%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SET795+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n008.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 14:40:22 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
% 0.00/0.13  % Problem    : SET795+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n008.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat Aug 26 10:57:17 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.3Ayw5pjfds/cvc5---1.0.5_7241.p...
% 0.21/0.55  ------- get file name : TPTP file name is SET795+4
% 0.21/0.55  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_7241.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 SET795+4
% 0.21/0.55  % SZS output start Proof for SET795+4
% 0.21/0.55  (
% 0.21/0.55  (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (B $$unsorted)) (=> (and (tptp.order R E) (tptp.member A E) (tptp.member B E) (tptp.apply R A B)) (tptp.least_upper_bound B (tptp.unordered_pair A B) R E)))))) (let ((_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 $$unsorted)) (=> (and (tptp.member M E) (tptp.upper_bound M R X)) (tptp.apply R A M)))))))) (let ((_let_3 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.upper_bound M R E) (forall ((X $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M))))))) (let ((_let_4 (forall ((R $$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 $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_5 (forall ((X $$unsorted) (A $$unsorted) (B $$unsorted)) (= (tptp.member X (tptp.unordered_pair A B)) (or (= X A) (= X B)))))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_7 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_8 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_9 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_10 (tptp.least_upper_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (not _let_6))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_13 _let_11 _let_10))) (let ((_let_17 (forall ((R $$unsorted) (E $$unsorted) (A $$unsorted) (B $$unsorted)) (or (not (tptp.order R E)) (not (tptp.member A E)) (not (tptp.member B E)) (not (tptp.apply R A B)) (tptp.least_upper_bound B (tptp.unordered_pair A B) R E))))) (let ((_let_18 (not _let_16))) (let ((_let_19 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_20 (or))) (let ((_let_21 (not _let_17))) (let ((_let_22 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_19) :args (_let_21))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_21) _let_17))) (REFL :args (_let_18)) :args _let_20)) _let_19 :args (_let_18 true _let_17)))) (let ((_let_23 (REFL :args (_let_16)))) (let ((_let_24 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 _let_9))) (let ((_let_25 (not _let_24))) (let ((_let_26 (or _let_25 _let_7))) (let ((_let_27 (not _let_7))) (let ((_let_28 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))))) (let ((_let_29 (not _let_26))) (let ((_let_30 (tptp.upper_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_31 (= _let_30 _let_28))) (let ((_let_32 (not _let_28))) (let ((_let_33 (forall ((R $$unsorted) (E $$unsorted) (M $$unsorted)) (= (tptp.upper_bound M R E) (forall ((X $$unsorted)) (or (not (tptp.member X E)) (tptp.apply R X M))))))) (let ((_let_34 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_35 (_let_33))) (let ((_let_36 ((tptp.upper_bound M R E)))) (let ((_let_37 (forall ((M $$unsorted)) (or (not (tptp.member M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.upper_bound M SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 M))))) (let ((_let_38 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9))) (let ((_let_39 (and _let_38 _let_30 _let_37))) (let ((_let_40 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))) (let ((_let_41 (tptp.upper_bound SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or (not (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) _let_42 _let_40))) (let ((_let_44 (forall ((X $$unsorted)) (or (not (tptp.member X (tptp.unordered_pair SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8))))) (let ((_let_45 (= _let_41 _let_44))) (let ((_let_46 (not _let_38))) (let ((_let_47 (or _let_46 _let_40))) (let ((_let_48 (_let_5))) (let ((_let_49 (ASSUME :args _let_48))) (let ((_let_50 ((tptp.member X (tptp.unordered_pair A B))))) (let ((_let_51 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48))) _let_49 :args (_let_38 false _let_5)))) (let ((_let_52 (_let_44))) (let ((_let_53 (not _let_37))) (let ((_let_54 (_let_53))) (let ((_let_55 (= _let_10 _let_39))) (let ((_let_56 (not _let_39))) (let ((_let_57 (forall ((A $$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)) (or (not (tptp.member M E)) (not (tptp.upper_bound M R X)) (tptp.apply R A M)))))))) (let ((_let_58 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_59 (_let_32))) (let ((_let_60 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_59)) :args _let_59)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_32) _let_28))) (REFL :args (_let_29)) :args _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_31)) :args ((or _let_30 _let_32 (not _let_31)))) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_39)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_55)) :args ((or _let_10 _let_56 (not _let_55)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_16 4)) _let_22 :args ((not _let_10) true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_58 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.least_upper_bound A X R E)))) :args (_let_57))) _let_58 :args (_let_55 false _let_57)) :args (_let_56 true _let_10 false _let_55)) _let_51 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_54)) :args _let_54)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_37))) (REFL :args ((not _let_43))) :args _let_20)) (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 _let_9) false))))) :args _let_52)) (REORDERING (CNF_OR_POS :args (_let_47)) :args ((or _let_46 _let_40 (not _let_47)))) _let_51 (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_42 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_8 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_45 false _let_33)) (CNF_OR_NEG :args (_let_43 2)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_43 1)) (CONG (REFL :args (_let_43)) (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_20)) :args ((or _let_41 _let_43))) :args (_let_43 true _let_47 false _let_38 false _let_44 false _let_45 true _let_40 false _let_41)) :args (_let_37 false _let_43)) :args ((not _let_30) true _let_39 false _let_38 false _let_37)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_34 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 _let_9 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_36)) :args _let_35)) _let_34 :args (_let_31 false _let_33)) :args (_let_32 true _let_30 false _let_31)) :args (_let_29 true _let_28)))) (let ((_let_61 (CNF_OR_NEG :args (_let_26 1)))) (let ((_let_62 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11))) (let ((_let_63 (or _let_8 _let_62))) (let ((_let_64 (= _let_24 _let_63))) (let ((_let_65 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5))) (let ((_let_66 (or _let_13 _let_65))) (let ((_let_67 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X X))))) (let ((_let_68 (and _let_67 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X)) (= X Y))) (forall ((X $$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_69 (= _let_14 _let_68))) (let ((_let_70 (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_71 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_72 (_let_67))) (let ((_let_73 (MACRO_SR_PRED_INTRO :args ((= (not _let_27) _let_7))))) (let ((_let_74 (ASSUME :args (_let_65)))) (let ((_let_75 (APPLY_UF tptp.apply))) (let ((_let_76 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5)))) (let ((_let_77 (ASSUME :args (_let_62)))) (let ((_let_78 (REFL :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2)))) (let ((_let_79 (ASSUME :args (_let_27)))) (let ((_let_80 (SYMM (FALSE_INTRO _let_79)))) (let ((_let_81 (ASSUME :args (_let_6)))) (let ((_let_82 (ASSUME :args (_let_8)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_81 _let_82 _let_79) :args (_let_6 _let_27 _let_8)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_80 (CONG _let_78 (SYMM _let_82) _let_76 :args _let_75) (TRUE_INTRO _let_81))) :args (_let_6 _let_8 _let_27)) :args ((not (and _let_6 _let_27 _let_8)) SB_LITERAL))) (CONG (REFL :args (_let_11)) _let_73 (REFL :args ((not _let_8))) :args _let_20)) (MACRO_RESOLUTION_TRUST (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_74 _let_77 _let_79) :args (_let_65 _let_27 _let_62)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS _let_80 (CONG _let_78 (SYMM _let_77) _let_76 :args _let_75) (TRUE_INTRO _let_74))) :args (_let_65 _let_62 _let_27)) :args ((not (and _let_65 _let_27 _let_62)) SB_LITERAL))) (CONG (REFL :args ((not _let_65))) _let_73 (REFL :args ((not _let_62))) :args _let_20)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_66)) :args ((or _let_13 _let_65 (not _let_66)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 2)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_13) _let_12))) :args _let_20)) :args ((or _let_12 _let_16))) _let_22 :args (_let_12 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_72) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_72)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_68 0)) :args ((or _let_67 (not _let_68)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_69)) :args ((or _let_15 _let_68 (not _let_69)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 0)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_15) _let_14))) :args _let_20)) :args ((or _let_14 _let_16))) _let_22 :args (_let_14 true _let_16)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_71 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.order R E)))) :args (_let_70))) _let_71 :args (_let_69 false _let_70)) :args (_let_68 false _let_14 false _let_69)) :args (_let_67 false _let_68)) :args (_let_66 false _let_67)) :args (_let_65 false _let_12 false _let_66)) (REORDERING (CNF_OR_POS :args (_let_63)) :args ((or _let_8 _let_62 (not _let_63)))) (REORDERING (CNF_EQUIV_POS1 :args (_let_64)) :args ((or _let_25 _let_63 (not _let_64)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_49 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_5 QUANTIFIERS_INST_E_MATCHING _let_50)) :args _let_48))) _let_49 :args (_let_64 false _let_5)) _let_61 (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_26 0)) (CONG (REFL :args (_let_26)) (MACRO_SR_PRED_INTRO :args ((= (not _let_25) _let_24))) :args _let_20)) :args ((or _let_24 _let_26))) :args ((or _let_26 _let_8) false _let_65 false _let_62 false _let_63 false _let_64 true _let_7 false _let_24)) _let_60 :args (_let_8 true _let_26)) (MACRO_RESOLUTION_TRUST _let_61 _let_60 :args (_let_27 true _let_26)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_16 3)) (CONG _let_23 (MACRO_SR_PRED_INTRO :args ((= (not _let_11) _let_6))) :args _let_20)) :args ((or _let_6 _let_16))) _let_22 :args (_let_6 true _let_16)) :args (false false _let_8 true _let_7 false _let_6)) :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 $$unsorted)) (= (tptp.member X (tptp.singleton A)) (= X A))) _let_5 (forall ((X $$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 $$unsorted)) (=> (tptp.member Y A) (tptp.member X Y))))) _let_4 (forall ((R $$unsorted) (E $$unsorted)) (= (tptp.total_order R E) (and (tptp.order R E) (forall ((X $$unsorted) (Y $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E)) (or (tptp.apply R X Y) (tptp.apply R Y X))))))) _let_3 (forall ((R $$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 $$unsorted)) (=> (tptp.member X E) (tptp.apply R X M)))))) (forall ((R $$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 $$unsorted)) (=> (and (tptp.member X E) (tptp.apply R X M)) (= M X)))))) _let_2 (forall ((A $$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_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.56  )
% 0.21/0.56  % SZS output end Proof for SET795+4
% 0.21/0.56  % cvc5---1.0.5 exiting
% 0.21/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------