TSTP Solution File: SYO473^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO473^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 300.03s 300.46s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO473^1 : TPTP v7.5.0. Released v4.0.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Mar 13 07:08:36 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.44/0.61 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.44/0.61 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4fc20>, <kernel.Type object at 0x1d4fb48>) of role type named mu_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring mu:Type
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4fc20>) of role type named meq_ind_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.44/0.61 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
% 0.44/0.61 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.44/0.61 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4fc20>, <kernel.DependentProduct object at 0x1d4fbd8>) of role type named meq_prop_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.61 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
% 0.44/0.61 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))))
% 0.44/0.61 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4fc68>, <kernel.DependentProduct object at 0x1d4fd88>) of role type named mnot_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.44/0.61 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.44/0.61 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.44/0.61 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4f440>) of role type named mor_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.61 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
% 0.44/0.61 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))))
% 0.44/0.61 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4f440>, <kernel.DependentProduct object at 0x1d4f6c8>) of role type named mand_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.61 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
% 0.44/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.44/0.61 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.44/0.61 FOF formula (<kernel.Constant object at 0x1d4f6c8>, <kernel.DependentProduct object at 0x1d4f4d0>) of role type named mimplies_type
% 0.44/0.61 Using role type
% 0.44/0.61 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.44/0.61 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
% 0.44/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.44/0.61 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4f4d0>, <kernel.DependentProduct object at 0x1d4f908>) of role type named mimplied_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.62 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
% 0.46/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.46/0.62 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4f908>, <kernel.DependentProduct object at 0x1d4fd88>) of role type named mequiv_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.62 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
% 0.46/0.62 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))))
% 0.46/0.62 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4f440>) of role type named mxor_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.62 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
% 0.46/0.62 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.46/0.62 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4fc20>, <kernel.DependentProduct object at 0x1d4f908>) of role type named mforall_ind_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.46/0.62 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
% 0.46/0.62 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.46/0.62 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4f908>, <kernel.DependentProduct object at 0x1d4f098>) of role type named mforall_prop_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.46/0.62 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
% 0.46/0.62 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))))
% 0.46/0.62 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.46/0.62 FOF formula (<kernel.Constant object at 0x1d4f098>, <kernel.DependentProduct object at 0x1d4fd88>) of role type named mexists_ind_type
% 0.46/0.62 Using role type
% 0.46/0.62 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.46/0.62 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
% 0.46/0.62 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)))))))
% 0.46/0.63 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4f0e0>) of role type named mexists_prop_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.46/0.63 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
% 0.46/0.63 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)))))))
% 0.46/0.63 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1d4f0e0>, <kernel.DependentProduct object at 0x1d4f488>) of role type named mtrue_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mtrue:(fofType->Prop)
% 0.46/0.63 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.46/0.63 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.46/0.63 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1d4f488>, <kernel.DependentProduct object at 0x1d4fb48>) of role type named mfalse_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mfalse:(fofType->Prop)
% 0.46/0.63 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.46/0.63 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.46/0.63 Defined: mfalse:=(mnot mtrue)
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1d4fd88>, <kernel.DependentProduct object at 0x1d4f6c8>) of role type named mbox_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.63 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
% 0.46/0.63 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)))))
% 0.46/0.63 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1bdbea8>, <kernel.DependentProduct object at 0x1d4f098>) of role type named mdia_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.63 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
% 0.46/0.63 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)))))
% 0.46/0.63 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1bdbc68>, <kernel.DependentProduct object at 0x1d4f320>) of role type named mreflexive_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.46/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.46/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.46/0.63 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1d4f320>, <kernel.DependentProduct object at 0x1d4f0e0>) of role type named msymmetric_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.64 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)))))
% 0.48/0.64 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1be3fc8>, <kernel.DependentProduct object at 0x1be39e0>) of role type named mserial_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.64 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))))))
% 0.48/0.64 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1be39e0>, <kernel.DependentProduct object at 0x1be3ab8>) of role type named mtransitive_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.64 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)))))
% 0.48/0.64 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1be3f38>, <kernel.DependentProduct object at 0x1d4f320>) of role type named meuclidean_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.64 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)))))
% 0.48/0.64 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1be37e8>, <kernel.DependentProduct object at 0x1d4f0e0>) of role type named mpartially_functional_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.64 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)))))
% 0.48/0.64 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))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1be37e8>, <kernel.DependentProduct object at 0x1d4f320>) of role type named mfunctional_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.48/0.64 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
% 0.48/0.65 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)))))))))
% 0.48/0.65 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))))))))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1be37e8>, <kernel.DependentProduct object at 0x1d4f098>) of role type named mweakly_dense_type
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.48/0.65 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
% 0.48/0.65 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)))))))))
% 0.48/0.65 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))))))))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1d4f6c8>, <kernel.DependentProduct object at 0x1d4f098>) of role type named mweakly_connected_type
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.48/0.65 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
% 0.48/0.65 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))))))
% 0.48/0.65 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)))))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1d4f200>, <kernel.DependentProduct object at 0x1d4f098>) of role type named mweakly_directed_type
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.48/0.65 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
% 0.48/0.65 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))))))))
% 0.48/0.65 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)))))))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1d4fb48>, <kernel.DependentProduct object at 0x1d58098>) of role type named mvalid_type
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring mvalid:((fofType->Prop)->Prop)
% 0.48/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.48/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.48/0.65 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.48/0.65 FOF formula (<kernel.Constant object at 0x1d4f6c8>, <kernel.DependentProduct object at 0x1d583b0>) of role type named minvalid_type
% 0.48/0.65 Using role type
% 0.48/0.65 Declaring minvalid:((fofType->Prop)->Prop)
% 0.48/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.48/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.48/0.66 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1d584d0>, <kernel.DependentProduct object at 0x1d58638>) of role type named msatisfiable_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.48/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.48/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.48/0.66 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1d583b0>, <kernel.DependentProduct object at 0x1d58200>) of role type named mcountersatisfiable_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.48/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.48/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.48/0.66 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.48/0.66 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^1.ax, trying next directory
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1bdbc68>, <kernel.DependentProduct object at 0x1be3a28>) of role type named rel_k_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring rel_k:(fofType->(fofType->Prop))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1be3710>, <kernel.DependentProduct object at 0x1be3b48>) of role type named mbox_k_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mbox_k:((fofType->Prop)->(fofType->Prop))
% 0.48/0.66 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
% 0.48/0.66 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)))))
% 0.48/0.66 Defined: mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V))))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1be3b48>, <kernel.DependentProduct object at 0x1be3a28>) of role type named mdia_k_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring mdia_k:((fofType->Prop)->(fofType->Prop))
% 0.48/0.66 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))) of role definition named mdia_k
% 0.48/0.66 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_k) (fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))))
% 0.48/0.66 Defined: mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi))))
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1be0f38>, <kernel.DependentProduct object at 0x2ac7578033b0>) of role type named p_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring p:(fofType->Prop)
% 0.48/0.66 FOF formula (<kernel.Constant object at 0x1be0998>, <kernel.DependentProduct object at 0x2ac757803ab8>) of role type named q_type
% 0.48/0.66 Using role type
% 0.48/0.66 Declaring q:(fofType->Prop)
% 0.48/0.66 FOF formula (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)))) (mbox_k ((mimplies (mbox_k ((mequiv p) q))) q)))) of role conjecture named prove
% 0.48/0.66 Conjecture to prove = (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)))) (mbox_k ((mimplies (mbox_k ((mequiv p) q))) q)))):Prop
% 0.48/0.66 Parameter mu_DUMMY:mu.
% 0.48/0.66 Parameter fofType_DUMMY:fofType.
% 0.48/0.66 We need to prove ['(mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)))) (mbox_k ((mimplies (mbox_k ((mequiv p) q))) q))))']
% 0.48/0.66 Parameter mu:Type.
% 0.48/0.66 Parameter fofType:Type.
% 0.48/0.66 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.48/0.66 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.48/0.66 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.66 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.66 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.66 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)).
% 0.48/0.66 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.48/0.66 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.48/0.66 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))).
% 0.48/0.66 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.66 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.66 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.66 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.66 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).
% 0.48/0.66 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).
% 0.48/0.66 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).
% 0.48/0.66 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).
% 0.48/0.66 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).
% 0.48/0.66 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).
% 14.88/15.07 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).
% 14.88/15.07 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 14.88/15.07 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 14.88/15.07 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 14.88/15.07 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 14.88/15.07 Parameter rel_k:(fofType->(fofType->Prop)).
% 14.88/15.07 Definition mbox_k:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_k W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 14.88/15.07 Definition mdia_k:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_k (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 14.88/15.07 Parameter p:(fofType->Prop).
% 14.88/15.07 Parameter q:(fofType->Prop).
% 14.88/15.07 Trying to prove (mvalid ((mimplies (mbox_k ((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)))) (mbox_k ((mimplies (mbox_k ((mequiv p) q))) q))))
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 14.88/15.07 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 14.88/15.07 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 14.88/15.07 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 14.88/15.07 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 14.88/15.07 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 14.88/15.07 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 14.88/15.07 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 14.88/15.07 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 14.88/15.07 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 14.88/15.07 Found x10:False
% 14.88/15.07 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 14.88/15.07 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 49.04/49.25 Found x30:False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 49.04/49.25 Found x30:False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 49.04/49.25 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 49.04/49.25 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 49.04/49.25 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 49.04/49.25 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 49.04/49.25 Found x30:False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 49.04/49.25 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 49.04/49.25 Found x30:False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 49.04/49.25 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 49.04/49.25 Found x10:False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 49.04/49.25 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 62.95/63.16 Found x10:False
% 62.95/63.16 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 62.95/63.16 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 62.95/63.16 Found x10:False
% 62.95/63.16 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 62.95/63.16 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 62.95/63.16 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 62.95/63.16 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 62.95/63.16 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 62.95/63.16 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 62.95/63.16 Found x10:False
% 62.95/63.16 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 62.95/63.16 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 62.95/63.16 Found x10:False
% 62.95/63.16 Found (fun (x3:(((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0))=> x10) as proof of False
% 85.41/85.61 Found (fun (x3:(((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0))=> x10) as proof of ((((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0)->False)
% 85.41/85.61 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 85.41/85.61 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 85.41/85.61 Found x10:False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 85.41/85.61 Found x10:False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 85.41/85.61 Found x10:False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 85.41/85.61 Found x10:False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 85.41/85.61 Found x30:False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 85.41/85.61 Found x30:False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 85.41/85.61 Found x30:False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 85.41/85.61 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 85.41/85.61 Found x30:False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 85.41/85.61 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 85.41/85.61 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 85.41/85.61 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 85.41/85.61 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 104.42/104.68 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 104.42/104.68 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 104.42/104.68 Found x10:False
% 104.42/104.68 Found (fun (x3:(((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0))=> x10) as proof of False
% 104.42/104.68 Found (fun (x3:(((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0))=> x10) as proof of ((((mor (mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p))))) (mnot ((mbox rel_k) (mnot q)))) V0)->False)
% 104.42/104.68 Found x10:False
% 104.42/104.68 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 104.42/104.68 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 104.42/104.68 Found or_introl10:=(or_introl1 (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 104.42/104.68 Found (or_introl1 (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 104.42/104.68 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 125.93/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 125.93/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 125.93/126.18 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 125.93/126.18 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.93/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.93/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.93/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 125.98/126.18 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 125.98/126.18 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found ((or_introl (((rel_k W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 125.98/126.18 Found x10:False
% 125.98/126.18 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 125.98/126.18 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 125.98/126.18 Found x10:False
% 125.98/126.18 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 125.98/126.18 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 125.98/126.18 Found x10:False
% 125.98/126.18 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of False
% 125.98/126.18 Found (fun (x4:((mdia_k q) V0))=> x10) as proof of (((mdia_k q) V0)->False)
% 125.98/126.18 Found x10:False
% 125.98/126.18 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of False
% 125.98/126.18 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V0))=> x10) as proof of (((mnot (mbox_k ((mequiv p) q))) V0)->False)
% 125.98/126.18 Found x1:(((rel_k W) V)->False)
% 125.98/126.18 Instantiate: V0:=W:fofType;V:=V1:fofType
% 125.98/126.18 Found x1 as proof of (((rel_k V0) V1)->False)
% 125.98/126.18 Found (or_introl10 x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 125.98/126.18 Found ((or_introl1 ((mnot q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 125.98/126.18 Found (((or_introl (((rel_k V0) V1)->False)) ((mnot q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 125.98/126.18 Found x30:False
% 125.98/126.18 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 135.89/136.14 Found x1:(((rel_k W) V)->False)
% 135.89/136.14 Instantiate: V0:=W:fofType;V:=V1:fofType
% 135.89/136.14 Found x1 as proof of (((rel_k V0) V1)->False)
% 135.89/136.14 Found (or_introl10 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 135.89/136.14 Found ((or_introl1 (((mequiv p) q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 135.89/136.14 Found (((or_introl (((rel_k V0) V1)->False)) (((mequiv p) q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 135.89/136.14 Found x10:False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 135.89/136.14 Found x10:False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 135.89/136.14 Found x10:False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of False
% 135.89/136.14 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 135.89/136.14 Found x10:False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 135.89/136.14 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 135.89/136.14 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 135.89/136.14 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of False
% 135.89/136.14 Found (fun (x4:((mnot (mbox_k ((mequiv p) q))) V))=> x30) as proof of (((mnot (mbox_k ((mequiv p) q))) V)->False)
% 135.89/136.14 Found x30:False
% 135.89/136.14 Found (fun (x4:((mdia_k q) V))=> x30) as proof of False
% 135.89/136.14 Found (fun (x4:((mdia_k q) V))=> x30) as proof of (((mdia_k q) V)->False)
% 135.89/136.14 Found x4:(((rel_k W) V0)->False)
% 135.89/136.14 Instantiate: V0:=V00:fofType;V:=W:fofType
% 135.89/136.14 Found x4 as proof of (((rel_k V) V00)->False)
% 135.89/136.14 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 135.89/136.14 Found ((or_introl1 ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 135.89/136.14 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 135.89/136.14 Found x4:(((rel_k W) V0)->False)
% 135.89/136.14 Instantiate: V0:=V00:fofType;V:=W:fofType
% 135.89/136.14 Found x4 as proof of (((rel_k V) V00)->False)
% 135.89/136.14 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 135.89/136.14 Found ((or_introl1 (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 135.89/136.14 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 135.89/136.14 Found x3:(((rel_k W) V0)->False)
% 135.89/136.14 Instantiate: V0:=V00:fofType;V:=W:fofType
% 135.89/136.14 Found x3 as proof of (((rel_k V) V00)->False)
% 135.89/136.14 Found (or_introl10 x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 135.89/136.14 Found ((or_introl1 ((mnot q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 135.89/136.14 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 167.79/168.04 Found x3:(((rel_k W) V0)->False)
% 167.79/168.04 Instantiate: V0:=V00:fofType;V:=W:fofType
% 167.79/168.04 Found x3 as proof of (((rel_k V) V00)->False)
% 167.79/168.04 Found (or_introl10 x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found ((or_introl1 (((mequiv p) q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found x4:(((rel_k W) V0)->False)
% 167.79/168.04 Instantiate: V0:=V00:fofType;V:=W:fofType
% 167.79/168.04 Found x4 as proof of (((rel_k V) V00)->False)
% 167.79/168.04 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 167.79/168.04 Found ((or_introl1 ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 167.79/168.04 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 167.79/168.04 Found x4:(((rel_k W) V0)->False)
% 167.79/168.04 Instantiate: V0:=V00:fofType;V:=W:fofType
% 167.79/168.04 Found x4 as proof of (((rel_k V) V00)->False)
% 167.79/168.04 Found (or_introl10 x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found ((or_introl1 (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 167.79/168.04 Found or_intror00:=(or_intror0 (((rel_k W) V1)->False)):((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k W) V1)->False)))
% 167.79/168.04 Found (or_intror0 (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found or_intror00:=(or_intror0 (((rel_k W) V1)->False)):((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k W) V1)->False)))
% 167.79/168.04 Found (or_intror0 (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror (((mequiv p) q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror (((mequiv p) q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror (((mequiv p) q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found ((or_intror (((mequiv p) q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or (((mequiv p) q) V0)) (((rel_k V) V0)->False)))
% 167.79/168.04 Found x10:False
% 167.79/168.04 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 167.79/168.04 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 167.79/168.04 Found x10:False
% 167.79/168.04 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 167.79/168.04 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 167.79/168.04 Found x10:False
% 167.79/168.04 Found (fun (x4:((mnot ((mbox rel_k) (mnot q))) V0))=> x10) as proof of False
% 167.79/168.04 Found (fun (x4:((mnot ((mbox rel_k) (mnot q))) V0))=> x10) as proof of (((mnot ((mbox rel_k) (mnot q))) V0)->False)
% 167.79/168.04 Found x10:False
% 167.79/168.04 Found (fun (x4:((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V0))=> x10) as proof of False
% 167.79/168.04 Found (fun (x4:((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V0))=> x10) as proof of (((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V0)->False)
% 167.79/168.04 Found x30:False
% 167.79/168.04 Found (fun (x4:((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V))=> x30) as proof of False
% 191.46/191.69 Found (fun (x4:((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V))=> x30) as proof of (((mnot ((mbox rel_k) ((mand ((mimplies p) q)) ((mor (mnot q)) p)))) V)->False)
% 191.46/191.69 Found x30:False
% 191.46/191.69 Found (fun (x4:((mnot ((mbox rel_k) (mnot q))) V))=> x30) as proof of False
% 191.46/191.69 Found (fun (x4:((mnot ((mbox rel_k) (mnot q))) V))=> x30) as proof of (((mnot ((mbox rel_k) (mnot q))) V)->False)
% 191.46/191.69 Found or_introl00:=(or_introl0 (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found (or_introl0 (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) (((mand ((mimplies p) q)) ((mor (mnot q)) p)) V0)))
% 191.46/191.69 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_k W) V1)->False)->((or (((rel_k W) V1)->False)) ((mnot q) V0)))
% 191.46/191.69 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V1)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) ((mnot q) V0)))
% 191.46/191.69 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 191.46/191.69 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mequiv p) q) V0)))
% 191.46/191.69 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 191.46/191.69 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 191.46/191.69 Found x3:((rel_k V) V0)
% 191.46/191.69 Instantiate: V1:=V0:fofType;V:=W:fofType
% 191.46/191.69 Found x3 as proof of ((rel_k W) V1)
% 191.46/191.69 Found (x5 x3) as proof of False
% 191.46/191.69 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of False
% 221.90/222.16 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.16 Found x3:((rel_k V) V0)
% 221.90/222.16 Instantiate: V1:=V0:fofType;V:=W:fofType
% 221.90/222.16 Found x3 as proof of ((rel_k W) V1)
% 221.90/222.16 Found (x5 x3) as proof of False
% 221.90/222.16 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of False
% 221.90/222.16 Found (fun (x5:(((rel_k W) V1)->False))=> (x5 x3)) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.16 Found x1:(((rel_k W) V)->False)
% 221.90/222.16 Instantiate: V0:=W:fofType;V:=V1:fofType
% 221.90/222.16 Found x1 as proof of (((rel_k V0) V1)->False)
% 221.90/222.16 Found (or_introl00 x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 221.90/222.16 Found ((or_introl0 ((mnot q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 221.90/222.16 Found (((or_introl (((rel_k V0) V1)->False)) ((mnot q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) ((mnot q) V1))
% 221.90/222.16 Found x1:(((rel_k W) V)->False)
% 221.90/222.16 Instantiate: V0:=W:fofType;V:=V1:fofType
% 221.90/222.16 Found x1 as proof of (((rel_k V0) V1)->False)
% 221.90/222.16 Found (or_introl00 x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 221.90/222.16 Found ((or_introl0 (((mequiv p) q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 221.90/222.17 Found (((or_introl (((rel_k V0) V1)->False)) (((mequiv p) q) V1)) x1) as proof of ((or (((rel_k V0) V1)->False)) (((mequiv p) q) V1))
% 221.90/222.17 Found x30:False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 221.90/222.17 Found x30:False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.17 Found x10:False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.17 Found x10:False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 221.90/222.17 Found x30:False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x30) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.17 Found x10:False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 221.90/222.17 Found x30:False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of False
% 221.90/222.17 Found (fun (x5:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1))=> x30) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V1)->False)
% 221.90/222.17 Found x10:False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of False
% 221.90/222.17 Found (fun (x5:(((rel_k W) V1)->False))=> x10) as proof of ((((rel_k W) V1)->False)->False)
% 221.90/222.17 Found x4:(((rel_k W) V0)->False)
% 221.90/222.17 Instantiate: V0:=V00:fofType;V:=W:fofType
% 221.90/222.17 Found x4 as proof of (((rel_k V) V00)->False)
% 221.90/222.17 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 221.90/222.17 Found ((or_introl0 ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 221.90/222.17 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 221.90/222.17 Found x4:(((rel_k W) V0)->False)
% 221.90/222.17 Instantiate: V0:=V00:fofType;V:=W:fofType
% 221.90/222.17 Found x4 as proof of (((rel_k V) V00)->False)
% 221.90/222.17 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 221.90/222.17 Found ((or_introl0 (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 221.90/222.17 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 221.90/222.17 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) (((mequiv p) q) V0)))
% 221.90/222.17 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) (((mequiv p) q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) (((mequiv p) q) V0)))
% 240.84/241.09 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_k W) V2)->False)->((or (((rel_k W) V2)->False)) ((mnot q) V0)))
% 240.84/241.09 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 240.84/241.09 Found ((or_introl (((rel_k W) V2)->False)) ((mnot q) V0)) as proof of ((((rel_k W) V2)->False)->((or (((rel_k V) V0)->False)) ((mnot q) V0)))
% 240.84/241.09 Found x3:(((rel_k W) V0)->False)
% 240.84/241.09 Instantiate: V0:=V00:fofType;V:=W:fofType
% 240.84/241.09 Found x3 as proof of (((rel_k V) V00)->False)
% 240.84/241.09 Found (or_introl00 x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found ((or_introl0 ((mnot q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found x3:(((rel_k W) V0)->False)
% 240.84/241.09 Instantiate: V0:=V00:fofType;V:=W:fofType
% 240.84/241.09 Found x3 as proof of (((rel_k V) V00)->False)
% 240.84/241.09 Found (or_introl00 x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found ((or_introl0 (((mequiv p) q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x3) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found x4:(((rel_k W) V0)->False)
% 240.84/241.09 Instantiate: V0:=V00:fofType;V:=W:fofType
% 240.84/241.09 Found x4 as proof of (((rel_k V) V00)->False)
% 240.84/241.09 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found ((or_introl0 ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found (((or_introl (((rel_k V) V00)->False)) ((mnot q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) ((mnot q) V00))
% 240.84/241.09 Found x10:False
% 240.84/241.09 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of False
% 240.84/241.09 Found (fun (x3:(((rel_k W) V0)->False))=> x10) as proof of ((((rel_k W) V0)->False)->False)
% 240.84/241.09 Found x10:False
% 240.84/241.09 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of False
% 240.84/241.09 Found (fun (x3:(((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0))=> x10) as proof of ((((mimplies (mbox_k ((mequiv p) q))) (mdia_k q)) V0)->False)
% 240.84/241.09 Found x4:(((rel_k W) V0)->False)
% 240.84/241.09 Instantiate: V0:=V00:fofType;V:=W:fofType
% 240.84/241.09 Found x4 as proof of (((rel_k V) V00)->False)
% 240.84/241.09 Found (or_introl00 x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found ((or_introl0 (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found (((or_introl (((rel_k V) V00)->False)) (((mequiv p) q) V00)) x4) as proof of ((or (((rel_k V) V00)->False)) (((mequiv p) q) V00))
% 240.84/241.09 Found or_intror10:=(or_intror1 (((rel_k W) V1)->False)):((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k W) V1)->False)))
% 240.84/241.09 Found (or_intror1 (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 240.84/241.09 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)->False)) as proof of ((((rel_k W) V1)->False)->((or ((mnot q) V0)) (((rel_k V) V0)->False)))
% 240.84/241.09 Found ((or_intror ((mnot q) V0)) (((rel_k W) V1)-
%------------------------------------------------------------------------------