TSTP Solution File: SEU176+2 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU176+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n016.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 16:29:49 EDT 2023
% Result : Theorem 0.21s 0.65s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU176+2 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n016.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 18:09:07 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.65 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.K1l4Be2K9j/cvc5---1.0.5_24321.p...
% 0.21/0.65 ------- get file name : TPTP file name is SEU176+2
% 0.21/0.65 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24321.smt2...
% 0.21/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.65 % SZS status Theorem for SEU176+2
% 0.21/0.65 % SZS output start Proof for SEU176+2
% 0.21/0.65 (
% 0.21/0.65 (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B))))))))) (let ((_let_2 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (=> (not (= B tptp.empty_set)) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B)))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (not (and (not (= B tptp.empty_set)) (= (tptp.complements_of_subsets A B) tptp.empty_set))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.complements_of_subsets A (tptp.complements_of_subsets A B)) B))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A (tptp.subset_complement A B)) B))))) (let ((_let_7 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (=> (tptp.element B _let_1) (tptp.element (tptp.complements_of_subsets A B) _let_1)))))) (let ((_let_8 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.meet_of_subsets A B) _let_1)))))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B (tptp.powerset _let_1)) (tptp.element (tptp.union_of_subsets A B) _let_1)))))) (let ((_let_10 (forall ((A $$unsorted)) (tptp.element (tptp.cast_to_subset A) (tptp.powerset A))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_12 (forall ((A $$unsorted)) (= (tptp.cast_to_subset A) A)))) (let ((_let_13 (tptp.meet_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_14 (tptp.cast_to_subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_15 (tptp.subset_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 _let_13))) (let ((_let_16 (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_17 (tptp.union_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_18 (= _let_17 _let_15))) (let ((_let_19 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14))) (let ((_let_20 (tptp.complements_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16))) (let ((_let_21 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_20))) (let ((_let_22 (= _let_15 (tptp.set_difference _let_14 _let_13)))) (let ((_let_23 (tptp.subset_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 _let_17))) (let ((_let_24 (= _let_23 (tptp.meet_of_subsets SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_20)))) (let ((_let_25 (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17))) (let ((_let_26 (= _let_25 (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17)))) (let ((_let_27 (= (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13) (tptp.set_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13)))) (let ((_let_28 (= _let_17 (tptp.subset_complement SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_25)))) (let ((_let_29 (= _let_23 (tptp.set_difference _let_14 _let_17)))) (let ((_let_30 (= tptp.empty_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_31 (tptp.powerset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_32 (tptp.powerset _let_31))) (let ((_let_33 (tptp.element SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_32))) (let ((_let_34 (not _let_33))) (let ((_let_35 (or _let_34 _let_30 _let_18))) (let ((_let_36 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (= (tptp.union_of_subsets A (tptp.complements_of_subsets A B)) (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.meet_of_subsets A B))))))) (let ((_let_37 (not _let_35))) (let ((_let_38 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_39 (or))) (let ((_let_40 (not _let_36))) (let ((_let_41 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_38) :args (_let_40))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_36))) (REFL :args (_let_37)) :args _let_39)) _let_38 :args (_let_37 true _let_36)))) (let ((_let_42 (forall ((A $$unsorted)) (= A (tptp.cast_to_subset A))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_12)) (MACRO_SR_EQ_INTRO :args (_let_12 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or _let_34 _let_21))) (let ((_let_45 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= B (tptp.complements_of_subsets A (tptp.complements_of_subsets A B))))))) (let ((_let_46 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_35 0)) (CONG (REFL :args (_let_35)) (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_33))) :args _let_39)) :args ((or _let_33 _let_35))) _let_41 :args (_let_33 true _let_35)))) (let ((_let_48 (tptp.element _let_13 _let_31))) (let ((_let_49 (not _let_48))) (let ((_let_50 (tptp.element _let_14 _let_31))) (let ((_let_51 (not _let_50))) (let ((_let_52 (or _let_51 _let_49 _let_22))) (let ((_let_53 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B _let_1)) (not (tptp.element C _let_1)) (= (tptp.subset_difference A B C) (tptp.set_difference B C))))))) (let ((_let_54 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_55 (_let_53))) (let ((_let_56 ((tptp.subset_difference A B C)))) (let ((_let_57 (or _let_34 _let_48))) (let ((_let_58 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B (tptp.powerset _let_1))) (tptp.element (tptp.meet_of_subsets A B) _let_1)))))) (let ((_let_59 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_57)) :args ((or _let_34 _let_48 (not _let_57)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_59 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_58))) _let_59 :args (_let_57 false _let_58)) :args (_let_48 false _let_33 false _let_57)))) (let ((_let_61 (_let_10))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cast_to_subset A)))) :args _let_61)) _let_62 :args (_let_50 false _let_10)))) (let ((_let_64 (= tptp.empty_set _let_16))) (let ((_let_65 (tptp.element _let_16 _let_32))) (let ((_let_66 (not _let_65))) (let ((_let_67 (or _let_66 _let_64 _let_24))) (let ((_let_68 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (= (tptp.subset_difference A (tptp.cast_to_subset A) (tptp.union_of_subsets A B)) (tptp.meet_of_subsets A (tptp.complements_of_subsets A B))))))) (let ((_let_69 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_70 (not _let_64))) (let ((_let_71 (or _let_34 _let_30 _let_70))) (let ((_let_72 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset (tptp.powerset A)))) (= tptp.empty_set B) (not (= tptp.empty_set (tptp.complements_of_subsets A B))))))) (let ((_let_73 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_74 (or _let_34 _let_65))) (let ((_let_75 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.powerset A)))) (or (not (tptp.element B _let_1)) (tptp.element (tptp.complements_of_subsets A B) _let_1)))))) (let ((_let_76 (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_34 _let_65 (not _let_74)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.complements_of_subsets A B)))) :args (_let_75))) _let_76 :args (_let_74 false _let_75)) :args (_let_65 false _let_33 false _let_74)))) (let ((_let_78 (tptp.element _let_17 _let_31))) (let ((_let_79 (not _let_78))) (let ((_let_80 (or _let_79 _let_26))) (let ((_let_81 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= (tptp.subset_complement A B) (tptp.set_difference A B)))))) (let ((_let_82 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_83 (_let_81))) (let ((_let_84 ((not (= (tptp.element B (tptp.powerset A)) false))))) (let ((_let_85 (or _let_66 _let_78))) (let ((_let_86 (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (or (not (tptp.element B (tptp.powerset _let_1))) (tptp.element (tptp.union_of_subsets A B) _let_1)))))) (let ((_let_87 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_88 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_85)) :args ((or _let_66 _let_78 (not _let_85)))) _let_77 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_87 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union_of_subsets A B)))) :args (_let_86))) _let_87 :args (_let_85 false _let_86)) :args (_let_78 false _let_65 false _let_85)))) (let ((_let_89 (or _let_49 _let_27))) (let ((_let_90 (or _let_79 _let_28))) (let ((_let_91 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.element B (tptp.powerset A))) (= B (tptp.subset_complement A (tptp.subset_complement A B))))))) (let ((_let_92 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_93 (or _let_51 _let_79 _let_29))) (let ((_let_94 (and _let_19 _let_21 _let_22 _let_24 _let_26 _let_27 _let_28 _let_29))) (let ((_let_95 (ASSUME :args (_let_22)))) (let ((_let_96 (APPLY_UF tptp.set_difference))) (let ((_let_97 (ASSUME :args (_let_19)))) (let ((_let_98 (SYMM (SYMM _let_97)))) (let ((_let_99 (ASSUME :args (_let_27)))) (let ((_let_100 (ASSUME :args (_let_21)))) (let ((_let_101 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_102 (ASSUME :args (_let_24)))) (let ((_let_103 (ASSUME :args (_let_29)))) (let ((_let_104 (ASSUME :args (_let_26)))) (let ((_let_105 (ASSUME :args (_let_28)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_94)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_95 _let_97 _let_99 _let_100 _let_102 _let_103 _let_104 _let_105) (SCOPE (TRANS (SYMM (SYMM _let_105)) (CONG _let_101 (TRANS (SYMM (SYMM _let_104)) (CONG _let_98 (REFL :args (_let_17)) :args _let_96) (SYMM _let_103) (SYMM (SYMM _let_102)) (CONG _let_101 (SYMM _let_100) :args (APPLY_UF tptp.meet_of_subsets))) :args (APPLY_UF tptp.subset_complement)) (SYMM (SYMM _let_99)) (CONG _let_98 (REFL :args (_let_13)) :args _let_96) (SYMM _let_95)) :args (_let_22 _let_19 _let_27 _let_21 _let_24 _let_29 _let_26 _let_28))) :args (_let_19 _let_21 _let_22 _let_24 _let_26 _let_27 _let_28 _let_29))) :args (true _let_94)) :args ((or _let_18 (not _let_19) (not _let_21) (not _let_22) (not _let_24) (not _let_26) (not _let_27) (not _let_28) (not _let_29)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_93)) :args ((or _let_51 _let_79 _let_29 (not _let_93)))) _let_63 _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_93 false _let_53)) :args (_let_29 false _let_50 false _let_78 false _let_93)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_90)) :args ((or _let_79 _let_28 (not _let_90)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_92 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset A)) false))))) :args (_let_91))) _let_92 :args (_let_90 false _let_91)) :args (_let_28 false _let_78 false _let_90)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_49 _let_27 (not _let_89)))) _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_13 QUANTIFIERS_INST_E_MATCHING _let_84)) :args _let_83)) _let_82 :args (_let_89 false _let_81)) :args (_let_27 false _let_48 false _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_80)) :args ((or _let_79 _let_26 (not _let_80)))) _let_88 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_17 QUANTIFIERS_INST_E_MATCHING _let_84)) :args _let_83)) _let_82 :args (_let_80 false _let_81)) :args (_let_26 false _let_78 false _let_80)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_67)) :args ((or _let_66 _let_64 _let_24 (not _let_67)))) _let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_71)) :args ((or _let_34 _let_30 _let_70 (not _let_71)))) _let_47 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 1)) _let_41 :args ((not _let_30) true _let_35)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_73 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_72))) _let_73 :args (_let_71 false _let_72)) :args (_let_70 false _let_33 true _let_30 false _let_71)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_69 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.union_of_subsets A B)))) :args (_let_68))) _let_69 :args (_let_67 false _let_68)) :args (_let_24 false _let_65 true _let_64 false _let_67)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_51 _let_49 _let_22 (not _let_52)))) _let_63 _let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_14 _let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_56)) :args _let_55)) _let_54 :args (_let_52 false _let_53)) :args (_let_22 false _let_50 false _let_48 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_34 _let_21 (not _let_44)))) _let_47 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.element B (tptp.powerset (tptp.powerset A))) false))))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_21 false _let_33 false _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.cast_to_subset A)))) :args (_let_42))) _let_43 :args (_let_19 false _let_42)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_35 2)) _let_41 :args ((not _let_18) true _let_35)) :args (false false _let_29 false _let_28 false _let_27 false _let_26 false _let_24 false _let_22 false _let_21 false _let_19 true _let_18)) :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 $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (= A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (= B (tptp.set_meet A)))) (let ((_let_2 (= A tptp.empty_set))) (and (=> (not _let_2) (= _let_1 (forall ((C $$unsorted)) (= (tptp.in C B) (forall ((D $$unsorted)) (=> (tptp.in D A) (tptp.in C D))))))) (=> _let_2 (= _let_1 (= B tptp.empty_set))))))) (forall ((A $$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)) (= (= B (tptp.powerset A)) (forall ((C $$unsorted)) (= (tptp.in C B) (tptp.subset C A))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.element B A))) (let ((_let_2 (tptp.empty A))) (and (=> (not _let_2) (= _let_1 (tptp.in B A))) (=> _let_2 (= _let_1 (tptp.empty B))))))) (forall ((A $$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 $$unsorted)) (= (tptp.in D C) (or (tptp.in D A) (tptp.in D B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (= C (tptp.cartesian_product2 A B)) (forall ((D $$unsorted)) (= (tptp.in D C) (exists ((E $$unsorted) (F $$unsorted)) (and (tptp.in E A) (tptp.in F B) (= D (tptp.ordered_pair E F)))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))))) (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)))))) _let_12 (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.union A)) (forall ((C $$unsorted)) (= (tptp.in C B) (exists ((D $$unsorted)) (and (tptp.in C D) (tptp.in D A))))))) (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))))))) _let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.ordered_pair A B) (tptp.unordered_pair (tptp.unordered_pair A B) (tptp.singleton A)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.powerset A))) (= (= C (tptp.complements_of_subsets A B)) (forall ((D $$unsorted)) (=> (tptp.element D (tptp.powerset A)) (= (tptp.in D C) (tptp.in (tptp.subset_complement A D) B))))))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.proper_subset A B) (and (tptp.subset A B) (not (= A B))))) true true true true _let_10 true true true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (tptp.element B _let_1) (tptp.element (tptp.subset_complement A B) _let_1)))) true true true true _let_9 _let_8 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.powerset A))) (=> (and (tptp.element B _let_1) (tptp.element C _let_1)) (tptp.element (tptp.subset_difference A B C) _let_1)))) _let_7 true (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (tptp.empty tptp.empty_set) (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.empty (tptp.ordered_pair A B)))) (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)) _let_6 _let_5 (forall ((A $$unsorted) (B $$unsorted)) (not (tptp.proper_subset A A))) (forall ((A $$unsorted)) (not (= (tptp.singleton A) tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.disjoint (tptp.singleton A) B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (not (tptp.in A B)) (tptp.disjoint (tptp.singleton A) B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in C A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (or (tptp.in C A) (tptp.subset A (tptp.set_difference B (tptp.singleton C)))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (=> (tptp.in C A) (tptp.in C B))) (tptp.element A (tptp.powerset B)))) (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 $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.union_of_subsets A B) (tptp.union B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.powerset A))) (= (tptp.meet_of_subsets A B) (tptp.set_meet B)))) _let_4 (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) (C $$unsorted) (D $$unsorted)) (= (tptp.in (tptp.ordered_pair A B) (tptp.cartesian_product2 C D)) (and (tptp.in A C) (tptp.in B D)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (not (and (= (tptp.unordered_pair A B) (tptp.unordered_pair C D)) (not (= A C)) (not (= A D))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (and (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B C)) (tptp.subset (tptp.cartesian_product2 C A) (tptp.cartesian_product2 C B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset C D)) (tptp.subset (tptp.cartesian_product2 A C) (tptp.cartesian_product2 B D)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_union2 A B) B))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (=> (tptp.in C B) (tptp.in (tptp.powerset C) B))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_intersection2 A B) A)) (forall ((A $$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 $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.subset B C)) (tptp.subset A C))) (= (tptp.powerset tptp.empty_set) (tptp.singleton tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_intersection2 A C) (tptp.set_intersection2 B C)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= (tptp.set_intersection2 A B) A))) (forall ((A $$unsorted)) (= (tptp.set_intersection2 A tptp.empty_set) tptp.empty_set)) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.element A B) (or (tptp.empty B) (tptp.in A B)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (forall ((C $$unsorted)) (= (tptp.in C A) (tptp.in C B))) (= A B))) (forall ((A $$unsorted)) (tptp.subset tptp.empty_set A)) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.subset A B) (tptp.subset (tptp.set_difference A C) (tptp.set_difference B C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (= (tptp.ordered_pair A B) (tptp.ordered_pair C D)) (and (= A C) (= B D)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.set_difference A B) A)) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A B) tptp.empty_set) (tptp.subset A B))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset (tptp.singleton A) B) (tptp.in A B))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.subset (tptp.unordered_pair A B) C) (and (tptp.in A C) (tptp.in B C)))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_union2 A (tptp.set_difference B A)) (tptp.set_union2 A B))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.singleton B))) (= (tptp.subset A _let_1) (or (= A tptp.empty_set) (= A _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) (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.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (= (tptp.disjoint B C) (tptp.subset B (tptp.subset_complement A C))))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset A B) (= B (tptp.set_union2 A (tptp.set_difference B A))))) _let_3 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (= (tptp.set_union2 (tptp.singleton A) B) B))) _let_2 _let_1 (forall ((A $$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) (C $$unsorted)) (=> (and (tptp.in A B) (tptp.element B (tptp.powerset C))) (tptp.element A C))) (forall ((A $$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 $$unsorted)) (tptp.in C (tptp.set_intersection2 A B))) _let_1))))) (forall ((A $$unsorted)) (=> (not (= A tptp.empty_set)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (forall ((C $$unsorted)) (=> (tptp.element C A) (=> (not (tptp.in C B)) (tptp.in C (tptp.subset_complement A B))))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset A)) (not (and (tptp.in B (tptp.subset_complement A C)) (tptp.in B C))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (not (and (tptp.in A B) (tptp.element B (tptp.powerset C)) (tptp.empty C)))) (forall ((A $$unsorted) (B $$unsorted)) (not (and (tptp.subset A B) (tptp.proper_subset B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (tptp.subset A B) (tptp.disjoint B C)) (tptp.disjoint A C))) (forall ((A $$unsorted) (B $$unsorted)) (= (= (tptp.set_difference A (tptp.singleton B)) A) (not (tptp.in B A)))) (forall ((A $$unsorted)) (= (tptp.unordered_pair A A) (tptp.singleton A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (= A tptp.empty_set))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.subset (tptp.singleton A) (tptp.singleton B)) (= A B))) (forall ((A $$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))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= A B))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.subset A (tptp.union B)))) (forall ((A $$unsorted)) (= (tptp.union (tptp.powerset A)) A)) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.in A B) (forall ((C $$unsorted) (D $$unsorted)) (=> (and (tptp.in C B) (tptp.subset D C)) (tptp.in D B))) (forall ((C $$unsorted)) (not (and (tptp.in C B) (forall ((D $$unsorted)) (not (and (tptp.in D B) (forall ((E $$unsorted)) (=> (tptp.subset E C) (tptp.in E D))))))))) (forall ((C $$unsorted)) (not (and (tptp.subset C B) (not (tptp.are_equipotent C B)) (not (tptp.in C B)))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (= (tptp.singleton A) (tptp.unordered_pair B C)) (= B C))) true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.66 )
% 0.21/0.66 % SZS output end Proof for SEU176+2
% 0.21/0.66 % cvc5---1.0.5 exiting
% 0.21/0.66 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------