TSTP Solution File: NUM042-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM042-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 10:42:06 EDT 2023
% Result : Unsatisfiable 1.72s 1.95s
% Output : Proof 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM042-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n005.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 : Fri Aug 25 12:14:08 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DRT5ka2Iox/cvc5---1.0.5_3056.p...
% 0.21/0.54 ------- get file name : TPTP file name is NUM042-1
% 0.21/0.54 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_3056.smt2...
% 0.21/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.72/1.95 % SZS status Unsatisfiable for NUM042-1
% 1.72/1.95 % SZS output start Proof for NUM042-1
% 1.72/1.96 (
% 1.72/1.96 (let ((_let_1 (tptp.domain_of (tptp.symmetrization_of tptp.x)))) (let ((_let_2 (tptp.irreflexive tptp.x _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.complement tptp.identity_relation))) (let ((_let_5 (tptp.subclass tptp.x _let_4))) (let ((_let_6 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation))) (tptp.irreflexive X Y))))) (let ((_let_8 (tptp.cross_product tptp.universal_class _let_6))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_14 (tptp.restrict tptp.x _let_1 _let_1))) (let ((_let_15 (tptp.not_subclass_element _let_14 _let_4))) (let ((_let_16 (tptp.member _let_15 _let_4))) (let ((_let_17 (tptp.member _let_15 tptp.x))) (let ((_let_18 (not _let_17))) (let ((_let_19 (not _let_5))) (let ((_let_20 (or _let_19 _let_18 _let_16))) (let ((_let_21 (_let_13))) (let ((_let_22 (ASSUME :args _let_21))) (let ((_let_23 (not _let_20))) (let ((_let_24 (tptp.cross_product _let_1 _let_1))) (let ((_let_25 (tptp.intersection _let_24 tptp.x))) (let ((_let_26 (tptp.member _let_15 _let_25))) (let ((_let_27 (not _let_26))) (let ((_let_28 (or _let_27 _let_17))) (let ((_let_29 (_let_10))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (= _let_14 _let_25))) (let ((_let_32 (tptp.member _let_15 _let_14))) (let ((_let_33 (_let_9))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (tptp.subclass _let_14 _let_4))) (let ((_let_36 (or _let_32 _let_35))) (let ((_let_37 (_let_12))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (not _let_35))) (let ((_let_40 (or _let_39 _let_2))) (let ((_let_41 (_let_7))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_2 _let_39 (not _let_40)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (tptp.x _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.irreflexive X Y) true))))) :args _let_41)) _let_42 :args (_let_40 false _let_7)) :args (_let_39 true _let_2 false _let_40)))) (let ((_let_44 (and _let_32 _let_31))) (let ((_let_45 (_let_32 _let_31))) (let ((_let_46 (ASSUME :args (_let_32)))) (let ((_let_47 (ASSUME :args (_let_31)))) (let ((_let_48 (not _let_16))) (let ((_let_49 (or _let_48 _let_35))) (let ((_let_50 (_let_11))) (let ((_let_51 (ASSUME :args _let_50))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_22 :args (tptp.x _let_4 _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subclass X Y) false)) (not (= (tptp.member U X) false))))) :args _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_19 _let_16 _let_18 _let_23))) (ASSUME :args (_let_5)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_35 _let_48 (not _let_49)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_14 _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_50)) _let_51 :args (_let_49 false _let_11)) :args (_let_48 true _let_35 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_28)) :args ((or _let_27 _let_17 (not _let_28)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_44)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_46 _let_47) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_15)) (SYMM _let_47) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_46))) :args _let_45)) :args _let_45)) :args (true _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_32 (not _let_36)))) _let_43 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (_let_14 _let_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_37)) _let_38 :args (_let_36 false _let_12)) :args (_let_32 true _let_35 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_34 :args (_let_1 _let_1 tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.restrict Xr X Y)))) :args _let_33))) _let_34 :args (_let_31 false _let_9)) :args (_let_26 false _let_32 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_15 _let_24 tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_29)) _let_30 :args (_let_28 false _let_10)) :args (_let_17 false _let_26 false _let_28)) :args (_let_23 false _let_5 true _let_16 false _let_17)) _let_22 :args (false true _let_20 false _let_13)) :args (_let_13 _let_12 _let_11 (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))) (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))) _let_10 (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))) _let_9 (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (tptp.function tptp.choice) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))) (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (tptp.intersection _let_6 (tptp.intersection _let_6 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))) (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (= (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.compose_class X) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose_class X))) (= (tptp.compose X Y) Z))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_8) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.composition_function)) (= (tptp.compose X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.compose X Y))) tptp.composition_function))) (tptp.subclass tptp.domain_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.domain_relation)) (= (tptp.domain_of X) Y))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.domain_of X)) tptp.domain_relation))) (forall ((X $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued1 X))) (forall ((X $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued2 X))) (forall ((X $$unsorted)) (= (tptp.domain X (tptp.image (tptp.inverse X) (tptp.singleton (tptp.single_valued1 X))) (tptp.single_valued2 X)) (tptp.single_valued3 X))) (= (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation _let_4)) tptp.element_relation) tptp.singleton_relation) (tptp.subclass tptp.application_function _let_8) (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))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.inverse X)) (tptp.symmetrization_of X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.irreflexive X Y)) (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation)))) _let_7 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.connected X Y)) (tptp.subclass (tptp.cross_product Y Y) (tptp.union tptp.identity_relation (tptp.symmetrization_of X))))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.subclass (tptp.cross_product Y Y) (tptp.union tptp.identity_relation (tptp.symmetrization_of X)))) (tptp.connected X Y))) (forall ((Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.restrict Xr Y Y))) (or (not (tptp.transitive Xr Y)) (tptp.subclass (tptp.compose _let_1 _let_1) _let_1)))) (forall ((Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.restrict Xr Y Y))) (or (not (tptp.subclass (tptp.compose _let_1 _let_1) _let_1)) (tptp.transitive Xr Y)))) (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.asymmetric Xr Y)) (= (tptp.restrict (tptp.intersection Xr (tptp.inverse Xr)) Y Y) tptp.null_class))) (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (= (tptp.restrict (tptp.intersection Xr (tptp.inverse Xr)) Y Y) tptp.null_class)) (tptp.asymmetric Xr Y))) (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.segment Xr Y Z) (tptp.domain_of (tptp.restrict Xr Y (tptp.singleton Z))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.well_ordering X Y)) (tptp.connected X Y))) (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (= U tptp.null_class) (tptp.member (tptp.least Xr U) U))) (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (not (tptp.member V U)) (tptp.member (tptp.least Xr U) U))) (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (= (tptp.segment Xr U (tptp.least Xr U)) tptp.null_class))) (forall ((Xr $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.well_ordering Xr Y)) (not (tptp.subclass U Y)) (not (tptp.member V U)) (not (tptp.member (tptp.ordered_pair V (tptp.least Xr U)) Xr)))) (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.connected Xr Y)) (not (= (tptp.not_well_ordering Xr Y) tptp.null_class)) (tptp.well_ordering Xr Y))) (forall ((Xr $$unsorted) (Y $$unsorted)) (or (not (tptp.connected Xr Y)) (tptp.subclass (tptp.not_well_ordering Xr Y) Y) (tptp.well_ordering Xr Y))) (forall ((V $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.not_well_ordering Xr Y))) (or (not (tptp.member V _let_1)) (not (= (tptp.segment Xr _let_1 V) tptp.null_class)) (not (tptp.connected Xr Y)) (tptp.well_ordering Xr Y)))) (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.section Xr Y Z)) (tptp.subclass Y Z))) (forall ((Xr $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.section Xr Y Z)) (tptp.subclass (tptp.domain_of (tptp.restrict Xr Z Y)) Y))) (forall ((Y $$unsorted) (Z $$unsorted) (Xr $$unsorted)) (or (not (tptp.subclass Y Z)) (not (tptp.subclass (tptp.domain_of (tptp.restrict Xr Z Y)) Y)) (tptp.section Xr Y Z))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.ordinal_numbers)) (tptp.well_ordering tptp.element_relation X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.ordinal_numbers)) (tptp.subclass (tptp.sum_class X) X))) (forall ((X $$unsorted)) (or (not (tptp.well_ordering tptp.element_relation X)) (not (tptp.subclass (tptp.sum_class X) X)) (not (tptp.member X tptp.universal_class)) (tptp.member X tptp.ordinal_numbers))) (forall ((X $$unsorted)) (or (not (tptp.well_ordering tptp.element_relation X)) (not (tptp.subclass (tptp.sum_class X) X)) (tptp.member X tptp.ordinal_numbers) (= X tptp.ordinal_numbers))) (= (tptp.union (tptp.singleton tptp.null_class) (tptp.image tptp.successor_relation tptp.ordinal_numbers)) tptp.kind_1_ordinals) (= (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers) tptp.limit_ordinals) (forall ((X $$unsorted)) (tptp.subclass (tptp.rest_of X) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X))) (tptp.member U (tptp.domain_of X)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X))) (= (tptp.restrict X U tptp.universal_class) V))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted)) (or (not (tptp.member U (tptp.domain_of X))) (not (= (tptp.restrict X U tptp.universal_class) V)) (tptp.member (tptp.ordered_pair U V) (tptp.rest_of X)))) (tptp.subclass tptp.rest_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.rest_relation)) (= (tptp.rest_of X) Y))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.ordered_pair X (tptp.rest_of X)) tptp.rest_relation))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.function Z))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.function X))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (tptp.member (tptp.domain_of X) tptp.ordinal_numbers))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (tptp.member X (tptp.recursion_equation_functions Z))) (= (tptp.compose Z (tptp.rest_of X)) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.function Z)) (not (tptp.function X)) (not (tptp.member (tptp.domain_of X) tptp.ordinal_numbers)) (not (= (tptp.compose Z (tptp.rest_of X)) X)) (tptp.member X (tptp.recursion_equation_functions Z)))) (tptp.subclass tptp.union_of_range_map _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.union_of_range_map)) (= (tptp.sum_class (tptp.range_of X)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.sum_class (tptp.range_of X)) Y)) (tptp.member _let_1 tptp.union_of_range_map)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply (tptp.recursion X tptp.successor_relation tptp.union_of_range_map) Y) (tptp.ordinal_add X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.recursion tptp.null_class (tptp.apply tptp.add_relation X) tptp.union_of_range_map) (tptp.ordinal_multiply X Y))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.omega)) (= (tptp.integer_of X) X))) (forall ((X $$unsorted)) (or (tptp.member X tptp.omega) (= (tptp.integer_of X) tptp.null_class))) _let_5 _let_3))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.72/1.96 )
% 1.72/1.97 % SZS output end Proof for NUM042-1
% 1.72/1.97 % cvc5---1.0.5 exiting
% 1.72/1.97 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------