TSTP Solution File: SET559-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET559-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 14:39:07 EDT 2023
% Result : Unsatisfiable 6.95s 7.32s
% Output : Proof 6.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.15 % Problem : SET559-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.16 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 14:36:55 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.53 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.6QqPvz1xtE/cvc5---1.0.5_22601.p...
% 0.23/0.55 ------- get file name : TPTP file name is SET559-6
% 0.23/0.56 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_22601.smt2...
% 0.23/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.95/7.32 % SZS status Unsatisfiable for SET559-6
% 6.95/7.32 % SZS output start Proof for SET559-6
% 6.95/7.32 (
% 6.95/7.32 (let ((_let_1 (tptp.domain_of tptp.xf2))) (let ((_let_2 (tptp.range_of tptp.xh))) (let ((_let_3 (tptp.cross_product _let_2 _let_2))) (let ((_let_4 (tptp.subclass _let_3 _let_1))) (let ((_let_5 (not _let_4))) (let ((_let_6 (tptp.compatible tptp.xh tptp.xf1 tptp.xf2))) (let ((_let_7 (tptp.operation tptp.xf2))) (let ((_let_8 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_9 (tptp.cross_product tptp.universal_class _let_8))) (let ((_let_10 (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))))) (let ((_let_11 (forall ((Xf $$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))))))) (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.domain_of _let_1))) (let ((_let_20 (tptp.not_subclass_element _let_3 _let_1))) (let ((_let_21 (tptp.first _let_20))) (let ((_let_22 (tptp.member _let_21 _let_19))) (let ((_let_23 (tptp.member _let_21 _let_2))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.subclass _let_2 _let_19))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_22))) (let ((_let_28 (_let_18))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 (not _let_27))) (let ((_let_31 (tptp.second _let_20))) (let ((_let_32 (tptp.ordered_pair _let_21 _let_31))) (let ((_let_33 (tptp.member _let_32 _let_3))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_23))) (let ((_let_36 (_let_15))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (= _let_20 _let_32))) (let ((_let_39 (tptp.member _let_20 _let_3))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (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_43 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or _let_39 _let_4))) (let ((_let_45 (_let_17))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (ASSUME :args (_let_5)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_4 _let_39 (not _let_44)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (_let_3 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_45)) _let_46 :args (_let_44 false _let_17)) :args (_let_39 true _let_4 false _let_44)))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_38 (not _let_41)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_20 _let_2 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.cross_product X Y)) false))))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_38 false _let_39 false _let_41)))) (let ((_let_50 (and _let_39 _let_38))) (let ((_let_51 (_let_39 _let_38))) (let ((_let_52 (ASSUME :args (_let_39)))) (let ((_let_53 (APPLY_UF tptp.member))) (let ((_let_54 (ASSUME :args (_let_38)))) (let ((_let_55 (SYMM _let_54))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_54) (SCOPE (TRUE_ELIM (TRANS (CONG _let_55 (REFL :args (_let_3)) :args _let_53) (TRUE_INTRO _let_52))) :args _let_51)) :args _let_51)) :args (true _let_50)) _let_48 _let_49 :args (_let_33 false _let_39 false _let_38)))) (let ((_let_57 (tptp.cross_product _let_19 _let_19))) (let ((_let_58 (tptp.member _let_32 _let_57))) (let ((_let_59 (tptp.member _let_31 _let_19))) (let ((_let_60 (not _let_59))) (let ((_let_61 (not _let_22))) (let ((_let_62 (or _let_61 _let_60 _let_58))) (let ((_let_63 (_let_13))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (= _let_1 _let_57))) (let ((_let_66 (tptp.member _let_20 _let_1))) (let ((_let_67 (not _let_58))) (let ((_let_68 (not _let_7))) (let ((_let_69 (or _let_68 _let_65))) (let ((_let_70 (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= _let_1 (tptp.cross_product _let_2 _let_2)))))))) (let ((_let_71 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (not _let_66))) (let ((_let_73 (or _let_72 _let_4))) (let ((_let_74 (_let_16))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 (and _let_72 _let_65 _let_38))) (let ((_let_77 (ASSUME :args (_let_72)))) (let ((_let_78 (ASSUME :args (_let_65)))) (let ((_let_79 (tptp.member _let_31 _let_2))) (let ((_let_80 (not _let_79))) (let ((_let_81 (or _let_26 _let_80 _let_59))) (let ((_let_82 ((not (= (tptp.subclass X Y) false)) (not (= (tptp.member U X) false))))) (let ((_let_83 (or _let_34 _let_79))) (let ((_let_84 (_let_14))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (not _let_6))) (let ((_let_87 (or _let_86 _let_25))) (let ((_let_88 (_let_10))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_86 _let_25 (not _let_87)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (tptp.xh tptp.xf1 tptp.xf2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.compatible Xh Xf1 Xf2) false))))) :args _let_88)) _let_89 :args (_let_87 false _let_10)) :args (_let_25 false _let_6 false _let_87)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_2 _let_19 _let_21 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_28)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_27)) :args ((or _let_26 _let_22 _let_24 _let_30))) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_62)) :args ((or _let_61 _let_60 _let_58 (not _let_62)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_26 _let_59 _let_80 (not _let_81)))) _let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_34 _let_79 (not _let_83)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_21 _let_31 _let_2 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_84)) _let_85 :args (_let_83 false _let_14)) :args (_let_79 false _let_33 false _let_83)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_2 _let_19 _let_31 QUANTIFIERS_INST_E_MATCHING _let_82)) :args _let_28)) _let_29 :args (_let_81 false _let_18)) :args (_let_59 false _let_25 false _let_79 false _let_81)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_77 _let_54 _let_78) (SCOPE (FALSE_ELIM (TRANS (CONG _let_55 (SYMM _let_78) :args _let_53) (FALSE_INTRO _let_77))) :args (_let_72 _let_38 _let_65))) :args (_let_72 _let_65 _let_38))) :args (true _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_72) _let_66))) (REFL :args ((not _let_65))) (REFL :args ((not _let_38))) (REFL :args (_let_67)) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_4 _let_72 (not _let_73)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (_let_3 _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_74)) _let_75 :args (_let_73 false _let_16)) :args (_let_72 true _let_4 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_68 _let_65 (not _let_69)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (tptp.xf2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.operation Xf) false))))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_65 false _let_7 false _let_69)) _let_49 :args (_let_67 true _let_66 false _let_65 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_64 :args (_let_21 _let_19 _let_31 _let_19 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) true))))) :args _let_63)) _let_64 :args (_let_62 false _let_13)) :args (_let_61 false _let_59 true _let_58 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_23 (not _let_35)))) _let_56 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_21 _let_31 _let_2 _let_2 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_36)) _let_37 :args (_let_35 false _let_15)) :args (_let_23 false _let_33 false _let_35)) :args (_let_30 false _let_25 true _let_22 false _let_23)) _let_29 :args (false true _let_27 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 $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) _let_15 _let_14 _let_13 _let_12 (tptp.subclass tptp.element_relation _let_8) (forall ((X $$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 $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_8) (forall ((X $$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_8 (tptp.intersection _let_8 (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 $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) _let_11 (forall ((Xf $$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 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) _let_10 (forall ((Xh $$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 $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_9) (forall ((X $$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_8) (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_9) (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_7 _let_6 _let_5)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 6.95/7.32 )
% 6.95/7.34 % SZS output end Proof for SET559-6
% 6.95/7.35 % cvc5---1.0.5 exiting
% 6.95/7.35 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------