TSTP Solution File: SYO576^7 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO576^7 : TPTP v7.5.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n028.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 00:52:08 EDT 2022
% Result : Timeout 288.66s 288.98s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO576^7 : TPTP v7.5.0. Released v5.5.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % RAMPerCPU : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % DateTime : Sun Mar 13 22:00:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.46/0.63 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.46/0.63 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^0.ax, trying next directory
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1496830>, <kernel.Type object at 0x1496e60>) of role type named mu_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mu:Type
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1496440>, <kernel.DependentProduct object at 0x1496320>) of role type named qmltpeq_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1491e60>, <kernel.DependentProduct object at 0x1491c20>) of role type named meq_prop_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.63 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
% 0.46/0.63 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))))
% 0.46/0.63 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1491a28>, <kernel.DependentProduct object at 0x14919e0>) of role type named mnot_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.46/0.63 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.46/0.63 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.46/0.63 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x14919e0>, <kernel.DependentProduct object at 0x1491d40>) of role type named mor_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.63 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
% 0.46/0.63 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))))
% 0.46/0.63 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1491d40>, <kernel.DependentProduct object at 0x1491098>) of role type named mbox_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox
% 0.46/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))))
% 0.46/0.63 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.46/0.63 FOF formula (<kernel.Constant object at 0x1491098>, <kernel.DependentProduct object at 0x14919e0>) of role type named mforall_prop_type
% 0.46/0.63 Using role type
% 0.46/0.63 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.46/0.63 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% 0.46/0.63 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% 0.46/0.63 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491e60>, <kernel.DependentProduct object at 0x1491518>) of role type named mtrue_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mtrue:(fofType->Prop)
% 0.49/0.64 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.49/0.64 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.49/0.64 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491518>, <kernel.DependentProduct object at 0x1491908>) of role type named mfalse_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mfalse:(fofType->Prop)
% 0.49/0.64 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.49/0.64 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.49/0.64 Defined: mfalse:=(mnot mtrue)
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491098>, <kernel.DependentProduct object at 0x1491ab8>) of role type named mand_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.64 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
% 0.49/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.49/0.64 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491ab8>, <kernel.DependentProduct object at 0x1491050>) of role type named mimplies_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.64 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
% 0.49/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.49/0.64 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491050>, <kernel.DependentProduct object at 0x1491b48>) of role type named mimplied_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.64 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
% 0.49/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.49/0.64 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491b48>, <kernel.DependentProduct object at 0x1491518>) of role type named mequiv_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.64 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
% 0.49/0.64 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))))
% 0.49/0.64 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.49/0.64 FOF formula (<kernel.Constant object at 0x1491518>, <kernel.DependentProduct object at 0x1491098>) of role type named mxor_type
% 0.49/0.64 Using role type
% 0.49/0.64 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.64 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
% 0.49/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.49/0.65 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x1491098>, <kernel.DependentProduct object at 0x1491b48>) of role type named mdia_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.49/0.65 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
% 0.49/0.65 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)))))
% 0.49/0.65 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x1491098>, <kernel.DependentProduct object at 0x1491050>) of role type named exists_in_world_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring exists_in_world:(mu->(fofType->Prop))
% 0.49/0.65 FOF formula (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))) of role axiom named nonempty_ax
% 0.49/0.65 A new axiom: (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V))))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x1491bd8>, <kernel.DependentProduct object at 0x14912d8>) of role type named mforall_ind_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.49/0.65 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
% 0.49/0.65 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)))))
% 0.49/0.65 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x14910e0>, <kernel.DependentProduct object at 0x1600170>) of role type named mexists_ind_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.49/0.65 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
% 0.49/0.65 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)))))))
% 0.49/0.65 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x1491050>, <kernel.DependentProduct object at 0x1600128>) of role type named mexists_prop_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.49/0.65 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
% 0.49/0.65 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)))))))
% 0.49/0.65 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.49/0.65 FOF formula (<kernel.Constant object at 0x1491560>, <kernel.DependentProduct object at 0x1600560>) of role type named mreflexive_type
% 0.49/0.65 Using role type
% 0.49/0.65 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.49/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.49/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.49/0.65 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x1600560>, <kernel.DependentProduct object at 0x16004d0>) of role type named msymmetric_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.66 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)))))
% 0.49/0.66 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x16004d0>, <kernel.DependentProduct object at 0x1600488>) of role type named mserial_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.66 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))))))
% 0.49/0.66 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x1600488>, <kernel.DependentProduct object at 0x1600368>) of role type named mtransitive_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.66 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)))))
% 0.49/0.66 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x1600368>, <kernel.DependentProduct object at 0x16002d8>) of role type named meuclidean_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.66 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)))))
% 0.49/0.66 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x16002d8>, <kernel.DependentProduct object at 0x16005a8>) of role type named mpartially_functional_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.66 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)))))
% 0.49/0.66 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))))
% 0.49/0.66 FOF formula (<kernel.Constant object at 0x16005a8>, <kernel.DependentProduct object at 0x1600a28>) of role type named mfunctional_type
% 0.49/0.66 Using role type
% 0.49/0.66 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.49/0.66 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
% 0.49/0.67 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)))))))))
% 0.49/0.67 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))))))))
% 0.49/0.67 FOF formula (<kernel.Constant object at 0x1600a28>, <kernel.DependentProduct object at 0x1600ab8>) of role type named mweakly_dense_type
% 0.49/0.67 Using role type
% 0.49/0.67 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.49/0.67 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
% 0.49/0.67 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)))))))))
% 0.49/0.67 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))))))))
% 0.49/0.67 FOF formula (<kernel.Constant object at 0x1600ab8>, <kernel.DependentProduct object at 0x16002d8>) of role type named mweakly_connected_type
% 0.49/0.67 Using role type
% 0.49/0.67 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.49/0.67 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
% 0.49/0.67 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))))))
% 0.49/0.67 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)))))
% 0.49/0.67 FOF formula (<kernel.Constant object at 0x16002d8>, <kernel.DependentProduct object at 0x1600ea8>) of role type named mweakly_directed_type
% 0.49/0.67 Using role type
% 0.49/0.67 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.49/0.67 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
% 0.49/0.67 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))))))))
% 0.49/0.67 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)))))))
% 0.49/0.67 FOF formula (<kernel.Constant object at 0x16003f8>, <kernel.DependentProduct object at 0x1600d40>) of role type named mvalid_type
% 0.49/0.67 Using role type
% 0.49/0.67 Declaring mvalid:((fofType->Prop)->Prop)
% 0.49/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.49/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.49/0.67 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.49/0.67 FOF formula (<kernel.Constant object at 0x16002d8>, <kernel.DependentProduct object at 0x16009e0>) of role type named msatisfiable_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.49/0.68 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.49/0.68 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.49/0.68 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x1600d40>, <kernel.DependentProduct object at 0x1600b00>) of role type named mcountersatisfiable_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.49/0.68 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.49/0.68 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.49/0.68 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x16002d8>, <kernel.DependentProduct object at 0x1600e60>) of role type named minvalid_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring minvalid:((fofType->Prop)->Prop)
% 0.49/0.68 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.49/0.68 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.49/0.68 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.49/0.68 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x1496170>, <kernel.DependentProduct object at 0x1496b00>) of role type named rel_s4_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring rel_s4:(fofType->(fofType->Prop))
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x1496b90>, <kernel.DependentProduct object at 0x1496200>) of role type named mbox_s4_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.49/0.68 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
% 0.49/0.68 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)))))
% 0.49/0.68 Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x1496200>, <kernel.DependentProduct object at 0x14968c0>) of role type named mdia_s4_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% 0.49/0.68 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% 0.49/0.68 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% 0.49/0.68 Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% 0.49/0.68 FOF formula (mreflexive rel_s4) of role axiom named a1
% 0.49/0.68 A new axiom: (mreflexive rel_s4)
% 0.49/0.68 FOF formula (mtransitive rel_s4) of role axiom named a2
% 0.49/0.68 A new axiom: (mtransitive rel_s4)
% 0.49/0.68 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^1.ax, trying next directory
% 0.49/0.68 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
% 0.49/0.68 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)))
% 0.49/0.68 FOF formula (<kernel.Constant object at 0x2b1c18018878>, <kernel.DependentProduct object at 0x2b1c18018bd8>) of role type named p_type
% 0.49/0.68 Using role type
% 0.49/0.68 Declaring p:(fofType->Prop)
% 0.49/0.68 FOF formula (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p)))) of role conjecture named con
% 0.49/0.68 Conjecture to prove = (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p)))):Prop
% 0.49/0.68 Parameter mu_DUMMY:mu.
% 0.49/0.68 Parameter fofType_DUMMY:fofType.
% 0.49/0.68 We need to prove ['(mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p))))']
% 0.49/0.68 Parameter mu:Type.
% 0.49/0.68 Parameter fofType:Type.
% 0.49/0.68 Parameter qmltpeq:(mu->(mu->(fofType->Prop))).
% 0.49/0.68 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.49/0.68 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 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))).
% 0.49/0.68 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.49/0.68 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.49/0.68 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.49/0.68 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.49/0.68 Parameter exists_in_world:(mu->(fofType->Prop)).
% 0.49/0.68 Axiom nonempty_ax:(forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))).
% 0.49/0.68 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)).
% 0.49/0.68 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.49/0.68 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)).
% 0.49/0.68 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.49/0.68 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.49/0.68 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.49/0.68 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).
% 0.49/0.68 Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.49/0.68 Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.49/0.68 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).
% 4.25/4.41 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).
% 4.25/4.41 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).
% 4.25/4.41 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).
% 4.25/4.41 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 4.25/4.41 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 4.25/4.41 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 4.25/4.41 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 4.25/4.41 Parameter rel_s4:(fofType->(fofType->Prop)).
% 4.25/4.41 Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 4.25/4.41 Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 4.25/4.41 Axiom a1:(mreflexive rel_s4).
% 4.25/4.41 Axiom a2:(mtransitive rel_s4).
% 4.25/4.41 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))).
% 4.25/4.41 Parameter p:(fofType->Prop).
% 4.25/4.41 Trying to prove (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p))))
% 4.25/4.41 Found a10:=(a1 W):((rel_s4 W) W)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (x1 (a1 W)) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 4.25/4.41 Found a10:=(a1 S):((rel_s4 S) S)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (x1 (a1 S)) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 4.25/4.41 Found a10:=(a1 W):((rel_s4 W) W)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.25/4.41 Found (x1 (a1 W)) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 4.25/4.41 Found a10:=(a1 S):((rel_s4 S) S)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.25/4.41 Found (x1 (a1 S)) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 4.25/4.41 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 4.25/4.41 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 4.25/4.41 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 4.25/4.41 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 4.25/4.41 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 4.25/4.41 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 4.25/4.41 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 8.02/8.19 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found a10:=(a1 W):((rel_s4 W) W)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (x3 (a1 W)) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 8.02/8.19 Found a10:=(a1 W):((rel_s4 W) W)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.02/8.19 Found (x3 (a1 W)) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 8.02/8.19 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 8.02/8.19 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found a10:=(a1 W):((rel_s4 W) W)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (x1 (a1 W)) as proof of False
% 8.02/8.19 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 8.02/8.19 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 8.02/8.19 Found a10:=(a1 W):((rel_s4 W) W)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.02/8.19 Found (x1 (a1 W)) as proof of False
% 8.02/8.19 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 8.02/8.19 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 8.02/8.19 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 8.02/8.19 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.02/8.19 Found a10:=(a1 S):((rel_s4 S) S)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (x3 (a1 S)) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 8.02/8.19 Found a10:=(a1 S):((rel_s4 S) S)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 8.02/8.19 Found (x3 (a1 S)) as proof of False
% 8.02/8.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 13.25/13.42 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 13.25/13.42 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 13.25/13.42 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 13.25/13.42 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found a10:=(a1 W):((rel_s4 W) W)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (x3 (a1 W)) as proof of False
% 13.25/13.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 13.25/13.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 13.25/13.42 Found a10:=(a1 W):((rel_s4 W) W)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 13.25/13.42 Found (x3 (a1 W)) as proof of False
% 13.25/13.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 13.25/13.42 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 13.25/13.42 Found a10:=(a1 S):((rel_s4 S) S)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (x1 (a1 S)) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 13.25/13.42 Found a10:=(a1 S):((rel_s4 S) S)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (a1 S) as proof of ((rel_s4 S) V)
% 13.25/13.42 Found (x1 (a1 S)) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 13.25/13.42 Found a10:=(a1 W):((rel_s4 W) W)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (x1 (a1 W)) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 13.25/13.42 Found a10:=(a1 W):((rel_s4 W) W)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (a1 W) as proof of ((rel_s4 W) V)
% 13.25/13.42 Found (x1 (a1 W)) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 13.25/13.42 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 13.25/13.42 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 13.25/13.42 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 13.25/13.42 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 19.71/19.87 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (x3 (a1 S)) as proof of False
% 19.71/19.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 19.71/19.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (x3 (a1 S)) as proof of False
% 19.71/19.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 19.71/19.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (x1 (a1 S)) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V)
% 19.71/19.87 Found (x1 (a1 S)) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 19.71/19.87 Found a10:=(a1 W):((rel_s4 W) W)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found a10:=(a1 V):((rel_s4 V) V)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (x1 (a1 V)) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 19.71/19.87 Found a10:=(a1 W):((rel_s4 W) W)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found a10:=(a1 W):((rel_s4 W) W)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found a10:=(a1 W):((rel_s4 W) W)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found (a1 W) as proof of ((rel_s4 W) V0)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found a10:=(a1 V):((rel_s4 V) V)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (a1 V) as proof of ((rel_s4 V) V0)
% 19.71/19.87 Found (x1 (a1 V)) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 19.71/19.87 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found a10:=(a1 S):((rel_s4 S) S)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 19.71/19.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.73/24.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.73/24.92 Found a10:=(a1 S):((rel_s4 S) S)
% 24.73/24.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.73/24.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.73/24.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.73/24.92 Found a10:=(a1 V):((rel_s4 V) V)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (x1 (a1 V)) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 24.73/24.92 Found a10:=(a1 V):((rel_s4 V) V)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (x1 (a1 V)) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 24.73/24.92 Found a10:=(a1 W):((rel_s4 W) W)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found a10:=(a1 W):((rel_s4 W) W)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found a10:=(a1 W):((rel_s4 W) W)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found a10:=(a1 W):((rel_s4 W) W)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.73/24.92 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.73/24.92 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.73/24.92 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found a10:=(a1 V):((rel_s4 V) V)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (x1 (a1 V)) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 24.73/24.92 Found a10:=(a1 V):((rel_s4 V) V)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (a1 V) as proof of ((rel_s4 V) V0)
% 24.73/24.92 Found (x1 (a1 V)) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 24.73/24.92 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 24.73/24.92 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.73/24.92 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.73/24.92 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found a10:=(a1 W):((rel_s4 W) W)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (x3 (a1 W)) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 28.85/29.02 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 28.85/29.02 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found a10:=(a1 W):((rel_s4 W) W)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (x3 (a1 W)) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 28.85/29.02 Found a10:=(a1 S):((rel_s4 S) S)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found a10:=(a1 W):((rel_s4 W) W)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (x3 (a1 W)) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 28.85/29.02 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 28.85/29.02 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found a10:=(a1 W):((rel_s4 W) W)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.85/29.02 Found (x3 (a1 W)) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 28.85/29.02 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 28.85/29.02 Found a10:=(a1 S):((rel_s4 S) S)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.85/29.02 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 28.85/29.02 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 28.85/29.02 Found a10:=(a1 V):((rel_s4 V) V)
% 28.85/29.02 Found (a1 V) as proof of ((rel_s4 V) V0)
% 36.91/37.11 Found (a1 V) as proof of ((rel_s4 V) V0)
% 36.91/37.11 Found (a1 V) as proof of ((rel_s4 V) V0)
% 36.91/37.11 Found (x1 (a1 V)) as proof of False
% 36.91/37.11 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 36.91/37.11 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 36.91/37.11 Found a10:=(a1 S):((rel_s4 S) S)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found a10:=(a1 S):((rel_s4 S) S)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 36.91/37.11 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found a10:=(a1 W):((rel_s4 W) W)
% 36.91/37.11 Found (a1 W) as proof of ((rel_s4 W) V)
% 36.91/37.11 Found (a1 W) as proof of ((rel_s4 W) V)
% 36.91/37.11 Found (a1 W) as proof of ((rel_s4 W) V)
% 36.91/37.11 Found (x1 (a1 W)) as proof of False
% 36.91/37.11 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 36.91/37.11 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 36.91/37.11 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 36.91/37.11 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 36.91/37.11 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found a10:=(a1 S):((rel_s4 S) S)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 36.91/37.11 Found (x3 (a1 S)) as proof of False
% 36.91/37.11 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 36.91/37.11 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 36.91/37.11 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 36.91/37.11 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 36.91/37.11 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 36.91/37.11 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found a10:=(a1 S):((rel_s4 S) S)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (x3 (a1 S)) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 42.63/42.89 Found a10:=(a1 S):((rel_s4 S) S)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (x3 (a1 S)) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 42.63/42.89 Found a10:=(a1 S):((rel_s4 S) S)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (a1 S) as proof of ((rel_s4 S) V0)
% 42.63/42.89 Found (x3 (a1 S)) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 42.63/42.89 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 42.63/42.89 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 42.63/42.89 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 42.63/42.89 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 42.63/42.89 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 42.63/42.89 Found a10:=(a1 V):((rel_s4 V) V)
% 42.63/42.89 Found (a1 V) as proof of ((rel_s4 V) V0)
% 42.63/42.89 Found (a1 V) as proof of ((rel_s4 V) V0)
% 42.63/42.89 Found (a1 V) as proof of ((rel_s4 V) V0)
% 42.63/42.89 Found (x1 (a1 V)) as proof of False
% 42.63/42.89 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 42.63/42.89 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 42.63/42.89 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 42.63/42.89 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 47.23/47.43 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found a10:=(a1 W):((rel_s4 W) W)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (x3 (a1 W)) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 47.23/47.43 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 47.23/47.43 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found a10:=(a1 W):((rel_s4 W) W)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (x3 (a1 W)) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 47.23/47.43 Found a10:=(a1 W):((rel_s4 W) W)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.23/47.43 Found (x3 (a1 W)) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 47.23/47.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 47.23/47.43 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 47.23/47.43 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.23/47.43 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 47.23/47.43 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 47.23/47.43 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 56.54/56.80 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 56.54/56.80 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (x3 (a1 W)) as proof of False
% 56.54/56.80 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 56.54/56.80 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found a10:=(a1 S):((rel_s4 S) S)
% 56.54/56.80 Found (a1 S) as proof of ((rel_s4 S) V)
% 56.54/56.80 Found (a1 S) as proof of ((rel_s4 S) V)
% 56.54/56.80 Found (a1 S) as proof of ((rel_s4 S) V)
% 56.54/56.80 Found (x1 (a1 S)) as proof of False
% 56.54/56.80 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 56.54/56.80 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 56.54/56.80 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 56.54/56.80 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V)
% 56.54/56.80 Found (x1 (a1 W)) as proof of False
% 56.54/56.80 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 56.54/56.80 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found x3:(((rel_s4 W) V0)->False)
% 56.54/56.80 Instantiate: V0:=V00:fofType;V:=W:fofType
% 56.54/56.80 Found x3 as proof of (((rel_s4 V) V00)->False)
% 56.54/56.80 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found a10:=(a1 W):((rel_s4 W) W)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found (a1 W) as proof of ((rel_s4 W) V0)
% 56.54/56.80 Found x3:(((rel_s4 W) V0)->False)
% 56.54/56.80 Instantiate: V0:=V00:fofType
% 56.54/56.80 Found x3 as proof of (((rel_s4 V) V00)->False)
% 56.54/56.80 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 56.54/56.80 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 56.54/56.80 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 56.54/56.80 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.90/62.12 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 61.90/62.12 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found a10:=(a1 W):((rel_s4 W) W)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found x2:((rel_s4 V) V0)
% 61.90/62.12 Instantiate: V1:=V0:fofType;V:=W:fofType
% 61.90/62.12 Found x2 as proof of ((rel_s4 W) V1)
% 61.90/62.12 Found (x4 x2) as proof of False
% 61.90/62.12 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 61.90/62.12 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 61.90/62.12 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 61.90/62.12 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.90/62.12 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 61.90/62.12 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.90/62.12 Found a10:=(a1 W):((rel_s4 W) W)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 61.90/62.12 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 61.90/62.12 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found x2:((rel_s4 V) V0)
% 61.90/62.12 Instantiate: V1:=V0:fofType
% 61.90/62.12 Found x2 as proof of ((rel_s4 W) V1)
% 61.90/62.12 Found (x4 x2) as proof of False
% 61.90/62.12 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 61.90/62.12 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 61.90/62.12 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 61.90/62.12 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.90/62.12 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 64.71/64.94 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 64.71/64.94 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 64.71/64.94 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 64.71/64.94 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 64.71/64.94 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 64.71/64.94 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 64.71/64.94 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 64.71/64.94 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 64.71/64.94 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 64.71/64.94 Found a10:=(a1 W):((rel_s4 W) W)
% 64.71/64.94 Found (a1 W) as proof of ((rel_s4 W) V1)
% 64.71/64.94 Found (a1 W) as proof of ((rel_s4 W) V1)
% 64.71/64.94 Found (a1 W) as proof of ((rel_s4 W) V1)
% 64.71/64.94 Found (x5 (a1 W)) as proof of False
% 64.71/64.94 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 64.71/64.94 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 64.71/64.94 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 64.71/64.94 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 64.71/64.94 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 64.71/64.94 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 68.02/68.25 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 68.02/68.25 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 68.02/68.25 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 68.02/68.25 Found a10:=(a1 W):((rel_s4 W) W)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (x5 (a1 W)) as proof of False
% 68.02/68.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 68.02/68.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 68.02/68.25 Found a10:=(a1 W):((rel_s4 W) W)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (a1 W) as proof of ((rel_s4 W) V1)
% 68.02/68.25 Found (x5 (a1 W)) as proof of False
% 68.02/68.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 68.02/68.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 68.02/68.25 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 68.02/68.25 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found a10:=(a1 S):((rel_s4 S) S)
% 68.02/68.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 68.02/68.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 68.02/68.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 68.02/68.25 Found (x3 (a1 S)) as proof of False
% 68.02/68.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 68.02/68.25 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 68.02/68.25 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 68.02/68.25 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 68.02/68.25 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 73.88/74.10 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 73.88/74.10 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 73.88/74.10 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 73.88/74.10 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 73.88/74.10 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 73.88/74.10 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 73.88/74.10 Found a10:=(a1 W):((rel_s4 W) W)
% 73.88/74.10 Found (a1 W) as proof of ((rel_s4 W) V1)
% 73.88/74.10 Found (a1 W) as proof of ((rel_s4 W) V1)
% 73.88/74.10 Found (a1 W) as proof of ((rel_s4 W) V1)
% 73.88/74.10 Found (x5 (a1 W)) as proof of False
% 73.88/74.10 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 73.88/74.10 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 73.88/74.10 Found a10:=(a1 S):((rel_s4 S) S)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 73.88/74.10 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 73.88/74.10 Found a10:=(a1 S):((rel_s4 S) S)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (x3 (a1 S)) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 73.88/74.10 Found a10:=(a1 S):((rel_s4 S) S)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (x3 (a1 S)) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 73.88/74.10 Found a10:=(a1 S):((rel_s4 S) S)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found a10:=(a1 S):((rel_s4 S) S)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 73.88/74.10 Found (x3 (a1 S)) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 73.88/74.10 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 73.88/74.10 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 85.21/85.48 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 85.21/85.48 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 85.21/85.48 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 85.21/85.48 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 85.21/85.48 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 85.21/85.48 Found x3:(((rel_s4 S) V0)->False)
% 85.21/85.48 Instantiate: V0:=V00:fofType;V:=S:fofType
% 85.21/85.48 Found x3 as proof of (((rel_s4 V) V00)->False)
% 85.21/85.48 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found a10:=(a1 S):((rel_s4 S) S)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found x3:(((rel_s4 S) V0)->False)
% 85.21/85.48 Instantiate: V0:=V00:fofType
% 85.21/85.48 Found x3 as proof of (((rel_s4 V) V00)->False)
% 85.21/85.48 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 85.21/85.48 Found a10:=(a1 S):((rel_s4 S) S)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V)
% 85.21/85.48 Found (x1 (a1 S)) as proof of False
% 85.21/85.48 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 85.21/85.48 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 85.21/85.48 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 85.21/85.48 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 85.21/85.48 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 85.21/85.48 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 85.21/85.48 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 85.21/85.48 Found a10:=(a1 S):((rel_s4 S) S)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 85.21/85.48 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 85.21/85.48 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 85.21/85.48 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 85.21/85.48 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 85.21/85.48 Found a10:=(a1 S):((rel_s4 S) S)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found (a1 S) as proof of ((rel_s4 S) V0)
% 85.21/85.48 Found x2:((rel_s4 V) V0)
% 85.21/85.48 Instantiate: V1:=V0:fofType;V:=S:fofType
% 85.21/85.48 Found x2 as proof of ((rel_s4 S) V1)
% 85.21/85.48 Found (x4 x2) as proof of False
% 85.21/85.48 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 85.21/85.48 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 85.21/85.48 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 89.88/90.13 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 89.88/90.13 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found a10:=(a1 S):((rel_s4 S) S)
% 89.88/90.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 89.88/90.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 89.88/90.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 89.88/90.13 Found x2:((rel_s4 V) V0)
% 89.88/90.13 Instantiate: V1:=V0:fofType
% 89.88/90.13 Found x2 as proof of ((rel_s4 S) V1)
% 89.88/90.13 Found (x4 x2) as proof of False
% 89.88/90.13 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 89.88/90.13 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 89.88/90.13 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 89.88/90.13 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 89.88/90.13 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 89.88/90.13 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 89.88/90.13 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 89.88/90.13 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 89.88/90.13 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 89.88/90.13 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 89.88/90.13 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 89.88/90.13 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 89.88/90.13 Found a10:=(a1 W):((rel_s4 W) W)
% 89.88/90.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 89.88/90.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 89.88/90.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 89.88/90.13 Found a10:=(a1 V):((rel_s4 V) V)
% 89.88/90.13 Found (a1 V) as proof of ((rel_s4 V) V00)
% 89.88/90.13 Found (a1 V) as proof of ((rel_s4 V) V00)
% 89.88/90.13 Found (a1 V) as proof of ((rel_s4 V) V00)
% 89.88/90.13 Found (x2 (a1 V)) as proof of False
% 89.88/90.13 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 89.88/90.13 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 93.39/93.63 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 93.39/93.63 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 93.39/93.63 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 93.39/93.63 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.39/93.63 Found a10:=(a1 V):((rel_s4 V) V)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (x1 (a1 V)) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 93.39/93.63 Found a10:=(a1 V):((rel_s4 V) V)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (x1 (a1 V)) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 93.39/93.63 Found a10:=(a1 W):((rel_s4 W) W)
% 93.39/93.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.39/93.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.39/93.63 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.39/93.63 Found a10:=(a1 S):((rel_s4 S) S)
% 93.39/93.63 Found (a1 S) as proof of ((rel_s4 S) V1)
% 93.39/93.63 Found (a1 S) as proof of ((rel_s4 S) V1)
% 93.39/93.63 Found (a1 S) as proof of ((rel_s4 S) V1)
% 93.39/93.63 Found (x5 (a1 S)) as proof of False
% 93.39/93.63 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 93.39/93.63 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 93.39/93.63 Found a10:=(a1 V):((rel_s4 V) V)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (a1 V) as proof of ((rel_s4 V) V0)
% 93.39/93.63 Found (x1 (a1 V)) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 93.39/93.63 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 93.39/93.63 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 93.39/93.63 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 93.39/93.63 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 97.99/98.20 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 97.99/98.20 Found a10:=(a1 W):((rel_s4 W) W)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found a10:=(a1 V):((rel_s4 V) V)
% 97.99/98.20 Found (a1 V) as proof of ((rel_s4 V) V00)
% 97.99/98.20 Found (a1 V) as proof of ((rel_s4 V) V00)
% 97.99/98.20 Found (a1 V) as proof of ((rel_s4 V) V00)
% 97.99/98.20 Found (x2 (a1 V)) as proof of False
% 97.99/98.20 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 97.99/98.20 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 97.99/98.20 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 97.99/98.20 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 97.99/98.20 Found a10:=(a1 W):((rel_s4 W) W)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.99/98.20 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 97.99/98.20 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 97.99/98.20 Found a10:=(a1 S):((rel_s4 S) S)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (x5 (a1 S)) as proof of False
% 97.99/98.20 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 97.99/98.20 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 97.99/98.20 Found a10:=(a1 S):((rel_s4 S) S)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (a1 S) as proof of ((rel_s4 S) V1)
% 97.99/98.20 Found (x5 (a1 S)) as proof of False
% 97.99/98.20 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 97.99/98.20 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 97.99/98.20 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 97.99/98.20 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.69/105.98 Found a10:=(a1 W):((rel_s4 W) W)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 105.69/105.98 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 105.69/105.98 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 105.69/105.98 Found a10:=(a1 W):((rel_s4 W) W)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found x3:(((rel_s4 W) V0)->False)
% 105.69/105.98 Instantiate: V0:=V00:fofType;V:=W:fofType
% 105.69/105.98 Found x3 as proof of (((rel_s4 V) V00)->False)
% 105.69/105.98 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found a10:=(a1 W):((rel_s4 W) W)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found a10:=(a1 S):((rel_s4 S) S)
% 105.69/105.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 105.69/105.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 105.69/105.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 105.69/105.98 Found (x5 (a1 S)) as proof of False
% 105.69/105.98 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 105.69/105.98 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 105.69/105.98 Found x2:((rel_s4 V) V0)
% 105.69/105.98 Instantiate: V1:=V0:fofType;V:=W:fofType
% 105.69/105.98 Found x2 as proof of ((rel_s4 W) V1)
% 105.69/105.98 Found (x4 x2) as proof of False
% 105.69/105.98 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 105.69/105.98 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 105.69/105.98 Found x3:(((rel_s4 W) V0)->False)
% 105.69/105.98 Instantiate: V0:=V00:fofType
% 105.69/105.98 Found x3 as proof of (((rel_s4 V) V00)->False)
% 105.69/105.98 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 105.69/105.98 Found a10:=(a1 W):((rel_s4 W) W)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found a10:=(a1 W):((rel_s4 W) W)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.69/105.98 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 105.69/105.98 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 105.69/105.98 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 105.69/105.98 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 105.69/105.98 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 113.08/113.34 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found x2:((rel_s4 V) V0)
% 113.08/113.34 Instantiate: V1:=V0:fofType
% 113.08/113.34 Found x2 as proof of ((rel_s4 W) V1)
% 113.08/113.34 Found (x4 x2) as proof of False
% 113.08/113.34 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 113.08/113.34 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found x3:(((rel_s4 W) V0)->False)
% 113.08/113.34 Instantiate: V0:=V00:fofType;V:=W:fofType
% 113.08/113.34 Found x3 as proof of (((rel_s4 V) V00)->False)
% 113.08/113.34 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 113.08/113.34 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 113.08/113.34 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 113.08/113.34 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 113.08/113.34 Found (or_comm_i00 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 113.08/113.34 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 113.08/113.34 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 113.08/113.34 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found x2:((rel_s4 V) V0)
% 113.08/113.34 Instantiate: V1:=V0:fofType;V:=W:fofType
% 113.08/113.34 Found x2 as proof of ((rel_s4 W) V1)
% 113.08/113.34 Found (x4 x2) as proof of False
% 113.08/113.34 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 113.08/113.34 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found a10:=(a1 W):((rel_s4 W) W)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found (a1 W) as proof of ((rel_s4 W) V0)
% 113.08/113.34 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 113.08/113.34 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found x3:(((rel_s4 W) V0)->False)
% 116.97/117.30 Instantiate: V0:=V00:fofType
% 116.97/117.30 Found x3 as proof of (((rel_s4 V) V00)->False)
% 116.97/117.30 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 116.97/117.30 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 116.97/117.30 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 116.97/117.30 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 116.97/117.30 Found (or_comm_i00 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 116.97/117.30 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 116.97/117.30 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 116.97/117.30 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 116.97/117.30 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 116.97/117.30 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found a10:=(a1 W):((rel_s4 W) W)
% 116.97/117.30 Found (a1 W) as proof of ((rel_s4 W) V0)
% 116.97/117.30 Found (a1 W) as proof of ((rel_s4 W) V0)
% 116.97/117.30 Found (a1 W) as proof of ((rel_s4 W) V0)
% 116.97/117.30 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 116.97/117.30 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 116.97/117.30 Found x2:((rel_s4 V) V0)
% 116.97/117.30 Instantiate: V1:=V0:fofType
% 116.97/117.30 Found x2 as proof of ((rel_s4 W) V1)
% 116.97/117.30 Found (x4 x2) as proof of False
% 116.97/117.30 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 116.97/117.30 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 116.97/117.30 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 116.97/117.30 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 116.97/117.30 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 123.40/123.63 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 123.40/123.63 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 123.40/123.63 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 123.40/123.63 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 123.40/123.63 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 123.40/123.63 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 123.40/123.63 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 123.40/123.63 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 123.40/123.63 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 123.40/123.63 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 123.40/123.63 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 128.27/128.55 Found a10:=(a1 W):((rel_s4 W) W)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 128.27/128.55 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 128.27/128.55 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 128.27/128.55 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 128.27/128.55 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 128.27/128.55 Found ((or_intror (p V0)) (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 128.27/128.55 Found a10:=(a1 W):((rel_s4 W) W)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.27/128.55 Found (x5 (a1 W)) as proof of False
% 128.27/128.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 128.27/128.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 128.27/128.55 Found a10:=(a1 S):((rel_s4 S) S)
% 128.27/128.55 Found (a1 S) as proof of ((rel_s4 S) V0)
% 128.27/128.55 Found (a1 S) as proof of ((rel_s4 S) V0)
% 128.27/128.55 Found (a1 S) as proof of ((rel_s4 S) V0)
% 128.27/128.55 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 128.27/128.55 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 128.27/128.55 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 128.27/128.55 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 128.27/128.55 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 128.27/128.55 Found a10:=(a1 W):((rel_s4 W) W)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 128.27/128.55 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 128.27/128.55 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 128.27/128.55 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 131.10/131.37 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 131.10/131.37 Found a10:=(a1 V):((rel_s4 V) V)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (x1 (a1 V)) as proof of False
% 131.10/131.37 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 131.10/131.37 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 131.10/131.37 Found a10:=(a1 V):((rel_s4 V) V)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V0)
% 131.10/131.37 Found (x1 (a1 V)) as proof of False
% 131.10/131.37 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 131.10/131.37 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 131.10/131.37 Found a10:=(a1 W):((rel_s4 W) W)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (x5 (a1 W)) as proof of False
% 131.10/131.37 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 131.10/131.37 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 131.10/131.37 Found a10:=(a1 W):((rel_s4 W) W)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 131.10/131.37 Found (x5 (a1 W)) as proof of False
% 131.10/131.37 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 131.10/131.37 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 131.10/131.37 Found a10:=(a1 V):((rel_s4 V) V)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V00)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V00)
% 131.10/131.37 Found (a1 V) as proof of ((rel_s4 V) V00)
% 131.10/131.37 Found (x2 (a1 V)) as proof of False
% 131.10/131.37 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 131.10/131.37 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 131.10/131.37 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 131.10/131.37 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 131.10/131.37 Found ((or_introl (((rel_s4 W) V2)->False)) (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 131.10/131.37 Found a10:=(a1 S):((rel_s4 S) S)
% 131.10/131.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.10/131.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.10/131.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 131.10/131.37 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 131.10/131.37 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 138.38/138.61 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 138.38/138.61 Found a10:=(a1 S):((rel_s4 S) S)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 138.38/138.61 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 138.38/138.61 Found ((or_introl (((rel_s4 W) V2)->False)) (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 138.38/138.61 Found a10:=(a1 W):((rel_s4 W) W)
% 138.38/138.61 Found (a1 W) as proof of ((rel_s4 W) V1)
% 138.38/138.61 Found (a1 W) as proof of ((rel_s4 W) V1)
% 138.38/138.61 Found (a1 W) as proof of ((rel_s4 W) V1)
% 138.38/138.61 Found (x5 (a1 W)) as proof of False
% 138.38/138.61 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 138.38/138.61 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 138.38/138.61 Found a10:=(a1 V):((rel_s4 V) V)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V00)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V00)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V00)
% 138.38/138.61 Found (x2 (a1 V)) as proof of False
% 138.38/138.61 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 138.38/138.61 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 138.38/138.61 Found a10:=(a1 V):((rel_s4 V) V)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V0)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V0)
% 138.38/138.61 Found (a1 V) as proof of ((rel_s4 V) V0)
% 138.38/138.61 Found (x1 (a1 V)) as proof of False
% 138.38/138.61 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 138.38/138.61 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 138.38/138.61 Found a10:=(a1 S):((rel_s4 S) S)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found a10:=(a1 S):((rel_s4 S) S)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found (a1 S) as proof of ((rel_s4 S) V0)
% 138.38/138.61 Found x3:(((rel_s4 S) V0)->False)
% 138.38/138.61 Instantiate: V0:=V00:fofType;V:=S:fofType
% 138.38/138.61 Found x3 as proof of (((rel_s4 V) V00)->False)
% 138.38/138.61 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 138.38/138.61 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 147.87/148.10 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 147.87/148.10 Found a10:=(a1 S):((rel_s4 S) S)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found x2:((rel_s4 V) V0)
% 147.87/148.10 Instantiate: V1:=V0:fofType;V:=S:fofType
% 147.87/148.10 Found x2 as proof of ((rel_s4 S) V1)
% 147.87/148.10 Found (x4 x2) as proof of False
% 147.87/148.10 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 147.87/148.10 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 147.87/148.10 Found x4:((rel_s4 V) V0)
% 147.87/148.10 Instantiate: V2:=V0:fofType;V:=W:fofType
% 147.87/148.10 Found x4 as proof of ((rel_s4 W) V2)
% 147.87/148.10 Found (x6 x4) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 147.87/148.10 Found a10:=(a1 S):((rel_s4 S) S)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found x3:(((rel_s4 S) V0)->False)
% 147.87/148.10 Instantiate: V0:=V00:fofType
% 147.87/148.10 Found x3 as proof of (((rel_s4 V) V00)->False)
% 147.87/148.10 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 147.87/148.10 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 147.87/148.10 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 147.87/148.10 Found a10:=(a1 S):((rel_s4 S) S)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found x4:((rel_s4 V) V0)
% 147.87/148.10 Instantiate: V2:=V0:fofType
% 147.87/148.10 Found x4 as proof of ((rel_s4 W) V2)
% 147.87/148.10 Found (x6 x4) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 147.87/148.10 Found x2:((rel_s4 V) V0)
% 147.87/148.10 Instantiate: V1:=V0:fofType
% 147.87/148.10 Found x2 as proof of ((rel_s4 S) V1)
% 147.87/148.10 Found (x4 x2) as proof of False
% 147.87/148.10 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 147.87/148.10 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 147.87/148.10 Found x4:((rel_s4 V) V0)
% 147.87/148.10 Instantiate: V2:=V0:fofType
% 147.87/148.10 Found x4 as proof of ((rel_s4 W) V2)
% 147.87/148.10 Found (x6 x4) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 147.87/148.10 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 147.87/148.10 Found a10:=(a1 V):((rel_s4 V) V)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (x1 (a1 V)) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 147.87/148.10 Found a10:=(a1 V):((rel_s4 V) V)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (x1 (a1 V)) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 147.87/148.10 Found a10:=(a1 S):((rel_s4 S) S)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found (a1 S) as proof of ((rel_s4 S) V0)
% 147.87/148.10 Found a10:=(a1 V):((rel_s4 V) V)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (x1 (a1 V)) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 147.87/148.10 Found a10:=(a1 V):((rel_s4 V) V)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (a1 V) as proof of ((rel_s4 V) V0)
% 147.87/148.10 Found (x1 (a1 V)) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 147.87/148.10 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 149.69/149.94 Found a10:=(a1 V):((rel_s4 V) V)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (x1 (a1 V)) as proof of False
% 149.69/149.94 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 149.69/149.94 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 149.69/149.94 Found a10:=(a1 V):((rel_s4 V) V)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (a1 V) as proof of ((rel_s4 V) V0)
% 149.69/149.94 Found (x1 (a1 V)) as proof of False
% 149.69/149.94 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 149.69/149.94 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 149.69/149.94 Found x3:(((rel_s4 S) V0)->False)
% 149.69/149.94 Instantiate: V0:=V00:fofType;V:=S:fofType
% 149.69/149.94 Found x3 as proof of (((rel_s4 V) V00)->False)
% 149.69/149.94 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 149.69/149.94 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 149.69/149.94 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 149.69/149.94 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 149.69/149.94 Found (or_comm_i00 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 149.69/149.94 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 149.69/149.94 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 149.69/149.94 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 149.69/149.94 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 149.69/149.94 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 149.69/149.94 Found a10:=(a1 S):((rel_s4 S) S)
% 149.69/149.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 149.69/149.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 149.69/149.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 149.69/149.94 Found or_introl20:=(or_introl2 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 149.69/149.94 Found (or_introl2 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 149.69/149.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 149.69/149.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 149.69/149.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 149.69/149.94 Found or_introl00:=(or_introl0 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 158.18/158.40 Found (or_introl0 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 158.18/158.40 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 158.18/158.40 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 158.18/158.40 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 158.18/158.40 Found a10:=(a1 S):((rel_s4 S) S)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found x2:((rel_s4 V) V0)
% 158.18/158.40 Instantiate: V1:=V0:fofType;V:=S:fofType
% 158.18/158.40 Found x2 as proof of ((rel_s4 S) V1)
% 158.18/158.40 Found (x4 x2) as proof of False
% 158.18/158.40 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 158.18/158.40 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 158.18/158.40 Found x4:((rel_s4 V) V0)
% 158.18/158.40 Instantiate: V2:=V0:fofType
% 158.18/158.40 Found x4 as proof of ((rel_s4 W) V2)
% 158.18/158.40 Found (x6 x4) as proof of False
% 158.18/158.40 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 158.18/158.40 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 158.18/158.40 Found a10:=(a1 S):((rel_s4 S) S)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found a10:=(a1 S):((rel_s4 S) S)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found x3:(((rel_s4 S) V0)->False)
% 158.18/158.40 Instantiate: V0:=V00:fofType
% 158.18/158.40 Found x3 as proof of (((rel_s4 V) V00)->False)
% 158.18/158.40 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 158.18/158.40 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 158.18/158.40 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 158.18/158.40 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 158.18/158.40 Found (or_comm_i00 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.18/158.40 Found ((or_comm_i0 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.18/158.40 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.18/158.40 Found a10:=(a1 S):((rel_s4 S) S)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 158.18/158.40 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 158.18/158.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 158.18/158.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 158.18/158.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 158.18/158.40 Found a10:=(a1 S):((rel_s4 S) S)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.18/158.40 Found x2:((rel_s4 V) V0)
% 158.18/158.40 Instantiate: V1:=V0:fofType
% 158.18/158.40 Found x2 as proof of ((rel_s4 S) V1)
% 158.18/158.40 Found (x4 x2) as proof of False
% 158.18/158.40 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 158.18/158.40 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 158.18/158.40 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 158.18/158.40 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 163.16/163.40 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 163.16/163.40 Found a10:=(a1 S):((rel_s4 S) S)
% 163.16/163.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 163.16/163.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 163.16/163.40 Found (a1 S) as proof of ((rel_s4 S) V0)
% 163.16/163.40 Found a10:=(a1 W):((rel_s4 W) W)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found a10:=(a1 V):((rel_s4 V) V)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (x2 (a1 V)) as proof of False
% 163.16/163.40 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 163.16/163.40 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 163.16/163.40 Found a10:=(a1 V):((rel_s4 V) V)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (a1 V) as proof of ((rel_s4 V) V00)
% 163.16/163.40 Found (x2 (a1 V)) as proof of False
% 163.16/163.40 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 163.16/163.40 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 163.16/163.40 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 163.16/163.40 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 163.16/163.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 163.16/163.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 163.16/163.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 163.16/163.40 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 163.16/163.40 Found a10:=(a1 W):((rel_s4 W) W)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found (a1 W) as proof of ((rel_s4 W) V0)
% 163.16/163.40 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 163.16/163.40 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 163.16/163.40 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 163.16/163.40 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 163.16/163.40 Found (or_introl1 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 163.16/163.40 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 163.16/163.40 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 168.68/168.94 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 168.68/168.94 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 168.68/168.94 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 168.68/168.94 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 168.68/168.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 168.68/168.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 168.68/168.94 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 168.68/168.94 Found or_introl20:=(or_introl2 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found (or_introl2 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found or_introl00:=(or_introl0 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found (or_introl0 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 168.68/168.94 Found a10:=(a1 W):((rel_s4 W) W)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found a10:=(a1 S):((rel_s4 S) S)
% 168.68/168.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.68/168.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.68/168.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.68/168.94 Found a10:=(a1 V):((rel_s4 V) V)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (x2 (a1 V)) as proof of False
% 168.68/168.94 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 168.68/168.94 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 168.68/168.94 Found a10:=(a1 V):((rel_s4 V) V)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (a1 V) as proof of ((rel_s4 V) V00)
% 168.68/168.94 Found (x2 (a1 V)) as proof of False
% 168.68/168.94 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 168.68/168.94 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 168.68/168.94 Found a10:=(a1 W):((rel_s4 W) W)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.68/168.94 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 171.85/172.18 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 171.85/172.18 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 171.85/172.18 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 171.85/172.18 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 171.85/172.18 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 171.85/172.18 Found (or_introl1 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 171.85/172.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 171.85/172.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 171.85/172.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 171.85/172.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 171.85/172.18 Found x3:(((rel_s4 W) V0)->False)
% 171.85/172.18 Instantiate: V0:=V00:fofType;V:=W:fofType
% 171.85/172.18 Found x3 as proof of (((rel_s4 V) V00)->False)
% 171.85/172.18 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot (mbox_s4 p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 171.85/172.18 Found ((or_ind20 ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V00)->False)->P)) (x6:(((mnot (mbox_s4 p)) V00)->P))=> ((((((or_ind (((rel_s4 W) V00)->False)) ((mnot (mbox_s4 p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V00)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 171.85/172.18 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 171.85/172.18 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 176.16/176.47 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 176.16/176.47 Found a10:=(a1 S):((rel_s4 S) S)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V0)
% 176.16/176.47 Found a10:=(a1 S):((rel_s4 S) S)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V1)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V1)
% 176.16/176.47 Found (a1 S) as proof of ((rel_s4 S) V1)
% 176.16/176.47 Found (x5 (a1 S)) as proof of False
% 176.16/176.47 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 176.16/176.47 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 176.16/176.47 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 176.16/176.47 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 176.16/176.47 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 176.16/176.47 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found x3:(((rel_s4 W) V0)->False)
% 176.16/176.47 Instantiate: V0:=V00:fofType
% 176.16/176.47 Found x3 as proof of (((rel_s4 V) V00)->False)
% 176.16/176.47 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 176.16/176.47 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 176.16/176.47 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 176.16/176.47 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 176.16/176.47 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot (mbox_s4 p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 176.16/176.47 Found ((or_ind20 ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 176.16/176.47 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 179.26/179.54 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 179.26/179.54 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V00)->False)->P)) (x6:(((mnot (mbox_s4 p)) V00)->P))=> ((((((or_ind (((rel_s4 W) V00)->False)) ((mnot (mbox_s4 p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V00)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 179.26/179.54 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 179.26/179.54 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 179.26/179.54 Found a10:=(a1 W):((rel_s4 W) W)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 179.26/179.54 Found a10:=(a1 W):((rel_s4 W) W)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 179.26/179.54 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 179.26/179.54 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 179.26/179.54 Found a10:=(a1 W):((rel_s4 W) W)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 179.26/179.54 Found a10:=(a1 S):((rel_s4 S) S)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (x5 (a1 S)) as proof of False
% 179.26/179.54 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 179.26/179.54 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 179.26/179.54 Found a10:=(a1 S):((rel_s4 S) S)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 179.26/179.54 Found (x5 (a1 S)) as proof of False
% 179.26/179.54 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 186.03/186.29 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 186.03/186.29 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 186.03/186.29 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 186.03/186.29 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 186.03/186.29 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 186.03/186.29 Found x2:((rel_s4 V) V0)
% 186.03/186.29 Instantiate: V1:=V0:fofType;V:=W:fofType
% 186.03/186.29 Found x2 as proof of ((rel_s4 W) V1)
% 186.03/186.29 Found (x4 x2) as proof of False
% 186.03/186.29 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 186.03/186.29 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 186.03/186.29 Found a10:=(a1 W):((rel_s4 W) W)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found a10:=(a1 W):((rel_s4 W) W)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found a10:=(a1 W):((rel_s4 W) W)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V1)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V1)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V1)
% 186.03/186.29 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 186.03/186.29 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 186.03/186.29 Found ((or_introl (((rel_s4 S) V2)->False)) (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 186.03/186.29 Found a10:=(a1 W):((rel_s4 W) W)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found (a1 W) as proof of ((rel_s4 W) V0)
% 186.03/186.29 Found a10:=(a1 S):((rel_s4 S) S)
% 186.03/186.29 Found (a1 S) as proof of ((rel_s4 S) V1)
% 186.03/186.29 Found (a1 S) as proof of ((rel_s4 S) V1)
% 186.03/186.29 Found (a1 S) as proof of ((rel_s4 S) V1)
% 186.03/186.29 Found (x5 (a1 S)) as proof of False
% 186.03/186.29 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 186.03/186.29 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 186.03/186.29 Found x3:(((rel_s4 W) V0)->False)
% 186.03/186.29 Instantiate: V0:=V00:fofType;V:=W:fofType
% 186.03/186.29 Found x3 as proof of (((rel_s4 V) V00)->False)
% 186.03/186.29 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 186.03/186.29 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 186.03/186.29 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 186.03/186.29 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 192.87/193.13 Found (or_comm_i10 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found ((or_comm_i1 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found x2:((rel_s4 V) V0)
% 192.87/193.13 Instantiate: V1:=V0:fofType
% 192.87/193.13 Found x2 as proof of ((rel_s4 W) V1)
% 192.87/193.13 Found (x4 x2) as proof of False
% 192.87/193.13 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 192.87/193.13 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 192.87/193.13 Found a10:=(a1 W):((rel_s4 W) W)
% 192.87/193.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.87/193.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.87/193.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 192.87/193.13 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 192.87/193.13 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 192.87/193.13 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 192.87/193.13 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 192.87/193.13 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 192.87/193.13 Found x3:(((rel_s4 W) V0)->False)
% 192.87/193.13 Instantiate: V0:=V00:fofType
% 192.87/193.13 Found x3 as proof of (((rel_s4 V) V00)->False)
% 192.87/193.13 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 192.87/193.13 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 192.87/193.13 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 192.87/193.13 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 192.87/193.13 Found (or_comm_i10 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found ((or_comm_i1 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 192.87/193.13 Found x4:((rel_s4 V) V0)
% 192.87/193.13 Instantiate: V2:=V0:fofType;V:=S:fofType
% 192.87/193.13 Found x4 as proof of ((rel_s4 S) V2)
% 192.87/193.13 Found (x6 x4) as proof of False
% 192.87/193.13 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 192.87/193.13 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 192.87/193.13 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 192.87/193.13 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 192.87/193.13 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 192.87/193.13 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 199.33/199.64 Found a10:=(a1 V):((rel_s4 V) V)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (x1 (a1 V)) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 199.33/199.64 Found a10:=(a1 V):((rel_s4 V) V)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (x1 (a1 V)) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 199.33/199.64 Found a10:=(a1 V):((rel_s4 V) V)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (x1 (a1 V)) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 199.33/199.64 Found a10:=(a1 V):((rel_s4 V) V)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (a1 V) as proof of ((rel_s4 V) V0)
% 199.33/199.64 Found (x1 (a1 V)) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 199.33/199.64 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 199.33/199.64 Found x4:((rel_s4 V) V0)
% 199.33/199.64 Instantiate: V2:=V0:fofType
% 199.33/199.64 Found x4 as proof of ((rel_s4 S) V2)
% 199.33/199.64 Found (x6 x4) as proof of False
% 199.33/199.64 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 199.33/199.64 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 199.33/199.64 Found a10:=(a1 W):((rel_s4 W) W)
% 199.33/199.64 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.33/199.64 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.33/199.64 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.33/199.64 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 199.33/199.64 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found x4:((rel_s4 V) V0)
% 199.33/199.64 Instantiate: V2:=V0:fofType
% 199.33/199.64 Found x4 as proof of ((rel_s4 S) V2)
% 199.33/199.64 Found (x6 x4) as proof of False
% 199.33/199.64 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 199.33/199.64 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 199.33/199.64 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 199.33/199.64 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 199.33/199.64 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 199.33/199.64 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 199.33/199.64 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 199.33/199.64 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 199.33/199.64 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.33/199.64 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 205.16/205.46 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 205.16/205.46 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 205.16/205.46 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 205.16/205.46 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 205.16/205.46 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 205.16/205.46 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 205.16/205.46 Found or_introl20:=(or_introl2 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found (or_introl2 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found or_introl00:=(or_introl0 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found (or_introl0 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 205.16/205.46 Found a10:=(a1 W):((rel_s4 W) W)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found (x3 (a1 W)) as proof of False
% 205.16/205.46 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 205.16/205.46 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 205.16/205.46 Found a10:=(a1 W):((rel_s4 W) W)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found a10:=(a1 W):((rel_s4 W) W)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 205.16/205.46 Found x4:((rel_s4 V) V0)
% 205.16/205.46 Instantiate: V2:=V0:fofType
% 205.16/205.46 Found x4 as proof of ((rel_s4 S) V2)
% 205.16/205.46 Found (x6 x4) as proof of False
% 205.16/205.46 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 205.16/205.46 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 205.16/205.46 Found a10:=(a1 W):((rel_s4 W) W)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 205.16/205.46 Found a10:=(a1 V):((rel_s4 V) V)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (x1 (a1 V)) as proof of False
% 205.16/205.46 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 205.16/205.46 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 205.16/205.46 Found a10:=(a1 V):((rel_s4 V) V)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (a1 V) as proof of ((rel_s4 V) V0)
% 205.16/205.46 Found (x1 (a1 V)) as proof of False
% 205.16/205.46 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 212.53/212.78 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 212.53/212.78 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 212.53/212.78 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 212.53/212.78 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 212.53/212.78 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 212.53/212.78 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 212.53/212.78 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 212.53/212.78 Found ((or_intror (p V0)) (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found (x3 (a1 W)) as proof of False
% 212.53/212.78 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 212.53/212.78 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V1)
% 212.53/212.78 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 212.53/212.78 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 212.53/212.78 Found a10:=(a1 S):((rel_s4 S) S)
% 212.53/212.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 212.53/212.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 212.53/212.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 212.53/212.78 Found a10:=(a1 W):((rel_s4 W) W)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 212.53/212.78 Found a10:=(a1 V):((rel_s4 V) V)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (x2 (a1 V)) as proof of False
% 212.53/212.78 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 212.53/212.78 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 212.53/212.78 Found a10:=(a1 V):((rel_s4 V) V)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (a1 V) as proof of ((rel_s4 V) V00)
% 212.53/212.78 Found (x2 (a1 V)) as proof of False
% 212.53/212.78 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 212.53/212.78 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 215.26/215.52 Found a10:=(a1 W):((rel_s4 W) W)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found a10:=(a1 W):((rel_s4 W) W)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V1)
% 215.26/215.52 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 S) V3)->False)->((or (((rel_s4 S) V3)->False)) (p V2)))
% 215.26/215.52 Found (or_introl1 (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 215.26/215.52 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 215.26/215.52 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 215.26/215.52 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 215.26/215.52 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 215.26/215.52 Found or_introl20:=(or_introl2 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found (or_introl2 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found a10:=(a1 S):((rel_s4 S) S)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found a10:=(a1 S):((rel_s4 S) S)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found (a1 S) as proof of ((rel_s4 S) V0)
% 215.26/215.52 Found a10:=(a1 W):((rel_s4 W) W)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V0)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V0)
% 215.26/215.52 Found (a1 W) as proof of ((rel_s4 W) V0)
% 215.26/215.52 Found or_introl00:=(or_introl0 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found (or_introl0 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 215.26/215.52 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 215.26/215.52 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 215.26/215.52 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 215.26/215.52 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 215.26/215.52 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 215.26/215.52 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found a10:=(a1 V):((rel_s4 V) V)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (x2 (a1 V)) as proof of False
% 218.97/219.26 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 218.97/219.26 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 218.97/219.26 Found x3:(((rel_s4 W) V0)->False)
% 218.97/219.26 Instantiate: V0:=V00:fofType;V:=W:fofType
% 218.97/219.26 Found x3 as proof of (((rel_s4 V) V00)->False)
% 218.97/219.26 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 218.97/219.26 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 218.97/219.26 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 218.97/219.26 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 218.97/219.26 Found x4:((rel_s4 V) V0)
% 218.97/219.26 Instantiate: V2:=V0:fofType;V:=W:fofType
% 218.97/219.26 Found x4 as proof of ((rel_s4 W) V2)
% 218.97/219.26 Found (x6 x4) as proof of False
% 218.97/219.26 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 218.97/219.26 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 218.97/219.26 Found a10:=(a1 V):((rel_s4 V) V)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V00)
% 218.97/219.26 Found (x2 (a1 V)) as proof of False
% 218.97/219.26 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 218.97/219.26 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 218.97/219.26 Found a10:=(a1 V):((rel_s4 V) V)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (x1 (a1 V)) as proof of False
% 218.97/219.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 218.97/219.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 218.97/219.26 Found a10:=(a1 V):((rel_s4 V) V)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 218.97/219.26 Found (x1 (a1 V)) as proof of False
% 218.97/219.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 218.97/219.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 218.97/219.26 Found a10:=(a1 W):((rel_s4 W) W)
% 218.97/219.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 218.97/219.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 218.97/219.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 218.97/219.26 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 218.97/219.26 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 218.97/219.26 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 218.97/219.26 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 218.97/219.26 Found a10:=(a1 V):((rel_s4 V) V)
% 218.97/219.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 220.15/220.43 Found (a1 V) as proof of ((rel_s4 V) V0)
% 220.15/220.43 Found (a1 V) as proof of ((rel_s4 V) V0)
% 220.15/220.43 Found (x1 (a1 V)) as proof of False
% 220.15/220.43 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 220.15/220.43 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 220.15/220.43 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 S) V3)->False)->((or (((rel_s4 S) V3)->False)) (p V2)))
% 220.15/220.43 Found (or_introl1 (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 220.15/220.43 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 220.15/220.43 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 220.15/220.43 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 220.15/220.43 Found ((or_introl (((rel_s4 S) V3)->False)) (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 220.15/220.43 Found a10:=(a1 W):((rel_s4 W) W)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found a10:=(a1 W):((rel_s4 W) W)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 220.15/220.43 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 220.15/220.43 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found ((or_introl (((rel_s4 W) V1)->False)) (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found a10:=(a1 S):((rel_s4 S) S)
% 220.15/220.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 220.15/220.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 220.15/220.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 220.15/220.43 Found x3:(((rel_s4 S) V0)->False)
% 220.15/220.43 Instantiate: V0:=V00:fofType;V:=S:fofType
% 220.15/220.43 Found x3 as proof of (((rel_s4 V) V00)->False)
% 220.15/220.43 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot ((mbox rel_s4) p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 220.15/220.43 Found ((or_ind20 ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found ((((fun (P:Prop) (x5:((((rel_s4 S) V1)->False)->P)) (x6:(((mnot ((mbox rel_s4) p)) V1)->P))=> ((((((or_ind (((rel_s4 S) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 220.15/220.43 Found ((((fun (P:Prop) (x5:((((rel_s4 S) V00)->False)->P)) (x6:(((mnot ((mbox rel_s4) p)) V00)->P))=> ((((((or_ind (((rel_s4 S) V00)->False)) ((mnot ((mbox rel_s4) p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V00)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found a10:=(a1 S):((rel_s4 S) S)
% 225.44/225.74 Found (a1 S) as proof of ((rel_s4 S) V1)
% 225.44/225.74 Found (a1 S) as proof of ((rel_s4 S) V1)
% 225.44/225.74 Found (a1 S) as proof of ((rel_s4 S) V1)
% 225.44/225.74 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (forall (V0:fofType), ((or (((rel_s4 V) V0)->False)) (p V0)))
% 225.44/225.74 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((mbox_s4 p) V)
% 225.44/225.74 Found x3:(((rel_s4 W) V0)->False)
% 225.44/225.74 Instantiate: V0:=V00:fofType
% 225.44/225.74 Found x3 as proof of (((rel_s4 V) V00)->False)
% 225.44/225.74 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found x4:((rel_s4 V) V0)
% 225.44/225.74 Instantiate: V2:=V0:fofType
% 225.44/225.74 Found x4 as proof of ((rel_s4 W) V2)
% 225.44/225.74 Found (x6 x4) as proof of False
% 225.44/225.74 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 225.44/225.74 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 225.44/225.74 Found x4:((rel_s4 V) V0)
% 225.44/225.74 Instantiate: V2:=V0:fofType
% 225.44/225.74 Found x4 as proof of ((rel_s4 W) V2)
% 225.44/225.74 Found (x6 x4) as proof of False
% 225.44/225.74 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 225.44/225.74 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 225.44/225.74 Found a10:=(a1 W):((rel_s4 W) W)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V0)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V0)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V0)
% 225.44/225.74 Found a10:=(a1 W):((rel_s4 W) W)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found a10:=(a1 W):((rel_s4 W) W)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found a10:=(a1 W):((rel_s4 W) W)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found a10:=(a1 W):((rel_s4 W) W)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found (a1 W) as proof of ((rel_s4 W) V1)
% 225.44/225.74 Found x3:(((rel_s4 W) V0)->False)
% 225.44/225.74 Instantiate: V0:=V00:fofType;V:=W:fofType
% 225.44/225.74 Found x3 as proof of (((rel_s4 V) V00)->False)
% 225.44/225.74 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found x3:(((rel_s4 S) V0)->False)
% 225.44/225.74 Instantiate: V0:=V00:fofType
% 225.44/225.74 Found x3 as proof of (((rel_s4 V) V00)->False)
% 225.44/225.74 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 225.44/225.74 Found (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot ((mbox rel_s4) p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 232.03/232.37 Found ((or_ind20 ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found ((((fun (P:Prop) (x5:((((rel_s4 S) V1)->False)->P)) (x6:(((mnot ((mbox rel_s4) p)) V1)->P))=> ((((((or_ind (((rel_s4 S) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V1)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found ((((fun (P:Prop) (x5:((((rel_s4 S) V00)->False)->P)) (x6:(((mnot ((mbox rel_s4) p)) V00)->P))=> ((((((or_ind (((rel_s4 S) V00)->False)) ((mnot ((mbox rel_s4) p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 S) V00)->False)) (p V00))) (fun (x5:((mnot ((mbox rel_s4) p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found a10:=(a1 S):((rel_s4 S) S)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found a10:=(a1 S):((rel_s4 S) S)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 232.03/232.37 Found a10:=(a1 S):((rel_s4 S) S)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V1)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V1)
% 232.03/232.37 Found (a1 S) as proof of ((rel_s4 S) V1)
% 232.03/232.37 Found x2:((rel_s4 V) V0)
% 232.03/232.37 Instantiate: V1:=V0:fofType;V:=S:fofType
% 232.03/232.37 Found x2 as proof of ((rel_s4 S) V1)
% 232.03/232.37 Found (x4 x2) as proof of False
% 232.03/232.37 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 232.03/232.37 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 232.03/232.37 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (forall (V0:fofType), ((or (((rel_s4 V) V0)->False)) (p V0)))
% 232.03/232.37 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((mbox_s4 p) V)
% 232.03/232.37 Found x4:((rel_s4 V) V0)
% 232.03/232.37 Instantiate: V2:=V0:fofType
% 232.03/232.37 Found x4 as proof of ((rel_s4 W) V2)
% 232.03/232.37 Found (x6 x4) as proof of False
% 232.03/232.37 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 232.03/232.37 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 232.03/232.37 Found a10:=(a1 W):((rel_s4 W) W)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found a10:=(a1 W):((rel_s4 W) W)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 232.03/232.37 Found x3:(((rel_s4 W) V0)->False)
% 232.03/232.37 Instantiate: V0:=V00:fofType
% 232.03/232.37 Found x3 as proof of (((rel_s4 V) V00)->False)
% 232.03/232.37 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 232.03/232.37 Found a10:=(a1 S):((rel_s4 S) S)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found a10:=(a1 S):((rel_s4 S) S)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found a10:=(a1 S):((rel_s4 S) S)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.03 Found x3:(((rel_s4 S) V0)->False)
% 239.74/240.03 Instantiate: V0:=V00:fofType;V:=S:fofType
% 239.74/240.03 Found x3 as proof of (((rel_s4 V) V00)->False)
% 239.74/240.03 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.03 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.03 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.03 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.03 Found (or_comm_i10 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.03 Found ((or_comm_i1 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.03 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.03 Found a10:=(a1 W):((rel_s4 W) W)
% 239.74/240.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 239.74/240.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 239.74/240.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 239.74/240.03 Found x2:((rel_s4 V) V0)
% 239.74/240.03 Instantiate: V1:=V0:fofType
% 239.74/240.03 Found x2 as proof of ((rel_s4 S) V1)
% 239.74/240.03 Found (x4 x2) as proof of False
% 239.74/240.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 239.74/240.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 239.74/240.03 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 239.74/240.03 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 239.74/240.04 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 239.74/240.04 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 239.74/240.04 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 239.74/240.04 Found a10:=(a1 S):((rel_s4 S) S)
% 239.74/240.04 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.04 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.04 Found (a1 S) as proof of ((rel_s4 S) V0)
% 239.74/240.04 Found x3:(((rel_s4 S) V0)->False)
% 239.74/240.04 Instantiate: V0:=V00:fofType
% 239.74/240.04 Found x3 as proof of (((rel_s4 V) V00)->False)
% 239.74/240.04 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.04 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.04 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.04 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 239.74/240.04 Found (or_comm_i10 (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.04 Found ((or_comm_i1 (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.04 Found (((or_comm_i (p V00)) (((rel_s4 V) V00)->False)) (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 239.74/240.04 Found x4:((rel_s4 V) V0)
% 239.74/240.04 Instantiate: V2:=V0:fofType;V:=W:fofType
% 239.74/240.04 Found x4 as proof of ((rel_s4 W) V2)
% 239.74/240.04 Found (x6 x4) as proof of False
% 239.74/240.04 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 239.74/240.04 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 239.74/240.04 Found a10:=(a1 W):((rel_s4 W) W)
% 246.83/247.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 246.83/247.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 246.83/247.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 246.83/247.18 Found or_introl00:=(or_introl0 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 246.83/247.18 Found (or_introl0 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found a10:=(a1 S):((rel_s4 S) S)
% 246.83/247.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 246.83/247.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 246.83/247.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 246.83/247.18 Found x4:((rel_s4 V) V0)
% 246.83/247.18 Instantiate: V2:=V0:fofType
% 246.83/247.18 Found x4 as proof of ((rel_s4 W) V2)
% 246.83/247.18 Found (x6 x4) as proof of False
% 246.83/247.18 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 246.83/247.18 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 246.83/247.18 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 246.83/247.18 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 246.83/247.18 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 246.83/247.18 Found x4:((rel_s4 V) V0)
% 246.83/247.18 Instantiate: V2:=V0:fofType
% 246.83/247.18 Found x4 as proof of ((rel_s4 W) V2)
% 246.83/247.18 Found (x6 x4) as proof of False
% 246.83/247.18 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 246.83/247.18 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 246.83/247.18 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 246.83/247.18 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 246.83/247.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 246.83/247.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 246.83/247.18 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 246.83/247.18 Found or_introl00:=(or_introl0 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 246.83/247.18 Found (or_introl0 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 246.83/247.18 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 252.74/253.08 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 252.74/253.08 Found a10:=(a1 W):((rel_s4 W) W)
% 252.74/253.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 252.74/253.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 252.74/253.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 252.74/253.08 Found a10:=(a1 V):((rel_s4 V) V)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found (x2 (a1 V)) as proof of False
% 252.74/253.08 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 252.74/253.08 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 252.74/253.08 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 252.74/253.08 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found a10:=(a1 S):((rel_s4 S) S)
% 252.74/253.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.74/253.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.74/253.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 252.74/253.08 Found a10:=(a1 V):((rel_s4 V) V)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found (a1 V) as proof of ((rel_s4 V) V00)
% 252.74/253.08 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 252.74/253.08 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 252.74/253.08 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 252.74/253.08 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 252.74/253.08 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 252.74/253.08 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 252.74/253.08 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 252.74/253.08 Found x4:((rel_s4 V) V0)
% 252.74/253.08 Instantiate: V2:=V0:fofType
% 252.74/253.08 Found x4 as proof of ((rel_s4 W) V2)
% 252.74/253.08 Found (x6 x4) as proof of False
% 252.74/253.08 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 252.74/253.08 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 252.74/253.08 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 252.74/253.08 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 252.74/253.08 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 252.74/253.08 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 252.74/253.08 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 252.74/253.08 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found a10:=(a1 W):((rel_s4 W) W)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 260.61/260.92 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found a10:=(a1 V):((rel_s4 V) V)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found (x2 (a1 V)) as proof of False
% 260.61/260.92 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 260.61/260.92 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found a10:=(a1 V):((rel_s4 V) V)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.61/260.92 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 260.61/260.92 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.61/260.92 Found (x3 (a1 S)) as proof of False
% 260.61/260.92 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 260.61/260.92 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found a10:=(a1 W):((rel_s4 W) W)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found (a1 W) as proof of ((rel_s4 W) V1)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found a10:=(a1 S):((rel_s4 S) S)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found (a1 S) as proof of ((rel_s4 S) V1)
% 260.61/260.92 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 260.61/260.92 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 260.61/260.92 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 260.61/260.92 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 266.51/266.87 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 266.51/266.87 Found ((or_intror (p V0)) (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 266.51/266.87 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 266.51/266.87 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found a10:=(a1 S):((rel_s4 S) S)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found a10:=(a1 S):((rel_s4 S) S)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V0)
% 266.51/266.87 Found (x3 (a1 S)) as proof of False
% 266.51/266.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 266.51/266.87 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 266.51/266.87 Found or_introl20:=(or_introl2 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 266.51/266.87 Found (or_introl2 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 266.51/266.87 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 266.51/266.87 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 266.51/266.87 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 266.51/266.87 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 266.51/266.87 Found x3:(((rel_s4 S) V0)->False)
% 266.51/266.87 Instantiate: V0:=V00:fofType;V:=S:fofType
% 266.51/266.87 Found x3 as proof of (((rel_s4 V) V00)->False)
% 266.51/266.87 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 266.51/266.87 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 266.51/266.87 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 266.51/266.87 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 266.51/266.87 Found a10:=(a1 W):((rel_s4 W) W)
% 266.51/266.87 Found (a1 W) as proof of ((rel_s4 W) V1)
% 266.51/266.87 Found (a1 W) as proof of ((rel_s4 W) V1)
% 266.51/266.87 Found (a1 W) as proof of ((rel_s4 W) V1)
% 266.51/266.87 Found a10:=(a1 S):((rel_s4 S) S)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found a10:=(a1 S):((rel_s4 S) S)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found (a1 S) as proof of ((rel_s4 S) V1)
% 266.51/266.87 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 266.51/266.87 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 266.51/266.87 Found x3:(((rel_s4 W) V0)->False)
% 266.51/266.87 Instantiate: V0:=V00:fofType;V:=W:fofType
% 266.51/266.87 Found x3 as proof of (((rel_s4 V) V00)->False)
% 266.51/266.87 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot (mbox_s4 p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 269.63/269.93 Found ((or_ind20 ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V00)->False)->P)) (x6:(((mnot (mbox_s4 p)) V00)->P))=> ((((((or_ind (((rel_s4 W) V00)->False)) ((mnot (mbox_s4 p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V00)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 269.63/269.93 Found a10:=(a1 S):((rel_s4 S) S)
% 269.63/269.93 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.63/269.93 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.63/269.93 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.63/269.93 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 269.63/269.93 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 269.63/269.93 Found a10:=(a1 V):((rel_s4 V) V)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (x1 (a1 V)) as proof of False
% 269.63/269.93 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 269.63/269.93 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 269.63/269.93 Found a10:=(a1 V):((rel_s4 V) V)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V00)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V00)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V00)
% 269.63/269.93 Found a10:=(a1 V):((rel_s4 V) V)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (a1 V) as proof of ((rel_s4 V) V0)
% 269.63/269.93 Found (x1 (a1 V)) as proof of False
% 269.63/269.93 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 269.63/269.93 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 269.63/269.93 Found or_introl20:=(or_introl2 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 269.63/269.93 Found (or_introl2 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 269.63/269.93 Found ((or_introl (((rel_s4 W) V3)->False)) (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 272.23/272.54 Found x3:(((rel_s4 S) V0)->False)
% 272.23/272.54 Instantiate: V0:=V00:fofType
% 272.23/272.54 Found x3 as proof of (((rel_s4 V) V00)->False)
% 272.23/272.54 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 272.23/272.54 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 272.23/272.54 Found a10:=(a1 S):((rel_s4 S) S)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found a10:=(a1 S):((rel_s4 S) S)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found (a1 S) as proof of ((rel_s4 S) V1)
% 272.23/272.54 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 272.23/272.54 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 272.23/272.54 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 272.23/272.54 Found a10:=(a1 W):((rel_s4 W) W)
% 272.23/272.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of (((mnot (mbox_s4 p)) V1)->((rel_s4 W) V0))
% 272.23/272.54 Found a10:=(a1 W):((rel_s4 W) W)
% 272.23/272.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((((rel_s4 W) V1)->False)->((rel_s4 W) V0))
% 272.23/272.54 Found ((or_ind20 (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found (((or_ind2 ((rel_s4 W) V0)) (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((rel_s4 W) V0)) (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 272.23/272.54 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 272.23/272.54 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (forall (V0:fofType), ((or (((rel_s4 V) V0)->False)) (p V0)))
% 274.19/274.51 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (((mbox rel_s4) p) V)
% 274.19/274.51 Found x3:(((rel_s4 W) V0)->False)
% 274.19/274.51 Instantiate: V0:=V00:fofType
% 274.19/274.51 Found x3 as proof of (((rel_s4 V) V00)->False)
% 274.19/274.51 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3)) as proof of (((mnot (mbox_s4 p)) V1)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found ((or_ind20 ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (((or_ind2 ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V1)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V00)->False)->P)) (x6:(((mnot (mbox_s4 p)) V00)->P))=> ((((((or_ind (((rel_s4 W) V00)->False)) ((mnot (mbox_s4 p)) V00)) P) x5) x6) (x V00))) ((or (((rel_s4 V) V00)->False)) (p V00))) ((or_introl (((rel_s4 W) V00)->False)) (p V00))) (fun (x5:((mnot (mbox_s4 p)) V00))=> (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found x4:((rel_s4 V) V0)
% 274.19/274.51 Instantiate: V2:=V0:fofType;V:=S:fofType
% 274.19/274.51 Found x4 as proof of ((rel_s4 S) V2)
% 274.19/274.51 Found (x6 x4) as proof of False
% 274.19/274.51 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 274.19/274.51 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 274.19/274.51 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 274.19/274.51 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found ((or_introl (((rel_s4 S) V1)->False)) (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 274.19/274.51 Found x3:(((rel_s4 S) V0)->False)
% 274.19/274.51 Instantiate: V0:=V00:fofType;V:=S:fofType
% 274.19/274.51 Found x3 as proof of (((rel_s4 V) V00)->False)
% 274.19/274.51 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 274.19/274.51 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 274.19/274.51 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 274.19/274.51 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found a10:=(a1 S):((rel_s4 S) S)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V0)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V0)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V0)
% 279.29/279.58 Found a10:=(a1 V):((rel_s4 V) V)
% 279.29/279.58 Found (a1 V) as proof of ((rel_s4 V) V00)
% 279.29/279.58 Found (a1 V) as proof of ((rel_s4 V) V00)
% 279.29/279.58 Found (a1 V) as proof of ((rel_s4 V) V00)
% 279.29/279.58 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 279.29/279.58 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 279.29/279.58 Found a10:=(a1 W):((rel_s4 W) W)
% 279.29/279.58 Found (a1 W) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (a1 W) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of (((mnot (mbox_s4 p)) V1)->((rel_s4 W) V0))
% 279.29/279.58 Found a10:=(a1 W):((rel_s4 W) W)
% 279.29/279.58 Found (a1 W) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((((rel_s4 W) V1)->False)->((rel_s4 W) V0))
% 279.29/279.58 Found ((or_ind20 (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found (((or_ind2 ((rel_s4 W) V0)) (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found ((((fun (P:Prop) (x5:((((rel_s4 W) V1)->False)->P)) (x6:(((mnot (mbox_s4 p)) V1)->P))=> ((((((or_ind (((rel_s4 W) V1)->False)) ((mnot (mbox_s4 p)) V1)) P) x5) x6) x4)) ((rel_s4 W) V0)) (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W))) (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W))) as proof of ((rel_s4 W) V0)
% 279.29/279.58 Found a10:=(a1 S):((rel_s4 S) S)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found a10:=(a1 S):((rel_s4 S) S)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found a10:=(a1 S):((rel_s4 S) S)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found a10:=(a1 S):((rel_s4 S) S)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found (a1 S) as proof of ((rel_s4 S) V1)
% 279.29/279.58 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 279.29/279.58 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 279.29/279.58 Found ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 279.29/279.58 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 279.29/279.58 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (forall (V0:fofType), ((or (((rel_s4 V) V0)->False)) (p V0)))
% 279.29/279.58 Found (fun (V00:fofType)=> ((fun (P:Type)=> ((False_rect P) x30)) ((or (((rel_s4 V) V00)->False)) (p V00)))) as proof of (((mbox rel_s4) p) V)
% 279.29/279.58 Found x4:((rel_s4 V) V0)
% 279.29/279.58 Instantiate: V2:=V0:fofType
% 279.29/279.58 Found x4 as proof of ((rel_s4 S) V2)
% 279.29/279.58 Found (x6 x4) as proof of False
% 279.29/279.58 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 288.66/288.98 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 288.66/288.98 Found x4:((rel_s4 V) V0)
% 288.66/288.98 Instantiate: V2:=V0:fofType
% 288.66/288.98 Found x4 as proof of ((rel_s4 S) V2)
% 288.66/288.98 Found (x6 x4) as proof of False
% 288.66/288.98 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 288.66/288.98 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 288.66/288.98 Found x3:(((rel_s4 S) V0)->False)
% 288.66/288.98 Instantiate: V0:=V00:fofType
% 288.66/288.98 Found x3 as proof of (((rel_s4 V) V00)->False)
% 288.66/288.98 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 288.66/288.98 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 288.66/288.98 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 288.66/288.98 Found a10:=(a1 V):((rel_s4 V) V)
% 288.66/288.98 Found (a1 V) as proof of ((rel_s4 V) V0)
% 288.66/288.98 Found (a1 V) as proof of ((rel_s4 V) V0)
% 288.66/288.98 Found (a1 V) as proof of ((rel_s4 V) V0)
% 288.66/288.98 Found (x1 (a1 V)) as proof of False
% 288.66/288.98 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 288.66/288.98 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 288.66/288.98 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 288.66/288.98 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found a10:=(a1 W):((rel_s4 W) W)
% 288.66/288.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 288.66/288.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 288.66/288.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 288.66/288.98 Found (x3 (a1 W)) as proof of False
% 288.66/288.98 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 288.66/288.98 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 288.66/288.98 Found a10:=(a1 S):((rel_s4 S) S)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found a10:=(a1 S):((rel_s4 S) S)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 288.66/288.98 Found a10:=(a1 S):((rel_s4 S) S)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 288.66/288.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 288.66/288.98 Found x4:((rel_s4 V) V0)
% 288.66/288.98 Instantiate: V2:=V0:fofType
% 288.66/288.98 Found x4 as proof of ((rel_s4 S) V2)
% 288.66/288.98 Found (x6 x4) as proof of False
% 288.66/288.98 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 288.66/288.98 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 288.66/288.98 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 288.66/288.98 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 288.66/288.98 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 288.66/288.98 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 288.66/288.98 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 288.66/288.98 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (x3 (a1 W)) as proof of False
% 298.63/298.94 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 298.63/298.94 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 298.63/298.94 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 298.63/298.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 298.63/298.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 298.63/298.94 Found ((or_introl (((rel_s4 W) V1)->False)) (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 298.63/298.94 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 298.63/298.94 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found ((or_intror (p V0)) (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found a10:=(a1 S):((rel_s4 S) S)
% 298.63/298.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 298.63/298.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 298.63/298.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found or_introl10:=(or_introl1 ((mnot (mbox_s4 p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)))
% 298.63/298.94 Found (or_introl1 ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 298.63/298.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 298.63/298.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 298.63/298.94 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot (mbox_s4 p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot (mbox_s4 p)) V1)))
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W) W)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found (a1 W) as proof of ((rel_s4 W) V0)
% 298.63/298.94 Found a10:=(a1 W):((rel_s4 W)
%------------------------------------------------------------------------------