%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 14:36:45 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET014+4 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n017.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   : Sat Aug 26 15:58:11 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xsuYHcsCaM/cvc5---1.0.5_16742.p...
% 0.20/0.55  ------- get file name : TPTP file name is SET014+4
% 0.20/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16742.smt2...
% 0.20/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.55  % SZS status Theorem for SET014+4
% 0.20/0.55  % SZS output start Proof for SET014+4
% 0.20/0.55  (
% 0.20/0.55  (let ((_let_1 (forall ((A $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (and (tptp.subset X A) (tptp.subset Y A)) (tptp.subset (tptp.union X Y) A))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_5 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_7 (or _let_6 _let_5))) (let ((_let_8 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_9 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 _let_8))) (let ((_let_10 (= _let_9 _let_7))) (let ((_let_11 (_let_3))) (let ((_let_12 (ASSUME :args _let_11))) (let ((_let_13 ((tptp.member X (tptp.union A B))))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_15 (not _let_9))) (let ((_let_16 (or _let_15 _let_14))) (let ((_let_17 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (tptp.subset _let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_20 (= _let_19 _let_17))) (let ((_let_21 (not _let_17))) (let ((_let_22 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_23 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.subset A B)))) (let ((_let_26 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (_let_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_20 false _let_22)))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_28 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (and _let_28 _let_27))) (let ((_let_30 (= _let_29 _let_19))) (let ((_let_31 (not _let_19))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_33 (= _let_27 _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_8))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34))) (let ((_let_38 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_39 (not _let_38))) (let ((_let_40 (or _let_39 _let_34))) (let ((_let_41 (or (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_38))) (let ((_let_42 (= _let_35 _let_41))) (let ((_let_43 (not _let_30))) (let ((_let_44 (_let_2))) (let ((_let_45 (ASSUME :args _let_44))) (let ((_let_46 (or))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_45) :args _let_44)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_43)) :args _let_46)) _let_45 :args (_let_43 true _let_1)))) (let ((_let_48 (_let_30))) (let ((_let_49 (REORDERING (CNF_EQUIV_NEG1 :args _let_48) :args ((or _let_29 _let_19 _let_30))))) (let ((_let_50 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_51 (= _let_28 _let_50))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_54 (not _let_53))) (let ((_let_55 (or _let_54 _let_52))) (let ((_let_56 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_8))) (let ((_let_57 (not _let_56))) (let ((_let_58 (or _let_57 _let_52))) (let ((_let_59 (or _let_53 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_60 (= _let_56 _let_59))) (let ((_let_61 (not _let_29))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_51 false _let_22)))) (let ((_let_63 (not _let_51))) (let ((_let_64 (not _let_50))) (let ((_let_65 (_let_51))) (let ((_let_66 (_let_64))) (let ((_let_67 (not _let_20))) (let ((_let_68 (_let_20))) (let ((_let_69 (REORDERING (CNF_EQUIV_POS1 :args _let_68) :args ((or _let_31 _let_17 _let_67))))) (let ((_let_70 (_let_17))) (let ((_let_71 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) true))))) (let ((_let_72 (ASSUME :args _let_70))) (let ((_let_73 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_60)) :args ((or _let_56 (not _let_59) (not _let_60)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_60 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_58)) :args ((or _let_52 _let_57 (not _let_58)))) (REORDERING (CNF_OR_NEG :args (_let_59 0)) :args ((or _let_54 _let_59))) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) (CNF_OR_NEG :args (_let_55 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_55 0)) (CONG (REFL :args (_let_55)) (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_53))) :args _let_46)) :args ((or _let_53 _let_55))) _let_69 _let_26 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_64) _let_50))) (REFL :args ((not _let_55))) :args _let_46)) _let_49 _let_47 (REORDERING (CNF_EQUIV_POS2 :args _let_65) :args ((or _let_28 _let_64 _let_63))) _let_62 (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_28 _let_61))) :args (_let_28 false _let_60 true _let_56 false _let_59 false _let_58 true _let_52 false _let_53 false _let_17 false _let_20 true _let_55 false _let_19 true _let_30 true _let_50 false _let_51 true _let_29)))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_33 false _let_22)))) (let ((_let_75 (not _let_33))) (let ((_let_76 (not _let_32))) (let ((_let_77 (_let_33))) (let ((_let_78 (_let_76))) (let ((_let_79 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_42)) :args ((or _let_35 (not _let_41) (not _let_42)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_42 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_37)) :args ((or _let_34 _let_36 (not _let_37)))) (REORDERING (CNF_OR_NEG :args (_let_41 1)) :args ((or _let_39 _let_41))) (CNF_OR_NEG :args (_let_40 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_40 0)) (CONG (REFL :args (_let_40)) (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) :args _let_46)) :args ((or _let_38 _let_40))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_78)) :args _let_78)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_32))) (REFL :args ((not _let_40))) :args _let_46)) (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_72 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71)) :args _let_70)) (REORDERING (CNF_EQUIV_POS2 :args _let_77) :args ((or _let_27 _let_76 _let_75))) _let_74 _let_69 _let_26 (CNF_AND_NEG :args (_let_29)) _let_73 _let_49 _let_47 :args (_let_29 false _let_42 true _let_35 false _let_41 true _let_34 false _let_38 true _let_40 false _let_37 true _let_32 false _let_33 false _let_17 false _let_20 true _let_27 false _let_28 false _let_19 true _let_30)))) (let ((_let_80 (_let_21))) (let ((_let_81 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_17))) (REFL :args (_let_18)) :args _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_68) :args ((or _let_19 _let_21 _let_67))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_48) _let_47 _let_79 :args (_let_31 true _let_30 false _let_29)) _let_26 :args (_let_21 true _let_19 false _let_20)) :args (_let_18 true _let_17)))) (let ((_let_82 (not _let_6))) (let ((_let_83 (or _let_82 _let_14))) (let ((_let_84 (_let_50))) (let ((_let_85 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_71))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 1)) _let_81 :args ((not _let_14) true _let_16)))) (let ((_let_87 (not _let_5))) (let ((_let_88 (or _let_87 _let_14))) (let ((_let_89 (_let_32))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_7)) :args ((or _let_6 _let_5 (not _let_7)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_88)) :args ((or _let_14 _let_87 (not _let_88)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_89) :args _let_85) :args _let_89)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_77) :args ((or (not _let_27) _let_32 _let_75))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_27 _let_61))) _let_79 :args (_let_27 false _let_29)) _let_74 :args (_let_32 false _let_27 false _let_33)) :args (_let_88 false _let_32)) :args (_let_87 true _let_14 false _let_88)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_83)) :args ((or _let_14 _let_82 (not _let_83)))) _let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args _let_85) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_65) :args ((or (not _let_28) _let_50 _let_63))) _let_73 _let_62 :args (_let_50 false _let_28 false _let_51)) :args (_let_83 false _let_50)) :args (_let_82 true _let_14 false _let_83)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_10)) :args ((or _let_15 _let_7 (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG (REFL :args (_let_16)) (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_9))) :args _let_46)) :args ((or _let_9 _let_16))) _let_81 :args (_let_9 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_12 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_13)) :args _let_11)) _let_12 :args (_let_10 false _let_3)) :args (_let_7 false _let_9 false _let_10)) :args (false true _let_5 true _let_6 false _let_7)) :args (_let_4 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) _let_3 (forall ((X $$unsorted)) (not (tptp.member X tptp.empty_set))) (forall ((B $$unsorted) (A $$unsorted) (E $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))) (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.product A)) (forall ((Y $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_2 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.56  )
% 0.20/0.56  % SZS output end Proof for SET014+4
% 0.20/0.56  % cvc5---1.0.5 exiting
% 0.20/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------