%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET582+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 14:39:11 EDT 2023

% Result   : Theorem 0.49s 0.69s
% Output   : Proof 0.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET582+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n023.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 16:25:26 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.49/0.69  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.kqSEsB1tQY/cvc5---1.0.5_7379.p...
% 0.49/0.69  ------- get file name : TPTP file name is SET582+3
% 0.49/0.69  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7379.smt2...
% 0.49/0.69  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.49/0.69  % SZS status Theorem for SET582+3
% 0.49/0.69  % SZS output start Proof for SET582+3
% 0.49/0.69  (
% 0.49/0.69  (let ((_let_1 (not (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (=> (forall ((E $$unsorted)) (= (not (tptp.member E B)) (= (tptp.member E C) (tptp.member E D)))) (= B (tptp.symmetric_difference C D))))))) (let ((_let_2 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.symmetric_difference B C) (tptp.symmetric_difference C B))))) (let ((_let_3 (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.symmetric_difference B C) (tptp.union (tptp.difference B C) (tptp.difference C B)))))) (let ((_let_4 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.difference B C)) (and (tptp.member D B) (not (tptp.member D C))))))) (let ((_let_5 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.union B C)) (or (tptp.member D B) (tptp.member D C)))))) (let ((_let_6 (forall ((B $$unsorted) (C $$unsorted)) (=> (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))) (= B C))))) (let ((_let_7 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_7))) (let ((_let_9 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_9))) (let ((_let_11 (or _let_10 _let_8))) (let ((_let_12 (tptp.union _let_9 _let_7))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_12))) (let ((_let_14 (= _let_13 _let_11))) (let ((_let_15 (_let_5))) (let ((_let_16 (ASSUME :args _let_15))) (let ((_let_17 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_16 :args (_let_9 _let_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING ((tptp.member D (tptp.union B C))))) :args _let_15)) _let_16 :args (_let_14 false _let_5)))) (let ((_let_18 (not _let_11))) (let ((_let_19 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_20 (not _let_19))) (let ((_let_21 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (and _let_21 _let_20))) (let ((_let_23 (= _let_8 _let_22))) (let ((_let_24 (not _let_8))) (let ((_let_25 (_let_4))) (let ((_let_26 (ASSUME :args _let_25))) (let ((_let_27 ((tptp.member D (tptp.difference B C))))) (let ((_let_28 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_23 false _let_4)))) (let ((_let_29 (not _let_22))) (let ((_let_30 (not _let_21))) (let ((_let_31 (and _let_19 _let_30))) (let ((_let_32 (= _let_10 _let_31))) (let ((_let_33 (= _let_21 _let_19))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (not _let_34))) (let ((_let_36 (= _let_35 _let_33))) (let ((_let_37 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_38 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 _let_37))) (let ((_let_39 (= _let_38 _let_34))) (let ((_let_40 (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (= _let_37 _let_40))) (let ((_let_42 (= _let_40 _let_12))) (let ((_let_43 (not _let_31))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_32 false _let_4)))) (let ((_let_45 (not _let_32))) (let ((_let_46 (not _let_10))) (let ((_let_47 (_let_32))) (let ((_let_48 (REORDERING (CNF_EQUIV_POS1 :args _let_47) :args ((or _let_46 _let_31 _let_45))))) (let ((_let_49 (forall ((E $$unsorted)) (= (not (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (= (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) (tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))) (let ((_let_50 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_37))) (let ((_let_51 (not _let_49))) (let ((_let_52 (or _let_51 _let_50))) (let ((_let_53 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (or (not (forall ((E $$unsorted)) (= (not (tptp.member E B)) (= (tptp.member E C) (tptp.member E D))))) (= B (tptp.symmetric_difference C D)))))) (let ((_let_54 (not _let_52))) (let ((_let_55 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_56 (or))) (let ((_let_57 (not _let_53))) (let ((_let_58 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_55) :args (_let_57))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_57) _let_53))) (REFL :args (_let_54)) :args _let_56)) _let_55 :args (_let_54 true _let_53)))) (let ((_let_59 (_let_49))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_59) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member E SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) :args _let_59)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_52 0)) (CONG (REFL :args (_let_52)) (MACRO_SR_PRED_INTRO :args ((= (not _let_51) _let_49))) :args _let_56)) :args ((or _let_49 _let_52))) _let_58 :args (_let_49 true _let_52)) :args (_let_36 false _let_49)))) (let ((_let_61 (not _let_36))) (let ((_let_62 (_let_33))) (let ((_let_63 (_let_36))) (let ((_let_64 (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS1 :args _let_63) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_34))) (REFL :args _let_62) :args _let_56)) :args ((or _let_34 _let_33 _let_61))))) (let ((_let_65 (forall ((D $$unsorted)) (= (tptp.member D (tptp.symmetric_difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_66 (not _let_39))) (let ((_let_67 (not _let_65))) (let ((_let_68 (or _let_67 _let_50))) (let ((_let_69 (forall ((B $$unsorted) (C $$unsorted)) (or (not (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C)))) (= B C))))) (let ((_let_70 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_71 (_let_67))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_71)) :args _let_71)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_65))) (REFL :args (_let_66)) :args _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_68)) :args ((or _let_50 _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_52 1)) _let_58 :args ((not _let_50) true _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_70 :args (_let_37 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args (_let_69)))) _let_70 :args (_let_68 false _let_69)) :args (_let_67 true _let_50 false _let_68)) :args (_let_66 true _let_65)))) (let ((_let_73 (_let_39))) (let ((_let_74 (CNF_EQUIV_NEG2 :args _let_73))) (let ((_let_75 (_let_22))) (let ((_let_76 (not _let_23))) (let ((_let_77 (_let_23))) (let ((_let_78 (not _let_14))) (let ((_let_79 (_let_14))) (let ((_let_80 (REORDERING (CNF_EQUIV_POS2 :args _let_79) :args ((or _let_13 _let_18 _let_78))))) (let ((_let_81 (_let_2))) (let ((_let_82 (ASSUME :args _let_81))) (let ((_let_83 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_82 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.symmetric_difference B C)))) :args _let_81)) _let_82 :args (_let_41 false _let_2)))) (let ((_let_84 (_let_3))) (let ((_let_85 (ASSUME :args _let_84))) (let ((_let_86 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_85 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.symmetric_difference B C)))) :args _let_84)) _let_85 :args (_let_42 false _let_3)))) (let ((_let_87 (not _let_13))) (let ((_let_88 (_let_87))) (let ((_let_89 (not _let_38))) (let ((_let_90 (not _let_42))) (let ((_let_91 (REFL :args (_let_90)))) (let ((_let_92 (not _let_41))) (let ((_let_93 (REFL :args (_let_92)))) (let ((_let_94 (and _let_41 _let_42 _let_89))) (let ((_let_95 (_let_89))) (let ((_let_96 (ASSUME :args _let_95))) (let ((_let_97 (APPLY_UF tptp.member))) (let ((_let_98 (ASSUME :args (_let_41)))) (let ((_let_99 (SYMM _let_98))) (let ((_let_100 (ASSUME :args (_let_42)))) (let ((_let_101 (SYMM _let_100))) (let ((_let_102 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_36)))) (let ((_let_103 (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_94)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_96 _let_98 _let_100) (SCOPE (FALSE_ELIM (TRANS (CONG _let_102 (TRANS _let_101 _let_99) :args _let_97) (FALSE_INTRO _let_96))) :args (_let_89 _let_41 _let_42))) :args (_let_41 _let_42 _let_89))) :args (true _let_94)) (CONG _let_93 _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_89) _let_38))) (REFL :args _let_88) :args _let_56)))) (let ((_let_104 (not _let_33))) (let ((_let_105 (REORDERING (CNF_EQUIV_POS2 :args _let_63) :args ((or _let_35 _let_104 _let_61))))) (let ((_let_106 (REORDERING (CNF_EQUIV_NEG1 :args _let_73) :args ((or _let_38 _let_34 _let_39))))) (let ((_let_107 (and _let_41 _let_42 _let_87))) (let ((_let_108 (ASSUME :args _let_88))) (let ((_let_109 (REORDERING (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_107)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_108 _let_100 _let_98) (SCOPE (FALSE_ELIM (TRANS (CONG _let_102 (TRANS (SYMM _let_99) (SYMM _let_101)) :args _let_97) (FALSE_INTRO _let_108))) :args (_let_87 _let_42 _let_41))) :args (_let_41 _let_42 _let_87))) :args (true _let_107)) (CONG _let_93 _let_91 (MACRO_SR_PRED_INTRO :args ((= (not _let_87) _let_13))) (REFL :args _let_95) :args _let_56)) :args ((or _let_92 _let_90 _let_89 _let_13))))) (let ((_let_110 (REORDERING (CNF_EQUIV_POS1 :args _let_77) :args ((or _let_24 _let_22 _let_76))))) (let ((_let_111 (REORDERING (CNF_EQUIV_POS1 :args _let_79) :args ((or _let_11 _let_87 _let_78))))) (let ((_let_112 (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_10 _let_8 _let_18))))) (let ((_let_113 (MACRO_RESOLUTION_TRUST _let_112 _let_111 _let_17 _let_110 _let_28 _let_109 _let_86 _let_83 (REORDERING (CNF_AND_POS :args (_let_22 1)) :args ((or _let_20 _let_29))) _let_106 _let_72 (REORDERING (CNF_EQUIV_POS1 :args _let_62) :args ((or _let_19 _let_30 _let_104))) _let_105 _let_60 (MACRO_RESOLUTION_TRUST _let_103 _let_86 _let_83 _let_80 _let_17 (CNF_OR_NEG :args (_let_11 1)) (REORDERING (CNF_EQUIV_POS2 :args _let_77) :args ((or _let_8 _let_29 _let_76))) _let_28 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_75) (CONG (REFL :args _let_75) (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_19))) :args _let_56)) :args ((or _let_19 _let_30 _let_22))) _let_74 _let_72 (REORDERING (CNF_EQUIV_NEG2 :args _let_62) :args ((or _let_33 _let_20 _let_30))) _let_64 _let_60 :args ((or _let_33 _let_30) false _let_42 false _let_41 false _let_13 false _let_14 false _let_11 false _let_8 false _let_23 false _let_22 true _let_38 true _let_39 true _let_19 false _let_34 false _let_36)) _let_48 _let_44 (REORDERING (CNF_AND_POS :args (_let_31 1)) :args ((or _let_30 _let_43))) :args (_let_30 false _let_11 false _let_14 true _let_8 false _let_23 false _let_13 false _let_42 false _let_41 true _let_22 false _let_38 true _let_39 false _let_19 true _let_34 false _let_36 false _let_33 true _let_10 false _let_32 true _let_31)))) (let ((_let_114 (_let_31))) (let ((_let_115 (MACRO_RESOLUTION_TRUST _let_103 _let_86 _let_83 _let_80 _let_17 _let_74 _let_72 (CNF_OR_NEG :args (_let_11 0)) _let_64 _let_60 (REORDERING (CNF_EQUIV_POS2 :args _let_47) :args ((or _let_10 _let_43 _let_45))) _let_44 (REORDERING (CNF_EQUIV_POS2 :args _let_62) :args ((or _let_21 _let_20 _let_104))) _let_113 (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_114) (CONG (REFL :args _let_114) (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_21))) :args _let_56)) :args ((or _let_21 _let_20 _let_31))) _let_113 :args (_let_20 false _let_42 false _let_41 false _let_13 false _let_14 true _let_38 true _let_39 false _let_11 false _let_34 false _let_36 false _let_10 false _let_32 true _let_33 true _let_21 false _let_31 true _let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_111 (MACRO_RESOLUTION_TRUST _let_109 _let_83 _let_86 (MACRO_RESOLUTION_TRUST _let_106 (MACRO_RESOLUTION_TRUST _let_105 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_62) :args ((or _let_21 _let_19 _let_33))) _let_113 _let_115 :args (_let_33 true _let_21 true _let_19)) _let_60 :args (_let_35 false _let_33 false _let_36)) _let_72 :args (_let_38 true _let_34 true _let_39)) :args (_let_13 false _let_41 false _let_42 false _let_38)) (MACRO_RESOLUTION_TRUST _let_112 (MACRO_RESOLUTION_TRUST _let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 0)) :args ((or _let_19 _let_43))) _let_115 :args (_let_43 true _let_19)) _let_44 :args (_let_46 true _let_31 false _let_32)) (MACRO_RESOLUTION_TRUST _let_110 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_22 0)) :args ((or _let_21 _let_29))) _let_113 :args (_let_29 true _let_21)) _let_28 :args (_let_24 true _let_22 false _let_23)) :args (_let_18 true _let_10 true _let_8)) _let_17 :args (false false _let_13 true _let_11 false _let_14)) :args (_let_6 _let_5 _let_4 _let_3 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (and (tptp.subset B C) (tptp.subset C B)))) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.union B C) (tptp.union C B))) _let_2 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))))) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.subset B C) (forall ((D $$unsorted)) (=> (tptp.member D B) (tptp.member D C))))) (forall ((B $$unsorted)) (tptp.subset B B)) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.49/0.69  )
% 0.49/0.69  % SZS output end Proof for SET582+3
% 0.49/0.70  % cvc5---1.0.5 exiting
% 0.49/0.70  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------