM (SYMM _let_83)))) (let ((_let_85 (TRANS (SYMM _let_84) (SYMM _let_82)))) (let ((_let_86 (tptp.subset _let_14 _let_35))) (let ((_let_87 (tptp.subset _let_12 _let_35))) (let ((_let_88 (not _let_87))) (let ((_let_89 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_35))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_90 _let_88 _let_86))) (let ((_let_92 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_93 (tptp.subset _let_12 _let_92))) (let ((_let_94 (= _let_35 _let_92))) (let ((_let_95 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_92))) (let ((_let_96 (not _let_95))) (let ((_let_97 (tptp.subset _let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_98 (not _let_97))) (let ((_let_99 (or _let_98 _let_96 _let_93))) (let ((_let_100 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_102 (_let_2))) (let ((_let_103 (ASSUME :args _let_102))) (let ((_let_104 ((tptp.set_union2 A B)))) (let ((_let_105 (_let_6))) (let ((_let_106 (ASSUME :args _let_105))) (let ((_let_107 (and _let_94 _let_93))) (let ((_let_108 (ASSUME :args (_let_93)))) (let ((_let_109 (APPLY_UF tptp.subset))) (let ((_let_110 (ASSUME :args (_let_94)))) (let ((_let_111 (and _let_15 _let_48 _let_47 _let_86))) (let ((_let_112 (ASSUME :args (_let_86)))) (let ((_let_113 (and _let_15 _let_48 _let_47 _let_52))) (let ((_let_114 (ASSUME :args (_let_52)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_102)) _let_103 :args (_let_38 false _let_2)))) (let ((_let_116 (_let_30))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_116)) :args _let_116)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_29)) :args ((or _let_28 _let_30 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 _let_36 (not _let_40)))) _let_115 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_113)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_114 _let_78 _let_83 _let_81) (SCOPE (FALSE_ELIM (TRANS (CONG _let_79 (TRANS _let_82 _let_84) :args _let_109) (FALSE_INTRO _let_114))) :args (_let_52 _let_48 _let_47 _let_15))) :args (_let_15 _let_48 _let_47 _let_52))) :args (true _let_113)) (CONG _let_75 _let_73 _let_71 (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_46))) (REFL :args (_let_49)) :args _let_68)) _let_21 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_51)) :args ((or _let_52 (not _let_50) _let_51))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_111)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_112 _let_81 _let_83 _let_78) (SCOPE (TRUE_ELIM (TRANS (CONG _let_85 _let_80 :args _let_109) (TRUE_INTRO _let_112))) :args (_let_86 _let_15 _let_47 _let_48))) :args (_let_15 _let_48 _let_47 _let_86))) :args (true _let_111)) :args ((or _let_74 _let_72 _let_70 _let_50 (not _let_86)))) _let_21 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_90 _let_88 _let_86 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_102)) _let_103 :args (_let_89 false _let_2)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_107)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_108 _let_110) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_12)) (SYMM (SYMM _let_110)) :args _let_109) (TRUE_INTRO _let_108))) :args (_let_93 _let_94))) :args (_let_94 _let_93))) :args (true _let_107)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_20)) :args _let_18)) _let_19 :args (_let_94 false _let_11)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_98 _let_96 _let_93 (not _let_99)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_105)) _let_106 :args (_let_97 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_102)) _let_103 :args (_let_95 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_92 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subset A B) false)) (not (= (tptp.subset B C) false))))) :args (_let_100))) _let_101 :args (_let_99 false _let_100)) :args (_let_93 false _let_97 false _let_95 false _let_99)) :args (_let_87 false _let_94 false _let_93)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_35 _let_12 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_43)) _let_42 :args (_let_91 false _let_41)) :args (_let_86 false _let_89 false _let_87 false _let_91)) :args (_let_50 false _let_15 false _let_48 false _let_47 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_54)) :args ((or _let_53 _let_55 (not _let_54)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_81 _let_83 _let_77 _let_78) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG _let_85 _let_80 :args (=)) (FALSE_INTRO _let_77)) :args ((= _let_53 false)))) :args (_let_15 _let_47 _let_65 _let_48))) :args (_let_65 _let_15 _let_48 _let_47))) :args (true _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_58))) _let_75 _let_73 _let_71 (REFL :args (_let_59)) :args _let_68)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_67) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_5) _let_4))) (REFL :args _let_69) :args _let_68)) _let_67 :args (_let_65 true _let_4)) _let_21 _let_64 _let_63 :args (_let_59 true _let_58 false _let_15 false _let_48 false _let_47)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_57 :args (_let_44 _let_45 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_56))) _let_57 :args (_let_54 false _let_10)) :args (_let_55 true _let_53 false _let_54)) :args (_let_52 false _let_50 true _let_51)) :args (_let_49 false _let_15 false _let_48 false _let_47 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_37 false _let_38 true _let_36 false _let_40)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33)) _let_32 :args (_let_29 false _let_31)) :args (_let_30 true _let_28 false _let_29)) :args (_let_27 true _let_26)))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 1)) _let_117 :args (_let_25 true _let_24)))) (let ((_let_119 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 _let_12))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_17))) (let ((_let_122 (forall ((C $$unsorted)) (let ((_let_1 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (or (not (tptp.in C _let_1)) (tptp.in C (tptp.set_union2 _let_1 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_123 (tptp.subset _let_12 _let_13))) (let ((_let_124 (= _let_123 _let_122))) (let ((_let_125 (_let_122))) (let ((_let_126 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_127 (not _let_126))) (let ((_let_128 (and _let_22 _let_127))) (let ((_let_129 (= _let_119 _let_128))) (let ((_let_130 (forall ((D $$unsorted)) (= (tptp.in D (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_131 (_let_8))) (let ((_let_132 (ASSUME :args _let_131))) (let ((_let_133 (_let_130))) (let ((_let_134 (or _let_127 _let_16))) (let ((_let_135 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.in C (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_136 (= _let_38 _let_135))) (let ((_let_137 (_let_135))) (let ((_let_138 (_let_128))) (let ((_let_139 (ASSUME :args (_let_17)))) (let ((_let_140 (ASSUME :args (_let_25)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_139 _let_81 _let_140) :args (_let_15 _let_25 _let_17)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_140)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50)) _let_82 :args (APPLY_UF tptp.in)) (TRUE_INTRO _let_139))) :args (_let_17 _let_15 _let_25)) :args ((not (and _let_15 _let_25 _let_17)) SB_LITERAL))) (CONG _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_16))) (REFL :args ((not _let_17))) :args _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_121)) :args ((or _let_17 _let_120 (not _let_121)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_129)) :args ((or _let_119 (not _let_128) (not _let_129)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_138) (CONG (REFL :args _let_138) (REFL :args (_let_23)) (MACRO_SR_PRED_INTRO :args ((= (not _let_127) _let_126))) :args _let_68)) :args ((or _let_23 _let_126 _let_128))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_68)) :args ((or _let_22 _let_24))) _let_117 :args (_let_22 true _let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_134)) :args ((or _let_16 _let_127 (not _let_134)))) _let_118 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_137) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C _let_14) true))))) :args _let_137)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_136)) :args ((or _let_39 _let_135 (not _let_136)))) _let_115 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33)) _let_32 :args (_let_136 false _let_31)) :args (_let_135 false _let_38 false _let_136)) :args (_let_134 false _let_135)) :args (_let_127 true _let_16 false _let_134)) :args (_let_128 false _let_22 true _let_126)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_133) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) :args _let_133)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_132 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_12 QUANTIFIERS_INST_CBQI_PROP)) :args _let_131))) _let_132 :args (_let_130 false _let_8)) :args (_let_129 false _let_130)) :args (_let_119 false _let_128 false _let_129)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_125) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_50 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C _let_13) true))))) :args _let_125)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_124)) :args ((or (not _let_123) _let_122 (not _let_124)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_102)) _let_103 :args (_let_123 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (_let_12 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33)) _let_32 :args (_let_124 false _let_31)) :args (_let_122 false _let_123 false _let_124)) :args (_let_121 false _let_122)) :args (_let_17 false _let_119 false _let_121)) _let_118 _let_21 :args (false false _let_17 true _let_16 false _let_15)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_10 (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) _let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) _let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) true true true true (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) _let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) _let_5 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.71/26.48  )
% 25.71/26.48  % SZS output end Proof for SEU135+2
% 25.71/26.48  % cvc5---1.0.5 exiting
% 25.71/26.48  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------