%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n010.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 0.21s 0.54s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET694+4 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n010.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 11:26:20 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.Wcpdti9xUj/cvc5---1.0.5_12299.p...
% 0.21/0.54  ------- get file name : TPTP file name is SET694+4
% 0.21/0.54  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12299.smt2...
% 0.21/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54  % SZS status Theorem for SET694+4
% 0.21/0.54  % SZS output start Proof for SET694+4
% 0.21/0.54  (
% 0.21/0.54  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (tptp.subset (tptp.union (tptp.power_set A) (tptp.power_set B)) (tptp.power_set (tptp.union A B)))))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.union A B)) (or (tptp.member X A) (tptp.member X B)))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset X A))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_6 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_7))) (let ((_let_11 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (= _let_11 _let_6))) (let ((_let_13 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_14 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_15 (_let_13))) (let ((_let_16 ((tptp.subset A B)))) (let ((_let_17 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_18 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_17))) (let ((_let_19 (= _let_18 _let_11))) (let ((_let_20 (_let_4))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 ((tptp.member X (tptp.power_set A))))) (let ((_let_23 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_23))) (let ((_let_25 (or _let_24 _let_18))) (let ((_let_26 (tptp.union _let_23 _let_17))) (let ((_let_27 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_26))) (let ((_let_28 (= _let_27 _let_25))) (let ((_let_29 (_let_3))) (let ((_let_30 (ASSUME :args _let_29))) (let ((_let_31 ((tptp.member X (tptp.union A B))))) (let ((_let_32 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_33 (tptp.power_set _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_33))) (let ((_let_35 (not _let_27))) (let ((_let_36 (or _let_35 _let_34))) (let ((_let_37 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.power_set (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))))) (let ((_let_38 (not _let_36))) (let ((_let_39 (tptp.subset _let_26 _let_33))) (let ((_let_40 (= _let_39 _let_37))) (let ((_let_41 (not _let_37))) (let ((_let_42 (not _let_39))) (let ((_let_43 (_let_2))) (let ((_let_44 (ASSUME :args _let_43))) (let ((_let_45 (or))) (let ((_let_46 (_let_41))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_46)) :args _let_46)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_41) _let_37))) (REFL :args (_let_38)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_40)) :args ((or _let_39 _let_41 (not _let_40)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_44) :args _let_43)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_42)) :args _let_45)) _let_44 :args (_let_42 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (_let_26 _let_33 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_15)) _let_14 :args (_let_40 false _let_13)) :args (_let_41 true _let_39 false _let_40)) :args (_let_38 true _let_37)))) (let ((_let_48 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_49 (= _let_24 _let_48))) (let ((_let_50 (not _let_24))) (let ((_let_51 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_52 (= _let_48 _let_51))) (let ((_let_53 (not _let_48))) (let ((_let_54 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_55 (or _let_9 _let_54))) (let ((_let_56 (not _let_55))) (let ((_let_57 (or _let_54 _let_7))) (let ((_let_58 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_32))) (let ((_let_59 (= _let_58 _let_57))) (let ((_let_60 (not _let_57))) (let ((_let_61 (or _let_9 _let_58))) (let ((_let_62 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_63 (not _let_61))) (let ((_let_64 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_32))) (let ((_let_65 (= _let_64 _let_62))) (let ((_let_66 (not _let_62))) (let ((_let_67 (= _let_34 _let_64))) (let ((_let_68 (not _let_64))) (let ((_let_69 (_let_66))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_69)) :args _let_69)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_62))) (REFL :args (_let_63)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_65)) :args ((or _let_64 _let_66 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_67)) :args ((or _let_34 _let_68 (not _let_67)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_36 1)) _let_47 :args ((not _let_34) true _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_32 QUANTIFIERS_INST_E_MATCHING _let_22)) :args _let_20)) _let_21 :args (_let_67 false _let_4)) :args (_let_68 true _let_34 false _let_67)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_32 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_15)) _let_14 :args (_let_65 false _let_13)) :args (_let_66 true _let_64 false _let_65)) :args (_let_63 true _let_62)))) (let ((_let_71 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_59)) :args ((or _let_58 _let_60 (not _let_59)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_61 1)) _let_70 :args ((not _let_58) true _let_61)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_29)) _let_30 :args (_let_59 false _let_3)) :args (_let_60 true _let_58 false _let_59)))) (let ((_let_72 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_61 0)) (CONG (REFL :args (_let_61)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_45)) :args ((or _let_8 _let_61))) _let_70 :args (_let_8 true _let_61)))) (let ((_let_73 (_let_51))) (let ((_let_74 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6) false)))))) (let ((_let_75 (not _let_10))) (let ((_let_76 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_76) :args _let_74) :args _let_76)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_10)) :args ((or _let_9 _let_7 _let_75))) _let_72 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 1)) _let_71 :args ((not _let_7) true _let_57)) :args (_let_75 false _let_8 true _let_7)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_12)) :args ((or (not _let_11) _let_6 (not _let_12)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_19)) :args ((or (not _let_18) _let_11 (not _let_19)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_18 (not _let_25)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_49)) :args ((or _let_50 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_52)) :args ((or _let_53 _let_51 (not _let_52)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_73) :args _let_74) :args _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_55)) :args ((or _let_9 _let_54 _let_56))) _let_72 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_57 0)) _let_71 :args ((not _let_54) true _let_57)) :args (_let_56 false _let_8 true _let_54)) :args ((not _let_51) true _let_55)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_15)) _let_14 :args (_let_52 false _let_13)) :args (_let_53 true _let_51 false _let_52)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_22)) :args _let_20)) _let_21 :args (_let_49 false _let_4)) :args (_let_50 true _let_48 false _let_49)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or _let_35 _let_25 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_36 0)) (CONG (REFL :args (_let_36)) (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_27))) :args _let_45)) :args ((or _let_27 _let_36))) _let_47 :args (_let_27 true _let_36)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_23 _let_17 QUANTIFIERS_INST_E_MATCHING _let_31)) :args _let_29)) _let_30 :args (_let_28 false _let_3)) :args (_let_25 false _let_27 false _let_28)) :args (_let_18 true _let_24 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_22)) :args _let_20)) _let_21 :args (_let_19 false _let_4)) :args (_let_11 false _let_18 false _let_19)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_14 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_16)) :args _let_15)) _let_14 :args (_let_12 false _let_13)) :args (_let_6 false _let_11 false _let_12)) :args (false true _let_10 false _let_6)) :args (_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) _let_4 (forall ((X $$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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for SET694+4
% 0.21/0.55  % cvc5---1.0.5 exiting
% 0.21/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------