TSTP Solution File: SET808+4 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET808+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.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 14:40:24 EDT 2023
% Result : Theorem 1.89s 2.23s
% Output : Proof 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET808+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n014.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 11:58:47 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.52 %----Proving TF0_NAR, FOF, or CNF
% 1.89/2.23 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.78YjeeSLdR/cvc5---1.0.5_9248.p...
% 1.89/2.23 ------- get file name : TPTP file name is SET808+4
% 1.89/2.23 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_9248.smt2...
% 1.89/2.23 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 1.89/2.23 % SZS status Theorem for SET808+4
% 1.89/2.23 % SZS output start Proof for SET808+4
% 1.89/2.23 (
% 1.89/2.23 (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.member A tptp.on) (tptp.subset A tptp.on)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_3 (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))))) (let ((_let_4 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))))) (let ((_let_6 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))))) (let ((_let_7 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_11 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_13 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19))) (let ((_let_14 (not _let_13))) (let ((_let_15 (not _let_11))) (let ((_let_16 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (not _let_16))) (let ((_let_18 (not _let_12))) (let ((_let_19 (not _let_9))) (let ((_let_20 (or _let_19 _let_18 _let_17 _let_15 _let_14 _let_10))) (let ((_let_21 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_9))) (let ((_let_24 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_25 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_26 (= _let_25 _let_24))) (let ((_let_27 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (_let_27))) (let ((_let_30 ((tptp.subset A B)))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (not _let_31))) (let ((_let_33 (or _let_32 _let_25))) (let ((_let_34 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_35 (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_37 (and _let_36 _let_35 _let_34))) (let ((_let_38 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_39 (= _let_38 _let_37))) (let ((_let_40 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_40))) (let ((_let_43 ((tptp.member A tptp.on)))) (let ((_let_44 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_45 (not _let_38))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((A $$unsorted)) (or (not (tptp.member A tptp.on)) (tptp.subset A tptp.on))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (or))) (let ((_let_51 (not _let_47))) (let ((_let_52 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_51))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_47))) (REFL :args (_let_48)) :args _let_50)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_39)) :args ((or _let_45 _let_37 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_38))) :args _let_50)) :args ((or _let_38 _let_46))) _let_52 :args (_let_38 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_43)) :args _let_42)) _let_41 :args (_let_39 false _let_40)) :args (_let_37 false _let_38 false _let_39)))) (let ((_let_54 (not _let_37))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 2)) :args ((or _let_34 _let_54))) _let_53 :args (_let_34 false _let_37)))) (let ((_let_56 (_let_34))) (let ((_let_57 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) (let ((_let_58 (ASSUME :args _let_56))) (let ((_let_59 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 tptp.on))) (let ((_let_60 (or _let_32 _let_59))) (let ((_let_61 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X tptp.on))))) (let ((_let_62 (not _let_60))) (let ((_let_63 (= _let_44 _let_61))) (let ((_let_64 (not _let_61))) (let ((_let_65 (_let_64))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_61))) (REFL :args (_let_62)) :args _let_50)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_63)) :args ((or _let_44 _let_64 (not _let_63)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 1)) _let_52 :args ((not _let_44) true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_63 false _let_27)) :args (_let_64 true _let_44 false _let_63)) :args (_let_62 true _let_61)))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_60 0)) (CONG (REFL :args (_let_60)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_31))) :args _let_50)) :args ((or _let_31 _let_60))) _let_66 :args (_let_31 true _let_60)))) (let ((_let_68 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_33)) :args ((or _let_32 _let_25 (not _let_33)))) _let_67 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_57)) :args _let_56)) _let_55 :args (_let_33 false _let_34)) :args (_let_25 false _let_31 false _let_33)))) (let ((_let_69 (not _let_25))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_26)) :args ((or _let_69 _let_24 (not _let_26)))) _let_68 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_30)) :args _let_29)) _let_28 :args (_let_26 false _let_27)) :args (_let_24 false _let_25 false _let_26)))) (let ((_let_71 (_let_24))) (let ((_let_72 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) (let ((_let_73 (ASSUME :args _let_71))) (let ((_let_74 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_75 (not _let_74))) (let ((_let_76 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_77 (not _let_76))) (let ((_let_78 (or _let_22 _let_77 _let_75 _let_15 _let_14 _let_10))) (let ((_let_79 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y Z)) (tptp.apply tptp.member_predicate X Z))))) (let ((_let_80 (not _let_78))) (let ((_let_81 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y X)))))) (let ((_let_82 (and _let_81 _let_79))) (let ((_let_83 (not _let_79))) (let ((_let_84 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20))) (let ((_let_85 (not _let_84))) (let ((_let_86 (tptp.apply tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21))) (let ((_let_87 (not _let_86))) (let ((_let_88 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_89 (not _let_88))) (let ((_let_90 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_91 (not _let_90))) (let ((_let_92 (or _let_91 _let_89 _let_87 _let_85))) (let ((_let_93 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_94 (or _let_91 _let_93))) (let ((_let_95 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_21 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_96 (or _let_89 _let_95))) (let ((_let_97 (not _let_95))) (let ((_let_98 (not _let_93))) (let ((_let_99 (or _let_98 _let_97 _let_87 _let_85))) (let ((_let_100 (REFL :args (_let_92)))) (let ((_let_101 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y X)))))) (let ((_let_102 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.apply tptp.member_predicate X Y)) (not (tptp.apply tptp.member_predicate Y Z)) (tptp.apply tptp.member_predicate X Z))))) (let ((_let_103 (and _let_101 _let_102))) (let ((_let_104 (tptp.strict_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_105 (= _let_104 _let_103))) (let ((_let_106 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_107 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_108 (_let_106))) (let ((_let_109 ((tptp.strict_order R E)))) (let ((_let_110 (forall ((A $$unsorted) (BOUND_VARIABLE_901 $$unsorted)) (or (not (tptp.subset A SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (not (tptp.member BOUND_VARIABLE_901 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y tptp.member_predicate A)))))))) (let ((_let_111 (and _let_104 _let_110))) (let ((_let_112 (= _let_35 _let_111))) (let ((_let_113 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted) (BOUND_VARIABLE_901 $$unsorted)) (or (not (tptp.subset A E)) (not (tptp.member BOUND_VARIABLE_901 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y R A))))))))))) (let ((_let_114 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_115 (_let_113))) (let ((_let_116 ((tptp.strict_well_order R E)))) (let ((_let_117 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_112)) :args ((or (not _let_35) _let_111 (not _let_112)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_37 1)) :args ((or _let_35 _let_54))) _let_53 :args (_let_35 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_114 :args (tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_116)) :args _let_115)) _let_114 :args (_let_112 false _let_113)) :args (_let_111 false _let_35 false _let_112)))) (let ((_let_118 (not _let_111))) (let ((_let_119 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_105)) :args ((or (not _let_104) _let_103 (not _let_105)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_111 0)) :args ((or _let_104 _let_118))) _let_117 :args (_let_104 false _let_111)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_107 :args (tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_109)) :args _let_108)) _let_107 :args (_let_105 false _let_106)) :args (_let_103 false _let_104 false _let_105)))) (let ((_let_120 (not _let_103))) (let ((_let_121 (_let_101))) (let ((_let_122 (not _let_81))) (let ((_let_123 (_let_122))) (let ((_let_124 (tptp.strict_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_125 (= _let_124 _let_82))) (let ((_let_126 (not _let_82))) (let ((_let_127 (forall ((A $$unsorted) (BOUND_VARIABLE_901 $$unsorted)) (or (not (tptp.subset A SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (not (tptp.member BOUND_VARIABLE_901 A)) (not (forall ((Y $$unsorted)) (not (tptp.least Y tptp.member_predicate A)))))))) (let ((_let_128 (and _let_124 _let_127))) (let ((_let_129 (forall ((Y $$unsorted)) (not (tptp.least Y tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))))) (let ((_let_130 (not _let_129))) (let ((_let_131 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_132 (not _let_131))) (let ((_let_133 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_134 (not _let_133))) (let ((_let_135 (or _let_134 _let_132 _let_130))) (let ((_let_136 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_137 (or _let_134 _let_69 _let_136))) (let ((_let_138 (not _let_136))) (let ((_let_139 (or _let_138 _let_132 _let_130))) (let ((_let_140 (REFL :args (_let_135)))) (let ((_let_141 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.subset B C)) (tptp.subset A C))))) (let ((_let_142 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_143 (_let_110))) (let ((_let_144 (not _let_127))) (let ((_let_145 (_let_144))) (let ((_let_146 (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_147 (= _let_146 _let_128))) (let ((_let_148 (not _let_128))) (let ((_let_149 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_150 (tptp.set 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0)) (CONG _let_100 (MACRO_SR_PRED_INTRO :args ((= (not _let_91) _let_90))) :args _let_50)) :args ((or _let_90 _let_92))) :args (_let_92 false _let_99 false _let_95 false _let_96 false _let_93 false _let_94 false _let_84 false _let_86 false _let_88 false _let_90)) :args (_let_81 false _let_92)) :args (_let_83 true _let_82 false _let_81)) :args (_let_80 true _let_79)))) (let ((_let_201 (REFL :args (_let_78)))) (let ((_let_202 (or _let_77 _let_12))) (let ((_let_203 (or _let_75 _let_16))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_15 _let_14 _let_10 _let_19 _let_18 _let_17 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_203)) :args ((or _let_75 _let_16 (not _let_203)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 2)) (CONG _let_201 (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_74))) :args _let_50)) :args ((or _let_74 _let_78))) _let_200 :args (_let_74 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_203 false _let_24)) :args (_let_16 false _let_74 false _let_203)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 4)) (CONG _let_201 (MACRO_SR_PRED_INTRO :args ((= (not _let_14) _let_13))) :args _let_50)) :args ((or _let_13 _let_78))) _let_200 :args (_let_13 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_190 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_19 QUANTIFIERS_INST_E_MATCHING _let_189)) :args _let_188)) _let_187 :args (_let_20 false _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_202)) :args ((or _let_77 _let_12 (not _let_202)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 1)) (CONG _let_201 (MACRO_SR_PRED_INTRO :args ((= (not _let_77) _let_76))) :args _let_50)) :args ((or _let_76 _let_78))) _let_200 :args (_let_76 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_202 false _let_24)) :args (_let_12 false _let_76 false _let_202)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 3)) (CONG _let_201 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_11))) :args _let_50)) :args ((or _let_11 _let_78))) _let_200 :args (_let_11 true _let_78)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_78 5)) _let_200 :args ((not _let_10) true _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_23)) :args ((or _let_22 _let_9 (not _let_23)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_78 0)) (CONG _let_201 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_50)) :args ((or _let_21 _let_78))) _let_200 :args (_let_21 true _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_72)) :args _let_71)) _let_70 :args (_let_23 false _let_24)) :args (_let_9 false _let_21 false _let_23)) :args (false false _let_16 false _let_13 false _let_20 false _let_12 false _let_11 true _let_10 false _let_9)) :args (_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_7 _let_6 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) _let_5 _let_4 _let_3 (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 2.06/2.24 )
% 2.06/2.24 % SZS output end Proof for SET808+4
% 2.06/2.24 % cvc5---1.0.5 exiting
% 2.06/2.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------