%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n007.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 14:40:20 EDT 2023

% Result   : Theorem 0.21s 0.55s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET789+4 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n007.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 15:14:41 EDT 2023
% 0.14/0.36  % CPUTime    : 
% 0.21/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.HSJjk6FLEB/cvc5---1.0.5_7143.p...
% 0.21/0.55  ------- get file name : TPTP file name is SET789+4
% 0.21/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7143.smt2...
% 0.21/0.55  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.55  % SZS status Theorem for SET789+4
% 0.21/0.55  % SZS output start Proof for SET789+4
% 0.21/0.55  (
% 0.21/0.55  (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (=> (and (tptp.order R E) (tptp.greatest M R E)) (forall ((X $$unsorted)) (=> (tptp.greatest X R E) (= M X)))))))) (let ((_let_2 (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_3 (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 ((_let_4 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X)) (= X Y))))) (let ((_let_5 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11 _let_9 _let_7 _let_5))) (let ((_let_15 (and (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X X))) _let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Z)))))) (let ((_let_16 (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_17 (= _let_16 _let_15))) (let ((_let_18 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.order R E) (and (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X X))) (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y X)) (= X Y))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X E)) (not (tptp.member Y E)) (not (tptp.member Z E)) (not (tptp.apply R X Y)) (not (tptp.apply R Y Z)) (tptp.apply R X Z)))))))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (tptp.greatest SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (not _let_20))) (let ((_let_22 (tptp.greatest SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_23 (not _let_22))) (let ((_let_24 (not _let_16))) (let ((_let_25 (or _let_24 _let_23 _let_21 _let_5))) (let ((_let_26 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted) (BOUND_VARIABLE_909 $$unsorted)) (or (not (tptp.order R E)) (not (tptp.greatest M R E)) (not (tptp.greatest BOUND_VARIABLE_909 R E)) (= M BOUND_VARIABLE_909))))) (let ((_let_27 (not _let_25))) (let ((_let_28 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_29 (or))) (let ((_let_30 (not _let_26))) (let ((_let_31 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_28) :args (_let_30))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_30) _let_26))) (REFL :args (_let_27)) :args _let_29)) _let_28 :args (_let_27 true _let_26)))) (let ((_let_32 (REFL :args (_let_25)))) (let ((_let_33 (not _let_14))) (let ((_let_34 (or _let_13 _let_8))) (let ((_let_35 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_36 (and _let_10 _let_35))) (let ((_let_37 (= _let_20 _let_36))) (let ((_let_38 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.greatest M R E) (and (tptp.member M E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X M)))))))) (let ((_let_39 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_40 (_let_38))) (let ((_let_41 ((tptp.greatest M R E)))) (let ((_let_42 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_37)) :args ((or _let_21 _let_36 (not _let_37)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 2)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_20))) :args _let_29)) :args ((or _let_20 _let_25))) _let_31 :args (_let_20 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_37 false _let_38)) :args (_let_36 false _let_20 false _let_37)))) (let ((_let_43 (not _let_36))) (let ((_let_44 (_let_35))) (let ((_let_45 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) (let ((_let_46 (forall ((X $$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_47 (and _let_12 _let_46))) (let ((_let_48 (= _let_22 _let_47))) (let ((_let_49 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_48)) :args ((or _let_23 _let_47 (not _let_48)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 1)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_29)) :args ((or _let_22 _let_25))) _let_31 :args (_let_22 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_39 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_41)) :args _let_40)) _let_39 :args (_let_48 false _let_38)) :args (_let_47 false _let_22 false _let_48)))) (let ((_let_50 (not _let_47))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 0)) :args ((or _let_12 _let_50))) _let_49 :args (_let_12 false _let_47)))) (let ((_let_52 (or _let_11 _let_6))) (let ((_let_53 (_let_46))) (let ((_let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 0)) :args ((or _let_10 _let_43))) _let_42 :args (_let_10 false _let_36)))) (let ((_let_55 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_55) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y) false))))) :args _let_55)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_5 _let_13 _let_11 _let_7 _let_9 _let_33))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_25 3)) _let_31 :args ((not _let_5) true _let_25)) _let_51 _let_54 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_52)) :args ((or _let_11 _let_6 (not _let_52)))) _let_54 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_53) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_53)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_47 1)) :args ((or _let_46 _let_50))) _let_49 :args (_let_46 false _let_47)) :args (_let_52 false _let_46)) :args (_let_6 false _let_10 false _let_52)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_34)) :args ((or _let_13 _let_8 (not _let_34)))) _let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_44) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_45)) :args _let_44)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_36 1)) :args ((or _let_35 _let_43))) _let_42 :args (_let_35 false _let_36)) :args (_let_34 false _let_35)) :args (_let_8 false _let_12 false _let_34)) :args (_let_33 true _let_5 false _let_12 false _let_10 false _let_6 false _let_8)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_15 1)) :args ((or _let_4 (not _let_15)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_17)) :args ((or _let_24 _let_15 (not _let_17)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_25 0)) (CONG _let_32 (MACRO_SR_PRED_INTRO :args ((= (not _let_24) _let_16))) :args _let_29)) :args ((or _let_16 _let_25))) _let_31 :args (_let_16 true _let_25)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_19 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.order R E)))) :args (_let_18))) _let_19 :args (_let_17 false _let_18)) :args (_let_15 false _let_16 false _let_17)) :args (_let_4 false _let_15)) :args (false true _let_14 false _let_4)) :args (_let_3 (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))))) _let_2 (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)))))) (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 $$unsorted)) (=> (and (tptp.member M E) (tptp.upper_bound M R X)) (tptp.apply R A M)))))) (forall ((A $$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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56  )
% 0.21/0.56  % SZS output end Proof for SET789+4
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------