%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n009.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 14:39:27 EDT 2023

% Result   : Theorem 0.49s 0.70s
% Output   : Proof 0.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SET611+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n009.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 12:34:50 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.49/0.70  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.lBqW451nAO/cvc5---1.0.5_21692.p...
% 0.49/0.70  ------- get file name : TPTP file name is SET611+3
% 0.49/0.70  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_21692.smt2...
% 0.49/0.70  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.49/0.70  % SZS status Theorem for SET611+3
% 0.49/0.70  % SZS output start Proof for SET611+3
% 0.49/0.70  (
% 0.49/0.70  (let ((_let_1 (not (forall ((B $$unsorted) (C $$unsorted)) (= (= (tptp.intersection B C) tptp.empty_set) (= (tptp.difference B C) B)))))) (let ((_let_2 (forall ((B $$unsorted)) (not (tptp.member B tptp.empty_set))))) (let ((_let_3 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.difference B C)) (and (tptp.member D B) (not (tptp.member D C))))))) (let ((_let_4 (forall ((B $$unsorted) (C $$unsorted) (D $$unsorted)) (= (tptp.member D (tptp.intersection B C)) (and (tptp.member D B) (tptp.member D C)))))) (let ((_let_5 (forall ((B $$unsorted) (C $$unsorted)) (=> (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C))) (= B C))))) (let ((_let_6 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 tptp.empty_set))) (let ((_let_7 (_let_2))) (let ((_let_8 (ASSUME :args _let_7))) (let ((_let_9 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 _let_9))) (let ((_let_11 (= tptp.empty_set _let_9))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_14 (and _let_13 _let_12))) (let ((_let_15 (= _let_10 _let_14))) (let ((_let_16 (_let_4))) (let ((_let_17 (ASSUME :args _let_16))) (let ((_let_18 ((tptp.member D (tptp.intersection B C))))) (let ((_let_19 (not _let_12))) (let ((_let_20 (and _let_13 _let_19))) (let ((_let_21 (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 _let_21))) (let ((_let_23 (= _let_22 _let_20))) (let ((_let_24 (not _let_20))) (let ((_let_25 (_let_3))) (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_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_23 false _let_3)))) (let ((_let_29 (= _let_13 _let_22))) (let ((_let_30 (not _let_22))) (let ((_let_31 (forall ((D $$unsorted)) (= (tptp.member D SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.member D (tptp.difference SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_32 (not _let_29))) (let ((_let_33 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_21))) (let ((_let_34 (not _let_31))) (let ((_let_35 (or _let_34 _let_33))) (let ((_let_36 (forall ((B $$unsorted) (C $$unsorted)) (or (not (forall ((D $$unsorted)) (= (tptp.member D B) (tptp.member D C)))) (= B C))))) (let ((_let_37 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_38 (_let_36))) (let ((_let_39 (= _let_11 _let_33))) (let ((_let_40 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_42 (and _let_41 _let_40))) (let ((_let_43 (forall ((D $$unsorted)) (= (tptp.member D (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member D tptp.empty_set))))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_11))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 _let_9))) (let ((_let_47 (= _let_46 _let_42))) (let ((_let_48 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 tptp.empty_set))) (let ((_let_49 (= _let_46 _let_48))) (let ((_let_50 (not _let_33))) (let ((_let_51 (forall ((B $$unsorted) (C $$unsorted)) (= (= tptp.empty_set (tptp.intersection B C)) (= B (tptp.difference B C)))))) (let ((_let_52 (not _let_39))) (let ((_let_53 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_54 (or))) (let ((_let_55 (not _let_51))) (let ((_let_56 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_53) :args (_let_55))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_51))) (REFL :args (_let_52)) :args _let_54)) _let_53 :args (_let_52 true _let_51)))) (let ((_let_57 (_let_39))) (let ((_let_58 (not _let_40))) (let ((_let_59 (and _let_41 _let_58))) (let ((_let_60 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 _let_21))) (let ((_let_61 (= _let_60 _let_59))) (let ((_let_62 (not _let_42))) (let ((_let_63 (and _let_33 _let_41))) (let ((_let_64 (ASSUME :args (_let_41)))) (let ((_let_65 (APPLY_UF tptp.member))) (let ((_let_66 (ASSUME :args (_let_33)))) (let ((_let_67 (_let_44))) (let ((_let_68 ((not (= (tptp.member B tptp.empty_set) false))))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args (_let_49)) :args ((or _let_46 _let_48 _let_49))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_8 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_7)) _let_8 :args ((not _let_48) false _let_2)) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_67)) :args _let_67)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) (REFL :args ((not _let_49))) :args _let_54)) (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or (not _let_46) _let_42 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING _let_18)) :args _let_16)) _let_17 :args (_let_47 false _let_4)) (REORDERING (CNF_OR_POS :args (_let_45)) :args ((or _let_11 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_37 :args (_let_9 tptp.empty_set QUANTIFIERS_INST_ENUM)) :args _let_38))) _let_37 :args (_let_45 false _let_36)) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_63)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_64 _let_66) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35)) (SYMM _let_66) :args _let_65) (TRUE_INTRO _let_64))) :args (_let_41 _let_33))) :args (_let_33 _let_41))) :args (true _let_63)) (REORDERING (CNF_EQUIV_POS1 :args (_let_61)) :args ((or _let_59 (not _let_60) (not _let_61)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_35 QUANTIFIERS_INST_E_MATCHING _let_27)) :args _let_25)) _let_26 :args (_let_61 false _let_3)) (REORDERING (CNF_AND_POS :args (_let_59 1)) :args ((or _let_58 (not _let_59)))) (REORDERING (CNF_AND_POS :args (_let_42 1)) :args ((or _let_40 _let_62))) (REORDERING (CNF_AND_POS :args (_let_42 0)) :args ((or _let_41 _let_62))) :args ((or _let_50 _let_62) true _let_60 false _let_61 true _let_59 false _let_40 false _let_41)) (CNF_EQUIV_NEG2 :args _let_57) _let_56 :args (_let_50 true _let_48 true _let_49 true _let_46 false _let_47 true _let_43 false _let_45 true _let_42 true _let_11 true _let_39)))) (let ((_let_70 (_let_34))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_70)) :args _let_70)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_31))) (REFL :args (_let_32)) :args _let_54)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_35)) :args ((or _let_33 _let_34 (not _let_35)))) _let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_37 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_21 QUANTIFIERS_INST_ENUM)) :args _let_38)) _let_37 :args (_let_35 false _let_36)) :args (_let_34 true _let_33 false _let_35)) :args (_let_32 true _let_31)))) (let ((_let_72 (_let_29))) (let ((_let_73 (not _let_23))) (let ((_let_74 (_let_23))) (let ((_let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_74) :args ((or _let_30 _let_20 _let_73))) _let_28 (REORDERING (CNF_AND_POS :args (_let_20 0)) :args ((or _let_13 _let_24))) (REORDERING (CNF_EQUIV_NEG1 :args _let_72) :args ((or _let_13 _let_22 _let_29))) _let_71 :args (_let_13 false _let_23 true _let_20 false _let_22 true _let_29)))) (let ((_let_76 (not _let_13))) (let ((_let_77 (_let_20))) (let ((_let_78 (and _let_11 _let_10))) (let ((_let_79 (ASSUME :args (_let_10)))) (let ((_let_80 (ASSUME :args (_let_11)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_8 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_68)) :args _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_78)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_80) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45)) (SYMM (SYMM _let_80)) :args _let_65) (TRUE_INTRO _let_79))) :args (_let_10 _let_11))) :args (_let_11 _let_10))) :args (true _let_78)) :args ((or (not _let_11) _let_6 (not _let_10)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_57) :args ((or _let_11 _let_33 _let_39))) _let_69 _let_56 :args (_let_11 true _let_33 true _let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_15)) :args ((or _let_10 (not _let_14) (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_14)) :args ((or _let_76 _let_19 _let_14))) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_77) (CONG (REFL :args _let_77) (REFL :args (_let_76)) (MACRO_SR_PRED_INTRO :args ((= (not _let_19) _let_12))) :args _let_54)) :args ((or _let_76 _let_12 _let_20))) _let_75 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_74) :args ((or _let_22 _let_24 _let_73))) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_72) _let_71 _let_75 :args (_let_30 true _let_29 false _let_13)) _let_28 :args (_let_24 true _let_22 false _let_23)) :args (_let_12 false _let_13 true _let_20)) :args (_let_14 false _let_13 false _let_12)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_17 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_45 QUANTIFIERS_INST_E_MATCHING _let_18)) :args _let_16)) _let_17 :args (_let_15 false _let_4)) :args (_let_10 false _let_14 false _let_15)) :args (_let_6 false _let_11 false _let_10)) _let_8 :args (false false _let_6 false _let_2)) :args (_let_5 _let_4 _let_3 _let_2 (forall ((B $$unsorted) (C $$unsorted)) (= (= B C) (and (tptp.subset B C) (tptp.subset C B)))) (forall ((B $$unsorted) (C $$unsorted)) (= (tptp.intersection B C) (tptp.intersection C B))) (forall ((B $$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)) (forall ((B $$unsorted)) (= (tptp.empty B) (forall ((C $$unsorted)) (not (tptp.member C B))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.49/0.71  )
% 0.49/0.71  % SZS output end Proof for SET611+3
% 0.49/0.71  % cvc5---1.0.5 exiting
% 0.49/0.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------