%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n016.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 16:31:01 EDT 2023

% Result   : Theorem 0.22s 0.76s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU340+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Wed Aug 23 20:16:08 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.76  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.xCrskk9Ki6/cvc5---1.0.5_4116.p...
% 0.22/0.76  ------- get file name : TPTP file name is SEU340+1
% 0.22/0.76  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4116.smt2...
% 0.22/0.76  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.76  % SZS status Theorem for SEU340+1
% 0.22/0.76  % SZS output start Proof for SEU340+1
% 0.22/0.76  (
% 0.22/0.76  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_4 (not (forall ((A $$unsorted)) (=> (and (tptp.transitive_relstr A) (tptp.rel_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.the_carrier A)) (=> (and (tptp.related A B C) (tptp.related A C D)) (tptp.related A B D))))))))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))))) (let ((_let_6 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_8 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.the_carrier A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.the_carrier A)) (= (tptp.related A B C) (tptp.in (tptp.ordered_pair B C) (tptp.the_InternalRel A))))))))))) (let ((_let_9 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_transitive_in A B) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in E B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D E) A)) (tptp.in (tptp.ordered_pair C E) A))))))))) (let ((_let_10 (forall ((A $$unsorted)) (=> (tptp.rel_str A) (= (tptp.transitive_relstr A) (tptp.is_transitive_in (tptp.the_InternalRel A) (tptp.the_carrier A))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))))) (let ((_let_12 (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.the_InternalRel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_2 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (or (not (tptp.in C _let_2)) (not (tptp.in D _let_2)) (not (tptp.in E _let_2)) (not (tptp.in (tptp.ordered_pair C D) _let_1)) (not (tptp.in (tptp.ordered_pair D E) _let_1)) (tptp.in (tptp.ordered_pair C E) _let_1))))))) (let ((_let_13 (tptp.the_InternalRel SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8) _let_13))) (let ((_let_15 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_16 (tptp.in _let_15 _let_13))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_19 (tptp.in _let_18 _let_13))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.the_carrier SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_22 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_21))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21))) (let ((_let_25 (not _let_24))) (let ((_let_26 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_21))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_25 _let_23 _let_20 _let_17 _let_14))) (let ((_let_29 (tptp.is_transitive_in _let_13 _let_21))) (let ((_let_30 (= _let_29 _let_12))) (let ((_let_31 (tptp.relation _let_13))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_30))) (let ((_let_34 (forall ((A $$unsorted) (BOUND_VARIABLE_963 $$unsorted)) (or (not (tptp.relation A)) (= (tptp.is_transitive_in A BOUND_VARIABLE_963) (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (or (not (tptp.in C BOUND_VARIABLE_963)) (not (tptp.in D BOUND_VARIABLE_963)) (not (tptp.in E BOUND_VARIABLE_963)) (not (tptp.in (tptp.ordered_pair C D) A)) (not (tptp.in (tptp.ordered_pair D E) A)) (tptp.in (tptp.ordered_pair C E) A)))))))) (let ((_let_35 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_36 (tptp.cartesian_product2 _let_21 _let_21))) (let ((_let_37 (tptp.element _let_13 (tptp.powerset _let_36)))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_31))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B)))) (tptp.relation C))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (tptp.relation_of2_as_subset _let_13 _let_21 _let_21))) (let ((_let_43 (not _let_42))) (let ((_let_44 (or _let_43 _let_37))) (let ((_let_45 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2_as_subset C A B)) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (tptp.rel_str SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_42))) (let ((_let_50 (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.rel_str A)) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_53 (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_54 (not _let_53))) (let ((_let_55 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_21))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.related SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_58 (not _let_57))) (let ((_let_59 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21))) (let ((_let_60 (not _let_59))) (let ((_let_61 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_21))) (let ((_let_62 (not _let_61))) (let ((_let_63 (tptp.transitive_relstr SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_64 (not _let_63))) (let ((_let_65 (or _let_64 _let_48 _let_62 _let_60 _let_58 _let_56 _let_54 _let_52))) (let ((_let_66 (forall ((A $$unsorted) (BOUND_VARIABLE_1166 $$unsorted) (BOUND_VARIABLE_1164 $$unsorted) (BOUND_VARIABLE_1162 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.transitive_relstr A)) (not (tptp.rel_str A)) (not (tptp.element BOUND_VARIABLE_1162 _let_1)) (not (tptp.element BOUND_VARIABLE_1166 _let_1)) (not (tptp.related A BOUND_VARIABLE_1162 BOUND_VARIABLE_1166)) (not (tptp.element BOUND_VARIABLE_1164 _let_1)) (not (tptp.related A BOUND_VARIABLE_1166 BOUND_VARIABLE_1164)) (tptp.related A BOUND_VARIABLE_1162 BOUND_VARIABLE_1164)))))) (let ((_let_67 (not _let_65))) (let ((_let_68 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_69 (or))) (let ((_let_70 (not _let_66))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_68) :args (_let_70))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_66))) (REFL :args (_let_67)) :args _let_69)) _let_68 :args (_let_67 true _let_66)))) (let ((_let_72 (REFL :args (_let_65)))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 1)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_48) _let_47))) :args _let_69)) :args ((or _let_47 _let_65))) _let_71 :args (_let_47 true _let_65)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_37 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_42 (not _let_49)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.rel_str A) false))))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_42 false _let_47 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_21 _let_21 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2_as_subset C A B) false))))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_37 false _let_42 false _let_44)))) (let ((_let_75 (= _let_63 _let_29))) (let ((_let_76 (or _let_48 _let_75))) (let ((_let_77 (forall ((A $$unsorted)) (or (not (tptp.rel_str A)) (= (tptp.transitive_relstr A) (tptp.is_transitive_in (tptp.the_InternalRel A) (tptp.the_carrier A))))))) (let ((_let_78 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_79 (not _let_28))) (let ((_let_80 (and _let_26 _let_24))) (let ((_let_81 (tptp.in _let_18 _let_36))) (let ((_let_82 (= _let_81 _let_80))) (let ((_let_83 (_let_5))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 ((tptp.cartesian_product2 C D) (tptp.ordered_pair A B)))) (let ((_let_86 (tptp.empty _let_36))) (let ((_let_87 (tptp.element _let_18 _let_36))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_86 _let_81))) (let ((_let_90 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element A B)) (tptp.empty B) (tptp.in A B))))) (let ((_let_91 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_92 (_let_90))) (let ((_let_93 ((not (= (tptp.element A B) false))))) (let ((_let_94 (or _let_20 _let_38 _let_87))) (let ((_let_95 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.in A B)) (not (tptp.element B (tptp.powerset C))) (tptp.element A C))))) (let ((_let_96 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_97 (_let_95))) (let ((_let_98 ((not (= (tptp.in A B) false)) (tptp.powerset C)))) (let ((_let_99 (= _let_57 _let_19))) (let ((_let_100 (or _let_48 _let_62 _let_60 _let_99))) (let ((_let_101 (forall ((A $$unsorted) (BOUND_VARIABLE_1008 $$unsorted) (BOUND_VARIABLE_1006 $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (or (not (tptp.rel_str A)) (not (tptp.element BOUND_VARIABLE_1006 _let_1)) (not (tptp.element BOUND_VARIABLE_1008 _let_1)) (= (tptp.related A BOUND_VARIABLE_1006 BOUND_VARIABLE_1008) (tptp.in (tptp.ordered_pair BOUND_VARIABLE_1006 BOUND_VARIABLE_1008) (tptp.the_InternalRel A)))))))) (let ((_let_102 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_103 (_let_101))) (let ((_let_104 ((tptp.related A BOUND_VARIABLE_1006 BOUND_VARIABLE_1008)))) (let ((_let_105 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 3)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_59))) :args _let_69)) :args ((or _let_59 _let_65))) _let_71 :args (_let_59 true _let_65)))) (let ((_let_106 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 2)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_61))) :args _let_69)) :args ((or _let_61 _let_65))) _let_71 :args (_let_61 true _let_65)))) (let ((_let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_99)) :args ((or _let_58 _let_19 (not _let_99)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 4)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_57))) :args _let_69)) :args ((or _let_57 _let_65))) _let_71 :args (_let_57 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_48 _let_62 _let_60 _let_99 (not _let_100)))) _let_73 _let_106 _let_105 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_103)) _let_102 :args (_let_100 false _let_101)) :args (_let_99 false _let_47 false _let_61 false _let_59 false _let_100)) :args (_let_19 false _let_57 false _let_99)))) (let ((_let_108 (not _let_86))) (let ((_let_109 (or _let_17 _let_38 _let_108))) (let ((_let_110 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.in A B)) (not (tptp.element B (tptp.powerset C))) (not (tptp.empty C)))))) (let ((_let_111 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_112 (= _let_53 _let_16))) (let ((_let_113 (or _let_48 _let_60 _let_56 _let_112))) (let ((_let_114 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 5)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_55))) :args _let_69)) :args ((or _let_55 _let_65))) _let_71 :args (_let_55 true _let_65)))) (let ((_let_115 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_112)) :args ((or _let_54 _let_16 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 6)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_69)) :args ((or _let_53 _let_65))) _let_71 :args (_let_53 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_113)) :args ((or _let_48 _let_60 _let_56 _let_112 (not _let_113)))) _let_73 _let_105 _let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_103)) _let_102 :args (_let_113 false _let_101)) :args (_let_112 false _let_47 false _let_59 false _let_55 false _let_113)) :args (_let_16 false _let_53 false _let_112)))) (let ((_let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_17 _let_38 _let_108 (not _let_109)))) _let_115 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_15 _let_13 _let_36 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in A B) false)) (tptp.powerset C)))) :args (_let_110))) _let_111 :args (_let_109 false _let_110)) :args (_let_108 false _let_16 false _let_37 false _let_109)))) (let ((_let_117 (and _let_24 _let_22))) (let ((_let_118 (tptp.in _let_15 _let_36))) (let ((_let_119 (= _let_118 _let_117))) (let ((_let_120 (tptp.element _let_15 _let_36))) (let ((_let_121 (not _let_120))) (let ((_let_122 (or _let_121 _let_86 _let_118))) (let ((_let_123 (or _let_17 _let_38 _let_120))) (let ((_let_124 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_119)) :args ((or _let_117 (not _let_118) (not _let_119)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_122)) :args ((or _let_86 _let_121 _let_118 (not _let_122)))) _let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_123)) :args ((or _let_17 _let_38 _let_120 (not _let_123)))) _let_115 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (_let_15 _let_13 _let_36 QUANTIFIERS_INST_E_MATCHING _let_98)) :args _let_97)) _let_96 :args (_let_123 false _let_95)) :args (_let_120 false _let_16 false _let_37 false _let_123)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_15 _let_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_93)) :args _let_92)) _let_91 :args (_let_122 false _let_90)) :args (_let_118 true _let_86 false _let_120 false _let_122)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_21 _let_21 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_83)) _let_84 :args (_let_119 false _let_5)) :args (_let_117 false _let_118 false _let_119)))) (let ((_let_125 (not _let_117))) (let ((_let_126 (= _let_52 _let_14))) (let ((_let_127 (not _let_14))) (let ((_let_128 (or _let_48 _let_62 _let_56 _let_126))) (let ((_let_129 (_let_12))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_129) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in C _let_21) false)) (not (= (tptp.in D _let_21) false)) (not (= (tptp.in E _let_21) false))))) :args _let_129)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_14 _let_17 _let_20 _let_25 _let_23 _let_27 _let_79))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_126)) :args ((or _let_52 _let_127 (not _let_126)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_65 7)) _let_71 :args ((not _let_52) true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_48 _let_62 _let_56 _let_126 (not _let_128)))) _let_73 _let_106 _let_114 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_102 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_104)) :args _let_103)) _let_102 :args (_let_128 false _let_101)) :args (_let_126 false _let_47 false _let_61 false _let_55 false _let_128)) :args (_let_127 true _let_52 false _let_126)) _let_115 _let_107 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_117 0)) :args ((or _let_24 _let_125))) _let_124 :args (_let_24 false _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_117 1)) :args ((or _let_22 _let_125))) _let_124 :args (_let_22 false _let_117)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 0)) :args ((or _let_26 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_82)) :args ((or _let_80 (not _let_81) (not _let_82)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_86 _let_88 _let_81 (not _let_89)))) _let_116 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_94)) :args ((or _let_20 _let_38 _let_87 (not _let_94)))) _let_107 _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (_let_18 _let_13 _let_36 QUANTIFIERS_INST_E_MATCHING _let_98)) :args _let_97)) _let_96 :args (_let_94 false _let_95)) :args (_let_87 false _let_19 false _let_37 false _let_94)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_91 :args (_let_18 _let_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_93)) :args _let_92)) _let_91 :args (_let_89 false _let_90)) :args (_let_81 true _let_86 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21 _let_21 QUANTIFIERS_INST_E_MATCHING _let_85)) :args _let_83)) _let_84 :args (_let_82 false _let_5)) :args (_let_80 false _let_81 false _let_82)) :args (_let_26 false _let_80)) :args (_let_79 true _let_14 false _let_16 false _let_19 false _let_24 false _let_22 false _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or (not _let_29) _let_12 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_75)) :args ((or _let_64 _let_29 (not _let_75)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_65 0)) (CONG _let_72 (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_63))) :args _let_69)) :args ((or _let_63 _let_65))) _let_71 :args (_let_63 true _let_65)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_48 _let_75 (not _let_76)))) _let_73 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_78 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.rel_str A) false))))) :args (_let_77))) _let_78 :args (_let_76 false _let_77)) :args (_let_75 false _let_47 false _let_76)) :args (_let_29 false _let_63 false _let_75)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_30 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_31 _let_38 (not _let_39)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_21 _let_21 _let_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) false))))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_31 false _let_37 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_13 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.is_transitive_in A BOUND_VARIABLE_963)))) :args (_let_34))) _let_35 :args (_let_33 false _let_34)) :args (_let_30 false _let_31 false _let_33)) :args (_let_12 false _let_29 false _let_30)) :args (false true _let_28 false _let_12)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) _let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) _let_9 _let_8 true true true true true true (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true true true _let_7 _let_6 true (exists ((A $$unsorted)) (tptp.rel_str A)) (exists ((A $$unsorted)) (tptp.one_sorted_str A)) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2 C A B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (tptp.relation_of2_as_subset C A B))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) _let_4 _let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) _let_2 _let_1 (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.77  )
% 0.22/0.77  % SZS output end Proof for SEU340+1
% 0.22/0.77  % cvc5---1.0.5 exiting
% 0.22/0.77  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------