TSTP Solution File: SEU108+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU108+1 : TPTP v8.1.2. Released v3.2.0.
% 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 16:29:17 EDT 2023
% Result : Theorem 0.86s 1.12s
% Output : Proof 0.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU108+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 15:13:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.86/1.12 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.epgcPbREnJ/cvc5---1.0.5_23097.p...
% 0.86/1.12 ------- get file name : TPTP file name is SEU108+1
% 0.86/1.12 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_23097.smt2...
% 0.86/1.12 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.86/1.12 % SZS status Theorem for SEU108+1
% 0.86/1.12 % SZS output start Proof for SEU108+1
% 0.86/1.12 (
% 0.86/1.12 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))))) (let ((_let_2 (forall ((A $$unsorted)) (tptp.preboolean (tptp.powerset A))))) (let ((_let_3 (not _let_2))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))))) (let ((_let_5 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (=> (and (tptp.in B A) (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.set_union2 B C))))))) (let ((_let_8 (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))))) (let ((_let_10 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_union2 A B C) _let_1)))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.subset_union2 A C B))))))) (let ((_let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A B) (tptp.set_union2 B A))))) (let ((_let_13 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_14 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_15 (tptp.in _let_14 _let_13))) (let ((_let_16 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_17 (tptp.in _let_16 _let_13))) (let ((_let_18 (and _let_17 _let_15))) (let ((_let_19 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_13))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_13))) (let ((_let_22 (not _let_21))) (let ((_let_23 (or _let_22 _let_20 _let_18))) (let ((_let_24 (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (or (not (tptp.in B _let_1)) (not (tptp.in C _let_1)) (and (tptp.in (tptp.set_union2 B C) _let_1) (tptp.in (tptp.set_difference B C) _let_1))))))) (let ((_let_25 (not _let_23))) (let ((_let_26 (tptp.preboolean _let_13))) (let ((_let_27 (= _let_26 _let_24))) (let ((_let_28 (not _let_24))) (let ((_let_29 (forall ((A $$unsorted)) (= (tptp.preboolean A) (forall ((B $$unsorted) (C $$unsorted)) (or (not (tptp.in B A)) (not (tptp.in C A)) (and (tptp.in (tptp.set_union2 B C) A) (tptp.in (tptp.set_difference B C) A)))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (not _let_26))) (let ((_let_32 (_let_3))) (let ((_let_33 (ASSUME :args _let_32))) (let ((_let_34 (or))) (let ((_let_35 (_let_28))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_35)) :args _let_35)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_24))) (REFL :args (_let_25)) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_27)) :args ((or _let_26 _let_28 (not _let_27)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args _let_32)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_3) _let_2))) (REFL :args (_let_31)) :args _let_34)) _let_33 :args (_let_31 true _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.preboolean A)))) :args (_let_29))) _let_30 :args (_let_27 false _let_29)) :args (_let_28 true _let_26 false _let_27)) :args (_let_25 true _let_24)))) (let ((_let_37 (tptp.empty _let_13))) (let ((_let_38 (tptp.element _let_16 _let_13))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_37 _let_17))) (let ((_let_41 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element A B)) (tptp.empty B) (tptp.in A B))))) (let ((_let_42 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_43 (_let_41))) (let ((_let_44 ((not (= (tptp.in A B) true))))) (let ((_let_45 (tptp.subset_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_46 (tptp.element _let_45 _let_13))) (let ((_let_47 (tptp.subset_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_48 (tptp.set_union2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_49 (= _let_48 _let_47))) (let ((_let_50 (= _let_45 _let_47))) (let ((_let_51 (= _let_16 _let_48))) (let ((_let_52 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_13))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_13))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_46))) (let ((_let_57 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (tptp.element (tptp.subset_union2 A B C) _let_1)))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (or _let_20 _let_52))) (let ((_let_60 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.in A B)) (tptp.element A B))))) (let ((_let_61 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_62 (_let_60))) (let ((_let_63 ((not (= (tptp.in A B) false))))) (let ((_let_64 (REFL :args (_let_23)))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_59)) :args ((or _let_20 _let_52 (not _let_59)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 1)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_34)) :args ((or _let_19 _let_23))) _let_36 :args (_let_19 true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_59 false _let_60)) :args (_let_52 false _let_19 false _let_59)))) (let ((_let_66 (or _let_22 _let_54))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_22 _let_54 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_23 0)) (CONG _let_64 (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_21))) :args _let_34)) :args ((or _let_21 _let_23))) _let_36 :args (_let_21 true _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_61 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_63)) :args _let_62)) _let_61 :args (_let_66 false _let_60)) :args (_let_54 false _let_21 false _let_66)))) (let ((_let_68 (or _let_53 _let_55 _let_49))) (let ((_let_69 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.set_union2 B C))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (or _let_55 _let_53 _let_50))) (let ((_let_72 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.subset_union2 A B C) (tptp.subset_union2 A C B))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (tptp.powerset A))) (let ((_let_75 (_let_12))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (and _let_51 _let_50 _let_49 _let_46))) (let ((_let_78 (ASSUME :args (_let_46)))) (let ((_let_79 (APPLY_UF tptp.element))) (let ((_let_80 (REFL :args (_let_13)))) (let ((_let_81 (ASSUME :args (_let_50)))) (let ((_let_82 (ASSUME :args (_let_49)))) (let ((_let_83 (ASSUME :args (_let_51)))) (let ((_let_84 (_let_8))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.powerset A)))) :args _let_84)) _let_85 :args ((not _let_37) false _let_8)))) (let ((_let_87 (tptp.element _let_14 _let_13))) (let ((_let_88 (not _let_87))) (let ((_let_89 (or _let_88 _let_37 _let_15))) (let ((_let_90 (tptp.subset_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_91 (tptp.element _let_90 _let_13))) (let ((_let_92 (= _let_14 _let_90))) (let ((_let_93 (or _let_55 _let_53 _let_91))) (let ((_let_94 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))))) (let ((_let_95 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_96 (or _let_55 _let_53 _let_92))) (let ((_let_97 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_99 (and _let_92 _let_91))) (let ((_let_100 (ASSUME :args (_let_91)))) (let ((_let_101 (ASSUME :args (_let_92)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_18)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_37 _let_15 _let_88 (not _let_89)))) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_99)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_100 _let_101) (SCOPE (TRUE_ELIM (TRANS (CONG (SYMM (SYMM _let_101)) _let_80 :args _let_79) (TRUE_INTRO _let_100))) :args (_let_91 _let_92))) :args (_let_92 _let_91))) :args (true _let_99)) :args ((or _let_87 (not _let_92) (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_96)) :args ((or _let_55 _let_53 _let_92 (not _let_96)))) _let_67 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_98 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((tptp.powerset A) (tptp.set_difference B C)))) :args (_let_97)))) _let_98 :args (_let_96 false _let_97)) :args (_let_92 false _let_54 false _let_52 false _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_55 _let_53 _let_91 (not _let_93)))) _let_67 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset_difference A B C)))) :args (_let_94))) _let_95 :args (_let_93 false _let_94)) :args (_let_91 false _let_54 false _let_52 false _let_93)) :args (_let_87 false _let_92 false _let_91)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_14 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_89 false _let_41)) :args (_let_15 true _let_37 false _let_87 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_40)) :args ((or _let_37 _let_17 _let_39 (not _let_40)))) _let_86 (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_77)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_78 _let_81 _let_82 _let_83) (SCOPE (TRUE_ELIM (TRANS (CONG (TRANS (SYMM (SYMM _let_83)) (SYMM (SYMM _let_82)) (SYMM _let_81)) _let_80 :args _let_79) (TRUE_INTRO _let_78))) :args (_let_46 _let_50 _let_49 _let_51))) :args (_let_51 _let_50 _let_49 _let_46))) :args (true _let_77)) :args ((or _let_38 (not _let_51) (not _let_50) (not _let_49) (not _let_46)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_union2 A B)))) :args _let_75)) _let_76 :args (_let_51 false _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_55 _let_53 _let_50 (not _let_71)))) _let_67 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element C _let_74) false)) (not (= (tptp.element B _let_74) false))))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_50 false _let_54 false _let_52 false _let_71)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_55 _let_53 _let_49 (not _let_68)))) _let_67 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset A)) false)) (tptp.set_union2 B C)))) :args (_let_69)))) _let_70 :args (_let_68 false _let_69)) :args (_let_49 false _let_54 false _let_52 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_55 _let_53 _let_46 (not _let_56)))) _let_67 _let_65 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset_union2 A B C)))) :args (_let_57))) _let_58 :args (_let_56 false _let_57)) :args (_let_46 false _let_54 false _let_52 false _let_56)) :args (_let_38 false _let_51 false _let_50 false _let_49 false _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_42 :args (_let_16 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_44)) :args _let_43)) _let_42 :args (_let_40 false _let_41)) :args (_let_17 true _let_37 false _let_38 false _let_40)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_23 2)) _let_36 :args ((not _let_18) true _let_23)) :args (false false _let_15 false _let_17 true _let_18)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (tptp.preboolean A) (and (tptp.cup_closed A) (tptp.diff_closed A)))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (and (tptp.cup_closed A) (tptp.diff_closed A)) (tptp.preboolean A))) _let_12 _let_11 _let_10 _let_9 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.finite A) (tptp.finite (tptp.set_difference A B)))) _let_8 (tptp.empty tptp.empty_set) (forall ((A $$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 $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.set_union2 A B)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A A) A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_union2 A B B) B)))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.cup_closed A) (tptp.cap_closed A) (tptp.diff_closed A) (tptp.preboolean A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (exists ((A $$unsorted)) (tptp.empty A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B) (tptp.relation B) (tptp.function B) (tptp.one_to_one B) (tptp.epsilon_transitive B) (tptp.epsilon_connected B) (tptp.ordinal B) (tptp.natural B) (tptp.finite B)))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) _let_7 _let_6 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) _let_5 (forall ((A $$unsorted)) (= (tptp.set_union2 A tptp.empty_set) A)) _let_4 _let_3 _let_1 (forall ((A $$unsorted)) (= (tptp.set_difference A tptp.empty_set) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (forall ((A $$unsorted)) (= (tptp.set_difference tptp.empty_set A) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$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)) (not (and (tptp.empty A) (not (= A B)) (tptp.empty B)))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.86/1.13 )
% 0.86/1.13 % SZS output end Proof for SEU108+1
% 0.86/1.13 % cvc5---1.0.5 exiting
% 0.86/1.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------