%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.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 16:29:29 EDT 2023

% Result   : Theorem 26.71s 27.04s
% Output   : Proof 26.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n017.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Wed Aug 23 18:55:24 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 26.71/27.04  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.AHcb6V6c7w/cvc5---1.0.5_21542.p...
% 26.71/27.04  ------- get file name : TPTP file name is SEU138+2
% 26.71/27.04  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21542.smt2...
% 26.71/27.04  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.71/27.04  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.71/27.04  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.71/27.04  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.71/27.04  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.71/27.04  % SZS status Theorem for SEU138+2
% 26.71/27.04  % SZS output start Proof for SEU138+2
% 26.71/27.04  (
% 26.71/27.04  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))) (let ((_let_14 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))))) (let ((_let_15 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))))) (let ((_let_16 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_17 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_20 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 _let_20))) (let ((_let_22 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_25 (and _let_24 _let_23))) (let ((_let_26 (= _let_21 _let_25))) (let ((_let_27 (not _let_21))) (let ((_let_28 (and _let_24 _let_27))) (let ((_let_29 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_30 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_24))) (let ((_let_33 (forall ((C $$unsorted)) (or (not (tptp.in C (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_34 (tptp.subset _let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_35 (= _let_34 _let_33))) (let ((_let_36 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 ((tptp.subset A B)))) (let ((_let_40 (_let_12))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (_let_33))) (let ((_let_43 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20))) (let ((_let_44 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 _let_43))) (let ((_let_45 (or _let_31 _let_44))) (let ((_let_46 (forall ((C $$unsorted)) (or (not (tptp.in C (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.in C (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_47 (not _let_45))) (let ((_let_48 (tptp.subset _let_29 _let_43))) (let ((_let_49 (= _let_48 _let_46))) (let ((_let_50 (not _let_46))) (let ((_let_51 (= tptp.empty_set (tptp.set_difference _let_29 _let_43)))) (let ((_let_52 (= _let_48 _let_51))) (let ((_let_53 (not _let_48))) (let ((_let_54 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (_let_54))) (let ((_let_57 ((tptp.subset A B)))) (let ((_let_58 (= _let_43 _let_29))) (let ((_let_59 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_60 (= _let_29 _let_59))) (let ((_let_61 (tptp.set_difference _let_43 _let_43))) (let ((_let_62 (= tptp.empty_set _let_61))) (let ((_let_63 (tptp.set_intersection2 _let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_64 (= _let_43 _let_63))) (let ((_let_65 (= _let_43 (tptp.set_union2 _let_43 _let_61)))) (let ((_let_66 (= _let_59 (tptp.set_union2 _let_63 (tptp.set_difference _let_59 _let_63))))) (let ((_let_67 (not _let_51))) (let ((_let_68 (not _let_58))) (let ((_let_69 (_let_3))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (or))) (let ((_let_72 (_let_18))) (let ((_let_73 (ASSUME :args _let_72))) (let ((_let_74 (tptp.subset _let_43 _let_43))) (let ((_let_75 (= _let_74 _let_62))) (let ((_let_76 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_77 _let_74))) (let ((_let_79 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (_let_79))) (let ((_let_82 ((tptp.set_difference A C) (tptp.set_difference B C)))) (let ((_let_83 (_let_17))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_74 (not _let_78)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_83))) _let_84 :args (_let_76 false _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_81)) _let_80 :args (_let_78 false _let_79)) :args (_let_74 false _let_76 false _let_78)))) (let ((_let_86 (not _let_74))) (let ((_let_87 (tptp.subset _let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_64))) (let ((_let_90 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= A (tptp.set_intersection2 A B)))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_7))) (let ((_let_93 (ASSUME :args _let_92))) (let ((_let_94 ((tptp.set_difference A B)))) (let ((_let_95 (or _let_86 _let_65))) (let ((_let_96 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= B (tptp.set_union2 A (tptp.set_difference B A))))))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_98 (_let_96))) (let ((_let_99 ((not (= (tptp.subset A B) false))))) (let ((_let_100 (tptp.subset _let_63 _let_59))) (let ((_let_101 (not _let_100))) (let ((_let_102 (or _let_101 _let_66))) (let ((_let_103 (tptp.subset _let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_104 (not _let_103))) (let ((_let_105 (or _let_104 _let_100))) (let ((_let_106 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_109 (tptp.set_difference _let_108 _let_20))) (let ((_let_110 (tptp.subset _let_109 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_111 (not _let_110))) (let ((_let_112 (tptp.subset _let_43 _let_109))) (let ((_let_113 (not _let_112))) (let ((_let_114 (or _let_113 _let_111 _let_103))) (let ((_let_115 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_116 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_117 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_118 (tptp.subset _let_117 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_119 (= _let_109 _let_117))) (let ((_let_120 (_let_5))) (let ((_let_121 (ASSUME :args _let_120))) (let ((_let_122 (and _let_119 _let_118))) (let ((_let_123 (ASSUME :args (_let_118)))) (let ((_let_124 (APPLY_UF tptp.subset))) (let ((_let_125 (ASSUME :args (_let_119)))) (let ((_let_126 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_108))) (let ((_let_127 (not _let_126))) (let ((_let_128 (or _let_127 _let_112))) (let ((_let_129 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_130 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_129))) (let ((_let_131 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_132 (= _let_131 _let_129))) (let ((_let_133 (= _let_108 _let_131))) (let ((_let_134 (_let_1))) (let ((_let_135 (ASSUME :args _let_134))) (let ((_let_136 (_let_19))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (_let_6))) (let ((_let_139 (ASSUME :args _let_138))) (let ((_let_140 (and _let_133 _let_132 _let_130))) (let ((_let_141 (ASSUME :args (_let_130)))) (let ((_let_142 (ASSUME :args (_let_132)))) (let ((_let_143 (ASSUME :args (_let_133)))) (let ((_let_144 (and _let_60 _let_62 _let_64 _let_65 _let_51 _let_66))) (let ((_let_145 (ASSUME :args (_let_60)))) (let ((_let_146 (ASSUME :args (_let_66)))) (let ((_let_147 (ASSUME :args (_let_64)))) (let ((_let_148 (SYMM (SYMM _let_147)))) (let ((_let_149 (ASSUME :args (_let_51)))) (let ((_let_150 (ASSUME :args (_let_62)))) (let ((_let_151 (ASSUME :args (_let_65)))) (let ((_let_152 (_let_50))) (let ((_let_153 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_152)) :args _let_152)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_46))) (REFL :args (_let_47)) :args _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_49)) :args ((or _let_48 _let_50 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or _let_53 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_144)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_145 _let_146 _let_147 _let_149 _let_150 _let_151) (SCOPE (TRANS (SYMM (SYMM _let_151)) (CONG _let_148 (TRANS (SYMM _let_150) (SYMM (SYMM _let_149)) (CONG _let_145 _let_148 :args (APPLY_UF tptp.set_difference))) :args (APPLY_UF tptp.set_union2)) (SYMM _let_146) (SYMM _let_145)) :args (_let_60 _let_66 _let_64 _let_51 _let_62 _let_65))) :args (_let_60 _let_62 _let_64 _let_65 _let_51 _let_66))) :args (true _let_144)) :args ((or _let_58 (not _let_60) (not _let_62) (not _let_64) (not _let_65) _let_67 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_102)) :args ((or _let_101 _let_66 (not _let_102)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_105)) :args ((or _let_104 _let_100 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_114)) :args ((or _let_103 _let_113 _let_111 (not _let_114)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_127 _let_112 (not _let_128)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_140)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_141 _let_142 _let_143) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (TRANS (SYMM (SYMM _let_143)) (SYMM (SYMM _let_142))) :args _let_124) (TRUE_INTRO _let_141))) :args (_let_130 _let_132 _let_133))) :args (_let_133 _let_132 _let_130))) :args (true _let_140)) :args ((or (not _let_133) (not _let_132) _let_126 (not _let_130)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_139 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference B A)))) :args _let_138)) _let_139 :args (_let_133 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_137 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_136)) _let_137 :args (_let_132 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_135 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_134)) _let_135 :args (_let_130 false _let_1)) :args (_let_126 false _let_133 false _let_132 false _let_130)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_108 _let_20 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_81)) _let_80 :args (_let_128 false _let_79)) :args (_let_112 false _let_126 false _let_128)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_122)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_123 _let_125) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_125)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) :args _let_124) (TRUE_INTRO _let_123))) :args (_let_118 _let_119))) :args (_let_119 _let_118))) :args (true _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_121 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_120)) _let_121 :args (_let_119 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_94)) :args _let_92)) _let_93 :args (_let_118 false _let_7)) :args (_let_110 false _let_119 false _let_118)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_116 :args (_let_43 _let_109 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_115))) _let_116 :args (_let_114 false _let_115)) :args (_let_103 false _let_112 false _let_110 false _let_114)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (_let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING ((tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) :args (_let_106))) _let_107 :args (_let_105 false _let_106)) :args (_let_100 false _let_103 false _let_105)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_63 _let_59 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_98)) _let_97 :args (_let_102 false _let_96)) :args (_let_66 false _let_100 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_86 _let_65 (not _let_95)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_43 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_99)) :args _let_98)) _let_97 :args (_let_95 false _let_96)) :args (_let_65 false _let_74 false _let_95)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_88 _let_64 (not _let_89)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_94)) :args _let_92)) _let_93 :args (_let_87 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_43 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_90))) _let_91 :args (_let_89 false _let_90)) :args (_let_64 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_75)) :args ((or _let_86 _let_62 (not _let_75)))) _let_85 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_43 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_75 false _let_54)) :args (_let_62 false _let_74 false _let_75)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_72)) _let_73 :args (_let_60 false _let_18)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_70) :args _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args (_let_68)) :args _let_71)) _let_70 :args (_let_68 true _let_2)) :args (_let_67 false _let_66 false _let_65 false _let_64 false _let_62 false _let_60 true _let_58)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_29 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_52 false _let_54)) :args (_let_53 true _let_51 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_29 _let_43 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_49 false _let_36)) :args (_let_50 true _let_48 false _let_49)) :args (_let_47 true _let_46)))) (let ((_let_154 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_71)) :args ((or _let_30 _let_45))) _let_153 :args (_let_30 true _let_45)))) (let ((_let_155 (= _let_44 _let_28))) (let ((_let_156 (not _let_28))) (let ((_let_157 (forall ((D $$unsorted)) (let ((_let_1 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (= (tptp.in D (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_1)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (tptp.in D _let_1)))))))) (let ((_let_158 (_let_14))) (let ((_let_159 (ASSUME :args _let_158))) (let ((_let_160 (_let_157))) (let ((_let_161 (not _let_24))) (let ((_let_162 (_let_28))) (let ((_let_163 (not _let_25))) (let ((_let_164 (and _let_24 _let_22))) (let ((_let_165 (= _let_30 _let_164))) (let ((_let_166 (forall ((D $$unsorted)) (= (tptp.in D (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))))) (let ((_let_167 (_let_15))) (let ((_let_168 (ASSUME :args _let_167))) (let ((_let_169 (_let_166))) (let ((_let_170 (forall ((D $$unsorted)) (= (tptp.in D (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (and (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_171 (_let_170))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_27 _let_25 (not _let_26)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_171) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_171)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_159 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args _let_158))) _let_159 :args (_let_170 false _let_14)) :args (_let_26 false _let_170)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_25 1)) :args ((or _let_23 _let_163))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_164 1)) :args ((or _let_22 (not _let_164)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_165)) :args ((or _let_31 _let_164 (not _let_165)))) _let_154 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_169) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D _let_29)))) :args _let_169)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_168 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_29 QUANTIFIERS_INST_CBQI_PROP)) :args _let_167))) _let_168 :args (_let_166 false _let_15)) :args (_let_165 false _let_166)) :args (_let_164 false _let_30 false _let_165)) :args (_let_22 false _let_164)) :args (_let_163 false _let_22)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_162) (CONG (REFL :args _let_162) (REFL :args (_let_161)) (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_21))) :args _let_71)) :args ((or _let_21 _let_28 _let_161))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_155)) :args ((or _let_44 _let_156 (not _let_155)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_45 1)) _let_153 :args ((not _let_44) true _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_160) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.in D _let_43)))) :args _let_160)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_159 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20 _let_43 QUANTIFIERS_INST_CBQI_PROP)) :args _let_158))) _let_159 :args (_let_157 false _let_14)) :args (_let_155 false _let_157)) :args (_let_156 true _let_44 false _let_155)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_24 (not _let_32)))) _let_154 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_42) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_64 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.in C _let_29) false))))) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_35)) :args ((or (not _let_34) _let_33 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_40)) _let_41 :args (_let_34 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_29 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_39)) :args _let_38)) _let_37 :args (_let_35 false _let_36)) :args (_let_33 false _let_34 false _let_35)) :args (_let_32 false _let_33)) :args (_let_24 false _let_30 false _let_32)) :args (_let_21 true _let_28 false _let_24)) :args (false false _let_26 true _let_25 false _let_21)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) _let_19 _let_18 _let_17 (forall ((A $$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 $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) _let_16 _let_15 _let_14 (forall ((A $$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 $$unsorted)) (= (tptp.set_intersection2 A A) A)) _let_13 (exists ((A $$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 $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) _let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_11 _let_10 _let_9 (forall ((A $$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)) _let_8 _let_7 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) _let_6 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$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))) _let_5 _let_4 _let_3 (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_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.71/27.05  )
% 26.71/27.05  % SZS output end Proof for SEU138+2
% 26.71/27.05  % cvc5---1.0.5 exiting
% 26.71/27.05  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------