TSTP Solution File: SYO565^7 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO565^7 : TPTP v7.5.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n025.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 00:52:06 EDT 2022
% Result : Timeout 291.04s 291.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYO565^7 : TPTP v7.5.0. Released v5.5.0.
% 0.07/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n025.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 21:10:48 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
% 0.38/0.60 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.38/0.60 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^0.ax, trying next directory
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4050>, <kernel.Type object at 0x2aeeae9a4908>) of role type named mu_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring mu:Type
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4cb0>, <kernel.DependentProduct object at 0x2aeeae9a4050>) of role type named qmltpeq_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4290>, <kernel.DependentProduct object at 0x2aeeae9a4368>) of role type named meq_prop_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.60 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))) of role definition named meq_prop
% 0.38/0.60 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))))
% 0.38/0.60 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4d88>, <kernel.DependentProduct object at 0x2aeeae9a4998>) of role type named mnot_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.38/0.60 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.38/0.60 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.38/0.60 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4998>, <kernel.DependentProduct object at 0x2aeeae9a4098>) of role type named mor_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.60 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% 0.38/0.60 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% 0.38/0.60 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x2aeeae9a4098>, <kernel.DependentProduct object at 0x2aeeae9a43f8>) of role type named mbox_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.60 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox
% 0.38/0.60 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% 0.38/0.60 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.38/0.60 FOF formula (<kernel.Constant object at 0x18acd40>, <kernel.DependentProduct object at 0x2aeeae9a4320>) of role type named mforall_prop_type
% 0.38/0.60 Using role type
% 0.38/0.60 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.38/0.60 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% 0.38/0.60 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% 0.38/0.60 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4950>, <kernel.DependentProduct object at 0x2aeeae9a47e8>) of role type named mtrue_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mtrue:(fofType->Prop)
% 0.38/0.61 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.38/0.61 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.38/0.61 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a49e0>, <kernel.DependentProduct object at 0x2aeeae9a4f38>) of role type named mfalse_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mfalse:(fofType->Prop)
% 0.38/0.61 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.38/0.61 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.38/0.61 Defined: mfalse:=(mnot mtrue)
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4098>, <kernel.DependentProduct object at 0x2aeeae9a4950>) of role type named mand_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) of role definition named mand
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.38/0.61 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4950>, <kernel.DependentProduct object at 0x2aeeae9a4f38>) of role type named mimplies_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) of role definition named mimplies
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.38/0.61 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4b48>, <kernel.DependentProduct object at 0x18b1998>) of role type named mimplied_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))) of role definition named mimplied
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.38/0.61 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4b48>, <kernel.DependentProduct object at 0x18b1ef0>) of role type named mequiv_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))) of role definition named mequiv
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mequiv) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))))
% 0.38/0.61 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.38/0.61 FOF formula (<kernel.Constant object at 0x2aeeae9a4b48>, <kernel.DependentProduct object at 0x18b15f0>) of role type named mxor_type
% 0.38/0.61 Using role type
% 0.38/0.61 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.61 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))) of role definition named mxor
% 0.38/0.61 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.38/0.62 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b15f0>, <kernel.DependentProduct object at 0x18b1ef0>) of role type named mdia_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.38/0.62 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))) of role definition named mdia
% 0.38/0.62 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mdia) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))))
% 0.38/0.62 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b15f0>, <kernel.DependentProduct object at 0x18b1320>) of role type named exists_in_world_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring exists_in_world:(mu->(fofType->Prop))
% 0.38/0.62 FOF formula (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))) of role axiom named nonempty_ax
% 0.38/0.62 A new axiom: (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b15a8>, <kernel.DependentProduct object at 0x18b1830>) of role type named mforall_ind_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.38/0.62 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))) of role definition named mforall_ind
% 0.38/0.62 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))))
% 0.38/0.62 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b1290>, <kernel.DependentProduct object at 0x18b17a0>) of role type named mexists_ind_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.38/0.62 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))) of role definition named mexists_ind
% 0.38/0.62 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mexists_ind) (fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))))
% 0.38/0.62 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b1cf8>, <kernel.DependentProduct object at 0x18b1a70>) of role type named mexists_prop_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.38/0.62 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))) of role definition named mexists_prop
% 0.38/0.62 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))))
% 0.38/0.62 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.38/0.62 FOF formula (<kernel.Constant object at 0x18b1830>, <kernel.DependentProduct object at 0x2aeea6ed13f8>) of role type named mreflexive_type
% 0.38/0.62 Using role type
% 0.38/0.62 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.38/0.62 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.38/0.62 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.47/0.63 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x18b1290>, <kernel.DependentProduct object at 0x2aeea6ed10e0>) of role type named msymmetric_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))) of role definition named msymmetric
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))))
% 0.47/0.63 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x18b1290>, <kernel.DependentProduct object at 0x2aeea6ed15f0>) of role type named mserial_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))) of role definition named mserial
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))))
% 0.47/0.63 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x18b1a70>, <kernel.DependentProduct object at 0x2aeea6ed1320>) of role type named mtransitive_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))) of role definition named mtransitive
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))))
% 0.47/0.63 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2aeea6ed1320>, <kernel.DependentProduct object at 0x2aeea6ed1248>) of role type named meuclidean_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))) of role definition named meuclidean
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))))
% 0.47/0.63 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2aeea6ed1248>, <kernel.DependentProduct object at 0x2aeea6ed1368>) of role type named mpartially_functional_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))) of role definition named mpartially_functional
% 0.47/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))))
% 0.47/0.63 Defined: mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2aeea6ed1368>, <kernel.DependentProduct object at 0x2aeea6ed18c0>) of role type named mfunctional_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))) of role definition named mfunctional
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))))
% 0.47/0.64 Defined: mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2aeea6ed18c0>, <kernel.DependentProduct object at 0x2aeea6ed1950>) of role type named mweakly_dense_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))) of role definition named mweakly_dense
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))))
% 0.47/0.64 Defined: mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2aeea6ed1950>, <kernel.DependentProduct object at 0x2aeea6ed1248>) of role type named mweakly_connected_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))) of role definition named mweakly_connected
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))))
% 0.47/0.64 Defined: mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2aeea6ed1248>, <kernel.DependentProduct object at 0x2aeea6ed1d40>) of role type named mweakly_directed_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))) of role definition named mweakly_directed
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))))
% 0.47/0.64 Defined: mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2aeea6ed1098>, <kernel.DependentProduct object at 0x2aeea6ed1bd8>) of role type named mvalid_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mvalid:((fofType->Prop)->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.47/0.64 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.47/0.65 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2aeea6ed1248>, <kernel.DependentProduct object at 0x2aeea6ed1878>) of role type named msatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.47/0.65 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2aeea6ed1bd8>, <kernel.DependentProduct object at 0x2aeea6ed1998>) of role type named mcountersatisfiable_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.47/0.65 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2aeea6ed1248>, <kernel.DependentProduct object at 0x2aeea6ed1cf8>) of role type named minvalid_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring minvalid:((fofType->Prop)->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.47/0.65 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.47/0.65 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x188fc68>, <kernel.DependentProduct object at 0x18ace60>) of role type named rel_s4_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring rel_s4:(fofType->(fofType->Prop))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x188fc68>, <kernel.DependentProduct object at 0x18ace60>) of role type named mbox_s4_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))) of role definition named mbox_s4
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))))
% 0.47/0.65 Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x188fc68>, <kernel.DependentProduct object at 0x2aeeae9a4d40>) of role type named mdia_s4_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% 0.47/0.65 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% 0.47/0.65 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% 0.47/0.65 Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% 0.47/0.65 FOF formula (mreflexive rel_s4) of role axiom named a1
% 0.47/0.65 A new axiom: (mreflexive rel_s4)
% 0.47/0.65 FOF formula (mtransitive rel_s4) of role axiom named a2
% 0.47/0.65 A new axiom: (mtransitive rel_s4)
% 0.47/0.65 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^1.ax, trying next directory
% 0.47/0.65 FOF formula (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))) of role axiom named cumulative_ax
% 0.47/0.65 A new axiom: (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W)))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0x18b2488>, <kernel.DependentProduct object at 0x18b2710>) of role type named a_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring a:(mu->(fofType->Prop))
% 0.47/0.66 FOF formula (mvalid ((mequiv (mbox_s4 (mforall_ind (fun (X:mu)=> (a X))))) (mdia_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (a X))))))) of role conjecture named con
% 0.47/0.66 Conjecture to prove = (mvalid ((mequiv (mbox_s4 (mforall_ind (fun (X:mu)=> (a X))))) (mdia_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (a X))))))):Prop
% 0.47/0.66 Parameter mu_DUMMY:mu.
% 0.47/0.66 Parameter fofType_DUMMY:fofType.
% 0.47/0.66 We need to prove ['(mvalid ((mequiv (mbox_s4 (mforall_ind (fun (X:mu)=> (a X))))) (mdia_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (a X)))))))']
% 0.47/0.66 Parameter mu:Type.
% 0.47/0.66 Parameter fofType:Type.
% 0.47/0.66 Parameter qmltpeq:(mu->(mu->(fofType->Prop))).
% 0.47/0.66 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.66 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.66 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.47/0.66 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.47/0.66 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.66 Parameter exists_in_world:(mu->(fofType->Prop)).
% 0.47/0.66 Axiom nonempty_ax:(forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))).
% 0.47/0.66 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.66 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.66 Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.66 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.66 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.66 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.66 Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.66 Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% 5.79/5.98 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).
% 5.79/5.98 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).
% 5.79/5.98 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).
% 5.79/5.98 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).
% 5.79/5.98 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).
% 5.79/5.98 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 5.79/5.98 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 5.79/5.98 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 5.79/5.98 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 5.79/5.98 Parameter rel_s4:(fofType->(fofType->Prop)).
% 5.79/5.98 Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 5.79/5.98 Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 5.79/5.98 Axiom a1:(mreflexive rel_s4).
% 5.79/5.98 Axiom a2:(mtransitive rel_s4).
% 5.79/5.98 Axiom cumulative_ax:(forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))).
% 5.79/5.98 Parameter a:(mu->(fofType->Prop)).
% 5.79/5.98 Trying to prove (mvalid ((mequiv (mbox_s4 (mforall_ind (fun (X:mu)=> (a X))))) (mdia_s4 (mforall_ind (fun (X:mu)=> (mbox_s4 (a X)))))))
% 5.79/5.98 Found a10:=(a1 W):((rel_s4 W) W)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (x2 (a1 W)) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 5.79/5.98 Found a10:=(a1 W):((rel_s4 W) W)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (x2 (a1 W)) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 5.79/5.98 Found a10:=(a1 S):((rel_s4 S) S)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (x2 (a1 S)) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 5.79/5.98 Found a10:=(a1 S):((rel_s4 S) S)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (a1 S) as proof of ((rel_s4 S) V)
% 5.79/5.98 Found (x2 (a1 S)) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 5.79/5.98 Found a10:=(a1 W):((rel_s4 W) W)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (a1 W) as proof of ((rel_s4 W) V)
% 5.79/5.98 Found (x2 (a1 W)) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 5.79/5.98 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (x2 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 S):((rel_s4 S) S)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (x2 (a1 S)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 S):((rel_s4 S) S)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (x2 (a1 S)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (x2 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (x2 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (x2 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 16.21/16.42 Found (x2 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 S):((rel_s4 S) S)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (x2 (a1 S)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 S):((rel_s4 S) S)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (x2 (a1 S)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 S):((rel_s4 S) S)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 16.21/16.42 Found (x2 (a1 S)) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 16.21/16.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 16.21/16.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 16.21/16.42 Found (x3 (a1 W)) as proof of False
% 16.21/16.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 16.21/16.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 16.21/16.42 Found a10:=(a1 W):((rel_s4 W) W)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (x3 (a1 W)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 22.37/22.53 Found a10:=(a1 S):((rel_s4 S) S)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V)
% 22.37/22.53 Found (x2 (a1 S)) as proof of False
% 22.37/22.53 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 22.37/22.53 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 22.37/22.53 Found a10:=(a1 W):((rel_s4 W) W)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (x3 (a1 W)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 22.37/22.53 Found a10:=(a1 W):((rel_s4 W) W)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (a1 W) as proof of ((rel_s4 W) V0)
% 22.37/22.53 Found (x3 (a1 W)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 22.37/22.53 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 22.37/22.53 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found a10:=(a1 S):((rel_s4 S) S)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (x3 (a1 S)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 22.37/22.53 Found a10:=(a1 S):((rel_s4 S) S)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (x3 (a1 S)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 22.37/22.53 Found a10:=(a1 S):((rel_s4 S) S)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (x3 (a1 S)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 22.37/22.53 Found a10:=(a1 S):((rel_s4 S) S)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (a1 S) as proof of ((rel_s4 S) V0)
% 22.37/22.53 Found (x3 (a1 S)) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 22.37/22.53 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 22.37/22.53 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 22.37/22.53 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 22.37/22.53 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found a10:=(a1 W):((rel_s4 W) W)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (x2 (a1 W)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 27.30/27.50 Found a10:=(a1 W):((rel_s4 W) W)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (x2 (a1 W)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 27.30/27.50 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 27.30/27.50 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found a10:=(a1 W):((rel_s4 W) W)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (x2 (a1 W)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 27.30/27.50 Found a10:=(a1 W):((rel_s4 W) W)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (a1 W) as proof of ((rel_s4 W) V)
% 27.30/27.50 Found (x2 (a1 W)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 27.30/27.50 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 27.30/27.50 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 27.30/27.50 Found a10:=(a1 S):((rel_s4 S) S)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (x2 (a1 S)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 27.30/27.50 Found a10:=(a1 S):((rel_s4 S) S)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (x2 (a1 S)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 27.30/27.50 Found a10:=(a1 S):((rel_s4 S) S)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (a1 S) as proof of ((rel_s4 S) V)
% 27.30/27.50 Found (x2 (a1 S)) as proof of False
% 27.30/27.50 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 36.06/36.25 Found a10:=(a1 S):((rel_s4 S) S)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V)
% 36.06/36.25 Found (x2 (a1 S)) as proof of False
% 36.06/36.25 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 36.06/36.25 Found a10:=(a1 W):((rel_s4 W) W)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (x3 (a1 W)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 W):((rel_s4 W) W)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (x3 (a1 W)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 W):((rel_s4 W) W)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (x3 (a1 W)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 W):((rel_s4 W) W)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 36.06/36.25 Found (x3 (a1 W)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 36.06/36.25 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 36.06/36.25 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 36.06/36.25 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 36.06/36.25 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 36.06/36.25 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 36.06/36.25 Found a10:=(a1 S):((rel_s4 S) S)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (x3 (a1 S)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 S):((rel_s4 S) S)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (x3 (a1 S)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 S):((rel_s4 S) S)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (x3 (a1 S)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 36.06/36.25 Found a10:=(a1 S):((rel_s4 S) S)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.06/36.25 Found (x3 (a1 S)) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 36.06/36.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 36.06/36.25 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 46.00/46.20 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found a10:=(a1 S):((rel_s4 S) S)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (x2 (a1 S)) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 46.00/46.20 Found a10:=(a1 S):((rel_s4 S) S)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V)
% 46.00/46.20 Found (x2 (a1 S)) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 46.00/46.20 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 46.00/46.20 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found a10:=(a1 W):((rel_s4 W) W)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found a10:=(a1 W):((rel_s4 W) W)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 46.00/46.20 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 46.00/46.20 Found a10:=(a1 W):((rel_s4 W) W)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found a10:=(a1 W):((rel_s4 W) W)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 46.00/46.20 Found a10:=(a1 S):((rel_s4 S) S)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found a10:=(a1 S):((rel_s4 S) S)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 46.00/46.20 Found a10:=(a1 W):((rel_s4 W) W)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 46.00/46.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 46.00/46.20 Found (x2 (a1 W)) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 46.00/46.20 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (x2 (a1 W)) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (x2 (a1 W)) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V)
% 58.27/58.45 Found (x2 (a1 W)) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (x2 (a1 S)) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V)
% 58.27/58.45 Found (x2 (a1 S)) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 58.27/58.45 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found a10:=(a1 S):((rel_s4 S) S)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 58.27/58.45 Found a10:=(a1 W):((rel_s4 W) W)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 58.27/58.45 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (x2 (a1 S)) as proof of False
% 65.43/65.63 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 65.43/65.63 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V)
% 65.43/65.63 Found (x2 (a1 S)) as proof of False
% 65.43/65.63 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 65.43/65.63 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found a10:=(a1 W):((rel_s4 W) W)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 65.43/65.63 Found (x3 (a1 W)) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.43/65.63 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 65.43/65.63 Found a10:=(a1 S):((rel_s4 S) S)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 65.43/65.63 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found a10:=(a1 W):((rel_s4 W) W)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found a10:=(a1 S):((rel_s4 S) S)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 72.56/72.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found a10:=(a1 W):((rel_s4 W) W)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 72.56/72.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 72.56/72.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found a10:=(a1 S):((rel_s4 S) S)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (x3 (a1 S)) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 72.56/72.80 Found a10:=(a1 S):((rel_s4 S) S)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (x3 (a1 S)) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 72.56/72.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 72.56/72.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 72.56/72.80 Found a10:=(a1 S):((rel_s4 S) S)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 72.56/72.80 Found (x3 (a1 S)) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 72.56/72.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 72.56/72.80 Found a10:=(a1 W):((rel_s4 W) W)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (x2 (a1 W)) as proof of False
% 72.56/72.80 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 72.56/72.80 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 72.56/72.80 Found a10:=(a1 W):((rel_s4 W) W)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 72.56/72.80 Found (x2 (a1 W)) as proof of False
% 72.56/72.80 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 78.60/78.80 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 78.60/78.80 Found a10:=(a1 S):((rel_s4 S) S)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (x3 (a1 S)) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 78.60/78.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 78.60/78.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found a10:=(a1 S):((rel_s4 S) S)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (x3 (a1 S)) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 78.60/78.80 Found a10:=(a1 S):((rel_s4 S) S)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (x3 (a1 S)) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 78.60/78.80 Found a10:=(a1 S):((rel_s4 S) S)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (x3 (a1 S)) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 78.60/78.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 78.60/78.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found a10:=(a1 S):((rel_s4 S) S)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (a1 S) as proof of ((rel_s4 S) V0)
% 78.60/78.80 Found (x3 (a1 S)) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 78.60/78.80 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 78.60/78.80 Found a10:=(a1 W):((rel_s4 W) W)
% 78.60/78.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.60/78.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.60/78.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.60/78.80 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 78.60/78.80 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 78.60/78.80 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found a10:=(a1 W):((rel_s4 W) W)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found a10:=(a1 S):((rel_s4 S) S)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found a10:=(a1 W):((rel_s4 W) W)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (x2 (a1 W)) as proof of False
% 84.96/85.21 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 84.96/85.21 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 84.96/85.21 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 84.96/85.21 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found a10:=(a1 S):((rel_s4 S) S)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found (a1 S) as proof of ((rel_s4 S) V0)
% 84.96/85.21 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 84.96/85.21 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found a10:=(a1 W):((rel_s4 W) W)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V)
% 84.96/85.21 Found (x2 (a1 W)) as proof of False
% 84.96/85.21 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 84.96/85.21 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 84.96/85.21 Found a10:=(a1 W):((rel_s4 W) W)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found (a1 W) as proof of ((rel_s4 W) V0)
% 84.96/85.21 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 84.96/85.21 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 84.96/85.21 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 84.96/85.21 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 93.46/93.71 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found a10:=(a1 W):((rel_s4 W) W)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 93.46/93.71 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found a10:=(a1 W):((rel_s4 W) W)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found a10:=(a1 W):((rel_s4 W) W)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.46/93.71 Found a10:=(a1 S):((rel_s4 S) S)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 93.46/93.71 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found a10:=(a1 S):((rel_s4 S) S)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.46/93.71 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 93.46/93.71 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 93.46/93.71 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 105.38/105.62 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 105.38/105.62 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 105.38/105.62 Found a10:=(a1 S):((rel_s4 S) S)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (x2 (a1 S)) as proof of False
% 105.38/105.62 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 105.38/105.62 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found a10:=(a1 S):((rel_s4 S) S)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found a10:=(a1 S):((rel_s4 S) S)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V)
% 105.38/105.62 Found (x2 (a1 S)) as proof of False
% 105.38/105.62 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 105.38/105.62 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found a10:=(a1 S):((rel_s4 S) S)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (x3 (a1 W)) as proof of False
% 105.38/105.62 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 105.38/105.62 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.38/105.62 Found (x3 (a1 W)) as proof of False
% 105.38/105.62 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 105.38/105.62 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 105.38/105.62 Found a10:=(a1 S):((rel_s4 S) S)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.38/105.62 Found a10:=(a1 W):((rel_s4 W) W)
% 105.38/105.62 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 S):((rel_s4 S) S)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found a10:=(a1 S):((rel_s4 S) S)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (x3 (a1 W)) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.86/124.13 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 123.86/124.13 Found a10:=(a1 W):((rel_s4 W) W)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 123.86/124.13 Found a10:=(a1 S):((rel_s4 S) S)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found a10:=(a1 S):((rel_s4 S) S)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 123.86/124.13 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 123.86/124.13 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 123.86/124.13 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 123.86/124.13 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 123.86/124.13 Found a10:=(a1 S):((rel_s4 S) S)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 123.86/124.13 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 W) V1)->False)))
% 123.86/124.13 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 131.73/131.98 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 131.73/131.98 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 131.73/131.98 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 131.73/131.98 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 131.73/131.98 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found a10:=(a1 S):((rel_s4 S) S)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (x3 (a1 S)) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 131.73/131.98 Found a10:=(a1 W):((rel_s4 W) W)
% 131.73/131.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 131.73/131.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 131.73/131.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 131.73/131.98 Found a10:=(a1 S):((rel_s4 S) S)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (x3 (a1 S)) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 131.73/131.98 Found a10:=(a1 S):((rel_s4 S) S)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (x3 (a1 S)) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 131.73/131.98 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 131.73/131.98 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found a10:=(a1 S):((rel_s4 S) S)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (x3 (a1 S)) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 131.73/131.98 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 131.73/131.98 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 131.73/131.98 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 131.73/131.98 Found a10:=(a1 S):((rel_s4 S) S)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.73/131.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (x3 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 141.24/141.47 Found a10:=(a1 W):((rel_s4 W) W)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (x3 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (x3 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found a10:=(a1 W):((rel_s4 W) W)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (x3 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 141.24/141.47 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 141.24/141.47 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 141.24/141.47 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 141.24/141.47 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 141.24/141.47 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 141.24/141.47 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (x2 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 141.24/141.47 Found a10:=(a1 W):((rel_s4 W) W)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found (a1 W) as proof of ((rel_s4 W) V0)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (x2 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 141.24/141.47 Found a10:=(a1 S):((rel_s4 S) S)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (a1 S) as proof of ((rel_s4 S) V)
% 141.24/141.47 Found (x2 (a1 S)) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 141.24/141.47 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 141.24/141.47 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 W) V1)->False)))
% 148.51/148.77 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.77 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.77 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.77 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.77 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.77 Found a10:=(a1 W):((rel_s4 W) W)
% 148.51/148.77 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.77 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.77 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.77 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 148.51/148.78 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found a10:=(a1 S):((rel_s4 S) S)
% 148.51/148.78 Found (a1 S) as proof of ((rel_s4 S) V)
% 148.51/148.78 Found (a1 S) as proof of ((rel_s4 S) V)
% 148.51/148.78 Found (a1 S) as proof of ((rel_s4 S) V)
% 148.51/148.78 Found (x2 (a1 S)) as proof of False
% 148.51/148.78 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 148.51/148.78 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 148.51/148.78 Found a10:=(a1 W):((rel_s4 W) W)
% 148.51/148.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 148.51/148.78 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 148.51/148.78 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 S) V1)->False)))
% 148.51/148.78 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.78 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.78 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.78 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 148.51/148.78 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 148.51/148.78 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 148.51/148.78 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found a10:=(a1 W):((rel_s4 W) W)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 155.59/155.86 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found a10:=(a1 W):((rel_s4 W) W)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 155.59/155.86 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found a10:=(a1 S):((rel_s4 S) S)
% 155.59/155.86 Found (a1 S) as proof of ((rel_s4 S) V0)
% 155.59/155.86 Found (a1 S) as proof of ((rel_s4 S) V0)
% 155.59/155.86 Found (a1 S) as proof of ((rel_s4 S) V0)
% 155.59/155.86 Found x3:(((rel_s4 W) V0)->False)
% 155.59/155.86 Instantiate: V0:=V00:fofType;V:=W:fofType
% 155.59/155.86 Found x3 as proof of (((rel_s4 V) V00)->False)
% 155.59/155.86 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found ((or_introl0 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 155.59/155.86 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 155.59/155.86 Found x4:(((rel_s4 W) V0)->False)
% 155.59/155.86 Instantiate: V0:=V00:fofType;V:=W:fofType
% 155.59/155.86 Found x4 as proof of (((rel_s4 V) V00)->False)
% 155.59/155.86 Found (or_introl00 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found ((or_introl0 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 155.59/155.86 Found a10:=(a1 W):((rel_s4 W) W)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found a10:=(a1 W):((rel_s4 W) W)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.59/155.86 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 155.59/155.86 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 164.13/164.45 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 164.13/164.45 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 164.13/164.45 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (x4 (a1 W)) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.13/164.45 Found x3:(((rel_s4 W) V0)->False)
% 164.13/164.45 Instantiate: V0:=V00:fofType
% 164.13/164.45 Found x3 as proof of (((rel_s4 V) V00)->False)
% 164.13/164.45 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found ((or_introl0 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found a10:=(a1 S):((rel_s4 S) S)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (x4 (a1 W)) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.13/164.45 Found x4:(((rel_s4 W) V0)->False)
% 164.13/164.45 Instantiate: V0:=V00:fofType
% 164.13/164.45 Found x4 as proof of (((rel_s4 V) V00)->False)
% 164.13/164.45 Found (or_introl00 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found ((or_introl0 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found a10:=(a1 S):((rel_s4 S) S)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (x4 (a1 W)) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (x4 (a1 W)) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.13/164.45 Found (x4 (a1 W)) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 164.13/164.45 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.13/164.45 Found a10:=(a1 W):((rel_s4 W) W)
% 164.13/164.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (x4 (a1 W)) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 171.23/171.48 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 S) V1)->False)))
% 171.23/171.48 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 171.23/171.48 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 171.23/171.48 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 171.23/171.48 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 171.23/171.48 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found a10:=(a1 S):((rel_s4 S) S)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (x4 (a1 W)) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found a10:=(a1 S):((rel_s4 S) S)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V1)
% 171.23/171.48 Found (x4 (a1 W)) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 171.23/171.48 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found a10:=(a1 W):((rel_s4 W) W)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found (a1 W) as proof of ((rel_s4 W) V0)
% 171.23/171.48 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 171.23/171.48 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 171.23/171.48 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 171.23/171.48 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 171.23/171.48 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 171.23/171.48 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 171.23/171.48 Found a10:=(a1 S):((rel_s4 S) S)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 171.23/171.48 Found (x3 (a1 S)) as proof of False
% 171.23/171.48 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 176.23/176.50 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 176.23/176.50 Found a10:=(a1 S):((rel_s4 S) S)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (x3 (a1 S)) as proof of False
% 176.23/176.50 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 176.23/176.50 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 176.23/176.50 Found a10:=(a1 W):((rel_s4 W) W)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found a10:=(a1 W):((rel_s4 W) W)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found a10:=(a1 S):((rel_s4 S) S)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 176.23/176.50 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found a10:=(a1 W):((rel_s4 W) W)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 176.23/176.50 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found a10:=(a1 W):((rel_s4 W) W)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found (a1 W) as proof of ((rel_s4 W) V0)
% 176.23/176.50 Found a10:=(a1 S):((rel_s4 S) S)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (x3 (a1 S)) as proof of False
% 176.23/176.50 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 176.23/176.50 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 176.23/176.50 Found or_introl10:=(or_introl1 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 176.23/176.50 Found (or_introl1 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 176.23/176.50 Found a10:=(a1 S):((rel_s4 S) S)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.23/176.50 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (x3 (a1 S)) as proof of False
% 187.37/187.65 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 187.37/187.65 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 187.37/187.65 Found a10:=(a1 S):((rel_s4 S) S)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found x3:(((rel_s4 S) V0)->False)
% 187.37/187.65 Instantiate: V0:=V00:fofType;V:=S:fofType
% 187.37/187.65 Found x3 as proof of (((rel_s4 V) V00)->False)
% 187.37/187.65 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found ((or_introl0 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found x4:((rel_s4 V) V0)
% 187.37/187.65 Instantiate: V1:=V0:fofType;V:=W:fofType
% 187.37/187.65 Found x4 as proof of ((rel_s4 W) V1)
% 187.37/187.65 Found (x5 x4) as proof of False
% 187.37/187.65 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 x4)) as proof of False
% 187.37/187.65 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 x4)) as proof of ((((rel_s4 W) V1)->False)->False)
% 187.37/187.65 Found x4:(((rel_s4 S) V0)->False)
% 187.37/187.65 Instantiate: V0:=V00:fofType;V:=S:fofType
% 187.37/187.65 Found x4 as proof of (((rel_s4 V) V00)->False)
% 187.37/187.65 Found (or_introl00 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found ((or_introl0 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found a10:=(a1 S):((rel_s4 S) S)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found x3:(((rel_s4 S) V0)->False)
% 187.37/187.65 Instantiate: V0:=V00:fofType
% 187.37/187.65 Found x3 as proof of (((rel_s4 V) V00)->False)
% 187.37/187.65 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found ((or_introl0 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 187.37/187.65 Found a10:=(a1 S):((rel_s4 S) S)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found (a1 S) as proof of ((rel_s4 S) V0)
% 187.37/187.65 Found x4:((rel_s4 V) V0)
% 187.37/187.65 Instantiate: V1:=V0:fofType
% 187.37/187.65 Found x4 as proof of ((rel_s4 W) V1)
% 187.37/187.65 Found (x5 x4) as proof of False
% 187.37/187.65 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 x4)) as proof of False
% 187.37/187.65 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 x4)) as proof of ((((rel_s4 W) V1)->False)->False)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (x2 (a1 W)) as proof of False
% 187.37/187.65 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 187.37/187.65 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V)
% 187.37/187.65 Found (x2 (a1 W)) as proof of False
% 187.37/187.65 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 187.37/187.65 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 187.37/187.65 Found a10:=(a1 W):((rel_s4 W) W)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found (a1 W) as proof of ((rel_s4 W) V0)
% 187.37/187.65 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V00)))
% 192.30/192.57 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V1)))
% 192.30/192.57 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 192.30/192.57 Found x4:(((rel_s4 S) V0)->False)
% 192.30/192.57 Instantiate: V0:=V00:fofType
% 192.30/192.57 Found x4 as proof of (((rel_s4 V) V00)->False)
% 192.30/192.57 Found (or_introl00 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 192.30/192.57 Found ((or_introl0 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 192.30/192.57 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 192.30/192.57 Found a10:=(a1 S):((rel_s4 S) S)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found a10:=(a1 S):((rel_s4 S) S)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (x4 (a1 S)) as proof of False
% 192.30/192.57 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 192.30/192.57 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 192.30/192.57 Found a10:=(a1 W):((rel_s4 W) W)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found a10:=(a1 W):((rel_s4 W) W)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found a10:=(a1 W):((rel_s4 W) W)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.30/192.57 Found a10:=(a1 S):((rel_s4 S) S)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V0)
% 192.30/192.57 Found a10:=(a1 S):((rel_s4 S) S)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (a1 S) as proof of ((rel_s4 S) V1)
% 192.30/192.57 Found (x4 (a1 S)) as proof of False
% 192.30/192.57 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 192.30/192.57 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 192.30/192.57 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V00)))
% 192.30/192.57 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 192.30/192.57 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V1)))
% 192.30/192.57 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 198.71/199.03 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 198.71/199.03 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 198.71/199.03 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (x2 (a1 W)) as proof of False
% 198.71/199.03 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 198.71/199.03 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (x4 (a1 S)) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (x4 (a1 S)) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (x4 (a1 S)) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V1)
% 198.71/199.03 Found (x4 (a1 S)) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 198.71/199.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V)
% 198.71/199.03 Found (x2 (a1 W)) as proof of False
% 198.71/199.03 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 198.71/199.03 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 198.71/199.03 Found a10:=(a1 S):((rel_s4 S) S)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 198.71/199.03 Found a10:=(a1 W):((rel_s4 W) W)
% 198.71/199.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 205.86/206.19 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found a10:=(a1 W):((rel_s4 W) W)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V0)))
% 205.86/206.19 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V0)))
% 205.86/206.19 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found a10:=(a1 W):((rel_s4 W) W)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (x4 (a1 S)) as proof of False
% 205.86/206.19 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 205.86/206.19 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V1)
% 205.86/206.19 Found (x4 (a1 S)) as proof of False
% 205.86/206.19 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of False
% 205.86/206.19 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found a10:=(a1 S):((rel_s4 S) S)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 205.86/206.19 Found a10:=(a1 W):((rel_s4 W) W)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.86/206.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V0)))
% 214.77/215.11 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 214.77/215.11 Found a10:=(a1 S):((rel_s4 S) S)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found a10:=(a1 S):((rel_s4 S) S)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V1)))
% 214.77/215.11 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 214.77/215.11 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V00)))
% 214.77/215.11 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 214.77/215.11 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 214.77/215.11 Found x4:((rel_s4 V) V0)
% 214.77/215.11 Instantiate: V1:=V0:fofType;V:=S:fofType
% 214.77/215.11 Found x4 as proof of ((rel_s4 S) V1)
% 214.77/215.11 Found (x5 x4) as proof of False
% 214.77/215.11 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 x4)) as proof of False
% 214.77/215.11 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 x4)) as proof of ((((rel_s4 S) V1)->False)->False)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found a10:=(a1 S):((rel_s4 S) S)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 214.77/215.11 Found a10:=(a1 W):((rel_s4 W) W)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 214.77/215.11 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V1)))
% 222.62/222.94 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 222.62/222.94 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V00)))
% 222.62/222.94 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 222.62/222.94 Found x4:((rel_s4 V) V0)
% 222.62/222.94 Instantiate: V1:=V0:fofType
% 222.62/222.94 Found x4 as proof of ((rel_s4 S) V1)
% 222.62/222.94 Found (x5 x4) as proof of False
% 222.62/222.94 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 x4)) as proof of False
% 222.62/222.94 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 x4)) as proof of ((((rel_s4 S) V1)->False)->False)
% 222.62/222.94 Found a10:=(a1 S):((rel_s4 S) S)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found a10:=(a1 W):((rel_s4 W) W)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found a10:=(a1 W):((rel_s4 W) W)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V0)))
% 222.62/222.94 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found a10:=(a1 W):((rel_s4 W) W)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 222.62/222.94 Found a10:=(a1 S):((rel_s4 S) S)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found a10:=(a1 S):((rel_s4 S) S)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 222.62/222.94 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) ((a X) V0)))
% 222.62/222.94 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 222.62/222.94 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 230.11/230.42 Found ((or_introl (((rel_s4 W) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V00)))
% 230.11/230.42 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 230.11/230.42 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V1)))
% 230.11/230.42 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 230.11/230.42 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 230.11/230.42 Found (x2 (a1 S)) as proof of False
% 230.11/230.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 230.11/230.42 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 230.11/230.42 Found a10:=(a1 S):((rel_s4 S) S)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found (a1 S) as proof of ((rel_s4 S) V0)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (x3 (a1 W)) as proof of False
% 230.11/230.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 230.11/230.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 230.11/230.42 Found a10:=(a1 W):((rel_s4 W) W)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 230.11/230.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (x3 (a1 W)) as proof of False
% 234.63/234.94 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 234.63/234.94 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 234.63/234.94 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V1)))
% 234.63/234.94 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 234.63/234.94 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V00)))
% 234.63/234.94 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 234.63/234.94 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 234.63/234.94 Found a10:=(a1 S):((rel_s4 S) S)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found a10:=(a1 S):((rel_s4 S) S)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (x2 (a1 S)) as proof of False
% 234.63/234.94 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 234.63/234.94 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 234.63/234.94 Found a10:=(a1 S):((rel_s4 S) S)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 234.63/234.94 Found (x2 (a1 S)) as proof of False
% 234.63/234.94 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 234.63/234.94 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 234.63/234.94 Found a10:=(a1 S):((rel_s4 S) S)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found a10:=(a1 W):((rel_s4 W) W)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found a10:=(a1 W):((rel_s4 W) W)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found a10:=(a1 W):((rel_s4 W) W)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 W) V1)->False)))
% 234.63/234.94 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 234.63/234.94 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 234.63/234.94 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 234.63/234.94 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 234.63/234.94 Found a10:=(a1 W):((rel_s4 W) W)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found a10:=(a1 W):((rel_s4 W) W)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 234.63/234.94 Found a10:=(a1 S):((rel_s4 S) S)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 234.63/234.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V)
% 244.26/244.54 Found (x2 (a1 S)) as proof of False
% 244.26/244.54 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of False
% 244.26/244.54 Found (fun (x2:(((rel_s4 S) V)->False))=> (x2 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (x3 (a1 W)) as proof of False
% 244.26/244.54 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 244.26/244.54 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (x3 (a1 W)) as proof of False
% 244.26/244.54 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 244.26/244.54 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V0)))
% 244.26/244.54 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V0)))
% 244.26/244.54 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 S):((rel_s4 S) S)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.26/244.54 Found a10:=(a1 W):((rel_s4 W) W)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 244.26/244.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V0)))
% 252.30/252.60 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 S):((rel_s4 S) S)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V00)))
% 252.30/252.60 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 252.30/252.60 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V1)))
% 252.30/252.60 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 252.30/252.60 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 252.30/252.60 Found a10:=(a1 S):((rel_s4 S) S)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found a10:=(a1 S):((rel_s4 S) S)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (x3 (a1 W)) as proof of False
% 252.30/252.60 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 252.30/252.60 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 W):((rel_s4 W) W)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found (a1 W) as proof of ((rel_s4 W) V0)
% 252.30/252.60 Found a10:=(a1 S):((rel_s4 S) S)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found or_introl00:=(or_introl0 ((a X) V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) ((a X) V00)))
% 257.59/257.90 Found (or_introl0 ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V1)->False)) ((a X) V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) ((a X) V00)))
% 257.59/257.90 Found a10:=(a1 S):((rel_s4 S) S)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found a10:=(a1 W):((rel_s4 W) W)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found or_introl00:=(or_introl0 ((a X) V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V1)))
% 257.59/257.90 Found (or_introl0 ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 257.59/257.90 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) ((a X) V1)))
% 257.59/257.90 Found a10:=(a1 W):((rel_s4 W) W)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found a10:=(a1 S):((rel_s4 S) S)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found a10:=(a1 S):((rel_s4 S) S)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 257.59/257.90 Found a10:=(a1 W):((rel_s4 W) W)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (x3 (a1 W)) as proof of False
% 257.59/257.90 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 257.59/257.90 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 257.59/257.90 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 W) V1)->False)))
% 257.59/257.90 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 257.59/257.90 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 257.59/257.90 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 257.59/257.90 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 257.59/257.90 Found ((or_intror ((a X) V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 257.59/257.90 Found a10:=(a1 W):((rel_s4 W) W)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 257.59/257.90 Found (x3 (a1 W)) as proof of False
% 257.59/257.90 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 257.59/257.90 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 257.59/257.90 Found a10:=(a1 W):((rel_s4 W) W)
% 257.59/257.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found a10:=(a1 W):((rel_s4 W) W)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 265.35/265.67 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found a10:=(a1 W):((rel_s4 W) W)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) ((a X) V0)))
% 265.35/265.67 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found ((or_introl (((rel_s4 S) V2)->False)) ((a X) V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 265.35/265.67 Found a10:=(a1 W):((rel_s4 W) W)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (x3 (a1 W)) as proof of False
% 265.35/265.67 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 265.35/265.67 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found a10:=(a1 W):((rel_s4 W) W)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 S) V1)->False)))
% 265.35/265.67 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 265.35/265.67 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 265.35/265.67 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 265.35/265.67 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 265.35/265.67 Found a10:=(a1 S):((rel_s4 S) S)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 265.35/265.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found a10:=(a1 W):((rel_s4 W) W)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found a10:=(a1 W):((rel_s4 W) W)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found x3:(((rel_s4 W) V0)->False)
% 281.57/281.90 Instantiate: V0:=V00:fofType;V:=W:fofType
% 281.57/281.90 Found x3 as proof of (((rel_s4 V) V00)->False)
% 281.57/281.90 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found ((or_introl1 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found x4:(((rel_s4 W) V0)->False)
% 281.57/281.90 Instantiate: V0:=V00:fofType;V:=W:fofType
% 281.57/281.90 Found x4 as proof of (((rel_s4 V) V00)->False)
% 281.57/281.90 Found (or_introl10 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found ((or_introl1 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found a10:=(a1 W):((rel_s4 W) W)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found a10:=(a1 W):((rel_s4 W) W)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found x3:(((rel_s4 W) V0)->False)
% 281.57/281.90 Instantiate: V0:=V00:fofType
% 281.57/281.90 Found x3 as proof of (((rel_s4 V) V00)->False)
% 281.57/281.90 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found ((or_introl1 ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found x4:(((rel_s4 W) V0)->False)
% 281.57/281.90 Instantiate: V0:=V00:fofType
% 281.57/281.90 Found x4 as proof of (((rel_s4 V) V00)->False)
% 281.57/281.90 Found (or_introl10 x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found ((or_introl1 ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found (((or_introl (((rel_s4 V) V00)->False)) ((a X) V00)) x4) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 281.57/281.90 Found a10:=(a1 W):((rel_s4 W) W)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found (a1 W) as proof of ((rel_s4 W) V0)
% 281.57/281.90 Found a10:=(a1 S):((rel_s4 S) S)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found (a1 S) as proof of ((rel_s4 S) V0)
% 281.57/281.90 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 281.57/281.90 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 281.57/281.90 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 281.57/281.90 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found a10:=(a1 W):((rel_s4 W) W)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found a10:=(a1 S):((rel_s4 S) S)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found a10:=(a1 S):((rel_s4 S) S)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 285.58/285.92 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 285.58/285.92 Found a10:=(a1 W):((rel_s4 W) W)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found x3:(((rel_s4 W) V0)->False)
% 285.58/285.92 Instantiate: V0:=V00:fofType;V:=W:fofType
% 285.58/285.92 Found x3 as proof of (((rel_s4 V) V00)->False)
% 285.58/285.92 Found (or_intror10 x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (or_comm_i00 (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found (((or_comm_i ((a X) V00)) (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found a10:=(a1 S):((rel_s4 S) S)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found x4:(((rel_s4 W) V0)->False)
% 285.58/285.92 Instantiate: V0:=V00:fofType;V:=W:fofType
% 285.58/285.92 Found x4 as proof of (((rel_s4 V) V00)->False)
% 285.58/285.92 Found (or_intror10 x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found ((or_intror1 (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 285.58/285.92 Found (or_comm_i00 (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found (((or_comm_i ((a X) V00)) (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 285.58/285.92 Found a10:=(a1 W):((rel_s4 W) W)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.58/285.92 Found a10:=(a1 S):((rel_s4 S) S)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.58/285.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (x2 (a1 W)) as proof of False
% 291.04/291.40 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 291.04/291.40 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V)
% 291.04/291.40 Found (x2 (a1 W)) as proof of False
% 291.04/291.40 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of False
% 291.04/291.40 Found (fun (x2:(((rel_s4 W) V)->False))=> (x2 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (x3 (a1 S)) as proof of False
% 291.04/291.40 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 291.04/291.40 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (x3 (a1 S)) as proof of False
% 291.04/291.40 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 291.04/291.40 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V1)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V1)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V1)
% 291.04/291.40 Found (x4 (a1 W)) as proof of False
% 291.04/291.40 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 291.04/291.40 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 291.04/291.40 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 291.04/291.40 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 291.04/291.40 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 291.04/291.40 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 291.04/291.40 Found a10:=(a1 S):((rel_s4 S) S)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 291.04/291.40 Found a10:=(a1 W):((rel_s4 W) W)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 291.04/291.40 Found x3:(((rel_s4 W) V0)->False)
% 291.04/291.40 Instantiate: V0:=V00:fofType
% 291.04/291.40 Found x3 as proof of (((rel_s4 V) V00)->False)
% 291.04/291.40 Found (or_intror10 x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 291.04/291.40 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 291.04/291.40 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 291.04/291.40 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 294.40/294.73 Found (or_comm_i00 (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found (((or_comm_i ((a X) V00)) (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found a10:=(a1 W):((rel_s4 W) W)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V1)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V1)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V1)
% 294.40/294.73 Found (x4 (a1 W)) as proof of False
% 294.40/294.73 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of False
% 294.40/294.73 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 294.40/294.73 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 S) V1)->False)))
% 294.40/294.73 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 294.40/294.73 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 294.40/294.73 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 294.40/294.73 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 294.40/294.73 Found ((or_intror ((a X) V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or ((a X) V0)) (((rel_s4 V) V0)->False)))
% 294.40/294.73 Found x4:(((rel_s4 W) V0)->False)
% 294.40/294.73 Instantiate: V0:=V00:fofType
% 294.40/294.73 Found x4 as proof of (((rel_s4 V) V00)->False)
% 294.40/294.73 Found (or_intror10 x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 294.40/294.73 Found ((or_intror1 (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 294.40/294.73 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 294.40/294.73 Found (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4) as proof of ((or ((a X) V00)) (((rel_s4 V) V00)->False))
% 294.40/294.73 Found (or_comm_i00 (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found (((or_comm_i ((a X) V00)) (((rel_s4 V) V00)->False)) (((or_intror ((a X) V00)) (((rel_s4 V) V00)->False)) x4)) as proof of ((or (((rel_s4 V) V00)->False)) ((a X) V00))
% 294.40/294.73 Found a10:=(a1 S):((rel_s4 S) S)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found a10:=(a1 W):((rel_s4 W) W)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found a10:=(a1 S):((rel_s4 S) S)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found (a1 S) as proof of ((rel_s4 S) V0)
% 294.40/294.73 Found or_introl00:=(or_introl0 ((a X) V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) ((a X) V0)))
% 294.40/294.73 Found (or_introl0 ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 294.40/294.73 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 294.40/294.73 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 294.40/294.73 Found ((or_introl (((rel_s4 W) V1)->False)) ((a X) V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) ((a X) V0)))
% 294.40/294.73 Found a10:=(a1 W):((rel_s4 W) W)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found a10:=(a1 W):((rel_s4 W) W)
% 294.40/294.73 Found (a1 W) as proof of ((rel_s4 W) V0)
% 294.40/294.73 Found (a1 W) as
%------------------------------------------------------------------------------