TSTP Solution File: SET018-4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n029.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 14:36:50 EDT 2023
% Result : Unsatisfiable 25.61s 26.05s
% Output : Proof 25.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 08:39:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.51 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.EY42hsw1ct/cvc5---1.0.5_2525.p...
% 0.21/0.53 ------- get file name : TPTP file name is SET018-4
% 0.21/0.53 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_2525.smt2...
% 0.21/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.24/10.66 --- Run --no-e-matching --full-saturate-quant at 5...
% 15.51/15.71 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.52/20.76 --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.51/25.79 --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.61/26.05 % SZS status Unsatisfiable for SET018-4
% 25.61/26.05 % SZS output start Proof for SET018-4
% 25.61/26.06 (
% 25.61/26.06 (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)) (= (tptp.ordered_pair X Y) (tptp.non_ordered_pair (tptp.singleton_set X) (tptp.non_ordered_pair X Y)))))) (let ((_let_11 (forall ((X $$unsorted)) (= (tptp.singleton_set X) (tptp.non_ordered_pair X X))))) (let ((_let_12 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.little_set (tptp.non_ordered_pair X Y))))) (let ((_let_13 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U Y)))))) (let ((_let_14 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (tptp.member U (tptp.non_ordered_pair X Y)) (not (tptp.little_set U)) (not (= U X)))))) (let ((_let_15 (forall ((U $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.member U (tptp.non_ordered_pair X Y))) (= U X) (= U Y))))) (let ((_let_16 (= tptp.a tptp.d))) (let ((_let_17 (= tptp.b tptp.c))) (let ((_let_18 (= tptp.a tptp.c))) (let ((_let_19 (ASSUME :args (_let_2)))) (let ((_let_20 (tptp.non_ordered_pair tptp.a tptp.b))) (let ((_let_21 (tptp.member tptp.d _let_20))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_16 _let_1))) (let ((_let_24 (_let_15))) (let ((_let_25 (ASSUME :args _let_24))) (let ((_let_26 (tptp.non_ordered_pair tptp.c tptp.d))) (let ((_let_27 (= _let_20 _let_26))) (let ((_let_28 (tptp.member tptp.d _let_26))) (let ((_let_29 (tptp.singleton_set tptp.a))) (let ((_let_30 (tptp.non_ordered_pair _let_29 _let_20))) (let ((_let_31 (tptp.member _let_26 _let_30))) (let ((_let_32 (= _let_29 _let_26))) (let ((_let_33 (not _let_31))) (let ((_let_34 (or _let_33 _let_32 _let_27))) (let ((_let_35 (tptp.singleton_set tptp.c))) (let ((_let_36 (tptp.non_ordered_pair _let_35 _let_26))) (let ((_let_37 (tptp.member _let_20 _let_36))) (let ((_let_38 (= _let_20 _let_35))) (let ((_let_39 (not _let_37))) (let ((_let_40 (or _let_39 _let_38 _let_27))) (let ((_let_41 (tptp.non_ordered_pair tptp.a tptp.a))) (let ((_let_42 (= _let_29 _let_41))) (let ((_let_43 (tptp.member tptp.c _let_26))) (let ((_let_44 (tptp.member tptp.c _let_41))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_18 _let_18))) (let ((_let_47 (tptp.member _let_26 _let_36))) (let ((_let_48 (= _let_3 _let_36))) (let ((_let_49 (= _let_4 _let_30))) (let ((_let_50 (tptp.little_set _let_26))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_47 _let_51))) (let ((_let_53 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member Y (tptp.non_ordered_pair X Y)) (not (tptp.little_set Y)))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_13)) (MACRO_SR_EQ_INTRO :args (_let_13 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((tptp.non_ordered_pair X Y)))) (let ((_let_57 (_let_12))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 ((tptp.non_ordered_pair X Y)))) (let ((_let_60 (_let_10))) (let ((_let_61 (ASSUME :args _let_60))) (let ((_let_62 ((tptp.ordered_pair X Y)))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_60)) _let_61 :args (_let_48 false _let_10)))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_62)) :args _let_60)) _let_61 :args (_let_49 false _let_10)))) (let ((_let_65 (ASSUME :args (_let_5)))) (let ((_let_66 (and _let_5 _let_49 _let_48 _let_47))) (let ((_let_67 (ASSUME :args (_let_47)))) (let ((_let_68 (APPLY_UF tptp.member))) (let ((_let_69 (ASSUME :args (_let_48)))) (let ((_let_70 (SYMM _let_69))) (let ((_let_71 (SYMM _let_65))) (let ((_let_72 (ASSUME :args (_let_49)))) (let ((_let_73 (SYMM (SYMM _let_72)))) (let ((_let_74 (tptp.member _let_20 _let_30))) (let ((_let_75 (tptp.little_set _let_20))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_74 _let_76))) (let ((_let_78 (and _let_5 _let_49 _let_48 _let_74))) (let ((_let_79 (ASSUME :args (_let_74)))) (let ((_let_80 (TRANS _let_70 _let_71 _let_73))) (let ((_let_81 (_let_11))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (tptp.a QUANTIFIERS_INST_CBQI_PROP)) :args _let_81)) _let_82 :args (_let_42 false _let_11)))) (let ((_let_84 (not _let_7))) (let ((_let_85 (or _let_43 _let_84))) (let ((_let_86 (forall ((X $$unsorted) (Y $$unsorted)) (or (tptp.member X (tptp.non_ordered_pair X Y)) (not (tptp.little_set X)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (_let_86))) (let ((_let_89 ((tptp.non_ordered_pair X Y)))) (let ((_let_90 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_84 _let_43 (not _let_85)))) (ASSUME :args (_let_7)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_89)) :args _let_88)) _let_87 :args (_let_85 false _let_86)) :args (_let_43 false _let_7 false _let_85)))) (let ((_let_91 (or))) (let ((_let_92 (not _let_32))) (let ((_let_93 (REFL :args (_let_92)))) (let ((_let_94 (not _let_42))) (let ((_let_95 (REFL :args (_let_94)))) (let ((_let_96 (ASSUME :args (_let_45)))) (let ((_let_97 (ASSUME :args (_let_42)))) (let ((_let_98 (SYMM (SYMM _let_97)))) (let ((_let_99 (ASSUME :args (_let_32)))) (let ((_let_100 (TRANS (SYMM _let_99) _let_98))) (let ((_let_101 (ASSUME :args (_let_43)))) (let ((_let_102 (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_96 _let_97 _let_99 _let_101) :args (_let_42 _let_43 _let_32 _let_45)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_101)) (CONG (REFL :args (tptp.c)) _let_100 :args _let_68) (FALSE_INTRO _let_96))) :args (_let_45 _let_42 _let_32 _let_43)) :args ((not (and _let_42 _let_43 _let_32 _let_45)) SB_LITERAL))) (CONG _let_95 (REFL :args ((not _let_43))) _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_91)))) (let ((_let_103 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.c tptp.a tptp.a QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_24))) _let_25 :args (_let_46 false _let_15)))) (let ((_let_104 (REORDERING (FACTORING (CNF_OR_POS :args (_let_46))) :args ((or _let_18 _let_45 (not _let_46)))))) (let ((_let_105 (not _let_18))) (let ((_let_106 (not _let_38))) (let ((_let_107 (REFL :args (_let_105)))) (let ((_let_108 (not _let_27))) (let ((_let_109 (= _let_29 _let_35))) (let ((_let_110 (ASSUME :args (_let_109)))) (let ((_let_111 (SYMM _let_110))) (let ((_let_112 (ASSUME :args (_let_38)))) (let ((_let_113 (_let_108))) (let ((_let_114 (ASSUME :args _let_113))) (let ((_let_115 (_let_18))) (let ((_let_116 (ASSUME :args _let_115))) (let ((_let_117 (SYMM _let_116))) (let ((_let_118 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_97 (MODUS_PONENS _let_116 (SCOPE (CONG (SYMM _let_117) :args (APPLY_UF tptp.singleton_set)) :args _let_115)) _let_112 _let_99 _let_114) :args (_let_42 _let_32 _let_108 _let_38 _let_18)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_114)) (TRUE_INTRO (TRANS (TRANS (SYMM (SYMM _let_112)) _let_111) _let_98 (SYMM _let_100))))) :args (_let_42 _let_109 _let_38 _let_32 _let_108)) :args ((not (and _let_42 _let_32 _let_108 _let_38 _let_18)) SB_LITERAL))) (CONG _let_95 _let_93 (MACRO_SR_PRED_INTRO :args ((= (not _let_108) _let_27))) (REFL :args (_let_106)) _let_107 :args _let_91)) :args ((or _let_94 _let_27 _let_92 _let_106 _let_105))) _let_83 _let_104 _let_103 _let_102 _let_90 _let_83 (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_27 _let_39 _let_38 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_20 _let_35 _let_26 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24)) _let_25 :args (_let_40 false _let_15)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_72 _let_65 _let_69) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_20)) _let_80 :args _let_68) (TRUE_INTRO _let_79))) :args (_let_74 _let_49 _let_5 _let_48))) :args (_let_5 _let_49 _let_48 _let_74))) :args (true _let_78)) _let_65 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_74 _let_76 (not _let_77)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_57)) _let_58 :args (_let_75 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_29 _let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_77 false _let_53)) :args (_let_74 false _let_75 false _let_77)) :args (_let_37 false _let_5 false _let_49 false _let_48 false _let_74)) (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_32 _let_27 (not _let_34)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (_let_26 _let_29 _let_20 QUANTIFIERS_INST_CBQI_PROP)) :args _let_24))) _let_25 :args (_let_34 false _let_15)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_66)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_67 _let_69 _let_65 _let_72) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_26)) (TRANS (SYMM _let_73) (SYMM _let_71) (SYMM _let_70)) :args _let_68) (TRUE_INTRO _let_67))) :args (_let_47 _let_48 _let_5 _let_49))) :args (_let_5 _let_49 _let_48 _let_47))) :args (true _let_66)) _let_65 _let_64 _let_63 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_47 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_59)) :args _let_57)) _let_58 :args (_let_50 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (_let_35 _let_26 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_47 false _let_50 false _let_52)) :args (_let_31 false _let_5 false _let_49 false _let_48 false _let_47)) :args (_let_27 false _let_42 false _let_18 false _let_46 false _let_44 false _let_43 false _let_42 false _let_38 false _let_40 false _let_37 false _let_32 false _let_34 false _let_31)))) (let ((_let_119 (not _let_6))) (let ((_let_120 (or _let_28 _let_119))) (let ((_let_121 (ASSUME :args (_let_22)))) (let ((_let_122 (ASSUME :args (_let_27)))) (let ((_let_123 (SYMM _let_122))) (let ((_let_124 (ASSUME :args (_let_28)))) (let ((_let_125 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_1 _let_22 _let_16 (not _let_23)))) _let_19 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_121 _let_122 _let_124) :args (_let_28 _let_27 _let_22)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_124)) (CONG (REFL :args (tptp.d)) _let_123 :args _let_68) (FALSE_INTRO _let_121))) :args (_let_22 _let_27 _let_28)) :args ((not (and _let_28 _let_27 _let_22)) SB_LITERAL))) (CONG (REFL :args ((not _let_28))) (REFL :args _let_113) (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_91)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_120)) :args ((or _let_119 _let_28 (not _let_120)))) (ASSUME :args (_let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.c tptp.d QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_120 false _let_53)) :args (_let_28 false _let_6 false _let_120)) _let_118 :args (_let_21 false _let_28 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.d tptp.a tptp.b QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_24))) _let_25 :args (_let_23 false _let_15)) :args (_let_16 true _let_1 false _let_21 false _let_23)))) (let ((_let_126 (tptp.member tptp.b _let_26))) (let ((_let_127 (not _let_126))) (let ((_let_128 (or _let_127 _let_17 _let_1))) (let ((_let_129 (tptp.member tptp.b _let_20))) (let ((_let_130 (not _let_8))) (let ((_let_131 (or _let_129 _let_130))) (let ((_let_132 (and _let_129 _let_27))) (let ((_let_133 (_let_129 _let_27))) (let ((_let_134 (ASSUME :args (_let_129)))) (let ((_let_135 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_128)) :args ((or _let_1 _let_127 _let_17 (not _let_128)))) _let_19 (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_132)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_134 _let_122) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (tptp.b)) _let_123 :args _let_68) (TRUE_INTRO _let_134))) :args _let_133)) :args _let_133)) :args (true _let_132)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_131)) :args ((or _let_130 _let_129 (not _let_131)))) (ASSUME :args (_let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (tptp.a tptp.b QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_131 false _let_53)) :args (_let_129 false _let_8 false _let_131)) _let_118 :args (_let_126 false _let_129 false _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_25 :args (tptp.b tptp.c tptp.d QUANTIFIERS_INST_CBQI_CONFLICT)) :args _let_24)) _let_25 :args (_let_128 false _let_15)) :args (_let_17 true _let_1 false _let_126 false _let_128)))) (let ((_let_136 (tptp.member _let_29 _let_36))) (let ((_let_137 (not _let_136))) (let ((_let_138 (or _let_137 _let_109 _let_32))) (let ((_let_139 (tptp.member _let_29 _let_30))) (let ((_let_140 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(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_9 _let_8 _let_7 _let_6 _let_5 _let_2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 25.61/26.06 )
% 25.61/26.06 % SZS output end Proof for SET018-4
% 25.61/26.06 % cvc5---1.0.5 exiting
% 25.61/26.06 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------