%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET351+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 14:38:35 EDT 2023

% Result   : Theorem 0.19s 0.54s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n010.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 15:09:50 EDT 2023
% 0.19/0.35  % CPUTime    : 
% 0.19/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.19/0.54  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.oH3e1YpSIg/cvc5---1.0.5_25395.p...
% 0.19/0.54  ------- get file name : TPTP file name is SET351+4
% 0.19/0.54  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_25395.smt2...
% 0.19/0.54  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.19/0.54  % SZS status Theorem for SET351+4
% 0.19/0.54  % SZS output start Proof for SET351+4
% 0.19/0.54  (
% 0.19/0.54  (let ((_let_1 (forall ((A $$unsorted)) (tptp.equal_set (tptp.sum (tptp.singleton A)) A)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (exists ((Y $$unsorted)) (and (tptp.member Y A) (tptp.member X Y))))))) (let ((_let_4 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))))) (let ((_let_5 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))))) (let ((_let_6 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_11 (not _let_10))) (let ((_let_12 (or _let_11 _let_8))) (let ((_let_13 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y)))))) (let ((_let_14 (not _let_12))) (let ((_let_15 (_let_4))) (let ((_let_16 (ASSUME :args _let_15))) (let ((_let_17 ((tptp.member X (tptp.singleton A))))) (let ((_let_18 (tptp.sum _let_9))) (let ((_let_19 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_18))) (let ((_let_20 (or _let_8 _let_19))) (let ((_let_21 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.sum (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))) (let ((_let_22 (not _let_20))) (let ((_let_23 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18))) (let ((_let_24 (= _let_23 _let_21))) (let ((_let_25 (not _let_21))) (let ((_let_26 (forall ((A $$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_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_28 (_let_26))) (let ((_let_29 ((tptp.subset A B)))) (let ((_let_30 (tptp.subset _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_31 (and _let_30 _let_23))) (let ((_let_32 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.sum (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_33 (= _let_30 _let_32))) (let ((_let_34 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_35 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_18))) (let ((_let_36 (not _let_35))) (let ((_let_37 (or _let_36 _let_34))) (let ((_let_38 (forall ((Y $$unsorted)) (or (not (tptp.member Y (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 Y)))))) (let ((_let_39 (not _let_38))) (let ((_let_40 (= _let_35 _let_39))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_42 (not _let_41))) (let ((_let_43 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 _let_9))) (let ((_let_44 (not _let_43))) (let ((_let_45 (or _let_44 _let_42))) (let ((_let_46 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_47 (= _let_43 _let_46))) (let ((_let_48 (or))) (let ((_let_49 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.sum A)) (not (forall ((Y $$unsorted)) (or (not (tptp.member Y A)) (not (tptp.member X Y))))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (_let_49))) (let ((_let_52 ((tptp.member X (tptp.sum A))))) (let ((_let_53 (_let_39))) (let ((_let_54 (REFL :args (_let_45)))) (let ((_let_55 (not _let_34))) (let ((_let_56 (ASSUME :args (_let_55)))) (let ((_let_57 (ASSUME :args (_let_46)))) (let ((_let_58 (ASSUME :args (_let_41)))) (let ((_let_59 (not _let_32))) (let ((_let_60 (_let_59))) (let ((_let_61 (tptp.equal_set _let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_62 (= _let_61 _let_31))) (let ((_let_63 (not _let_31))) (let ((_let_64 (_let_5))) (let ((_let_65 (ASSUME :args _let_64))) (let ((_let_66 (not _let_61))) (let ((_let_67 (_let_2))) (let ((_let_68 (ASSUME :args _let_67))) (let ((_let_69 (_let_25))) (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_25) _let_21))) (REFL :args (_let_22)) :args _let_48)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_24)) :args ((or _let_23 _let_25 (not _let_24)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_62)) :args ((or _let_61 _let_63 (not _let_62)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_68) :args _let_67)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_2) _let_1))) (REFL :args (_let_66)) :args _let_48)) _let_68 :args (_let_66 true _let_1)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_65 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_64)) _let_65 :args (_let_62 false _let_5)) :args (_let_63 true _let_61 false _let_62)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_33)) :args ((or _let_30 _let_59 (not _let_33)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_60)) :args _let_60)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_59) _let_32))) (REFL :args ((not _let_37))) :args _let_48)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_56 _let_57 _let_58) :args (_let_55 _let_41 _let_46)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_58)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6)) (SYMM _let_57) :args (APPLY_UF tptp.member)) (FALSE_INTRO _let_56))) :args (_let_55 _let_46 _let_41)) :args ((not (and _let_55 _let_41 _let_46)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_34))) (REFL :args (_let_42)) (REFL :args ((not _let_46))) :args _let_48)) (REORDERING (CNF_EQUIV_POS1 :args (_let_47)) :args ((or _let_44 _let_46 (not _let_47)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_17)) :args _let_15))) _let_16 :args (_let_47 false _let_4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 1)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_48)) :args ((or _let_41 _let_45))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_45 0)) (CONG _let_54 (MACRO_SR_PRED_INTRO :args ((= (not _let_44) _let_43))) :args _let_48)) :args ((or _let_43 _let_45))) (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_53)) :args _let_53)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_39) _let_38))) (REFL :args ((not _let_45))) :args _let_48)) (REORDERING (CNF_EQUIV_POS1 :args (_let_40)) :args ((or _let_36 _let_39 (not _let_40)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_9 QUANTIFIERS_INST_E_MATCHING _let_52)) :args _let_51)) _let_50 :args (_let_40 false _let_49)) (CNF_OR_NEG :args (_let_37 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_37 0)) (CONG (REFL :args (_let_37)) (MACRO_SR_PRED_INTRO :args ((= (not _let_36) _let_35))) :args _let_48)) :args ((or _let_35 _let_37))) :args (_let_37 false _let_46 false _let_47 false _let_41 false _let_43 true _let_45 true _let_38 false _let_40 true _let_34 false _let_35)) :args (_let_32 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (_let_18 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_33 false _let_26)) :args (_let_30 false _let_32 false _let_33)) :args ((not _let_23) true _let_31 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_27 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_18 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_29)) :args _let_28)) _let_27 :args (_let_24 false _let_26)) :args (_let_25 true _let_23 false _let_24)) :args (_let_22 true _let_21)))) (let ((_let_71 (not _let_13))) (let ((_let_72 (= _let_19 _let_71))) (let ((_let_73 (not _let_72))) (let ((_let_74 (_let_13))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_74) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 Y) false))))) :args _let_74)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_EQUIV_POS2 :args (_let_72)) (CONG (REFL :args (_let_73)) (REFL :args (_let_19)) (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_13))) :args _let_48)) :args ((or _let_19 _let_13 _let_73))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_20 1)) _let_70 :args ((not _let_19) true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9 QUANTIFIERS_INST_E_MATCHING _let_52)) :args _let_51)) _let_50 :args (_let_72 false _let_49)) :args (_let_13 true _let_19 false _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_12)) :args ((or _let_8 _let_11 _let_14))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_20 0)) (CONG (REFL :args (_let_20)) (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_48)) :args ((or _let_7 _let_20))) _let_70 :args (_let_7 true _let_20)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_16 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING _let_17)) :args _let_15))) _let_16 :args (_let_10 false _let_4)) :args (_let_14 false _let_7 false _let_10)) :args (false false _let_13 true _let_12)) :args (_let_6 _let_5 (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)))) (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 $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) _let_4 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))) _let_3 (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.19/0.54  )
% 0.19/0.54  % SZS output end Proof for SET351+4
% 0.19/0.54  % cvc5---1.0.5 exiting
% 0.19/0.55  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------