%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET028-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 14:36:59 EDT 2023

% Result   : Unsatisfiable 50.06s 50.28s
% Output   : Proof 50.06s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET028-3 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n023.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 10:50:41 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EikS4bRceK/cvc5---1.0.5_343.p...
% 0.21/0.52  ------- get file name : TPTP file name is SET028-3
% 0.21/0.52  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_343.smt2...
% 0.21/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.52/10.71  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.59/15.78  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.65/20.84  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.71/25.88  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.80/30.97  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.82/36.05  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.90/41.12  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 46.31/46.57  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 50.06/50.28  % SZS status Unsatisfiable for SET028-3
% 50.06/50.28  % SZS output start Proof for SET028-3
% 50.06/50.28  (
% 50.06/50.28  (let ((_let_1 (tptp.singleton_set tptp.element))) (let ((_let_2 (tptp.image _let_1 tptp.a_function))) (let ((_let_3 (tptp.sigma _let_2))) (let ((_let_4 (tptp.apply tptp.a_function tptp.element))) (let ((_let_5 (tptp.subset _let_4 _let_3))) (let ((_let_6 (not _let_5))) (let ((_let_7 (forall ((X $$unsorted)) (or (not (tptp.little_set X)) (tptp.member X (tptp.singleton_set X)))))) (let ((_let_8 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.second X)))))) (let ((_let_9 (forall ((X $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (tptp.little_set (tptp.first X)))))) (let ((_let_10 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member Z (tptp.second (tptp.f28 Z Xf Y))))))) (let ((_let_11 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= (tptp.first (tptp.f28 Z Xf Y)) Y))))) (let ((_let_12 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.member (tptp.f28 Z Xf Y) Xf))))) (let ((_let_13 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (tptp.ordered_pair_predicate (tptp.f28 Z Xf Y)))))) (let ((_let_14 (forall ((Z $$unsorted) (X $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.image X Xf)) (not (tptp.little_set Z)) (not (tptp.ordered_pair_predicate Y)) (not (tptp.member Y Xf)) (not (tptp.member (tptp.first Y) X)) (not (= (tptp.second Y) Z)))))) (let ((_let_15 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (not (tptp.member (tptp.f17 X Y) Y)))))) (let ((_let_16 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.subset X Y) (tptp.member (tptp.f17 X Y) X))))) (let ((_let_17 (forall ((Z $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member Z (tptp.sigma X)) (not (tptp.member Y X)) (not (tptp.member Z Y)))))) (let ((_let_18 (tptp.f17 _let_4 _let_3))) (let ((_let_19 (tptp.f28 _let_18 tptp.a_function tptp.element))) (let ((_let_20 (tptp.second _let_19))) (let ((_let_21 (tptp.member _let_18 _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (tptp.member _let_20 _let_2))) (let ((_let_24 (not _let_23))) (let ((_let_25 (tptp.member _let_18 _let_3))) (let ((_let_26 (or _let_25 _let_24 _let_22))) (let ((_let_27 (_let_17))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (not _let_26))) (let ((_let_30 (tptp.first _let_19))) (let ((_let_31 (tptp.member _let_30 _let_1))) (let ((_let_32 (not _let_31))) (let ((_let_33 (tptp.member _let_19 tptp.a_function))) (let ((_let_34 (not _let_33))) (let ((_let_35 (tptp.ordered_pair_predicate _let_19))) (let ((_let_36 (not _let_35))) (let ((_let_37 (tptp.little_set _let_20))) (let ((_let_38 (not _let_37))) (let ((_let_39 (or _let_23 _let_38 _let_36 _let_34 _let_32))) (let ((_let_40 (forall ((X $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.second Y))) (or (tptp.member _let_1 (tptp.image X Xf)) (not (tptp.little_set _let_1)) (not (tptp.ordered_pair_predicate Y)) (not (tptp.member Y Xf)) (not (tptp.member (tptp.first Y) X))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (= tptp.element _let_30))) (let ((_let_43 (tptp.member tptp.element _let_1))) (let ((_let_44 (tptp.member _let_18 _let_4))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_42))) (let ((_let_47 (forall ((Z $$unsorted) (Xf $$unsorted) (Y $$unsorted)) (or (not (tptp.member Z (tptp.apply Xf Y))) (= Y (tptp.first (tptp.f28 Z Xf Y))))))) (let ((_let_48 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_49 (or _let_5 _let_44))) (let ((_let_50 (_let_16))) (let ((_let_51 (ASSUME :args _let_50))) (let ((_let_52 (ASSUME :args (_let_6)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_49)) :args ((or _let_5 _let_44 (not _let_49)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (_let_4 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset X Y) true))))) :args _let_50)) _let_51 :args (_let_49 false _let_16)) :args (_let_44 true _let_5 false _let_49)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_42 (not _let_46)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_48 :args (_let_18 tptp.a_function tptp.element QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.apply Xf Y)) false))))) :args (_let_47))) _let_48 :args (_let_46 false _let_47)) :args (_let_42 false _let_44 false _let_46)))) (let ((_let_55 (tptp.little_set tptp.element))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_56 _let_43))) (let ((_let_58 (_let_7))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (tptp.little_set _let_30))) (let ((_let_61 (or _let_36 _let_60))) (let ((_let_62 (_let_9))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 (or _let_45 _let_35))) (let ((_let_65 (_let_13))) (let ((_let_66 (ASSUME :args _let_65))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_64)) :args ((or _let_45 _let_35 (not _let_64)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_66 :args (_let_18 tptp.a_function tptp.element QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.apply Xf Y)) false))))) :args _let_65)) _let_66 :args (_let_64 false _let_13)) :args (_let_35 false _let_44 false _let_64)))) (let ((_let_68 (and _let_42 _let_60))) (let ((_let_69 (ASSUME :args (_let_60)))) (let ((_let_70 (ASSUME :args (_let_42)))) (let ((_let_71 (SYMM _let_70))) (let ((_let_72 (and _let_43 _let_42))) (let ((_let_73 (_let_43 _let_42))) (let ((_let_74 (ASSUME :args (_let_43)))) (let ((_let_75 (or _let_36 _let_37))) (let ((_let_76 (_let_8))) (let ((_let_77 (ASSUME :args _let_76))) (let ((_let_78 (or _let_45 _let_33))) (let ((_let_79 (_let_12))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (or _let_45 _let_21))) (let ((_let_82 (_let_10))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (not _let_25))) (let ((_let_85 (or _let_5 _let_84))) (let ((_let_86 (_let_15))) (let ((_let_87 (ASSUME :args _let_86))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (_let_18 _let_2 _let_20 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_27)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_22 _let_24 _let_29))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_5 _let_84 (not _let_85)))) _let_52 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (_let_4 _let_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset X Y) true))))) :args _let_86)) _let_87 :args (_let_85 false _let_15)) :args (_let_84 true _let_5 false _let_85)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_45 _let_21 (not _let_81)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (_let_18 tptp.a_function tptp.element QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.apply Xf Y)) false))))) :args _let_82)) _let_83 :args (_let_81 false _let_10)) :args (_let_21 false _let_44 false _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_39)) :args ((or _let_36 _let_34 _let_38 _let_23 _let_32 (not _let_39)))) _let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_45 _let_33 (not _let_78)))) _let_53 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_18 tptp.a_function tptp.element QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member Z (tptp.apply Xf Y)) false))))) :args _let_79)) _let_80 :args (_let_78 false _let_12)) :args (_let_33 false _let_44 false _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_75)) :args ((or _let_36 _let_37 (not _let_75)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_77 :args (_let_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.ordered_pair_predicate X) false))))) :args _let_76)) _let_77 :args (_let_75 false _let_8)) :args (_let_37 false _let_35 false _let_75)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_72)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_74 _let_70) (SCOPE (TRUE_ELIM (TRANS (CONG _let_71 (REFL :args (_let_1)) :args (APPLY_UF tptp.member)) (TRUE_INTRO _let_74))) :args _let_73)) :args _let_73)) :args (true _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_56 _let_43 (not _let_57)))) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_68)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_69 _let_70) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM _let_71) :args (APPLY_UF tptp.little_set)) (TRUE_INTRO _let_69))) :args (_let_60 _let_42))) :args (_let_42 _let_60))) :args (true _let_68)) :args ((or _let_55 (not _let_42) (not _let_60)))) _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_36 _let_60 (not _let_61)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (_let_19 QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_62)) _let_63 :args (_let_61 false _let_9)) :args (_let_60 false _let_35 false _let_61)) :args (_let_55 false _let_42 false _let_60)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (tptp.element QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton_set X)))) :args _let_58)) _let_59 :args (_let_57 false _let_7)) :args (_let_43 false _let_55 false _let_57)) _let_54 :args (_let_31 false _let_43 false _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (_let_1 tptp.a_function _let_19 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.member (tptp.first Y) X) false)) (tptp.image X Xf)))) :args (_let_40))) _let_41 :args (_let_39 false _let_40)) :args (_let_23 false _let_35 false _let_33 false _let_37 false _let_31 false _let_39)) :args (_let_29 true _let_25 false _let_21 false _let_23)) _let_28 :args (false true _let_26 false _let_17)) :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 $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))) (forall ((X $$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 $$unsorted)) (or (not (tptp.ordered_pair_predicate X)) (= X (tptp.ordered_pair (tptp.f2 X) (tptp.f3 X))))) (forall ((X $$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 $$unsorted)) (or (not (tptp.member Z (tptp.sigma X))) (tptp.member Z (tptp.f16 Z X)))) _let_17 (forall ((U $$unsorted)) (or (not (tptp.little_set U)) (tptp.little_set (tptp.sigma U)))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted)) (or (not (tptp.subset X Y)) (not (tptp.member U X)) (tptp.member U Y))) _let_16 _let_15 (forall ((X $$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 $$unsorted)) (or (not (tptp.member Z (tptp.image X Xf))) (= (tptp.second (tptp.f22 Z X Xf)) Z))) _let_14 (forall ((X $$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 $$unsorted)) (or (tptp.one_to_one_function Xf) (not (tptp.function Xf)) (not (tptp.function (tptp.converse Xf))))) _let_13 _let_12 _let_11 _let_10 (forall ((Z $$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))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.little_set X)) (not (tptp.little_set Y)) (= (tptp.first (tptp.ordered_pair X Y)) X))) (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_9 _let_8 _let_7 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.ordered_pair X Y))) (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))) _let_6))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 50.06/50.28  )
% 50.06/50.29  % SZS output end Proof for SET028-3
% 50.06/50.29  % cvc5---1.0.5 exiting
% 50.06/50.29  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------