0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.13	% Command    : do_cvc5 %s %d
0.14/0.34	% Computer   : n027.cluster.edu
0.14/0.34	% Model      : x86_64 x86_64
0.14/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.34	% Memory     : 8042.1875MB
0.14/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.34	% CPULimit   : 1200
0.14/0.34	% WCLimit    : 120
0.14/0.34	% DateTime   : Tue Jul 13 13:45:25 EDT 2021
0.14/0.35	% CPUTime    : 
0.21/0.49	%----THF division
0.21/0.50	------- cvc5-thf casc 28 : /export/starexec/sandbox2/benchmark/theBenchmark.p at 120...
0.21/0.50	--- Run --ho-elim --full-saturate-quant at 10...
1.41/1.57	% SZS status Theorem for theBenchmark
1.41/1.58	% SZS output start Proof for theBenchmark
1.41/1.58	(proof
1.41/1.58	(let ((_let_1 (gt n4))) (let ((_let_2 (gt n2))) (let ((_let_3 (mbox_s4 true))) (let ((_let_4 (mvalid _let_3))) (let ((_let_5 (gt n1))) (let ((_let_6 (gt n3))) (let ((_let_7 (gt n5))) (let ((_let_8 (succ n0))) (let ((_let_9 (succ _let_8))) (let ((_let_10 (succ _let_9))) (let ((_let_11 (succ _let_10))) (let ((_let_12 (mbox_s4 ((gt loopcounter) n1)))) (let ((_let_13 (not (mvalid (mbox_s4 ((mimplies _let_3) ((mand (mbox_s4 ((mimplies (mbox_s4 (mnot _let_12))) _let_3))) (mbox_s4 ((mimplies _let_12) _let_3))))))))) (let ((_let_14 (= mdia_s4 (lambda ((Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (mbox_s4 (mnot Phi))) __flatten_var_0))))) (let ((_let_15 (= mbox_s4 (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not ((rel_s4 W) V)) (Phi V))))))) (let ((_let_16 (= minvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (not (Phi W))))))) (let ((_let_17 (= mcountersatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (not (Phi W))))))) (let ((_let_18 (= msatisfiable (lambda ((Phi (-> $$unsorted Bool))) (exists ((W $$unsorted)) (Phi W)))))) (let ((_let_19 (= mvalid (lambda ((Phi (-> $$unsorted Bool))) (forall ((W $$unsorted)) (Phi W)))))) (let ((_let_20 (= mweakly_directed (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) (exists ((V $$unsorted)) (and ((R T) V) ((R U) V)))))))))) (let ((_let_21 (= mweakly_connected (lambda ((R (-> $$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_22 (= 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_23 (= mfunctional (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) (and ((R S) T) (forall ((U $$unsorted)) (=> ((R S) U) (= T U)))))))))) (let ((_let_24 (= mpartially_functional (lambda ((R (-> $$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_25 (= meuclidean (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted) (U $$unsorted)) (let ((_let_1 (R S))) (=> (and (_let_1 T) (_let_1 U)) ((R T) U)))))))) (let ((_let_26 (= mtransitive (lambda ((R (-> $$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_27 (= mserial (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) (exists ((T $$unsorted)) ((R S) T))))))) (let ((_let_28 (= msymmetric (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted) (T $$unsorted)) (=> ((R S) T) ((R T) S))))))) (let ((_let_29 (= mreflexive (lambda ((R (-> $$unsorted $$unsorted Bool))) (forall ((S $$unsorted)) ((R S) S)))))) (let ((_let_30 (= mexists_prop (lambda ((Phi (-> (-> $$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_31 (= mexists_ind (lambda ((Phi (-> mu $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mnot (Phi X)) __flatten_var_0)))) __flatten_var_0))))) (let ((_let_32 (= mforall_ind (lambda ((Phi (-> mu $$unsorted Bool)) (W $$unsorted)) (forall ((X mu)) (=> ((exists_in_world X) W) ((Phi X) W))))))) (let ((_let_33 (= mdia (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mbox R) (mnot Phi))) __flatten_var_0))))) (let ((_let_34 (= mxor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mequiv Phi) Psi)) __flatten_var_0))))) (let ((_let_35 (= mequiv (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)) __flatten_var_0))))) (let ((_let_36 (= mimplied (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mor (mnot Psi)) Phi) __flatten_var_0))))) (let ((_let_37 (= mimplies (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) (((mor (mnot Phi)) Psi) __flatten_var_0))))) (let ((_let_38 (= mand (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (__flatten_var_0 $$unsorted)) ((mnot ((mor (mnot Phi)) (mnot Psi))) __flatten_var_0))))) (let ((_let_39 (= mfalse (mnot mtrue)))) (let ((_let_40 (= mtrue (lambda ((W $$unsorted)) true)))) (let ((_let_41 (= mforall_prop (lambda ((Phi (-> (-> $$unsorted Bool) $$unsorted Bool)) (W $$unsorted)) (forall ((P (-> $$unsorted Bool))) ((Phi P) W)))))) (let ((_let_42 (= mbox (lambda ((R (-> $$unsorted $$unsorted Bool)) (Phi (-> $$unsorted Bool)) (W $$unsorted)) (forall ((V $$unsorted)) (or (not ((R W) V)) (Phi V))))))) (let ((_let_43 (= mor (lambda ((Phi (-> $$unsorted Bool)) (Psi (-> $$unsorted Bool)) (W $$unsorted)) (or (Phi W) (Psi W)))))) (let ((_let_44 (= mnot (lambda ((Phi (-> $$unsorted Bool)) (W $$unsorted)) (not (Phi W)))))) (let ((_let_45 (= meq_prop (lambda ((X (-> $$unsorted Bool)) (Y (-> $$unsorted Bool)) (W $$unsorted)) (= (X W) (Y W)))))) (let ((_let_46 (ho_3 k_19 skv_39))) (let ((_let_47 (ho_3 (ho_5 k_4 skv_40) skv_39))) (let ((_let_48 (not _let_47))) (let ((_let_49 (or _let_48 _let_46))) (let ((_let_50 (forall ((BOUND_VARIABLE_131428 $$unsorted) (BOUND_VARIABLE_131432 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_131428) BOUND_VARIABLE_131432)) (ho_3 k_19 BOUND_VARIABLE_131432))))) (let ((_let_51 (ASSUME |:args| (_let_45)))) (let ((_let_52 (ASSUME |:args| (_let_44)))) (let ((_let_53 (ASSUME |:args| (_let_43)))) (let ((_let_54 (ASSUME |:args| (_let_42)))) (let ((_let_55 (ASSUME |:args| (_let_41)))) (let ((_let_56 (EQ_RESOLVE (ASSUME |:args| (_let_40)) (MACRO_SR_EQ_INTRO |:args| (_let_40 7 12))))) (let ((_let_57 (EQ_RESOLVE (ASSUME |:args| (_let_39)) (MACRO_SR_EQ_INTRO _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_39 7 12))))) (let ((_let_58 (EQ_RESOLVE (ASSUME |:args| (_let_38)) (MACRO_SR_EQ_INTRO _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_38 7 12))))) (let ((_let_59 (EQ_RESOLVE (ASSUME |:args| (_let_37)) (MACRO_SR_EQ_INTRO _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_37 7 12))))) (let ((_let_60 (EQ_RESOLVE (ASSUME |:args| (_let_36)) (MACRO_SR_EQ_INTRO _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_36 7 12))))) (let ((_let_61 (EQ_RESOLVE (ASSUME |:args| (_let_35)) (MACRO_SR_EQ_INTRO _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_35 7 12))))) (let ((_let_62 (EQ_RESOLVE (ASSUME |:args| (_let_34)) (MACRO_SR_EQ_INTRO _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_34 7 12))))) (let ((_let_63 (EQ_RESOLVE (ASSUME |:args| (_let_33)) (MACRO_SR_EQ_INTRO _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 |:args| (_let_33 7 12))))) (let ((_let_64 (EQ_RESOLVE (ASSUME |:args| (_let_32)) (MACRO_SR_EQ_INTRO |:args| (_let_32 7 12))))) (let ((_let_65 (EQ_RESOLVE (ASSUME |:args| (_let_31)) (MACRO_SR_EQ_INTRO _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 |:args| (_let_31 7 12))))) (let ((_let_66 (EQ_RESOLVE (ASSUME |:args| (_let_30)) (MACRO_SR_EQ_INTRO _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 |:args| (_let_30 7 12))))) (let ((_let_67 (ASSUME |:args| (_let_29)))) (let ((_let_68 (EQ_RESOLVE (ASSUME |:args| (_let_28)) (MACRO_SR_EQ_INTRO |:args| (_let_28 7 12))))) (let ((_let_69 (EQ_RESOLVE (ASSUME |:args| (_let_27)) (MACRO_SR_EQ_INTRO |:args| (_let_27 7 12))))) (let ((_let_70 (EQ_RESOLVE (ASSUME |:args| (_let_26)) (MACRO_SR_EQ_INTRO |:args| (_let_26 7 12))))) (let ((_let_71 (EQ_RESOLVE (ASSUME |:args| (_let_25)) (MACRO_SR_EQ_INTRO |:args| (_let_25 7 12))))) (let ((_let_72 (EQ_RESOLVE (ASSUME |:args| (_let_24)) (MACRO_SR_EQ_INTRO |:args| (_let_24 7 12))))) (let ((_let_73 (EQ_RESOLVE (ASSUME |:args| (_let_23)) (MACRO_SR_EQ_INTRO |:args| (_let_23 7 12))))) (let ((_let_74 (EQ_RESOLVE (ASSUME |:args| (_let_22)) (MACRO_SR_EQ_INTRO |:args| (_let_22 7 12))))) (let ((_let_75 (EQ_RESOLVE (ASSUME |:args| (_let_21)) (MACRO_SR_EQ_INTRO |:args| (_let_21 7 12))))) (let ((_let_76 (EQ_RESOLVE (ASSUME |:args| (_let_20)) (MACRO_SR_EQ_INTRO |:args| (_let_20 7 12))))) (let ((_let_77 (ASSUME |:args| (_let_19)))) (let ((_let_78 (EQ_RESOLVE (ASSUME |:args| (_let_18)) (MACRO_SR_EQ_INTRO |:args| (_let_18 7 12))))) (let ((_let_79 (EQ_RESOLVE (ASSUME |:args| (_let_17)) (MACRO_SR_EQ_INTRO |:args| (_let_17 7 12))))) (let ((_let_80 (ASSUME |:args| (_let_16)))) (let ((_let_81 (ASSUME |:args| (_let_15)))) (let ((_let_82 (EQ_RESOLVE (ASSUME |:args| (_let_14)) (MACRO_SR_EQ_INTRO _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _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 |:args| (_let_14 7 12))))) (let ((_let_83 (EQ_RESOLVE (ASSUME |:args| (_let_4)) (TRANS (MACRO_SR_EQ_INTRO _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _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 |:args| (_let_4 7 12)) (PREPROCESS |:args| ((= (forall ((BOUND_VARIABLE_131428 $$unsorted) (BOUND_VARIABLE_131432 $$unsorted)) (or (not ((rel_s4 BOUND_VARIABLE_131428) BOUND_VARIABLE_131432)) (true BOUND_VARIABLE_131432))) _let_50))))))) (let ((_let_84 (_let_50))) (let ((_let_85 (ho_5 k_4 skv_36))) (let ((_let_86 (or (not (ho_3 _let_85 skv_40)) (not (forall ((BOUND_VARIABLE_172500 $$unsorted)) (or (not (ho_3 (ho_5 k_4 skv_40) BOUND_VARIABLE_172500)) (not (forall ((BOUND_VARIABLE_172501 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172500) BOUND_VARIABLE_172501)) (ho_3 (ho_2 (ho_10 k_14 loopcounter) n1) BOUND_VARIABLE_172501))))))) _let_48 _let_46))) (let ((_let_87 (ho_3 k_19 skv_37))) (let ((_let_88 (ho_3 (ho_5 k_4 skv_38) skv_37))) (let ((_let_89 (not _let_88))) (let ((_let_90 (or (not (ho_3 _let_85 skv_38)) (not (forall ((BOUND_VARIABLE_172484 $$unsorted)) (or (not (ho_3 (ho_5 k_4 skv_38) BOUND_VARIABLE_172484)) (ho_3 (ho_2 (ho_10 k_14 loopcounter) n1) BOUND_VARIABLE_172484)))) _let_89 _let_87))) (let ((_let_91 (and _let_86 _let_90))) (let ((_let_92 (or _let_89 _let_87))) (let ((_let_93 (20))) (let ((_let_94 (or (not (ho_3 (ho_5 k_4 skv_35) skv_36)) (not (forall ((BOUND_VARIABLE_172520 $$unsorted)) (or (not (ho_3 (ho_5 k_4 skv_36) BOUND_VARIABLE_172520)) (ho_3 k_19 BOUND_VARIABLE_172520)))) _let_91))) (let ((_let_95 (forall ((BOUND_VARIABLE_172471 $$unsorted) (BOUND_VARIABLE_172475 $$unsorted) (BOUND_VARIABLE_172476 $$unsorted) (BOUND_VARIABLE_172477 $$unsorted) (BOUND_VARIABLE_172478 $$unsorted) (BOUND_VARIABLE_172479 $$unsorted)) (let ((_let_1 (ho_5 k_4 BOUND_VARIABLE_172475))) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172471) BOUND_VARIABLE_172475)) (not (forall ((BOUND_VARIABLE_172520 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172475) BOUND_VARIABLE_172520)) (ho_3 k_19 BOUND_VARIABLE_172520)))) (and (or (not (ho_3 _let_1 BOUND_VARIABLE_172479)) (not (forall ((BOUND_VARIABLE_172500 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172479) BOUND_VARIABLE_172500)) (not (forall ((BOUND_VARIABLE_172501 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172500) BOUND_VARIABLE_172501)) (ho_3 (ho_2 (ho_10 k_14 loopcounter) n1) BOUND_VARIABLE_172501))))))) (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172479) BOUND_VARIABLE_172478)) (ho_3 k_19 BOUND_VARIABLE_172478)) (or (not (ho_3 _let_1 BOUND_VARIABLE_172477)) (not (forall ((BOUND_VARIABLE_172484 $$unsorted)) (or (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172477) BOUND_VARIABLE_172484)) (ho_3 (ho_2 (ho_10 k_14 loopcounter) n1) BOUND_VARIABLE_172484)))) (not (ho_3 (ho_5 k_4 BOUND_VARIABLE_172477) BOUND_VARIABLE_172476)) (ho_3 k_19 BOUND_VARIABLE_172476)))))))) (let ((_let_96 (not _let_94))) (let ((_let_97 (not _let_95))) (let ((_let_98 (EQ_RESOLVE (ASSUME |:args| (_let_13)) (TRANS (MACRO_SR_EQ_INTRO _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _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 |:args| (_let_13 7 12)) (PREPROCESS |:args| ((= (not (forall ((BOUND_VARIABLE_172471 $$unsorted) (BOUND_VARIABLE_172475 $$unsorted) (BOUND_VARIABLE_172476 $$unsorted) (BOUND_VARIABLE_172477 $$unsorted) (BOUND_VARIABLE_172478 $$unsorted) (BOUND_VARIABLE_172479 $$unsorted)) (let ((_let_1 (rel_s4 BOUND_VARIABLE_172475))) (or (not ((rel_s4 BOUND_VARIABLE_172471) BOUND_VARIABLE_172475)) (not (forall ((BOUND_VARIABLE_172520 $$unsorted)) (or (not ((rel_s4 BOUND_VARIABLE_172475) BOUND_VARIABLE_172520)) (true BOUND_VARIABLE_172520)))) (and (or (not (_let_1 BOUND_VARIABLE_172479)) (not (forall ((BOUND_VARIABLE_172500 $$unsorted)) (or (not ((rel_s4 BOUND_VARIABLE_172479) BOUND_VARIABLE_172500)) (not (forall ((BOUND_VARIABLE_172501 $$unsorted)) (or (not ((rel_s4 BOUND_VARIABLE_172500) BOUND_VARIABLE_172501)) (((gt loopcounter) n1) BOUND_VARIABLE_172501))))))) (not ((rel_s4 BOUND_VARIABLE_172479) BOUND_VARIABLE_172478)) (true BOUND_VARIABLE_172478)) (or (not (_let_1 BOUND_VARIABLE_172477)) (not (forall ((BOUND_VARIABLE_172484 $$unsorted)) (or (not ((rel_s4 BOUND_VARIABLE_172477) BOUND_VARIABLE_172484)) (((gt loopcounter) n1) BOUND_VARIABLE_172484)))) (not ((rel_s4 BOUND_VARIABLE_172477) BOUND_VARIABLE_172476)) (true BOUND_VARIABLE_172476))))))) _let_97))))))) (let ((_let_99 (MACRO_RESOLUTION_TRUST (CNF_AND_NEG |:args| (_let_91)) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_94 2)) (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_98) |:args| (_let_97))) (CONG (MACRO_SR_PRED_INTRO |:args| ((= (not _let_97) _let_95))) (REFL |:args| (_let_96)) |:args| _let_93)) _let_98 |:args| (_let_96 true _let_95)) |:args| ((not _let_91) true _let_94)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_92)) |:args| ((or _let_87 _let_89 (not _let_92)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 |:args| (skv_38 skv_37)) |:args| _let_84)) _let_83 |:args| (_let_92 false _let_50)) (CNF_OR_NEG |:args| (_let_90 3)) (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_90 2)) (CONG (REFL |:args| (_let_90)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_89) _let_88))) |:args| _let_93)) |:args| ((or _let_88 _let_90))) |:args| (_let_90 false _let_92 true _let_87 false _let_88)) |:args| ((not _let_86) true _let_91 false _let_90)))) (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS |:args| (_let_49)) |:args| ((or _let_46 _let_48 (not _let_49)))) (MACRO_RESOLUTION_TRUST (CNF_OR_NEG |:args| (_let_86 3)) _let_99 |:args| ((not _let_46) true _let_86)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG |:args| (_let_86 2)) (CONG (REFL |:args| (_let_86)) (MACRO_SR_PRED_INTRO |:args| ((= (not _let_48) _let_47))) |:args| _let_93)) |:args| ((or _let_47 _let_86))) _let_99 |:args| (_let_47 true _let_86)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_83 |:args| (skv_40 skv_39)) |:args| _let_84)) _let_83 |:args| (_let_49 false _let_50)) |:args| (false true _let_46 false _let_47 false _let_49)) |:args| (_let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _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 (forall ((V $$unsorted)) (exists ((X mu)) ((exists_in_world X) V))) _let_15 _let_14 (mtransitive rel_s4) (mreflexive rel_s4) (forall ((X mu) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (exists_in_world X))) (=> (and ((rel_s4 V) W) (_let_1 V)) (_let_1 W)))) (mvalid (mbox_s4 (mforall_ind (lambda ((X mu) (__flatten_var_0 $$unsorted)) ((mbox_s4 (mforall_ind (lambda ((C mu) (__flatten_var_0 $$unsorted)) ((mbox_s4 ((mimplies (mbox_s4 ((leq n0) X))) (mbox_s4 ((leq ((uniform_int_rnd C) X)) X)))) __flatten_var_0)))) __flatten_var_0))))) (mvalid (mbox_s4 (mforall_ind (lambda ((A mu) (__flatten_var_0 $$unsorted)) ((mbox_s4 (mforall_ind (lambda ((B mu) (__flatten_var_0 $$unsorted)) ((mbox_s4 (mforall_ind (lambda ((C mu) (__flatten_var_0 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1.41/1.58	)
1.41/1.58	% SZS output end Proof for theBenchmark
1.41/1.59	EOF