TSTP Solution File: SET034-3 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET034-3 : 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 14:37:01 EDT 2023
% Result : Unsatisfiable 0.95s 1.13s
% Output : Proof 0.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET034-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.15/0.37 % Computer : n029.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sat Aug 26 15:55:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.52 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XnmY7nNE3W/cvc5---1.0.5_24202.p...
% 0.23/0.55 ------- get file name : TPTP file name is SET034-3
% 0.23/0.55 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24202.smt2...
% 0.23/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.95/1.13 % SZS status Unsatisfiable for SET034-3
% 0.95/1.13 % SZS output start Proof for SET034-3
% 0.95/1.14 (
% 0.95/1.14 (let ((_let_1 (tptp.compose tptp.another_function tptp.a_function))) (let ((_let_2 (tptp.function _let_1))) (let ((_let_3 (not _let_2))) (let ((_let_4 (tptp.function tptp.another_function))) (let ((_let_5 (tptp.function tptp.a_function))) (let ((_let_6 (forall ((Y $$unsorted) (X $$unsorted)) (tptp.relation (tptp.compose Y X))))) (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 $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.member (tptp.ordered_pair (tptp.f31 Z Xf Xg) (tptp.f30 Z Xf Xg)) Xg))))) (let ((_let_10 (forall ((Z $$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))))) (let ((_let_11 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (= Z (tptp.ordered_pair (tptp.f29 Z Xf Xg) (tptp.f30 Z Xf Xg))))))) (let ((_let_12 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f31 Z Xf Xg)))))) (let ((_let_13 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f30 Z Xf Xg)))))) (let ((_let_14 (forall ((Z $$unsorted) (Xf $$unsorted) (Xg $$unsorted)) (or (not (tptp.member Z (tptp.compose Xf Xg))) (tptp.little_set (tptp.f29 Z Xf Xg)))))) (let ((_let_15 (forall ((Xf $$unsorted)) (or (tptp.function Xf) (not (tptp.relation Xf)) (not (tptp.single_valued_set Xf)))))) (let ((_let_16 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.single_valued_set Xf))))) (let ((_let_17 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (not (= (tptp.f20 X) (tptp.f21 X))))))) (let ((_let_18 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f21 X)) X))))) (let ((_let_19 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.member (tptp.ordered_pair (tptp.f19 X) (tptp.f20 X)) X))))) (let ((_let_20 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f21 X)))))) (let ((_let_21 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f20 X)))))) (let ((_let_22 (forall ((X $$unsorted)) (or (tptp.single_valued_set X) (tptp.little_set (tptp.f19 X)))))) (let ((_let_23 (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))))) (let ((_let_24 (tptp.f20 _let_1))) (let ((_let_25 (tptp.f19 _let_1))) (let ((_let_26 (tptp.ordered_pair _let_25 _let_24))) (let ((_let_27 (tptp.f30 _let_26 tptp.another_function tptp.a_function))) (let ((_let_28 (tptp.f29 _let_26 tptp.another_function tptp.a_function))) (let ((_let_29 (tptp.ordered_pair _let_28 _let_27))) (let ((_let_30 (= _let_26 _let_29))) (let ((_let_31 (tptp.f31 _let_26 tptp.another_function tptp.a_function))) (let ((_let_32 (tptp.member (tptp.ordered_pair _let_31 _let_27) tptp.a_function))) (let ((_let_33 (= _let_24 (tptp.second _let_26)))) (let ((_let_34 (= _let_27 (tptp.second _let_29)))) (let ((_let_35 (tptp.f21 _let_1))) (let ((_let_36 (tptp.ordered_pair _let_25 _let_35))) (let ((_let_37 (tptp.f31 _let_36 tptp.another_function tptp.a_function))) (let ((_let_38 (tptp.member (tptp.ordered_pair _let_37 _let_24) tptp.a_function))) (let ((_let_39 (= _let_37 _let_31))) (let ((_let_40 (tptp.member _let_26 _let_1))) (let ((_let_41 (not _let_40))) (let ((_let_42 (or _let_41 _let_30))) (let ((_let_43 (_let_11))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 ((not (= (tptp.member Z (tptp.compose Xf Xg)) false))))) (let ((_let_46 (tptp.single_valued_set _let_1))) (let ((_let_47 (or _let_46 _let_40))) (let ((_let_48 (_let_19))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 (not _let_46))) (let ((_let_51 (tptp.relation _let_1))) (let ((_let_52 (not _let_51))) (let ((_let_53 (or _let_2 _let_52 _let_50))) (let ((_let_54 (_let_15))) (let ((_let_55 (ASSUME :args _let_54))) (let ((_let_56 (_let_6))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_2 _let_52 _let_50 (not _let_53)))) (ASSUME :args (_let_3)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.compose Y X)))) :args _let_56)) _let_57 :args (_let_51 false _let_6)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_55 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.function Xf) true))))) :args _let_54)) _let_55 :args (_let_53 false _let_15)) :args (_let_50 true _let_2 false _let_51 false _let_53)))) (let ((_let_59 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_40 (not _let_47)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_49 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.single_valued_set X) true))))) :args _let_48)) _let_49 :args (_let_47 false _let_19)) :args (_let_40 true _let_46 false _let_47)))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_41 _let_30 (not _let_42)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_26 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_45)) :args _let_43)) _let_44 :args (_let_42 false _let_11)) :args (_let_30 false _let_40 false _let_42)))) (let ((_let_61 (or _let_41 _let_32))) (let ((_let_62 (_let_9))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 ((not (= (tptp.member Z (tptp.compose Xf Xg)) false))))) (let ((_let_65 (tptp.little_set _let_24))) (let ((_let_66 (not _let_65))) (let ((_let_67 (tptp.little_set _let_25))) (let ((_let_68 (not _let_67))) (let ((_let_69 (or _let_68 _let_66 _let_33))) (let ((_let_70 (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_71 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_70))) (let ((_let_73 ((tptp.ordered_pair X Y)))) (let ((_let_74 (or _let_46 _let_65))) (let ((_let_75 (_let_21))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_46 _let_65 (not _let_74)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.single_valued_set X) true))))) :args _let_75)) _let_76 :args (_let_74 false _let_21)) :args (_let_65 true _let_46 false _let_74)))) (let ((_let_78 (or _let_46 _let_67))) (let ((_let_79 (_let_22))) (let ((_let_80 (ASSUME :args _let_79))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_78)) :args ((or _let_46 _let_67 (not _let_78)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.single_valued_set X) true))))) :args _let_79)) _let_80 :args (_let_78 false _let_22)) :args (_let_67 true _let_46 false _let_78)))) (let ((_let_82 (tptp.little_set _let_27))) (let ((_let_83 (not _let_82))) (let ((_let_84 (tptp.little_set _let_28))) (let ((_let_85 (not _let_84))) (let ((_let_86 (or _let_85 _let_83 _let_34))) (let ((_let_87 (or _let_41 _let_82))) (let ((_let_88 (_let_13))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 ((not (= (tptp.member Z (tptp.compose Xf Xg)) false))))) (let ((_let_91 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_41 _let_82 (not _let_87)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_26 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_90)) :args _let_88)) _let_89 :args (_let_87 false _let_13)) :args (_let_82 false _let_40 false _let_87)))) (let ((_let_92 (or _let_41 _let_84))) (let ((_let_93 (_let_14))) (let ((_let_94 (ASSUME :args _let_93))) (let ((_let_95 ((not (= (tptp.member Z (tptp.compose Xf Xg)) false))))) (let ((_let_96 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_92)) :args ((or _let_41 _let_84 (not _let_92)))) _let_59 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_26 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_95)) :args _let_93)) _let_94 :args (_let_92 false _let_14)) :args (_let_84 false _let_40 false _let_92)))) (let ((_let_97 (tptp.f30 _let_36 tptp.another_function tptp.a_function))) (let ((_let_98 (= _let_24 _let_97))) (let ((_let_99 (tptp.member (tptp.ordered_pair _let_37 _let_97) tptp.a_function))) (let ((_let_100 (not _let_99))) (let ((_let_101 (not _let_38))) (let ((_let_102 (tptp.little_set _let_97))) (let ((_let_103 (not _let_102))) (let ((_let_104 (tptp.little_set _let_37))) (let ((_let_105 (not _let_104))) (let ((_let_106 (tptp.single_valued_set tptp.a_function))) (let ((_let_107 (not _let_106))) (let ((_let_108 (or _let_107 _let_105 _let_66 _let_103 _let_101 _let_100 _let_98))) (let ((_let_109 (_let_23))) (let ((_let_110 (ASSUME :args _let_109))) (let ((_let_111 ((not (= (tptp.member (tptp.ordered_pair U W) X) false)) (not (= (tptp.little_set V) false))))) (let ((_let_112 (tptp.f29 _let_36 tptp.another_function tptp.a_function))) (let ((_let_113 (tptp.ordered_pair _let_112 _let_97))) (let ((_let_114 (= _let_97 (tptp.second _let_113)))) (let ((_let_115 (= _let_35 (tptp.second _let_36)))) (let ((_let_116 (= _let_36 _let_113))) (let ((_let_117 (= _let_24 _let_35))) (let ((_let_118 (not _let_98))) (let ((_let_119 (tptp.little_set _let_112))) (let ((_let_120 (not _let_119))) (let ((_let_121 (or _let_120 _let_103 _let_114))) (let ((_let_122 (tptp.member _let_36 _let_1))) (let ((_let_123 (not _let_122))) (let ((_let_124 (or _let_123 _let_102))) (let ((_let_125 (or _let_46 _let_122))) (let ((_let_126 (_let_18))) (let ((_let_127 (ASSUME :args _let_126))) (let ((_let_128 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_125)) :args ((or _let_46 _let_122 (not _let_125)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_127 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.single_valued_set X) true))))) :args _let_126)) _let_127 :args (_let_125 false _let_18)) :args (_let_122 true _let_46 false _let_125)))) (let ((_let_129 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_124)) :args ((or _let_123 _let_102 (not _let_124)))) _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_36 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_90)) :args _let_88)) _let_89 :args (_let_124 false _let_13)) :args (_let_102 false _let_122 false _let_124)))) (let ((_let_130 (or _let_123 _let_119))) (let ((_let_131 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_130)) :args ((or _let_123 _let_119 (not _let_130)))) _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_94 :args (_let_36 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_95)) :args _let_93)) _let_94 :args (_let_130 false _let_14)) :args (_let_119 false _let_122 false _let_130)))) (let ((_let_132 (tptp.little_set _let_35))) (let ((_let_133 (not _let_132))) (let ((_let_134 (or _let_68 _let_133 _let_115))) (let ((_let_135 (or _let_46 _let_132))) (let ((_let_136 (_let_20))) (let ((_let_137 (ASSUME :args _let_136))) (let ((_let_138 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_135)) :args ((or _let_46 _let_132 (not _let_135)))) _let_58 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_137 :args (_let_1 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.single_valued_set X) true))))) :args _let_136)) _let_137 :args (_let_135 false _let_20)) :args (_let_132 true _let_46 false _let_135)))) (let ((_let_139 (or _let_123 _let_116))) (let ((_let_140 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_139)) :args ((or _let_123 _let_116 (not _let_139)))) _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_44 :args (_let_36 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_45)) :args _let_43)) _let_44 :args (_let_139 false _let_11)) :args (_let_116 false _let_122 false _let_139)))) (let ((_let_141 (not _let_117))) (let ((_let_142 (or _let_46 _let_141))) (let ((_let_143 (_let_17))) (let ((_let_144 (ASSUME :args _let_143))) (let ((_let_145 (not _let_114))) (let ((_let_146 (not _let_115))) (let ((_let_147 (not _let_116))) (let ((_let_148 (or))) (let ((_let_149 (and _let_141 _let_116 _let_115 _let_114))) (let ((_let_150 (ASSUME :args (_let_141)))) (let ((_let_151 (ASSUME :args (_let_115)))) (let ((_let_152 (APPLY_UF tptp.second))) (let ((_let_153 (ASSUME :args (_let_116)))) (let ((_let_154 (SYMM _let_153))) (let ((_let_155 (ASSUME :args (_let_114)))) (let ((_let_156 (or _let_123 _let_99))) (let ((_let_157 (or _let_123 _let_104))) (let ((_let_158 (_let_12))) (let ((_let_159 (ASSUME :args _let_158))) (let ((_let_160 ((not (= (tptp.member Z (tptp.compose Xf Xg)) false))))) (let ((_let_161 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_157)) :args ((or _let_123 _let_104 (not _let_157)))) _let_128 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_159 :args (_let_36 tptp.another_function tptp.a_function QUANTIFIERS_INST_E_MATCHING _let_160)) :args 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(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 $$unsorted)) (or (tptp.relation Z) (not (tptp.ordered_pair_predicate (tptp.f18 Z))))) _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 (forall ((Xf $$unsorted)) (or (not (tptp.function Xf)) (tptp.relation Xf))) _let_16 _let_15 (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 $$unsorted)) (or (tptp.closed Xs Xf) (not (tptp.little_set Xs)) (not (tptp.little_set Xf)) (not (tptp.maps Xf (tptp.cross_product Xs Xs) Xs)))) _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 (forall ((Z $$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)))) (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))) (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)))) _let_6 (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))))) _let_5 _let_4 _let_3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.95/1.14 )
% 0.95/1.14 % SZS output end Proof for SET034-3
% 0.95/1.14 % cvc5---1.0.5 exiting
% 0.95/1.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------