%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET255-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n003.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 14:38:22 EDT 2023

% Result   : Unsatisfiable 4.56s 4.74s
% Output   : Proof 4.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET255-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat Aug 26 13:59:54 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.22/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.50  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.UlSPuWl1cq/cvc5---1.0.5_19019.p...
% 0.22/0.52  ------- get file name : TPTP file name is SET255-6
% 0.22/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_19019.smt2...
% 0.22/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 4.56/4.74  % SZS status Unsatisfiable for SET255-6
% 4.56/4.74  % SZS output start Proof for SET255-6
% 4.56/4.74  (
% 4.56/4.74  (let ((_let_1 (tptp.restrict tptp.x tptp.y2 tptp.z))) (let ((_let_2 (tptp.restrict tptp.x tptp.y1 tptp.z))) (let ((_let_3 (tptp.subclass _let_2 _let_1))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.subclass tptp.y1 tptp.y2))) (let ((_let_6 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_7 (tptp.cross_product tptp.universal_class _let_6))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))) (let ((_let_9 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))) (let ((_let_11 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_12 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))))) (let ((_let_13 (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))))) (let ((_let_14 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))))) (let ((_let_15 (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))))) (let ((_let_16 (forall ((X $$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 $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_19 (tptp.not_subclass_element _let_2 _let_1))) (let ((_let_20 (tptp.first _let_19))) (let ((_let_21 (tptp.member _let_20 tptp.y2))) (let ((_let_22 (tptp.member _let_20 tptp.y1))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_5))) (let ((_let_25 (or _let_24 _let_23 _let_21))) (let ((_let_26 (_let_18))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (not _let_25))) (let ((_let_29 (tptp.cross_product tptp.y1 tptp.z))) (let ((_let_30 (tptp.second _let_19))) (let ((_let_31 (tptp.ordered_pair _let_20 _let_30))) (let ((_let_32 (tptp.member _let_31 _let_29))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_22))) (let ((_let_35 (_let_15))) (let ((_let_36 (ASSUME :args _let_35))) (let ((_let_37 (= _let_19 _let_31))) (let ((_let_38 (tptp.member _let_19 _let_29))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37))) (let ((_let_41 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= Z (tptp.ordered_pair (tptp.first Z) (tptp.second Z))))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (tptp.intersection _let_29 tptp.x))) (let ((_let_44 (tptp.member _let_19 _let_43))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_38))) (let ((_let_47 (_let_11))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (= _let_2 _let_43))) (let ((_let_50 (tptp.member _let_19 _let_2))) (let ((_let_51 (_let_8))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 ((tptp.restrict Xr X Y)))) (let ((_let_54 (or _let_50 _let_3))) (let ((_let_55 (_let_17))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (ASSUME :args (_let_4)))) (let ((_let_58 (and _let_50 _let_49))) (let ((_let_59 (_let_50 _let_49))) (let ((_let_60 (ASSUME :args (_let_50)))) (let ((_let_61 (APPLY_UF tptp.member))) (let ((_let_62 (ASSUME :args (_let_49)))) (let ((_let_63 (REFL :args (_let_19)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_58)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_60 _let_62) (SCOPE (TRUE_ELIM (TRANS (CONG _let_63 (SYMM _let_62) :args _let_61) (TRUE_INTRO _let_60))) :args _let_59)) :args _let_59)) :args (true _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_3 _let_50 (not _let_54)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_2 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_55)) _let_56 :args (_let_54 false _let_17)) :args (_let_50 true _let_3 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.y1 tptp.z tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_53)) :args _let_51))) _let_52 :args (_let_49 false _let_8)) :args (_let_44 false _let_50 false _let_49)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_38 (not _let_46)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_19 _let_29 tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_47)) _let_48 :args (_let_46 false _let_11)) :args (_let_38 false _let_44 false _let_46)))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_37 (not _let_40)))) _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_19 tptp.y1 tptp.z QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.cross_product X Y)) false))))) :args (_let_41))) _let_42 :args (_let_40 false _let_41)) :args (_let_37 false _let_38 false _let_40)))) (let ((_let_67 (and _let_38 _let_37))) (let ((_let_68 (_let_38 _let_37))) (let ((_let_69 (ASSUME :args (_let_38)))) (let ((_let_70 (ASSUME :args (_let_37)))) (let ((_let_71 (SYMM _let_70))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_69 _let_70) (SCOPE (TRUE_ELIM (TRANS (CONG _let_71 (REFL :args (_let_29)) :args _let_61) (TRUE_INTRO _let_69))) :args _let_68)) :args _let_68)) :args (true _let_67)) _let_65 _let_66 :args (_let_32 false _let_38 false _let_37)))) (let ((_let_73 (tptp.cross_product tptp.y2 tptp.z))) (let ((_let_74 (tptp.member _let_31 _let_73))) (let ((_let_75 (tptp.member _let_30 tptp.z))) (let ((_let_76 (not _let_75))) (let ((_let_77 (not _let_21))) (let ((_let_78 (or _let_77 _let_76 _let_74))) (let ((_let_79 (_let_13))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (tptp.member _let_19 _let_73))) (let ((_let_82 (not _let_74))) (let ((_let_83 (tptp.intersection _let_73 tptp.x))) (let ((_let_84 (tptp.member _let_19 _let_83))) (let ((_let_85 (tptp.member _let_19 tptp.x))) (let ((_let_86 (not _let_85))) (let ((_let_87 (not _let_81))) (let ((_let_88 (or _let_87 _let_86 _let_84))) (let ((_let_89 (_let_9))) (let ((_let_90 (ASSUME :args _let_89))) (let ((_let_91 (= _let_1 _let_83))) (let ((_let_92 (tptp.member _let_19 _let_1))) (let ((_let_93 (not _let_84))) (let ((_let_94 (not _let_92))) (let ((_let_95 (or _let_94 _let_3))) (let ((_let_96 (_let_16))) (let ((_let_97 (ASSUME :args _let_96))) (let ((_let_98 (or))) (let ((_let_99 (and _let_94 _let_91))) (let ((_let_100 (_let_94 _let_91))) (let ((_let_101 (ASSUME :args (_let_94)))) (let ((_let_102 (ASSUME :args (_let_91)))) (let ((_let_103 (or _let_45 _let_85))) (let ((_let_104 (_let_10))) (let ((_let_105 (ASSUME :args _let_104))) (let ((_let_106 (and _let_87 _let_37))) (let ((_let_107 (_let_87 _let_37))) (let ((_let_108 (ASSUME :args (_let_87)))) (let ((_let_109 (or _let_33 _let_75))) (let ((_let_110 (_let_14))) (let ((_let_111 (ASSUME :args _let_110))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.y1 tptp.y2 _let_20 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subclass X Y) false)) (not (= (tptp.member U X) false))))) :args _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_21 _let_23 _let_28))) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_77 _let_76 _let_74 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_109)) :args ((or _let_33 _let_75 (not _let_109)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_111 :args (_let_20 _let_30 tptp.y1 tptp.z QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_110)) _let_111 :args (_let_109 false _let_14)) :args (_let_75 false _let_32 false _let_109)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_106)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_108 _let_70) (SCOPE (FALSE_ELIM (TRANS (CONG _let_71 (REFL :args (_let_73)) :args _let_61) (FALSE_INTRO _let_108))) :args _let_107)) :args _let_107)) :args (true _let_106)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_81))) (REFL :args ((not _let_37))) (REFL :args (_let_82)) :args _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_87 _let_86 _let_84 (not _let_88)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_103)) :args ((or _let_45 _let_85 (not _let_103)))) _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_105 :args (_let_19 _let_29 tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_104)) _let_105 :args (_let_103 false _let_10)) :args (_let_85 false _let_44 false _let_103)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_99)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_101 _let_102) (SCOPE (FALSE_ELIM (TRANS (CONG _let_63 (SYMM _let_102) :args _let_61) (FALSE_INTRO _let_101))) :args _let_100)) :args _let_100)) :args (true _let_99)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_94) _let_92))) (REFL :args ((not _let_91))) (REFL :args (_let_93)) :args _let_98)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_95)) :args ((or _let_3 _let_94 (not _let_95)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_97 :args (_let_2 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_96)) _let_97 :args (_let_95 false _let_16)) :args (_let_94 true _let_3 false _let_95)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.y2 tptp.z tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_53)) :args _let_51))) _let_52 :args (_let_91 false _let_8)) :args (_let_93 true _let_92 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_90 :args (_let_19 _let_73 tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) true))))) :args _let_89)) _let_90 :args (_let_88 false _let_9)) :args (_let_87 false _let_85 true _let_84 false _let_88)) _let_66 :args (_let_82 true _let_81 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_20 tptp.y2 _let_30 tptp.z QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) true))))) :args _let_79)) _let_80 :args (_let_78 false _let_13)) :args (_let_77 false _let_75 true _let_74 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_22 (not _let_34)))) _let_72 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (_let_20 _let_30 tptp.y1 tptp.z QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_35)) _let_36 :args (_let_34 false _let_15)) :args (_let_22 false _let_32 false _let_34)) :args (_let_28 false _let_5 true _let_21 false _let_22)) _let_27 :args (false true _let_25 false _let_18)) :args (_let_18 _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))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) _let_15 _let_14 _let_13 _let_12 (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)))) _let_11 _let_10 _let_9 (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 $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) _let_8 (forall ((X $$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 $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (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 $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (tptp.function tptp.choice) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (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)) (tptp.subclass (tptp.compose_class X) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X))) (= (tptp.compose X Y) Z))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_7) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.composition_function)) (= (tptp.compose X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.compose X Y))) tptp.composition_function))) (tptp.subclass tptp.domain_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.domain_relation)) (= (tptp.domain_of X) Y))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.domain_of X)) tptp.domain_relation))) (forall ((X $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued1 X))) (forall ((X $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued2 X))) (forall ((X $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))) (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation) tptp.singleton_relation) (tptp.subclass tptp.application_function _let_7) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (tptp.member Y (tptp.domain_of X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (= (tptp.apply X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class)))) (not (tptp.member Y (tptp.domain_of X))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.apply X Y))) tptp.application_function))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subclass (tptp.range_of Xf) Y))) (forall ((Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.subclass (tptp.range_of Xf) Y)) (tptp.maps Xf (tptp.domain_of Xf) Y))) _let_5 _let_4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 4.56/4.74  )
% 4.56/4.76  % SZS output end Proof for SET255-6
% 4.56/4.76  % cvc5---1.0.5 exiting
% 4.56/4.76  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------