%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU293+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n025.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 16:30:40 EDT 2023

% Result   : Theorem 26.54s 26.73s
% Output   : Proof 26.57s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.17  % Problem    : SEU293+2 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.18  % Command    : do_cvc5 %s %d
% 0.18/0.39  % Computer : n025.cluster.edu
% 0.18/0.39  % Model    : x86_64 x86_64
% 0.18/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.39  % Memory   : 8042.1875MB
% 0.18/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.39  % CPULimit   : 300
% 0.18/0.39  % WCLimit    : 300
% 0.18/0.39  % DateTime   : Wed Aug 23 21:51:06 EDT 2023
% 0.18/0.39  % CPUTime    : 
% 0.24/0.50  %----Proving TF0_NAR, FOF, or CNF
% 26.54/26.73  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.CY2M0YKUS5/cvc5---1.0.5_31822.p...
% 26.54/26.73  ------- get file name : TPTP file name is SEU293+2
% 26.54/26.73  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_31822.smt2...
% 26.54/26.73  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.54/26.73  --- Run --no-e-matching --full-saturate-quant at 5...
% 26.54/26.73  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 26.54/26.73  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 26.54/26.73  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 26.54/26.73  % SZS status Theorem for SEU293+2
% 26.54/26.73  % SZS output start Proof for SEU293+2
% 26.54/26.73  (
% 26.54/26.73  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (= B (tptp.apply C A)))))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (not (= B tptp.empty_set)) (forall ((E $$unsorted)) (= (tptp.in E (tptp.relation_inverse_image D C)) (and (tptp.in E A) (tptp.in (tptp.apply D E) C)))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_inverse_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_rng C)) (tptp.in (tptp.ordered_pair A D) C) (tptp.in D B)))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))) (let ((_let_6 (tptp.relation tptp.empty_set))) (let ((_let_7 (tptp.empty tptp.empty_set))) (let ((_let_8 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (= A tptp.empty_set))) (let ((_let_3 (= B tptp.empty_set))) (=> (tptp.relation_of2_as_subset C A B) (and (=> (=> _let_3 _let_2) (= _let_1 (= A (tptp.relation_dom_as_subset A B C)))) (=> _let_3 (or _let_2 (= _let_1 (= C tptp.empty_set)))))))))))) (let ((_let_11 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.relation_dom A)) (tptp.in (tptp.apply A D) B)))))))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))))) (let ((_let_13 (tptp.relation_inverse_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_14 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_13))) (let ((_let_15 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_16 (tptp.in _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_17 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_18 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 _let_17))) (let ((_let_19 (and _let_18 _let_16))) (let ((_let_20 (= _let_14 _let_19))) (let ((_let_21 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_22 (and _let_21 _let_16))) (let ((_let_23 (= _let_14 _let_22))) (let ((_let_24 (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (not (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 D) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)))))) (let ((_let_25 (not _let_24))) (let ((_let_26 (= _let_14 _let_25))) (let ((_let_27 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_28 (not _let_27))) (let ((_let_29 (tptp.in (tptp.ordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_30 (not _let_29))) (let ((_let_31 (or (not (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48 (tptp.relation_rng SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) _let_30 _let_28))) (let ((_let_32 (= _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_48))) (let ((_let_33 (and _let_18 _let_32))) (let ((_let_34 (= _let_29 _let_33))) (let ((_let_35 (tptp.relation_dom_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_35))) (let ((_let_37 (= _let_35 _let_17))) (let ((_let_38 (not _let_14))) (let ((_let_39 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_40 (tptp.relation_of2_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_41 (not _let_40))) (let ((_let_42 (tptp.quasi_total SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_43 (not _let_42))) (let ((_let_44 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43 _let_41 _let_39 _let_23))) (let ((_let_47 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (BOUND_VARIABLE_10189 $$unsorted)) (or (not (tptp.function D)) (not (tptp.quasi_total D A B)) (not (tptp.relation_of2_as_subset D A B)) (= tptp.empty_set B) (= (tptp.in BOUND_VARIABLE_10189 (tptp.relation_inverse_image D C)) (and (tptp.in BOUND_VARIABLE_10189 A) (tptp.in (tptp.apply D BOUND_VARIABLE_10189) C))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 4)) _let_52 :args ((not _let_23) true _let_46)))) (let ((_let_54 (_let_23))) (let ((_let_55 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_26))) (let ((_let_58 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (= (tptp.in A (tptp.relation_inverse_image C B)) (not (forall ((D $$unsorted)) (or (not (tptp.in D (tptp.relation_rng C))) (not (tptp.in (tptp.ordered_pair A D) C)) (not (tptp.in D B)))))))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 (tptp.powerset (tptp.cartesian_product2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_55))) (let ((_let_63 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B)))) (tptp.relation C))))) (let ((_let_64 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_65 (or _let_41 _let_60))) (let ((_let_66 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2_as_subset C A B)) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))))) (let ((_let_67 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_68 (REFL :args (_let_46)))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 2)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_40))) :args _let_50)) :args ((or _let_40 _let_46))) _let_52 :args (_let_40 true _let_46)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_55 _let_61 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_41 _let_60 (not _let_65)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_67 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2_as_subset C A B) false))))) :args (_let_66))) _let_67 :args (_let_65 false _let_66)) :args (_let_60 false _let_40 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_63))) _let_64 :args (_let_62 false _let_63)) :args (_let_55 false _let_60 false _let_62)))) (let ((_let_71 (_let_25))) (let ((_let_72 (REFL :args (_let_31)))) (let ((_let_73 (or _let_56 _let_45 _let_34))) (let ((_let_74 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation C)) (not (tptp.function C)) (= (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (= B (tptp.apply C A)))))))) (let ((_let_75 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_50)) :args ((or _let_44 _let_46))) _let_52 :args (_let_44 true _let_46)))) (let ((_let_77 (not _let_33))) (let ((_let_78 (= _let_42 _let_36))) (let ((_let_79 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_80 (and _let_39 (not _let_79)))) (let ((_let_81 (or _let_80 _let_78))) (let ((_let_82 (not _let_39))) (let ((_let_83 (and _let_81 (or _let_82 _let_79 (= _let_42 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))))) (let ((_let_84 (or _let_41 _let_83))) (let ((_let_85 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (= tptp.empty_set A))) (let ((_let_3 (= tptp.empty_set B))) (or (not (tptp.relation_of2_as_subset C A B)) (and (or (and _let_3 (not _let_2)) (= _let_1 (= A (tptp.relation_dom_as_subset A B C)))) (or (not _let_3) _let_2 (= _let_1 (= tptp.empty_set C))))))))))) (let ((_let_86 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_87 (not _let_80))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or _let_43 _let_36 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 1)) (CONG _let_68 (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_42))) :args _let_50)) :args ((or _let_42 _let_46))) _let_52 :args (_let_42 true _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_80 _let_78 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_80 0)) :args ((or _let_39 _let_87))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 3)) _let_52 :args (_let_82 true _let_46)) :args (_let_87 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_83 0)) :args ((or _let_81 (not _let_83)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_84)) :args ((or _let_41 _let_83 (not _let_84)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_86 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation_of2_as_subset C A B) false))))) :args (_let_85))) _let_86 :args (_let_84 false _let_85)) :args (_let_83 false _let_40 false _let_84)) :args (_let_81 false _let_83)) :args (_let_78 true _let_80 false _let_81)) :args (_let_36 false _let_42 false _let_78)))) (let ((_let_89 (tptp.relation_of2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_90 _let_37))) (let ((_let_92 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2 C A B)) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))))) (let ((_let_93 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_94 (= _let_40 _let_89))) (let ((_let_95 (_let_4))) (let ((_let_96 (ASSUME :args _let_95))) (let ((_let_97 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_90 _let_37 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_94)) :args ((or _let_41 _let_89 (not _let_94)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_96 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.relation_of2_as_subset C A B)))) :args _let_95)) _let_96 :args (_let_94 false _let_4)) :args (_let_89 false _let_40 false _let_94)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_CBQI_PROP)) :args (_let_92))) _let_93 :args (_let_91 false _let_92)) :args (_let_37 false _let_89 false _let_91)))) (let ((_let_98 (not _let_37))) (let ((_let_99 (not _let_18))) (let ((_let_100 (not _let_36))) (let ((_let_101 (and _let_36 _let_18 _let_37))) (let ((_let_102 (ASSUME :args (_let_18)))) (let ((_let_103 (APPLY_UF tptp.in))) (let ((_let_104 (ASSUME :args (_let_37)))) (let ((_let_105 (SYMM _let_104))) (let ((_let_106 (ASSUME :args (_let_36)))) (let ((_let_107 (SYMM _let_106))) (let ((_let_108 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19)))) (let ((_let_109 (and _let_27 _let_32))) (let ((_let_110 (_let_27 _let_32))) (let ((_let_111 (ASSUME :args (_let_27)))) (let ((_let_112 (ASSUME :args (_let_32)))) (let ((_let_113 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_22)) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_111 _let_112) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_112)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17)) :args _let_103) (TRUE_INTRO _let_111))) :args _let_110)) :args _let_110)) :args (true _let_109)) :args ((or _let_16 _let_28 (not _let_32)))) (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_101)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_102 _let_104 _let_106) (SCOPE (TRUE_ELIM (TRANS (CONG _let_108 (TRANS (SYMM _let_107) (SYMM _let_105)) :args _let_103) (TRUE_INTRO _let_102))) :args (_let_18 _let_37 _let_36))) :args (_let_36 _let_18 _let_37))) :args (true _let_101)) :args ((or _let_21 _let_100 _let_99 _let_98))) _let_97 _let_88 (REORDERING (CNF_AND_POS :args (_let_33 1)) :args ((or _let_32 _let_77))) (REORDERING (CNF_AND_POS :args (_let_33 0)) :args ((or _let_18 _let_77))) (REORDERING (CNF_EQUIV_POS1 :args (_let_34)) :args ((or _let_30 _let_33 (not _let_34)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_45 _let_56 _let_34 (not _let_73)))) _let_76 _let_70 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((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D)))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_rng A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair D C) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.well_orders A B) (and (tptp.is_reflexive_in A B) (tptp.is_transitive_in A B) (tptp.is_antisymmetric_in A B) (tptp.is_connected_in A B) (tptp.is_well_founded_in A B)))))) (forall ((A $$unsorted)) (= (tptp.being_limit_ordinal A) (= A (tptp.union A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_field A) (tptp.set_union2 (tptp.relation_dom A) (tptp.relation_rng A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_connected_in A B) (forall ((C $$unsorted) (D $$unsorted)) (not (and (tptp.in C B) (tptp.in D B) (not (= C D)) (not (tptp.in (tptp.ordered_pair C D) A)) (not (tptp.in (tptp.ordered_pair D C) A))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.relation_restriction A B) (tptp.set_intersection2 A (tptp.cartesian_product2 B B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.relation_inverse A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.in (tptp.ordered_pair D C) A)))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.relation_isomorphism A B C) (and (= (tptp.relation_dom C) (tptp.relation_field A)) (= (tptp.relation_rng C) (tptp.relation_field B)) (tptp.one_to_one C) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.relation_field A))) (= (tptp.in (tptp.ordered_pair D E) A) (and (tptp.in D _let_1) (tptp.in E _let_1) (tptp.in (tptp.ordered_pair (tptp.apply C D) (tptp.apply C E)) B))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (and (tptp.in B _let_1) (tptp.in C _let_1) (= (tptp.apply A B) (tptp.apply A C))) (= B C))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_composition A B)) (forall ((D $$unsorted) (E $$unsorted)) (= (tptp.in (tptp.ordered_pair D E) C) (exists ((F $$unsorted)) (and (tptp.in (tptp.ordered_pair D F) A) (tptp.in (tptp.ordered_pair F E) B)))))))))))) (forall ((A $$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))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (= (tptp.function_inverse A) (tptp.relation_inverse A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (tptp.is_reflexive_in A (tptp.relation_field A))))) true true true true true true true true true (forall ((A $$unsorted)) (tptp.relation (tptp.inclusion_relation A))) true true (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) true true (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_restriction A B)))) true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_inverse A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_dom_as_subset A B C) (tptp.powerset A)))) true true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.relation_composition A B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_rng_as_subset A B C) (tptp.powerset B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.union_of_subsets A B) _let_1)))) (forall ((A $$unsorted)) (tptp.relation (tptp.identity_relation A))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.meet_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation A) (tptp.relation (tptp.relation_dom_restriction A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.relation (tptp.relation_rng_restriction A B)))) true true true _let_9 (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 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition B A))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_7 _let_6 _let_8) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.relation_empty_yielding A)) (and (tptp.relation _let_1) (tptp.relation_empty_yielding _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.relation A) (tptp.function A) (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.succ A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_7 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (tptp.relation _let_1) (tptp.function _let_1)))) (and _let_6 _let_8 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_7 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_union2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.succ A))) (=> (tptp.ordinal A) (and (not (tptp.empty _let_1)) (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_difference A B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.unordered_pair A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction A B))) (=> (and (tptp.relation A) (tptp.function A)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.union A))) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive _let_1) (tptp.epsilon_connected _let_1) (tptp.ordinal _let_1))))) (and _let_7 _let_6) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_rng_restriction A B))) (=> (and (tptp.relation B) (tptp.function B)) (and (tptp.relation _let_1) (tptp.function _let_1))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_composition A B))) (=> (and (tptp.empty A) (tptp.relation B)) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (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.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_inverse (tptp.relation_inverse A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.reflexive A) (forall ((B $$unsorted)) (=> (tptp.in B (tptp.relation_field A)) (tptp.in (tptp.ordered_pair B B) A)))))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_rng_restriction A B)) (tptp.relation_dom B)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C D) A)) (tptp.in (tptp.ordered_pair B D) A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (tptp.well_ordering B) (tptp.equipotent A (tptp.relation_field B)) (forall ((C $$unsorted)) (=> (tptp.relation C) (not (tptp.well_orders C A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair C B) A)) (= B C)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field A))) (not (and (tptp.in B _let_1) (tptp.in C _let_1) (not (= B C)) (not (tptp.in (tptp.ordered_pair B C) A)) (not (tptp.in (tptp.ordered_pair C B) A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in B (tptp.relation_dom (tptp.relation_dom_restriction C A))) (and (tptp.in B (tptp.relation_dom C)) (tptp.in B A))))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C) (tptp.quasi_total C A B)))) (exists ((A $$unsorted)) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A) (tptp.empty A) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (and (tptp.relation_of2 C A B) (tptp.relation C) (tptp.function C)))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A) (tptp.function A))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_rng_as_subset A B C) (tptp.relation_rng C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))) _let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (= (tptp.ordinal_subset A B) (tptp.subset A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (tptp.are_equipotent A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (tptp.ordinal_subset A A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (tptp.equipotent A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.in C A))) (=> (and _let_1 (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) _let_1 (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E)))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.in D A))) (= (tptp.in (tptp.ordered_pair D E) C) (and _let_1 _let_1 (exists ((J $$unsorted)) (and (= D J) (tptp.in E J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair E K) B)))))))))))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.singleton B))) (let ((_let_2 (tptp.in B A))) (=> (and _let_2 (= C _let_1) _let_2 (= D _let_1)) (= C D))))) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.in C A))) (= (tptp.in (tptp.ordered_pair C D) B) (and _let_1 _let_1 (= D (tptp.singleton C)))))))))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted)) (and (tptp.ordinal B) (tptp.in B A))) (exists ((B $$unsorted)) (and (tptp.ordinal B) (tptp.in B A) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (=> (tptp.in C A) (tptp.ordinal_subset B C)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (exists ((D $$unsorted)) (and (tptp.relation D) (forall ((E $$unsorted) (F $$unsorted)) (= (tptp.in (tptp.ordered_pair E F) D) (and (tptp.in E A) (tptp.in F A) (tptp.in (tptp.ordered_pair (tptp.apply C E) (tptp.apply C F)) B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.in C A))) (=> (and _let_1 (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) _let_1 (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E)))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (let ((_let_1 (tptp.in E A))) (and _let_1 _let_1 (exists ((J $$unsorted)) (and (= E J) (tptp.in D J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair D K) B)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (forall ((C $$unsorted)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= (tptp.ordered_pair G H) E) (tptp.in G A) (exists ((I $$unsorted)) (and (= G I) (tptp.in H I) (forall ((J $$unsorted)) (=> (tptp.in J I) (tptp.in (tptp.ordered_pair H J) B))))))) (= D F) (exists ((K $$unsorted) (L $$unsorted)) (and (= (tptp.ordered_pair K L) F) (tptp.in K A) (exists ((M $$unsorted)) (and (= K M) (tptp.in L M) (forall ((N $$unsorted)) (=> (tptp.in N M) (tptp.in (tptp.ordered_pair L N) B)))))))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 A C)) (= F E) (exists ((O $$unsorted) (P $$unsorted)) (and (= (tptp.ordered_pair O P) E) (tptp.in O A) (exists ((Q $$unsorted)) (and (= O Q) (tptp.in P Q) (forall ((R $$unsorted)) (=> (tptp.in R Q) (tptp.in (tptp.ordered_pair P R) B)))))))))))))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.singleton B))) (let ((_let_2 (tptp.in B A))) (=> (and _let_2 (= C _let_1) _let_2 (= D _let_1)) (= C D))))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (let ((_let_1 (tptp.in D A))) (and _let_1 _let_1 (= C (tptp.singleton D)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) D) (tptp.in F A) (= G (tptp.singleton F)))) (= C E) (exists ((H $$unsorted) (I $$unsorted)) (and (= (tptp.ordered_pair H I) E) (tptp.in H A) (= I (tptp.singleton H))))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.cartesian_product2 A B)) (= E D) (exists ((J $$unsorted) (K $$unsorted)) (and (= (tptp.ordered_pair J K) D) (tptp.in J A) (= K (tptp.singleton J))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (=> (forall ((D $$unsorted) (E $$unsorted) (F $$unsorted)) (=> (and (= D E) (exists ((G $$unsorted) (H $$unsorted)) (and (= E (tptp.ordered_pair G H)) (tptp.in (tptp.ordered_pair (tptp.apply C G) (tptp.apply C H)) B))) (= D F) (exists ((I $$unsorted) (J $$unsorted)) (and (= F (tptp.ordered_pair I J)) (tptp.in (tptp.ordered_pair (tptp.apply C I) (tptp.apply C J)) B)))) (= E F))) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (exists ((F $$unsorted)) (and (tptp.in F (tptp.cartesian_product2 A A)) (= F E) (exists ((K $$unsorted) (L $$unsorted)) (and (= E (tptp.ordered_pair K L)) (tptp.in (tptp.ordered_pair (tptp.apply C K) (tptp.apply C L)) B))))))))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (= B C) (tptp.ordinal C) (= B D) (tptp.ordinal D)) (= C D))) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in D A) (= D C) (tptp.ordinal C)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (= C D) (exists ((F $$unsorted)) (and (tptp.ordinal F) (= D F) (tptp.in F A))) (= C E) (exists ((G $$unsorted)) (and (tptp.ordinal G) (= E G) (tptp.in G A)))) (= D E))) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.succ B)) (= E D) (exists ((H $$unsorted)) (and (tptp.ordinal H) (= D H) (tptp.in H A))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (forall ((C $$unsorted)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 A C)) (exists ((F $$unsorted) (G $$unsorted)) (and (= (tptp.ordered_pair F G) E) (tptp.in F A) (exists ((H $$unsorted)) (and (= F H) (tptp.in G H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair G I) B)))))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.cartesian_product2 A B)) (exists ((E $$unsorted) (F $$unsorted)) (and (= (tptp.ordered_pair E F) D) (tptp.in E A) (= F (tptp.singleton E))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation B) (tptp.relation C) (tptp.function C)) (exists ((D $$unsorted)) (forall ((E $$unsorted)) (= (tptp.in E D) (and (tptp.in E (tptp.cartesian_product2 A A)) (exists ((F $$unsorted) (G $$unsorted)) (and (= E (tptp.ordered_pair F G)) (tptp.in (tptp.ordered_pair (tptp.apply C F) (tptp.apply C G)) B))))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (forall ((C $$unsorted)) (= (tptp.in C B) (and (tptp.in C A) (tptp.ordinal C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (exists ((C $$unsorted)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.succ B)) (exists ((E $$unsorted)) (and (tptp.ordinal E) (= D E) (tptp.in E A))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation B)) (=> (and (forall ((C $$unsorted) (D $$unsorted) (E $$unsorted)) (=> (and (tptp.in C A) (exists ((F $$unsorted)) (and (= C F) (tptp.in D F) (forall ((G $$unsorted)) (=> (tptp.in G F) (tptp.in (tptp.ordered_pair D G) B))))) (exists ((H $$unsorted)) (and (= C H) (tptp.in E H) (forall ((I $$unsorted)) (=> (tptp.in I H) (tptp.in (tptp.ordered_pair E I) B)))))) (= D E))) (forall ((C $$unsorted)) (not (and (tptp.in C A) (forall ((D $$unsorted)) (not (exists ((J $$unsorted)) (and (= C J) (tptp.in D J) (forall ((K $$unsorted)) (=> (tptp.in K J) (tptp.in (tptp.ordered_pair D K) B))))))))))) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (= (tptp.relation_dom C) A) (forall ((D $$unsorted)) (=> (tptp.in D A) (exists ((L $$unsorted)) (and (= D L) (tptp.in (tptp.apply C D) L) (forall ((M $$unsorted)) (=> (tptp.in M L) (tptp.in (tptp.ordered_pair (tptp.apply C D) M) B)))))))))))) (forall ((A $$unsorted)) (=> (and (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.singleton B))) (=> (and (tptp.in B A) (= C _let_1) (= D _let_1)) (= C D)))) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted)) (not (= C (tptp.singleton B)))))))) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) (tptp.singleton C)))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.function B) (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) (tptp.singleton C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.equipotent A B) (tptp.equipotent B A))) (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)))) (forall ((A $$unsorted)) (tptp.in A (tptp.succ A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_rng (tptp.relation_rng_restriction B C))) (and (tptp.in A B) (tptp.in A (tptp.relation_rng C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng_restriction A B) B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.relation_rng B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset 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(tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.relation_dom_restriction (tptp.relation_rng_restriction A C) B) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_image C B)) (exists ((D $$unsorted)) (and (tptp.in D (tptp.relation_dom C)) (tptp.in (tptp.ordered_pair D A) C) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_image B A) (tptp.relation_rng B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (tptp.subset (tptp.relation_image B (tptp.relation_inverse_image B A)) A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_image B A) (tptp.relation_image B (tptp.set_intersection2 (tptp.relation_dom B) A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A (tptp.relation_dom B)) (tptp.subset A (tptp.relation_inverse_image B (tptp.relation_image B A)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A (tptp.relation_dom A)) (tptp.relation_rng A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_image B (tptp.relation_inverse_image B A)) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation_of2_as_subset D C A) (=> (tptp.subset (tptp.relation_rng D) B) (tptp.relation_of2_as_subset D C B)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_image B (tptp.relation_rng A))))))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_inverse_image B A) (tptp.relation_dom B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation_of2_as_subset D C A) (=> (tptp.subset A B) (tptp.relation_of2_as_subset D C B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_restriction C B)) (and (tptp.in A C) (tptp.in A (tptp.cartesian_product2 B B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (not (and (not (= A tptp.empty_set)) (tptp.subset A (tptp.relation_rng B)) (= (tptp.relation_inverse_image B A) tptp.empty_set))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.subset A B) (tptp.subset (tptp.relation_inverse_image C A) (tptp.relation_inverse_image C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_dom_restriction (tptp.relation_rng_restriction A B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_restriction B A) (tptp.relation_rng_restriction A (tptp.relation_dom_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in A (tptp.relation_field (tptp.relation_restriction C B))) (and (tptp.in A (tptp.relation_field C)) (tptp.in A B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (tptp.in B (tptp.relation_rng C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_field (tptp.relation_restriction B A)))) (=> (tptp.relation B) (and (tptp.subset _let_1 (tptp.relation_field B)) (tptp.subset _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in A (tptp.relation_dom (tptp.relation_composition C B))) (and (tptp.in A (tptp.relation_dom C)) (tptp.in (tptp.apply C A) (tptp.relation_dom B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (forall ((E $$unsorted)) (=> (and (tptp.relation E) (tptp.function E)) (=> (tptp.in C A) (or (= B tptp.empty_set) (= (tptp.apply (tptp.relation_composition D E) C) (tptp.apply E (tptp.apply D C))))))))) (forall ((A $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.proper_subset A B) (tptp.in A B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (tptp.subset A (tptp.cartesian_product2 (tptp.relation_dom A) (tptp.relation_rng A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (tptp.subset (tptp.fiber (tptp.relation_restriction C A) B) (tptp.fiber C B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (let ((_let_1 (tptp.relation_composition C B))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 A) (tptp.apply B (tptp.apply C A))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C B A) (= (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair D E) C)))))) (= (tptp.relation_dom_as_subset B A C) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.reflexive B) (tptp.reflexive (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.apply (tptp.relation_composition B C) A) (tptp.apply C (tptp.apply B A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in A B) (tptp.ordinal A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (= (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair E D) C)))))) (= (tptp.relation_rng_as_subset A B C) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.connected B) (tptp.connected (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (and (not (tptp.in A B)) (not (= A B)) (not (tptp.in B A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.transitive B) (tptp.transitive (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset A B) (and (tptp.subset (tptp.relation_dom A) (tptp.relation_dom B)) (tptp.subset (tptp.relation_rng A) (tptp.relation_rng B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.antisymmetric B) (tptp.antisymmetric (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.relation_restriction B A))) (=> (tptp.relation B) (=> (tptp.well_orders B A) (and (= (tptp.relation_field _let_1) A) (tptp.well_ordering _let_1)))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.relation B) (tptp.well_orders B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (not (and (forall ((B $$unsorted)) (not (and (tptp.in B A) (= B tptp.empty_set)))) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (not (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in (tptp.apply B C) 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 $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.reflexive (tptp.inclusion_relation A))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_field C))) (=> (tptp.relation C) (=> (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A _let_1) (tptp.in B _let_1)))))) (forall ((A $$unsorted)) (=> (forall ((B $$unsorted)) (=> (tptp.in B A) (and (tptp.ordinal B) (tptp.subset B A)))) (tptp.ordinal A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_founded_relation B) (tptp.well_founded_relation (tptp.relation_restriction B A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.ordinal B) (not (and (tptp.subset A B) (not (= A tptp.empty_set)) (forall ((C $$unsorted)) (=> (tptp.ordinal C) (not (and (tptp.in C A) (forall ((D $$unsorted)) (=> (tptp.ordinal D) (=> (tptp.in D A) (tptp.ordinal_subset C D)))))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (tptp.well_ordering B) (tptp.well_ordering (tptp.relation_restriction B A))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (= (tptp.in A B) (tptp.ordinal_subset (tptp.succ A) B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.identity_relation A)) (and (= (tptp.relation_dom B) A) (forall ((C $$unsorted)) (=> (tptp.in C A) (= (tptp.apply B C) C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in B A) (= (tptp.apply (tptp.identity_relation A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (tptp.relation A) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (=> (and (tptp.well_ordering B) (tptp.subset A (tptp.relation_field B))) (= (tptp.relation_field (tptp.relation_restriction B A)) A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.in B C) (tptp.in C A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted)) (tptp.transitive (tptp.inclusion_relation 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 $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (= (tptp.being_limit_ordinal A) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (=> (tptp.in B A) (tptp.in (tptp.succ B) A))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.being_limit_ordinal A))) (=> (tptp.ordinal A) (and (not (and (not _let_1) (forall ((B $$unsorted)) (=> (tptp.ordinal B) (not (= A (tptp.succ B))))))) (not (and (exists ((B $$unsorted)) (and (tptp.ordinal B) (= A (tptp.succ B)))) _let_1)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_composition A B)) (tptp.relation_rng B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) _let_2 (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_rng A) (tptp.relation_dom B)) (= (tptp.relation_dom (tptp.relation_composition A B)) (tptp.relation_dom A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (=> (tptp.subset (tptp.relation_dom A) (tptp.relation_rng B)) (= (tptp.relation_rng (tptp.relation_composition B A)) (tptp.relation_rng A))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (tptp.relation_isomorphism B A (tptp.function_inverse C))))))))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.connected (tptp.inclusion_relation A)))) (forall ((A $$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)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.relation_isomorphism A B C) (and (=> (tptp.reflexive A) (tptp.reflexive B)) (=> (tptp.transitive A) (tptp.transitive B)) (=> (tptp.connected A) (tptp.connected B)) (=> (tptp.antisymmetric A) (tptp.antisymmetric B)) (=> (tptp.well_founded_relation A) (tptp.well_founded_relation B)))))))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (forall ((B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (= (= B (tptp.function_inverse A)) (and (= (tptp.relation_dom B) (tptp.relation_rng A)) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (and (tptp.in C (tptp.relation_rng A)) (= D (tptp.apply B C))))) (let ((_let_2 (and (tptp.in D (tptp.relation_dom A)) (= C (tptp.apply A D))))) (and (=> _let_1 _let_2) (=> _let_2 _let_1)))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (and (tptp.well_ordering A) (tptp.relation_isomorphism A B C)) (tptp.well_ordering B)))))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function_inverse A))) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (and (= (tptp.relation_rng A) (tptp.relation_dom _let_1)) (= (tptp.relation_dom A) (tptp.relation_rng _let_1))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (forall ((B $$unsorted) (C $$unsorted)) (not (tptp.in (tptp.ordered_pair B C) A))) (= A tptp.empty_set)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.function_inverse B))) (=> (and (tptp.relation B) (tptp.function B)) (=> (and (tptp.one_to_one B) (tptp.in A (tptp.relation_rng B))) (and (= A (tptp.apply B (tptp.apply _let_1 A))) (= A (tptp.apply (tptp.relation_composition _let_1 B) A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (tptp.is_well_founded_in A (tptp.relation_field A))))) (forall ((A $$unsorted)) (tptp.antisymmetric (tptp.inclusion_relation A))) (and (= (tptp.relation_dom tptp.empty_set) tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (tptp.one_to_one A) (tptp.one_to_one (tptp.function_inverse A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted)) (=> (tptp.relation A) (=> (or (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)) (= A tptp.empty_set)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (= (tptp.relation_dom A) tptp.empty_set) (= (tptp.relation_rng A) tptp.empty_set)))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (forall ((C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (= B (tptp.relation_dom_restriction C A)) (and (= (tptp.relation_dom B) (tptp.set_intersection2 (tptp.relation_dom C) A)) (forall ((D $$unsorted)) (=> (tptp.in D (tptp.relation_dom B)) (= (tptp.apply B D) (tptp.apply C D)))))))))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.function D) (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (tptp.in C A) (or (= B tptp.empty_set) (tptp.in (tptp.apply D C) (tptp.relation_rng D)))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_founded_relation (tptp.inclusion_relation A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom_restriction C A))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 B) (tptp.apply C B)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.identity_relation A))) (and (= (tptp.relation_dom _let_1) A) (= (tptp.relation_rng _let_1) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in B A) (= (tptp.apply (tptp.relation_dom_restriction C A) B) (tptp.apply C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair A B))) (=> (tptp.relation D) (= (tptp.in _let_1 (tptp.relation_composition (tptp.identity_relation C) D)) (and (tptp.in A C) (tptp.in _let_1 D)))))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ordered_pair A B))) (and (= (tptp.pair_first _let_1) A) (= (tptp.pair_second _let_1) B)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (tptp.in D C)))))))))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (tptp.well_ordering (tptp.inclusion_relation A)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (tptp.in A (tptp.relation_dom (tptp.relation_dom_restriction C B))) (and (tptp.in A B) (tptp.in A (tptp.relation_dom C)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_dom_restriction B A) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) _let_1 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_orders A (tptp.relation_field A)) (tptp.well_ordering A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom (tptp.relation_dom_restriction B A)) (tptp.set_intersection2 (tptp.relation_dom B) A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_dom_restriction B A) (tptp.relation_composition (tptp.identity_relation A) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_rng (tptp.relation_dom_restriction B A)) (tptp.relation_rng B)))) (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.function D))) (=> (and _let_1 (tptp.quasi_total D A B) (tptp.relation_of2_as_subset D A B)) (=> (tptp.subset B C) (or (and (= B tptp.empty_set) (not (= A tptp.empty_set))) (and _let_1 (tptp.quasi_total D A C) (tptp.relation_of2_as_subset D A C))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.57/26.74  )
% 26.57/26.74  % SZS output end Proof for SEU293+2
% 26.57/26.74  % cvc5---1.0.5 exiting
% 26.57/26.74  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------