TSTP Solution File: SYO474^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO474^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : 0s
% DateTime : Tue Mar 29 00:51:50 EDT 2022
% Result : Timeout 292.85s 293.18s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYO474^1 : TPTP v7.5.0. Released v4.0.0.
% 0.06/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sun Mar 13 07:38:22 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.38/0.59 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.38/0.59 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20febd8>, <kernel.Type object at 0x20fe4d0>) of role type named mu_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring mu:Type
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20fe9e0>, <kernel.DependentProduct object at 0x20febd8>) of role type named meq_ind_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.38/0.59 FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% 0.38/0.59 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.38/0.59 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20febd8>, <kernel.DependentProduct object at 0x20fe8c0>) of role type named meq_prop_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))) of role definition named meq_prop
% 0.38/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))))
% 0.38/0.59 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20fe950>, <kernel.DependentProduct object at 0x20fe9e0>) of role type named mnot_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.38/0.59 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.38/0.59 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.38/0.59 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20fe9e0>, <kernel.DependentProduct object at 0x20fe248>) of role type named mor_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% 0.38/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% 0.38/0.59 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20fe248>, <kernel.DependentProduct object at 0x20feef0>) of role type named mand_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) of role definition named mand
% 0.38/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.38/0.59 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.38/0.59 FOF formula (<kernel.Constant object at 0x20feef0>, <kernel.DependentProduct object at 0x20fe758>) of role type named mimplies_type
% 0.38/0.59 Using role type
% 0.38/0.59 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) of role definition named mimplies
% 0.38/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.38/0.59 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20fe758>, <kernel.DependentProduct object at 0x20fe170>) of role type named mimplied_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))) of role definition named mimplied
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.38/0.61 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20fe170>, <kernel.DependentProduct object at 0x20fe9e0>) of role type named mequiv_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))) of role definition named mequiv
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))))
% 0.38/0.61 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20fe9e0>, <kernel.DependentProduct object at 0x20fe248>) of role type named mxor_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))) of role definition named mxor
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.38/0.61 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20febd8>, <kernel.DependentProduct object at 0x20fe170>) of role type named mforall_ind_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.38/0.61 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% 0.38/0.61 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.38/0.61 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2b5bfc979cf8>, <kernel.DependentProduct object at 0x20fe878>) of role type named mforall_prop_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.38/0.61 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% 0.38/0.61 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% 0.38/0.61 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20fe878>, <kernel.DependentProduct object at 0x20feef0>) of role type named mexists_ind_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.38/0.61 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))) of role definition named mexists_ind
% 0.38/0.61 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))))
% 0.38/0.61 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20feef0>, <kernel.DependentProduct object at 0x20fea70>) of role type named mexists_prop_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.38/0.61 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))) of role definition named mexists_prop
% 0.38/0.61 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))))
% 0.38/0.61 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20dc638>, <kernel.DependentProduct object at 0x20fe170>) of role type named mtrue_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mtrue:(fofType->Prop)
% 0.38/0.61 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.38/0.61 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.38/0.61 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20dca28>, <kernel.DependentProduct object at 0x20fe320>) of role type named mfalse_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mfalse:(fofType->Prop)
% 0.38/0.61 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.38/0.61 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.38/0.61 Defined: mfalse:=(mnot mtrue)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x20dcb90>, <kernel.DependentProduct object at 0x20fe320>) of role type named mbox_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox
% 0.38/0.62 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% 0.38/0.62 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x20dcb90>, <kernel.DependentProduct object at 0x20feef0>) of role type named mdia_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.62 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))) of role definition named mdia
% 0.38/0.62 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))))
% 0.38/0.62 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x20feb48>, <kernel.DependentProduct object at 0x20fe3b0>) of role type named mreflexive_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.38/0.62 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.38/0.62 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.38/0.62 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x20fe3b0>, <kernel.DependentProduct object at 0x20fe488>) of role type named msymmetric_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))) of role definition named msymmetric
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))))
% 0.47/0.63 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x20fe488>, <kernel.DependentProduct object at 0x20fe878>) of role type named mserial_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))) of role definition named mserial
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))))
% 0.47/0.63 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x20fe878>, <kernel.DependentProduct object at 0x20fe9e0>) of role type named mtransitive_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))) of role definition named mtransitive
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))))
% 0.47/0.63 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x20fe9e0>, <kernel.DependentProduct object at 0x20fe488>) of role type named meuclidean_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))) of role definition named meuclidean
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))))
% 0.47/0.63 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x20fe320>, <kernel.DependentProduct object at 0x20fff80>) of role type named mpartially_functional_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))) of role definition named mpartially_functional
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))))
% 0.47/0.63 Defined: mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x20fe3b0>, <kernel.DependentProduct object at 0x20ffcb0>) of role type named mfunctional_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))) of role definition named mfunctional
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))))
% 0.47/0.64 Defined: mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x20fe3b0>, <kernel.DependentProduct object at 0x20fff80>) of role type named mweakly_dense_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))) of role definition named mweakly_dense
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))))
% 0.47/0.64 Defined: mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x20fe3b0>, <kernel.DependentProduct object at 0x20ffa70>) of role type named mweakly_connected_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))) of role definition named mweakly_connected
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))))
% 0.47/0.64 Defined: mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x20ffa70>, <kernel.DependentProduct object at 0x20ffc20>) of role type named mweakly_directed_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))) of role definition named mweakly_directed
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))))
% 0.47/0.64 Defined: mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x20ffe18>, <kernel.DependentProduct object at 0x20ff638>) of role type named mvalid_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mvalid:((fofType->Prop)->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.47/0.64 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x20ffa70>, <kernel.DependentProduct object at 0x2b5bf4eb9200>) of role type named minvalid_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring minvalid:((fofType->Prop)->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.47/0.65 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x20ffa70>, <kernel.DependentProduct object at 0x2b5bf4eb9560>) of role type named msatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.47/0.65 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b5bf4eb93f8>, <kernel.DependentProduct object at 0x2b5bf4eb9638>) of role type named mcountersatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.47/0.65 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.47/0.65 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^1.ax, trying next directory
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x20f9c68>, <kernel.DependentProduct object at 0x20dca70>) of role type named rel_k_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring rel_k:(fofType->(fofType->Prop))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x20f9c68>, <kernel.DependentProduct object at 0x20dccf8>) of role type named mbox_k_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mbox_k:((fofType->Prop)->(fofType->Prop))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_k) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V))))) of role definition named mbox_k
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_k) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V)))))
% 0.47/0.65 Defined: mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x20dccf8>, <kernel.DependentProduct object at 0x20dca70>) of role type named mdia_k_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mdia_k:((fofType->Prop)->(fofType->Prop))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))) of role definition named mdia_k
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))))
% 0.47/0.65 Defined: mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2b5bfc98c710>, <kernel.DependentProduct object at 0x2b5bfc98cef0>) of role type named p_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring p:(fofType->Prop)
% 0.47/0.65 FOF formula (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)))) ((mimplies (mdia_k (mbox_k p))) (mbox_k p)))) of role conjecture named prove
% 0.47/0.65 Conjecture to prove = (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)))) ((mimplies (mdia_k (mbox_k p))) (mbox_k p)))):Prop
% 0.47/0.65 Parameter mu_DUMMY:mu.
% 0.47/0.65 Parameter fofType_DUMMY:fofType.
% 0.47/0.65 We need to prove ['(mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)))) ((mimplies (mdia_k (mbox_k p))) (mbox_k p))))']
% 0.47/0.65 Parameter mu:Type.
% 0.47/0.65 Parameter fofType:Type.
% 0.47/0.65 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.47/0.65 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.65 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.65 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.65 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.65 Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.65 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.47/0.65 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.47/0.65 Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.65 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.65 Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% 19.87/20.06 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 19.87/20.06 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 19.87/20.06 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 19.87/20.06 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 19.87/20.06 Parameter rel_k:(fofType->(fofType->Prop)).
% 19.87/20.06 Definition mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 19.87/20.06 Definition mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 19.87/20.06 Parameter p:(fofType->Prop).
% 19.87/20.06 Trying to prove (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)))) ((mimplies (mdia_k (mbox_k p))) (mbox_k p))))
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 19.87/20.06 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 19.87/20.06 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 19.87/20.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 19.87/20.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 19.87/20.06 Found x10:False
% 19.87/20.06 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 34.20/34.39 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 34.20/34.39 Found x10:False
% 34.20/34.39 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 34.20/34.39 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 34.20/34.39 Found x30:False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 34.20/34.39 Found x30:False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 34.20/34.39 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 34.20/34.39 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found (or_introl1 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 34.20/34.39 Found x10:False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 34.20/34.39 Found x10:False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 34.20/34.39 Found x30:False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 34.20/34.39 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 34.20/34.39 Found x30:False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 34.20/34.39 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 34.20/34.39 Found x10:False
% 34.20/34.39 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 34.20/34.39 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 34.20/34.39 Found x10:False
% 34.20/34.39 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 34.20/34.39 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 34.20/34.39 Found x30:False
% 34.20/34.39 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 34.20/34.39 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 55.86/56.10 Found x30:False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 55.86/56.10 Found or_introl00:=(or_introl0 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found (or_introl0 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 55.86/56.10 Found x30:False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 55.86/56.10 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 55.86/56.10 Found x30:False
% 55.86/56.10 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 55.86/56.10 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 55.86/56.10 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 55.86/56.10 Found x10:False
% 55.86/56.10 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 77.40/77.60 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 77.40/77.60 Found x10:False
% 77.40/77.60 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 77.40/77.60 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 77.40/77.60 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found x10:False
% 77.40/77.60 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 77.40/77.60 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 77.40/77.60 Found x10:False
% 77.40/77.60 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 77.40/77.60 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 77.40/77.60 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 77.40/77.60 Found x10:False
% 77.40/77.60 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 77.40/77.60 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 83.55/83.76 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 83.55/83.76 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 83.55/83.76 Found x30:False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 83.55/83.76 Found x30:False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 83.55/83.76 Found x30:False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 83.55/83.76 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 83.55/83.76 Found x30:False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 83.55/83.76 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 83.55/83.76 Found x10:False
% 83.55/83.76 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 83.55/83.76 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 83.59/83.76 Found x10:False
% 83.59/83.76 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 83.59/83.76 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 83.59/83.76 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 83.59/83.76 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found (or_introl1 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found (or_introl1 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 104.95/105.15 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found (or_introl1 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 104.95/105.15 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 116.84/117.06 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V0))=> x10) as proof of (((mbox_k p) V0)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0))=> x10) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V0)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 116.84/117.06 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 116.84/117.06 Found x10:False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of False
% 116.84/117.06 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 116.84/117.06 Found x1:(((rel_k W) V)->False)
% 116.84/117.06 Instantiate: V0:=W:fofType;V:=V1:fofType
% 116.84/117.06 Found x1 as proof of (((rel_k V0) V1)->False)
% 116.84/117.06 Found (or_introl10 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 116.84/117.06 Found ((or_introl1 (((mimplies p) (mbox_k p)) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 116.84/117.06 Found (((or_introl (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of False
% 116.84/117.06 Found (fun (x4:((mnot (mbox_k ((mimplies p) (mbox_k p)))) V))=> x30) as proof of (((mnot (mbox_k ((mimplies p) (mbox_k p)))) V)->False)
% 116.84/117.06 Found x30:False
% 116.84/117.06 Found (fun (x4:((mbox_k p) V))=> x30) as proof of False
% 129.23/129.50 Found (fun (x4:((mbox_k p) V))=> x30) as proof of (((mbox_k p) V)->False)
% 129.23/129.50 Found x10:False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 129.23/129.50 Found x10:False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 129.23/129.50 Found x4:(((rel_k W) V0)->False)
% 129.23/129.50 Instantiate: V0:=V00:fofType;V:=W:fofType
% 129.23/129.50 Found x4 as proof of (((rel_k V) V00)->False)
% 129.23/129.50 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found ((or_introl1 (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found x3:(((rel_k W) V0)->False)
% 129.23/129.50 Instantiate: V0:=V00:fofType;V:=W:fofType
% 129.23/129.50 Found x3 as proof of (((rel_k V) V00)->False)
% 129.23/129.50 Found (or_introl10 x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found ((or_introl1 (((mimplies p) (mbox_k p)) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found x10:False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 129.23/129.50 Found x10:False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 129.23/129.50 Found x30:False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 129.23/129.50 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 129.23/129.50 Found x30:False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 129.23/129.50 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 129.23/129.50 Found x4:(((rel_k W) V0)->False)
% 129.23/129.50 Instantiate: V0:=V00:fofType;V:=W:fofType
% 129.23/129.50 Found x4 as proof of (((rel_k V) V00)->False)
% 129.23/129.50 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found ((or_introl1 (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 129.23/129.50 Found or_introl00:=(or_introl0 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found (or_introl0 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 129.23/129.50 Found or_intror00:=(or_intror0 (((rel_k W) V1)->False)):((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)))
% 129.23/129.50 Found (or_intror0 (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 157.50/157.75 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 157.50/157.75 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 157.50/157.75 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 157.50/157.75 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 157.50/157.75 Found x10:False
% 157.50/157.75 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 157.50/157.75 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 157.50/157.75 Found x10:False
% 157.50/157.75 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 157.50/157.75 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 157.50/157.75 Found x30:False
% 157.50/157.75 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 157.50/157.75 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 157.50/157.75 Found x30:False
% 157.50/157.75 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 157.50/157.75 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 157.50/157.75 Found or_introl00:=(or_introl0 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found (or_introl0 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)))
% 157.50/157.75 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 157.50/157.75 Found or_introl00:=(or_introl0 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V1)->False)->((or (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found (or_introl0 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 157.50/157.75 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 178.82/179.14 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 178.82/179.14 Found ((or_introl (((rel_k S) V1)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 178.82/179.14 Found x3:((rel_k V) V0)
% 178.82/179.14 Instantiate: V1:=V0:fofType;V:=W:fofType
% 178.82/179.14 Found x3 as proof of ((rel_k W) V1)
% 178.82/179.14 Found (x5 x3) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of ((((rel_k W) V1)->False)->False)
% 178.82/179.14 Found or_intror10:=(or_intror1 ((mbox_k p) V1)):(((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V1)))
% 178.82/179.14 Found (or_intror1 ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 178.82/179.14 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 178.82/179.14 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 178.82/179.14 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 178.82/179.14 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 178.82/179.14 Found x1:(((rel_k W) V)->False)
% 178.82/179.14 Instantiate: V0:=W:fofType;V:=V1:fofType
% 178.82/179.14 Found x1 as proof of (((rel_k V0) V1)->False)
% 178.82/179.14 Found (or_introl00 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 178.82/179.14 Found ((or_introl0 (((mimplies p) (mbox_k p)) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 178.82/179.14 Found (((or_introl (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 178.82/179.14 Found x30:False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 178.82/179.14 Found x30:False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 178.82/179.14 Found x30:False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 178.82/179.14 Found x10:False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of False
% 178.82/179.14 Found (fun (x5:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V1)->False)
% 178.82/179.14 Found x30:False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 178.82/179.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 178.82/179.14 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 185.68/185.97 Found x1:(((rel_k S) V)->False)
% 185.68/185.97 Instantiate: V0:=S:fofType;V:=V1:fofType
% 185.68/185.97 Found x1 as proof of (((rel_k V0) V1)->False)
% 185.68/185.97 Found (or_introl10 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 185.68/185.97 Found ((or_introl1 (((mimplied (mbox_k p)) p) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 185.68/185.97 Found (((or_introl (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 185.68/185.97 Found x4:(((rel_k W) V0)->False)
% 185.68/185.97 Instantiate: V0:=V00:fofType;V:=W:fofType
% 185.68/185.97 Found x4 as proof of (((rel_k V) V00)->False)
% 185.68/185.97 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 185.68/185.97 Found ((or_introl0 (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 185.68/185.97 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 185.68/185.97 Found x30:False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 185.68/185.97 Found x30:False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of ((((rel_k S) V1)->False)->False)
% 185.68/185.97 Found x10:False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of ((((rel_k S) V1)->False)->False)
% 185.68/185.97 Found x10:False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 185.68/185.97 Found x30:False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 185.68/185.97 Found x10:False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of ((((rel_k S) V1)->False)->False)
% 185.68/185.97 Found x10:False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of False
% 185.68/185.97 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 185.68/185.97 Found x30:False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of False
% 185.68/185.97 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of ((((rel_k S) V1)->False)->False)
% 185.68/185.97 Found x10:False
% 185.68/185.97 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 185.68/185.97 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 198.93/199.21 Found x10:False
% 198.93/199.21 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of False
% 198.93/199.21 Found (fun (x4:(((mbox rel_k) p) V0))=> x10) as proof of ((((mbox rel_k) p) V0)->False)
% 198.93/199.21 Found x30:False
% 198.93/199.21 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 198.93/199.21 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 198.93/199.21 Found x30:False
% 198.93/199.21 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 198.93/199.21 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 198.93/199.21 Found x3:(((rel_k W) V0)->False)
% 198.93/199.21 Instantiate: V0:=V00:fofType;V:=W:fofType
% 198.93/199.21 Found x3 as proof of (((rel_k V) V00)->False)
% 198.93/199.21 Found (or_introl00 x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found ((or_introl0 (((mimplies p) (mbox_k p)) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found x10:False
% 198.93/199.21 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 198.93/199.21 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 198.93/199.21 Found x10:False
% 198.93/199.21 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of False
% 198.93/199.21 Found (fun (x3:(((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mimplies p) (mbox_k p)))) (mbox_k p)) V0)->False)
% 198.93/199.21 Found x4:(((rel_k S) V0)->False)
% 198.93/199.21 Instantiate: V0:=V00:fofType;V:=S:fofType
% 198.93/199.21 Found x4 as proof of (((rel_k V) V00)->False)
% 198.93/199.21 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found ((or_introl1 (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found (((or_introl (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found x4:(((rel_k W) V0)->False)
% 198.93/199.21 Instantiate: V0:=V00:fofType;V:=W:fofType
% 198.93/199.21 Found x4 as proof of (((rel_k V) V00)->False)
% 198.93/199.21 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found ((or_introl0 (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found (((or_introl (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 198.93/199.21 Found or_intror10:=(or_intror1 ((mbox_k p) V1)):(((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V1)))
% 198.93/199.21 Found (or_intror1 ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 198.93/199.21 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 198.93/199.21 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 198.93/199.21 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 198.93/199.21 Found x3:(((rel_k S) V0)->False)
% 198.93/199.21 Instantiate: V0:=V00:fofType;V:=S:fofType
% 198.93/199.21 Found x3 as proof of (((rel_k V) V00)->False)
% 198.93/199.21 Found (or_introl10 x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found ((or_introl1 (((mimplied (mbox_k p)) p) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found (((or_introl (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 198.93/199.21 Found or_intror10:=(or_intror1 (((rel_k W) V1)->False)):((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)))
% 198.93/199.21 Found (or_intror1 (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 198.93/199.21 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplies p) (mbox_k p)) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mimplies p) (mbox_k p)) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found x30:False
% 251.29/251.57 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of False
% 251.29/251.57 Found (fun (x4:((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mimplied (mbox_k p)) p))) V)->False)
% 251.29/251.57 Found x30:False
% 251.29/251.57 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of False
% 251.29/251.57 Found (fun (x4:(((mbox rel_k) p) V))=> x30) as proof of ((((mbox rel_k) p) V)->False)
% 251.29/251.57 Found x4:(((rel_k S) V0)->False)
% 251.29/251.57 Instantiate: V0:=V00:fofType;V:=S:fofType
% 251.29/251.57 Found x4 as proof of (((rel_k V) V00)->False)
% 251.29/251.57 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 251.29/251.57 Found ((or_introl1 (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 251.29/251.57 Found (((or_introl (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 251.29/251.57 Found or_intror00:=(or_intror0 (((rel_k S) V1)->False)):((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k S) V1)->False)))
% 251.29/251.57 Found (or_intror0 (((rel_k S) V1)->False)) as proof of ((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplied (mbox_k p)) p) V0)) (((rel_k S) V1)->False)) as proof of ((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplied (mbox_k p)) p) V0)) (((rel_k S) V1)->False)) as proof of ((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplied (mbox_k p)) p) V0)) (((rel_k S) V1)->False)) as proof of ((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found ((or_intror (((mimplied (mbox_k p)) p) V0)) (((rel_k S) V1)->False)) as proof of ((((rel_k S) V1)->False)->((or (((mimplied (mbox_k p)) p) V0)) (((rel_k V) V0)->False)))
% 251.29/251.57 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 251.29/251.57 Found x10:False
% 251.29/251.57 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of False
% 251.29/251.57 Found (fun (x3:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V0)->False)
% 251.29/251.57 Found x10:False
% 251.29/251.57 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of False
% 251.29/251.57 Found (fun (x3:(((rel_k S) V0)->False))=> x10) as proof of ((((rel_k S) V0)->False)->False)
% 251.29/251.57 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)))
% 262.21/262.53 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 262.21/262.53 Found x1:(((rel_k W) V)->False)
% 262.21/262.53 Instantiate: V0:=W:fofType;V:=V1:fofType
% 262.21/262.53 Found x1 as proof of (((rel_k V0) V1)->False)
% 262.21/262.53 Found (or_intror00 x1) as proof of ((or (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False))
% 262.21/262.53 Found ((or_intror0 (((rel_k V0) V1)->False)) x1) as proof of ((or (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False))
% 262.21/262.53 Found (((or_intror (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) x1) as proof of ((or (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False))
% 262.21/262.53 Found (((or_intror (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) x1) as proof of ((or (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False))
% 262.21/262.53 Found (or_comm_i00 (((or_intror (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) x1)) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 262.21/262.53 Found ((or_comm_i0 (((rel_k V0) V1)->False)) (((or_intror (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) x1)) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 262.21/262.53 Found (((or_comm_i (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) (((or_intror (((mimplies p) (mbox_k p)) V1)) (((rel_k V0) V1)->False)) x1)) as proof of ((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1))
% 262.21/262.53 Found x3:((rel_k V) V0)
% 262.21/262.53 Instantiate: V1:=V0:fofType;V:=W:fofType
% 262.21/262.53 Found x3 as proof of ((rel_k W) V1)
% 262.21/262.53 Found (x5 x3) as proof of False
% 262.21/262.53 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of False
% 262.21/262.53 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of ((((rel_k W) V1)->False)->False)
% 262.21/262.53 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V2)->False)->((or (((rel_k S) V2)->False)) (((mimplied (mbox_k p)) p) V0)))
% 262.21/262.53 Found (or_introl1 (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k S) V2)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k S) V2)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 262.21/262.53 Found ((or_introl (((rel_k S) V2)->False)) (((mimplied (mbox_k p)) p) V0)) as proof of ((((rel_k S) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplied (mbox_k p)) p) V0)))
% 262.21/262.53 Found x3:((rel_k V) V0)
% 262.21/262.53 Instantiate: V1:=V0:fofType;V:=S:fofType
% 262.21/262.53 Found x3 as proof of ((rel_k S) V1)
% 262.21/262.53 Found (x5 x3) as proof of False
% 262.21/262.53 Found (fun (x5:(((rel_k S) V1)->False))=> (x5 x3)) as proof of False
% 262.21/262.53 Found (fun (x5:(((rel_k S) V1)->False))=> (x5 x3)) as proof of ((((rel_k S) V1)->False)->False)
% 262.21/262.53 Found or_intror20:=(or_intror2 ((mbox_k p) V1)):(((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V1)))
% 262.21/262.53 Found (or_intror2 ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 262.21/262.53 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 262.21/262.53 Found ((or_intror ((mnot p) V0)) ((mbox_k p) V1)) as proof of (((mbox_k p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 262.21/262.53 Found x4:(((rel_k W) V0)->False)
% 262.21/262.53 Instantiate: V0:=V00:fofType;V:=W:fofType
% 262.21/262.53 Found x4 as proof of (((rel_k V) V00)->False)
% 262.21/262.53 Found (or_intror00 x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found ((or_intror0 (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (or_comm_i00 (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 269.19/269.47 Found ((or_comm_i0 (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 269.19/269.47 Found (((or_comm_i (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 269.19/269.47 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found (or_introl1 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found ((or_introl (((rel_k W) V1)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 269.19/269.47 Found x3:(((rel_k W) V0)->False)
% 269.19/269.47 Instantiate: V0:=V00:fofType;V:=W:fofType
% 269.19/269.47 Found x3 as proof of (((rel_k V) V00)->False)
% 269.19/269.47 Found (or_intror00 x3) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found ((or_intror0 (((rel_k V) V00)->False)) x3) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x3) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x3) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 269.19/269.47 Found (or_comm_i00 (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x3)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 269.19/269.47 Found ((or_comm_i0 (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x3)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 279.57/279.89 Found (((or_comm_i (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x3)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 279.57/279.89 Found or_intror10:=(or_intror1 (((mbox rel_k) p) V1)):((((mbox rel_k) p) V1)->((or ((mnot p) V0)) (((mbox rel_k) p) V1)))
% 279.57/279.89 Found (or_intror1 (((mbox rel_k) p) V1)) as proof of ((((mbox rel_k) p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 279.57/279.89 Found ((or_intror ((mnot p) V0)) (((mbox rel_k) p) V1)) as proof of ((((mbox rel_k) p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 279.57/279.89 Found ((or_intror ((mnot p) V0)) (((mbox rel_k) p) V1)) as proof of ((((mbox rel_k) p) V1)->((or ((mnot p) V0)) ((mbox_k p) V0)))
% 279.57/279.89 Found x1:(((rel_k S) V)->False)
% 279.57/279.89 Instantiate: V0:=S:fofType;V:=V1:fofType
% 279.57/279.89 Found x1 as proof of (((rel_k V0) V1)->False)
% 279.57/279.89 Found (or_introl00 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 279.57/279.89 Found ((or_introl0 (((mimplied (mbox_k p)) p) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 279.57/279.89 Found (((or_introl (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mimplied (mbox_k p)) p) V1))
% 279.57/279.89 Found x4:(((rel_k W) V0)->False)
% 279.57/279.89 Instantiate: V0:=V00:fofType;V:=W:fofType
% 279.57/279.89 Found x4 as proof of (((rel_k V) V00)->False)
% 279.57/279.89 Found (or_intror00 x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 279.57/279.89 Found ((or_intror0 (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 279.57/279.89 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 279.57/279.89 Found (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4) as proof of ((or (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False))
% 279.57/279.89 Found (or_comm_i00 (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 279.57/279.89 Found ((or_comm_i0 (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 279.57/279.89 Found (((or_comm_i (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) (((or_intror (((mimplies p) (mbox_k p)) V00)) (((rel_k V) V00)->False)) x4)) as proof of ((or (((rel_k V) V00)->False)) (((mimplies p) (mbox_k p)) V00))
% 279.57/279.89 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V1)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found (or_introl1 (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found or_introl10:=(or_introl1 (((mimplies p) (mbox_k p)) V1)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found (or_introl1 (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 279.57/279.89 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V1)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V0) V1)->False)) (((mimplies p) (mbox_k p)) V1)))
% 292.85/293.18 Found x30:False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 292.85/293.18 Found x30:False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of ((((rel_k S) V1)->False)->False)
% 292.85/293.18 Found x10:False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of ((((rel_k S) V1)->False)->False)
% 292.85/293.18 Found x10:False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 292.85/293.18 Found x30:False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x30) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 292.85/293.18 Found x10:False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of False
% 292.85/293.18 Found (fun (x5:(((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1))=> x10) as proof of ((((mimplied ((mbox rel_k) p)) ((mbox rel_k) ((mimplied (mbox_k p)) p))) V1)->False)
% 292.85/293.18 Found x10:False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x10) as proof of ((((rel_k S) V1)->False)->False)
% 292.85/293.18 Found x30:False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of False
% 292.85/293.18 Found (fun (x5:(((rel_k S) V1)->False))=> x30) as proof of ((((rel_k S) V1)->False)->False)
% 292.85/293.18 Found x4:(((rel_k S) V0)->False)
% 292.85/293.18 Instantiate: V0:=V00:fofType;V:=S:fofType
% 292.85/293.18 Found x4 as proof of (((rel_k V) V00)->False)
% 292.85/293.18 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 292.85/293.18 Found ((or_introl0 (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 292.85/293.18 Found (((or_introl (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mimplied (mbox_k p)) p) V00))
% 292.85/293.18 Found or_introl00:=(or_introl0 (((mimplies p) (mbox_k p)) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found (or_introl0 (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found ((or_introl (((rel_k W) V2)->False)) (((mimplies p) (mbox_k p)) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mimplies p) (mbox_k p)) V0)))
% 292.85/293.18 Found or_introl10:=(or_introl1 (((mimplied (mbox_k p)) p) V0)):((((rel_k S) V2)->False)->((or (((rel_k S) V2)->False)) (((mimplied
%------------------------------------------------------------------------------