%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET124-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:37:51 EDT 2023

% Result   : Unsatisfiable 0.38s 1.05s
% Output   : Proof 0.89s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem    : SET124-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.08/0.16  % Command    : do_cvc5 %s %d
% 0.17/0.37  % Computer : n009.cluster.edu
% 0.17/0.37  % Model    : x86_64 x86_64
% 0.17/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37  % Memory   : 8042.1875MB
% 0.17/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit   : 300
% 0.17/0.38  % WCLimit    : 300
% 0.17/0.38  % DateTime   : Sat Aug 26 08:55:20 EDT 2023
% 0.17/0.38  % CPUTime    : 
% 0.36/0.53  %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.53  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.ZIfg2wjjsx/cvc5---1.0.5_32017.p...
% 0.38/0.54  ------- get file name : TPTP file name is SET124-6
% 0.38/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_32017.smt2...
% 0.38/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/1.05  % SZS status Unsatisfiable for SET124-6
% 0.38/1.05  % SZS output start Proof for SET124-6
% 0.38/1.05  (
% 0.38/1.05  (let ((_let_1 (tptp.set_builder tptp.x tptp.z))) (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 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union (tptp.singleton X) Y) (tptp.set_builder X Y))))) (let ((_let_6 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))))) (let ((_let_8 (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_9 (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))))) (let ((_let_10 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))))) (let ((_let_11 (forall ((X $$unsorted)) (= (tptp.unordered_pair X X) (tptp.singleton X))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))))) (let ((_let_13 (tptp.unordered_pair tptp.x tptp.x))) (let ((_let_14 (tptp.singleton tptp.x))) (let ((_let_15 (= _let_14 _let_13))) (let ((_let_16 (tptp.member tptp.x _let_13))) (let ((_let_17 (tptp.member tptp.x _let_14))) (let ((_let_18 (_let_11))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (not _let_4))) (let ((_let_21 (or _let_20 _let_16))) (let ((_let_22 (_let_12))) (let ((_let_23 (ASSUME :args _let_22))) (let ((_let_24 (ASSUME :args (_let_4)))) (let ((_let_25 (not _let_17))) (let ((_let_26 (tptp.complement _let_14))) (let ((_let_27 (tptp.member tptp.x _let_26))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_28 _let_25))) (let ((_let_30 (_let_9))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (tptp.complement tptp.z))) (let ((_let_33 (tptp.intersection _let_26 _let_32))) (let ((_let_34 (tptp.member tptp.x _let_33))) (let ((_let_35 (not _let_34))) (let ((_let_36 (or _let_35 _let_27))) (let ((_let_37 (_let_10))) (let ((_let_38 (ASSUME :args _let_37))) (let ((_let_39 (tptp.complement _let_33))) (let ((_let_40 (tptp.member tptp.x _let_39))) (let ((_let_41 (or _let_20 _let_40 _let_34))) (let ((_let_42 (_let_8))) (let ((_let_43 (ASSUME :args _let_42))) (let ((_let_44 (tptp.union _let_14 tptp.z))) (let ((_let_45 (= _let_44 _let_39))) (let ((_let_46 (= _let_1 _let_44))) (let ((_let_47 (not _let_40))) (let ((_let_48 (_let_7))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (_let_5))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (ASSUME :args (_let_3)))) (let ((_let_53 (or))) (let ((_let_54 (and _let_3 _let_46 _let_45))) (let ((_let_55 (_let_3 _let_46 _let_45))) (let ((_let_56 (APPLY_UF tptp.member))) (let ((_let_57 (ASSUME :args (_let_46)))) (let ((_let_58 (ASSUME :args (_let_45)))) (let ((_let_59 (REFL :args (tptp.x)))) (let ((_let_60 (ASSUME :args (_let_25)))) (let ((_let_61 (ASSUME :args (_let_15)))) (let ((_let_62 (ASSUME :args (_let_16)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_60 _let_61 _let_62) :args (_let_15 _let_16 _let_25)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_62)) (CONG _let_59 (SYMM _let_61) :args _let_56) (FALSE_INTRO _let_60))) :args (_let_25 _let_15 _let_16)) :args ((not (and _let_15 _let_16 _let_25)) SB_LITERAL))) (CONG (REFL :args ((not _let_15))) (REFL :args ((not _let_16))) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_17))) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_25 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_36)) :args ((or _let_35 _let_27 (not _let_36)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_20 _let_40 _let_34 (not _let_41)))) _let_24 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_54)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_52 _let_57 _let_58) (SCOPE (FALSE_ELIM (TRANS (CONG _let_59 (TRANS (SYMM _let_58) (SYMM _let_57)) :args _let_56) (FALSE_INTRO _let_52))) :args _let_55)) :args _let_55)) :args (true _let_54)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args ((not _let_46))) (REFL :args ((not _let_45))) (REFL :args (_let_47)) :args _let_53)) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_51 :args (tptp.x tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_builder X Y)))) :args _let_50))) _let_51 :args (_let_46 false _let_5)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_14 tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union X Y)))) :args _let_48))) _let_49 :args (_let_45 false _let_7)) :args (_let_47 true _let_2 false _let_46 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (tptp.x _let_33 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) true))))) :args _let_42)) _let_43 :args (_let_41 false _let_8)) :args (_let_34 false _let_4 true _let_40 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_38 :args (tptp.x _let_26 _let_32 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.intersection X Y)) false))))) :args _let_37)) _let_38 :args (_let_36 false _let_10)) :args (_let_27 false _let_34 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.x _let_14 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.complement X)) false))))) :args _let_30)) _let_31 :args (_let_29 false _let_9)) :args (_let_25 false _let_27 false _let_29)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_21)) :args ((or _let_20 _let_16 (not _let_21)))) _let_24 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (tptp.x tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_22)) _let_23 :args (_let_21 false _let_12)) :args (_let_16 false _let_4 false _let_21)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton X)))) :args _let_18))) _let_19 :args (_let_15 false _let_11)) :args (false true _let_17 false _let_16 false _let_15)) :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 $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))) _let_12 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.member (tptp.unordered_pair X Y) tptp.universal_class)) _let_11 (forall ((X $$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)))) _let_10 (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_9 _let_8 _let_7 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))) (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_6) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.sum_class X) tptp.universal_class))) (forall ((X $$unsorted)) (= (tptp.complement (tptp.image tptp.element_relation (tptp.complement X))) (tptp.power_class X))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (tptp.member (tptp.power_class U) tptp.universal_class))) (forall ((Yr $$unsorted) (Xr $$unsorted)) (tptp.subclass (tptp.compose Yr Xr) (tptp.cross_product tptp.universal_class tptp.universal_class))) (forall ((Y $$unsorted) (Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted)) (or (not (tptp.member (tptp.ordered_pair Y Z) (tptp.compose Yr Xr))) (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y)))))) (forall ((Z $$unsorted) (Yr $$unsorted) (Xr $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair Y Z))) (or (not (tptp.member Z (tptp.image Yr (tptp.image Xr (tptp.singleton Y))))) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 (tptp.compose Yr Xr))))) (forall ((X $$unsorted)) (or (not (tptp.single_valued_class X)) (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation))) (forall ((X $$unsorted)) (or (not (tptp.subclass (tptp.compose X (tptp.inverse X)) tptp.identity_relation)) (tptp.single_valued_class X))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class)))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation))) (forall ((Xf $$unsorted)) (or (not (tptp.subclass Xf (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.subclass (tptp.compose Xf (tptp.inverse Xf)) tptp.identity_relation)) (tptp.function Xf))) (forall ((Xf $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X tptp.universal_class)) (tptp.member (tptp.image Xf X) tptp.universal_class))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (tptp.member (tptp.regular X) X))) (forall ((X $$unsorted)) (or (= X tptp.null_class) (= (tptp.intersection X (tptp.regular X)) tptp.null_class))) (forall ((Xf $$unsorted) (Y $$unsorted)) (= (tptp.sum_class (tptp.image Xf (tptp.singleton Y))) (tptp.apply Xf Y))) (tptp.function tptp.choice) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (= Y tptp.null_class) (tptp.member (tptp.apply tptp.choice Y) Y))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one Xf)) (tptp.function (tptp.inverse Xf)))) (forall ((Xf $$unsorted)) (or (not (tptp.function (tptp.inverse Xf))) (not (tptp.function Xf)) (tptp.one_to_one Xf))) (= (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))))) _let_5 _let_4 _let_3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.38/1.05  )
% 0.89/1.07  % SZS output end Proof for SET124-6
% 0.89/1.07  % cvc5---1.0.5 exiting
% 0.89/1.07  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------