%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET016+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 14:36:47 EDT 2023

% Result   : Theorem 0.21s 0.68s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET016+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % 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 11:06:37 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.68  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.FdERc3RdqW/cvc5---1.0.5_31665.p...
% 0.21/0.68  ------- get file name : TPTP file name is SET016+4
% 0.21/0.68  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_31665.smt2...
% 0.21/0.68  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.68  % SZS status Theorem for SET016+4
% 0.21/0.68  % SZS output start Proof for SET016+4
% 0.21/0.68  (
% 0.21/0.68  (let ((_let_1 (not (forall ((A $$unsorted) (B $$unsorted) (U $$unsorted) (V $$unsorted)) (=> (tptp.equal_set (tptp.unordered_pair (tptp.singleton A) (tptp.unordered_pair A B)) (tptp.unordered_pair (tptp.singleton U) (tptp.unordered_pair U V))) (= A U)))))) (let ((_let_2 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))))) (let ((_let_3 (forall ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))))) (let ((_let_4 (forall ((A $$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.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (= _let_7 _let_6))) (let ((_let_9 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 _let_6))) (let ((_let_12 (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_13 (= _let_7 _let_12))) (let ((_let_14 (or _let_13 _let_8))) (let ((_let_15 (tptp.unordered_pair _let_12 _let_6))) (let ((_let_16 (tptp.member _let_7 _let_15))) (let ((_let_17 (= _let_16 _let_14))) (let ((_let_18 (_let_2))) (let ((_let_19 (ASSUME :args _let_18))) (let ((_let_20 ((tptp.member X (tptp.unordered_pair A B))))) (let ((_let_21 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_22 (tptp.unordered_pair _let_7 _let_21))) (let ((_let_23 (tptp.member _let_7 _let_22))) (let ((_let_24 (not _let_23))) (let ((_let_25 (or _let_24 _let_16))) (let ((_let_26 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.unordered_pair (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (tptp.member X (tptp.unordered_pair (tptp.singleton SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))))) (let ((_let_27 (tptp.subset _let_22 _let_15))) (let ((_let_28 (= _let_27 _let_26))) (let ((_let_29 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (and _let_27 (tptp.subset _let_15 _let_22)))) (let ((_let_32 (tptp.equal_set _let_22 _let_15))) (let ((_let_33 (= _let_32 _let_31))) (let ((_let_34 (_let_4))) (let ((_let_35 (ASSUME :args _let_34))) (let ((_let_36 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_37 (not _let_32))) (let ((_let_38 (or _let_37 _let_36))) (let ((_let_39 (forall ((A $$unsorted) (B $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.equal_set (tptp.unordered_pair (tptp.singleton A) (tptp.unordered_pair A B)) (tptp.unordered_pair (tptp.singleton U) (tptp.unordered_pair U V)))) (= A U))))) (let ((_let_40 (not _let_38))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (or))) (let ((_let_43 (not _let_39))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_41) :args (_let_43))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_43) _let_39))) (REFL :args (_let_40)) :args _let_42)) _let_41 :args (_let_40 true _let_39)))) (let ((_let_45 (_let_26))) (let ((_let_46 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_7))) (let ((_let_47 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_12))) (let ((_let_48 (not _let_13))) (let ((_let_49 (_let_3))) (let ((_let_50 (ASSUME :args _let_49))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_ENUM)) :args _let_49))) _let_50 :args (_let_46 false _let_3)))) (let ((_let_52 (= _let_36 _let_47))) (let ((_let_53 (not _let_47))) (let ((_let_54 (not _let_36))) (let ((_let_55 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_38 1)) _let_44 :args (_let_54 true _let_38)))) (let ((_let_56 (ASSUME :args (_let_46)))) (let ((_let_57 (TRUE_INTRO _let_56))) (let ((_let_58 (APPLY_UF tptp.member))) (let ((_let_59 (ASSUME :args (_let_13)))) (let ((_let_60 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_61 (ASSUME :args (_let_53)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_13 _let_8 (not _let_14)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_56 _let_59 _let_61) :args (_let_46 _let_53 _let_13)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_61)) (CONG _let_60 (SYMM _let_59) :args _let_58) _let_57)) :args (_let_46 _let_13 _let_53)) :args ((not (and _let_46 _let_53 _let_13)) SB_LITERAL))) (CONG (REFL :args ((not _let_46))) (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_47))) (REFL :args (_let_48)) :args _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_52)) :args ((or _let_36 _let_53 (not _let_52)))) _let_55 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_ENUM)) :args _let_49))) _let_50 :args (_let_52 false _let_3)) :args (_let_53 true _let_36 false _let_52)) _let_51 :args (_let_48 true _let_47 false _let_46)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or (not _let_16) _let_14 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_25)) :args ((or _let_24 _let_16 (not _let_25)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_7 _let_7 _let_21 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18))) _let_19 :args (_let_23 false _let_2)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_45) :args (_let_7 QUANTIFIERS_INST_ENUM)) :args _let_45)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_28)) :args ((or (not _let_27) _let_26 (not _let_28)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_31 0)) :args ((or _let_27 (not _let_31)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_33)) :args ((or _let_37 _let_31 (not _let_33)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_38 0)) (CONG (REFL :args (_let_38)) (MACRO_SR_PRED_INTRO :args ((= (not _let_37) _let_32))) :args _let_42)) :args ((or _let_32 _let_38))) _let_44 :args (_let_32 true _let_38)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_35 :args (_let_22 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_34)) _let_35 :args (_let_33 false _let_4)) :args (_let_31 false _let_32 false _let_33)) :args (_let_27 false _let_31)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_30 :args (_let_22 _let_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_29))) _let_30 :args (_let_28 false _let_29)) :args (_let_26 false _let_27 false _let_28)) :args (_let_25 false _let_26)) :args (_let_16 false _let_23 false _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (_let_7 _let_12 _let_6 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18)) _let_19 :args (_let_17 false _let_2)) :args (_let_14 false _let_16 false _let_17)) :args (_let_8 true _let_13 false _let_14)))) (let ((_let_63 (or _let_36 _let_9))) (let ((_let_64 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_6))) (let ((_let_65 (= _let_64 _let_63))) (let ((_let_66 (and _let_46 _let_8))) (let ((_let_67 (_let_46 _let_8))) (let ((_let_68 (ASSUME :args (_let_8)))) (let ((_let_69 (SYMM (SYMM _let_68)))) (let ((_let_70 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_36 _let_9 (not _let_63)))) _let_55 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_65)) :args ((or _let_63 (not _let_64) (not _let_65)))) (MACRO_RESOLUTION_TRUST (RESOLUTION (CNF_AND_NEG :args (_let_66)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_56 _let_68) (SCOPE (TRUE_ELIM (TRANS (CONG _let_60 (SYMM _let_69) :args _let_58) _let_57)) :args _let_67)) :args _let_67)) :args (true _let_66)) _let_51 _let_62 :args (_let_64 false _let_46 false _let_8)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18)) _let_19 :args (_let_65 false _let_2)) :args (_let_63 false _let_64 false _let_65)) :args (_let_9 true _let_36 false _let_63)))) (let ((_let_71 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_72 (= _let_71 _let_10))) (let ((_let_73 (not _let_10))) (let ((_let_74 (not _let_71))) (let ((_let_75 (REFL :args ((not _let_9))))) (let ((_let_76 (and _let_54 _let_9))) (let ((_let_77 (ASSUME :args (_let_54)))) (let ((_let_78 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))) (let ((_let_79 (ASSUME :args (_let_9)))) (let ((_let_80 (SYMM _let_79))) (let ((_let_81 (ASSUME :args (_let_11)))) (let ((_let_82 (ASSUME :args (_let_73)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_81 _let_68 _let_79 _let_82) :args (_let_8 _let_9 _let_73 _let_11)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_82)) (CONG _let_78 (TRANS (CONG _let_80 :args (APPLY_UF tptp.singleton)) _let_69) :args _let_58) (TRUE_INTRO _let_81))) :args (_let_11 _let_8 _let_9 _let_73)) :args ((not (and _let_8 _let_9 _let_73 _let_11)) SB_LITERAL))) (CONG (REFL :args ((not _let_8))) _let_75 (MACRO_SR_PRED_INTRO :args ((= (not _let_73) _let_10))) (REFL :args ((not _let_11))) :args _let_42)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_20)) :args _let_18))) _let_19 :args (_let_11 false _let_2)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_72)) :args ((or _let_71 _let_73 (not _let_72)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (RESOLUTION (CNF_AND_NEG :args (_let_76)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_79 _let_77) (SCOPE (FALSE_ELIM (MACRO_SR_PRED_TRANSFORM (TRANS (CONG _let_80 _let_78 :args (=)) (FALSE_INTRO _let_77)) :args ((= _let_71 false)))) :args (_let_9 _let_54))) :args (_let_54 _let_9))) :args (true _let_76)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_54) _let_36))) _let_75 (REFL :args (_let_74)) :args _let_42)) _let_55 _let_70 :args (_let_74 true _let_36 false _let_9)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_ENUM)) :args _let_49))) _let_50 :args (_let_72 false _let_3)) :args (_let_73 true _let_71 false _let_72)) _let_70 _let_62 :args (false false _let_11 true _let_10 false _let_9 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 $$unsorted)) (= (tptp.member X (tptp.intersection A B)) (and (tptp.member X A) (tptp.member X B)))) (forall ((X $$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_3 _let_2 (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_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.69  )
% 0.21/0.69  % SZS output end Proof for SET016+4
% 0.21/0.69  % cvc5---1.0.5 exiting
% 0.21/0.69  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------