%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET079-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n026.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 14:37:29 EDT 2023

% Result   : Unsatisfiable 13.28s 13.53s
% Output   : Proof 13.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET079-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 09:25:03 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.51  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.en1HkEW9kK/cvc5---1.0.5_26696.p...
% 0.22/0.52  ------- get file name : TPTP file name is SET079-6
% 0.22/0.53  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_26696.smt2...
% 0.22/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.59/10.77  --- Run --no-e-matching --full-saturate-quant at 5...
% 13.28/13.53  % SZS status Unsatisfiable for SET079-6
% 13.28/13.53  % SZS output start Proof for SET079-6
% 13.28/13.53  (
% 13.28/13.53  (let ((_let_1 (tptp.singleton tptp.x))) (let ((_let_2 (= _let_1 tptp.null_class))) (let ((_let_3 (tptp.member tptp.x tptp.universal_class))) (let ((_let_4 (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) (let ((_let_5 (= _let_4 tptp.identity_relation))) (let ((_let_6 (tptp.complement tptp.element_relation))) (let ((_let_7 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_8 (= (tptp.intersection _let_7 (tptp.intersection _let_7 (tptp.complement (tptp.compose _let_6 (tptp.inverse tptp.element_relation))))) tptp.subset_relation))) (let ((_let_9 (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_11 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_14 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_15 (tptp.unordered_pair tptp.x tptp.x))) (let ((_let_16 (= _let_1 _let_15))) (let ((_let_17 (tptp.member tptp.x _let_15))) (let ((_let_18 (= tptp.universal_class tptp.x))) (let ((_let_19 (tptp.member tptp.universal_class tptp.element_relation))) (let ((_let_20 (= tptp.element_relation _let_1))) (let ((_let_21 (_let_12))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.x QUANTIFIERS_INST_ENUM)) :args _let_21))) _let_22 :args (_let_16 false _let_12)))) (let ((_let_24 (not _let_3))) (let ((_let_25 (or _let_24 _let_17))) (let ((_let_26 (_let_13))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_17 (not _let_25)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.x tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_26)) _let_27 :args (_let_25 false _let_13)) :args (_let_17 false _let_3 false _let_25)))) (let ((_let_29 (tptp.unordered_pair tptp.universal_class tptp.universal_class))) (let ((_let_30 (tptp.member tptp.x _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_18 _let_18))) (let ((_let_33 (_let_14))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (= _let_1 _let_29))) (let ((_let_36 (tptp.regular _let_29))) (let ((_let_37 (tptp.intersection _let_29 _let_36))) (let ((_let_38 (tptp.member tptp.x _let_37))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_30))) (let ((_let_41 (= _let_1 _let_37))) (let ((_let_42 (or _let_35 _let_41))) (let ((_let_43 (and _let_16 _let_17 _let_35))) (let ((_let_44 (ASSUME :args (_let_17)))) (let ((_let_45 (TRUE_INTRO _let_44))) (let ((_let_46 (APPLY_UF tptp.member))) (let ((_let_47 (ASSUME :args (_let_16)))) (let ((_let_48 (SYMM (SYMM _let_47)))) (let ((_let_49 (ASSUME :args (_let_35)))) (let ((_let_50 (REFL :args (tptp.x)))) (let ((_let_51 (_let_11))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (forall ((X $$unsorted)) (let ((_let_1 (tptp.singleton tptp.x))) (or (= X _let_1) (= (tptp.intersection X (tptp.regular X)) _let_1)))))) (let ((_let_54 (SYMM (ASSUME :args (_let_8))))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_9)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO (AND_INTRO (SYMM (ASSUME :args (_let_2))) (EQ_RESOLVE (SYMM (ASSUME :args (_let_5))) (MACRO_SR_EQ_INTRO _let_54 :args ((= tptp.identity_relation _let_4) SB_DEFAULT SBA_FIXPOINT))) _let_54) :args ((forall ((X $$unsorted)) (or (= tptp.null_class X) (= tptp.null_class (tptp.intersection X (tptp.regular X))))) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_56 (_let_53))) (let ((_let_57 (or))) (let ((_let_58 (REFL :args ((not _let_17))))) (let ((_let_59 (REFL :args ((not _let_16))))) (let ((_let_60 (ASSUME :args (_let_41)))) (let ((_let_61 (ASSUME :args (_let_39)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_32))) :args ((or _let_31 _let_18 (not _let_32)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_47 _let_60 _let_61) :args (_let_16 _let_17 _let_41 _let_39)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_61)) (CONG _let_50 (TRANS (SYMM _let_60) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_16 _let_41 _let_39)) :args ((not (and _let_16 _let_17 _let_41 _let_39)) SB_LITERAL))) (CONG _let_59 _let_58 (REFL :args ((not _let_41))) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_57)) _let_28 _let_23 (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_35 _let_41 (not _let_42)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_29 QUANTIFIERS_INST_ENUM)) :args _let_56))) _let_55 :args (_let_42 false _let_53)) (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_30 _let_39 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.x _let_29 _let_36 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_51)) _let_52 :args (_let_40 false _let_11)) (RESOLUTION (CNF_AND_NEG :args (_let_43)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_44 _let_47 _let_49) (SCOPE (TRUE_ELIM (TRANS (CONG _let_50 (TRANS (SYMM (SYMM (SYMM _let_49))) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_16 _let_35))) :args (_let_16 _let_17 _let_35))) :args (true _let_43)) _let_28 _let_23 :args (_let_30 false _let_17 false _let_16 false _let_41 false _let_42 true _let_38 false _let_40 true _let_35 false _let_17 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.x tptp.universal_class tptp.universal_class QUANTIFIERS_INST_CBQI_PROP)) :args _let_33))) _let_34 :args (_let_32 false _let_14)) :args (_let_18 false _let_30 false _let_32)))) (let ((_let_63 (not _let_19))) (let ((_let_64 (tptp.member tptp.universal_class _let_6))) (let ((_let_65 (not _let_64))) (let ((_let_66 (or _let_65 _let_63))) (let ((_let_67 (_let_10))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (tptp.regular _let_6))) (let ((_let_70 (tptp.intersection _let_6 _let_69))) (let ((_let_71 (tptp.member tptp.universal_class _let_70))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_64))) (let ((_let_74 (= _let_1 _let_70))) (let ((_let_75 (= _let_6 _let_1))) (let ((_let_76 (or _let_75 _let_74))) (let ((_let_77 (REFL :args ((not _let_18))))) (let ((_let_78 (ASSUME :args (_let_74)))) (let ((_let_79 (ASSUME :args (_let_18)))) (let ((_let_80 (SYMM (SYMM _let_79)))) (let ((_let_81 (ASSUME :args (_let_72)))) (let ((_let_82 (ASSUME :args (_let_75)))) (let ((_let_83 (ASSUME :args (_let_65)))) (let ((_let_84 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_63 _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_47 _let_82 _let_79 _let_83) :args (_let_65 _let_75 _let_16 _let_17 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_83)) (CONG _let_80 (REFL :args (_let_6)) :args _let_46) (CONG _let_50 (TRANS (SYMM (SYMM _let_82)) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_16 _let_75 _let_18 _let_65)) :args ((not (and _let_65 _let_75 _let_16 _let_17 _let_18)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) (REFL :args ((not _let_75))) _let_59 _let_58 _let_77 :args _let_57)) _let_62 _let_28 _let_23 (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_75 _let_74 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_6 QUANTIFIERS_INST_ENUM)) :args _let_56))) _let_55 :args (_let_76 false _let_53)) (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_79 _let_47 _let_78 _let_81) :args (_let_74 _let_16 _let_17 _let_18 _let_72)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_81)) (CONG _let_80 (TRANS (SYMM _let_78) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_18 _let_16 _let_74 _let_72)) :args ((not (and _let_74 _let_16 _let_17 _let_18 _let_72)) SB_LITERAL))) (CONG (REFL :args ((not _let_74))) _let_59 _let_58 _let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_71))) :args _let_57)) _let_62 _let_28 _let_23 (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_64 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.universal_class _let_6 _let_69 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_51)) _let_52 :args (_let_73 false _let_11)) :args (_let_64 false _let_18 false _let_17 false _let_16 false _let_75 false _let_76 true _let_74 false _let_18 false _let_17 false _let_16 true _let_71 false _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_68 :args (tptp.universal_class tptp.element_relation QUANTIFIERS_INST_ENUM)) :args _let_67)) _let_68 :args (_let_66 false _let_10)) :args (_let_63 false _let_64 false _let_66)))) (let ((_let_85 (tptp.regular tptp.element_relation))) (let ((_let_86 (tptp.intersection tptp.element_relation _let_85))) (let ((_let_87 (= _let_1 _let_86))) (let ((_let_88 (or _let_20 _let_87))) (let ((_let_89 (tptp.member tptp.universal_class _let_86))) (let ((_let_90 (not _let_87))) (let ((_let_91 (not _let_89))) (let ((_let_92 (or _let_91 _let_19))) (let ((_let_93 (ASSUME :args (_let_87)))) (let ((_let_94 (ASSUME :args (_let_91)))) (let ((_let_95 (ASSUME :args (_let_20)))) (let ((_let_96 (ASSUME :args (_let_63)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_47 _let_95 _let_79 _let_96) :args (_let_63 _let_20 _let_16 _let_17 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_96)) (CONG _let_80 (REFL :args (tptp.element_relation)) :args _let_46) (CONG _let_50 (TRANS (SYMM (SYMM _let_95)) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_16 _let_20 _let_18 _let_63)) :args ((not (and _let_63 _let_20 _let_16 _let_17 _let_18)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_19))) (REFL :args ((not _let_20))) _let_59 _let_58 _let_77 :args _let_57)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_20 _let_87 (not _let_88)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_44 _let_79 _let_47 _let_93 _let_94) :args (_let_87 _let_16 _let_17 _let_18 _let_91)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_94)) (CONG _let_80 (TRANS (SYMM _let_93) _let_48) :args _let_46) _let_45)) :args (_let_17 _let_18 _let_16 _let_87 _let_91)) :args ((not (and _let_87 _let_16 _let_17 _let_18 _let_91)) SB_LITERAL))) (CONG (REFL :args (_let_90)) _let_59 _let_58 _let_77 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_89))) :args _let_57)) _let_23 _let_28 _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_19 _let_91 (not _let_92)))) _let_84 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.universal_class tptp.element_relation _let_85 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_51)) _let_52 :args (_let_92 false _let_11)) :args (_let_91 true _let_19 false _let_92)) :args (_let_90 false _let_16 false _let_17 false _let_18 true _let_89)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (tptp.element_relation QUANTIFIERS_INST_ENUM)) :args _let_56))) _let_55 :args (_let_88 false _let_53)) :args (_let_20 true _let_87 false _let_88)) _let_84 _let_62 _let_28 _let_23 :args (false false _let_20 true _let_19 false _let_18 false _let_17 false _let_16)) :args ((forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (forall ((X $$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_14 _let_13 (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)) _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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_7) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) _let_11 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) _let_10 (forall ((Z $$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_7) (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))) _let_9 (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))) _let_8 _let_5 (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))))) _let_3 _let_2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 13.28/13.53  )
% 13.28/13.54  % SZS output end Proof for SET079-6
% 13.28/13.54  % cvc5---1.0.5 exiting
% 13.28/13.54  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------