%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n024.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 14:40:21 EDT 2023

% Result   : Theorem 0.22s 0.55s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET793+4 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sat Aug 26 10:13:24 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.22/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.55  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.VDmrNWHKJM/cvc5---1.0.5_9240.p...
% 0.22/0.55  ------- get file name : TPTP file name is SET793+4
% 0.22/0.55  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_9240.smt2...
% 0.22/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.55  % SZS status Theorem for SET793+4
% 0.22/0.55  % SZS output start Proof for SET793+4
% 0.22/0.55  (
% 0.22/0.55  (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (=> (and (tptp.total_order R E) (tptp.max M R E)) (tptp.greatest M R E)))))) (let ((_let_2 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.max M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R M X)) (= M X)))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.greatest M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M)))))))) (let ((_let_4 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.total_order R E) (and (tptp.order R E) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (or (tptp.apply R X Y) (tptp.apply R Y X))))))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_7 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7))) (let ((_let_8 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_9 (not _let_8))) (let ((_let_10 (or _let_9 _let_5))) (let ((_let_11 (not _let_5))) (let ((_let_12 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_13 (not _let_10))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (and _let_14 _let_12))) (let ((_let_16 (not _let_12))) (let ((_let_17 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 X)) (= X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))))) (let ((_let_18 (and _let_14 _let_17))) (let ((_let_19 (tptp.max SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_20 (= _let_19 _let_18))) (let ((_let_21 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.max M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (not (tptp.apply R M X)) (= M X)))))))) (let ((_let_22 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_23 (tptp.greatest SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_24 (not _let_19))) (let ((_let_25 (tptp.total_order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_26 (not _let_25))) (let ((_let_27 (or _let_26 _let_24 _let_23))) (let ((_let_28 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (or (not (tptp.total_order R E)) (not (tptp.max M R E)) (tptp.greatest M R E))))) (let ((_let_29 (not _let_27))) (let ((_let_30 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_31 (or))) (let ((_let_32 (not _let_28))) (let ((_let_33 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_30) :args (_let_32))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_31)) _let_30 :args (_let_29 true _let_28)))) (let ((_let_34 (REFL :args (_let_27)))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_20)) :args ((or _let_24 _let_18 (not _let_20)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 1)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_19))) :args _let_31)) :args ((or _let_19 _let_27))) _let_33 :args (_let_19 true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_22 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.max M R E)))) :args (_let_21)))) _let_22 :args (_let_20 false _let_21)) :args (_let_18 false _let_19 false _let_20)))) (let ((_let_36 (not _let_18))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 0)) :args ((or _let_14 _let_36))) _let_35 :args (_let_14 false _let_18)))) (let ((_let_38 (= _let_23 _let_15))) (let ((_let_39 (not _let_15))) (let ((_let_40 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.greatest M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X M)))))))) (let ((_let_41 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_42 (_let_16))) (let ((_let_43 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_42)) :args _let_42)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_16) _let_12))) (REFL :args (_let_13)) :args _let_31)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_15)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_38)) :args ((or _let_23 _let_39 (not _let_38)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_27 2)) _let_33 :args ((not _let_23) true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_41 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.greatest M R E)))) :args (_let_40))) _let_41 :args (_let_38 false _let_40)) :args (_let_39 true _let_23 false _let_38)) _let_37 :args (_let_16 true _let_15 false _let_14)) :args (_let_13 true _let_12)))) (let ((_let_44 (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_10 1)) _let_43 :args (_let_11 true _let_10)))) (let ((_let_45 (not _let_14))) (let ((_let_46 (or _let_45 _let_9 _let_6 _let_5))) (let ((_let_47 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X))))) (let ((_let_48 (and (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) _let_47))) (let ((_let_49 (= _let_25 _let_48))) (let ((_let_50 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.total_order R E) (and (tptp.order R E) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (tptp.apply R X Y) (tptp.apply R Y X)))))))) (let ((_let_51 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_52 (_let_47))) (let ((_let_53 (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_10 0)) (CONG (REFL :args (_let_10)) (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_31)) :args ((or _let_8 _let_10))) _let_43 :args (_let_8 true _let_10)))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_46)) :args ((or _let_45 _let_9 _let_5 _let_6 (not _let_46)))) _let_37 _let_53 _let_44 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_52) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X) true))))) :args _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_48 1)) :args ((or _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_49)) :args ((or _let_26 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_27 0)) (CONG _let_34 (MACRO_SR_PRED_INTRO :args ((= (not _let_26) _let_25))) :args _let_31)) :args ((or _let_25 _let_27))) _let_33 :args (_let_25 true _let_27)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.total_order R E)))) :args (_let_50))) _let_51 :args (_let_49 false _let_50)) :args (_let_48 false _let_25 false _let_49)) :args (_let_47 false _let_48)) :args (_let_46 false _let_47)) :args (_let_6 false _let_14 false _let_8 true _let_5 false _let_46)))) (let ((_let_55 (not _let_6))) (let ((_let_56 (or _let_9 _let_55 _let_7))) (let ((_let_57 (_let_17))) (let ((_let_58 (ASSUME :args (_let_11)))) (let ((_let_59 (ASSUME :args (_let_7)))) (let ((_let_60 (ASSUME :args (_let_6)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_58 _let_59 _let_60) :args (_let_11 _let_6 _let_7)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (TRUE_INTRO _let_60)) (CONG (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)) _let_59 (SYMM _let_59) :args (APPLY_UF tptp.apply)) (FALSE_INTRO _let_58))) :args (_let_11 _let_7 _let_6)) :args ((not (and _let_11 _let_6 _let_7)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_5))) (REFL :args (_let_55)) (REFL :args ((not _let_7))) :args _let_31)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_56)) :args ((or _let_9 _let_55 _let_7 (not _let_56)))) _let_53 _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_57) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_18 1)) :args ((or _let_17 _let_36))) _let_35 :args (_let_17 false _let_18)) :args (_let_56 false _let_17)) :args (_let_7 false _let_8 false _let_6 false _let_56)) _let_54 _let_44 :args (false false _let_7 false _let_6 true _let_5)) :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))))))) _let_4 (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))))) _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_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)))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.22/0.56  )
% 0.22/0.56  % SZS output end Proof for SET793+4
% 0.22/0.56  % cvc5---1.0.5 exiting
% 0.22/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------