TSTP Solution File: SEU146+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU146+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n025.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 16:29:32 EDT 2023
% Result : Theorem 0.23s 0.62s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU146+2 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 23 13:49:36 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.23/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.23/0.62 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.fLMX6fSOEO/cvc5---1.0.5_28420.p...
% 0.23/0.62 ------- get file name : TPTP file name is SEU146+2
% 0.23/0.62 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28420.smt2...
% 0.23/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.23/0.62 % SZS status Theorem for SEU146+2
% 0.23/0.62 % SZS output start Proof for SEU146+2
% 0.23/0.62 (
% 0.23/0.62 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)))) (let ((_let_3 (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)))) (let ((_let_6 (not (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1)))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subset A B)) (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C))))))) (let ((_let_14 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_16 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_17 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_18 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_19 (not _let_18))) (let ((_let_20 (or _let_19 _let_17 _let_16))) (let ((_let_21 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (tptp.set_intersection2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_24 (tptp.subset _let_23 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_25 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_23))) (let ((_let_26 (_let_5))) (let ((_let_27 (ASSUME :args _let_26))) (let ((_let_28 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_25))) (let ((_let_31 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (= A (tptp.set_intersection2 A B)))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (forall ((C $$unsorted)) (or (not (tptp.in C SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.in C (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_34 (= _let_28 _let_33))) (let ((_let_35 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (or (not (tptp.in C A)) (tptp.in C B))))))) (let ((_let_36 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_36 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_35))) _let_36 :args (_let_34 false _let_35)))) (let ((_let_38 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_39 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_40 (or _let_39 _let_38))) (let ((_let_41 (= _let_28 _let_40))) (let ((_let_42 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14))) (let ((_let_43 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (tptp.subset tptp.empty_set _let_14))) (let ((_let_47 (not _let_34))) (let ((_let_48 (_let_34))) (let ((_let_49 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= tptp.empty_set A) (= A _let_1))))))) (let ((_let_50 (not _let_41))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (or))) (let ((_let_53 (not _let_49))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_51) :args (_let_53))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_49))) (REFL :args (_let_50)) :args _let_52)) _let_51 :args (_let_50 true _let_49)))) (let ((_let_55 (_let_41))) (let ((_let_56 (not _let_33))) (let ((_let_57 (_let_56))) (let ((_let_58 (_let_3))) (let ((_let_59 (ASSUME :args _let_58))) (let ((_let_60 (not _let_46))) (let ((_let_61 (not _let_39))) (let ((_let_62 (_let_61))) (let ((_let_63 (_let_29))) (let ((_let_64 (ASSUME :args _let_63))) (let ((_let_65 (APPLY_UF tptp.subset))) (let ((_let_66 (ASSUME :args (_let_39)))) (let ((_let_67 (ASSUME :args (_let_46)))) (let ((_let_68 (not _let_40))) (let ((_let_69 (not _let_42))) (let ((_let_70 (not _let_38))) (let ((_let_71 (ASSUME :args (_let_69)))) (let ((_let_72 (ASSUME :args (_let_38)))) (let ((_let_73 (ASSUME :args (_let_43)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_48) :args ((or _let_28 _let_56 _let_47))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_71 _let_72 _let_73) :args (_let_38 _let_43 _let_69)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_73)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8)) (SYMM (SYMM _let_72)) :args (APPLY_UF tptp.in)) (FALSE_INTRO _let_71))) :args (_let_69 _let_38 _let_43)) :args ((not (and _let_38 _let_43 _let_69)) SB_LITERAL))) (CONG (REFL :args (_let_70)) (REFL :args (_let_44)) (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_42))) :args _let_52)) (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_39 _let_38 _let_68))) (REORDERING (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_64 _let_66 _let_67) :args (_let_39 _let_29 _let_46)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_67)) (CONG (SYMM (SYMM _let_66)) (REFL :args (_let_14)) :args _let_65) (FALSE_INTRO _let_64))) :args (_let_29 _let_39 _let_46)) :args ((not (and _let_39 _let_29 _let_46)) SB_LITERAL))) (CONG (REFL :args _let_62) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) (REFL :args (_let_60)) :args _let_52)) :args ((or _let_28 _let_61 _let_60))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (_let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset tptp.empty_set A) true))))) :args _let_58)) _let_59 :args (_let_46 false _let_3)) (CNF_OR_NEG :args (_let_45 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG (REFL :args (_let_45)) (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_52)) :args ((or _let_43 _let_45))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_33))) (REFL :args ((not _let_45))) :args _let_52)) (REORDERING (CNF_EQUIV_NEG1 :args _let_55) :args ((or _let_28 _let_40 _let_41))) _let_54 (REORDERING (CNF_EQUIV_POS1 :args _let_48) :args ((or _let_29 _let_33 _let_47))) _let_37 :args (_let_33 false _let_38 true _let_39 false _let_46 true _let_42 false _let_43 true _let_45 false _let_40 true _let_41 true _let_28 false _let_34)) _let_37 :args (_let_28 false _let_33 false _let_34)))) (let ((_let_75 (and _let_25 _let_24))) (let ((_let_76 (ASSUME :args (_let_24)))) (let ((_let_77 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_78 (ASSUME :args (_let_25)))) (let ((_let_79 (tptp.subset _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_80 (= _let_79 _let_17))) (let ((_let_81 (not _let_17))) (let ((_let_82 (_let_9))) (let ((_let_83 (ASSUME :args _let_82))) (let ((_let_84 (tptp.proper_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_85 (not _let_84))) (let ((_let_86 (not _let_79))) (let ((_let_87 (or _let_86 _let_85))) (let ((_let_88 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.subset A B)) (not (tptp.proper_subset B A)))))) (let ((_let_89 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_90 (and _let_28 _let_70))) (let ((_let_91 (= _let_84 _let_90))) (let ((_let_92 (_let_10))) (let ((_let_93 (ASSUME :args _let_92))) (let ((_let_94 (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_55) _let_54 _let_74 :args (_let_68 true _let_41 false _let_28)))) (let ((_let_95 (_let_90))) (let ((_let_96 (tptp.subset _let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_97 (and _let_96 _let_16))) (let ((_let_98 (not _let_16))) (let ((_let_99 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_15))) (let ((_let_100 (= _let_99 _let_97))) (let ((_let_101 (not _let_97))) (let ((_let_102 (_let_12))) (let ((_let_103 (ASSUME :args _let_102))) (let ((_let_104 (= tptp.empty_set _let_15))) (let ((_let_105 (not _let_99))) (let ((_let_106 (= _let_28 _let_104))) (let ((_let_107 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (= tptp.empty_set (tptp.set_difference A B)))))) (let ((_let_108 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_109 (and _let_61 _let_104))) (let ((_let_110 (ASSUME :args _let_62))) (let ((_let_111 (ASSUME :args (_let_104)))) (let ((_let_112 (_let_2))) (let ((_let_113 (ASSUME :args _let_112))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.in C A) true)) (tptp.set_difference B (tptp.singleton C))))) :args (_let_13))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_20)) :args ((or _let_16 _let_17 _let_19 _let_22))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_97)) :args ((or (not _let_96) _let_97 _let_98))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_113 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_difference A B)))) :args _let_112)) _let_113 :args (_let_96 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_100)) :args ((or _let_99 _let_101 (not _let_100)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_109)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_111 _let_110) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG (SYMM _let_111) _let_77 :args (=)) (FALSE_INTRO _let_110)) :args ((= _let_99 false)))) :args (_let_104 _let_61))) :args (_let_61 _let_104))) :args (true _let_109)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_61) _let_39))) (REFL :args ((not _let_104))) (REFL :args (_let_105)) :args _let_52)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 0)) _let_94 :args (_let_61 true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_106)) :args ((or _let_29 _let_104 (not _let_106)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_108 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_107))) _let_108 :args (_let_106 false _let_107)) :args (_let_104 false _let_28 false _let_106)) :args (_let_105 true _let_39 false _let_104)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_103 :args (_let_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_102))) _let_103 :args (_let_100 false _let_12)) :args (_let_101 true _let_99 false _let_100)) :args (_let_98 false _let_96 true _let_97)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_80)) :args ((or _let_79 _let_81 (not _let_80)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_87)) :args ((or _let_85 _let_86 (not _let_87)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_91)) :args ((or _let_84 (not _let_90) (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_95) (CONG (REFL :args _let_95) (REFL :args _let_63) (MACRO_SR_PRED_INTRO :args ((= (not _let_70) _let_38))) :args _let_52)) :args ((or _let_38 _let_29 _let_90))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 1)) _let_94 :args (_let_70 true _let_40)) _let_74 :args (_let_90 true _let_38 false _let_28)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args _let_92)) _let_93 :args (_let_91 false _let_10)) :args (_let_84 false _let_90 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_89 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.proper_subset B A) false))))) :args (_let_88))) _let_89 :args (_let_87 false _let_88)) :args (_let_86 false _let_84 false _let_87)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.subset (tptp.singleton A) B)))) :args _let_82)) _let_83 :args (_let_80 false _let_9)) :args (_let_81 true _let_79 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_75)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_76 _let_78) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_78)) _let_77 :args _let_65) (TRUE_INTRO _let_76))) :args (_let_24 _let_25))) :args (_let_25 _let_24))) :args (true _let_75)) :args ((or (not _let_25) _let_18 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_30)) :args ((or _let_29 _let_25 (not _let_30)))) _let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.subset A B) false))))) :args (_let_31))) _let_32 :args (_let_30 false _let_31)) :args (_let_25 false _let_28 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A B)))) :args _let_26)) _let_27 :args (_let_24 false _let_5)) :args (_let_18 false _let_25 false _let_24)) :args (_let_22 true _let_16 true _let_17 false _let_18)) _let_21 :args (false true _let_20 false _let_13)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.proper_subset A B) (not (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.unordered_pair A B) (tptp.unordered_pair B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) _let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) (forall ((A $$unsorted)) (= (= A tptp.empty_set) (forall ((B $$unsorted)) (not (tptp.in B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.unordered_pair A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (= D A) (= D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_union2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) _let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_intersection2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.set_difference A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (and (tptp.in D A) (not (tptp.in D B))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) _let_10 true true true true true true (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.empty A)) (not (tptp.empty (tptp.set_union2 B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) _let_9 _let_8 _let_7 _let_6 (exists ((A $$unsorted)) (tptp.empty A)) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) _let_5 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset A C)) (tptp.subset A (tptp.set_intersection2 B C)))) (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) _let_4 (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) _let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) _let_2 (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (and (tptp.in C A) (tptp.in C B)))))) (not (and (exists ((C $$unsorted)) (and (tptp.in C A) (tptp.in C B))) _let_1))))) (forall ((A $$unsorted)) (=> (tptp.subset A tptp.empty_set) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference (tptp.set_union2 A B) B) (tptp.set_difference A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_difference A (tptp.set_difference A B)) (tptp.set_intersection2 A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.disjoint A B))) (and (not (and (not _let_1) (forall ((C $$unsorted)) (not (tptp.in C (tptp.set_intersection2 A B)))))) (not (and (exists ((C $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) _let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.in A B) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_difference A B) A))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C B)) (tptp.subset (tptp.set_union2 A C) B))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.23/0.63 )
% 0.23/0.63 % SZS output end Proof for SEU146+2
% 0.23/0.63 % cvc5---1.0.5 exiting
% 0.23/0.63 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------