%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM156-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n027.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 10:42:31 EDT 2023

% Result   : Unsatisfiable 31.15s 31.64s
% Output   : Proof 31.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : NUM156-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.36  % Computer : n027.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri Aug 25 11:34:48 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.23/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.51  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ZuD1jhI3FX/cvc5---1.0.5_4610.p...
% 0.23/0.54  ------- get file name : TPTP file name is NUM156-1
% 0.23/0.54  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_4610.smt2...
% 0.23/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.44/10.76  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.44/15.88  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.64/20.99  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.65/26.09  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.78/31.23  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 31.15/31.64  % SZS status Unsatisfiable for NUM156-1
% 31.15/31.64  % SZS output start Proof for NUM156-1
% 31.15/31.64  (
% 31.15/31.64  (let ((_let_1 (not (tptp.member tptp.null_class tptp.kind_1_ordinals)))) (let ((_let_2 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_3 (tptp.intersection (tptp.complement tptp.kind_1_ordinals) tptp.ordinal_numbers))) (let ((_let_4 (= _let_3 tptp.limit_ordinals))) (let ((_let_5 (tptp.image tptp.successor_relation tptp.ordinal_numbers))) (let ((_let_6 (tptp.singleton tptp.null_class))) (let ((_let_7 (tptp.union _let_6 _let_5))) (let ((_let_8 (= _let_7 tptp.kind_1_ordinals))) (let ((_let_9 (tptp.cross_product tptp.universal_class _let_2))) (let ((_let_10 (tptp.intersection (tptp.complement (tptp.compose tptp.element_relation (tptp.complement tptp.identity_relation))) tptp.element_relation))) (let ((_let_11 (= _let_10 tptp.singleton_relation))) (let ((_let_12 (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation))) (let ((_let_13 (= _let_12 tptp.identity_relation))) (let ((_let_14 (= (tptp.intersection _let_2 (tptp.intersection _let_2 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation))) (let ((_let_15 (tptp.inductive tptp.omega))) (let ((_let_16 (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))) (let ((_let_18 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))))) (let ((_let_19 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_21 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_22 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_23 (forall ((X $$unsorted)) (tptp.subclass X tptp.universal_class)))) (let ((_let_24 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_25 (tptp.unordered_pair tptp.null_class tptp.null_class))) (let ((_let_26 (= _let_6 _let_25))) (let ((_let_27 (tptp.member tptp.null_class _let_6))) (let ((_let_28 (tptp.member tptp.null_class _let_25))) (let ((_let_29 (_let_21))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 (not _let_27))) (let ((_let_32 (tptp.complement _let_6))) (let ((_let_33 (tptp.member tptp.null_class _let_32))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_31))) (let ((_let_36 (_let_19))) (let ((_let_37 (ASSUME :args _let_36))) (let ((_let_38 (tptp.complement _let_5))) (let ((_let_39 (tptp.intersection _let_32 _let_38))) (let ((_let_40 (tptp.member tptp.null_class _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_33))) (let ((_let_43 (_let_20))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (tptp.complement _let_39))) (let ((_let_46 (tptp.member tptp.null_class _let_45))) (let ((_let_47 (tptp.member tptp.null_class tptp.universal_class))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46 _let_40))) (let ((_let_50 (_let_18))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (= _let_7 _let_45))) (let ((_let_53 (tptp.member tptp.null_class _let_7))) (let ((_let_54 (not _let_46))) (let ((_let_55 (_let_17))) (let ((_let_56 (ASSUME :args _let_55))) (let ((_let_57 (SYMM (ASSUME :args (_let_14))))) (let ((_let_58 (EQ_RESOLVE (SYMM (ASSUME :args (_let_13))) (MACRO_SR_EQ_INTRO _let_57 :args ((= tptp.identity_relation _let_12) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (EQ_RESOLVE (SYMM (ASSUME :args (_let_11))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_58 _let_57) :args ((= tptp.singleton_relation _let_10) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (SYMM (ASSUME :args (_let_8))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO (AND_INTRO (EQ_RESOLVE (SYMM (ASSUME :args (_let_4))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_60 _let_59 _let_58 _let_57) :args ((= tptp.limit_ordinals _let_3) SB_DEFAULT SBA_FIXPOINT))) _let_60 _let_59 _let_58 _let_57) :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (or))) (let ((_let_63 (not _let_53))) (let ((_let_64 (and _let_63 _let_52))) (let ((_let_65 (_let_63 _let_52))) (let ((_let_66 (APPLY_UF tptp.member))) (let ((_let_67 (ASSUME :args (_let_52)))) (let ((_let_68 (REFL :args (tptp.null_class)))) (let ((_let_69 (tptp.member tptp.null_class tptp.omega))) (let ((_let_70 (not _let_69))) (let ((_let_71 (tptp.subclass tptp.omega tptp.universal_class))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_70 _let_47))) (let ((_let_74 (_let_24))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 (_let_23))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (not _let_15))) (let ((_let_79 (or _let_78 _let_69))) (let ((_let_80 (_let_16))) (let ((_let_81 (ASSUME :args _let_80))) (let ((_let_82 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_70 _let_47 _let_72 (not _let_73)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_78 _let_69 (not _let_79)))) (ASSUME :args (_let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_81 :args (tptp.omega QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.inductive X) false))))) :args _let_80)) _let_81 :args (_let_79 false _let_16)) :args (_let_69 false _let_15 false _let_79)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (tptp.omega QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_76)) _let_77 :args (_let_71 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (tptp.omega tptp.universal_class tptp.null_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_74)) _let_75 :args (_let_73 false _let_24)) :args (_let_47 false _let_69 false _let_71 false _let_73)))) (let ((_let_83 (or _let_48 _let_28))) (let ((_let_84 (_let_22))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (ASSUME :args (_let_28)))) (let ((_let_87 (ASSUME :args (_let_26)))) (let ((_let_88 (ASSUME :args (_let_31)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_86 _let_87 _let_88) :args (_let_26 _let_31 _let_28)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_88)) (CONG _let_68 (SYMM (SYMM _let_87)) :args _let_66) (TRUE_INTRO _let_86))) :args (_let_28 _let_26 _let_31)) :args ((not (and _let_26 _let_31 _let_28)) SB_LITERAL))) (CONG (REFL :args ((not _let_26))) (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_27))) (REFL :args ((not _let_28))) :args _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_48 _let_28 (not _let_83)))) _let_82 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (tptp.null_class tptp.null_class QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_84)) _let_85 :args (_let_83 false _let_22)) :args (_let_28 false _let_47 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_34 _let_31 (not _let_35)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_33 (not _let_42)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_46 _let_40 (not _let_49)))) _let_82 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_64)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_61 _let_67) (SCOPE (FALSE_ELIM (TRANS (CONG _let_68 (SYMM _let_67) :args _let_66) (FALSE_INTRO _let_61))) :args _let_65)) :args _let_65)) :args (true _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_53))) (REFL :args ((not _let_52))) (REFL :args (_let_54)) :args _let_62)) _let_61 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_56 :args (_let_6 _let_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union X Y)))) :args _let_55))) _let_56 :args (_let_52 false _let_17)) :args (_let_54 true _let_53 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.null_class _let_39 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) true))))) :args _let_50)) _let_51 :args (_let_49 false _let_18)) :args (_let_40 false _let_47 true _let_46 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.null_class _let_32 _let_38 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_43)) _let_44 :args (_let_42 false _let_20)) :args (_let_33 false _let_40 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (tptp.null_class _let_6 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) false))))) :args _let_36)) _let_37 :args (_let_35 false _let_19)) :args (_let_31 false _let_33 false _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_30 :args (tptp.null_class QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_29))) _let_30 :args (_let_26 false _let_21)) :args (false false _let_28 true _let_27 false _let_26)) :args (_let_24 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (tptp.subclass X Y))) _let_23 (forall ((X $$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_22 (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_21 (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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_2) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) _let_20 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) _let_19 _let_18 _let_17 (forall ((X $$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_2) (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)))) _let_16 (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))) _let_15 (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_14 _let_13 (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 $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (= (tptp.compose X Y) Z)) (tptp.member _let_1 (tptp.compose_class X))))) (tptp.subclass tptp.composition_function _let_9) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.composition_function)) (= (tptp.compose X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.compose X Y))) tptp.composition_function))) (tptp.subclass tptp.domain_relation _let_2) (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_11 (tptp.subclass tptp.application_function _let_9) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (tptp.member Y (tptp.domain_of X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) tptp.application_function)) (= (tptp.apply X Y) Z))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y Z)) (tptp.cross_product tptp.universal_class (tptp.cross_product tptp.universal_class tptp.universal_class)))) (not (tptp.member Y (tptp.domain_of X))) (tptp.member (tptp.ordered_pair X (tptp.ordered_pair Y (tptp.apply X Y))) tptp.application_function))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (= (tptp.domain_of Xf) X))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subclass (tptp.range_of Xf) Y))) (forall ((Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.subclass (tptp.range_of Xf) Y)) (tptp.maps Xf (tptp.domain_of Xf) Y))) (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))) _let_8 _let_4 (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_2) (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 $$unsorted)) (or (not (tptp.function Z)) (not (tptp.function X)) (not (tptp.member (tptp.domain_of X) tptp.ordinal_numbers)) (not (= (tptp.compose Z (tptp.rest_of X)) X)) (tptp.member X (tptp.recursion_equation_functions Z)))) (tptp.subclass tptp.union_of_range_map _let_2) (forall ((X $$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_1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 31.15/31.64  )
% 31.15/31.64  % SZS output end Proof for NUM156-1
% 31.23/31.65  % cvc5---1.0.5 exiting
% 31.23/31.65  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------