%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET692+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n032.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 14:39:56 EDT 2023

% Result   : Theorem 0.16s 0.43s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET692+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11  % Command    : do_cvc5 %s %d
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Sat Aug 26 11:37:29 EDT 2023
% 0.11/0.31  % CPUTime    : 
% 0.16/0.40  %----Proving TF0_NAR, FOF, or CNF
% 0.16/0.43  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.PERX7zSMfP/cvc5---1.0.5_16957.p...
% 0.16/0.43  ------- get file name : TPTP file name is SET692+4
% 0.16/0.43  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_16957.smt2...
% 0.16/0.43  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.16/0.43  % SZS status Theorem for SET692+4
% 0.16/0.43  % SZS output start Proof for SET692+4
% 0.16/0.43  (
% 0.16/0.43  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A (tptp.intersection A B)) (tptp.subset A B))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((A $$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_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (and _let_7 _let_6))) (let ((_let_9 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _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.intersection A B))))) (let ((_let_15 (tptp.equal_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_16 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (= _let_15 _let_16))) (let ((_let_18 (not _let_17))) (let ((_let_19 (_let_2))) (let ((_let_20 (ASSUME :args _let_19))) (let ((_let_21 (or))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_20) :args _let_19)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_18)) :args _let_21)) _let_20 :args (_let_18 true _let_1)))) (let ((_let_23 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_24 (= _let_16 _let_23))) (let ((_let_25 (not _let_16))) (let ((_let_26 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_27 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.subset A B)))) (let ((_let_30 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_24 false _let_26)))) (let ((_let_31 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_32 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_33 (not _let_32))) (let ((_let_34 (or _let_33 _let_31))) (let ((_let_35 (tptp.subset _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_37 (and _let_36 _let_35))) (let ((_let_38 (= _let_15 _let_37))) (let ((_let_39 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_40 (= _let_36 _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_9))) (let ((_let_42 (or _let_33 _let_41))) (let ((_let_43 (and _let_32 _let_31))) (let ((_let_44 (= _let_41 _let_43))) (let ((_let_45 (not _let_23))) (let ((_let_46 (not _let_24))) (let ((_let_47 (_let_24))) (let ((_let_48 (REORDERING (CNF_EQUIV_POS2 :args _let_47) :args ((or _let_16 _let_45 _let_46))))) (let ((_let_49 (_let_23))) (let ((_let_50 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) (let ((_let_51 (_let_17))) (let ((_let_52 (CNF_EQUIV_NEG2 :args _let_51))) (let ((_let_53 (_let_4))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_53)) _let_54 :args (_let_38 false _let_4)))) (let ((_let_56 (not _let_38))) (let ((_let_57 (not _let_37))) (let ((_let_58 (_let_38))) (let ((_let_59 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_60 (= _let_35 _let_59))) (let ((_let_61 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_62 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_9))) (let ((_let_63 (not _let_62))) (let ((_let_64 (or _let_63 _let_61))) (let ((_let_65 (and _let_61 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_66 (= _let_62 _let_65))) (let ((_let_67 (not _let_59))) (let ((_let_68 (_let_67))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_40 false _let_26)))) (let ((_let_70 (not _let_40))) (let ((_let_71 (not _let_39))) (let ((_let_72 (_let_40))) (let ((_let_73 (_let_71))) (let ((_let_74 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_43)) :args ((or _let_33 _let_43 (not _let_31)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_44)) :args ((or _let_41 (not _let_43) (not _let_44)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_14)) :args _let_12)) _let_13 :args (_let_44 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_33 _let_31 (not _let_34)))) (CNF_OR_NEG :args (_let_42 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_42 0)) (CONG (REFL :args (_let_42)) (MACRO_SR_PRED_INTRO :args ((= (not _let_33) _let_32))) :args _let_21)) :args ((or _let_32 _let_42))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_73)) :args _let_73)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_39))) (REFL :args ((not _let_42))) :args _let_21)) (REORDERING (CNF_EQUIV_POS2 :args _let_72) :args ((or _let_36 _let_71 _let_70))) _let_69 (CNF_AND_NEG :args (_let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_60)) :args ((or _let_35 _let_67 (not _let_60)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_59))) (REFL :args ((not _let_64))) :args _let_21)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_65 0)) :args ((or _let_61 (not _let_65)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_66)) :args ((or _let_63 _let_65 (not _let_66)))) (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_66 false _let_3)) (CNF_OR_NEG :args (_let_64 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_64 0)) (CONG (REFL :args (_let_64)) (MACRO_SR_PRED_INTRO :args ((= (not _let_63) _let_62))) :args _let_21)) :args ((or _let_62 _let_64))) :args (_let_64 false _let_65 false _let_66 true _let_61 false _let_62)) :args (_let_59 false _let_64)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_60 false _let_26)) :args (_let_35 false _let_59 false _let_60)) (REORDERING (CNF_EQUIV_POS2 :args _let_58) :args ((or _let_15 _let_57 _let_56))) _let_55 _let_52 _let_22 (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_49) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 _let_30 :args (_let_45 true _let_43 false _let_44 false _let_31 true _let_41 false _let_32 true _let_42 true _let_39 false _let_40 true _let_36 false _let_35 true _let_37 false _let_38 true _let_15 true _let_17 false _let_34 false _let_16 false _let_24)))) (let ((_let_75 (not _let_7))) (let ((_let_76 (or _let_75 _let_6))) (let ((_let_77 (or _let_75 _let_10))) (let ((_let_78 (not _let_15))) (let ((_let_79 (not _let_76))) (let ((_let_80 (_let_45))) (let ((_let_81 (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_80)) :args _let_80)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_23))) (REFL :args (_let_79)) :args _let_21)))) (let ((_let_82 (_let_39))) (let ((_let_83 (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_AND_POS :args (_let_8 1)) :args ((or _let_6 _let_83))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_76 1)) (MACRO_RESOLUTION_TRUST _let_81 _let_74 :args (_let_79 true _let_23)) :args ((not _let_6) true _let_76)) :args (_let_83 true _let_6)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_77)) :args ((or _let_75 _let_10 (not _let_77)))) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_82) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_82)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_76 0)) (CONG (REFL :args (_let_76)) (MACRO_SR_PRED_INTRO :args ((= (not _let_75) _let_7))) :args _let_21)) :args ((or _let_7 _let_76))) (REORDERING (CNF_EQUIV_POS1 :args _let_72) :args ((or (not _let_36) _let_39 _let_70))) _let_69 _let_81 (REORDERING (CNF_AND_POS :args (_let_37 0)) :args ((or _let_36 _let_57))) _let_48 _let_30 (REORDERING (CNF_EQUIV_POS1 :args _let_58) :args ((or _let_78 _let_37 _let_56))) _let_55 _let_52 _let_22 :args ((or _let_78 _let_10) false _let_77 false _let_7 false _let_39 false _let_40 true _let_76 false _let_36 true _let_23 false _let_24 false _let_37 false _let_38 true _let_16 true _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_51) :args ((or _let_15 _let_16 _let_17))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_47) :args ((or _let_25 _let_23 _let_46))) _let_74 _let_30 :args (_let_25 true _let_23 false _let_24)) _let_22 :args (_let_15 true _let_16 true _let_17)) :args (_let_10 false _let_15)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 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))) _let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))) (forall ((X $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.16/0.44  )
% 0.16/0.44  % SZS output end Proof for SET692+4
% 0.16/0.44  % cvc5---1.0.5 exiting
% 0.16/0.44  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------