%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET096-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 14:37:39 EDT 2023

% Result   : Unsatisfiable 2.00s 2.24s
% Output   : Proof 2.00s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET096-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n006.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 11:31:22 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.49  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.0MP2qv1V7l/cvc5---1.0.5_28721.p...
% 0.21/0.52  ------- get file name : TPTP file name is SET096-7
% 0.21/0.52  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28721.smt2...
% 0.21/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 2.00/2.24  % SZS status Unsatisfiable for SET096-7
% 2.00/2.24  % SZS output start Proof for SET096-7
% 2.00/2.25  (
% 2.00/2.25  (let ((_let_1 (tptp.singleton tptp.y))) (let ((_let_2 (not (= _let_1 tptp.x)))) (let ((_let_3 (not (= tptp.x tptp.null_class)))) (let ((_let_4 (tptp.subclass tptp.x _let_1))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.subclass (tptp.singleton X) Y))))) (let ((_let_6 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y (tptp.singleton X))) (= Y X))))) (let ((_let_7 (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= X tptp.null_class))))) (let ((_let_8 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_9 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member (tptp.not_subclass_element X Y) X) (tptp.subclass X Y))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.member U X)) (tptp.member U Y))))) (let ((_let_12 (tptp.member tptp.y tptp.x))) (let ((_let_13 (tptp.not_subclass_element tptp.x tptp.null_class))) (let ((_let_14 (tptp.member _let_13 tptp.x))) (let ((_let_15 (= tptp.y _let_13))) (let ((_let_16 (tptp.subclass _let_1 tptp.x))) (let ((_let_17 (not _let_12))) (let ((_let_18 (or _let_17 _let_16))) (let ((_let_19 (_let_5))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (= tptp.x _let_1))) (let ((_let_22 (not _let_16))) (let ((_let_23 (not _let_4))) (let ((_let_24 (or _let_23 _let_22 _let_21))) (let ((_let_25 (_let_9))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 (ASSUME :args (_let_4)))) (let ((_let_28 (tptp.subclass tptp.x tptp.null_class))) (let ((_let_29 (or _let_14 _let_28))) (let ((_let_30 (_let_10))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (= tptp.null_class tptp.x))) (let ((_let_33 (not _let_28))) (let ((_let_34 (or _let_33 _let_32))) (let ((_let_35 (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= tptp.null_class X))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_28 _let_14 (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_32 _let_33 (not _let_34)))) (SYMM (ASSUME :args (_let_3))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X tptp.null_class) false))))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)) :args (_let_33 true _let_32 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.x tptp.null_class QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) true))))) :args _let_30)) _let_31 :args (_let_29 false _let_10)) :args (_let_14 true _let_28 false _let_29)))) (let ((_let_38 (tptp.member _let_13 _let_1))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_15))) (let ((_let_41 (_let_6))) (let ((_let_42 (ASSUME :args _let_41))) (let ((_let_43 (not _let_14))) (let ((_let_44 (or _let_23 _let_43 _let_38))) (let ((_let_45 (_let_11))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (ASSUME :args (_let_17)))) (let ((_let_48 (ASSUME :args (_let_15)))) (let ((_let_49 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_47 _let_48 _let_49) :args (_let_17 _let_14 _let_15)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_49)) (CONG (SYMM _let_48) (REFL :args (tptp.x)) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_47))) :args (_let_17 _let_15 _let_14)) :args ((not (and _let_17 _let_14 _let_15)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_17) _let_12))) (REFL :args (_let_43)) (REFL :args ((not _let_15))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_15 (not _let_40)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_23 _let_43 _let_38 (not _let_44)))) _let_27 _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.x _let_1 _let_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subclass X Y) false)) (not (= (tptp.member U X) false))))) :args _let_45)) _let_46 :args (_let_44 false _let_11)) :args (_let_38 false _let_4 false _let_14 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_13 tptp.y QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Y (tptp.singleton X)) false))))) :args _let_41))) _let_42 :args (_let_40 false _let_6)) :args (_let_15 false _let_38 false _let_40)) _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_16 _let_17 (not _let_18)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_21 _let_23 _let_22 (not _let_24)))) (SYMM (ASSUME :args (_let_2))) _let_27 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (tptp.x _let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subclass X Y) false))))) :args _let_25)) _let_26 :args (_let_24 false _let_9)) :args (_let_22 true _let_21 false _let_4 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.y tptp.x QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.subclass (tptp.singleton X) Y) true))))) :args _let_19)) _let_20 :args (_let_18 false _let_5)) :args (_let_17 true _let_16 false _let_18)) :args (false false _let_15 false _let_14 true _let_12)) :args (_let_11 _let_10 (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))) _let_9 (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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_8) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.element_relation)) (tptp.member X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (not (tptp.member X Y)) (tptp.member _let_1 tptp.element_relation)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z X))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.intersection X Y))) (tptp.member Z Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z X)) (not (tptp.member Z Y)) (tptp.member Z (tptp.intersection X Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (tptp.member Z (tptp.complement X)) (tptp.member Z X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))) (tptp.union X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.intersection (tptp.complement (tptp.intersection X Y)) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y)))) (tptp.symmetric_difference X Y))) (forall ((Xr $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.intersection Xr (tptp.cross_product X Y)) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Xr $$unsorted)) (= (tptp.intersection (tptp.cross_product X Y) Xr) (tptp.restrict Xr X Y))) (forall ((X $$unsorted) (Z $$unsorted)) (or (not (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class)) (not (tptp.member Z (tptp.domain_of X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z tptp.universal_class)) (= (tptp.restrict X (tptp.singleton Z) tptp.universal_class) tptp.null_class) (tptp.member Z (tptp.domain_of X)))) (forall ((X $$unsorted)) (tptp.subclass (tptp.rotate X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.rotate X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X))) (forall ((V $$unsorted) (W $$unsorted) (U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V W) U) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.rotate X))))) (forall ((X $$unsorted)) (tptp.subclass (tptp.flip X) (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair U V) W) (tptp.flip X))) (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X))) (forall ((V $$unsorted) (U $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ordered_pair (tptp.ordered_pair U V) W))) (or (not (tptp.member (tptp.ordered_pair (tptp.ordered_pair V U) W) X)) (not (tptp.member _let_1 (tptp.cross_product (tptp.cross_product tptp.universal_class tptp.universal_class) tptp.universal_class))) (tptp.member _let_1 (tptp.flip X))))) (forall ((Y $$unsorted)) (= (tptp.domain_of (tptp.flip (tptp.cross_product Y tptp.universal_class))) (tptp.inverse Y))) (forall ((Z $$unsorted)) (= (tptp.domain_of (tptp.inverse Z)) (tptp.range_of Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.first (tptp.not_subclass_element (tptp.restrict Z X (tptp.singleton Y)) tptp.null_class)) (tptp.domain Z X Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.second (tptp.not_subclass_element (tptp.restrict Z (tptp.singleton X) Y) tptp.null_class)) (tptp.range Z X Y))) (forall ((Xr $$unsorted) (X $$unsorted)) (= (tptp.range_of (tptp.restrict Xr X tptp.universal_class)) (tptp.image Xr X))) (forall ((X $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_8) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) tptp.successor_relation)) (= (tptp.successor X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (= (tptp.successor X) Y)) (not (tptp.member _let_1 (tptp.cross_product tptp.universal_class tptp.universal_class))) (tptp.member _let_1 tptp.successor_relation)))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.member tptp.null_class X))) (forall ((X $$unsorted)) (or (not (tptp.inductive X)) (tptp.subclass (tptp.image tptp.successor_relation X) X))) (forall ((X $$unsorted)) (or (not (tptp.member tptp.null_class X)) (not (tptp.subclass (tptp.image tptp.successor_relation X) X)) (tptp.inductive X))) (tptp.inductive tptp.omega) (forall ((Y $$unsorted)) (or (not (tptp.inductive Y)) (tptp.subclass tptp.omega Y))) (tptp.member tptp.omega tptp.universal_class) (forall ((X $$unsorted)) (= (tptp.domain_of (tptp.restrict tptp.element_relation tptp.universal_class X)) (tptp.sum_class X))) (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_8 (tptp.intersection _let_8 (tptp.complement (tptp.compose (tptp.complement tptp.element_relation) (tptp.inverse tptp.element_relation))))) tptp.subset_relation) (= (tptp.intersection (tptp.inverse tptp.subset_relation) tptp.subset_relation) tptp.identity_relation) (forall ((Xr $$unsorted)) (= (tptp.complement (tptp.domain_of (tptp.intersection Xr tptp.identity_relation))) (tptp.diagonalise Xr))) (forall ((X $$unsorted)) (= (tptp.intersection (tptp.domain_of X) (tptp.diagonalise (tptp.compose (tptp.inverse tptp.element_relation) X))) (tptp.cantor X))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.operation Xf)) (= (tptp.cross_product _let_2 _let_2) _let_1))))) (forall ((Xf $$unsorted)) (or (not (tptp.operation Xf)) (tptp.subclass (tptp.range_of Xf) (tptp.domain_of (tptp.domain_of Xf))))) (forall ((Xf $$unsorted)) (let ((_let_1 (tptp.domain_of Xf))) (let ((_let_2 (tptp.domain_of _let_1))) (or (not (tptp.function Xf)) (not (= (tptp.cross_product _let_2 _let_2) _let_1)) (not (tptp.subclass (tptp.range_of Xf) _let_2)) (tptp.operation Xf))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.function Xh))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh)))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.compatible Xh Xf1 Xf2)) (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2))))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.function Xh)) (not (= (tptp.domain_of (tptp.domain_of Xf1)) (tptp.domain_of Xh))) (not (tptp.subclass (tptp.range_of Xh) (tptp.domain_of (tptp.domain_of Xf2)))) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf1))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.operation Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (tptp.compatible Xh Xf1 Xf2))) (forall ((Xh $$unsorted) (Xf1 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ordered_pair X Y))) (or (not (tptp.homomorphism Xh Xf1 Xf2)) (not (tptp.member _let_1 (tptp.domain_of Xf1))) (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh X) (tptp.apply Xh Y))) (tptp.apply Xh (tptp.apply Xf1 _let_1)))))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (tptp.member (tptp.ordered_pair (tptp.not_homomorphism1 Xh Xf1 Xf2) (tptp.not_homomorphism2 Xh Xf1 Xf2)) (tptp.domain_of Xf1)) (tptp.homomorphism Xh Xf1 Xf2))) (forall ((Xf1 $$unsorted) (Xf2 $$unsorted) (Xh $$unsorted)) (let ((_let_1 (tptp.not_homomorphism2 Xh Xf1 Xf2))) (let ((_let_2 (tptp.not_homomorphism1 Xh Xf1 Xf2))) (or (not (tptp.operation Xf1)) (not (tptp.operation Xf2)) (not (tptp.compatible Xh Xf1 Xf2)) (not (= (tptp.apply Xf2 (tptp.ordered_pair (tptp.apply Xh _let_2) (tptp.apply Xh _let_1))) (tptp.apply Xh (tptp.apply Xf1 (tptp.ordered_pair _let_2 _let_1))))) (tptp.homomorphism Xh Xf1 Xf2))))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member X (tptp.unordered_pair X Y)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (tptp.member Y (tptp.unordered_pair X Y)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member U tptp.universal_class))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y))) (tptp.member V tptp.universal_class))) (forall ((X $$unsorted)) (tptp.subclass X X)) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y Z)) (tptp.subclass X Z))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= X Y) (tptp.member (tptp.not_subclass_element X Y) X) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (= X Y) (tptp.member (tptp.not_subclass_element Y X) Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y) (tptp.member (tptp.not_subclass_element X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member (tptp.not_subclass_element X Y) Y)) (not (tptp.member (tptp.not_subclass_element Y X) X)) (= X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (not (tptp.member Y (tptp.intersection (tptp.complement X) X)))) (forall ((Z $$unsorted)) (not (tptp.member Z tptp.null_class))) (forall ((X $$unsorted)) (tptp.subclass tptp.null_class X)) _let_7 (forall ((Z $$unsorted)) (or (= Z tptp.null_class) (tptp.member (tptp.not_subclass_element Z tptp.null_class) Z))) (tptp.member tptp.null_class tptp.universal_class) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair X Y) (tptp.unordered_pair Y X))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.subclass (tptp.singleton X) (tptp.unordered_pair X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.subclass (tptp.singleton Y) (tptp.unordered_pair X Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (tptp.member Y tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton X)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member X tptp.universal_class) (= (tptp.unordered_pair X Y) (tptp.singleton Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (= (tptp.unordered_pair X Y) tptp.null_class) (tptp.member X tptp.universal_class) (tptp.member Y tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (= (tptp.unordered_pair X Y) (tptp.unordered_pair X Z))) (not (tptp.member (tptp.ordered_pair Y Z) (tptp.cross_product tptp.universal_class tptp.universal_class))) (= Y Z))) (forall ((X $$unsorted) (Z $$unsorted) (Y $$unsorted)) (or (not (= (tptp.unordered_pair X Z) (tptp.unordered_pair Y Z))) (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product tptp.universal_class tptp.universal_class))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (not (= (tptp.unordered_pair X Y) tptp.null_class)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.member (tptp.ordered_pair X Y) (tptp.cross_product U V))) (not (= (tptp.unordered_pair X Y) tptp.null_class)))) (forall ((X $$unsorted) (Z $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Z)) (not (tptp.member Y Z)) (tptp.subclass (tptp.unordered_pair X Y) Z))) (forall ((X $$unsorted)) (tptp.member (tptp.singleton X) tptp.universal_class)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.singleton Y))) (tptp.member _let_1 (tptp.unordered_pair X _let_1)))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.singleton X)))) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (not (= (tptp.singleton X) tptp.null_class)))) (tptp.member tptp.null_class (tptp.singleton tptp.null_class)) _let_6 (forall ((X $$unsorted)) (or (tptp.member X tptp.universal_class) (= (tptp.singleton X) tptp.null_class))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.singleton X) (tptp.singleton Y))) (not (tptp.member X tptp.universal_class)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.singleton X) (tptp.singleton Y))) (not (tptp.member Y tptp.universal_class)) (= X Y))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (or (not (= (tptp.unordered_pair Y Z) (tptp.singleton X))) (not (tptp.member X tptp.universal_class)) (= X Y) (= X Z))) (forall ((Y $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member (tptp.member_of (tptp.singleton Y)) tptp.universal_class))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.singleton Y))) (or (not (tptp.member Y tptp.universal_class)) (= (tptp.singleton (tptp.member_of _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.member_of X))) (or (tptp.member _let_1 tptp.universal_class) (= _let_1 X)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.member_of X))) (or (= (tptp.singleton _let_1) X) (= _let_1 X)))) (forall ((U $$unsorted)) (or (not (tptp.member U tptp.universal_class)) (= (tptp.member_of (tptp.singleton U)) U))) (forall ((X $$unsorted)) (or (tptp.member (tptp.member_of1 X) tptp.universal_class) (= (tptp.member_of X) X))) (forall ((X $$unsorted)) (or (= (tptp.singleton (tptp.member_of1 X)) X) (= (tptp.member_of X) X))) (forall ((X $$unsorted)) (or (not (= (tptp.singleton (tptp.member_of X)) X)) (tptp.member X tptp.universal_class))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.member_of X))) (or (not (= (tptp.singleton _let_1) X)) (not (tptp.member Y X)) (= _let_1 Y)))) _let_5 _let_4 _let_3 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.00/2.25  )
% 2.00/2.26  % SZS output end Proof for SET096-7
% 2.00/2.26  % cvc5---1.0.5 exiting
% 2.00/2.26  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------