%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET067-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n028.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 14:37:21 EDT 2023

% Result   : Unsatisfiable 4.80s 5.04s
% Output   : Proof 4.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET067-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command    : do_cvc5 %s %d
% 0.12/0.34  % Computer : n028.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Sat Aug 26 09:16:22 EDT 2023
% 0.12/0.34  % CPUTime    : 
% 0.19/0.46  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.47  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.Hn2PEq9JHg/cvc5---1.0.5_27377.p...
% 0.19/0.48  ------- get file name : TPTP file name is SET067-7
% 0.19/0.49  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_27377.smt2...
% 0.19/0.49  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.80/5.04  % SZS status Unsatisfiable for SET067-7
% 4.80/5.04  % SZS output start Proof for SET067-7
% 4.80/5.04  (
% 4.80/5.04  (let ((_let_1 (tptp.unordered_pair tptp.x tptp.y))) (let ((_let_2 (tptp.singleton tptp.x))) (let ((_let_3 (tptp.subclass _let_2 _let_1))) (let ((_let_4 (not _let_3))) (let ((_let_5 (forall ((Z $$unsorted)) (not (tptp.member Z tptp.null_class))))) (let ((_let_6 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_7 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))) (let ((_let_8 (tptp.function tptp.choice))) (let ((_let_9 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))) (let ((_let_10 (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))))) (let ((_let_11 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_14 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_15 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_18 (tptp.unordered_pair tptp.x tptp.x))) (let ((_let_19 (tptp.unordered_pair _let_18 _let_18))) (let ((_let_20 (tptp.singleton _let_18))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (tptp.member _let_20 tptp.universal_class))) (let ((_let_23 (tptp.member _let_19 tptp.universal_class))) (let ((_let_24 (_let_12))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 ((tptp.singleton X)))) (let ((_let_27 (tptp.image tptp.choice _let_20))) (let ((_let_28 (tptp.member _let_27 tptp.universal_class))) (let ((_let_29 (not _let_22))) (let ((_let_30 (not _let_8))) (let ((_let_31 (or _let_30 _let_29 _let_28))) (let ((_let_32 (_let_10))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (tptp.sum_class _let_27))) (let ((_let_35 (tptp.member _let_34 tptp.universal_class))) (let ((_let_36 (not _let_28))) (let ((_let_37 (or _let_36 _let_35))) (let ((_let_38 (_let_11))) (let ((_let_39 (ASSUME :args _let_38))) (let ((_let_40 (tptp.apply tptp.choice _let_18))) (let ((_let_41 (= tptp.x _let_40))) (let ((_let_42 (= _let_40 _let_34))) (let ((_let_43 (tptp.member tptp.x tptp.universal_class))) (let ((_let_44 (not _let_35))) (let ((_let_45 (tptp.member _let_40 _let_18))) (let ((_let_46 (not _let_45))) (let ((_let_47 (or _let_46 _let_41 _let_41))) (let ((_let_48 (_let_15))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 ((not (= (tptp.member U (tptp.unordered_pair X Y)) false))))) (let ((_let_51 (= tptp.null_class _let_18))) (let ((_let_52 (tptp.member _let_18 tptp.universal_class))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51 _let_45))) (let ((_let_55 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (= _let_2 _let_18))) (let ((_let_58 (tptp.not_subclass_element _let_2 _let_1))) (let ((_let_59 (tptp.member _let_58 _let_2))) (let ((_let_60 (tptp.member _let_58 tptp.null_class))) (let ((_let_61 (not _let_51))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24))) _let_25 :args (_let_57 false _let_12)))) (let ((_let_63 (or _let_59 _let_3))) (let ((_let_64 (_let_17))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (ASSUME :args (_let_4)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_3 _let_59 (not _let_63)))) _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_2 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_64)) _let_65 :args (_let_63 false _let_17)) :args (_let_59 true _let_3 false _let_63)))) (let ((_let_68 (not _let_60))) (let ((_let_69 (_let_5))) (let ((_let_70 (ASSUME :args _let_69))) (let ((_let_71 (or))) (let ((_let_72 (ASSUME :args (_let_59)))) (let ((_let_73 (TRUE_INTRO _let_72))) (let ((_let_74 (APPLY_UF tptp.member))) (let ((_let_75 (ASSUME :args (_let_57)))) (let ((_let_76 (SYMM _let_75))) (let ((_let_77 (ASSUME :args (_let_51)))) (let ((_let_78 (REFL :args (_let_58)))) (let ((_let_79 (ASSUME :args (_let_68)))) (let ((_let_80 (_let_13))) (let ((_let_81 (ASSUME :args _let_80))) (let ((_let_82 ((tptp.unordered_pair X Y)))) (let ((_let_83 (_let_9))) (let ((_let_84 (ASSUME :args _let_83))) (let ((_let_85 (tptp.member tptp.x _let_1))) (let ((_let_86 (not _let_43))) (let ((_let_87 (or _let_86 _let_85))) (let ((_let_88 (_let_14))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (= tptp.x _let_58))) (let ((_let_91 (tptp.member _let_58 _let_1))) (let ((_let_92 (not _let_85))) (let ((_let_93 (tptp.member _let_58 _let_18))) (let ((_let_94 (not _let_93))) (let ((_let_95 (or _let_94 _let_90 _let_90))) (let ((_let_96 (and _let_59 _let_57))) (let ((_let_97 (_let_59 _let_57))) (let ((_let_98 (not _let_91))) (let ((_let_99 (or _let_98 _let_3))) (let ((_let_100 (_let_16))) (let ((_let_101 (ASSUME :args _let_100))) (let ((_let_102 (not _let_90))) (let ((_let_103 (and _let_98 _let_90))) (let ((_let_104 (_let_98 _let_90))) (let ((_let_105 (ASSUME :args (_let_98)))) (let ((_let_106 (ASSUME :args (_let_90)))) (let ((_let_107 (and _let_86 _let_42 _let_41))) (let ((_let_108 (ASSUME :args (_let_86)))) (let ((_let_109 (REFL :args (tptp.universal_class)))) (let ((_let_110 (ASSUME :args (_let_41)))) (let ((_let_111 (ASSUME :args (_let_42)))) (let ((_let_112 (not _let_23))) (let ((_let_113 (not _let_21))) (let ((_let_114 (ASSUME :args (_let_23)))) (let ((_let_115 (ASSUME :args (_let_21)))) (let ((_let_116 (ASSUME :args (_let_29)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_114 _let_115 _let_116) :args (_let_21 _let_29 _let_23)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_116)) (CONG (SYMM (SYMM _let_115)) _let_109 :args _let_74) (TRUE_INTRO _let_114))) :args (_let_23 _let_21 _let_29)) :args ((not (and _let_21 _let_29 _let_23)) SB_LITERAL))) (CONG (REFL :args (_let_113)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_22))) (REFL :args (_let_112)) :args _let_71)) :args ((or _let_22 _let_113 _let_112))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (_let_18 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_80)) _let_81 :args (_let_23 false _let_13)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_31)) :args ((or _let_30 _let_28 _let_29 (not _let_31)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_36 _let_35 (not _let_37)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_107)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_108 _let_110 _let_111) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_111) (SYMM _let_110)) _let_109 :args _let_74) (FALSE_INTRO _let_108))) :args (_let_86 _let_41 _let_42))) :args (_let_86 _let_42 _let_41))) :args (true _let_107)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_43))) (REFL :args ((not _let_42))) (REFL :args ((not _let_41))) (REFL :args (_let_44)) :args _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_86 _let_85 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_103)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_105 _let_106) (SCOPE (FALSE_ELIM (TRANS (CONG (SYMM (SYMM _let_106)) (REFL :args (_let_1)) :args _let_74) (FALSE_INTRO _let_105))) :args _let_104)) :args _let_104)) :args (true _let_103)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_98) _let_91))) (REFL :args (_let_102)) (REFL :args (_let_92)) :args _let_71)) :args ((or _let_91 _let_92 _let_102))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_99)) :args ((or _let_3 _let_98 (not _let_99)))) _let_66 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_101 :args (_let_2 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_100)) _let_101 :args (_let_99 false _let_16)) :args (_let_98 true _let_3 false _let_99)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_95))) :args ((or _let_94 _let_90 (not _let_95)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_96)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_72 _let_75) (SCOPE (TRUE_ELIM (TRANS (CONG _let_78 _let_76 :args _let_74) _let_73)) :args _let_97)) :args _let_97)) :args (true _let_96)) _let_67 _let_62 :args (_let_93 false _let_59 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_58 tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48))) _let_49 :args (_let_95 false _let_15)) :args (_let_90 false _let_93 false _let_95)) :args (_let_92 true _let_91 false _let_90)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_88)) _let_89 :args (_let_87 false _let_14)) :args (_let_86 true _let_85 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_84 :args (tptp.choice _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply Xf Y)))) :args _let_83))) _let_84 :args (_let_42 false _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_47))) :args ((or _let_46 _let_41 (not _let_47)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_53 _let_51 _let_45 (not _let_54)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_82)) :args _let_80)) _let_81 :args (_let_52 false _let_13)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_79 _let_77 _let_75 _let_72) :args (_let_59 _let_57 _let_51 _let_68)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_79)) (CONG _let_78 (TRANS (SYMM (SYMM _let_77)) _let_76) :args _let_74) _let_73)) :args (_let_68 _let_51 _let_57 _let_59)) :args ((not (and _let_59 _let_57 _let_51 _let_68)) SB_LITERAL))) (CONG (REFL :args ((not _let_59))) (REFL :args ((not _let_57))) (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_68) _let_60))) :args _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_58 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Z tptp.null_class) false))))) :args _let_69)) _let_70 :args (_let_68 false _let_5)) _let_67 _let_62 :args (_let_61 true _let_60 false _let_59 false _let_57)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y tptp.universal_class) false))))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_45 false _let_52 true _let_51 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_40 tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48))) _let_49 :args (_let_47 false _let_15)) :args (_let_41 false _let_45 false _let_47)) :args (_let_44 true _let_43 false _let_42 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (_let_27 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sum_class X)))) :args _let_38)) _let_39 :args (_let_37 false _let_11)) :args (_let_36 true _let_35 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_33 :args (tptp.choice _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.image Xf X)))) :args _let_32)) _let_33 :args (_let_31 false _let_10)) :args (_let_29 false _let_8 true _let_28 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_26)) :args _let_24))) _let_25 :args (_let_21 false _let_12)) :args (false false _let_23 true _let_22 false _let_21)) :args ((forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) _let_17 _let_16 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))) _let_15 _let_14 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) _let_13 _let_12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))) (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) _let_11 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) _let_10 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) _let_9 _let_8 _let_7 (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))) (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (tptp.intersection _let_6 (tptp.intersection _let_6 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))) (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (= (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V tptp.universal_class))) (forall ((X $$unsorted)) (tptp.subclass X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (tptp.member (tptp.not_subclass_element X Y) X) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (= X Y) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y) (tptp.member (tptp.not_subclass_element X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (not (tptp.member Y (tptp.intersection (tptp.complement X) X)))) _let_5 (forall ((X $$unsorted)) (tptp.subclass tptp.null_class X)) (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= X tptp.null_class))) (forall ((Z $$unsorted)) (or (= Z tptp.null_class) (tptp.member (tptp.not_subclass_element Z tptp.null_class) Z))) (tptp.member tptp.null_class tptp.universal_class) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair X Y) (tptp.unordered_pair Y X))) _let_4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.80/5.04  )
% 4.80/5.06  % SZS output end Proof for SET067-7
% 4.80/5.06  % cvc5---1.0.5 exiting
% 4.80/5.06  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------