TSTP Solution File: SEU053+1 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n012.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 16:29:09 EDT 2023
% Result : Theorem 0.96s 1.14s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU053+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n012.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 13:44:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.96/1.14 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.DhUQtYchId/cvc5---1.0.5_12479.p...
% 0.96/1.14 ------- get file name : TPTP file name is SEU053+1
% 0.96/1.14 ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_12479.smt2...
% 0.96/1.14 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.96/1.14 % SZS status Theorem for SEU053+1
% 0.96/1.14 % SZS output start Proof for SEU053+1
% 0.96/1.14 (
% 0.96/1.14 (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (not (= A B)) (tptp.disjoint (tptp.singleton A) (tptp.singleton B)))))) (let ((_let_2 (forall ((A $$unsorted)) (=> (tptp.relation A) (= (tptp.relation_image A tptp.empty_set) tptp.empty_set))))) (let ((_let_3 (not (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (=> (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.relation_image A (tptp.set_intersection2 B C)) (tptp.set_intersection2 (tptp.relation_image A B) (tptp.relation_image A C)))) (tptp.one_to_one A))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation B) (tptp.function B)) (=> (tptp.in A (tptp.relation_dom B)) (= (tptp.relation_image B (tptp.singleton A)) (tptp.singleton (tptp.apply B A)))))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A A) A)))) (let ((_let_6 (tptp.relation tptp.empty_set))) (let ((_let_7 (tptp.empty tptp.empty_set))) (let ((_let_8 (forall ((A $$unsorted)) (not (tptp.empty (tptp.singleton A)))))) (let ((_let_9 (and _let_7 _let_6 (tptp.relation_empty_yielding tptp.empty_set)))) (let ((_let_10 (forall ((A $$unsorted)) (=> (and (tptp.relation A) (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (and (tptp.in B _let_1) (tptp.in C _let_1) (= (tptp.apply A B) (tptp.apply A C))) (= B C))))))))) (let ((_let_11 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= (tptp.set_intersection2 A B) tptp.empty_set))))) (let ((_let_12 (= tptp.empty_set (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 tptp.empty_set)))) (let ((_let_13 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_14 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_15 (= _let_14 _let_13))) (let ((_let_16 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_17 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_16))) (let ((_let_18 (= _let_17 (tptp.singleton _let_14)))) (let ((_let_19 (tptp.singleton _let_13))) (let ((_let_20 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_21 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_20))) (let ((_let_22 (= _let_21 _let_19))) (let ((_let_23 (tptp.empty _let_19))) (let ((_let_24 (tptp.set_intersection2 _let_20 _let_16))) (let ((_let_25 (= tptp.empty_set _let_24))) (let ((_let_26 (tptp.set_intersection2 _let_20 _let_20))) (let ((_let_27 (= _let_20 _let_26))) (let ((_let_28 (= (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_24) (tptp.set_intersection2 _let_21 _let_17)))) (let ((_let_29 (= (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 _let_26) (tptp.set_intersection2 _let_21 _let_21)))) (let ((_let_30 (tptp.relation SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_31 (not _let_30))) (let ((_let_32 (or _let_31 _let_12))) (let ((_let_33 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (= tptp.empty_set (tptp.relation_image A tptp.empty_set)))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (tptp.one_to_one SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_36 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.set_intersection2 B C)) (tptp.set_intersection2 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 B) (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 C)))))) (let ((_let_37 (not _let_36))) (let ((_let_38 (tptp.function SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_31 _let_39 _let_37 _let_35))) (let ((_let_41 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (not (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.relation_image A (tptp.set_intersection2 B C)) (tptp.set_intersection2 (tptp.relation_image A B) (tptp.relation_image A C))))) (tptp.one_to_one A))))) (let ((_let_42 (not _let_40))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (or))) (let ((_let_45 (not _let_41))) (let ((_let_46 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_43) :args (_let_45))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_41))) (REFL :args (_let_42)) :args _let_44)) _let_43 :args (_let_42 true _let_41)))) (let ((_let_47 (REFL :args (_let_40)))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_31) _let_30))) :args _let_44)) :args ((or _let_30 _let_40))) _let_46 :args (_let_30 true _let_40)))) (let ((_let_49 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_50 (not _let_15))) (let ((_let_51 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (let ((_let_52 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 _let_51))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.in SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 _let_51))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_50 _let_49))) (let ((_let_57 (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10))) (or (not (tptp.in B _let_1)) (not (tptp.in C _let_1)) (not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 B) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 C))) (= B C)))))) (let ((_let_58 (not _let_56))) (let ((_let_59 (= _let_35 _let_57))) (let ((_let_60 (not _let_57))) (let ((_let_61 (or _let_31 _let_39 _let_59))) (let ((_let_62 (forall ((A $$unsorted)) (or (not (tptp.relation A)) (not (tptp.function A)) (= (tptp.one_to_one A) (forall ((B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (or (not (tptp.in B _let_1)) (not (tptp.in C _let_1)) (not (= (tptp.apply A B) (tptp.apply A C))) (= B C))))))))) (let ((_let_63 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 1)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_44)) :args ((or _let_38 _let_40))) _let_46 :args (_let_38 true _let_40)))) (let ((_let_65 (_let_60))) (let ((_let_66 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_65)) :args _let_65)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_57))) (REFL :args (_let_58)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_35 _let_60 (not _let_59)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_40 3)) _let_46 :args ((not _let_35) true _let_40)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_61)) :args ((or _let_31 _let_39 _let_59 (not _let_61)))) _let_48 _let_64 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_62))) _let_63 :args (_let_61 false _let_62)) :args (_let_59 false _let_30 false _let_38 false _let_61)) :args (_let_60 true _let_35 false _let_59)) :args (_let_58 true _let_57)))) (let ((_let_67 (REFL :args (_let_56)))) (let ((_let_68 (or _let_31 _let_39 _let_55 _let_18))) (let ((_let_69 (forall ((A $$unsorted) (B $$unsorted)) (or (not (tptp.relation B)) (not (tptp.function B)) (not (tptp.in A (tptp.relation_dom B))) (= (tptp.relation_image B (tptp.singleton A)) (tptp.singleton (tptp.apply B A))))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_69))) (let ((_let_72 ((not (= (tptp.in A (tptp.relation_dom B)) false))))) (let ((_let_73 (or _let_31 _let_39 _let_53 _let_22))) (let ((_let_74 (not _let_23))) (let ((_let_75 (_let_8))) (let ((_let_76 (ASSUME :args _let_75))) (let ((_let_77 (tptp.disjoint _let_20 _let_16))) (let ((_let_78 (= _let_77 _let_25))) (let ((_let_79 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.disjoint A B) (= tptp.empty_set (tptp.set_intersection2 A B)))))) (let ((_let_80 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_81 (or _let_49 _let_77))) (let ((_let_82 (forall ((A $$unsorted) (B $$unsorted)) (or (= A B) (tptp.disjoint (tptp.singleton A) (tptp.singleton B)))))) (let ((_let_83 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_84 (forall ((A $$unsorted)) (= A (tptp.set_intersection2 A A))))) (let ((_let_85 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 2)) (CONG _let_47 (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_36))) :args _let_44)) :args ((or _let_36 _let_40))) _let_46 :args (_let_36 true _let_40)))) (let ((_let_87 (_let_36))) (let ((_let_88 (ASSUME :args _let_87))) (let ((_let_89 (ASSUME :args (_let_7)))) (let ((_let_90 (ASSUME :args (_let_12)))) (let ((_let_91 (APPLY_UF tptp.relation_image))) (let ((_let_92 (ASSUME :args (_let_25)))) (let ((_let_93 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10)))) (let ((_let_94 (ASSUME :args (_let_28)))) (let ((_let_95 (ASSUME :args (_let_18)))) (let ((_let_96 (ASSUME :args (_let_15)))) (let ((_let_97 (ASSUME :args (_let_22)))) (let ((_let_98 (SYMM _let_97))) (let ((_let_99 (ASSUME :args (_let_29)))) (let ((_let_100 (ASSUME :args (_let_27)))) (let ((_let_101 (ASSUME :args (_let_74)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_89 _let_90 _let_92 _let_94 _let_97 _let_95 _let_96 _let_99 _let_100 _let_101) :args (_let_7 _let_12 _let_15 _let_18 _let_22 _let_74 _let_25 _let_27 _let_28 _let_29)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_101)) (CONG (TRANS _let_98 (CONG _let_93 (SYMM (SYMM _let_100)) :args _let_91) (SYMM (SYMM _let_99)) (CONG (REFL :args (_let_21)) (TRANS (SYMM _let_98) (CONG (SYMM _let_96) :args (APPLY_UF tptp.singleton)) (SYMM _let_95)) :args (APPLY_UF tptp.set_intersection2)) (SYMM _let_94) (CONG _let_93 (SYMM _let_92) :args _let_91) (SYMM _let_90)) :args (APPLY_UF tptp.empty)) (TRUE_INTRO _let_89))) :args (_let_7 _let_12 _let_25 _let_28 _let_22 _let_18 _let_15 _let_29 _let_27 _let_74)) :args ((not (and _let_7 _let_12 _let_15 _let_18 _let_22 _let_74 _let_25 _let_27 _let_28 _let_29)) SB_LITERAL))) (CONG (REFL :args ((not _let_7))) (REFL :args ((not _let_12))) (REFL :args (_let_50)) (REFL :args ((not _let_18))) (REFL :args ((not _let_22))) (MACRO_SR_PRED_INTRO :args ((= (not _let_74) _let_23))) (REFL :args ((not _let_25))) (REFL :args ((not _let_27))) (REFL :args ((not _let_28))) (REFL :args ((not _let_29))) :args _let_44)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_20 _let_20 QUANTIFIERS_INST_E_MATCHING ((tptp.set_intersection2 (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 B) (tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 C))))) :args _let_87)) _let_86 :args (_let_29 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_88 :args (_let_20 _let_16 QUANTIFIERS_INST_E_MATCHING ((tptp.relation_image SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 (tptp.set_intersection2 B C))))) :args _let_87)) _let_86 :args (_let_28 false _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (_let_20 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.set_intersection2 A A)))) :args (_let_84))) _let_85 :args (_let_27 false _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_78)) :args ((or (not _let_77) _let_25 (not _let_78)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_49 _let_77 (not _let_81)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_56 3)) _let_66 :args ((not _let_49) true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_83 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING ((tptp.singleton A) (tptp.singleton B)))) :args (_let_82)))) _let_83 :args (_let_81 false _let_82)) :args (_let_77 true _let_49 false _let_81)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_80 :args (_let_20 _let_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.disjoint A B)))) :args (_let_79))) _let_80 :args (_let_78 false _let_79)) :args (_let_25 false _let_77 false _let_78)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 :args (_let_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.singleton A)))) :args _let_75)) _let_76 :args (_let_74 false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_31 _let_39 _let_53 _let_22 (not _let_73)))) _let_48 _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 1)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_44)) :args ((or _let_52 _let_56))) _let_66 :args (_let_52 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_72)) :args _let_71)) _let_70 :args (_let_73 false _let_69)) :args (_let_22 false _let_30 false _let_38 false _let_52 false _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_31 _let_39 _let_55 _let_18 (not _let_68)))) _let_48 _let_64 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_44)) :args ((or _let_54 _let_56))) _let_66 :args (_let_54 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_70 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING _let_72)) :args _let_71)) _let_70 :args (_let_68 false _let_69)) :args (_let_18 false _let_30 false _let_38 false _let_54 false _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_67 (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_15))) :args _let_44)) :args ((or _let_15 _let_56))) _let_66 :args (_let_15 true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_31 _let_12 (not _let_32)))) _let_48 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.relation A) false))))) :args (_let_33))) _let_34 :args (_let_32 false _let_33)) :args (_let_12 false _let_30 false _let_32)) (AND_ELIM (ASSUME :args (_let_9)) :args (0)) :args (false false _let_29 false _let_28 false _let_27 false _let_25 true _let_23 false _let_22 false _let_18 false _let_15 false _let_12 false _let_7)) :args ((forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.function A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.function A))) (let ((_let_2 (tptp.relation A))) (=> (and _let_2 (tptp.empty A) _let_1) (and _let_2 _let_1 (tptp.one_to_one A)))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.set_intersection2 A B) (tptp.set_intersection2 B A))) (forall ((A $$unsorted) (B $$unsorted)) (= (= B (tptp.singleton A)) (forall ((C $$unsorted)) (= (tptp.in C B) (= C A))))) _let_11 _let_10 (forall ((A $$unsorted)) (exists ((B $$unsorted)) (tptp.element B A))) _let_9 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.relation A) (tptp.relation B)) (tptp.relation (tptp.set_intersection2 A B)))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) _let_7 _let_8 (and _let_7 _let_6) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_dom A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_dom A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) _let_5 (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.disjoint_nonempty A A)))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$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)) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.empty A) (tptp.function A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (exists ((A $$unsorted)) (not (tptp.empty A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.function A) (tptp.one_to_one A))) (exists ((A $$unsorted)) (and (tptp.relation A) (tptp.relation_empty_yielding A))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (= (tptp.disjoint_nonempty A B) (tptp.disjoint A B)))) (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset A A)) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (=> (tptp.disjoint_nonempty A B) (tptp.disjoint_nonempty B A)))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.disjoint A B) (tptp.disjoint B A))) _let_4 _let_3 _let_2 _let_1 (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (tptp.element A B))) (forall ((A $$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)) (= (tptp.element A (tptp.powerset B)) (tptp.subset A B))) (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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.96/1.15 )
% 0.96/1.15 % SZS output end Proof for SEU053+1
% 0.96/1.15 % cvc5---1.0.5 exiting
% 1.01/1.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------