%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n004.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
% 0.00/0.13  % Problem    : SET693+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n004.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 15:33:37 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dJkffTGf2V/cvc5---1.0.5_9334.p...
% 0.21/0.54  ------- get file name : TPTP file name is SET693+4
% 0.21/0.54  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9334.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 SET693+4
% 0.21/0.54  % SZS output start Proof for SET693+4
% 0.21/0.54  (
% 0.21/0.54  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A (tptp.union A B)) (tptp.subset B A))))) (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 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_7 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (= _let_7 _let_6))) (let ((_let_9 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_10 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_11 (_let_9))) (let ((_let_12 ((tptp.subset A B)))) (let ((_let_13 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_10 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_12)) :args _let_11)) _let_10 :args (_let_8 false _let_9)))) (let ((_let_14 (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (tptp.equal_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_16 (= _let_15 _let_7))) (let ((_let_17 (not _let_16))) (let ((_let_18 (_let_2))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 (or))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_19) :args _let_18)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_17)) :args _let_20)) _let_19 :args (_let_17 true _let_1)))) (let ((_let_22 (tptp.subset _let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_23 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14))) (let ((_let_24 (and _let_23 _let_22))) (let ((_let_25 (= _let_15 _let_24))) (let ((_let_26 (not _let_15))) (let ((_let_27 (_let_4))) (let ((_let_28 (ASSUME :args _let_27))) (let ((_let_29 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_28 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_27)) _let_28 :args (_let_25 false _let_4)))) (let ((_let_30 (not _let_24))) (let ((_let_31 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_32 (= _let_22 _let_31))) (let ((_let_33 (not _let_22))) (let ((_let_34 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_10 :args (_let_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_12)) :args _let_11)) _let_10 :args (_let_32 false _let_9)))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_36 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_14))) (let ((_let_37 (not _let_36))) (let ((_let_38 (or _let_37 _let_35))) (let ((_let_39 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_40 (not _let_39))) (let ((_let_41 (or _let_40 _let_35))) (let ((_let_42 (or _let_35 _let_39))) (let ((_let_43 (= _let_36 _let_42))) (let ((_let_44 (not _let_31))) (let ((_let_45 (not _let_32))) (let ((_let_46 (_let_32))) (let ((_let_47 (_let_31))) (let ((_let_48 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) true))))) (let ((_let_49 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.union SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))))) (let ((_let_50 (= _let_23 _let_49))) (let ((_let_51 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 _let_14))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_53 (not _let_52))) (let ((_let_54 (or _let_53 _let_51))) (let ((_let_55 (or _let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_56 (= _let_51 _let_55))) (let ((_let_57 (_let_3))) (let ((_let_58 (ASSUME :args _let_57))) (let ((_let_59 ((tptp.member X (tptp.union A B))))) (let ((_let_60 (not _let_49))) (let ((_let_61 (_let_60))) (let ((_let_62 (not _let_25))) (let ((_let_63 (_let_25))) (let ((_let_64 (_let_16))) (let ((_let_65 (not _let_8))) (let ((_let_66 (not _let_6))) (let ((_let_67 (_let_8))) (let ((_let_68 (_let_66))) (let ((_let_69 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_43)) :args ((or _let_36 (not _let_42) (not _let_43)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_59)) :args _let_57)) _let_58 :args (_let_43 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_38)) :args ((or _let_35 _let_37 (not _let_38)))) (REORDERING (CNF_OR_NEG :args (_let_42 1)) :args ((or _let_40 _let_42))) (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_20)) :args ((or _let_39 _let_41))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_68)) :args _let_68)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_66) _let_6))) (REFL :args ((not _let_41))) :args _let_20)) (REORDERING (CNF_EQUIV_POS2 :args _let_67) :args ((or _let_7 _let_66 _let_65))) _let_13 (CNF_EQUIV_NEG2 :args _let_64) _let_21 (REORDERING (CNF_EQUIV_POS2 :args _let_63) :args ((or _let_15 _let_30 _let_62))) _let_29 (CNF_AND_NEG :args (_let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_50)) :args ((or _let_23 _let_60 (not _let_50)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_61)) :args _let_61)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_60) _let_49))) (REFL :args ((not _let_54))) :args _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_56)) :args ((or _let_51 (not _let_55) (not _let_56)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_59)) :args _let_57)) _let_58 :args (_let_56 false _let_3)) (REORDERING (CNF_OR_NEG :args (_let_55 0)) :args ((or _let_53 _let_55))) (CNF_OR_NEG :args (_let_54 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_54 0)) (CONG (REFL :args (_let_54)) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_20)) :args ((or _let_52 _let_54))) :args (_let_54 false _let_56 false _let_55 true _let_51 false _let_52)) :args (_let_49 false _let_54)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_10 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_12)) :args _let_11)) _let_10 :args (_let_50 false _let_9)) :args (_let_23 false _let_49 false _let_50)) (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_47) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_47)) (REORDERING (CNF_EQUIV_POS2 :args _let_46) :args ((or _let_22 _let_44 _let_45))) _let_34 :args (_let_44 false _let_43 true _let_36 false _let_42 true _let_35 false _let_39 true _let_41 true _let_6 false _let_8 true _let_7 true _let_16 false _let_15 false _let_25 false _let_24 false _let_23 false _let_38 false _let_22 false _let_32)))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_71 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_72 (not _let_71))) (let ((_let_73 (or _let_72 _let_70))) (let ((_let_74 (not _let_73))) (let ((_let_75 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 _let_14))) (let ((_let_76 (not _let_75))) (let ((_let_77 (or _let_76 _let_70))) (let ((_let_78 (not _let_77))) (let ((_let_79 (_let_44))) (let ((_let_80 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_79)) :args _let_79)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_31))) (REFL :args (_let_78)) :args _let_20)) _let_69 :args (_let_78 true _let_31)))) (let ((_let_81 (or _let_70 _let_71))) (let ((_let_82 (= _let_75 _let_81))) (let ((_let_83 (CNF_OR_NEG :args (_let_77 1)))) (let ((_let_84 (_let_6))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_67) :args ((or (not _let_7) _let_6 _let_65))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_84) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_48)) :args _let_84)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_73)) :args ((or _let_70 _let_72 _let_74))) (MACRO_RESOLUTION_TRUST _let_83 _let_80 :args ((not _let_70) true _let_77)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_81)) :args ((or _let_70 _let_71 (not _let_81)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_82)) :args ((or _let_76 _let_81 (not _let_82)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING _let_59)) :args _let_57)) _let_58 :args (_let_82 false _let_3)) _let_83 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_77 0)) (CONG (REFL :args (_let_77)) (MACRO_SR_PRED_INTRO :args ((= (not _let_76) _let_75))) :args _let_20)) :args ((or _let_75 _let_77))) :args ((or _let_77 _let_71) false _let_81 false _let_82 true _let_70 false _let_75)) _let_80 :args (_let_71 true _let_77)) :args (_let_74 true _let_70 false _let_71)) :args (_let_66 true _let_73)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_NEG1 :args _let_64) :args ((or _let_15 _let_7 _let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_63) :args ((or _let_26 _let_24 _let_62))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_24 1)) :args ((or _let_22 _let_30))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_46) :args ((or _let_33 _let_31 _let_45))) _let_69 _let_34 :args (_let_33 true _let_31 false _let_32)) :args (_let_30 true _let_22)) _let_29 :args (_let_26 true _let_24 false _let_25)) _let_21 :args (_let_7 true _let_15 true _let_16)) _let_13 :args (false true _let_6 false _let_7 false _let_8)) :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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.55  )
% 0.21/0.55  % SZS output end Proof for SET693+4
% 0.21/0.55  % cvc5---1.0.5 exiting
% 0.21/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------