%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n013.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 0.22s 0.52s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET804+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat Aug 26 12:15:17 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.52  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.eAA4ZU9ewj/cvc5---1.0.5_12297.p...
% 0.22/0.52  ------- get file name : TPTP file name is SET804+4
% 0.22/0.52  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_12297.smt2...
% 0.22/0.52  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.52  % SZS status Theorem for SET804+4
% 0.22/0.52  % SZS output start Proof for SET804+4
% 0.22/0.52  (
% 0.22/0.52  (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted)) (=> (tptp.order R E) (forall ((M1 $$unsorted) (M2 $$unsorted)) (=> (and (tptp.min M1 R E) (tptp.min M2 R E) (not (= M1 M2))) (not (exists ((M $$unsorted)) (tptp.least M R E)))))))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.min M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R X M)) (= M X)))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.least M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X)))))))) (let ((_let_4 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_5 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_6 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6))) (let ((_let_7 (tptp.min SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_8 (not _let_7))) (let ((_let_9 (tptp.min SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_10 (not _let_9))) (let ((_let_11 (tptp.least SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_12 (not _let_11))) (let ((_let_13 (not (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)))) (let ((_let_14 (or _let_13 _let_12 _let_10 _let_8 _let_4))) (let ((_let_15 (not _let_4))) (let ((_let_16 (forall ((R $$unsorted) (E $$unsorted) (BOUND_VARIABLE_929 $$unsorted) (BOUND_VARIABLE_927 $$unsorted) (BOUND_VARIABLE_923 $$unsorted)) (or (not (tptp.order R E)) (not (tptp.least BOUND_VARIABLE_923 R E)) (not (tptp.min BOUND_VARIABLE_927 R E)) (not (tptp.min BOUND_VARIABLE_929 R E)) (= BOUND_VARIABLE_927 BOUND_VARIABLE_929))))) (let ((_let_17 (not _let_14))) (let ((_let_18 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_19 (or))) (let ((_let_20 (not _let_16))) (let ((_let_21 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (SCOPE (SKOLEMIZE _let_18) :args (_let_20)) (REWRITE :args ((=> _let_20 (not (or _let_13 _let_12 _let_10 _let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)))))))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_20) _let_16))) (REFL :args (_let_17)) :args _let_19)) _let_18 :args (_let_17 true _let_16)))) (let ((_let_22 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_23 (not _let_22))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_23 _let_5))) (let ((_let_27 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (= X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_28 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_29 (and _let_28 _let_27))) (let ((_let_30 (= _let_7 _let_29))) (let ((_let_31 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.min M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (not (tptp.apply R X M)) (= M X)))))))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (_let_31))) (let ((_let_34 ((tptp.min M R E)))) (let ((_let_35 (REFL :args (_let_14)))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_30)) :args ((or _let_8 _let_29 (not _let_30)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 3)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_8) _let_7))) :args _let_19)) :args ((or _let_7 _let_14))) _let_21 :args (_let_7 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33))) _let_32 :args (_let_30 false _let_31)) :args (_let_29 false _let_7 false _let_30)))) (let ((_let_37 (not _let_29))) (let ((_let_38 (_let_27))) (let ((_let_39 (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false)))))) (let ((_let_40 (not _let_28))) (let ((_let_41 (or _let_40 _let_22))) (let ((_let_42 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 X))))) (let ((_let_43 (and _let_24 _let_42))) (let ((_let_44 (= _let_11 _let_43))) (let ((_let_45 (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_46 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_47 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_44)) :args ((or _let_12 _let_43 (not _let_44)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 1)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_12) _let_11))) :args _let_19)) :args ((or _let_11 _let_14))) _let_21 :args (_let_11 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_46 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.least M R E)))) :args (_let_45))) _let_46 :args (_let_44 false _let_45)) :args (_let_43 false _let_11 false _let_44)))) (let ((_let_48 (not _let_43))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_43 1)) :args ((or _let_42 _let_48))) _let_47 :args (_let_42 false _let_43)))) (let ((_let_50 (_let_42))) (let ((_let_51 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) (let ((_let_52 (ASSUME :args _let_50))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_43 0)) :args ((or _let_24 _let_48))) _let_47 :args (_let_24 false _let_43)))) (let ((_let_54 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_6 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_25 _let_55 _let_6))) (let ((_let_57 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)) (= X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_58 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_59 (and _let_58 _let_57))) (let ((_let_60 (= _let_9 _let_59))) (let ((_let_61 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_60)) :args ((or _let_10 _let_59 (not _let_60)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_14 2)) (CONG _let_35 (MACRO_SR_PRED_INTRO :args ((= (not _let_10) _let_9))) :args _let_19)) :args ((or _let_9 _let_14))) _let_21 :args (_let_9 true _let_14)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_32 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_34)) :args _let_33))) _let_32 :args (_let_60 false _let_31)) :args (_let_59 false _let_9 false _let_60)))) (let ((_let_62 (not _let_59))) (let ((_let_63 (_let_57))) (let ((_let_64 (not _let_58))) (let ((_let_65 (or _let_64 _let_54))) (let ((_let_66 (ASSUME :args (_let_6)))) (let ((_let_67 (ASSUME :args (_let_5)))) (let ((_let_68 (ASSUME :args (_let_15)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_67 _let_66 _let_68) :args (_let_15 _let_5 _let_6)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_68)) (TRUE_INTRO (TRANS (SYMM (SYMM _let_67)) (SYMM _let_66))))) :args (_let_5 _let_6 _let_15)) :args ((not (and _let_15 _let_5 _let_6)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_4))) (REFL :args ((not _let_5))) (REFL :args ((not _let_6))) :args _let_19)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_25 _let_55 _let_6 (not _let_56)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_65)) :args ((or _let_64 _let_54 (not _let_65)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 0)) :args ((or _let_58 _let_62))) _let_61 :args (_let_58 false _let_59)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_65 false _let_42)) :args (_let_54 false _let_58 false _let_65)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_63) :args _let_39) :args _let_63))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_59 1)) :args ((or _let_57 _let_62))) _let_61 :args (_let_57 false _let_59)) :args (_let_56 false _let_57)) :args (_let_6 false _let_24 false _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_26)) :args ((or _let_25 _let_23 _let_5 (not _let_26)))) _let_53 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_41)) :args ((or _let_40 _let_22 (not _let_41)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 0)) :args ((or _let_28 _let_37))) _let_36 :args (_let_28 false _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_52 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_51)) :args _let_50)) _let_49 :args (_let_41 false _let_42)) :args (_let_22 false _let_28 false _let_41)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_38) :args _let_39) :args _let_38))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_29 1)) :args ((or _let_27 _let_37))) _let_36 :args (_let_27 false _let_29)) :args (_let_26 false _let_27)) :args (_let_5 false _let_24 false _let_22 false _let_26)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_14 4)) _let_21 :args (_let_15 true _let_14)) :args (false false _let_6 false _let_5 true _let_4)) :args ((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 $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M))))) (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.lower_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R M X))))) (forall ((R $$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 $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R M X)) (= M X)))))) _let_2 (forall ((A $$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)))))) (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_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.52  )
% 0.22/0.52  % SZS output end Proof for SET804+4
% 0.22/0.52  % cvc5---1.0.5 exiting
% 0.22/0.52  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------