%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n015.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 14:40:23 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : SET802+4 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.16  % Command    : do_cvc5 %s %d
% 0.14/0.37  % Computer : n015.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Sat Aug 26 16:33:53 EDT 2023
% 0.14/0.37  % CPUTime    : 
% 0.20/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.61  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.TFiP7oF8aB/cvc5---1.0.5_23922.p...
% 0.20/0.61  ------- get file name : TPTP file name is SET802+4
% 0.20/0.61  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_23922.smt2...
% 0.20/0.61  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.61  % SZS status Theorem for SET802+4
% 0.20/0.61  % SZS output start Proof for SET802+4
% 0.20/0.61  (
% 0.20/0.61  (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted)) (=> (tptp.order R E) (forall ((X $$unsorted)) (=> (tptp.subset X E) (forall ((M $$unsorted)) (= (tptp.least M R X) (and (tptp.member M X) (tptp.greatest_lower_bound M X R E))))))))))) (let ((_let_2 (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.greatest_lower_bound A X R E) (and (tptp.member A X) (tptp.lower_bound A R X) (forall ((M $$unsorted)) (=> (and (tptp.member M E) (tptp.lower_bound M R X)) (tptp.apply R M A)))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X)))))))) (let ((_let_4 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.lower_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X))))))) (let ((_let_5 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 X))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_8 (not _let_7))) (let ((_let_9 (or _let_8 _let_6))) (let ((_let_10 (tptp.lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_11 (= _let_10 _let_5))) (let ((_let_12 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.lower_bound M R E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R M X))))))) (let ((_let_13 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_14 (_let_12))) (let ((_let_15 ((tptp.lower_bound M R E)))) (let ((_let_16 (not _let_10))) (let ((_let_17 (or (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_16 _let_6))) (let ((_let_18 (forall ((M $$unsorted)) (or (not (tptp.member M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.lower_bound M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_19 (not _let_17))) (let ((_let_20 (tptp.lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_21 (and _let_7 _let_20 _let_18))) (let ((_let_22 (not _let_18))) (let ((_let_23 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X))))) (let ((_let_24 (= _let_20 _let_23))) (let ((_let_25 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_15)) :args _let_14)) _let_13 :args (_let_24 false _let_12)))) (let ((_let_26 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X))))) (let ((_let_27 (and _let_7 _let_26))) (let ((_let_28 (tptp.least SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_29 (= _let_28 _let_27))) (let ((_let_30 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R M X)))))))) (let ((_let_31 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_32 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_31 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.least M R E)))) :args (_let_30))) _let_31 :args (_let_29 false _let_30)))) (let ((_let_33 (tptp.greatest_lower_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_34 (and _let_7 _let_33))) (let ((_let_35 (= _let_28 _let_34))) (let ((_let_36 (= _let_33 _let_21))) (let ((_let_37 (or (not (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_35))) (let ((_let_38 (forall ((R $$unsorted) (E $$unsorted) (BOUND_VARIABLE_1071 $$unsorted) (BOUND_VARIABLE_1069 $$unsorted)) (or (not (tptp.order R E)) (not (tptp.subset BOUND_VARIABLE_1069 E)) (= (tptp.least BOUND_VARIABLE_1071 R BOUND_VARIABLE_1069) (and (tptp.member BOUND_VARIABLE_1071 BOUND_VARIABLE_1069) (tptp.greatest_lower_bound BOUND_VARIABLE_1071 BOUND_VARIABLE_1069 R E))))))) (let ((_let_39 (not _let_37))) (let ((_let_40 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_41 (or))) (let ((_let_42 (not _let_38))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_37 2)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_40) :args (_let_42))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_38))) (REFL :args (_let_39)) :args _let_41)) _let_40 :args (_let_39 true _let_38)) :args ((not _let_35) true _let_37)))) (let ((_let_44 (_let_35))) (let ((_let_45 (not _let_29))) (let ((_let_46 (not _let_27))) (let ((_let_47 (_let_29))) (let ((_let_48 (not _let_34))) (let ((_let_49 (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.greatest_lower_bound A X R E) (and (tptp.member A X) (tptp.lower_bound A R X) (forall ((M $$unsorted)) (or (not (tptp.member M E)) (not (tptp.lower_bound M R X)) (tptp.apply R M A)))))))) (let ((_let_50 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_50 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.greatest_lower_bound A X R E)))) :args (_let_49))) _let_50 :args (_let_36 false _let_49)))) (let ((_let_52 (not _let_36))) (let ((_let_53 (not _let_33))) (let ((_let_54 (_let_36))) (let ((_let_55 (ALPHA_EQUIV :args (_let_26 (= X X))))) (let ((_let_56 (not _let_21))) (let ((_let_57 (not _let_24))) (let ((_let_58 (not _let_20))) (let ((_let_59 (_let_24))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_59) :args ((or _let_58 _let_23 _let_57))) _let_25 (REORDERING (CNF_AND_POS :args (_let_21 1)) :args ((or _let_20 _let_56))) (EQUIV_ELIM2 _let_55) (REORDERING (CNF_EQUIV_POS1 :args _let_54) :args ((or _let_53 _let_21 _let_52))) _let_51 (REORDERING (CNF_AND_NEG :args (_let_27)) :args ((or _let_8 _let_27 (not _let_26)))) (REORDERING (CNF_AND_POS :args (_let_34 1)) :args ((or _let_33 _let_48))) (REORDERING (CNF_AND_POS :args (_let_34 0)) :args ((or _let_7 _let_48))) (REORDERING (CNF_EQUIV_POS2 :args _let_47) :args ((or _let_28 _let_46 _let_45))) _let_32 (REORDERING (CNF_EQUIV_NEG1 :args _let_44) :args ((or _let_28 _let_34 _let_35))) _let_43 :args (_let_28 false _let_24 false _let_20 true _let_23 false _let_21 false _let_36 true _let_26 false _let_33 false _let_7 true _let_27 false _let_29 false _let_34 true _let_35)))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args _let_47) :args ((or (not _let_28) _let_27 _let_45))) _let_60 _let_32 :args (_let_27 false _let_28 false _let_29)))) (let ((_let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 0)) :args ((or _let_7 _let_46))) _let_61 :args (_let_7 false _let_27)))) (let ((_let_63 (_let_22))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_63)) :args _let_63)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_22) _let_18))) (REFL :args (_let_19)) :args _let_41)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_NEG :args (_let_21)) :args ((or _let_8 _let_21 _let_58 _let_22))) _let_62 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_54) :args ((or _let_33 _let_56 _let_52))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_34)) (MACRO_RESOLUTION_TRUST (CNF_EQUIV_NEG2 :args _let_44) _let_43 _let_60 :args (_let_48 true _let_35 false _let_28)) _let_62 :args (_let_53 true _let_34 false _let_7)) _let_51 :args (_let_56 true _let_33 false _let_36)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args _let_59) :args ((or _let_20 (not _let_23) _let_57))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 _let_55) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_27 1)) :args ((or _let_26 _let_46))) _let_61 :args (_let_26 false _let_27)) :args (_let_23 false _let_26)) _let_25 :args (_let_20 false _let_23 false _let_24)) :args (_let_22 false _let_7 true _let_21 false _let_20)) :args (_let_19 true _let_18)))) (let ((_let_65 (not _let_9))) (let ((_let_66 (_let_5))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_66) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5) false))))) :args _let_66)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_9)) :args ((or _let_8 _let_6 _let_65))) _let_62 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_17 2)) _let_64 :args ((not _let_6) true _let_17)) :args (_let_65 false _let_7 true _let_6)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_11)) :args ((or _let_16 _let_5 (not _let_11)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_17 1)) (CONG (REFL :args (_let_17)) (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_10))) :args _let_41)) :args ((or _let_10 _let_17))) _let_64 :args (_let_10 true _let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_15)) :args _let_14)) _let_13 :args (_let_11 false _let_12)) :args (_let_5 false _let_10 false _let_11)) :args (false true _let_9 false _let_5)) :args ((forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))) (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.equal_set A B) (and (tptp.subset A B) (tptp.subset B A)))) (forall ((X $$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 $$unsorted)) (= (tptp.member B (tptp.difference E A)) (and (tptp.member B E) (not (tptp.member B A))))) (forall ((X $$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))))) (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.order R E) (and (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y X)) (= X Y)))) (forall ((X $$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 ((R $$unsorted) (E $$unsorted)) (= (tptp.total_order R E) (and (tptp.order R E) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (or (tptp.apply R X Y) (tptp.apply R Y X))))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.upper_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M))))) _let_4 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.greatest M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M)))))) _let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.max M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R M X)) (= M X)))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.min M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R X M)) (= M X)))))) (forall ((A $$unsorted) (X $$unsorted) (R $$unsorted) (E $$unsorted)) (= (tptp.least_upper_bound A X R E) (and (tptp.member A X) (tptp.upper_bound A R X) (forall ((M $$unsorted)) (=> (and (tptp.member M E) (tptp.upper_bound M R X)) (tptp.apply R A M)))))) _let_2 _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.20/0.61  )
% 0.20/0.61  % SZS output end Proof for SET802+4
% 0.20/0.61  % cvc5---1.0.5 exiting
% 0.20/0.62  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------