TSTP Solution File: NUM141-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM141-1 : 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 10:42:29 EDT 2023
% Result : Unsatisfiable 31.75s 32.00s
% Output : Proof 31.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM141-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:43:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.jD1AkvhCNn/cvc5---1.0.5_16896.p...
% 0.21/0.53 ------- get file name : TPTP file name is NUM141-1
% 0.21/0.53 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16896.smt2...
% 0.21/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.59/10.89 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.78/15.97 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.83/21.01 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.81/26.06 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.95/31.21 --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.75/32.00 % SZS status Unsatisfiable for NUM141-1
% 31.75/32.00 % SZS output start Proof for NUM141-1
% 31.75/32.01 (
% 31.75/32.01 (let ((_let_1 (tptp.successor tptp.x))) (let ((_let_2 (tptp.member tptp.x _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.member tptp.x tptp.universal_class))) (let ((_let_5 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_6 (tptp.cross_product tptp.universal_class _let_5))) (let ((_let_7 (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))) (let ((_let_9 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_11 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))))) (let ((_let_12 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_14 (tptp.unordered_pair tptp.x tptp.x))) (let ((_let_15 (tptp.singleton tptp.x))) (let ((_let_16 (= _let_15 _let_14))) (let ((_let_17 (tptp.member tptp.x _let_15))) (let ((_let_18 (tptp.member tptp.x _let_14))) (let ((_let_19 (_let_12))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (not _let_17))) (let ((_let_22 (tptp.complement _let_15))) (let ((_let_23 (tptp.member tptp.x _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_21))) (let ((_let_26 (_let_10))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (tptp.complement tptp.x))) (let ((_let_29 (tptp.intersection _let_28 _let_22))) (let ((_let_30 (tptp.member tptp.x _let_29))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_23))) (let ((_let_33 (_let_11))) (let ((_let_34 (ASSUME :args _let_33))) (let ((_let_35 (tptp.complement _let_29))) (let ((_let_36 (tptp.member tptp.x _let_35))) (let ((_let_37 (not _let_4))) (let ((_let_38 (or _let_37 _let_36 _let_30))) (let ((_let_39 (_let_9))) (let ((_let_40 (ASSUME :args _let_39))) (let ((_let_41 (tptp.union tptp.x _let_15))) (let ((_let_42 (= _let_41 _let_35))) (let ((_let_43 (= _let_1 _let_41))) (let ((_let_44 (not _let_36))) (let ((_let_45 (_let_8))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (_let_7))) (let ((_let_48 (ASSUME :args _let_47))) (let ((_let_49 (ASSUME :args (_let_3)))) (let ((_let_50 (or))) (let ((_let_51 (and _let_3 _let_43 _let_42))) (let ((_let_52 (_let_3 _let_43 _let_42))) (let ((_let_53 (APPLY_UF tptp.member))) (let ((_let_54 (ASSUME :args (_let_43)))) (let ((_let_55 (ASSUME :args (_let_42)))) (let ((_let_56 (REFL :args (tptp.x)))) (let ((_let_57 (ASSUME :args (_let_4)))) (let ((_let_58 (or _let_37 _let_18))) (let ((_let_59 (_let_13))) (let ((_let_60 (ASSUME :args _let_59))) (let ((_let_61 (ASSUME :args (_let_18)))) (let ((_let_62 (ASSUME :args (_let_16)))) (let ((_let_63 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_61 _let_62 _let_63) :args (_let_16 _let_21 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_63)) (CONG _let_56 (SYMM (SYMM _let_62)) :args _let_53) (TRUE_INTRO _let_61))) :args (_let_18 _let_16 _let_21)) :args ((not (and _let_16 _let_21 _let_18)) SB_LITERAL))) (CONG (REFL :args ((not _let_16))) (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_17))) (REFL :args ((not _let_18))) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_37 _let_18 (not _let_58)))) _let_57 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_60 :args (tptp.x tptp.x QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_59)) _let_60 :args (_let_58 false _let_13)) :args (_let_18 false _let_4 false _let_58)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_21 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_23 (not _let_32)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_37 _let_36 _let_30 (not _let_38)))) _let_57 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_51)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_49 _let_54 _let_55) (SCOPE (FALSE_ELIM (TRANS (CONG _let_56 (TRANS (SYMM _let_55) (SYMM _let_54)) :args _let_53) (FALSE_INTRO _let_49))) :args _let_52)) :args _let_52)) :args (true _let_51)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args ((not _let_43))) (REFL :args ((not _let_42))) (REFL :args (_let_44)) :args _let_50)) _let_49 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.successor X)))) :args _let_47))) _let_48 :args (_let_43 false _let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.x _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union X Y)))) :args _let_45))) _let_46 :args (_let_42 false _let_8)) :args (_let_44 true _let_2 false _let_43 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_40 :args (tptp.x _let_29 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) true))))) :args _let_39)) _let_40 :args (_let_38 false _let_9)) :args (_let_30 false _let_4 true _let_36 false _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (tptp.x _let_28 _let_22 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_33)) _let_34 :args (_let_32 false _let_11)) :args (_let_23 false _let_30 false _let_32)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.x _let_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) false))))) :args _let_26)) _let_27 :args (_let_25 false _let_10)) :args (_let_21 false _let_23 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_19))) _let_20 :args (_let_16 false _let_12)) :args (false false _let_18 true _let_17 false _let_16)) :args ((forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= X Y)) (tptp.subclass Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) _let_13 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) _let_12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair (tptp.singleton X) (tptp.unordered_pair X (tptp.singleton Y))) (tptp.ordered_pair X Y))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U X))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V Y))) (forall ((U $$unsorted) (X $$unsorted) (V $$unsorted) (Y $$unsorted)) (or (not (tptp.member U X)) (not (tptp.member V Y)) (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_5) (forall ((X $$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_11 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) _let_10 _let_9 _let_8 (forall ((X $$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 $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) _let_7 (tptp.subclass tptp.successor_relation _let_5) (forall ((X $$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_5 (tptp.intersection _let_5 (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 $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_6) (forall ((X $$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_5) (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_6) (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 $$unsorted)) (or (not (tptp.irreflexive X Y)) (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass (tptp.restrict X Y Y) (tptp.complement tptp.identity_relation))) (tptp.irreflexive X Y))) (forall ((X $$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_5) (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 $$unsorted)) (or (not (tptp.function Z)) (not (tptp.function X)) (not (tptp.member (tptp.domain_of X) tptp.ordinal_numbers)) (not (= (tptp.compose Z (tptp.rest_of X)) X)) (tptp.member X (tptp.recursion_equation_functions Z)))) (tptp.subclass tptp.union_of_range_map _let_5) (forall ((X $$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_4 _let_3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.75/32.01 )
% 31.75/32.01 % SZS output end Proof for NUM141-1
% 31.75/32.01 % cvc5---1.0.5 exiting
% 31.75/32.01 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------