TSTP Solution File: SET372+4 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET372+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n010.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 14:38:39 EDT 2023
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET372+4 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : do_cvc5 %s %d
% 0.13/0.34 % Computer : n010.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:39:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.56 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.OMHQbZSyLi/cvc5---1.0.5_18310.p...
% 0.20/0.56 ------- get file name : TPTP file name is SET372+4
% 0.20/0.56 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_18310.smt2...
% 0.20/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.56 % SZS status Theorem for SET372+4
% 0.20/0.56 % SZS output start Proof for SET372+4
% 0.20/0.56 (
% 0.20/0.56 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.equal_set (tptp.power_set (tptp.intersection A B)) (tptp.intersection (tptp.power_set A) (tptp.power_set B)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_7))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (and _let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_11 (= _let_8 _let_10))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_8))) (let ((_let_15 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_16 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (_let_18))) (let ((_let_21 ((tptp.subset A B)))) (let ((_let_22 (tptp.power_set _let_7))) (let ((_let_23 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_22))) (let ((_let_24 (= _let_23 _let_16))) (let ((_let_25 (_let_4))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 ((tptp.member X (tptp.power_set A))))) (let ((_let_28 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_30 (tptp.intersection _let_29 _let_28))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_30))) (let ((_let_32 (not _let_23))) (let ((_let_33 (or _let_32 _let_31))) (let ((_let_34 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.power_set (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.intersection (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_35 (not _let_33))) (let ((_let_36 (tptp.subset _let_22 _let_30))) (let ((_let_37 (= _let_36 _let_34))) (let ((_let_38 (not _let_34))) (let ((_let_39 (tptp.subset _let_30 _let_22))) (let ((_let_40 (and _let_36 _let_39))) (let ((_let_41 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.power_set (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_42 (= _let_39 _let_41))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_22))) (let ((_let_44 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_30))) (let ((_let_45 (not _let_44))) (let ((_let_46 (or _let_45 _let_43))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_28))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_29))) (let ((_let_49 (and _let_48 _let_47))) (let ((_let_50 (= _let_44 _let_49))) (let ((_let_51 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7))) (let ((_let_52 (= _let_43 _let_51))) (let ((_let_53 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_54 (= _let_51 _let_53))) (let ((_let_55 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_56 (= _let_48 _let_55))) (let ((_let_57 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_58 (= _let_47 _let_57))) (let ((_let_59 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_7))) (let ((_let_60 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_61 (not _let_60))) (let ((_let_62 (or _let_61 _let_59))) (let ((_let_63 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_64 (= _let_55 _let_63))) (let ((_let_65 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_66 (= _let_57 _let_65))) (let ((_let_67 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_68 (or _let_61 _let_67))) (let ((_let_69 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_70 (or _let_61 _let_69))) (let ((_let_71 (and _let_67 _let_69))) (let ((_let_72 (= _let_59 _let_71))) (let ((_let_73 (or))) (let ((_let_74 (_let_3))) (let ((_let_75 (ASSUME :args _let_74))) (let ((_let_76 ((tptp.member X (tptp.intersection A B))))) (let ((_let_77 (not _let_49))) (let ((_let_78 (not _let_53))) (let ((_let_79 (_let_78))) (let ((_let_80 (_let_63))) (let ((_let_81 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7) false)))))) (let ((_let_82 (_let_65))) (let ((_let_83 (not _let_41))) (let ((_let_84 (_let_83))) (let ((_let_85 (tptp.equal_set _let_22 _let_30))) (let ((_let_86 (= _let_85 _let_40))) (let ((_let_87 (not _let_40))) (let ((_let_88 (_let_5))) (let ((_let_89 (ASSUME :args _let_88))) (let ((_let_90 (not _let_85))) (let ((_let_91 (_let_2))) (let ((_let_92 (ASSUME :args _let_91))) (let ((_let_93 (_let_38))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_93)) :args _let_93)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_38) _let_34))) (REFL :args (_let_35)) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_37)) :args ((or _let_36 _let_38 (not _let_37)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_86)) :args ((or _let_85 _let_87 (not _let_86)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_92) :args _let_91)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_90)) :args _let_73)) _let_92 :args (_let_90 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_22 _let_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_88)) _let_89 :args (_let_86 false _let_5)) :args (_let_87 true _let_85 false _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_39 _let_83 (not _let_42)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_84)) :args _let_84)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_83) _let_41))) (REFL :args ((not _let_46))) :args _let_73)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_71)) (REORDERING (CNF_OR_POS :args (_let_70)) :args ((or _let_61 _let_69 (not _let_70)))) (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_61 _let_67 (not _let_68)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_72)) :args ((or _let_59 (not _let_71) (not _let_72)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_74)) _let_75 :args (_let_72 false _let_3)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args _let_81) :args _let_82)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_80) :args _let_81) :args _let_80)) (CNF_OR_NEG :args (_let_62 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_62 0)) (CONG (REFL :args (_let_62)) (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_60))) :args _let_73)) :args ((or _let_60 _let_62))) (REORDERING (CNF_EQUIV_POS1 :args (_let_66)) :args ((or (not _let_57) _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_66 false _let_18)) (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or (not _let_55) _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_64 false _let_18)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_78) _let_53))) (REFL :args ((not _let_62))) :args _let_73)) (REORDERING (CNF_EQUIV_POS1 :args (_let_58)) :args ((or (not _let_47) _let_57 (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_58 false _let_4)) (REORDERING (CNF_EQUIV_POS1 :args (_let_56)) :args ((or (not _let_48) _let_55 (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_56 false _let_4)) (REORDERING (CNF_EQUIV_POS2 :args (_let_54)) :args ((or _let_51 _let_78 (not _let_54)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_54 false _let_18)) (REORDERING (CNF_AND_POS :args (_let_49 1)) :args ((or _let_47 _let_77))) (REORDERING (CNF_AND_POS :args (_let_49 0)) :args ((or _let_48 _let_77))) (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_43 (not _let_51) (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_7 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_52 false _let_4)) (REORDERING (CNF_EQUIV_POS1 :args (_let_50)) :args ((or _let_45 _let_49 (not _let_50)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_29 _let_28 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_74)) _let_75 :args (_let_50 false _let_3)) (CNF_OR_NEG :args (_let_46 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_44))) :args _let_73)) :args ((or _let_44 _let_46))) :args (_let_46 false _let_69 false _let_67 true _let_71 false _let_72 false _let_70 false _let_68 true _let_59 false _let_60 false _let_65 false _let_66 false _let_63 false _let_64 true _let_62 false _let_57 false _let_58 false _let_55 false _let_56 true _let_53 false _let_54 false _let_47 false _let_48 true _let_51 false _let_52 false _let_49 false _let_50 true _let_43 false _let_44)) :args (_let_41 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_30 _let_22 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_42 false _let_18)) :args (_let_39 false _let_41 false _let_42)) :args ((not _let_36) true _let_40 false _let_39)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_22 _let_30 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_37 false _let_18)) :args (_let_38 true _let_36 false _let_37)) :args (_let_35 true _let_34)))) (let ((_let_95 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or (not _let_16) _let_15 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_24)) :args ((or _let_32 _let_16 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_33 0)) (CONG (REFL :args (_let_33)) (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_23))) :args _let_73)) :args ((or _let_23 _let_33))) _let_94 :args (_let_23 true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_24 false _let_4)) :args (_let_16 false _let_23 false _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_17 false _let_18)) :args (_let_15 false _let_16 false _let_17)))) (let ((_let_96 (_let_15))) (let ((_let_97 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false))))) (let ((_let_98 (ASSUME :args _let_96))) (let ((_let_99 (or _let_13 _let_9))) (let ((_let_100 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_101 (not _let_99))) (let ((_let_102 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_103 (= _let_102 _let_100))) (let ((_let_104 (not _let_100))) (let ((_let_105 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_29))) (let ((_let_106 (= _let_105 _let_102))) (let ((_let_107 (not _let_102))) (let ((_let_108 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_28))) (let ((_let_109 (and _let_105 _let_108))) (let ((_let_110 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_111 (= _let_108 _let_110))) (let ((_let_112 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_113 (= _let_110 _let_112))) (let ((_let_114 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_115 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_116 (not _let_115))) (let ((_let_117 (or _let_116 _let_114))) (let ((_let_118 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_7))) (let ((_let_119 (or _let_116 _let_118))) (let ((_let_120 (and (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_114))) (let ((_let_121 (= _let_118 _let_120))) (let ((_let_122 (not _let_112))) (let ((_let_123 (_let_122))) (let ((_let_124 (= _let_31 _let_109))) (let ((_let_125 (not _let_109))) (let ((_let_126 (_let_104))) (let ((_let_127 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_126)) :args _let_126)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_104) _let_100))) (REFL :args (_let_101)) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_103)) :args ((or _let_102 _let_104 (not _let_103)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_106)) :args ((or _let_105 _let_107 (not _let_106)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_109)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_124)) :args ((or _let_31 _let_125 (not _let_124)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_33 1)) _let_94 :args ((not _let_31) true _let_33)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_29 _let_28 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_74)) _let_75 :args (_let_124 false _let_3)) :args (_let_125 true _let_31 false _let_124)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_111)) :args ((or _let_108 (not _let_110) (not _let_111)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_113)) :args ((or _let_110 _let_122 (not _let_113)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_123)) :args _let_123)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_122) _let_112))) (REFL :args ((not _let_117))) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_121)) :args ((or (not _let_118) _let_120 (not _let_121)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_74)) _let_75 :args (_let_121 false _let_3)) (REORDERING (CNF_AND_POS :args (_let_120 1)) :args ((or _let_114 (not _let_120)))) (REORDERING (CNF_OR_POS :args (_let_119)) :args ((or _let_116 _let_118 (not _let_119)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_119 false _let_15)) (CNF_OR_NEG :args (_let_117 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_117 0)) (CONG (REFL :args (_let_117)) (MACRO_SR_PRED_INTRO :args ((= (not _let_116) _let_115))) :args _let_73)) :args ((or _let_115 _let_117))) :args (_let_117 false _let_121 true _let_120 false _let_118 false _let_119 true _let_114 false _let_115)) :args (_let_112 false _let_117)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_113 false _let_18)) :args (_let_110 false _let_112 false _let_113)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_111 false _let_4)) :args (_let_108 false _let_110 false _let_111)) :args ((not _let_105) true _let_109 false _let_108)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_106 false _let_4)) :args (_let_107 true _let_105 false _let_106)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_21)) :args _let_20)) _let_19 :args (_let_103 false _let_18)) :args (_let_104 true _let_102 false _let_103)) :args (_let_101 true _let_100)))) (let ((_let_128 (not _let_10))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or (not _let_8) _let_10 (not _let_11)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_75 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_76)) :args _let_74)) _let_75 :args (_let_11 false _let_3)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_10 0)) :args ((or _let_9 _let_128))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_99 1)) _let_127 :args ((not _let_9) true _let_99)) :args (_let_128 true _let_9)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_8 (not _let_14)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_99 0)) (CONG (REFL :args (_let_99)) (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_73)) :args ((or _let_12 _let_99))) _let_127 :args (_let_12 true _let_99)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_97)) :args _let_96)) _let_95 :args (_let_14 false _let_15)) :args (_let_8 false _let_12 false _let_14)) :args (false false _let_11 true _let_10 false _let_8)) :args (_let_6 _let_5 _let_4 _let_3 (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_2 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56 )
% 0.20/0.56 % SZS output end Proof for SET372+4
% 0.20/0.56 % cvc5---1.0.5 exiting
% 0.20/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------