%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU291+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 2.55s 2.81s
% Output   : Proof 2.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.16  % Problem    : SEU291+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.17  % Command    : do_cvc5 %s %d
% 0.16/0.38  % Computer : n025.cluster.edu
% 0.16/0.38  % Model    : x86_64 x86_64
% 0.16/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38  % Memory   : 8042.1875MB
% 0.16/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38  % CPULimit   : 300
% 0.16/0.38  % WCLimit    : 300
% 0.16/0.38  % DateTime   : Thu Aug 24 00:27:21 EDT 2023
% 0.16/0.38  % CPUTime    : 
% 0.23/0.55  %----Proving TF0_NAR, FOF, or CNF
% 2.55/2.81  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.bvOe8uIhaY/cvc5---1.0.5_20640.p...
% 2.55/2.81  ------- get file name : TPTP file name is SEU291+2
% 2.55/2.81  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_20640.smt2...
% 2.55/2.81  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.55/2.81  % SZS status Theorem for SEU291+2
% 2.55/2.81  % SZS output start Proof for SEU291+2
% 2.55/2.81  (
% 2.55/2.81  (let ((_let_1 (not (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)))))))))) (let ((_let_2 (tptp.relation_dom tptp.empty_set))) (let ((_let_3 (and (= _let_2 tptp.empty_set) (= (tptp.relation_rng tptp.empty_set) tptp.empty_set)))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))) (let ((_let_6 (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 $$unsorted)) (not (tptp.in (tptp.ordered_pair D E) C)))))) (= (tptp.relation_dom_as_subset B A C) B)))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (tptp.relation_of2_as_subset D C A) (=> (tptp.subset A B) (tptp.relation_of2_as_subset D C B)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))) (let ((_let_9 (tptp.relation tptp.empty_set))) (let ((_let_10 (tptp.empty tptp.empty_set))) (let ((_let_11 (tptp.relation_empty_yielding tptp.empty_set))) (let ((_let_12 (forall ((A $$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_13 (= tptp.empty_set _let_2))) (let ((_let_14 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_15 (= tptp.empty_set _let_14))) (let ((_let_16 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_17 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_16))) (let ((_let_18 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_19 (= _let_16 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_14)))) (let ((_let_20 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_21 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_22 (= _let_21 _let_15))) (let ((_let_23 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_24 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_25 (tptp.relation_of2_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_26 (tptp.quasi_total SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17))) (let ((_let_27 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_28 (and _let_27 _let_26 _let_25))) (let ((_let_29 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_30 (not _let_29))) (let ((_let_31 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_32 (and _let_31 _let_30))) (let ((_let_33 (not _let_21))) (let ((_let_34 (tptp.relation_of2_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_35 (not _let_34))) (let ((_let_36 (tptp.quasi_total SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_37 (not _let_36))) (let ((_let_38 (not _let_27))) (let ((_let_39 (or _let_38 _let_37 _let_35 _let_33 _let_32 _let_28))) (let ((_let_40 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.function D))) (or (not _let_1) (not (tptp.quasi_total D A B)) (not (tptp.relation_of2_as_subset D A B)) (not (tptp.subset B C)) (and (= tptp.empty_set B) (not (= tptp.empty_set A))) (and _let_1 (tptp.quasi_total D A C) (tptp.relation_of2_as_subset D A C))))))) (let ((_let_41 (not _let_39))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (or))) (let ((_let_44 (not _let_40))) (let ((_let_45 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_42) :args (_let_44))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_40))) (REFL :args (_let_41)) :args _let_43)) _let_42 :args (_let_41 true _let_40)))) (let ((_let_46 (REFL :args (_let_39)))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 3)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_21))) :args _let_43)) :args ((or _let_21 _let_39))) _let_45 :args (_let_21 true _let_39)))) (let ((_let_48 (or _let_33 _let_17))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= A (tptp.set_intersection2 A B)))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (not _let_18))) (let ((_let_52 (not _let_26))) (let ((_let_53 (or _let_35 _let_33 _let_25))) (let ((_let_54 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (tptp.relation_of2_as_subset D C A)) (not (tptp.subset A B)) (tptp.relation_of2_as_subset D C B))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 2)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) :args _let_43)) :args ((or _let_34 _let_39))) _let_45 :args (_let_34 true _let_39)))) (let ((_let_57 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_35 _let_33 _let_25 (not _let_53)))) _let_56 _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.relation_of2_as_subset D C A) false)) (not (= (tptp.subset A B) false))))) :args (_let_54))) _let_55 :args (_let_53 false _let_54)) :args (_let_25 false _let_34 false _let_21 false _let_53)))) (let ((_let_58 (not _let_25))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_28)) :args ((or _let_38 _let_28 _let_52 _let_58))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 0)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_27))) :args _let_43)) :args ((or _let_27 _let_39))) _let_45 :args (_let_27 true _let_39)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 5)) _let_45 :args ((not _let_28) true _let_39)) _let_57 :args (_let_52 false _let_27 true _let_28 false _let_25)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_39 1)) (CONG _let_46 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_43)) :args ((or _let_36 _let_39))) _let_45 :args (_let_36 true _let_39)))) (let ((_let_61 (_let_51))) (let ((_let_62 (ASSUME :args (_let_52)))) (let ((_let_63 (ASSUME :args (_let_18)))) (let ((_let_64 (ASSUME :args (_let_36)))) (let ((_let_65 (_let_4))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (and _let_20 _let_30))) (let ((_let_68 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 (tptp.relation_dom_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_69 (= _let_26 _let_68))) (let ((_let_70 (or _let_67 _let_69))) (let ((_let_71 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_72 (not _let_20))) (let ((_let_73 (and _let_70 (or _let_72 _let_29 (= _let_26 _let_71))))) (let ((_let_74 (or _let_58 _let_73))) (let ((_let_75 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.quasi_total C A B))) (let ((_let_2 (= tptp.empty_set A))) (let ((_let_3 (= tptp.empty_set B))) (or (not (tptp.relation_of2_as_subset C A B)) (and (or (and _let_3 (not _let_2)) (= _let_1 (= A (tptp.relation_dom_as_subset A B C)))) (or (not _let_3) _let_2 (= _let_1 (= tptp.empty_set C))))))))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (_let_75))) (let ((_let_78 ((not (= (tptp.relation_of2_as_subset C A B) false))))) (let ((_let_79 (not _let_69))) (let ((_let_80 (forall ((D $$unsorted)) (or (not (tptp.in D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (not (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair D E) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))))))) (let ((_let_81 (= _let_80 _let_68))) (let ((_let_82 (or _let_58 _let_81))) (let ((_let_83 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.relation_of2_as_subset C B A)) (= (forall ((D $$unsorted)) (or (not (tptp.in D B)) (not (forall ((E $$unsorted)) (not (tptp.in (tptp.ordered_pair D E) C)))))) (= B (tptp.relation_dom_as_subset B A C))))))) (let ((_let_84 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_85 (_let_83))) (let ((_let_86 ((not (= (tptp.relation_of2_as_subset C B A) false))))) (let ((_let_87 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 (tptp.relation_dom_as_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)))) (let ((_let_88 (= _let_87 _let_80))) (let ((_let_89 (or _let_35 _let_88))) (let ((_let_90 (= _let_36 _let_87))) (let ((_let_91 (or _let_32 _let_90))) (let ((_let_92 (and _let_91 (or (not _let_31) _let_29 (= _let_36 _let_71))))) (let ((_let_93 (or _let_35 _let_92))) (let ((_let_94 (= tptp.empty_set _let_16))) (let ((_let_95 (ASSUME :args (_let_15)))) (let ((_let_96 (ASSUME :args (_let_20)))) (let ((_let_97 (SYMM _let_96))) (let ((_let_98 (ASSUME :args (_let_13)))) (let ((_let_99 (SYMM (SYMM _let_98)))) (let ((_let_100 (SYMM _let_95))) (let ((_let_101 (ASSUME :args (_let_17)))) (let ((_let_102 (ASSUME :args _let_61))) (let ((_let_103 (ASSUME :args (_let_19)))) (let ((_let_104 (SYMM _let_100))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_98 (MODUS_PONENS (AND_INTRO _let_103 _let_95 _let_96) (SCOPE (TRANS _let_104 (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16)) (TRANS _let_97 _let_104) :args (APPLY_UF tptp.set_difference)) (SYMM _let_103)) :args (_let_19 _let_15 _let_20))) _let_101 _let_95 _let_96 _let_102) :args (_let_13 _let_51 _let_15 _let_17 _let_20 _let_19)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_102)) (TRUE_INTRO (TRANS (TRANS (SYMM (SYMM _let_101)) (SYMM (ASSUME :args (_let_94)))) _let_99 (SYMM (TRANS _let_100 _let_99)) (SYMM (TRANS _let_97 _let_95)))))) :args (_let_13 _let_94 _let_17 _let_15 _let_20 _let_51)) :args ((not (and _let_13 _let_51 _let_15 _let_17 _let_20 _let_19)) SB_LITERAL))) (CONG (REFL :args ((not _let_13))) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_18))) (REFL :args ((not _let_15))) (REFL :args ((not _let_17))) (REFL :args (_let_72)) (REFL :args ((not _let_19))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_67 0)) :args ((or _let_20 (not _let_67)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_67 _let_69 (not _let_70)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_69)) :args ((or _let_26 (not _let_68) _let_79))) _let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_81)) :args ((or (not _let_80) _let_68 (not _let_81)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_88)) :args ((or _let_80 (not _let_87) (not _let_88)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_90)) :args ((or _let_37 _let_87 (not _let_90)))) _let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_32 _let_90 (not _let_91)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_39 4)) _let_45 :args ((not _let_32) true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_92 0)) :args ((or _let_91 (not _let_92)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_35 _let_92 (not _let_93)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_93 false _let_75)) :args (_let_92 false _let_34 false _let_93)) :args (_let_91 false _let_92)) :args (_let_90 true _let_32 false _let_91)) :args (_let_87 false _let_36 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_35 _let_88 (not _let_89)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85))) _let_84 :args (_let_89 false _let_83)) :args (_let_88 false _let_34 false _let_89)) :args (_let_80 false _let_87 false _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_82)) :args ((or _let_58 _let_81 (not _let_82)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_84 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_86)) :args _let_85)) _let_84 :args (_let_82 false _let_83)) :args (_let_81 false _let_25 false _let_82)) :args (_let_68 false _let_80 false _let_81)) :args (_let_79 true _let_26 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_73 0)) :args ((or _let_70 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_58 _let_73 (not _let_74)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_78)) :args _let_77)) _let_76 :args (_let_74 false _let_75)) :args (_let_73 false _let_25 false _let_74)) :args (_let_70 false _let_73)) :args (_let_67 true _let_69 false _let_70)) :args (_let_20 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_66 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_65))) _let_66 :args (_let_19 false _let_4)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_62 _let_63 _let_64) :args (_let_36 _let_52 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_64)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18)) (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15)) (SYMM (SYMM _let_63)) :args (APPLY_UF tptp.quasi_total)) (FALSE_INTRO _let_62))) :args (_let_52 _let_18 _let_36)) :args ((not (and _let_36 _let_52 _let_18)) SB_LITERAL))) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_52) _let_26))) (REFL :args _let_61) :args _let_43)) _let_60 _let_59 :args (_let_51 false _let_36 true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_48)) :args ((or 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:args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted)) (=> (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)) (tptp.ordinal A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A) (tptp.ordinal A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.ordinal A) (tptp.ordinal B)) (or (tptp.ordinal_subset A B) (tptp.ordinal_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.identity_relation A)) (forall ((C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair C D) B) (and (tptp.in C A) (= C D))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_dom_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in D B) (tptp.in _let_1 A)))))))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in E (tptp.relation_dom A)) (tptp.in E B) (= D (tptp.apply A E)))))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (forall ((C $$unsorted)) (=> (tptp.relation C) (= (= C (tptp.relation_rng_restriction A B)) (forall ((D $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.ordered_pair D E))) (= (tptp.in _let_1 C) (and (tptp.in E A) (tptp.in _let_1 B)))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.antisymmetric A) (tptp.is_antisymmetric_in A (tptp.relation_field A))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D (tptp.relation_dom A)) (tptp.in (tptp.apply A D) B)))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair E D) A) (tptp.in E B))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.relation_inverse_image A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted)) (and (tptp.in (tptp.ordered_pair D E) A) (tptp.in E B))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.connected A) (tptp.is_connected_in A (tptp.relation_field A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.transitive A) (tptp.is_transitive_in A (tptp.relation_field A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (= D (tptp.unordered_triple A B C)) (forall ((E $$unsorted)) (= (tptp.in E D) (not (and (not (= E A)) (not (= E B)) (not (= E C)))))))) (forall ((A $$unsorted)) (= (tptp.function A) (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.in (tptp.ordered_pair B C) A) (tptp.in (tptp.ordered_pair B D) A)) (= C D))))) _let_12 (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.ordered_pair B C))) (forall ((B $$unsorted)) (= (= B (tptp.pair_first A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.ordered_pair C D)) (= B C))))))) (forall ((A $$unsorted)) (= (tptp.succ A) (tptp.set_union2 A (tptp.singleton A)))) (forall ((A $$unsorted)) (= (tptp.relation A) (forall ((B $$unsorted)) (not (and (tptp.in B A) (forall ((C $$unsorted) (D $$unsorted)) (not (= B (tptp.ordered_pair C D))))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_reflexive_in A B) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.ordered_pair C C) A))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2 C A B) (tptp.subset C (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (= B (tptp.set_meet A)))) (let ((_let_2 (= A tptp.empty_set))) (and (=> (not _let_2) (= _let_1 (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> _let_2 (= _let_1 (= B tptp.empty_set))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted) (C $$unsorted)) (= (= C (tptp.fiber A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (not (= D B)) (tptp.in (tptp.ordered_pair D B) A)))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (= B (tptp.inclusion_relation A)) (and (= (tptp.relation_field B) A) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C A) (tptp.in D A)) (= (tptp.in (tptp.ordered_pair C D) B) (tptp.subset C D)))))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted)) (=> (exists ((B $$unsorted) (C $$unsorted)) (= A (tptp.ordered_pair B C))) (forall ((B $$unsorted)) (= (= B (tptp.pair_second A)) (forall ((C $$unsorted) (D $$unsorted)) (=> (= A (tptp.ordered_pair C D)) (= B D))))))) (forall ((A $$unsorted)) (= (tptp.epsilon_transitive A) (forall ((B $$unsorted)) (=> (tptp.in B A) (tptp.subset B A))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (= A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair C D))) (= (tptp.in _let_1 A) (tptp.in _let_1 B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_founded_relation A) (forall ((B $$unsorted)) (not (and (tptp.subset B (tptp.relation_field A)) (not (= B tptp.empty_set)) (forall ((C $$unsorted)) (not (and (tptp.in C B) (tptp.disjoint (tptp.fiber A C) B)))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) (forall ((A $$unsorted)) (= (tptp.epsilon_connected A) (forall ((B $$unsorted) (C $$unsorted)) (not (and (tptp.in B A) (tptp.in C A) (not (tptp.in B C)) (not (= B C)) (not (tptp.in C B))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (=> (tptp.relation B) (= (tptp.subset A B) (forall ((C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.ordered_pair C D))) (=> (tptp.in _let_1 A) (tptp.in _let_1 B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_well_founded_in A B) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (= C tptp.empty_set)) (forall ((D $$unsorted)) (not (and (tptp.in D C) (tptp.disjoint (tptp.fiber A D) C))))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (= C (tptp.apply A B)))) (let ((_let_2 (tptp.in B (tptp.relation_dom A)))) (and (=> _let_2 (= _let_1 (tptp.in (tptp.ordered_pair B C) A))) (=> (not _let_2) (= _let_1 (= C tptp.empty_set))))))))) (forall ((A $$unsorted)) (= (tptp.ordinal A) (and (tptp.epsilon_transitive A) (tptp.epsilon_connected A)))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (= B (tptp.relation_dom A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (tptp.in (tptp.ordered_pair C D) A)))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (forall ((B $$unsorted)) (= (tptp.is_antisymmetric_in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.in D B) (tptp.in (tptp.ordered_pair C D) A) (tptp.in (tptp.ordered_pair D C) A)) (= C D))))))) (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.well_ordering A) (and (tptp.reflexive A) (tptp.transitive A) (tptp.antisymmetric A) (tptp.connected A) (tptp.well_founded_relation A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equipotent A B) (exists ((C $$unsorted)) (and (tptp.relation C) (tptp.function C) (tptp.one_to_one C) (= (tptp.relation_dom C) A) (= (tptp.relation_rng C) B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (forall ((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 $$unsorted)) (not (and (tptp.in C B) (tptp.in D B) (not (= C D)) (not (tptp.in 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(tptp.ordered_pair (tptp.apply C D) (tptp.apply C E)) B))))))))))))) (forall ((A $$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 $$unsorted)) (=> (tptp.relation B) (tptp.relation (tptp.relation_rng_restriction A B)))) true true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (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 $$unsorted)) (let ((_let_1 (tptp.relation_inverse A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (and _let_10 _let_9 _let_11) (forall ((A $$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 $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_10 (forall ((A $$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_9 _let_11 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) _let_10 (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_10 _let_9) (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 $$unsorted)) (=> (tptp.relation C) (not (tptp.well_orders C A)))))))) _let_8 (forall ((A $$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))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_dom_as_subset A B C) (tptp.relation_dom C)))) (forall ((A $$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 $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (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 $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (= (tptp.relation_rng (tptp.relation_rng_restriction A B)) (tptp.set_intersection2 (tptp.relation_rng B) A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (and (tptp.subset (tptp.relation_dom C) A) (tptp.subset (tptp.relation_rng C) B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (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 $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$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))))))) (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)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.relation B) (tptp.subset (tptp.relation_inverse_image B A) (tptp.relation_dom B)))) _let_7 (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 $$unsorted)) (=> (tptp.epsilon_transitive A) (forall ((B $$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 $$unsorted)) (let ((_let_1 (tptp.relation_composition C B))) (=> (and (tptp.relation C) (tptp.function C)) (=> (tptp.in A (tptp.relation_dom _let_1)) (= (tptp.apply _let_1 A) (tptp.apply B (tptp.apply C A))))))))) _let_6 (forall ((A $$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))))))))))) _let_5 (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 $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$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 $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B)))))) _let_4 (forall ((A $$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))) _let_3 (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)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.relation C) (tptp.function C)) (= (tptp.in (tptp.ordered_pair A B) C) (and (tptp.in A (tptp.relation_dom C)) (= B (tptp.apply C A)))))) (forall ((A $$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 $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) _let_1 (forall ((A $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.55/2.82  )
% 2.55/2.82  % SZS output end Proof for SEU291+2
% 2.55/2.82  % cvc5---1.0.5 exiting
% 2.55/2.82  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------