TSTP Solution File: SET805+4 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : SET805+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n017.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 14:40:24 EDT 2023
% Result : Theorem 0.21s 0.60s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET805+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : do_cvc5 %s %d
% 0.15/0.35 % Computer : n017.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 09:12:26 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.49 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.60 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.5fHfzHZaMS/cvc5---1.0.5_3407.p...
% 0.21/0.60 ------- get file name : TPTP file name is SET805+4
% 0.21/0.60 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_3407.smt2...
% 0.21/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.60 % SZS status Theorem for SET805+4
% 0.21/0.60 % SZS output start Proof for SET805+4
% 0.21/0.60 (
% 0.21/0.60 (let ((_let_1 (not (forall ((R $$unsorted) (E $$unsorted)) (=> (tptp.order R E) (forall ((X $$unsorted)) (=> (tptp.subset X E) (tptp.order R X)))))))) (let ((_let_2 (forall ((R $$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 $$unsorted)) (=> (and (tptp.member X E) (tptp.member Y E) (tptp.member Z E)) (=> (and (tptp.apply R X Y) (tptp.apply R Y Z)) (tptp.apply R X Z))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (=> (tptp.member X A) (tptp.member X B))))))) (let ((_let_4 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y Z)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Z))))) (let ((_let_5 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_6 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13))) (let ((_let_7 (not _let_6))) (let ((_let_8 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12))) (let ((_let_9 (not _let_8))) (let ((_let_10 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_13 (not _let_12))) (let ((_let_14 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_15 (not _let_14))) (let ((_let_16 (or _let_15 _let_13 _let_11 _let_9 _let_7 _let_5))) (let ((_let_17 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X)) (= X Y))))) (let ((_let_18 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X X))))) (let ((_let_19 (and _let_18 _let_17 _let_4))) (let ((_let_20 (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_21 (= _let_20 _let_19))) (let ((_let_22 (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_23 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_24 (_let_22))) (let ((_let_25 ((tptp.order R E)))) (let ((_let_26 (tptp.order SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_27 (tptp.subset SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_28 (not _let_27))) (let ((_let_29 (not _let_20))) (let ((_let_30 (or _let_29 _let_28 _let_26))) (let ((_let_31 (forall ((R $$unsorted) (E $$unsorted) (BOUND_VARIABLE_1052 $$unsorted)) (or (not (tptp.order R E)) (not (tptp.subset BOUND_VARIABLE_1052 E)) (tptp.order R BOUND_VARIABLE_1052))))) (let ((_let_32 (not _let_30))) (let ((_let_33 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_34 (or))) (let ((_let_35 (not _let_31))) (let ((_let_36 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_33) :args (_let_35))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_35) _let_31))) (REFL :args (_let_32)) :args _let_34)) _let_33 :args (_let_32 true _let_31)))) (let ((_let_37 (REFL :args (_let_30)))) (let ((_let_38 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_21)) :args ((or _let_29 _let_19 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 0)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_29) _let_20))) :args _let_34)) :args ((or _let_20 _let_30))) _let_36 :args (_let_20 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_21 false _let_22)) :args (_let_19 false _let_20 false _let_21)))) (let ((_let_39 (not _let_19))) (let ((_let_40 (not _let_16))) (let ((_let_41 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_10))) (let ((_let_44 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))))) (let ((_let_45 (= _let_27 _let_44))) (let ((_let_46 (forall ((A $$unsorted) (B $$unsorted)) (= (tptp.subset A B) (forall ((X $$unsorted)) (or (not (tptp.member X A)) (tptp.member X B))))))) (let ((_let_47 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_48 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_45)) :args ((or _let_28 _let_44 (not _let_45)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_30 1)) (CONG _let_37 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_34)) :args ((or _let_27 _let_30))) _let_36 :args (_let_27 true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_47 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.subset A B)))) :args (_let_46))) _let_47 :args (_let_45 false _let_46)) :args (_let_44 false _let_27 false _let_45)))) (let ((_let_49 (_let_44))) (let ((_let_50 ((not (= (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4) false))))) (let ((_let_51 (ASSUME :args _let_49))) (let ((_let_52 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_53 (not _let_52))) (let ((_let_54 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_55 (not _let_54))) (let ((_let_56 (or _let_55 _let_53 _let_42 _let_9 _let_7 _let_5))) (let ((_let_57 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Z SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (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_58 (not _let_56))) (let ((_let_59 (forall ((X $$unsorted) (Y $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y)) (not (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 Y X)) (= X Y))))) (let ((_let_60 (forall ((X $$unsorted)) (or (not (tptp.member X SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4)) (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X X))))) (let ((_let_61 (and _let_60 _let_59 _let_57))) (let ((_let_62 (not _let_57))) (let ((_let_63 (= SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_64 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14))) (let ((_let_65 (not _let_64))) (let ((_let_66 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15))) (let ((_let_67 (not _let_66))) (let ((_let_68 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_69 (not _let_68))) (let ((_let_70 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_71 (not _let_70))) (let ((_let_72 (or _let_71 _let_69 _let_67 _let_65 _let_63))) (let ((_let_73 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_74 (or _let_71 _let_73))) (let ((_let_75 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_76 (or _let_69 _let_75))) (let ((_let_77 (not _let_75))) (let ((_let_78 (not _let_73))) (let ((_let_79 (or _let_78 _let_77 _let_67 _let_65 _let_63))) (let ((_let_80 (REFL :args (_let_72)))) (let ((_let_81 (_let_17))) (let ((_let_82 (not _let_59))) (let ((_let_83 (_let_82))) (let ((_let_84 (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16))) (let ((_let_85 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_86 (not _let_85))) (let ((_let_87 (or _let_86 _let_84))) (let ((_let_88 (tptp.member SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3))) (let ((_let_89 (or _let_86 _let_88))) (let ((_let_90 (not _let_88))) (let ((_let_91 (or _let_90 _let_84))) (let ((_let_92 (_let_18))) (let ((_let_93 (not _let_60))) (let ((_let_94 (_let_93))) (let ((_let_95 (= _let_26 _let_61))) (let ((_let_96 (not _let_61))) (let ((_let_97 (_let_62))) (let ((_let_98 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_97)) :args _let_97)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_62) _let_57))) (REFL :args (_let_58)) :args _let_34)) (MACRO_RESOLUTION_TRUST (CNF_AND_NEG :args (_let_61)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_95)) :args ((or _let_26 _let_96 (not _let_95)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_30 2)) _let_36 :args ((not _let_26) true _let_30)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_23 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_25)) :args _let_24)) _let_23 :args (_let_95 false _let_22)) :args (_let_96 true _let_26 false _let_95)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_94)) :args _let_94)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_93) _let_60))) (REFL :args ((not _let_87))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_91)) :args ((or _let_84 _let_90 (not _let_91)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_92) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X X) true))))) :args _let_92)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 0)) :args ((or _let_18 _let_39))) _let_38 :args (_let_18 false _let_19)) :args (_let_91 false _let_18)) (REORDERING (CNF_OR_POS :args (_let_89)) :args ((or _let_86 _let_88 (not _let_89)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_16 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_89 false _let_44)) (CNF_OR_NEG :args (_let_87 1)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_87 0)) (CONG (REFL :args (_let_87)) (MACRO_SR_PRED_INTRO :args ((= (not _let_86) _let_85))) :args _let_34)) :args ((or _let_85 _let_87))) :args (_let_87 false _let_91 false _let_88 false _let_89 true _let_84 false _let_85)) :args (_let_60 false _let_87)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME :args _let_83)) :args _let_83)) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_82) _let_59))) (REFL :args ((not _let_72))) :args _let_34)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_79)) :args ((or _let_67 _let_65 _let_63 _let_78 _let_77 (not _let_79)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_81) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Y) false))))) :args _let_81)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 1)) :args ((or _let_17 _let_39))) _let_38 :args (_let_17 false _let_19)) :args (_let_79 false _let_17)) (REORDERING (CNF_OR_POS :args (_let_76)) :args ((or _let_69 _let_75 (not _let_76)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_15 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_76 false _let_44)) (REORDERING (CNF_OR_POS :args (_let_74)) :args ((or _let_71 _let_73 (not _let_74)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_14 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_74 false _let_44)) (CNF_OR_NEG :args (_let_72 4)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 3)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_65) _let_64))) :args _let_34)) :args ((or _let_64 _let_72))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 2)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_67) _let_66))) :args _let_34)) :args ((or _let_66 _let_72))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 1)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_69) _let_68))) :args _let_34)) :args ((or _let_68 _let_72))) (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_72 0)) (CONG _let_80 (MACRO_SR_PRED_INTRO :args ((= (not _let_71) _let_70))) :args _let_34)) :args ((or _let_70 _let_72))) :args (_let_72 false _let_79 false _let_75 false _let_76 false _let_73 false _let_74 true _let_63 false _let_64 false _let_66 false _let_68 false _let_70)) :args (_let_59 false _let_72)) :args (_let_62 true _let_61 false _let_60 false _let_59)) :args (_let_58 true _let_57)))) (let ((_let_99 (REFL :args (_let_56)))) (let ((_let_100 (or _let_53 _let_12))) (let ((_let_101 (or _let_55 _let_14))) (let ((_let_102 (_let_4))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_102) :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.apply SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 X Z) true)) (not (= (tptp.member Y SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3) false))))) :args _let_102)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_16)) :args ((or _let_9 _let_7 _let_5 _let_15 _let_13 _let_11 _let_40))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 3)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_9) _let_8))) :args _let_34)) :args ((or _let_8 _let_56))) _let_98 :args (_let_8 true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 4)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_7) _let_6))) :args _let_34)) :args ((or _let_6 _let_56))) _let_98 :args (_let_6 true _let_56)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG :args (_let_56 5)) _let_98 :args ((not _let_5) true _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_101)) :args ((or _let_55 _let_14 (not _let_101)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 0)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args _let_34)) :args ((or _let_54 _let_56))) _let_98 :args (_let_54 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_11 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_101 false _let_44)) :args (_let_14 false _let_54 false _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_100)) :args ((or _let_53 _let_12 (not _let_100)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 1)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_53) _let_52))) :args _let_34)) :args ((or _let_52 _let_56))) _let_98 :args (_let_52 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_12 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_100 false _let_44)) :args (_let_12 false _let_52 false _let_100)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_43)) :args ((or _let_42 _let_10 (not _let_43)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_56 2)) (CONG _let_99 (MACRO_SR_PRED_INTRO :args ((= (not _let_42) _let_41))) :args _let_34)) :args ((or _let_41 _let_56))) _let_98 :args (_let_41 true _let_56)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_51 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_13 QUANTIFIERS_INST_E_MATCHING_SIMPLE _let_50)) :args _let_49)) _let_48 :args (_let_43 false _let_44)) :args (_let_10 false _let_41 false _let_43)) :args (_let_40 false _let_8 false _let_6 true _let_5 false _let_14 false _let_12 false _let_10)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_19 2)) :args ((or _let_4 _let_39))) _let_38 :args (_let_4 false _let_19)) :args (false true _let_16 false _let_4)) :args (_let_3 (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))))) _let_2 (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)))))) (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)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.60 )
% 0.21/0.60 % SZS output end Proof for SET805+4
% 0.21/0.60 % cvc5---1.0.5 exiting
% 0.21/0.61 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------