%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n031.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 14:37:59 EDT 2023

% Result   : Theorem 0.18s 0.48s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET159+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n031.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 15:56:23 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.18/0.45  %----Proving TF0_NAR, FOF, or CNF
% 0.18/0.48  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.xDdtzKcugI/cvc5---1.0.5_28824.p...
% 0.18/0.48  ------- get file name : TPTP file name is SET159+4
% 0.18/0.48  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_28824.smt2...
% 0.18/0.48  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.18/0.48  % SZS status Theorem for SET159+4
% 0.18/0.48  % SZS output start Proof for SET159+4
% 0.18/0.48  (
% 0.18/0.48  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (tptp.equal_set (tptp.union (tptp.union A B) C) (tptp.union A (tptp.union B C)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$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.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (or _let_7 _let_6))) (let ((_let_9 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_11 (= _let_10 _let_8))) (let ((_let_12 (_let_3))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 ((tptp.member X (tptp.union A B))))) (let ((_let_15 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_16 (or _let_15 _let_10))) (let ((_let_17 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_17))) (let ((_let_19 (= _let_18 _let_16))) (let ((_let_20 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (tptp.union _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_21))) (let ((_let_23 (not _let_18))) (let ((_let_24 (or _let_23 _let_22))) (let ((_let_25 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (tptp.member X (tptp.union (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_26 (not _let_24))) (let ((_let_27 (tptp.subset _let_17 _let_21))) (let ((_let_28 (= _let_27 _let_25))) (let ((_let_29 (not _let_25))) (let ((_let_30 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (_let_30))) (let ((_let_33 ((tptp.subset A B)))) (let ((_let_34 (tptp.subset _let_21 _let_17))) (let ((_let_35 (and _let_34 _let_27))) (let ((_let_36 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))))) (let ((_let_37 (= _let_34 _let_36))) (let ((_let_38 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_17))) (let ((_let_39 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_21))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_38))) (let ((_let_42 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_20))) (let ((_let_44 (or _let_43 _let_42))) (let ((_let_45 (= _let_39 _let_44))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_48 (or _let_47 _let_46))) (let ((_let_49 (= _let_38 _let_48))) (let ((_let_50 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_51 (or _let_50 _let_42))) (let ((_let_52 (= _let_46 _let_51))) (let ((_let_53 (or _let_47 _let_50))) (let ((_let_54 (= _let_43 _let_53))) (let ((_let_55 (or))) (let ((_let_56 (not _let_36))) (let ((_let_57 (_let_56))) (let ((_let_58 (tptp.equal_set _let_21 _let_17))) (let ((_let_59 (= _let_58 _let_35))) (let ((_let_60 (not _let_35))) (let ((_let_61 (_let_4))) (let ((_let_62 (ASSUME :args _let_61))) (let ((_let_63 (not _let_58))) (let ((_let_64 (_let_2))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (_let_29))) (let ((_let_67 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_66)) :args _let_66)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_25))) (REFL :args (_let_26)) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_28)) :args ((or _let_27 _let_29 (not _let_28)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_35)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_58 _let_60 (not _let_59)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_65) :args _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_63)) :args _let_55)) _let_65 :args (_let_63 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_62 :args (_let_21 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_61)) _let_62 :args (_let_59 false _let_4)) :args (_let_60 true _let_58 false _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_37)) :args ((or _let_34 _let_56 (not _let_37)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_57)) :args _let_57)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_56) _let_36))) (REFL :args ((not _let_41))) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_54)) :args ((or (not _let_43) _let_53 (not _let_54)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_54 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_44)) :args ((or _let_43 _let_42 (not _let_44)))) (REORDERING (CNF_OR_POS :args (_let_53)) :args ((or _let_47 _let_50 (not _let_53)))) (REORDERING (CNF_OR_NEG :args (_let_51 1)) :args ((or (not _let_42) _let_51))) (CNF_OR_NEG :args (_let_51 0)) (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_46 (not _let_51) (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_52 false _let_3)) (CNF_OR_NEG :args (_let_48 1)) (CNF_OR_NEG :args (_let_48 0)) (REORDERING (CNF_EQUIV_POS2 :args (_let_49)) :args ((or _let_38 (not _let_48) (not _let_49)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_49 false _let_3)) (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_40 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_45 false _let_3)) (CNF_OR_NEG :args (_let_41 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_41 0)) (CONG (REFL :args (_let_41)) (MACRO_SR_PRED_INTRO :args ((= (not _let_40) _let_39))) :args _let_55)) :args ((or _let_39 _let_41))) :args (_let_41 false _let_54 false _let_43 true _let_53 true _let_42 true _let_50 true _let_51 false _let_52 true _let_46 true _let_47 true _let_48 false _let_49 false _let_44 false _let_45 true _let_38 false _let_39)) :args (_let_36 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_21 _let_17 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_37 false _let_30)) :args (_let_34 false _let_36 false _let_37)) :args ((not _let_27) true _let_35 false _let_34)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (_let_17 _let_21 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_33)) :args _let_32)) _let_31 :args (_let_28 false _let_30)) :args (_let_29 true _let_27 false _let_28)) :args (_let_26 true _let_25)))) (let ((_let_68 (or _let_15 _let_7))) (let ((_let_69 (not _let_15))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_20))) (let ((_let_71 (= _let_70 _let_68))) (let ((_let_72 (not _let_68))) (let ((_let_73 (or _let_70 _let_6))) (let ((_let_74 (= _let_22 _let_73))) (let ((_let_75 (not _let_73))) (let ((_let_76 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_74)) :args ((or _let_22 _let_75 (not _let_74)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_24 1)) _let_67 :args ((not _let_22) true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_20 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_74 false _let_3)) :args (_let_75 true _let_22 false _let_74)))) (let ((_let_77 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_71)) :args ((or _let_70 _let_72 (not _let_71)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_73 0)) _let_76 :args ((not _let_70) true _let_73)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_71 false _let_3)) :args (_let_72 true _let_70 false _let_71)))) (let ((_let_78 (not _let_8))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or (not _let_10) _let_8 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_8)) :args ((or _let_6 _let_7 _let_78))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_73 1)) _let_76 :args ((not _let_6) true _let_73)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_68 1)) _let_77 :args ((not _let_7) true _let_68)) :args (_let_78 true _let_6 true _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_15 _let_10 (not _let_16)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_68 0)) :args ((or _let_69 _let_68))) _let_77 :args (_let_69 true _let_68)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_19)) :args ((or _let_23 _let_16 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_24 0)) (CONG (REFL :args (_let_24)) (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_18))) :args _let_55)) :args ((or _let_18 _let_24))) _let_67 :args (_let_18 true _let_24)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_19 false _let_3)) :args (_let_16 false _let_18 false _let_19)) :args (_let_10 true _let_15 false _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_11 false _let_3)) :args (false true _let_8 false _let_10 false _let_11)) :args (_let_5 _let_4 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.18/0.48  )
% 0.18/0.48  % SZS output end Proof for SET159+4
% 0.18/0.48  % cvc5---1.0.5 exiting
% 0.18/0.49  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------