TSTP Solution File: SET017-7 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET017-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n031.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 14:36:49 EDT 2023
% Result : Unsatisfiable 0.21s 0.63s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SET017-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.15 % Command : do_cvc5 %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 16:54:23 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.qyONMcAUK2/cvc5---1.0.5_10006.p...
% 0.21/0.53 ------- get file name : TPTP file name is SET017-7
% 0.21/0.53 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_10006.smt2...
% 0.21/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.63 % SZS status Unsatisfiable for SET017-7
% 0.21/0.63 % SZS output start Proof for SET017-7
% 0.21/0.63 (
% 0.21/0.63 (let ((_let_1 (= tptp.y tptp.z))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.cross_product tptp.universal_class tptp.universal_class))) (let ((_let_4 (tptp.member (tptp.ordered_pair tptp.y tptp.z) _let_3))) (let ((_let_5 (tptp.unordered_pair tptp.x tptp.z))) (let ((_let_6 (tptp.unordered_pair tptp.x tptp.y))) (let ((_let_7 (= _let_6 _let_5))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.unordered_pair X Y) (tptp.unordered_pair Y X))))) (let ((_let_9 (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))))) (let ((_let_10 (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))))) (let ((_let_11 (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.member Y tptp.universal_class)) (tptp.member Y (tptp.unordered_pair X Y)))))) (let ((_let_12 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.unordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_13 (= tptp.x tptp.z))) (let ((_let_14 (= tptp.x tptp.y))) (let ((_let_15 (ASSUME :args (_let_2)))) (let ((_let_16 (tptp.member tptp.z _let_6))) (let ((_let_17 (not _let_16))) (let ((_let_18 (or _let_17 _let_13 _let_1))) (let ((_let_19 (_let_12))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 ((not (= (tptp.member U (tptp.unordered_pair X Y)) false))))) (let ((_let_22 (tptp.member tptp.z _let_5))) (let ((_let_23 (tptp.member tptp.z tptp.universal_class))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_22))) (let ((_let_26 (_let_11))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 ((tptp.unordered_pair X Y)))) (let ((_let_29 (not _let_4))) (let ((_let_30 (or _let_29 _let_23))) (let ((_let_31 (_let_9))) (let ((_let_32 (ASSUME :args _let_31))) (let ((_let_33 (ASSUME :args (_let_4)))) (let ((_let_34 (ASSUME :args (_let_7)))) (let ((_let_35 (and _let_7 _let_22))) (let ((_let_36 (ASSUME :args (_let_22)))) (let ((_let_37 (APPLY_UF tptp.member))) (let ((_let_38 (SYMM _let_34))) (let ((_let_39 (tptp.unordered_pair tptp.z tptp.x))) (let ((_let_40 (tptp.member tptp.y _let_39))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_1 _let_14))) (let ((_let_43 (= _let_5 _let_39))) (let ((_let_44 (tptp.member tptp.y _let_6))) (let ((_let_45 (_let_8))) (let ((_let_46 (ASSUME :args _let_45))) (let ((_let_47 (tptp.member tptp.y tptp.universal_class))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_44))) (let ((_let_50 (or _let_29 _let_47))) (let ((_let_51 (_let_10))) (let ((_let_52 (ASSUME :args _let_51))) (let ((_let_53 (and _let_7 _let_44 _let_43))) (let ((_let_54 (ASSUME :args (_let_44)))) (let ((_let_55 (ASSUME :args (_let_43)))) (let ((_let_56 (ASSUME :args (_let_13)))) (let ((_let_57 (ASSUME :args (_let_14)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_56 _let_57 _let_15) :args (_let_2 _let_14 _let_13)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_15)) (TRUE_INTRO (TRANS (SYMM _let_57) (SYMM (SYMM _let_56)))))) :args (_let_13 _let_14 _let_2)) :args ((not (and _let_2 _let_14 _let_13)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args ((not _let_14))) (REFL :args ((not _let_13))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_1 _let_41 _let_14 (not _let_42)))) _let_15 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_53)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_54 _let_34 _let_55) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (tptp.y)) (TRANS (SYMM _let_55) _let_38) :args _let_37) (TRUE_INTRO _let_54))) :args (_let_44 _let_7 _let_43))) :args (_let_7 _let_44 _let_43))) :args (true _let_53)) _let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_48 _let_44 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_50)) :args ((or _let_29 _let_47 (not _let_50)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (tptp.y tptp.z tptp.universal_class tptp.universal_class QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_51)) _let_52 :args (_let_50 false _let_10)) :args (_let_47 false _let_4 false _let_50)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.y tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_26)) _let_27 :args (_let_49 false _let_11)) :args (_let_44 false _let_47 false _let_49)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (tptp.x tptp.z QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.unordered_pair X Y)))) :args _let_45)) _let_46 :args (_let_43 false _let_8)) :args (_let_40 false _let_7 false _let_44 false _let_43)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.y tptp.z tptp.x QUANTIFIERS_INST_E_MATCHING _let_21)) :args _let_19))) _let_20 :args (_let_42 false _let_12)) :args (_let_14 true _let_1 false _let_40 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_18)) :args ((or _let_1 _let_17 _let_13 (not _let_18)))) _let_15 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_35)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_36 _let_34) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (tptp.z)) (SYMM _let_38) :args _let_37) (TRUE_INTRO _let_36))) :args (_let_22 _let_7))) :args (_let_7 _let_22))) :args (true _let_35)) _let_34 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_22 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_23 (not _let_30)))) _let_33 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (tptp.y tptp.z tptp.universal_class tptp.universal_class QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.ordered_pair U V) (tptp.cross_product X Y)) false))))) :args _let_31)) _let_32 :args (_let_30 false _let_9)) :args (_let_23 false _let_4 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (tptp.z tptp.x QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_28)) :args _let_26)) _let_27 :args (_let_25 false _let_11)) :args (_let_22 false _let_23 false _let_25)) :args (_let_16 false _let_7 false _let_22)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_20 :args (tptp.z tptp.x tptp.y QUANTIFIERS_INST_E_MATCHING _let_21)) :args _let_19))) _let_20 :args (_let_18 false _let_12)) :args (_let_13 true _let_1 false _let_16 false _let_18)) _let_15 :args (false false _let_14 false _let_13 true _let_1)) :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 $$unsorted)) (or (not (tptp.subclass X Y)) (not (tptp.subclass Y X)) (= X Y))) _let_12 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X tptp.universal_class)) (tptp.member X (tptp.unordered_pair X Y)))) _let_11 (forall ((X $$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))) _let_10 _let_9 (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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (= (tptp.ordered_pair (tptp.first Z) (tptp.second Z)) Z))) (tptp.subclass tptp.element_relation _let_3) (forall ((X $$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 $$unsorted)) (= (tptp.union X (tptp.singleton X)) (tptp.successor X))) (tptp.subclass tptp.successor_relation _let_3) (forall ((X $$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_3 (tptp.intersection _let_3 (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)) (forall ((X $$unsorted)) (or (not (tptp.subclass X tptp.null_class)) (= X tptp.null_class))) (forall ((Z $$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) _let_8 (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))) _let_7 _let_4 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.63 )
% 0.21/0.64 % SZS output end Proof for SET017-7
% 0.21/0.64 % cvc5---1.0.5 exiting
% 0.21/0.64 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------