TSTP Solution File: SET071-7 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET071-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 14:37:23 EDT 2023
% Result : Unsatisfiable 0.90s 1.16s
% Output : Proof 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET071-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 09:39:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.bhQ12sTA1H/cvc5---1.0.5_23875.p...
% 0.21/0.52 ------- get file name : TPTP file name is SET071-7
% 0.21/0.52 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23875.smt2...
% 0.21/0.52 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.90/1.16 % SZS status Unsatisfiable for SET071-7
% 0.90/1.16 % SZS output start Proof for SET071-7
% 0.90/1.16 (
% 0.90/1.16 (let ((_let_1 (tptp.member tptp.y tptp.universal_class))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.member tptp.x tptp.universal_class))) (let ((_let_4 (not _let_3))) (let ((_let_5 (tptp.unordered_pair tptp.x tptp.y))) (let ((_let_6 (not (= _let_5 tptp.null_class)))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member X tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton Y)))))) (let ((_let_8 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_9 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))))) (let ((_let_10 (tptp.function tptp.choice))) (let ((_let_11 (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))))) (let ((_let_12 (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))))) (let ((_let_13 (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))))) (let ((_let_14 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)))) (let ((_let_16 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_17 (tptp.singleton tptp.y))) (let ((_let_18 (= _let_5 _let_17))) (let ((_let_19 (tptp.unordered_pair _let_17 _let_17))) (let ((_let_20 (= (tptp.singleton _let_17) _let_19))) (let ((_let_21 (tptp.singleton _let_5))) (let ((_let_22 (tptp.member _let_21 tptp.universal_class))) (let ((_let_23 (tptp.member _let_19 tptp.universal_class))) (let ((_let_24 (or _let_3 _let_18))) (let ((_let_25 (_let_7))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_3 _let_18 (not _let_24)))) (ASSUME :args (_let_4)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_25)) _let_26 :args (_let_24 false _let_7)) :args (_let_18 true _let_3 false _let_24)))) (let ((_let_28 (_let_14))) (let ((_let_29 (ASSUME :args _let_28))) (let ((_let_30 ((tptp.singleton X)))) (let ((_let_31 (tptp.image tptp.choice _let_21))) (let ((_let_32 (tptp.member _let_31 tptp.universal_class))) (let ((_let_33 (not _let_22))) (let ((_let_34 (not _let_10))) (let ((_let_35 (or _let_34 _let_33 _let_32))) (let ((_let_36 (_let_12))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (tptp.sum_class _let_31))) (let ((_let_39 (tptp.member _let_38 tptp.universal_class))) (let ((_let_40 (not _let_32))) (let ((_let_41 (or _let_40 _let_39))) (let ((_let_42 (_let_13))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (tptp.apply tptp.choice _let_5))) (let ((_let_45 (= _let_44 _let_38))) (let ((_let_46 (= tptp.y _let_44))) (let ((_let_47 (not _let_39))) (let ((_let_48 (_let_11))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (tptp.unordered_pair tptp.y tptp.y))) (let ((_let_51 (tptp.member _let_44 _let_50))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_52 _let_46 _let_46))) (let ((_let_54 (_let_16))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (tptp.member _let_44 _let_5))) (let ((_let_57 (= _let_17 _let_50))) (let ((_let_58 (= tptp.null_class _let_5))) (let ((_let_59 (tptp.member _let_5 tptp.universal_class))) (let ((_let_60 (not _let_59))) (let ((_let_61 (or _let_60 _let_58 _let_56))) (let ((_let_62 (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= tptp.null_class Y) (tptp.member (tptp.apply tptp.choice Y) Y))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (_let_15))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 ((tptp.unordered_pair X Y)))) (let ((_let_67 (and _let_18 _let_57 _let_56))) (let ((_let_68 (ASSUME :args (_let_56)))) (let ((_let_69 (APPLY_UF tptp.member))) (let ((_let_70 (ASSUME :args (_let_18)))) (let ((_let_71 (SYMM (SYMM _let_70)))) (let ((_let_72 (ASSUME :args (_let_57)))) (let ((_let_73 (ASSUME :args (_let_2)))) (let ((_let_74 (or))) (let ((_let_75 (and _let_2 _let_46 _let_45))) (let ((_let_76 (_let_2 _let_46 _let_45))) (let ((_let_77 (REFL :args (tptp.universal_class)))) (let ((_let_78 (ASSUME :args (_let_46)))) (let ((_let_79 (ASSUME :args (_let_45)))) (let ((_let_80 (not _let_23))) (let ((_let_81 (not _let_20))) (let ((_let_82 (not _let_18))) (let ((_let_83 (ASSUME :args (_let_23)))) (let ((_let_84 (ASSUME :args (_let_20)))) (let ((_let_85 (ASSUME :args (_let_33)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_83 _let_84 _let_70 _let_85) :args (_let_18 _let_20 _let_33 _let_23)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_85)) (CONG (CONG _let_71 :args (APPLY_UF tptp.singleton)) _let_77 :args _let_69) (CONG (SYMM (SYMM _let_84)) _let_77 :args _let_69) (TRUE_INTRO _let_83))) :args (_let_23 _let_20 _let_18 _let_33)) :args ((not (and _let_18 _let_20 _let_33 _let_23)) SB_LITERAL))) (CONG (REFL :args (_let_82)) (REFL :args (_let_81)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_22))) (REFL :args (_let_80)) :args _let_74)) :args ((or _let_82 _let_22 _let_81 _let_80))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_17 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_64)) _let_65 :args (_let_23 false _let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_32 _let_33 (not _let_35)))) (ASSUME :args (_let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_75)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_73 _let_78 _let_79) (SCOPE (FALSE_ELIM (TRANS (CONG (TRANS (SYMM _let_79) (SYMM _let_78)) _let_77 :args _let_69) (FALSE_INTRO _let_73))) :args _let_76)) :args _let_76)) :args (true _let_75)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args ((not _let_46))) (REFL :args ((not _let_45))) (REFL :args (_let_47)) :args _let_74)) _let_73 (MACRO_RESOLUTION_TRUST (REORDERING (FACTORING (CNF_OR_POS :args (_let_53))) :args ((or _let_46 _let_52 (not _let_53)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_67)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_68 _let_70 _let_72) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_44)) (TRANS (SYMM _let_72) (SYMM _let_71)) :args _let_69) (TRUE_INTRO _let_68))) :args (_let_56 _let_18 _let_57))) :args (_let_18 _let_57 _let_56))) :args (true _let_67)) _let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28))) _let_29 :args (_let_57 false _let_14)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_58 _let_60 _let_56 (not _let_61)))) (SYMM (ASSUME :args (_let_6))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_66)) :args _let_64)) _let_65 :args (_let_59 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (_let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member Y tptp.universal_class) false))))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_56 true _let_58 false _let_59 false _let_61)) :args (_let_51 false _let_18 false _let_57 false _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_44 tptp.y tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member U (tptp.unordered_pair X Y)) false))))) :args _let_54))) _let_55 :args (_let_53 false _let_16)) :args (_let_46 false _let_51 false _let_53)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (tptp.choice _let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.apply Xf Y)))) :args _let_48))) _let_49 :args (_let_45 false _let_11)) :args (_let_47 true _let_1 false _let_46 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (_let_31 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.sum_class X)))) :args _let_42)) _let_43 :args (_let_41 false _let_13)) :args (_let_40 true _let_39 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.choice _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.image Xf X)))) :args _let_36)) _let_37 :args (_let_35 false _let_12)) :args (_let_33 false _let_10 true _let_32 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_29 :args (_let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_28))) _let_29 :args (_let_20 false _let_14)) _let_27 :args (false false _let_23 true _let_22 false _let_20 false _let_18)) :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 $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))) _let_16 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) _let_15 _let_14 (forall ((X $$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_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 $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) _let_13 (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) _let_12 (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) _let_11 _let_10 _let_9 (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))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (= (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V tptp.universal_class))) (forall ((X $$unsorted)) (tptp.subclass X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (tptp.member (tptp.not_subclass_element X Y) X) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (= X Y) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y) (tptp.member (tptp.not_subclass_element X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (not (tptp.member Y (tptp.intersection (tptp.complement X) X)))) (forall ((Z $$unsorted)) (not (tptp.member Z tptp.null_class))) (forall ((X $$unsorted)) (tptp.subclass tptp.null_class X)) (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= X tptp.null_class))) (forall ((Z $$unsorted)) (or (= Z tptp.null_class) (tptp.member (tptp.not_subclass_element Z tptp.null_class) Z))) (tptp.member tptp.null_class tptp.universal_class) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair X Y) (tptp.unordered_pair Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.subclass (tptp.singleton X) (tptp.unordered_pair X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.subclass (tptp.singleton Y) (tptp.unordered_pair X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (tptp.member Y tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton X)))) _let_7 _let_6 _let_4 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.90/1.16 )
% 0.90/1.17 % SZS output end Proof for SET071-7
% 0.90/1.17 % cvc5---1.0.5 exiting
% 0.90/1.17 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------