TSTP Solution File: SYO490^6 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO490^6 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n021.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 00:51:54 EDT 2022
% Result : Timeout 294.02s 294.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO490^6 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n021.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 10:09:11 EDT 2022
% 0.12/0.33 % 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
% 0.19/0.55 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.19/0.55 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x1fc4b90>, <kernel.Type object at 0x1fc4128>) of role type named mu_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring mu:Type
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x1fc4ef0>, <kernel.DependentProduct object at 0x1fc4b90>) of role type named meq_ind_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.19/0.55 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
% 0.19/0.55 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.19/0.55 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x2af4cfcec050>, <kernel.DependentProduct object at 0x1fc4ef0>) of role type named meq_prop_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.55 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
% 0.19/0.55 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))))
% 0.19/0.55 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x2af4cfcec098>, <kernel.DependentProduct object at 0x1fc4128>) of role type named mnot_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.19/0.55 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.19/0.55 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.19/0.55 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x1fc4dd0>, <kernel.DependentProduct object at 0x1fc4128>) of role type named mor_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.55 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
% 0.19/0.55 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))))
% 0.19/0.55 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x1fc4d40>, <kernel.DependentProduct object at 0x1fc4b90>) of role type named mand_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.55 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
% 0.19/0.55 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.19/0.55 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.19/0.55 FOF formula (<kernel.Constant object at 0x1fc43f8>, <kernel.DependentProduct object at 0x1f9e5a8>) of role type named mimplies_type
% 0.19/0.55 Using role type
% 0.19/0.55 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.55 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
% 0.19/0.55 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.19/0.55 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x1fc43f8>, <kernel.DependentProduct object at 0x1f9ea28>) of role type named mimplied_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.56 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
% 0.19/0.56 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.19/0.56 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x1fc4dd0>, <kernel.DependentProduct object at 0x1f9ec68>) of role type named mequiv_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.56 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
% 0.19/0.56 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))))
% 0.19/0.56 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x2af4cfce5ea8>, <kernel.DependentProduct object at 0x1f9ecb0>) of role type named mxor_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.56 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
% 0.19/0.56 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.19/0.56 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x1f9e5f0>, <kernel.DependentProduct object at 0x1f9e638>) of role type named mforall_ind_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.19/0.56 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
% 0.19/0.56 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.19/0.56 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x1f9e638>, <kernel.DependentProduct object at 0x1f9ea70>) of role type named mforall_prop_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.19/0.56 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
% 0.19/0.56 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))))
% 0.19/0.56 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.19/0.56 FOF formula (<kernel.Constant object at 0x1f9ea70>, <kernel.DependentProduct object at 0x1f9eb48>) of role type named mexists_ind_type
% 0.19/0.56 Using role type
% 0.19/0.56 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.19/0.56 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
% 0.19/0.56 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)))))))
% 0.19/0.57 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1f9ec68>, <kernel.DependentProduct object at 0x1f9e9e0>) of role type named mexists_prop_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.19/0.57 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
% 0.19/0.57 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)))))))
% 0.19/0.57 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1fbb200>, <kernel.DependentProduct object at 0x1f9ed40>) of role type named mtrue_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mtrue:(fofType->Prop)
% 0.19/0.57 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.19/0.57 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.19/0.57 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1fbb200>, <kernel.DependentProduct object at 0x1f9ed40>) of role type named mfalse_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mfalse:(fofType->Prop)
% 0.19/0.57 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.19/0.57 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.19/0.57 Defined: mfalse:=(mnot mtrue)
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1fbbbd8>, <kernel.DependentProduct object at 0x1f9ed40>) of role type named mbox_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.57 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
% 0.19/0.57 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)))))
% 0.19/0.57 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1f9ed40>, <kernel.DependentProduct object at 0x1f9ea70>) of role type named mdia_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.19/0.57 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
% 0.19/0.57 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)))))
% 0.19/0.57 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1f9ec68>, <kernel.DependentProduct object at 0x1fc1950>) of role type named mreflexive_type
% 0.19/0.57 Using role type
% 0.19/0.57 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.19/0.57 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.19/0.57 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.19/0.57 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.19/0.57 FOF formula (<kernel.Constant object at 0x1f9eb90>, <kernel.DependentProduct object at 0x1fc1440>) of role type named msymmetric_type
% 0.19/0.57 Using role type
% 0.19/0.58 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.58 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)))))
% 0.19/0.58 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.19/0.58 FOF formula (<kernel.Constant object at 0x1fc0950>, <kernel.DependentProduct object at 0x1fc13b0>) of role type named mserial_type
% 0.19/0.58 Using role type
% 0.19/0.58 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.58 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))))))
% 0.19/0.58 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.19/0.58 FOF formula (<kernel.Constant object at 0x1f9ec68>, <kernel.DependentProduct object at 0x1fc1e60>) of role type named mtransitive_type
% 0.19/0.58 Using role type
% 0.19/0.58 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.58 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)))))
% 0.19/0.58 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.19/0.58 FOF formula (<kernel.Constant object at 0x1fc1e60>, <kernel.DependentProduct object at 0x1fc1cf8>) of role type named meuclidean_type
% 0.19/0.58 Using role type
% 0.19/0.58 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.58 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)))))
% 0.19/0.58 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.19/0.58 FOF formula (<kernel.Constant object at 0x1fc1cf8>, <kernel.DependentProduct object at 0x1fc1680>) of role type named mpartially_functional_type
% 0.19/0.58 Using role type
% 0.19/0.58 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.58 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)))))
% 0.19/0.58 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))))
% 0.19/0.58 FOF formula (<kernel.Constant object at 0x1fc1680>, <kernel.DependentProduct object at 0x1fc1f38>) of role type named mfunctional_type
% 0.19/0.58 Using role type
% 0.19/0.58 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.19/0.58 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
% 0.19/0.59 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)))))))))
% 0.19/0.59 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))))))))
% 0.19/0.59 FOF formula (<kernel.Constant object at 0x1fc1f38>, <kernel.DependentProduct object at 0x1fc1b48>) of role type named mweakly_dense_type
% 0.19/0.59 Using role type
% 0.19/0.59 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.19/0.59 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
% 0.19/0.59 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)))))))))
% 0.19/0.59 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))))))))
% 0.19/0.59 FOF formula (<kernel.Constant object at 0x1fc1b48>, <kernel.DependentProduct object at 0x1fc1c20>) of role type named mweakly_connected_type
% 0.19/0.59 Using role type
% 0.19/0.59 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.19/0.59 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
% 0.19/0.59 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))))))
% 0.19/0.59 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)))))
% 0.19/0.59 FOF formula (<kernel.Constant object at 0x1fc1c20>, <kernel.DependentProduct object at 0x1fc1560>) of role type named mweakly_directed_type
% 0.19/0.59 Using role type
% 0.19/0.59 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.19/0.59 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
% 0.19/0.59 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))))))))
% 0.19/0.59 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)))))))
% 0.19/0.59 FOF formula (<kernel.Constant object at 0x1fc17a0>, <kernel.DependentProduct object at 0x1fc1440>) of role type named mvalid_type
% 0.19/0.59 Using role type
% 0.19/0.59 Declaring mvalid:((fofType->Prop)->Prop)
% 0.19/0.59 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.19/0.59 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.19/0.59 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.19/0.59 FOF formula (<kernel.Constant object at 0x1fc1c20>, <kernel.DependentProduct object at 0x2af4c8234200>) of role type named minvalid_type
% 0.19/0.59 Using role type
% 0.19/0.59 Declaring minvalid:((fofType->Prop)->Prop)
% 0.19/0.59 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.19/0.60 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.19/0.60 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x1fc1cf8>, <kernel.DependentProduct object at 0x2af4c82345f0>) of role type named msatisfiable_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.19/0.60 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.19/0.60 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.19/0.60 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x1fc1290>, <kernel.DependentProduct object at 0x2af4c82345f0>) of role type named mcountersatisfiable_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.19/0.60 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.19/0.60 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.19/0.60 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.19/0.60 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^6.ax, trying next directory
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x1fc4cb0>, <kernel.DependentProduct object at 0x1fc45f0>) of role type named rel_s5_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring rel_s5:(fofType->(fofType->Prop))
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x1fc4b00>, <kernel.DependentProduct object at 0x1fc4950>) of role type named mbox_s5_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring mbox_s5:((fofType->Prop)->(fofType->Prop))
% 0.19/0.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s5) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V))))) of role definition named mbox_s5
% 0.19/0.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s5) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V)))))
% 0.19/0.60 Defined: mbox_s5:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V))))
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x1fc4950>, <kernel.DependentProduct object at 0x1fc43f8>) of role type named mdia_s5_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring mdia_s5:((fofType->Prop)->(fofType->Prop))
% 0.19/0.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s5) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi))))) of role definition named mdia_s5
% 0.19/0.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s5) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi)))))
% 0.19/0.60 Defined: mdia_s5:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi))))
% 0.19/0.60 FOF formula (mreflexive rel_s5) of role axiom named a1
% 0.19/0.60 A new axiom: (mreflexive rel_s5)
% 0.19/0.60 FOF formula (mtransitive rel_s5) of role axiom named a2
% 0.19/0.60 A new axiom: (mtransitive rel_s5)
% 0.19/0.60 FOF formula (msymmetric rel_s5) of role axiom named a3
% 0.19/0.60 A new axiom: (msymmetric rel_s5)
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x2af4cfd07950>, <kernel.Constant object at 0x2af4cfd07170>) of role type named a_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring a:mu
% 0.19/0.60 FOF formula (<kernel.Constant object at 0x2af4cfd07b90>, <kernel.DependentProduct object at 0x2af4cfd07fc8>) of role type named r_type
% 0.19/0.60 Using role type
% 0.19/0.60 Declaring r:(mu->(mu->(fofType->Prop)))
% 0.19/0.60 FOF formula (mvalid ((mimplies (mexists_ind (fun (X:mu)=> (mdia_s5 ((r a) X))))) (mdia_s5 (mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))))))) of role conjecture named prove
% 0.19/0.60 Conjecture to prove = (mvalid ((mimplies (mexists_ind (fun (X:mu)=> (mdia_s5 ((r a) X))))) (mdia_s5 (mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))))))):Prop
% 0.19/0.60 Parameter fofType_DUMMY:fofType.
% 0.19/0.60 We need to prove ['(mvalid ((mimplies (mexists_ind (fun (X:mu)=> (mdia_s5 ((r a) X))))) (mdia_s5 (mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))))))']
% 0.19/0.60 Parameter mu:Type.
% 0.19/0.60 Parameter fofType:Type.
% 0.19/0.60 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.19/0.60 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.19/0.60 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.19/0.60 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.19/0.60 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.19/0.60 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)).
% 0.19/0.60 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.19/0.60 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.19/0.60 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))).
% 0.19/0.60 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.19/0.60 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.19/0.60 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.19/0.60 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.19/0.60 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).
% 0.19/0.60 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).
% 0.19/0.60 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).
% 0.19/0.60 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).
% 0.19/0.60 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).
% 5.33/5.51 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).
% 5.33/5.51 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).
% 5.33/5.51 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 5.33/5.51 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 5.33/5.51 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 5.33/5.51 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 5.33/5.51 Parameter rel_s5:(fofType->(fofType->Prop)).
% 5.33/5.51 Definition mbox_s5:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s5 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 5.33/5.51 Definition mdia_s5:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s5 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 5.33/5.51 Axiom a1:(mreflexive rel_s5).
% 5.33/5.51 Axiom a2:(mtransitive rel_s5).
% 5.33/5.51 Axiom a3:(msymmetric rel_s5).
% 5.33/5.51 Parameter a:mu.
% 5.33/5.51 Parameter r:(mu->(mu->(fofType->Prop))).
% 5.33/5.51 Trying to prove (mvalid ((mimplies (mexists_ind (fun (X:mu)=> (mdia_s5 ((r a) X))))) (mdia_s5 (mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))))))
% 5.33/5.51 Found a10:=(a1 W):((rel_s5 W) W)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (x1 (a1 W)) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 5.33/5.51 Found a10:=(a1 S):((rel_s5 S) S)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (x1 (a1 S)) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 5.33/5.51 Found a10:=(a1 W):((rel_s5 W) W)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (a1 W) as proof of ((rel_s5 W) V)
% 5.33/5.51 Found (x1 (a1 W)) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 5.33/5.51 Found a10:=(a1 S):((rel_s5 S) S)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (a1 S) as proof of ((rel_s5 S) V)
% 5.33/5.51 Found (x1 (a1 S)) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 5.33/5.51 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 5.33/5.51 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 5.33/5.51 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 5.33/5.51 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 5.33/5.51 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 7.22/7.38 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found a10:=(a1 W):((rel_s5 W) W)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (x3 (a1 W)) as proof of False
% 7.22/7.38 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 7.22/7.38 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 7.22/7.38 Found a10:=(a1 W):((rel_s5 W) W)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (a1 W) as proof of ((rel_s5 W) V0)
% 7.22/7.38 Found (x3 (a1 W)) as proof of False
% 7.22/7.38 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 7.22/7.38 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 7.22/7.38 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 7.22/7.38 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 12.62/12.84 Found a10:=(a1 S):((rel_s5 S) S)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (x3 (a1 S)) as proof of False
% 12.62/12.84 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 12.62/12.84 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 12.62/12.84 Found a10:=(a1 S):((rel_s5 S) S)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V0)
% 12.62/12.84 Found (x3 (a1 S)) as proof of False
% 12.62/12.84 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 12.62/12.84 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 12.62/12.84 Found a10:=(a1 W):((rel_s5 W) W)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (x1 (a1 W)) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 12.62/12.84 Found a10:=(a1 W):((rel_s5 W) W)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (a1 W) as proof of ((rel_s5 W) V)
% 12.62/12.84 Found (x1 (a1 W)) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 12.62/12.84 Found a10:=(a1 S):((rel_s5 S) S)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (x1 (a1 S)) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 12.62/12.84 Found a10:=(a1 S):((rel_s5 S) S)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (a1 S) as proof of ((rel_s5 S) V)
% 12.62/12.84 Found (x1 (a1 S)) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 12.62/12.84 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 12.62/12.84 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 12.62/12.84 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 12.62/12.84 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 15.50/15.67 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found a10:=(a1 W):((rel_s5 W) W)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (x3 (a1 W)) as proof of False
% 15.50/15.67 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 15.50/15.67 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 15.50/15.67 Found a10:=(a1 W):((rel_s5 W) W)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (a1 W) as proof of ((rel_s5 W) V0)
% 15.50/15.67 Found (x3 (a1 W)) as proof of False
% 15.50/15.67 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 15.50/15.67 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 15.50/15.67 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 15.50/15.67 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 25.26/25.43 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 25.26/25.43 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 25.26/25.43 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 25.26/25.43 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (x3 (a1 S)) as proof of False
% 25.26/25.43 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 25.26/25.43 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (x3 (a1 S)) as proof of False
% 25.26/25.43 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 25.26/25.43 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (x1 (a1 W)) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V)
% 25.26/25.43 Found (x1 (a1 W)) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (x1 (a1 S)) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V)
% 25.26/25.43 Found (x1 (a1 S)) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 25.26/25.43 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found a10:=(a1 S):((rel_s5 S) S)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found (a1 S) as proof of ((rel_s5 S) V0)
% 25.26/25.43 Found a10:=(a1 W):((rel_s5 W) W)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 25.26/25.43 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found a10:=(a1 W):((rel_s5 W) W)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found a10:=(a1 W):((rel_s5 W) W)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found a10:=(a1 W):((rel_s5 W) W)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found a10:=(a1 W):((rel_s5 W) W)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found (a1 W) as proof of ((rel_s5 W) V0)
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found a10:=(a1 S):((rel_s5 S) S)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found (a1 S) as proof of ((rel_s5 S) V0)
% 33.95/34.17 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 33.95/34.17 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found a10:=(a1 W):((rel_s5 W) W)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (x3 (a1 W)) as proof of False
% 36.45/36.69 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.45/36.69 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 36.45/36.69 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 36.45/36.69 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 36.45/36.69 Found a10:=(a1 W):((rel_s5 W) W)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (a1 W) as proof of ((rel_s5 W) V0)
% 36.45/36.69 Found (x3 (a1 W)) as proof of False
% 36.45/36.69 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.45/36.69 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 36.45/36.69 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 36.45/36.69 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 38.32/38.48 Found a10:=(a1 W):((rel_s5 W) W)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (x3 (a1 W)) as proof of False
% 38.32/38.48 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 38.32/38.48 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 38.32/38.48 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found a10:=(a1 W):((rel_s5 W) W)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 38.32/38.48 Found (x3 (a1 W)) as proof of False
% 38.32/38.48 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 38.32/38.48 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 38.32/38.48 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 38.32/38.48 Found a10:=(a1 S):((rel_s5 S) S)
% 38.32/38.48 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (x3 (a1 S)) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 43.74/43.90 Found a10:=(a1 S):((rel_s5 S) S)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (x3 (a1 S)) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 43.74/43.90 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found a10:=(a1 S):((rel_s5 S) S)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (x3 (a1 S)) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 43.74/43.90 Found a10:=(a1 S):((rel_s5 S) S)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (a1 S) as proof of ((rel_s5 S) V0)
% 43.74/43.90 Found (x3 (a1 S)) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 43.74/43.90 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 43.74/43.90 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 43.74/43.90 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found a10:=(a1 W):((rel_s5 W) W)
% 47.56/47.76 Found (a1 W) as proof of ((rel_s5 W) V)
% 47.56/47.76 Found (a1 W) as proof of ((rel_s5 W) V)
% 47.56/47.76 Found (a1 W) as proof of ((rel_s5 W) V)
% 47.56/47.76 Found (x1 (a1 W)) as proof of False
% 47.56/47.76 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 47.56/47.76 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 47.56/47.76 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 47.56/47.76 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 47.56/47.76 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found a10:=(a1 S):((rel_s5 S) S)
% 60.76/60.99 Found (a1 S) as proof of ((rel_s5 S) V)
% 60.76/60.99 Found (a1 S) as proof of ((rel_s5 S) V)
% 60.76/60.99 Found (a1 S) as proof of ((rel_s5 S) V)
% 60.76/60.99 Found (x1 (a1 S)) as proof of False
% 60.76/60.99 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 60.76/60.99 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 60.76/60.99 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 60.76/60.99 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 60.76/60.99 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 60.76/60.99 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found a10:=(a1 W):((rel_s5 W) W)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (x3 (a1 W)) as proof of False
% 65.72/65.92 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.72/65.92 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 65.72/65.92 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 65.72/65.92 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 65.72/65.92 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 65.72/65.92 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 65.72/65.92 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 65.72/65.92 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 65.72/65.92 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 65.72/65.92 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 65.72/65.92 Found a10:=(a1 W):((rel_s5 W) W)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (a1 W) as proof of ((rel_s5 W) V0)
% 65.72/65.92 Found (x3 (a1 W)) as proof of False
% 65.72/65.92 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.72/65.92 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 65.72/65.92 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 65.72/65.92 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 65.72/65.92 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 65.72/65.92 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 70.64/70.84 Found a10:=(a1 W):((rel_s5 W) W)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (x3 (a1 W)) as proof of False
% 70.64/70.84 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 70.64/70.84 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 70.64/70.84 Found a10:=(a1 W):((rel_s5 W) W)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 70.64/70.84 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 70.64/70.84 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 70.64/70.84 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 70.64/70.84 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 70.64/70.84 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 70.64/70.84 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 70.64/70.84 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 70.64/70.84 Found a10:=(a1 W):((rel_s5 W) W)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (x3 (a1 W)) as proof of False
% 70.64/70.84 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 70.64/70.84 Found (fun (x3:(((rel_s5 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V0)->False)->False)
% 70.64/70.84 Found a10:=(a1 W):((rel_s5 W) W)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found (a1 W) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 70.64/70.84 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 70.64/70.84 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found a10:=(a1 S):((rel_s5 S) S)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (x3 (a1 S)) as proof of False
% 77.12/77.34 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 77.12/77.34 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 77.12/77.34 Found a10:=(a1 S):((rel_s5 S) S)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 77.12/77.34 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 77.12/77.34 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 77.12/77.34 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 77.12/77.34 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found a10:=(a1 S):((rel_s5 S) S)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 77.12/77.34 Found (x3 (a1 S)) as proof of False
% 77.12/77.34 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 77.12/77.34 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 77.12/77.34 Found a10:=(a1 W):((rel_s5 W) W)
% 77.12/77.34 Found (a1 W) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found (a1 W) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found (a1 W) as proof of ((rel_s5 W) V0)
% 77.12/77.34 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 77.12/77.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 81.28/81.56 Found a10:=(a1 S):((rel_s5 S) S)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (x3 (a1 S)) as proof of False
% 81.28/81.56 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 81.28/81.56 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 81.28/81.56 Found a10:=(a1 S):((rel_s5 S) S)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found or_intror10:=(or_intror1 (((rel_s5 S) V1)->False)):((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)))
% 81.28/81.56 Found (or_intror1 (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 81.28/81.56 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 81.28/81.56 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 81.28/81.56 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 81.28/81.56 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found a10:=(a1 W):((rel_s5 W) W)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V)
% 81.28/81.56 Found (x1 (a1 W)) as proof of False
% 81.28/81.56 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of False
% 81.28/81.56 Found (fun (x1:(((rel_s5 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s5 W) V)->False)->False)
% 81.28/81.56 Found or_intror10:=(or_intror1 (((rel_s5 W) V1)->False)):((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)))
% 81.28/81.56 Found (or_intror1 (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 81.28/81.56 Found a10:=(a1 W):((rel_s5 W) W)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V0)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V0)
% 81.28/81.56 Found (a1 W) as proof of ((rel_s5 W) V0)
% 81.28/81.56 Found a10:=(a1 S):((rel_s5 S) S)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (a1 S) as proof of ((rel_s5 S) V0)
% 81.28/81.56 Found (x3 (a1 S)) as proof of False
% 81.28/81.56 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 81.28/81.56 Found (fun (x3:(((rel_s5 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V0)->False)->False)
% 86.27/86.48 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 86.27/86.48 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 86.27/86.48 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found a10:=(a1 W):((rel_s5 W) W)
% 86.27/86.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 86.27/86.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 86.27/86.48 Found (a1 W) as proof of ((rel_s5 W) V0)
% 86.27/86.48 Found a10:=(a1 S):((rel_s5 S) S)
% 86.27/86.48 Found (a1 S) as proof of ((rel_s5 S) V0)
% 86.27/86.48 Found (a1 S) as proof of ((rel_s5 S) V0)
% 86.27/86.48 Found (a1 S) as proof of ((rel_s5 S) V0)
% 86.27/86.48 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 86.27/86.48 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 88.47/88.70 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 88.47/88.70 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 88.47/88.70 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 88.47/88.70 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 88.47/88.70 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 88.47/88.70 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 88.47/88.70 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 88.47/88.70 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 88.47/88.70 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 88.47/88.70 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 88.47/88.70 Found or_intror10:=(or_intror1 (((rel_s5 S) V1)->False)):((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)))
% 88.47/88.70 Found (or_intror1 (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 88.47/88.70 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 88.47/88.70 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 88.47/88.70 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 88.47/88.70 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 88.47/88.70 Found a10:=(a1 W):((rel_s5 W) W)
% 88.47/88.70 Found (a1 W) as proof of ((rel_s5 W) V0)
% 88.47/88.70 Found (a1 W) as proof of ((rel_s5 W) V0)
% 88.47/88.70 Found (a1 W) as proof of ((rel_s5 W) V0)
% 88.47/88.70 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found or_intror10:=(or_intror1 (((rel_s5 W) V1)->False)):((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)))
% 89.77/89.98 Found (or_intror1 (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 89.77/89.98 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 89.77/89.98 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 89.77/89.98 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 89.77/89.98 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 89.77/89.98 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 89.77/89.98 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 91.51/91.77 Found a10:=(a1 S):((rel_s5 S) S)
% 91.51/91.77 Found (a1 S) as proof of ((rel_s5 S) V0)
% 91.51/91.77 Found (a1 S) as proof of ((rel_s5 S) V0)
% 91.51/91.77 Found (a1 S) as proof of ((rel_s5 S) V0)
% 91.51/91.77 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 91.51/91.77 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 91.51/91.77 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 91.51/91.77 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 94.68/94.95 Found a10:=(a1 W):((rel_s5 W) W)
% 94.68/94.95 Found (a1 W) as proof of ((rel_s5 W) V1)
% 94.68/94.95 Found (a1 W) as proof of ((rel_s5 W) V1)
% 94.68/94.95 Found (a1 W) as proof of ((rel_s5 W) V1)
% 94.68/94.95 Found (x5 (a1 W)) as proof of False
% 94.68/94.95 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 94.68/94.95 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 94.68/94.95 Found a10:=(a1 S):((rel_s5 S) S)
% 94.68/94.95 Found (a1 S) as proof of ((rel_s5 S) V0)
% 94.68/94.95 Found (a1 S) as proof of ((rel_s5 S) V0)
% 94.68/94.95 Found (a1 S) as proof of ((rel_s5 S) V0)
% 94.68/94.95 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 94.68/94.95 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 94.68/94.95 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 94.68/94.95 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 94.68/94.95 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 94.68/94.95 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 94.68/94.95 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 94.68/94.95 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 94.68/94.95 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 94.68/94.95 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 97.39/97.63 Found a10:=(a1 S):((rel_s5 S) S)
% 97.39/97.63 Found (a1 S) as proof of ((rel_s5 S) V)
% 97.39/97.63 Found (a1 S) as proof of ((rel_s5 S) V)
% 97.39/97.63 Found (a1 S) as proof of ((rel_s5 S) V)
% 97.39/97.63 Found (x1 (a1 S)) as proof of False
% 97.39/97.63 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of False
% 97.39/97.63 Found (fun (x1:(((rel_s5 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s5 S) V)->False)->False)
% 97.39/97.63 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 97.39/97.63 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 97.39/97.63 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 97.39/97.63 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 97.39/97.63 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 97.39/97.63 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 100.10/100.34 Found a10:=(a1 W):((rel_s5 W) W)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (x5 (a1 W)) as proof of False
% 100.10/100.34 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 100.10/100.34 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 100.10/100.34 Found a10:=(a1 W):((rel_s5 W) W)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (a1 W) as proof of ((rel_s5 W) V1)
% 100.10/100.34 Found (x5 (a1 W)) as proof of False
% 100.10/100.34 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 100.10/100.34 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 100.10/100.34 Found a10:=(a1 S):((rel_s5 S) S)
% 100.10/100.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 100.10/100.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 100.10/100.34 Found (a1 S) as proof of ((rel_s5 S) V0)
% 100.10/100.34 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 100.10/100.34 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 102.85/103.14 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 102.85/103.14 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 102.85/103.14 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 102.85/103.14 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 102.85/103.14 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 102.85/103.14 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 102.85/103.14 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 102.85/103.14 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 102.85/103.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 102.85/103.14 Found a10:=(a1 W):((rel_s5 W) W)
% 102.85/103.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 102.85/103.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 102.85/103.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 102.85/103.14 Found (x5 (a1 W)) as proof of False
% 105.71/105.96 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 105.71/105.96 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 105.71/105.96 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 105.71/105.96 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 105.71/105.96 Found x3:(((rel_s5 S) V0)->False)
% 105.71/105.96 Instantiate: V0:=V00:fofType;V:=S:fofType
% 105.71/105.96 Found x3 as proof of (((rel_s5 V) V00)->False)
% 105.71/105.96 Found (or_introl00 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 105.71/105.96 Found ((or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 105.71/105.96 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 105.71/105.96 Found x3:(((rel_s5 W) V0)->False)
% 105.71/105.96 Instantiate: V0:=V00:fofType;V:=W:fofType
% 105.71/105.96 Found x3 as proof of (((rel_s5 V) V00)->False)
% 105.71/105.96 Found (or_introl00 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 105.71/105.96 Found ((or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 105.71/105.96 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 105.71/105.96 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 105.71/105.96 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 110.31/110.61 Found a10:=(a1 S):((rel_s5 S) S)
% 110.31/110.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 110.31/110.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 110.31/110.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 110.31/110.61 Found (x5 (a1 S)) as proof of False
% 110.31/110.61 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 110.31/110.61 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 110.31/110.61 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 110.31/110.61 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 110.31/110.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 110.31/110.61 Found x3:(((rel_s5 S) V0)->False)
% 110.31/110.61 Instantiate: V0:=V00:fofType
% 110.31/110.61 Found x3 as proof of (((rel_s5 V) V00)->False)
% 110.31/110.61 Found (or_introl00 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 110.31/110.61 Found ((or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 110.31/110.61 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 110.31/110.61 Found x3:(((rel_s5 W) V0)->False)
% 110.31/110.61 Instantiate: V0:=V00:fofType
% 110.31/110.61 Found x3 as proof of (((rel_s5 V) V00)->False)
% 110.31/110.61 Found (or_introl00 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 110.31/110.61 Found ((or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 110.31/110.61 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 114.40/114.62 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 114.40/114.62 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 114.40/114.62 Found a10:=(a1 S):((rel_s5 S) S)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (x5 (a1 S)) as proof of False
% 114.40/114.62 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 114.40/114.62 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 114.40/114.62 Found a10:=(a1 S):((rel_s5 S) S)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (a1 S) as proof of ((rel_s5 S) V1)
% 114.40/114.62 Found (x5 (a1 S)) as proof of False
% 114.40/114.62 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 114.40/114.62 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 114.40/114.62 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 114.40/114.62 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 114.40/114.62 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 136.19/136.43 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 136.19/136.43 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 136.19/136.43 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 136.19/136.43 Found x2:((rel_s5 V) V0)
% 136.19/136.43 Instantiate: V1:=V0:fofType;V:=S:fofType
% 136.19/136.43 Found x2 as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (x4 x2) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 136.19/136.43 Found x2:((rel_s5 V) V0)
% 136.19/136.43 Instantiate: V1:=V0:fofType;V:=W:fofType
% 136.19/136.43 Found x2 as proof of ((rel_s5 W) V1)
% 136.19/136.43 Found (x4 x2) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 136.19/136.43 Found a10:=(a1 S):((rel_s5 S) S)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (x5 (a1 S)) as proof of False
% 136.19/136.43 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 136.19/136.43 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 136.19/136.43 Found x2:((rel_s5 V) V0)
% 136.19/136.43 Instantiate: V1:=V0:fofType
% 136.19/136.43 Found x2 as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (x4 x2) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 136.19/136.43 Found x2:((rel_s5 V) V0)
% 136.19/136.43 Instantiate: V1:=V0:fofType
% 136.19/136.43 Found x2 as proof of ((rel_s5 W) V1)
% 136.19/136.43 Found (x4 x2) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 136.19/136.43 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 136.19/136.43 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 136.19/136.43 Found a10:=(a1 S):((rel_s5 S) S)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (a1 S) as proof of ((rel_s5 S) V1)
% 136.19/136.43 Found (x4 (a1 S)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 136.19/136.43 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 136.19/136.43 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 136.19/136.43 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 136.19/136.43 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 136.19/136.43 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 136.19/136.43 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 136.19/136.43 Found a10:=(a1 W):((rel_s5 W) W)
% 136.19/136.43 Found (a1 W) as proof of ((rel_s5 W) V1)
% 136.19/136.43 Found (a1 W) as proof of ((rel_s5 W) V1)
% 136.19/136.43 Found (a1 W) as proof of ((rel_s5 W) V1)
% 136.19/136.43 Found (x4 (a1 W)) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 136.19/136.43 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 151.40/151.65 Found a10:=(a1 W):((rel_s5 W) W)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found a10:=(a1 S):((rel_s5 S) S)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (x4 (a1 S)) as proof of False
% 151.40/151.65 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 151.40/151.65 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 151.40/151.65 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found a10:=(a1 S):((rel_s5 S) S)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (x3 (a1 S)) as proof of False
% 151.40/151.65 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of False
% 151.40/151.65 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)
% 151.40/151.65 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0))
% 151.40/151.65 Found a10:=(a1 W):((rel_s5 W) W)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (x4 (a1 W)) as proof of False
% 151.40/151.65 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 151.40/151.65 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 151.40/151.65 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 151.40/151.65 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 151.40/151.65 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 151.40/151.65 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 151.40/151.65 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 151.40/151.65 Found a10:=(a1 W):((rel_s5 W) W)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V1)
% 151.40/151.65 Found (x3 (a1 W)) as proof of False
% 151.40/151.65 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of False
% 151.40/151.65 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 151.40/151.65 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 151.40/151.65 Found a10:=(a1 W):((rel_s5 W) W)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found a10:=(a1 W):((rel_s5 W) W)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (a1 W) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a1 V0) as proof of ((rel_s5 V0) W)
% 151.40/151.65 Found (a300 (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found ((a30 W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found (((a3 V0) W) (a1 V0)) as proof of ((rel_s5 W) V0)
% 151.40/151.65 Found a10:=(a1 S):((rel_s5 S) S)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 151.40/151.65 Found (a1 S) as proof of ((rel_s5 S) V1)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V1)
% 164.44/164.68 Found (x3 (a1 S)) as proof of False
% 164.44/164.68 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of False
% 164.44/164.68 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)
% 164.44/164.68 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0))
% 164.44/164.68 Found a10:=(a1 W):((rel_s5 W) W)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V1)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V1)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V1)
% 164.44/164.68 Found (x3 (a1 W)) as proof of False
% 164.44/164.68 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of False
% 164.44/164.68 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 164.44/164.68 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 164.44/164.68 Found a10:=(a1 W):((rel_s5 W) W)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found a10:=(a1 S):((rel_s5 S) S)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found a10:=(a1 W):((rel_s5 W) W)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found a10:=(a1 W):((rel_s5 W) W)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 164.44/164.68 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 164.44/164.68 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 164.44/164.68 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 164.44/164.68 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found a10:=(a1 S):((rel_s5 S) S)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found (a1 S) as proof of ((rel_s5 S) V0)
% 164.44/164.68 Found or_intror00:=(or_intror0 (((rel_s5 S) V1)->False)):((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)))
% 164.44/164.68 Found (or_intror0 (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 164.44/164.68 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 164.44/164.68 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 164.44/164.68 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 164.44/164.68 Found a10:=(a1 W):((rel_s5 W) W)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found (a1 W) as proof of ((rel_s5 W) V0)
% 164.44/164.68 Found or_intror00:=(or_intror0 (((rel_s5 W) V1)->False)):((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)))
% 168.59/168.91 Found (or_intror0 (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found or_intror10:=(or_intror1 (((rel_s5 W) V2)->False)):((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)))
% 168.59/168.91 Found (or_intror1 (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found a10:=(a1 V0):((rel_s5 V0) V0)
% 168.59/168.91 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 168.59/168.91 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 168.59/168.91 Found (a1 V0) as proof of ((rel_s5 V0) S)
% 168.59/168.91 Found (a300 (a1 V0)) as proof of ((rel_s5 S) V0)
% 168.59/168.91 Found ((a30 S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 168.59/168.91 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 168.59/168.91 Found (((a3 V0) S) (a1 V0)) as proof of ((rel_s5 S) V0)
% 168.59/168.91 Found a10:=(a1 W):((rel_s5 W) W)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found or_intror10:=(or_intror1 (((rel_s5 W) V2)->False)):((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)))
% 168.59/168.91 Found (or_intror1 (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 168.59/168.91 Found a10:=(a1 W):((rel_s5 W) W)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found (a1 W) as proof of ((rel_s5 W) V0)
% 168.59/168.91 Found a10:=(a1 S):((rel_s5 S) S)
% 168.59/168.91 Found (a1 S) as proof of ((rel_s5 S) V0)
% 168.59/168.91 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found a10:=(a1 W):((rel_s5 W) W)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found or_intror10:=(or_intror1 (((rel_s5 W) V2)->False)):((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)))
% 178.52/178.79 Found (or_intror1 (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found a10:=(a1 W):((rel_s5 W) W)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found a10:=(a1 S):((rel_s5 S) S)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found a10:=(a1 S):((rel_s5 S) S)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found a10:=(a1 W):((rel_s5 W) W)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found a10:=(a1 S):((rel_s5 S) S)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found (a1 S) as proof of ((rel_s5 S) V0)
% 178.52/178.79 Found a10:=(a1 W):((rel_s5 W) W)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found (a1 W) as proof of ((rel_s5 W) V0)
% 178.52/178.79 Found or_intror00:=(or_intror0 (((rel_s5 S) V1)->False)):((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)))
% 178.52/178.79 Found (or_intror0 (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V1)->False)) as proof of ((((rel_s5 S) V1)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 178.52/178.79 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 178.52/178.79 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found or_intror00:=(or_intror0 (((rel_s5 W) V1)->False)):((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)))
% 181.98/182.27 Found (or_intror0 (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V1)->False)) as proof of ((((rel_s5 W) V1)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 181.98/182.27 Found or_intror10:=(or_intror1 (((rel_s5 W) V2)->False)):((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)))
% 181.98/182.27 Found (or_intror1 (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 181.98/182.27 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 186.98/187.28 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 186.98/187.28 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 186.98/187.28 Found ((or_intror ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 W) V2)->False)) as proof of ((((rel_s5 W) V2)->False)->((or ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) (((rel_s5 V) V0)->False)))
% 186.98/187.28 Found a10:=(a1 S):((rel_s5 S) S)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 186.98/187.28 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 186.98/187.28 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 186.98/187.28 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 186.98/187.28 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 186.98/187.28 Found a10:=(a1 W):((rel_s5 W) W)
% 186.98/187.28 Found (a1 W) as proof of ((rel_s5 W) V0)
% 186.98/187.28 Found (a1 W) as proof of ((rel_s5 W) V0)
% 186.98/187.28 Found (a1 W) as proof of ((rel_s5 W) V0)
% 186.98/187.28 Found a10:=(a1 S):((rel_s5 S) S)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found a10:=(a1 S):((rel_s5 S) S)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (a1 S) as proof of ((rel_s5 S) V0)
% 186.98/187.28 Found (x3 (a1 S)) as proof of False
% 186.98/187.28 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))) as proof of False
% 188.57/188.88 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)
% 188.57/188.88 Found (or_intror10 (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 188.57/188.88 Found ((or_intror1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 188.57/188.88 Found (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 188.57/188.88 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 188.57/188.88 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of (forall (V0:fofType), ((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 188.57/188.88 Found (fun (x3:(((rel_s5 S) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((mbox_s5 (mexists_ind (fun (x30:mu)=> (mexists_ind (r x30))))) V)
% 188.57/188.88 Found (fun (x3:(((rel_s5 S) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((((rel_s5 S) V0)->False)->((mbox_s5 (mexists_ind (fun (x30:mu)=> (mexists_ind (r x30))))) V))
% 188.57/188.88 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 188.57/188.88 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 191.86/192.16 Found or_intror10:=(or_intror1 (((rel_s5 S) V2)->False)):((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)))
% 191.86/192.16 Found (or_intror1 (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found or_intror10:=(or_intror1 (((rel_s5 S) V2)->False)):((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)))
% 191.86/192.16 Found (or_intror1 (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 191.86/192.16 Found a10:=(a1 W):((rel_s5 W) W)
% 191.86/192.16 Found (a1 W) as proof of ((rel_s5 W) V0)
% 191.86/192.16 Found (a1 W) as proof of ((rel_s5 W) V0)
% 191.86/192.16 Found (a1 W) as proof of ((rel_s5 W) V0)
% 191.86/192.16 Found (x3 (a1 W)) as proof of False
% 191.86/192.16 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))) as proof of False
% 191.86/192.16 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)
% 191.86/192.16 Found (or_intror10 (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 193.37/193.65 Found ((or_intror1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 193.37/193.65 Found (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 193.37/193.65 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 193.37/193.65 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of (forall (V0:fofType), ((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 193.37/193.65 Found (fun (x3:(((rel_s5 W) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))) V)
% 193.37/193.65 Found (fun (x3:(((rel_s5 W) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((((rel_s5 W) V0)->False)->((mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))) V))
% 193.37/193.65 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 193.37/193.65 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found a10:=(a1 S):((rel_s5 S) S)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found a10:=(a1 S):((rel_s5 S) S)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found (a1 S) as proof of ((rel_s5 S) V0)
% 200.09/200.37 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 200.09/200.37 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 200.09/200.37 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 200.09/200.37 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 204.02/204.29 Found a10:=(a1 S):((rel_s5 S) S)
% 204.02/204.29 Found (a1 S) as proof of ((rel_s5 S) V0)
% 204.02/204.29 Found (a1 S) as proof of ((rel_s5 S) V0)
% 204.02/204.29 Found (a1 S) as proof of ((rel_s5 S) V0)
% 204.02/204.29 Found (x3 (a1 S)) as proof of False
% 204.02/204.29 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))) as proof of False
% 204.02/204.29 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)
% 204.02/204.29 Found (or_intror10 (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 204.02/204.29 Found ((or_intror1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 204.02/204.29 Found (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 204.02/204.29 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 204.02/204.29 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of (forall (V0:fofType), ((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 204.02/204.29 Found (fun (x3:(((rel_s5 S) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((mbox_s5 (mexists_ind (fun (x30:mu)=> (mexists_ind (r x30))))) V)
% 204.02/204.29 Found (fun (x3:(((rel_s5 S) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V00))=> (x3 (a1 S))))) as proof of ((((rel_s5 S) V0)->False)->((mbox_s5 (mexists_ind (fun (x30:mu)=> (mexists_ind (r x30))))) V))
% 204.02/204.29 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 204.02/204.29 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 204.02/204.29 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 204.02/204.29 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 204.02/204.29 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 204.02/204.29 Found or_introl00:=(or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 206.68/206.96 Found (or_introl0 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 206.68/206.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 206.68/206.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 206.68/206.96 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 206.68/206.96 Found or_intror10:=(or_intror1 (((rel_s5 S) V2)->False)):((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)))
% 206.68/206.96 Found (or_intror1 (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 206.68/206.96 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 206.68/206.96 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 206.68/206.96 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 206.68/206.96 Found a10:=(a1 W):((rel_s5 W) W)
% 206.68/206.96 Found (a1 W) as proof of ((rel_s5 W) V0)
% 206.68/206.96 Found (a1 W) as proof of ((rel_s5 W) V0)
% 206.68/206.96 Found (a1 W) as proof of ((rel_s5 W) V0)
% 206.68/206.96 Found (x3 (a1 W)) as proof of False
% 206.68/206.96 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))) as proof of False
% 206.68/206.96 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)
% 206.68/206.96 Found (or_intror10 (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 206.68/206.96 Found ((or_intror1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 206.68/206.96 Found (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W)))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 206.68/206.96 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 206.68/206.96 Found (fun (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of (forall (V0:fofType), ((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found (fun (x3:(((rel_s5 W) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))) V)
% 210.84/211.16 Found (fun (x3:(((rel_s5 W) V0)->False)) (V00:fofType)=> (((or_intror (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V00))=> (x3 (a1 W))))) as proof of ((((rel_s5 W) V0)->False)->((mbox_s5 (mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))))) V))
% 210.84/211.16 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 210.84/211.16 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 210.84/211.16 Found a10:=(a1 S):((rel_s5 S) S)
% 210.84/211.16 Found (a1 S) as proof of ((rel_s5 S) V0)
% 210.84/211.16 Found (a1 S) as proof of ((rel_s5 S) V0)
% 210.84/211.16 Found (a1 S) as proof of ((rel_s5 S) V0)
% 210.84/211.16 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 210.84/211.16 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 216.93/217.26 Found a10:=(a1 S):((rel_s5 S) S)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found a10:=(a1 S):((rel_s5 S) S)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found (a1 S) as proof of ((rel_s5 S) V0)
% 216.93/217.26 Found a10:=(a1 W):((rel_s5 W) W)
% 216.93/217.26 Found (a1 W) as proof of ((rel_s5 W) V1)
% 216.93/217.26 Found (a1 W) as proof of ((rel_s5 W) V1)
% 216.93/217.26 Found (a1 W) as proof of ((rel_s5 W) V1)
% 216.93/217.26 Found (x5 (a1 W)) as proof of False
% 216.93/217.26 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 216.93/217.26 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 216.93/217.26 Found x3:(((rel_s5 S) V0)->False)
% 216.93/217.26 Instantiate: V0:=V00:fofType;V:=S:fofType
% 216.93/217.26 Found x3 as proof of (((rel_s5 V) V00)->False)
% 216.93/217.26 Found (or_introl10 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 216.93/217.26 Found ((or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 216.93/217.26 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 216.93/217.26 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 216.93/217.26 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 216.93/217.26 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 219.50/219.80 Found x3:(((rel_s5 W) V0)->False)
% 219.50/219.80 Instantiate: V0:=V00:fofType;V:=W:fofType
% 219.50/219.80 Found x3 as proof of (((rel_s5 V) V00)->False)
% 219.50/219.80 Found (or_introl10 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 219.50/219.80 Found ((or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 219.50/219.80 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 219.50/219.80 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 219.50/219.80 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 219.50/219.80 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 219.50/219.80 Found or_intror10:=(or_intror1 (((rel_s5 S) V2)->False)):((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)))
% 219.50/219.80 Found (or_intror1 (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 219.50/219.80 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 219.50/219.80 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 224.80/225.14 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 224.80/225.14 Found ((or_intror ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 S) V2)->False)) as proof of ((((rel_s5 S) V2)->False)->((or ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) (((rel_s5 V) V0)->False)))
% 224.80/225.14 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 224.80/225.14 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 224.80/225.14 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 224.80/225.14 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 224.80/225.14 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 224.80/225.14 Found x2:((rel_s5 V) V0)
% 224.80/225.14 Instantiate: V1:=V0:fofType;V:=W:fofType
% 224.80/225.14 Found x2 as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (x4 x2) as proof of False
% 224.80/225.14 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 224.80/225.14 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 224.80/225.14 Found x2:((rel_s5 V) V0)
% 224.80/225.14 Instantiate: V1:=V0:fofType;V:=S:fofType
% 224.80/225.14 Found x2 as proof of ((rel_s5 S) V1)
% 224.80/225.14 Found (x4 x2) as proof of False
% 224.80/225.14 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 224.80/225.14 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 224.80/225.14 Found a10:=(a1 S):((rel_s5 S) S)
% 224.80/225.14 Found (a1 S) as proof of ((rel_s5 S) V0)
% 224.80/225.14 Found (a1 S) as proof of ((rel_s5 S) V0)
% 224.80/225.14 Found (a1 S) as proof of ((rel_s5 S) V0)
% 224.80/225.14 Found a10:=(a1 W):((rel_s5 W) W)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (x5 (a1 W)) as proof of False
% 224.80/225.14 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 224.80/225.14 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 224.80/225.14 Found a10:=(a1 W):((rel_s5 W) W)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (a1 W) as proof of ((rel_s5 W) V1)
% 224.80/225.14 Found (x5 (a1 W)) as proof of False
% 224.80/225.14 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 226.34/226.63 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 226.34/226.63 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)):((((rel_s5 W) V1)->False)->((or (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) as proof of ((((rel_s5 W) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)))
% 226.34/226.63 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V1)))
% 226.34/226.63 Found x3:(((rel_s5 S) V0)->False)
% 226.34/226.63 Instantiate: V0:=V00:fofType
% 226.34/226.63 Found x3 as proof of (((rel_s5 V) V00)->False)
% 226.34/226.63 Found (or_introl10 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 226.34/226.63 Found ((or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 226.34/226.63 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00))
% 226.34/226.63 Found x3:(((rel_s5 W) V0)->False)
% 226.34/226.63 Instantiate: V0:=V00:fofType
% 226.34/226.63 Found x3 as proof of (((rel_s5 V) V00)->False)
% 226.34/226.63 Found (or_introl10 x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 226.34/226.63 Found ((or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 228.75/229.05 Found (((or_introl (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00)) x3) as proof of ((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V00))
% 228.75/229.05 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)):((((rel_s5 W) V2)->False)->((or (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found ((or_introl (((rel_s5 W) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)) as proof of ((((rel_s5 W) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)))
% 228.75/229.05 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 228.75/229.05 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 228.75/229.05 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 228.75/229.05 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 228.75/229.05 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 238.31/238.61 Found x2:((rel_s5 V) V0)
% 238.31/238.61 Instantiate: V1:=V0:fofType
% 238.31/238.61 Found x2 as proof of ((rel_s5 W) V1)
% 238.31/238.61 Found (x4 x2) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 238.31/238.61 Found x2:((rel_s5 V) V0)
% 238.31/238.61 Instantiate: V1:=V0:fofType
% 238.31/238.61 Found x2 as proof of ((rel_s5 S) V1)
% 238.31/238.61 Found (x4 x2) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 238.31/238.61 Found a10:=(a1 W):((rel_s5 W) W)
% 238.31/238.61 Found (a1 W) as proof of ((rel_s5 W) V1)
% 238.31/238.61 Found (a1 W) as proof of ((rel_s5 W) V1)
% 238.31/238.61 Found (a1 W) as proof of ((rel_s5 W) V1)
% 238.31/238.61 Found (x5 (a1 W)) as proof of False
% 238.31/238.61 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 238.31/238.61 Found (fun (x5:(((rel_s5 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 238.31/238.61 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 238.31/238.61 Found x2:((rel_s5 V) V0)
% 238.31/238.61 Instantiate: V1:=V0:fofType;V:=S:fofType
% 238.31/238.61 Found x2 as proof of ((rel_s5 S) V1)
% 238.31/238.61 Found (x4 x2) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 238.31/238.61 Found x2:((rel_s5 V) V0)
% 238.31/238.61 Instantiate: V1:=V0:fofType;V:=W:fofType
% 238.31/238.61 Found x2 as proof of ((rel_s5 W) V1)
% 238.31/238.61 Found (x4 x2) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 238.31/238.61 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 238.31/238.61 Found a10:=(a1 S):((rel_s5 S) S)
% 238.31/238.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 238.31/238.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 238.31/238.61 Found (a1 S) as proof of ((rel_s5 S) V1)
% 238.31/238.61 Found (x5 (a1 S)) as proof of False
% 242.73/243.06 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 242.73/243.06 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 242.73/243.06 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 242.73/243.06 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 242.73/243.06 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 242.73/243.06 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 242.73/243.06 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 242.73/243.06 Found x4:((rel_s5 V) V0)
% 242.73/243.06 Instantiate: V2:=V0:fofType;V:=W:fofType
% 242.73/243.06 Found x4 as proof of ((rel_s5 W) V2)
% 249.90/250.20 Found (x6 x4) as proof of False
% 249.90/250.20 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of False
% 249.90/250.20 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 W) V2)->False)->False)
% 249.90/250.20 Found x2:((rel_s5 V) V0)
% 249.90/250.20 Instantiate: V1:=V0:fofType
% 249.90/250.20 Found x2 as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (x4 x2) as proof of False
% 249.90/250.20 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of False
% 249.90/250.20 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 S) V1)->False)->False)
% 249.90/250.20 Found x2:((rel_s5 V) V0)
% 249.90/250.20 Instantiate: V1:=V0:fofType
% 249.90/250.20 Found x2 as proof of ((rel_s5 W) V1)
% 249.90/250.20 Found (x4 x2) as proof of False
% 249.90/250.20 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of False
% 249.90/250.20 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s5 W) V1)->False)->False)
% 249.90/250.20 Found a10:=(a1 S):((rel_s5 S) S)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (x5 (a1 S)) as proof of False
% 249.90/250.20 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 249.90/250.20 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 249.90/250.20 Found a10:=(a1 S):((rel_s5 S) S)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (a1 S) as proof of ((rel_s5 S) V1)
% 249.90/250.20 Found (x5 (a1 S)) as proof of False
% 249.90/250.20 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 249.90/250.20 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 249.90/250.20 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V0) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V1)))
% 249.90/250.20 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)):((((rel_s5 S) V1)->False)->((or (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 249.90/250.20 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 249.90/250.20 Found ((or_introl (((rel_s5 S) V1)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)) as proof of ((((rel_s5 S) V1)->False)->((or (((rel_s5 V) V00)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V00)))
% 265.02/265.37 Found x4:((rel_s5 V) V0)
% 265.02/265.37 Instantiate: V2:=V0:fofType
% 265.02/265.37 Found x4 as proof of ((rel_s5 W) V2)
% 265.02/265.37 Found (x6 x4) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 W) V2)->False)->False)
% 265.02/265.37 Found x4:((rel_s5 V) V0)
% 265.02/265.37 Instantiate: V2:=V0:fofType
% 265.02/265.37 Found x4 as proof of ((rel_s5 W) V2)
% 265.02/265.37 Found (x6 x4) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 W) V2)->False)->False)
% 265.02/265.37 Found a10:=(a1 W):((rel_s5 W) W)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (x4 (a1 W)) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 265.02/265.37 Found or_introl10:=(or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)):((((rel_s5 S) V2)->False)->((or (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found (or_introl1 ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found ((or_introl (((rel_s5 S) V2)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)) as proof of ((((rel_s5 S) V2)->False)->((or (((rel_s5 V) V0)->False)) ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)))
% 265.02/265.37 Found a10:=(a1 S):((rel_s5 S) S)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (x4 (a1 S)) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 265.02/265.37 Found a10:=(a1 S):((rel_s5 S) S)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (x5 (a1 S)) as proof of False
% 265.02/265.37 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 265.02/265.37 Found (fun (x5:(((rel_s5 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 265.02/265.37 Found x4:((rel_s5 V) V0)
% 265.02/265.37 Instantiate: V2:=V0:fofType
% 265.02/265.37 Found x4 as proof of ((rel_s5 W) V2)
% 265.02/265.37 Found (x6 x4) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of False
% 265.02/265.37 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 W) V2)->False)->False)
% 265.02/265.37 Found a10:=(a1 W):((rel_s5 W) W)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (a1 W) as proof of ((rel_s5 W) V1)
% 265.02/265.37 Found (x4 (a1 W)) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 265.02/265.37 Found a10:=(a1 S):((rel_s5 S) S)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (a1 S) as proof of ((rel_s5 S) V1)
% 265.02/265.37 Found (x4 (a1 S)) as proof of False
% 265.02/265.37 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 277.59/277.93 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 277.59/277.93 Found a10:=(a1 W):((rel_s5 W) W)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (x3 (a1 W)) as proof of False
% 277.59/277.93 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of False
% 277.59/277.93 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 277.59/277.93 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 277.59/277.93 Found a10:=(a1 S):((rel_s5 S) S)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (x3 (a1 S)) as proof of False
% 277.59/277.93 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of False
% 277.59/277.93 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)
% 277.59/277.93 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0))
% 277.59/277.93 Found x4:((rel_s5 V) V0)
% 277.59/277.93 Instantiate: V2:=V0:fofType;V:=S:fofType
% 277.59/277.93 Found x4 as proof of ((rel_s5 S) V2)
% 277.59/277.93 Found (x6 x4) as proof of False
% 277.59/277.93 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of False
% 277.59/277.93 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 S) V2)->False)->False)
% 277.59/277.93 Found a10:=(a1 W):((rel_s5 W) W)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (x4 (a1 W)) as proof of False
% 277.59/277.93 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 277.59/277.93 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 277.59/277.93 Found a10:=(a1 S):((rel_s5 S) S)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (x4 (a1 S)) as proof of False
% 277.59/277.93 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 277.59/277.93 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 277.59/277.93 Found a10:=(a1 W):((rel_s5 W) W)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V0)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V0)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V0)
% 277.59/277.93 Found a10:=(a1 W):((rel_s5 W) W)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (a1 W) as proof of ((rel_s5 W) V1)
% 277.59/277.93 Found (x3 (a1 W)) as proof of False
% 277.59/277.93 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of False
% 277.59/277.93 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 277.59/277.93 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 277.59/277.93 Found a10:=(a1 S):((rel_s5 S) S)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (a1 S) as proof of ((rel_s5 S) V1)
% 277.59/277.93 Found (x3 (a1 S)) as proof of False
% 277.59/277.93 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of False
% 283.94/284.36 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)
% 283.94/284.36 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0))
% 283.94/284.36 Found a10:=(a1 W):((rel_s5 W) W)
% 283.94/284.36 Found (a1 W) as proof of ((rel_s5 W) V2)
% 283.94/284.36 Found (a1 W) as proof of ((rel_s5 W) V2)
% 283.94/284.36 Found (a1 W) as proof of ((rel_s5 W) V2)
% 283.94/284.36 Found (x6 (a1 W)) as proof of False
% 283.94/284.36 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of False
% 283.94/284.36 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of ((((rel_s5 W) V2)->False)->False)
% 283.94/284.36 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)):((((rel_s5 W) V3)->False)->((or (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found x4:((rel_s5 V) V0)
% 283.94/284.36 Instantiate: V2:=V0:fofType
% 283.94/284.36 Found x4 as proof of ((rel_s5 S) V2)
% 283.94/284.36 Found (x6 x4) as proof of False
% 283.94/284.36 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of False
% 283.94/284.36 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 S) V2)->False)->False)
% 283.94/284.36 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)):((((rel_s5 W) V3)->False)->((or (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 283.94/284.36 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 294.02/294.40 Found x4:((rel_s5 V) V0)
% 294.02/294.40 Instantiate: V2:=V0:fofType
% 294.02/294.40 Found x4 as proof of ((rel_s5 S) V2)
% 294.02/294.40 Found (x6 x4) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 S) V2)->False)->False)
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (x4 (a1 W)) as proof of False
% 294.02/294.40 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 294.02/294.40 Found (fun (x4:(((rel_s5 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->False)
% 294.02/294.40 Found a10:=(a1 S):((rel_s5 S) S)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (x4 (a1 S)) as proof of False
% 294.02/294.40 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 294.02/294.40 Found (fun (x4:(((rel_s5 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->False)
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V1)
% 294.02/294.40 Found (x3 (a1 W)) as proof of False
% 294.02/294.40 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of False
% 294.02/294.40 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 294.02/294.40 Found (fun (x3:(((rel_s5 W) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x3 (a1 W))) as proof of ((((rel_s5 W) V1)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found a10:=(a1 S):((rel_s5 S) S)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (a1 S) as proof of ((rel_s5 S) V1)
% 294.02/294.40 Found (x3 (a1 S)) as proof of False
% 294.02/294.40 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of False
% 294.02/294.40 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0)
% 294.02/294.40 Found (fun (x3:(((rel_s5 S) V1)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (x30:mu)=> (mexists_ind (r x30))) X)))) V0))=> (x3 (a1 S))) as proof of ((((rel_s5 S) V1)->False)->((mexists_ind (fun (x30:mu)=> (mexists_ind (r x30)))) V0))
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (x6 (a1 W)) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of ((((rel_s5 W) V2)->False)->False)
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V2)
% 294.02/294.40 Found (x6 (a1 W)) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of False
% 294.02/294.40 Found (fun (x6:(((rel_s5 W) V2)->False))=> (x6 (a1 W))) as proof of ((((rel_s5 W) V2)->False)->False)
% 294.02/294.40 Found a10:=(a1 W):((rel_s5 W) W)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found (a1 W) as proof of ((rel_s5 W) V0)
% 294.02/294.40 Found or_introl10:=(or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)):((((rel_s5 W) V3)->False)->((or (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 294.02/294.40 Found (or_introl1 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found a10:=(a1 W):((rel_s5 W) W)
% 299.89/300.28 Found (a1 W) as proof of ((rel_s5 W) V2)
% 299.89/300.28 Found (a1 W) as proof of ((rel_s5 W) V2)
% 299.89/300.28 Found (a1 W) as proof of ((rel_s5 W) V2)
% 299.89/300.28 Found (x5 (a1 W)) as proof of False
% 299.89/300.28 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 299.89/300.28 Found (fun (x5:(((rel_s5 W) V2)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0)
% 299.89/300.28 Found (fun (x5:(((rel_s5 W) V2)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y)))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s5 W) V2)->False)->((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V0))
% 299.89/300.28 Found or_introl00:=(or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)):((((rel_s5 W) V3)->False)->((or (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found (or_introl0 ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found ((or_introl (((rel_s5 W) V3)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)) as proof of ((((rel_s5 W) V3)->False)->((or (((rel_s5 V1) V2)->False)) ((mexists_ind (fun (X:mu)=> (mexists_ind (fun (Y:mu)=> ((r X) Y))))) V2)))
% 299.89/300.28 Found x4:((rel_s5 V) V0)
% 299.89/300.28 Instantiate: V2:=V0:fofType
% 299.89/300.28 Found x4 as proof of ((rel_s5 S) V2)
% 299.89/300.28 Found (x6 x4) as proof of False
% 299.89/300.28 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of False
% 299.89/300.28 Found (fun (x6:(((rel_s5 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s5 S) V2)->False)->False)
% 299.89/300.28 Found a10:=(a1 W):((rel_s5 W) W)
% 299.89/300.28 Found (a1 W) as proof of ((rel_s5 W) V1)
% 299.89/300.28 Found (a1 W) as proof of ((rel_s5 W) V1)
% 299.89/300.28 Found (a1 W) as proof of ((
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