0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command    : do_cvc5 %s %d
0.13/0.34	% Computer   : n021.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 14:30:41 EDT 2021
0.13/0.34	% CPUTime    : 
0.19/0.47	%----THF division
0.19/0.48	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.19/0.48	--- Run --ho-elim --full-saturate-quant at 10...
10.29/10.50	--- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
10.86/11.04	% SZS status Theorem for theBenchmark
10.86/11.05	% SZS output start Proof for theBenchmark
10.86/11.05	(proof
10.86/11.05	(let ((_let_1 (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (((mequiv ((subset A) B)) (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (member X))) (((mimplies (_let_1 A)) (_let_1 B)) __flatten_var_0))))) __flatten_var_0))) __flatten_var_0)))))) (let ((_let_2 (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mnot ((member X) empty_set)) __flatten_var_0)))))) (let ((_let_3 (forall ((V $$unsorted)) ((exists_in_world empty_set) V)))) (let ((_let_4 (not (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) (((subset empty_set) A) __flatten_var_0))))))) (let ((_let_5 (= mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (mbox_s4 (mnot Phi))) __flatten_var_0))))) (let ((_let_6 (= mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not ((rel_s4 W) V)) (Phi V))))))) (let ((_let_7 (= minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (Phi W))))))) (let ((_let_8 (= mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (Phi W))))))) (let ((_let_9 (= msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (Phi W)))))) (let ((_let_10 (= mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (Phi W)))))) (let ((_let_11 (= mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) (exists ((V $$unsorted)) (and ((R T) V) ((R U) V)))))))))) (let ((_let_12 (= mweakly_connected (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) (or ((R T) U) (= T U) ((R U) T))))))))) (let ((_let_13 (= mweakly_dense (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (=> ((R S) T) (exists ((U $$unsorted)) (and ((R S) U) ((R U) T))))))))) (let ((_let_14 (= mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and ((R S) T) (forall ((U $$unsorted)) (=> ((R S) U) (= T U)))))))))) (let ((_let_15 (= mpartially_functional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) (= T U)))))))) (let ((_let_16 (= meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) ((R T) U)))))))) (let ((_let_17 (= mtransitive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) ((R T) U)) (_let_1 U)))))))) (let ((_let_18 (= mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) ((R S) T))))))) (let ((_let_19 (= msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> ((R S) T) ((R T) S))))))) (let ((_let_20 (= mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) ((R S) S)))))) (let ((_let_21 (= mexists_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (mforall_prop (lambda ((P (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (Phi P)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_22 (= mexists_ind (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mnot (Phi X)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_23 (= mforall_ind (lambda ((Phi (-> mu $$unsorted Bool)) (W $$unsorted)) (forall ((X mu)) (=> ((exists_in_world X) W) ((Phi X) W))))))) (let ((_let_24 (= mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mbox R) (mnot Phi))) __flatten_var_0))))) (let ((_let_25 (= mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_26 (= mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_27 (= mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mor (mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_28 (= mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mor (mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_29 (= mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mor (mnot Phi)) (mnot Psi))) __flatten_var_0))))) (let ((_let_30 (= mfalse (mnot mtrue)))) (let ((_let_31 (= mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_32 (= mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) ((Phi P) W)))))) (let ((_let_33 (= mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not ((R W) V)) (Phi V))))))) (let ((_let_34 (= mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (Phi W) (Psi W)))))) (let ((_let_35 (= mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (Phi W)))))) (let ((_let_36 (= meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (X W) (Y W)))))) (let ((_let_37 (forall ((BOUND_VARIABLE_3903 $$unsorted) (BOUND_VARIABLE_3907 mu)) (or (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_3907) BOUND_VARIABLE_3903)) (not (ho_3 (ho_2 (ho_7 k_6 BOUND_VARIABLE_3907) empty_set) BOUND_VARIABLE_3903)))))) (let ((_let_38 (ho_7 k_6 skv_47))) (let ((_let_39 (ho_3 (ho_2 _let_38 empty_set) skv_21))) (let ((_let_40 (not _let_39))) (let ((_let_41 (ho_3 (ho_2 k_1 skv_47) skv_21))) (let ((_let_42 (not _let_41))) (let ((_let_43 (or _let_42 _let_40))) (let ((_let_44 (ASSUME |:args| (_let_36)))) (let ((_let_45 (ASSUME |:args| (_let_35)))) (let ((_let_46 (ASSUME |:args| (_let_34)))) (let ((_let_47 (ASSUME |:args| (_let_33)))) (let ((_let_48 (ASSUME |:args| (_let_32)))) (let ((_let_49 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (MACRO_SR_EQ_INTRO |:args| (_let_31 7 12))))) (let ((_let_50 (EQ_RESOLVE (ASSUME |:args| (_let_30)) (MACRO_SR_EQ_INTRO _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_30 7 12))))) (let ((_let_51 (EQ_RESOLVE (ASSUME |:args| (_let_29)) (MACRO_SR_EQ_INTRO _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_29 7 12))))) (let ((_let_52 (EQ_RESOLVE (ASSUME |:args| (_let_28)) (MACRO_SR_EQ_INTRO _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_28 7 12))))) (let ((_let_53 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_27 7 12))))) (let ((_let_54 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_26 7 12))))) (let ((_let_55 (EQ_RESOLVE (ASSUME |:args| (_let_25)) (MACRO_SR_EQ_INTRO _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_25 7 12))))) (let ((_let_56 (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_24 7 12))))) (let ((_let_57 (EQ_RESOLVE (ASSUME |:args| (_let_23)) (MACRO_SR_EQ_INTRO |:args| (_let_23 7 12))))) (let ((_let_58 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_22 7 12))))) (let ((_let_59 (EQ_RESOLVE (ASSUME |:args| (_let_21)) (MACRO_SR_EQ_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_21 7 12))))) (let ((_let_60 (ASSUME |:args| (_let_20)))) (let ((_let_61 (EQ_RESOLVE (ASSUME |:args| (_let_19)) (MACRO_SR_EQ_INTRO |:args| (_let_19 7 12))))) (let ((_let_62 (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))))) (let ((_let_63 (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO |:args| (_let_17 7 12))))) (let ((_let_64 (EQ_RESOLVE (ASSUME |:args| (_let_16)) (MACRO_SR_EQ_INTRO |:args| (_let_16 7 12))))) (let ((_let_65 (EQ_RESOLVE (ASSUME |:args| (_let_15)) (MACRO_SR_EQ_INTRO |:args| (_let_15 7 12))))) (let ((_let_66 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO |:args| (_let_14 7 12))))) (let ((_let_67 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (MACRO_SR_EQ_INTRO |:args| (_let_13 7 12))))) (let ((_let_68 (EQ_RESOLVE (ASSUME |:args| (_let_12)) (MACRO_SR_EQ_INTRO |:args| (_let_12 7 12))))) (let ((_let_69 (EQ_RESOLVE (ASSUME |:args| (_let_11)) (MACRO_SR_EQ_INTRO |:args| (_let_11 7 12))))) (let ((_let_70 (ASSUME |:args| (_let_10)))) (let ((_let_71 (EQ_RESOLVE (ASSUME |:args| (_let_9)) (MACRO_SR_EQ_INTRO |:args| (_let_9 7 12))))) (let ((_let_72 (EQ_RESOLVE (ASSUME |:args| (_let_8)) (MACRO_SR_EQ_INTRO |:args| (_let_8 7 12))))) (let ((_let_73 (ASSUME |:args| (_let_7)))) (let ((_let_74 (ASSUME |:args| (_let_6)))) (let ((_let_75 (EQ_RESOLVE (ASSUME |:args| (_let_5)) (MACRO_SR_EQ_INTRO _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_5 7 12))))) (let ((_let_76 (EQ_RESOLVE (ASSUME |:args| (_let_2)) (TRANS (MACRO_SR_EQ_INTRO _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_2 7 12)) (PREPROCESS |:args| ((= (forall ((BOUND_VARIABLE_3903 $$unsorted) (BOUND_VARIABLE_3907 mu)) (or (not ((exists_in_world BOUND_VARIABLE_3907) BOUND_VARIABLE_3903)) (not (((member BOUND_VARIABLE_3907) empty_set) BOUND_VARIABLE_3903)))) _let_37))))))) (let ((_let_77 (not _let_43))) (let ((_let_78 (or _let_42 _let_40 (ho_3 (ho_2 _let_38 skv_22) skv_21)))) (let ((_let_79 (forall ((BOUND_VARIABLE_4514 mu)) (let ((_let_1 (ho_7 k_6 BOUND_VARIABLE_4514))) (or (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_4514) skv_21)) (not (ho_3 (ho_2 _let_1 empty_set) skv_21)) (ho_3 (ho_2 _let_1 skv_22) skv_21)))))) (let ((_let_80 (not _let_78))) (let ((_let_81 (ho_3 (ho_2 (ho_7 k_9 empty_set) skv_22) skv_21))) (let ((_let_82 (not _let_79))) (let ((_let_83 (or _let_82 _let_81))) (let ((_let_84 (ho_7 k_6 empty_set))) (let ((_let_85 (ho_3 (ho_2 k_1 empty_set) skv_21))) (let ((_let_86 (not _let_85))) (let ((_let_87 (not _let_81))) (let ((_let_88 (and (or _let_87 _let_86 (not (ho_3 (ho_2 _let_84 empty_set) skv_21)) (ho_3 (ho_2 _let_84 skv_22) skv_21)) _let_83))) (let ((_let_89 (ho_3 (ho_2 k_1 skv_22) skv_21))) (let ((_let_90 (not _let_89))) (let ((_let_91 (or _let_86 _let_90 _let_88))) (let ((_let_92 (forall ((BOUND_VARIABLE_4504 $$unsorted) (BOUND_VARIABLE_4508 mu) (BOUND_VARIABLE_4509 mu) (BOUND_VARIABLE_4510 mu)) (let ((_let_1 (ho_3 (ho_2 (ho_7 k_9 BOUND_VARIABLE_4508) BOUND_VARIABLE_4510) BOUND_VARIABLE_4504))) (let ((_let_2 (ho_7 k_6 BOUND_VARIABLE_4509))) (or (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_4510) BOUND_VARIABLE_4504)) (and (or (not _let_1) (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_4509) BOUND_VARIABLE_4504)) (not (ho_3 (ho_2 _let_2 BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) (ho_3 (ho_2 _let_2 BOUND_VARIABLE_4510) BOUND_VARIABLE_4504)) (or (not (forall ((BOUND_VARIABLE_4514 mu)) (let ((_let_1 (ho_7 k_6 BOUND_VARIABLE_4514))) (or (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_4514) BOUND_VARIABLE_4504)) (not (ho_3 (ho_2 _let_1 BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) (ho_3 (ho_2 _let_1 BOUND_VARIABLE_4510) BOUND_VARIABLE_4504))))) _let_1)))))))) (let ((_let_93 (EQ_RESOLVE (ASSUME |:args| (_let_1)) (TRANS (MACRO_SR_EQ_INTRO _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_1 7 12)) (PREPROCESS |:args| ((= (forall ((BOUND_VARIABLE_4504 $$unsorted) (BOUND_VARIABLE_4508 mu) (BOUND_VARIABLE_4509 mu) (BOUND_VARIABLE_4510 mu)) (let ((_let_1 (((subset BOUND_VARIABLE_4508) BOUND_VARIABLE_4510) BOUND_VARIABLE_4504))) (let ((_let_2 (member BOUND_VARIABLE_4509))) (or (not ((exists_in_world BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) (not ((exists_in_world BOUND_VARIABLE_4510) BOUND_VARIABLE_4504)) (and (or (not _let_1) (not ((exists_in_world BOUND_VARIABLE_4509) BOUND_VARIABLE_4504)) (not ((_let_2 BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) ((_let_2 BOUND_VARIABLE_4510) BOUND_VARIABLE_4504)) (or (not (forall ((BOUND_VARIABLE_4514 mu)) (let ((_let_1 (member BOUND_VARIABLE_4514))) (or (not ((exists_in_world BOUND_VARIABLE_4514) BOUND_VARIABLE_4504)) (not ((_let_1 BOUND_VARIABLE_4508) BOUND_VARIABLE_4504)) ((_let_1 BOUND_VARIABLE_4510) BOUND_VARIABLE_4504))))) _let_1)))))) _let_92))))))) (let ((_let_94 (forall ((V $$unsorted)) (ho_3 (ho_2 k_1 empty_set) V)))) (let ((_let_95 (EQ_RESOLVE (ASSUME |:args| (_let_3)) (PREPROCESS |:args| ((= _let_3 _let_94)))))) (let ((_let_96 (or _let_90 _let_81))) (let ((_let_97 (forall ((BOUND_VARIABLE_12431 $$unsorted) (BOUND_VARIABLE_12435 mu)) (or (not (ho_3 (ho_2 k_1 BOUND_VARIABLE_12435) BOUND_VARIABLE_12431)) (ho_3 (ho_2 (ho_7 k_9 empty_set) BOUND_VARIABLE_12435) BOUND_VARIABLE_12431))))) (let ((_let_98 (not _let_96))) (let ((_let_99 (not _let_97))) (let ((_let_100 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 |:args| (_let_4 7 12)) (PREPROCESS |:args| ((= (not (forall ((BOUND_VARIABLE_12431 $$unsorted) (BOUND_VARIABLE_12435 mu)) (or (not ((exists_in_world BOUND_VARIABLE_12435) BOUND_VARIABLE_12431)) (((subset empty_set) BOUND_VARIABLE_12435) BOUND_VARIABLE_12431)))) _let_99))))))) (let ((_let_101 (20))) (let ((_let_102 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_100) |:args| (_let_99))) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_99) _let_97))) (REFL |:args| (_let_98)) |:args| _let_101)) _let_100 |:args| (_let_98 true _let_97)))) (let ((_let_103 (_let_82))) (let ((_let_104 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE (ASSUME |:args| _let_103)) |:args| _let_103)) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_82) _let_79))) (REFL |:args| (_let_80)) |:args| _let_101)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_83)) |:args| ((or _let_81 _let_82 (not _let_83)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_96 1)) _let_102 |:args| (_let_87 true _let_96)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS |:args| (_let_88 1)) |:args| ((or _let_83 (not _let_88)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_91)) |:args| ((or _let_90 _let_86 _let_88 (not _let_91)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_96 0)) (CONG (REFL |:args| (_let_96)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_90) _let_89))) |:args| _let_101)) |:args| ((or _let_89 _let_96))) _let_102 |:args| (_let_89 true _let_96)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_95 |:args| (skv_21)) |:args| (_let_94))) _let_95 |:args| (_let_85 false _let_94)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_93 |:args| (skv_21 empty_set empty_set skv_22)) |:args| (_let_92))) _let_93 |:args| (_let_91 false _let_92)) |:args| (_let_88 false _let_89 false _let_85 false _let_91)) |:args| (_let_83 false _let_88)) |:args| (_let_82 true _let_81 false _let_83)) |:args| (_let_80 true _let_79)))) (let ((_let_105 (REFL |:args| (_let_78)))) (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_76 |:args| (skv_21 skv_47)) |:args| (_let_37))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_43)) |:args| ((or _let_42 _let_40 _let_77))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_78 0)) (CONG _let_105 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_42) _let_41))) |:args| _let_101)) |:args| ((or _let_41 _let_78))) _let_104 |:args| (_let_41 true _let_78)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_78 1)) (CONG _let_105 (MACRO_SR_PRED_INTRO |:args| ((= (not _let_40) _let_39))) |:args| _let_101)) |:args| ((or _let_39 _let_78))) _let_104 |:args| (_let_39 true _let_78)) |:args| (_let_77 false _let_41 false _let_39)) _let_76 |:args| (false true _let_43 false _let_37)) |:args| (_let_36 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23 _let_22 _let_21 _let_20 _let_19 _let_18 _let_17 _let_16 _let_15 _let_14 _let_13 _let_12 _let_11 _let_10 _let_9 _let_8 _let_7 (forall ((V $$unsorted)) (exists ((X mu)) ((exists_in_world X) V))) _let_6 _let_5 (mtransitive rel_s4) (mreflexive rel_s4) (forall ((X mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (exists_in_world X))) (=> (and ((rel_s4 V) W) (_let_1 V)) (_let_1 W)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) 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((member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (forall ((V $$unsorted) (V1 mu)) ((exists_in_world (singleton V1)) V)) (forall ((V $$unsorted) (V1 mu)) ((exists_in_world (power_set V1)) V)) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (((mequiv ((equal_set A) B)) ((mand ((subset A) B)) ((subset B) A))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (unordered_pair C))) (((mimplies ((qmltpeq A) B)) ((qmltpeq (_let_1 A)) (_let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (forall ((V $$unsorted) (V2 mu) (V1 mu)) ((exists_in_world ((unordered_pair V2) V1)) V)) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (((mimplies ((mand ((qmltpeq A) B)) ((equal_set A) C))) ((equal_set B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (member C))) (((mimplies ((mand ((qmltpeq A) B)) (_let_1 A))) (_let_1 B)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) (((mequiv ((member X) (sum A))) (mexists_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) (((mand ((member Y) A)) ((member X) Y)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((E mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (member B))) (((mequiv (_let_1 ((difference E) A))) ((mand (_let_1 E)) (mnot (_let_1 A)))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (forall ((V $$unsorted) (V2 mu) (V1 mu)) ((exists_in_world ((difference V2) V1)) V)) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (((mimplies ((qmltpeq A) B)) ((qmltpeq ((intersection A) C)) ((intersection B) C))) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (member X))) (((mequiv (_let_1 ((intersection A) B))) ((mand (_let_1 A)) (_let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (member X))) (((mequiv (_let_1 ((union A) B))) ((mor (_let_1 A)) (_let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) (((mequiv ((member X) (power_set A))) ((subset X) A)) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (((mimplies ((mand ((qmltpeq A) B)) ((subset A) C))) ((subset B) C)) __flatten_var_0))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (((mimplies ((qmltpeq A) B)) ((qmltpeq (sum A)) (sum B))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (qmltpeq X))) (((mequiv ((member X) ((unordered_pair A) B))) ((mor (_let_1 A)) (_let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (union C))) (((mimplies ((qmltpeq A) B)) ((qmltpeq (_let_1 A)) (_let_1 B))) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (forall ((V $$unsorted) (V1 mu)) ((exists_in_world (product V1)) V)) (mvalid (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((Y mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((Z mu) (__flatten_var_0 $$unsorted)) (let ((_let_1 (qmltpeq X))) (((mimplies ((mand (_let_1 Y)) ((qmltpeq Y) Z))) (_let_1 Z)) __flatten_var_0)))) __flatten_var_0))) __flatten_var_0)))) (forall ((V $$unsorted) (V2 mu) (V1 mu)) ((exists_in_world ((union V2) V1)) V)) (mvalid (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) (((mimplies ((qmltpeq A) B)) ((qmltpeq (product A)) (product B))) __flatten_var_0))) __flatten_var_0)))) (not false))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
10.86/11.05	)
10.86/11.05	% SZS output end Proof for theBenchmark
10.86/11.06	EOF