TSTP Solution File: SET191-6 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET191-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n004.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 14:38:08 EDT 2023
% Result : Unsatisfiable 65.92s 66.14s
% Output : Proof 65.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET191-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n004.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 14:49:08 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.20/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.mtSEYppHJQ/cvc5---1.0.5_13367.p...
% 0.20/0.53 ------- get file name : TPTP file name is SET191-6
% 0.20/0.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_13367.smt2...
% 0.20/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.46/10.73 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.54/15.78 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.55/20.82 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.64/25.86 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.75/30.96 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.78/36.02 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.79/41.07 --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.14/46.38 --- Run --prenex-quant=none --full-saturate-quant at 5...
% 51.19/51.43 --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 56.27/56.47 --- Run --relevant-triggers --full-saturate-quant at 5...
% 61.35/61.54 --- Run --finite-model-find --e-matching --sort-inference --uf-ss-fair at 5...
% 65.92/66.14 % SZS status Unsatisfiable for SET191-6
% 65.92/66.15 % SZS output start Proof for SET191-6
% 65.92/66.15 (
% 65.92/66.15 (let ((_let_1 (tptp.subclass tptp.x tptp.y))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.complement tptp.x))) (let ((_let_4 (tptp.union _let_3 tptp.y))) (let ((_let_5 (= _let_4 tptp.universal_class))) (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 (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation))) (let ((_let_9 (= _let_8 tptp.singleton_relation))) (let ((_let_10 (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) (let ((_let_11 (= _let_10 tptp.identity_relation))) (let ((_let_12 (= (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))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))) (let ((_let_14 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))) (let ((_let_15 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_16 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))))) (let ((_let_17 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_18 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_19 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_20 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_21 (tptp.complement tptp.y))) (let ((_let_22 (tptp.complement _let_3))) (let ((_let_23 (tptp.intersection _let_22 _let_21))) (let ((_let_24 (tptp.complement _let_23))) (let ((_let_25 (= _let_4 _let_24))) (let ((_let_26 (tptp.not_subclass_element tptp.x tptp.y))) (let ((_let_27 (tptp.member _let_26 _let_4))) (let ((_let_28 (tptp.member _let_26 _let_24))) (let ((_let_29 (_let_13))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (tptp.member _let_26 tptp.x))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.subclass tptp.x _let_4))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_32 _let_27))) (let ((_let_36 (_let_20))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (or _let_31 _let_1))) (let ((_let_39 (_let_19))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (ASSUME :args (_let_2)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_1 _let_31 (not _let_38)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_39)) _let_40 :args (_let_38 false _let_19)) :args (_let_31 true _let_1 false _let_38)))) (let ((_let_43 (forall ((X $$unsorted)) (tptp.subclass X (tptp.union (tptp.complement tptp.x) tptp.y))))) (let ((_let_44 (SYMM (ASSUME :args (_let_12))))) (let ((_let_45 (EQ_RESOLVE (SYMM (ASSUME :args (_let_11))) (MACRO_SR_EQ_INTRO _let_44 :args ((= tptp.identity_relation _let_10) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_46 (AND_INTRO (SYMM (ASSUME :args (_let_5))) (EQ_RESOLVE (SYMM (ASSUME :args (_let_9))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_45 _let_44) :args ((= tptp.singleton_relation _let_8) SB_DEFAULT SBA_FIXPOINT))) _let_45 _let_44))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO _let_46 :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_27 (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_43))) _let_47 :args (_let_33 false _let_43)) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.x _let_4 _let_26 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_36)) _let_37 :args (_let_35 false _let_20)) :args (_let_27 false _let_33 false _let_31 false _let_35)))) (let ((_let_49 (tptp.member _let_26 _let_23))) (let ((_let_50 (not _let_49))) (let ((_let_51 (not _let_28))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (_let_15))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (tptp.member _let_26 _let_21))) (let ((_let_56 (not _let_55))) (let ((_let_57 (tptp.member _let_26 _let_22))) (let ((_let_58 (not _let_57))) (let ((_let_59 (or _let_58 _let_56 _let_49))) (let ((_let_60 (_let_16))) (let ((_let_61 (ASSUME :args _let_60))) (let ((_let_62 (tptp.member _let_26 _let_3))) (let ((_let_63 (not _let_27))) (let ((_let_64 (or _let_63 _let_57 _let_62))) (let ((_let_65 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.union (tptp.complement tptp.x) tptp.y))) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))) (let ((_let_66 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_46 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_67 (_let_65))) (let ((_let_68 (not _let_62))) (let ((_let_69 (or _let_68 _let_32))) (let ((_let_70 (tptp.member _let_26 tptp.y))) (let ((_let_71 (or _let_63 _let_55 _let_70))) (let ((_let_72 (not _let_70))) (let ((_let_73 (or _let_72 _let_1))) (let ((_let_74 (_let_18))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 (ASSUME :args (_let_51)))) (let ((_let_77 (ASSUME :args (_let_25)))) (let ((_let_78 (ASSUME :args (_let_27)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_76 _let_77 _let_78) :args (_let_25 _let_27 _let_51)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_78)) (CONG (REFL :args (_let_26)) (SYMM (SYMM _let_77)) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_76))) :args (_let_51 _let_25 _let_27)) :args ((not (and _let_25 _let_27 _let_51)) SB_LITERAL))) (CONG (REFL :args ((not _let_25))) (REFL :args (_let_63)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_28))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_50 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_56 _let_58 _let_49 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_70 _let_63 _let_55 (not _let_71)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_1 _let_72 (not _let_73)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_74)) _let_75 :args (_let_73 false _let_18)) :args (_let_72 true _let_1 false _let_73)) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_26 tptp.y QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_67)) _let_66 :args (_let_71 false _let_65)) :args (_let_55 true _let_70 false _let_27 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_62 _let_63 _let_57 (not _let_64)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_69)) :args ((or _let_32 _let_68 (not _let_69)))) _let_42 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_26 tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) _let_54 :args (_let_69 false _let_15)) :args (_let_68 false _let_31 false _let_69)) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_26 _let_3 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_67)) _let_66 :args (_let_64 false _let_65)) :args (_let_57 true _let_62 false _let_27 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (_let_26 _let_22 _let_21 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_60)) _let_61 :args (_let_59 false _let_16)) :args (_let_49 false _let_55 false _let_57 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_26 _let_23 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_53)) _let_54 :args (_let_52 false _let_15)) :args (_let_51 false _let_49 false _let_52)) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_3 tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union X Y)))) :args _let_29))) _let_30 :args (_let_25 false _let_13)) :args (false true _let_28 false _let_27 false _let_25)) :args (_let_20 _let_19 _let_18 _let_17 (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))) (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 $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) _let_16 _let_15 _let_14 _let_13 (forall ((X $$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 $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$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 $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) _let_12 _let_11 (forall ((Xr $$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 $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))) _let_9 (tptp.subclass tptp.application_function _let_7) (forall ((X $$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_2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 65.92/66.15 )
% 65.92/66.16 % SZS output end Proof for SET191-6
% 65.92/66.16 % cvc5---1.0.5 exiting
% 65.92/66.16 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------