%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n006.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 14:40:25 EDT 2023

% Result   : Theorem 0.17s 0.50s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11  % Command    : do_cvc5 %s %d
% 0.11/0.32  % Computer : n006.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sat Aug 26 11:12:52 EDT 2023
% 0.11/0.32  % CPUTime    : 
% 0.17/0.43  %----Proving TF0_NAR, FOF, or CNF
% 0.17/0.50  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.dVRxcG9cxM/cvc5---1.0.5_5931.p...
% 0.17/0.50  ------- get file name : TPTP file name is SET812+4
% 0.17/0.50  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_5931.smt2...
% 0.17/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.17/0.50  % SZS status Theorem for SET812+4
% 0.17/0.50  % SZS output start Proof for SET812+4
% 0.17/0.50  (
% 0.17/0.50  (let ((_let_1 (not (forall ((A $$unsorted)) (=> (tptp.member A tptp.on) (tptp.equal_set A (tptp.intersection A (tptp.power_set A)))))))) (let ((_let_2 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.subset X A)))))))) (let ((_let_3 (forall ((X $$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 ((X $$unsorted) (A $$unsorted)) (= (tptp.member X (tptp.power_set A)) (tptp.subset 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 $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_8 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_9 (and _let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_8)))) (let ((_let_10 (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8))) (let ((_let_11 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 _let_10))) (let ((_let_12 (not _let_11))) (let ((_let_13 (or _let_12 _let_7))) (let ((_let_14 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_15 (not _let_13))) (let ((_let_16 (tptp.subset _let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_17 (= _let_16 _let_14))) (let ((_let_18 (not _let_14))) (let ((_let_19 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_20 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_21 (_let_19))) (let ((_let_22 ((tptp.subset A B)))) (let ((_let_23 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_24 (and _let_23 _let_16))) (let ((_let_25 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.member X (tptp.intersection SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.power_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))))) (let ((_let_26 (= _let_23 _let_25))) (let ((_let_27 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_10))) (let ((_let_28 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_29 (not _let_28))) (let ((_let_30 (or _let_29 _let_27))) (let ((_let_31 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))) (let ((_let_32 (or _let_29 _let_31))) (let ((_let_33 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_8))) (let ((_let_34 (and _let_28 _let_33))) (let ((_let_35 (= _let_27 _let_34))) (let ((_let_36 (= _let_33 _let_31))) (let ((_let_37 (or))) (let ((_let_38 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) (tptp.subset X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2))))) (let ((_let_39 (and (tptp.set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) (tptp.strict_well_order tptp.member_predicate SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) _let_38))) (let ((_let_40 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 tptp.on))) (let ((_let_41 (= _let_40 _let_39))) (let ((_let_42 (forall ((A $$unsorted)) (= (tptp.member A tptp.on) (and (tptp.set A) (tptp.strict_well_order tptp.member_predicate A) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.subset X A)))))))) (let ((_let_43 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_44 (tptp.equal_set SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10))) (let ((_let_45 (not _let_40))) (let ((_let_46 (or _let_45 _let_44))) (let ((_let_47 (forall ((A $$unsorted)) (or (not (tptp.member A tptp.on)) (tptp.equal_set A (tptp.intersection A (tptp.power_set A))))))) (let ((_let_48 (not _let_46))) (let ((_let_49 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_50 (not _let_47))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_49) :args (_let_50))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_50) _let_47))) (REFL :args (_let_48)) :args _let_37)) _let_49 :args (_let_48 true _let_47)))) (let ((_let_52 (_let_38))) (let ((_let_53 (_let_3))) (let ((_let_54 (ASSUME :args _let_53))) (let ((_let_55 ((tptp.member X (tptp.intersection A B))))) (let ((_let_56 (_let_4))) (let ((_let_57 (ASSUME :args _let_56))) (let ((_let_58 (not _let_25))) (let ((_let_59 (_let_58))) (let ((_let_60 (= _let_44 _let_24))) (let ((_let_61 (not _let_24))) (let ((_let_62 (_let_5))) (let ((_let_63 (ASSUME :args _let_62))) (let ((_let_64 (_let_18))) (let ((_let_65 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_64)) :args _let_64)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_18) _let_14))) (REFL :args (_let_15)) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_17)) :args ((or _let_16 _let_18 (not _let_17)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_24)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_60)) :args ((or _let_44 _let_61 (not _let_60)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_46 1)) _let_51 :args ((not _let_44) true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_63 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.equal_set A B)))) :args _let_62)) _let_63 :args (_let_60 false _let_5)) :args (_let_61 true _let_44 false _let_60)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_26)) :args ((or _let_23 _let_58 (not _let_26)))) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_58) _let_25))) (REFL :args ((not _let_30))) :args _let_37)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_34)) :args ((or _let_29 _let_34 (not _let_33)))) (REORDERING (CNF_EQUIV_POS2 :args (_let_36)) :args ((or _let_33 (not _let_31) (not _let_36)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_57 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING ((tptp.member X (tptp.power_set A))))) :args _let_56)) _let_57 :args (_let_36 false _let_4)) (REORDERING (CNF_EQUIV_POS2 :args (_let_35)) :args ((or _let_27 (not _let_34) (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53)) _let_54 :args (_let_35 false _let_3)) (REORDERING (CNF_OR_POS :args (_let_32)) :args ((or _let_29 _let_31 (not _let_32)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2) false))))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_39 2)) :args ((or _let_38 (not _let_39)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_41)) :args ((or _let_45 _let_39 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_46 0)) (CONG (REFL :args (_let_46)) (MACRO_SR_PRED_INTRO :args ((= (not _let_45) _let_40))) :args _let_37)) :args ((or _let_40 _let_46))) _let_51 :args (_let_40 true _let_46)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_43 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.member A tptp.on)))) :args (_let_42))) _let_43 :args (_let_41 false _let_42)) :args (_let_39 false _let_40 false _let_41)) :args (_let_38 false _let_39)) :args (_let_32 false _let_38)) (CNF_OR_NEG :args (_let_30 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG (REFL :args (_let_30)) (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_28))) :args _let_37)) :args ((or _let_28 _let_30))) :args (_let_30 false _let_33 false _let_36 true _let_34 false _let_35 false _let_31 false _let_32 true _let_27 false _let_28)) :args (_let_25 false _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_10 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_21)) _let_20 :args (_let_26 false _let_19)) :args (_let_23 false _let_25 false _let_26)) :args ((not _let_16) true _let_24 false _let_23)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_20 :args (_let_10 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_22)) :args _let_21)) _let_20 :args (_let_17 false _let_19)) :args (_let_18 true _let_16 false _let_17)) :args (_let_15 true _let_14)))) (let ((_let_66 (= _let_11 _let_9))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_9 0)) :args ((or _let_7 (not _let_9)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_66)) :args ((or _let_12 _let_9 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_13 0)) (CONG (REFL :args (_let_13)) (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_37)) :args ((or _let_11 _let_13))) _let_65 :args (_let_11 true _let_13)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_54 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_8 QUANTIFIERS_INST_E_MATCHING _let_55)) :args _let_53)) _let_54 :args (_let_66 false _let_3)) :args (_let_9 false _let_11 false _let_66)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_13 1)) _let_65 :args ((not _let_7) true _let_13)) :args (false false _let_9 true _let_7)) :args (_let_6 _let_5 _let_4 _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 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_well_order R E) (and (tptp.strict_order R E) (forall ((A $$unsorted)) (=> (and (tptp.subset A E) (exists ((X $$unsorted)) (tptp.member X A))) (exists ((Y $$unsorted)) (tptp.least Y R A))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (or (= M X) (tptp.apply R M X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.apply tptp.member_predicate X Y) (tptp.member X Y))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.strict_order R E) (and (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (not (and (tptp.apply R X Y) (tptp.apply R Y X))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))) (forall ((X $$unsorted)) (=> (tptp.set X) (forall ((Y $$unsorted)) (=> (tptp.member Y X) (tptp.set Y))))) (forall ((X $$unsorted) (R $$unsorted) (A $$unsorted) (Y $$unsorted)) (= (tptp.member Y (tptp.initial_segment X R A)) (and (tptp.member Y A) (tptp.apply R Y X)))) (forall ((A $$unsorted) (X $$unsorted)) (= (tptp.member X (tptp.suc A)) (tptp.member X (tptp.union A (tptp.singleton A))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.17/0.51  )
% 0.17/0.51  % SZS output end Proof for SET812+4
% 0.17/0.51  % cvc5---1.0.5 exiting
% 0.17/0.51  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------