%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET042-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 14:37:05 EDT 2023

% Result   : Unsatisfiable 0.20s 0.62s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET042-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 11:08:39 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.agxwyoTb0T/cvc5---1.0.5_9238.p...
% 0.20/0.53  ------- get file name : TPTP file name is SET042-3
% 0.20/0.53  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9238.smt2...
% 0.20/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.62  % SZS status Unsatisfiable for SET042-3
% 0.20/0.62  % SZS output start Proof for SET042-3
% 0.20/0.63  (
% 0.20/0.63  (let ((_let_1 (tptp.ordered_pair tptp.a tptp.b))) (let ((_let_2 (tptp.member _let_1 (tptp.cross_product tptp.set_a tptp.set_b)))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.member tptp.b tptp.set_b))) (let ((_let_5 (tptp.member tptp.a tptp.set_a))) (let ((_let_6 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.ordered_pair X Y))))) (let ((_let_7 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.second (tptp.ordered_pair X Y)) Y))))) (let ((_let_8 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.first (tptp.ordered_pair X Y)) X))))) (let ((_let_9 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.cross_product X Y)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Z)) (not (tptp.member (tptp.first Z) X)) (not (tptp.member (tptp.second Z) Y)))))) (let ((_let_10 (forall ((X $$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))))))) (let ((_let_11 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X Y)) (tptp.little_set X))))) (let ((_let_12 (tptp.second _let_1))) (let ((_let_13 (tptp.member _let_12 tptp.set_b))) (let ((_let_14 (not _let_13))) (let ((_let_15 (tptp.first _let_1))) (let ((_let_16 (tptp.member _let_15 tptp.set_a))) (let ((_let_17 (not _let_16))) (let ((_let_18 (tptp.ordered_pair_predicate _let_1))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.little_set _let_1))) (let ((_let_21 (not _let_20))) (let ((_let_22 (or _let_2 _let_21 _let_19 _let_17 _let_14))) (let ((_let_23 (_let_9))) (let ((_let_24 (ASSUME :args _let_23))) (let ((_let_25 (tptp.little_set tptp.b))) (let ((_let_26 (not _let_25))) (let ((_let_27 (tptp.little_set tptp.a))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or _let_18 _let_28 _let_26))) (let ((_let_30 (forall ((Y $$unsorted) (Z $$unsorted)) (or (tptp.ordered_pair_predicate (tptp.ordered_pair Y Z)) (not (tptp.little_set Y)) (not (tptp.little_set Z)))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (not _let_4))) (let ((_let_33 (or _let_32 _let_25))) (let ((_let_34 (_let_11))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 ((not (= (tptp.member X Y) false))))) (let ((_let_37 (ASSUME :args (_let_4)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_25 (not _let_33)))) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.b tptp.set_b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_34)) _let_35 :args (_let_33 false _let_11)) :args (_let_25 false _let_4 false _let_33)))) (let ((_let_39 (not _let_5))) (let ((_let_40 (or _let_39 _let_27))) (let ((_let_41 (ASSUME :args (_let_5)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_27 (not _let_40)))) _let_41 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (tptp.a tptp.set_a QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_34)) _let_35 :args (_let_40 false _let_11)) :args (_let_27 false _let_5 false _let_40)))) (let ((_let_43 (_let_6))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (= tptp.a _let_15))) (let ((_let_46 (or _let_28 _let_26 _let_45))) (let ((_let_47 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= X (tptp.first (tptp.ordered_pair X Y))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (and _let_5 _let_45))) (let ((_let_50 (_let_5 _let_45))) (let ((_let_51 (APPLY_UF tptp.member))) (let ((_let_52 (ASSUME :args (_let_45)))) (let ((_let_53 (= tptp.b _let_12))) (let ((_let_54 (or _let_28 _let_26 _let_53))) (let ((_let_55 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= Y (tptp.second (tptp.ordered_pair X Y))))))) (let ((_let_56 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_57 (and _let_4 _let_53))) (let ((_let_58 (_let_4 _let_53))) (let ((_let_59 (ASSUME :args (_let_53)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_22)) :args ((or _let_2 _let_21 _let_19 _let_17 _let_14 (not _let_22)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_57)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_37 _let_59) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_59) (REFL :args (tptp.set_b)) :args _let_51) (TRUE_INTRO _let_37))) :args _let_58)) :args _let_58)) :args (true _let_57)) :args ((or _let_32 _let_13 (not _let_53)))) _let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_54)) :args ((or _let_28 _let_26 _let_53 (not _let_54)))) _let_42 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_56 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair X Y)))) :args (_let_55))) _let_56 :args (_let_54 false _let_55)) :args (_let_53 false _let_27 false _let_25 false _let_54)) :args (_let_13 false _let_4 false _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_49)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_41 _let_52) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_52) (REFL :args (tptp.set_a)) :args _let_51) (TRUE_INTRO _let_41))) :args _let_50)) :args _let_50)) :args (true _let_49)) :args ((or _let_39 _let_16 (not _let_45)))) _let_41 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_28 _let_26 _let_45 (not _let_46)))) _let_42 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair X Y)))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_45 false _let_27 false _let_25 false _let_46)) :args (_let_16 false _let_5 false _let_45)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair X Y)))) :args _let_43)) _let_44 :args (_let_20 false _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_29)) :args ((or _let_18 _let_28 _let_26 (not _let_29)))) _let_42 _let_38 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.ordered_pair Y Z)))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)) :args (_let_18 false _let_27 false _let_25 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_24 :args (_let_1 tptp.set_a tptp.set_b QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.cross_product X Y)) true))))) :args _let_23)) _let_24 :args (_let_22 false _let_9)) (ASSUME :args (_let_3)) :args (false false _let_13 false _let_16 false _let_20 false _let_18 false _let_22 true _let_2)) :args (_let_11 (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 $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))) (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))) (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 $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))) _let_10 (forall ((Z $$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 $$unsorted)) (or (not (tptp.member Z (tptp.cross_product X Y))) (tptp.member (tptp.second Z) Y))) _let_9 (forall ((Z $$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)))))))) (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))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (= (tptp.non_ordered_pair Z X) (tptp.non_ordered_pair Z Y))) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.little_set U)) (not (tptp.little_set V)) (not (= (tptp.ordered_pair X Y) (tptp.ordered_pair U V))) (= Y V))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.subset Y X)) (= X Y))) _let_8 _let_7 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.first X)))) (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.second X)))) (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (tptp.member X (tptp.singleton_set X)))) _let_6 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set X))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.subset Y Z)) (tptp.subset X Z))) (forall ((Xf $$unsorted) (Y $$unsorted)) (tptp.subset (tptp.apply Xf Y) (tptp.sigma (tptp.image (tptp.singleton_set Y) Xf)))) (forall ((Y $$unsorted) (Xf $$unsorted)) (tptp.subset (tptp.image (tptp.singleton_set Y) Xf) (tptp.apply Xf Y))) (forall ((Y $$unsorted) (X $$unsorted)) (or (not (tptp.function Y)) (tptp.little_set (tptp.apply Y X)))) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.relation (tptp.compose Y X))) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.subset (tptp.range_of (tptp.compose Y X)) (tptp.range_of Y))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.subset (tptp.range_of X) (tptp.domain_of Y))) (= (tptp.domain_of X) (tptp.domain_of (tptp.compose Y X))))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.function X)) (not (tptp.function Y)) (tptp.function (tptp.compose Y X)))) (forall ((Xf $$unsorted) (U $$unsorted) (V $$unsorted) (Xg $$unsorted) (W $$unsorted)) (or (not (tptp.maps Xf U V)) (not (tptp.maps Xg V W)) (tptp.maps (tptp.compose Xg Xf) U W))) (forall ((X $$unsorted) (Y $$unsorted) (Xf $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (not (tptp.function Xf)) (not (tptp.member (tptp.ordered_pair X Y) Xf)) (= (tptp.apply Xf X) Y))) (forall ((Xf $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (not (= (tptp.apply Xf X) Y)) (tptp.member (tptp.ordered_pair X Y) Xf))) (forall ((Xf $$unsorted) (Xd $$unsorted) (Xr $$unsorted) (X $$unsorted)) (or (not (tptp.maps Xf Xd Xr)) (not (tptp.member X Xd)) (tptp.member (tptp.apply Xf X) Xr))) (forall ((Xf $$unsorted) (X $$unsorted) (Xg $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (tptp.subset (tptp.apply Xg (tptp.apply Xf X)) (tptp.apply (tptp.compose Xg Xf) X)))) (forall ((Xf $$unsorted) (Xg $$unsorted) (X $$unsorted)) (or (not (tptp.function Xf)) (tptp.subset (tptp.apply (tptp.compose Xg Xf) X) (tptp.apply Xg (tptp.apply Xf X))))) (forall ((Xf $$unsorted) (X $$unsorted) (Xg $$unsorted)) (or (not (tptp.function Xf)) (not (tptp.member X (tptp.domain_of Xf))) (= (tptp.apply Xg (tptp.apply Xf X)) (tptp.apply (tptp.compose Xg Xf) X)))) _let_5 _let_4 _let_3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.63  )
% 0.20/0.63  % SZS output end Proof for SET042-3
% 0.20/0.63  % cvc5---1.0.5 exiting
% 0.20/0.64  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------