TSTP Solution File: SET018-3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET018-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n020.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 0.58s 0.87s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.17 % Problem : SET018-3 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.18 % Command : do_cvc5 %s %d
% 0.15/0.42 % Computer : n020.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8042.1875MB
% 0.15/0.42 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Aug 26 12:39:30 EDT 2023
% 0.15/0.42 % CPUTime :
% 0.24/0.59 %----Proving TF0_NAR, FOF, or CNF
% 0.24/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.UKnGNKMG95/cvc5---1.0.5_15689.p...
% 0.24/0.62 ------- get file name : TPTP file name is SET018-3
% 0.24/0.63 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_15689.smt2...
% 0.24/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.58/0.87 % SZS status Unsatisfiable for SET018-3
% 0.58/0.87 % SZS output start Proof for SET018-3
% 0.58/0.89 (
% 0.58/0.89 (let ((_let_1 (= tptp.b tptp.d))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.ordered_pair tptp.c tptp.d))) (let ((_let_4 (tptp.ordered_pair tptp.a tptp.b))) (let ((_let_5 (= _let_4 _let_3))) (let ((_let_6 (tptp.little_set tptp.d))) (let ((_let_7 (tptp.little_set tptp.c))) (let ((_let_8 (tptp.little_set tptp.b))) (let ((_let_9 (tptp.little_set tptp.a))) (let ((_let_10 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (= (tptp.non_ordered_pair Z X) (tptp.non_ordered_pair Z Y))) (= X Y))))) (let ((_let_11 (forall ((X $$unsorted) (U $$unsorted) (Y $$unsorted) (V $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set U)) (not (= (tptp.ordered_pair X Y) (tptp.ordered_pair U V))) (= X U))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))))) (let ((_let_13 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))))) (let ((_let_14 (tptp.non_ordered_pair tptp.a tptp.b))) (let ((_let_15 (= _let_4 (tptp.non_ordered_pair (tptp.singleton_set tptp.a) _let_14)))) (let ((_let_16 (tptp.non_ordered_pair tptp.c tptp.d))) (let ((_let_17 (tptp.singleton_set tptp.c))) (let ((_let_18 (tptp.non_ordered_pair _let_17 _let_16))) (let ((_let_19 (= _let_3 _let_18))) (let ((_let_20 (= tptp.a tptp.c))) (let ((_let_21 (= _let_18 (tptp.non_ordered_pair _let_17 _let_14)))) (let ((_let_22 (ASSUME :args (_let_5)))) (let ((_let_23 (_let_12))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 ((tptp.ordered_pair X Y)))) (let ((_let_26 (not _let_5))) (let ((_let_27 (not _let_9))) (let ((_let_28 (not _let_7))) (let ((_let_29 (or _let_28 _let_27 _let_26 _let_20))) (let ((_let_30 (_let_11))) (let ((_let_31 (ASSUME :args _let_30))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_27 _let_28 _let_26 _let_20 (not _let_29)))) (ASSUME :args (_let_9)) (ASSUME :args (_let_7)) _let_22 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.c tptp.a tptp.d tptp.b QUANTIFIERS_INST_E_MATCHING ((tptp.ordered_pair X Y) (tptp.ordered_pair U V)))) :args _let_30))) _let_31 :args (_let_29 false _let_11)) :args (_let_20 false _let_9 false _let_7 false _let_5 false _let_29)))) (let ((_let_33 (= _let_14 _let_16))) (let ((_let_34 (not _let_21))) (let ((_let_35 (tptp.little_set _let_16))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.little_set _let_14))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_38 _let_36 _let_34 _let_33))) (let ((_let_40 (_let_10))) (let ((_let_41 (ASSUME :args _let_40))) (let ((_let_42 (= _let_14 (tptp.non_ordered_pair tptp.a tptp.d)))) (let ((_let_43 (not _let_33))) (let ((_let_44 (not _let_42))) (let ((_let_45 (not _let_6))) (let ((_let_46 (not _let_8))) (let ((_let_47 (or _let_46 _let_45 _let_44 _let_1))) (let ((_let_48 (or))) (let ((_let_49 (REFL :args ((not _let_20))))) (let ((_let_50 (and _let_20 _let_44))) (let ((_let_51 (ASSUME :args (_let_44)))) (let ((_let_52 (APPLY_UF tptp.non_ordered_pair))) (let ((_let_53 (ASSUME :args (_let_20)))) (let ((_let_54 (SYMM (SYMM _let_53)))) (let ((_let_55 (REFL :args (_let_14)))) (let ((_let_56 (_let_13))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 ((tptp.non_ordered_pair X Y)))) (let ((_let_59 (ASSUME :args (_let_34)))) (let ((_let_60 (ASSUME :args (_let_15)))) (let ((_let_61 (ASSUME :args (_let_19)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_59 (MODUS_PONENS (AND_INTRO _let_53 _let_60 _let_22 _let_61) (SCOPE (TRANS (SYMM _let_61) (SYMM _let_22) (SYMM (SYMM _let_60)) (CONG (CONG _let_54 :args (APPLY_UF tptp.singleton_set)) _let_55 :args _let_52)) :args (_let_20 _let_15 _let_5 _let_19)))) :args (_let_5 _let_15 _let_19 _let_20 _let_34)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO (SYMM (SYMM (ASSUME :args (_let_21)))))) (FALSE_INTRO _let_59))) :args (_let_34 _let_21)) :args ((not (and _let_5 _let_15 _let_19 _let_20 _let_34)) SB_LITERAL))) (CONG (REFL :args (_let_26)) (REFL :args ((not _let_15))) (REFL :args ((not _let_19))) _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_21))) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_38 _let_36 _let_33 _let_34 (not _let_39)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_56)) _let_57 :args (_let_37 false _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_58)) :args _let_56)) _let_57 :args (_let_35 false _let_13)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_50)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_51 _let_53) (SCOPE (FALSE_ELIM (TRANS (CONG _let_55 (CONG (SYMM _let_54) (REFL :args (tptp.d)) :args _let_52) :args (=)) (FALSE_INTRO _let_51))) :args (_let_44 _let_20))) :args (_let_20 _let_44))) :args (true _let_50)) (CONG _let_49 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_42))) (REFL :args (_let_43)) :args _let_48)) _let_32 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_1 _let_46 _let_45 _let_44 (not _let_47)))) (ASSUME :args (_let_2)) (ASSUME :args (_let_8)) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (tptp.b tptp.d tptp.a QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.little_set Y) false)) (tptp.non_ordered_pair Z X)))) :args _let_40)) _let_41 :args (_let_47 false _let_10)) :args (_let_44 true _let_1 false _let_8 false _let_6 false _let_47)) :args (_let_43 false _let_20 true _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_14 _let_16 _let_17 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.little_set X) false)) (tptp.non_ordered_pair Z Y)))) :args _let_40))) _let_41 :args (_let_39 false _let_10)) :args (_let_34 false _let_37 false _let_35 true _let_33 false _let_39)) _let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_23)) _let_24 :args (_let_19 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_23)) _let_24 :args (_let_15 false _let_12)) _let_22 :args (false true _let_21 false _let_20 false _let_19 false _let_15 false _let_5)) :args ((forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.little_set (tptp.f1 X Y)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.f1 X Y))) (or (tptp.member _let_1 X) (tptp.member _let_1 Y) (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.f1 X Y))) (or (not (tptp.member _let_1 X)) (not (tptp.member _let_1 Y)) (= X Y)))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.non_ordered_pair X Y))) (= U X) (= U Y))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U X)))) (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))) _let_13 (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))) _let_12 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f2 X)))) (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.f3 X)))) (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate X) (not (tptp.little_set Y)) (not (tptp.little_set Z)) (not (= X (tptp.ordered_pair Y Z))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f4 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.little_set (tptp.f5 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (= X (tptp.ordered_pair (tptp.f4 Z X) (tptp.f5 Z X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.first X))) (tptp.member Z (tptp.f4 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.first X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z U)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f6 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.little_set (tptp.f7 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (= X (tptp.ordered_pair (tptp.f6 Z X) (tptp.f7 Z X))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.second X))) (tptp.member Z (tptp.f7 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted)) (or (tptp.member Z (tptp.second X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= X (tptp.ordered_pair U V))) (not (tptp.member Z V)))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.estin)) (tptp.member (tptp.first Z) (tptp.second Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.estin) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) (tptp.second Z))))) (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 $$unsorted)) (or (tptp.member Z (tptp.intersection X Y)) (not (tptp.member Z X)) (not (tptp.member Z Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.complement X))) (not (tptp.member Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.complement X)) (not (tptp.little_set Z)) (tptp.member Z X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.union X Y) (tptp.complement (tptp.intersection (tptp.complement X) (tptp.complement Y))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.ordered_pair_predicate (tptp.f8 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (tptp.member (tptp.f8 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.domain_of X))) (= Z (tptp.first (tptp.f8 Z X))))) (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.domain_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.first Xp))))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.first Z) X))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.second Z) Y))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.cross_product X Y)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) X)) (not (tptp.member (tptp.second Z) Y)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.converse X))) (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.converse X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.ordered_pair (tptp.second Z) (tptp.first Z)) X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f9 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f10 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.little_set (tptp.f11 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (= Z (tptp.ordered_pair (tptp.f9 Z X) (tptp.ordered_pair (tptp.f10 Z X) (tptp.f11 Z X)))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.rotate_right X))) (tptp.member (tptp.ordered_pair (tptp.f10 Z X) (tptp.ordered_pair (tptp.f11 Z X) (tptp.f9 Z X))) X))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.rotate_right X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair V (tptp.ordered_pair W U)) X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f12 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f13 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.little_set (tptp.f14 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (= Z (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f13 Z X) (tptp.f14 Z X)))))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.flip_range_of X))) (tptp.member (tptp.ordered_pair (tptp.f12 Z X) (tptp.ordered_pair (tptp.f14 Z X) (tptp.f13 Z X))) X))) (forall ((Z $$unsorted) (X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.flip_range_of X)) (not (tptp.little_set Z)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair U (tptp.ordered_pair V W)))) (not (tptp.member (tptp.ordered_pair U (tptp.ordered_pair W V)) X)))) (forall ((X $$unsorted)) (= (tptp.successor X) (tptp.union X (tptp.singleton_set X)))) (forall ((Z $$unsorted)) (not (tptp.member Z tptp.empty_set))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.universal_set) (not (tptp.little_set Z)))) (tptp.little_set tptp.infinity) (tptp.member tptp.empty_set tptp.infinity) (forall ((X $$unsorted)) (or (not (tptp.member X tptp.infinity)) (tptp.member (tptp.successor X) tptp.infinity))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member (tptp.f16 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member Z (tptp.f16 Z X)))) (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.sigma X)) (not (tptp.member Y X)) (not (tptp.member Z Y)))) (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.sigma U)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (tptp.member (tptp.f17 X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (not (tptp.member (tptp.f17 X Y) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (tptp.subset X Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.proper_subset X Y)) (not (= X Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.proper_subset X Y) (not (tptp.subset X Y)) (= X Y))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.powerset X))) (tptp.subset Z X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (tptp.member Z (tptp.powerset X)) (not (tptp.little_set Z)) (not (tptp.subset Z X)))) (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.powerset U)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.relation Z)) (not (tptp.member X Z)) (tptp.ordered_pair_predicate X))) (forall ((Z $$unsorted)) (or (tptp.relation Z) (tptp.member (tptp.f18 Z) Z))) (forall ((Z $$unsorted)) (or (tptp.relation Z) (not (tptp.ordered_pair_predicate (tptp.f18 Z))))) (forall ((X $$unsorted) (U $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.single_valued_set X)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (tptp.little_set W)) (not (tptp.member (tptp.ordered_pair U V) X)) (not (tptp.member (tptp.ordered_pair U W) X)) (= V W))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f19 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f20 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f21 X)))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f20 X)) X))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f21 X)) X))) (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (not (= (tptp.f20 X) (tptp.f21 X))))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.relation Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.single_valued_set Xf))) (forall ((Xf $$unsorted)) (or (tptp.function Xf) (not (tptp.relation Xf)) (not (tptp.single_valued_set Xf)))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.ordered_pair_predicate (tptp.f22 Z X Xf)))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.f22 Z X Xf) Xf))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (tptp.member (tptp.first (tptp.f22 Z X Xf)) X))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (= (tptp.second (tptp.f22 Z X Xf)) Z))) (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.image X Xf)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Y)) (not (tptp.member Y Xf)) (not (tptp.member (tptp.first Y) X)) (not (= (tptp.second Y) Z)))) (forall ((X $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.function Xf)) (tptp.little_set (tptp.image X Xf)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.disjoint X Y)) (not (tptp.member U X)) (not (tptp.member U Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.disjoint X Y) (tptp.member (tptp.f23 X Y) Y))) (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.member (tptp.f24 X) X))) (forall ((X $$unsorted)) (or (= X tptp.empty_set) (tptp.disjoint (tptp.f24 X) X))) (tptp.function tptp.f25) (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.f26 X) X))) (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (= X tptp.empty_set) (tptp.member (tptp.ordered_pair X (tptp.f26 X)) tptp.f25))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.ordered_pair_predicate (tptp.f27 Z X)))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (tptp.member (tptp.f27 Z X) X))) (forall ((Z $$unsorted) (X $$unsorted)) (or (not (tptp.member Z (tptp.range_of X))) (= Z (tptp.second (tptp.f27 Z X))))) (forall ((Z $$unsorted) (X $$unsorted) (Xp $$unsorted)) (or (tptp.member Z (tptp.range_of X)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Xp)) (not (tptp.member Xp X)) (not (= Z (tptp.second Xp))))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (tptp.ordered_pair_predicate Z))) (forall ((Z $$unsorted)) (or (not (tptp.member Z tptp.identity_relation)) (= (tptp.first Z) (tptp.second Z)))) (forall ((Z $$unsorted)) (or (tptp.member Z tptp.identity_relation) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (= (tptp.first Z) (tptp.second Z))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.restrict X Y) (tptp.intersection X (tptp.cross_product Y tptp.universal_set)))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function Xf))) (forall ((Xf $$unsorted)) (or (not (tptp.one_to_one_function Xf)) (tptp.function (tptp.converse Xf)))) (forall ((Xf $$unsorted)) (or (tptp.one_to_one_function Xf) (not (tptp.function Xf)) (not (tptp.function (tptp.converse Xf))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.ordered_pair_predicate (tptp.f28 Z Xf Y)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member (tptp.f28 Z Xf Y) Xf))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= (tptp.first (tptp.f28 Z Xf Y)) Y))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member Z (tptp.second (tptp.f28 Z Xf Y))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.apply Xf Y)) (not (tptp.ordered_pair_predicate W)) (not (tptp.member W Xf)) (not (= (tptp.first W) Y)) (not (tptp.member Z (tptp.second W))))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.apply_to_two_arguments Xf X Y) (tptp.apply Xf (tptp.ordered_pair X Y)))) (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 $$unsorted)) (or (not (tptp.maps Xf X Y)) (tptp.subset (tptp.range_of Xf) Y))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.maps Xf X Y) (not (tptp.function Xf)) (not (= (tptp.domain_of Xf) X)) (not (tptp.subset (tptp.range_of Xf) Y)))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.little_set Xf))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (not (tptp.closed Xs Xf)) (tptp.maps Xf (tptp.cross_product Xs Xs) Xs))) (forall ((Xs $$unsorted) (Xf $$unsorted)) (or (tptp.closed Xs Xf) (not (tptp.little_set Xs)) (not (tptp.little_set Xf)) (not (tptp.maps Xf (tptp.cross_product Xs Xs) Xs)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f29 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f30 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f31 Z Xf Xg)))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (= Z (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f30 Z Xf Xg))))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f31 Z Xf Xg)) Xf))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f31 Z Xf Xg) (tptp.f30 Z Xf Xg)) Xg))) (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted) (X $$unsorted) (Y $$unsorted) (W $$unsorted)) (or (tptp.member Z (tptp.compose Xf Xg)) (not (tptp.little_set Z)) (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set W)) (not (= Z (tptp.ordered_pair X Y))) (not (tptp.member (tptp.ordered_pair X W) Xf)) (not (tptp.member (tptp.ordered_pair W Y) Xg)))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs1 Xf1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.closed Xs2 Xf2))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (tptp.maps Xh Xs1 Xs2))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2)) (not (tptp.member X Xs1)) (not (tptp.member Y Xs1)) (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 X Y)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh X) (tptp.apply Xh Y))))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2) Xs1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (tptp.member (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2) Xs1))) (forall ((Xh $$unsorted) (Xs1 $$unsorted) (Xf1 $$unsorted) (Xs2 $$unsorted) (Xf2 $$unsorted)) (let ((_let_1 (tptp.f33 Xh Xs1 Xf1 Xs2 Xf2))) (let ((_let_2 (tptp.f32 Xh Xs1 Xf1 Xs2 Xf2))) (or (tptp.homomorphism Xh Xs1 Xf1 Xs2 Xf2) (not (tptp.closed Xs1 Xf1)) (not (tptp.closed Xs2 Xf2)) (not (tptp.maps Xh Xs1 Xs2)) (not (= (tptp.apply Xh (tptp.apply_to_two_arguments Xf1 _let_2 _let_1)) (tptp.apply_to_two_arguments Xf2 (tptp.apply Xh _let_2) (tptp.apply Xh _let_1)))))))) _let_11 _let_10 _let_9 _let_8 _let_7 _let_6 _let_5 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.58/0.89 )
% 0.58/0.89 % SZS output end Proof for SET018-3
% 0.68/0.90 % cvc5---1.0.5 exiting
% 0.68/0.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------