TSTP Solution File: SYO440^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO440^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 00:51:27 EDT 2022
% Result : Timeout 290.99s 291.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO440^1 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % RAMPerCPU : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % DateTime : Sat Mar 12 17:18:34 EST 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 0.42/0.59 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.42/0.59 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x2b86744430e0>, <kernel.Type object at 0x2b8674443758>) of role type named mu_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring mu:Type
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x2b8674443320>, <kernel.DependentProduct object at 0x2b8674443bd8>) of role type named meq_ind_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.42/0.59 FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% 0.42/0.59 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.42/0.59 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x2b8674443cf8>, <kernel.DependentProduct object at 0x2b8674443b00>) of role type named meq_prop_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))) of role definition named meq_prop
% 0.42/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))))
% 0.42/0.59 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x1b7a638>, <kernel.DependentProduct object at 0x1b7a3f8>) of role type named mnot_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.42/0.59 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.42/0.59 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.42/0.59 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x1b7a5f0>, <kernel.DependentProduct object at 0x1b7a6c8>) of role type named mor_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% 0.42/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% 0.42/0.59 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x1b7a3f8>, <kernel.DependentProduct object at 0x1b75c68>) of role type named mand_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) of role definition named mand
% 0.42/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.42/0.59 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.42/0.59 FOF formula (<kernel.Constant object at 0x1b75e60>, <kernel.DependentProduct object at 0x1b7a5f0>) of role type named mimplies_type
% 0.42/0.59 Using role type
% 0.42/0.59 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.59 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) of role definition named mimplies
% 0.42/0.59 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.42/0.60 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1b75e60>, <kernel.DependentProduct object at 0x1b7a3f8>) of role type named mimplied_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.42/0.60 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1b75f38>, <kernel.DependentProduct object at 0x1b7a5f0>) of role type named mequiv_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 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))))
% 0.42/0.60 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1b7a3f8>, <kernel.DependentProduct object at 0x2b8674443878>) of role type named mxor_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.60 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
% 0.42/0.60 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.42/0.60 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x1b7a638>, <kernel.DependentProduct object at 0x2b8674443320>) of role type named mforall_ind_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.42/0.60 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% 0.42/0.60 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.42/0.60 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2b8674443320>, <kernel.DependentProduct object at 0x1b7d680>) of role type named mforall_prop_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.42/0.60 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% 0.42/0.60 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% 0.42/0.60 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.42/0.60 FOF formula (<kernel.Constant object at 0x2b8674443cf8>, <kernel.DependentProduct object at 0x1b7d9e0>) of role type named mexists_ind_type
% 0.42/0.60 Using role type
% 0.42/0.60 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.42/0.60 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
% 0.42/0.60 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)))))))
% 0.42/0.61 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2b8674443758>, <kernel.DependentProduct object at 0x1b7d170>) of role type named mexists_prop_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.42/0.61 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))) of role definition named mexists_prop
% 0.42/0.61 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mexists_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))))
% 0.42/0.61 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2b8674443758>, <kernel.DependentProduct object at 0x1b7d170>) of role type named mtrue_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mtrue:(fofType->Prop)
% 0.42/0.61 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.42/0.61 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.42/0.61 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x2b8674443bd8>, <kernel.DependentProduct object at 0x1b7df80>) of role type named mfalse_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mfalse:(fofType->Prop)
% 0.42/0.61 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.42/0.61 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.42/0.61 Defined: mfalse:=(mnot mtrue)
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1b7d290>, <kernel.DependentProduct object at 0x1b7d8c0>) of role type named mbox_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 FOF formula (((eq ((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))) mbox) (fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))) of role definition named mbox
% 0.42/0.61 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)))))
% 0.42/0.61 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1b7d8c0>, <kernel.DependentProduct object at 0x1b7db48>) of role type named mdia_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.42/0.61 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
% 0.42/0.61 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)))))
% 0.42/0.61 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1b7db90>, <kernel.DependentProduct object at 0x1b7d0e0>) of role type named mreflexive_type
% 0.42/0.61 Using role type
% 0.42/0.61 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.42/0.61 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.42/0.61 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.42/0.61 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.42/0.61 FOF formula (<kernel.Constant object at 0x1b7d0e0>, <kernel.DependentProduct object at 0x1b7db00>) of role type named msymmetric_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 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
% 0.42/0.62 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)))))
% 0.42/0.62 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1b786c8>, <kernel.DependentProduct object at 0x1b78cf8>) of role type named mserial_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 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
% 0.42/0.62 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))))))
% 0.42/0.62 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1b78908>, <kernel.DependentProduct object at 0x1b7db00>) of role type named mtransitive_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 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
% 0.42/0.62 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)))))
% 0.42/0.62 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1b78128>, <kernel.DependentProduct object at 0x1b7d9e0>) of role type named meuclidean_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 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
% 0.42/0.62 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)))))
% 0.42/0.62 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1b78128>, <kernel.DependentProduct object at 0x1b7db00>) of role type named mpartially_functional_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 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
% 0.42/0.62 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)))))
% 0.42/0.62 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))))
% 0.42/0.62 FOF formula (<kernel.Constant object at 0x1b78128>, <kernel.DependentProduct object at 0x1b7db90>) of role type named mfunctional_type
% 0.42/0.62 Using role type
% 0.42/0.62 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.42/0.62 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))) of role definition named mfunctional
% 0.48/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))))
% 0.48/0.63 Defined: mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1b7db90>, <kernel.DependentProduct object at 0x1b7df80>) of role type named mweakly_dense_type
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.48/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))) of role definition named mweakly_dense
% 0.48/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))))
% 0.48/0.63 Defined: mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1b7db00>, <kernel.DependentProduct object at 0x1b7df80>) of role type named mweakly_connected_type
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.48/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))) of role definition named mweakly_connected
% 0.48/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))))
% 0.48/0.63 Defined: mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1b7d320>, <kernel.DependentProduct object at 0x1b7df80>) of role type named mweakly_directed_type
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.48/0.63 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))) of role definition named mweakly_directed
% 0.48/0.63 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))))
% 0.48/0.63 Defined: mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1b7ddd0>, <kernel.DependentProduct object at 0x1cef098>) of role type named mvalid_type
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring mvalid:((fofType->Prop)->Prop)
% 0.48/0.63 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.48/0.63 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.48/0.63 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.48/0.63 FOF formula (<kernel.Constant object at 0x1b7db00>, <kernel.DependentProduct object at 0x1cef3b0>) of role type named minvalid_type
% 0.48/0.63 Using role type
% 0.48/0.63 Declaring minvalid:((fofType->Prop)->Prop)
% 0.48/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.48/0.64 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.48/0.64 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1cef4d0>, <kernel.DependentProduct object at 0x1cef638>) of role type named msatisfiable_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.48/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.48/0.64 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.48/0.64 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1cef3b0>, <kernel.DependentProduct object at 0x1cef200>) of role type named mcountersatisfiable_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.48/0.64 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.48/0.64 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.48/0.64 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.48/0.64 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1b7a638>, <kernel.DependentProduct object at 0x2b8674443f80>) of role type named rel_s4_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring rel_s4:(fofType->(fofType->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b8674443c20>, <kernel.DependentProduct object at 0x2b8674443440>) of role type named mbox_s4_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.48/0.64 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
% 0.48/0.64 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)))))
% 0.48/0.64 Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2b8674443440>, <kernel.DependentProduct object at 0x2b8674443638>) of role type named mdia_s4_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% 0.48/0.64 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% 0.48/0.64 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% 0.48/0.64 Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% 0.48/0.64 FOF formula (mreflexive rel_s4) of role axiom named a1
% 0.48/0.64 A new axiom: (mreflexive rel_s4)
% 0.48/0.64 FOF formula (mtransitive rel_s4) of role axiom named a2
% 0.48/0.64 A new axiom: (mtransitive rel_s4)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x1b58e18>, <kernel.DependentProduct object at 0x1e1a878>) of role type named p_type
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring p:(fofType->Prop)
% 0.48/0.64 FOF formula (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p)))) of role conjecture named prove
% 0.48/0.64 Conjecture to prove = (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p)))):Prop
% 0.48/0.64 Parameter mu_DUMMY:mu.
% 0.48/0.64 Parameter fofType_DUMMY:fofType.
% 0.48/0.64 We need to prove ['(mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p))))']
% 0.48/0.64 Parameter mu:Type.
% 0.48/0.64 Parameter fofType:Type.
% 0.48/0.64 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.48/0.64 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.48/0.64 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.64 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.64 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.64 Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.48/0.64 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.48/0.64 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.48/0.64 Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.48/0.64 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% 0.48/0.64 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).
% 3.87/4.06 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).
% 3.87/4.06 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 3.87/4.06 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 3.87/4.06 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 3.87/4.06 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 3.87/4.06 Parameter rel_s4:(fofType->(fofType->Prop)).
% 3.87/4.06 Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 3.87/4.06 Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 3.87/4.06 Axiom a1:(mreflexive rel_s4).
% 3.87/4.06 Axiom a2:(mtransitive rel_s4).
% 3.87/4.06 Parameter p:(fofType->Prop).
% 3.87/4.06 Trying to prove (mvalid ((mimplies (mdia_s4 (mbox_s4 (mdia_s4 (mbox_s4 p))))) (mdia_s4 (mbox_s4 p))))
% 3.87/4.06 Found a10:=(a1 W):((rel_s4 W) W)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (x1 (a1 W)) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 3.87/4.06 Found a10:=(a1 W):((rel_s4 W) W)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 3.87/4.06 Found (x1 (a1 W)) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 3.87/4.06 Found a10:=(a1 S):((rel_s4 S) S)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (x1 (a1 S)) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 3.87/4.06 Found a10:=(a1 S):((rel_s4 S) S)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 3.87/4.06 Found (x1 (a1 S)) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 3.87/4.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 3.87/4.06 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 3.87/4.06 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 3.87/4.06 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)))
% 3.87/4.06 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)))
% 3.87/4.06 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)))
% 3.87/4.06 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 3.87/4.06 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 3.87/4.06 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)))
% 3.87/4.06 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)))
% 3.87/4.06 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)))
% 3.87/4.06 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)))
% 3.87/4.06 Found a10:=(a1 W):((rel_s4 W) W)
% 3.87/4.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (x3 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 8.96/9.16 Found a10:=(a1 W):((rel_s4 W) W)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (x3 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 8.96/9.16 Found a10:=(a1 W):((rel_s4 W) W)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (x1 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 8.96/9.16 Found a10:=(a1 W):((rel_s4 W) W)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V)
% 8.96/9.16 Found (x1 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 8.96/9.16 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 8.96/9.16 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 8.96/9.16 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 8.96/9.16 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 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)))
% 8.96/9.16 Found a10:=(a1 W):((rel_s4 W) W)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (x3 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 8.96/9.16 Found a10:=(a1 W):((rel_s4 W) W)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (a1 W) as proof of ((rel_s4 W) V0)
% 8.96/9.16 Found (x3 (a1 W)) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 8.96/9.16 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 14.77/14.94 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 14.77/14.94 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 Found a10:=(a1 S):((rel_s4 S) S)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (x3 (a1 S)) as proof of False
% 14.77/14.94 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 14.77/14.94 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 14.77/14.94 Found a10:=(a1 S):((rel_s4 S) S)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V0)
% 14.77/14.94 Found (x3 (a1 S)) as proof of False
% 14.77/14.94 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 14.77/14.94 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 14.77/14.94 Found a10:=(a1 W):((rel_s4 W) W)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (x1 (a1 W)) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 14.77/14.94 Found a10:=(a1 W):((rel_s4 W) W)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (a1 W) as proof of ((rel_s4 W) V)
% 14.77/14.94 Found (x1 (a1 W)) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 14.77/14.94 Found a10:=(a1 S):((rel_s4 S) S)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (x1 (a1 S)) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 14.77/14.94 Found a10:=(a1 S):((rel_s4 S) S)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (a1 S) as proof of ((rel_s4 S) V)
% 14.77/14.94 Found (x1 (a1 S)) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 14.77/14.94 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 14.77/14.94 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 14.77/14.94 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 14.77/14.94 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 14.77/14.94 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)))
% 20.98/21.13 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)))
% 20.98/21.13 Found a10:=(a1 S):((rel_s4 S) S)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (x3 (a1 S)) as proof of False
% 20.98/21.13 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 20.98/21.13 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 20.98/21.13 Found a10:=(a1 S):((rel_s4 S) S)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (x3 (a1 S)) as proof of False
% 20.98/21.13 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 20.98/21.13 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 V):((rel_s4 V) V)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (x1 (a1 V)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 S):((rel_s4 S) S)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (x1 (a1 S)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 S):((rel_s4 S) S)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V)
% 20.98/21.13 Found (x1 (a1 S)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 V):((rel_s4 V) V)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (x1 (a1 V)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 20.98/21.13 Found a10:=(a1 V):((rel_s4 V) V)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (x1 (a1 V)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 W):((rel_s4 W) W)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found (a1 W) as proof of ((rel_s4 W) V0)
% 20.98/21.13 Found a10:=(a1 S):((rel_s4 S) S)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found (a1 S) as proof of ((rel_s4 S) V0)
% 20.98/21.13 Found a10:=(a1 V):((rel_s4 V) V)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (a1 V) as proof of ((rel_s4 V) V0)
% 20.98/21.13 Found (x1 (a1 V)) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 20.98/21.13 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 24.71/24.91 Found a10:=(a1 S):((rel_s4 S) S)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found a10:=(a1 W):((rel_s4 W) W)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found a10:=(a1 W):((rel_s4 W) W)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found a10:=(a1 S):((rel_s4 S) S)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found a10:=(a1 S):((rel_s4 S) S)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found (a1 S) as proof of ((rel_s4 S) V0)
% 24.71/24.91 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.71/24.91 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.71/24.91 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.71/24.91 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 Found a10:=(a1 W):((rel_s4 W) W)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (x3 (a1 W)) as proof of False
% 24.71/24.91 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 24.71/24.91 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 24.71/24.91 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 24.71/24.91 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 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)))
% 24.71/24.91 Found a10:=(a1 W):((rel_s4 W) W)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (a1 W) as proof of ((rel_s4 W) V0)
% 24.71/24.91 Found (x3 (a1 W)) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 34.92/35.15 Found a10:=(a1 W):((rel_s4 W) W)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (x3 (a1 W)) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 34.92/35.15 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 34.92/35.15 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 34.92/35.15 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)))
% 34.92/35.15 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)))
% 34.92/35.15 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)))
% 34.92/35.15 Found a10:=(a1 W):((rel_s4 W) W)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 34.92/35.15 Found (x3 (a1 W)) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 34.92/35.15 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 34.92/35.15 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 34.92/35.15 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 34.92/35.15 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)))
% 34.92/35.15 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)))
% 34.92/35.15 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)))
% 34.92/35.15 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)))
% 34.92/35.15 Found a10:=(a1 V):((rel_s4 V) V)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (x1 (a1 V)) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 34.92/35.15 Found a10:=(a1 V):((rel_s4 V) V)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (x1 (a1 V)) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 34.92/35.15 Found a10:=(a1 V):((rel_s4 V) V)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (a1 V) as proof of ((rel_s4 V) V0)
% 34.92/35.15 Found (x1 (a1 V)) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 34.92/35.15 Found a10:=(a1 W):((rel_s4 W) W)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V)
% 34.92/35.15 Found (a1 W) as proof of ((rel_s4 W) V)
% 34.92/35.15 Found (x1 (a1 W)) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 34.92/35.15 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 34.92/35.15 Found a10:=(a1 S):((rel_s4 S) S)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found a10:=(a1 S):((rel_s4 S) S)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 34.92/35.15 Found a10:=(a1 S):((rel_s4 S) S)
% 34.92/35.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 40.22/40.39 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 Found a10:=(a1 S):((rel_s4 S) S)
% 40.22/40.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.22/40.39 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 40.22/40.39 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 40.22/40.39 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 40.22/40.39 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 Found a10:=(a1 W):((rel_s4 W) W)
% 40.22/40.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.22/40.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.22/40.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.22/40.39 Found (x3 (a1 W)) as proof of False
% 40.22/40.39 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 40.22/40.39 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.22/40.39 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 40.22/40.39 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 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)))
% 40.22/40.39 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 40.22/40.39 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 40.22/40.39 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 Found a10:=(a1 W):((rel_s4 W) W)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (x3 (a1 W)) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 43.31/43.55 Found a10:=(a1 W):((rel_s4 W) W)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (x3 (a1 W)) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 43.31/43.55 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 43.31/43.55 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 43.31/43.55 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 43.31/43.55 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 43.31/43.55 Found a10:=(a1 W):((rel_s4 W) W)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (x3 (a1 W)) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 43.31/43.55 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 43.31/43.55 Found a10:=(a1 W):((rel_s4 W) W)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.31/43.55 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 43.31/43.55 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 43.31/43.55 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)))
% 43.31/43.55 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 Found a10:=(a1 S):((rel_s4 S) S)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (x3 (a1 S)) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 47.46/47.67 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 47.46/47.67 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 Found a10:=(a1 W):((rel_s4 W) W)
% 47.46/47.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.46/47.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.46/47.67 Found (a1 W) as proof of ((rel_s4 W) V0)
% 47.46/47.67 Found a10:=(a1 S):((rel_s4 S) S)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (x3 (a1 S)) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 47.46/47.67 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 47.46/47.67 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 47.46/47.67 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 47.46/47.67 Found a10:=(a1 S):((rel_s4 S) S)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (a1 S) as proof of ((rel_s4 S) V0)
% 47.46/47.67 Found (x3 (a1 S)) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 47.46/47.67 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 47.46/47.67 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 47.46/47.67 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 47.46/47.67 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)))
% 47.46/47.67 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)))
% 53.03/53.23 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)))
% 53.03/53.23 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)))
% 53.03/53.23 Found a10:=(a1 W):((rel_s4 W) W)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V)
% 53.03/53.23 Found (x1 (a1 W)) as proof of False
% 53.03/53.23 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 53.03/53.23 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 53.03/53.23 Found a10:=(a1 W):((rel_s4 W) W)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found x3:(((rel_s4 W) V0)->False)
% 53.03/53.23 Instantiate: V0:=V00:fofType;V:=W:fofType
% 53.03/53.23 Found x3 as proof of (((rel_s4 V) V00)->False)
% 53.03/53.23 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found a10:=(a1 S):((rel_s4 S) S)
% 53.03/53.23 Found (a1 S) as proof of ((rel_s4 S) V0)
% 53.03/53.23 Found (a1 S) as proof of ((rel_s4 S) V0)
% 53.03/53.23 Found (a1 S) as proof of ((rel_s4 S) V0)
% 53.03/53.23 Found (x3 (a1 S)) as proof of False
% 53.03/53.23 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 53.03/53.23 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 53.03/53.23 Found a10:=(a1 W):((rel_s4 W) W)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found x3:(((rel_s4 W) V0)->False)
% 53.03/53.23 Instantiate: V0:=V00:fofType
% 53.03/53.23 Found x3 as proof of (((rel_s4 V) V00)->False)
% 53.03/53.23 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 53.03/53.23 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 53.03/53.23 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 53.03/53.23 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)))
% 53.03/53.23 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)))
% 53.03/53.23 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)))
% 53.03/53.23 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 53.03/53.23 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 53.03/53.23 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)))
% 53.03/53.23 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)))
% 53.03/53.23 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)))
% 53.03/53.23 Found a10:=(a1 V):((rel_s4 V) V)
% 53.03/53.23 Found (a1 V) as proof of ((rel_s4 V) V0)
% 53.03/53.23 Found (a1 V) as proof of ((rel_s4 V) V0)
% 53.03/53.23 Found (a1 V) as proof of ((rel_s4 V) V0)
% 53.03/53.23 Found (x1 (a1 V)) as proof of False
% 53.03/53.23 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 53.03/53.23 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 53.03/53.23 Found a10:=(a1 W):((rel_s4 W) W)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found (a1 W) as proof of ((rel_s4 W) V0)
% 53.03/53.23 Found x2:((rel_s4 V) V0)
% 53.03/53.23 Instantiate: V1:=V0:fofType;V:=W:fofType
% 53.03/53.23 Found x2 as proof of ((rel_s4 W) V1)
% 53.03/53.23 Found (x4 x2) as proof of False
% 53.03/53.23 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 53.03/53.23 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 57.13/57.33 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 57.13/57.33 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 Found a10:=(a1 W):((rel_s4 W) W)
% 57.13/57.33 Found (a1 W) as proof of ((rel_s4 W) V0)
% 57.13/57.33 Found (a1 W) as proof of ((rel_s4 W) V0)
% 57.13/57.33 Found (a1 W) as proof of ((rel_s4 W) V0)
% 57.13/57.33 Found x2:((rel_s4 V) V0)
% 57.13/57.33 Instantiate: V1:=V0:fofType
% 57.13/57.33 Found x2 as proof of ((rel_s4 W) V1)
% 57.13/57.33 Found (x4 x2) as proof of False
% 57.13/57.33 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 57.13/57.33 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 57.13/57.33 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 57.13/57.33 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 57.13/57.33 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 57.13/57.33 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 57.13/57.33 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 57.13/57.33 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)))
% 57.13/57.33 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 Found a10:=(a1 W):((rel_s4 W) W)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (x5 (a1 W)) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 61.35/61.55 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 61.35/61.55 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 61.35/61.55 Found (or_introl0 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 61.35/61.55 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 Found a10:=(a1 W):((rel_s4 W) W)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (x5 (a1 W)) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 61.35/61.55 Found a10:=(a1 W):((rel_s4 W) W)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (a1 W) as proof of ((rel_s4 W) V1)
% 61.35/61.55 Found (x5 (a1 W)) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 61.35/61.55 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 61.35/61.55 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 61.35/61.55 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 61.35/61.55 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)))
% 76.63/76.83 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)))
% 76.63/76.83 Found a10:=(a1 W):((rel_s4 W) W)
% 76.63/76.83 Found (a1 W) as proof of ((rel_s4 W) V1)
% 76.63/76.83 Found (a1 W) as proof of ((rel_s4 W) V1)
% 76.63/76.83 Found (a1 W) as proof of ((rel_s4 W) V1)
% 76.63/76.83 Found (x5 (a1 W)) as proof of False
% 76.63/76.83 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 76.63/76.83 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 76.63/76.83 Found a10:=(a1 S):((rel_s4 S) S)
% 76.63/76.83 Found (a1 S) as proof of ((rel_s4 S) V)
% 76.63/76.83 Found (a1 S) as proof of ((rel_s4 S) V)
% 76.63/76.83 Found (a1 S) as proof of ((rel_s4 S) V)
% 76.63/76.83 Found (x1 (a1 S)) as proof of False
% 76.63/76.83 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 76.63/76.83 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 76.63/76.83 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 76.63/76.83 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 76.63/76.83 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 76.63/76.83 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 76.63/76.83 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 76.63/76.83 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)))
% 80.20/80.41 Found or_intror00:=(or_intror0 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 80.20/80.41 Found (or_intror0 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 Found a10:=(a1 W):((rel_s4 W) W)
% 80.20/80.41 Found (a1 W) as proof of ((rel_s4 W) V0)
% 80.20/80.41 Found (a1 W) as proof of ((rel_s4 W) V0)
% 80.20/80.41 Found (a1 W) as proof of ((rel_s4 W) V0)
% 80.20/80.41 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 80.20/80.41 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 Found a10:=(a1 S):((rel_s4 S) S)
% 80.20/80.41 Found (a1 S) as proof of ((rel_s4 S) V0)
% 80.20/80.41 Found (a1 S) as proof of ((rel_s4 S) V0)
% 80.20/80.41 Found (a1 S) as proof of ((rel_s4 S) V0)
% 80.20/80.41 Found (x3 (a1 S)) as proof of False
% 80.20/80.41 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 80.20/80.41 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 80.20/80.41 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 80.20/80.41 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 Found a10:=(a1 V):((rel_s4 V) V)
% 80.20/80.41 Found (a1 V) as proof of ((rel_s4 V) V00)
% 80.20/80.41 Found (a1 V) as proof of ((rel_s4 V) V00)
% 80.20/80.41 Found (a1 V) as proof of ((rel_s4 V) V00)
% 80.20/80.41 Found (x2 (a1 V)) as proof of False
% 80.20/80.41 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 80.20/80.41 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 80.20/80.41 Found or_intror10:=(or_intror1 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 80.20/80.41 Found (or_intror1 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 80.20/80.41 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)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 Found a10:=(a1 S):((rel_s4 S) S)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found a10:=(a1 V):((rel_s4 V) V)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (x1 (a1 V)) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 83.76/83.96 Found a10:=(a1 V):((rel_s4 V) V)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (x1 (a1 V)) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 83.76/83.96 Found a10:=(a1 W):((rel_s4 W) W)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found a10:=(a1 V):((rel_s4 V) V)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V0)
% 83.76/83.96 Found (x1 (a1 V)) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 83.76/83.96 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 83.76/83.96 Found a10:=(a1 S):((rel_s4 S) S)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (x3 (a1 S)) as proof of False
% 83.76/83.96 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 83.76/83.96 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 83.76/83.96 Found a10:=(a1 W):((rel_s4 W) W)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found (a1 W) as proof of ((rel_s4 W) V0)
% 83.76/83.96 Found a10:=(a1 V):((rel_s4 V) V)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V00)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V00)
% 83.76/83.96 Found (a1 V) as proof of ((rel_s4 V) V00)
% 83.76/83.96 Found (x2 (a1 V)) as proof of False
% 83.76/83.96 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 83.76/83.96 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 83.76/83.96 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 83.76/83.96 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 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)))
% 83.76/83.96 Found a10:=(a1 S):((rel_s4 S) S)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (a1 S) as proof of ((rel_s4 S) V0)
% 83.76/83.96 Found (x3 (a1 S)) as proof of False
% 83.76/83.96 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 83.76/83.96 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 93.51/93.75 Found a10:=(a1 W):((rel_s4 W) W)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found a10:=(a1 S):((rel_s4 S) S)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found a10:=(a1 W):((rel_s4 W) W)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 93.51/93.75 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 93.51/93.75 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)))
% 93.51/93.75 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)))
% 93.51/93.75 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)))
% 93.51/93.75 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)))
% 93.51/93.75 Found a10:=(a1 S):((rel_s4 S) S)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (x3 (a1 S)) as proof of False
% 93.51/93.75 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 93.51/93.75 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 93.51/93.75 Found a10:=(a1 W):((rel_s4 W) W)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found x3:(((rel_s4 W) V0)->False)
% 93.51/93.75 Instantiate: V0:=V00:fofType;V:=W:fofType
% 93.51/93.75 Found x3 as proof of (((rel_s4 V) V00)->False)
% 93.51/93.75 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found a10:=(a1 W):((rel_s4 W) W)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found x2:((rel_s4 V) V0)
% 93.51/93.75 Instantiate: V1:=V0:fofType;V:=W:fofType
% 93.51/93.75 Found x2 as proof of ((rel_s4 W) V1)
% 93.51/93.75 Found (x4 x2) as proof of False
% 93.51/93.75 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 93.51/93.75 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 93.51/93.75 Found x3:(((rel_s4 S) V0)->False)
% 93.51/93.75 Instantiate: V0:=V00:fofType;V:=S:fofType
% 93.51/93.75 Found x3 as proof of (((rel_s4 V) V00)->False)
% 93.51/93.75 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found a10:=(a1 S):((rel_s4 S) S)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 93.51/93.75 Found x3:(((rel_s4 W) V0)->False)
% 93.51/93.75 Instantiate: V0:=V00:fofType
% 93.51/93.75 Found x3 as proof of (((rel_s4 V) V00)->False)
% 93.51/93.75 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 93.51/93.75 Found a10:=(a1 W):((rel_s4 W) W)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 93.51/93.75 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 93.51/93.75 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 93.51/93.75 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)))
% 97.95/98.15 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)))
% 97.95/98.15 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)))
% 97.95/98.15 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 97.95/98.15 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 97.95/98.15 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)))
% 97.95/98.15 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)))
% 97.95/98.15 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)))
% 97.95/98.15 Found a10:=(a1 W):((rel_s4 W) W)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found x2:((rel_s4 V) V0)
% 97.95/98.15 Instantiate: V1:=V0:fofType
% 97.95/98.15 Found x2 as proof of ((rel_s4 W) V1)
% 97.95/98.15 Found (x4 x2) as proof of False
% 97.95/98.15 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 97.95/98.15 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 97.95/98.15 Found x3:(((rel_s4 S) V0)->False)
% 97.95/98.15 Instantiate: V0:=V00:fofType
% 97.95/98.15 Found x3 as proof of (((rel_s4 V) V00)->False)
% 97.95/98.15 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 97.95/98.15 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 97.95/98.15 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 97.95/98.15 Found a10:=(a1 W):((rel_s4 W) W)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found a10:=(a1 W):((rel_s4 W) W)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found (a1 W) as proof of ((rel_s4 W) V0)
% 97.95/98.15 Found a10:=(a1 S):((rel_s4 S) S)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V0)
% 97.95/98.15 Found x3:(((rel_s4 W) V0)->False)
% 97.95/98.15 Instantiate: V0:=V00:fofType;V:=W:fofType
% 97.95/98.15 Found x3 as proof of (((rel_s4 V) V00)->False)
% 97.95/98.15 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 97.95/98.15 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 97.95/98.15 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 97.95/98.15 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 97.95/98.15 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))
% 97.95/98.15 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))
% 97.95/98.15 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))
% 97.95/98.15 Found a10:=(a1 S):((rel_s4 S) S)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V)
% 97.95/98.15 Found (a1 S) as proof of ((rel_s4 S) V)
% 97.95/98.15 Found (x1 (a1 S)) as proof of False
% 97.95/98.15 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 97.95/98.15 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 97.95/98.15 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 97.95/98.15 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 97.95/98.15 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)))
% 97.95/98.15 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)))
% 97.95/98.15 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)))
% 101.80/102.03 Found a10:=(a1 W):((rel_s4 W) W)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found a10:=(a1 W):((rel_s4 W) W)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found x2:((rel_s4 V) V0)
% 101.80/102.03 Instantiate: V1:=V0:fofType;V:=W:fofType
% 101.80/102.03 Found x2 as proof of ((rel_s4 W) V1)
% 101.80/102.03 Found (x4 x2) as proof of False
% 101.80/102.03 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 101.80/102.03 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 101.80/102.03 Found a10:=(a1 S):((rel_s4 S) S)
% 101.80/102.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 101.80/102.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 101.80/102.03 Found (a1 S) as proof of ((rel_s4 S) V0)
% 101.80/102.03 Found x2:((rel_s4 V) V0)
% 101.80/102.03 Instantiate: V1:=V0:fofType;V:=S:fofType
% 101.80/102.03 Found x2 as proof of ((rel_s4 S) V1)
% 101.80/102.03 Found (x4 x2) as proof of False
% 101.80/102.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 101.80/102.03 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 101.80/102.03 Found a10:=(a1 W):((rel_s4 W) W)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found a10:=(a1 W):((rel_s4 W) W)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found (a1 W) as proof of ((rel_s4 W) V0)
% 101.80/102.03 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 101.80/102.03 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 101.80/102.03 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 101.80/102.03 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 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)))
% 101.80/102.03 Found x3:(((rel_s4 W) V0)->False)
% 101.80/102.03 Instantiate: V0:=V00:fofType
% 101.80/102.03 Found x3 as proof of (((rel_s4 V) V00)->False)
% 101.80/102.03 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 101.80/102.03 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 101.80/102.03 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 101.80/102.03 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 101.80/102.03 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))
% 101.80/102.03 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))
% 105.89/106.11 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))
% 105.89/106.11 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 105.89/106.11 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 Found a10:=(a1 W):((rel_s4 W) W)
% 105.89/106.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.89/106.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.89/106.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 105.89/106.11 Found or_intror10:=(or_intror1 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 105.89/106.11 Found (or_intror1 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 Found x2:((rel_s4 V) V0)
% 105.89/106.11 Instantiate: V1:=V0:fofType
% 105.89/106.11 Found x2 as proof of ((rel_s4 W) V1)
% 105.89/106.11 Found (x4 x2) as proof of False
% 105.89/106.11 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 105.89/106.11 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 105.89/106.11 Found a10:=(a1 S):((rel_s4 S) S)
% 105.89/106.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.89/106.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.89/106.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 105.89/106.11 Found x2:((rel_s4 V) V0)
% 105.89/106.11 Instantiate: V1:=V0:fofType
% 105.89/106.11 Found x2 as proof of ((rel_s4 S) V1)
% 105.89/106.11 Found (x4 x2) as proof of False
% 105.89/106.11 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 105.89/106.11 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 105.89/106.11 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 105.89/106.11 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 105.89/106.11 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 105.89/106.11 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 105.89/106.11 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 105.89/106.11 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)))
% 105.89/106.11 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 110.63/110.84 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 110.63/110.84 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 110.63/110.84 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 110.63/110.84 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 110.63/110.84 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 110.63/110.84 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 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)))
% 110.63/110.84 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 114.25/114.46 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 Found a10:=(a1 S):((rel_s4 S) S)
% 114.25/114.46 Found (a1 S) as proof of ((rel_s4 S) V1)
% 114.25/114.46 Found (a1 S) as proof of ((rel_s4 S) V1)
% 114.25/114.46 Found (a1 S) as proof of ((rel_s4 S) V1)
% 114.25/114.46 Found (x5 (a1 S)) as proof of False
% 114.25/114.46 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 114.25/114.46 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 114.25/114.46 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 114.25/114.46 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 114.25/114.46 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 Found a10:=(a1 W):((rel_s4 W) W)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V0)
% 114.25/114.46 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 114.25/114.46 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 Found a10:=(a1 W):((rel_s4 W) W)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 114.25/114.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 114.25/114.46 Found (x5 (a1 W)) as proof of False
% 114.25/114.46 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 114.25/114.46 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 114.25/114.46 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 114.25/114.46 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 114.25/114.46 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)))
% 117.17/117.42 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 117.17/117.42 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 117.17/117.42 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 Found a10:=(a1 S):((rel_s4 S) S)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (x5 (a1 S)) as proof of False
% 117.17/117.42 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 117.17/117.42 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 117.17/117.42 Found or_introl00:=(or_introl0 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 117.17/117.42 Found (or_introl0 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 Found a10:=(a1 S):((rel_s4 S) S)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (a1 S) as proof of ((rel_s4 S) V1)
% 117.17/117.42 Found (x5 (a1 S)) as proof of False
% 117.17/117.42 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 117.17/117.42 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 117.17/117.42 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 117.17/117.42 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 117.17/117.42 Found a10:=(a1 W):((rel_s4 W) W)
% 117.17/117.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 117.17/117.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 117.17/117.42 Found (a1 W) as proof of ((rel_s4 W) V0)
% 117.17/117.42 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 117.17/117.42 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 117.17/117.42 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)))
% 117.17/117.42 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 119.70/119.90 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 119.70/119.90 Found (or_introl0 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 Found a10:=(a1 W):((rel_s4 W) W)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (x5 (a1 W)) as proof of False
% 119.70/119.90 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 119.70/119.90 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.70/119.90 Found a10:=(a1 W):((rel_s4 W) W)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.70/119.90 Found (x5 (a1 W)) as proof of False
% 119.70/119.90 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 119.70/119.90 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.70/119.90 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V1)))
% 119.70/119.90 Found (or_introl1 (p V1)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 119.70/119.90 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 119.70/119.90 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)))
% 133.63/133.84 Found a10:=(a1 S):((rel_s4 S) S)
% 133.63/133.84 Found (a1 S) as proof of ((rel_s4 S) V1)
% 133.63/133.84 Found (a1 S) as proof of ((rel_s4 S) V1)
% 133.63/133.84 Found (a1 S) as proof of ((rel_s4 S) V1)
% 133.63/133.84 Found (x5 (a1 S)) as proof of False
% 133.63/133.84 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 133.63/133.84 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 133.63/133.84 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V2)->False)->((or (((rel_s4 W) V2)->False)) (p V0)))
% 133.63/133.84 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 133.63/133.84 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)))
% 133.63/133.84 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)))
% 133.63/133.84 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)))
% 133.63/133.84 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)))
% 133.63/133.84 Found a10:=(a1 W):((rel_s4 W) W)
% 133.63/133.84 Found (a1 W) as proof of ((rel_s4 W) V1)
% 133.63/133.84 Found (a1 W) as proof of ((rel_s4 W) V1)
% 133.63/133.84 Found (a1 W) as proof of ((rel_s4 W) V1)
% 133.63/133.84 Found (x5 (a1 W)) as proof of False
% 133.63/133.84 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 133.63/133.84 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 133.63/133.84 Found x4:((rel_s4 V) V0)
% 133.63/133.84 Instantiate: V2:=V0:fofType;V:=W:fofType
% 133.63/133.84 Found x4 as proof of ((rel_s4 W) V2)
% 133.63/133.84 Found (x6 x4) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 133.63/133.84 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 133.63/133.84 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 133.63/133.84 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)))
% 133.63/133.84 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)))
% 133.63/133.84 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)))
% 133.63/133.84 Found x4:((rel_s4 V) V0)
% 133.63/133.84 Instantiate: V2:=V0:fofType
% 133.63/133.84 Found x4 as proof of ((rel_s4 W) V2)
% 133.63/133.84 Found (x6 x4) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 133.63/133.84 Found x4:((rel_s4 V) V0)
% 133.63/133.84 Instantiate: V2:=V0:fofType
% 133.63/133.84 Found x4 as proof of ((rel_s4 W) V2)
% 133.63/133.84 Found (x6 x4) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 133.63/133.84 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 133.63/133.84 Found a10:=(a1 V):((rel_s4 V) V)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (x1 (a1 V)) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 133.63/133.84 Found a10:=(a1 V):((rel_s4 V) V)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (x1 (a1 V)) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 133.63/133.84 Found a10:=(a1 V):((rel_s4 V) V)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (a1 V) as proof of ((rel_s4 V) V0)
% 133.63/133.84 Found (x1 (a1 V)) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 133.63/133.84 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 142.83/143.09 Found a10:=(a1 V):((rel_s4 V) V)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (x1 (a1 V)) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 142.83/143.09 Found a10:=(a1 V):((rel_s4 V) V)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (x1 (a1 V)) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 142.83/143.09 Found a10:=(a1 V):((rel_s4 V) V)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (a1 V) as proof of ((rel_s4 V) V0)
% 142.83/143.09 Found (x1 (a1 V)) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 142.83/143.09 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 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)))
% 142.83/143.09 Found x4:((rel_s4 V) V0)
% 142.83/143.09 Instantiate: V2:=V0:fofType
% 142.83/143.09 Found x4 as proof of ((rel_s4 W) V2)
% 142.83/143.09 Found (x6 x4) as proof of False
% 142.83/143.09 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 142.83/143.09 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 142.83/143.09 Found or_introl10:=(or_introl1 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 142.83/143.09 Found (or_introl1 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 142.83/143.09 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 142.83/143.09 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 142.83/143.09 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 142.83/143.09 Found or_intror00:=(or_intror0 (((rel_s4 S) V1)->False)):((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 S) V1)->False)))
% 142.83/143.09 Found (or_intror0 (((rel_s4 S) V1)->False)) as proof of ((((rel_s4 S) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 142.83/143.09 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 Found a10:=(a1 W):((rel_s4 W) W)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found a10:=(a1 V):((rel_s4 V) V)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (x2 (a1 V)) as proof of False
% 145.90/146.12 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 145.90/146.12 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 145.90/146.12 Found a10:=(a1 S):((rel_s4 S) S)
% 145.90/146.12 Found (a1 S) as proof of ((rel_s4 S) V0)
% 145.90/146.12 Found (a1 S) as proof of ((rel_s4 S) V0)
% 145.90/146.12 Found (a1 S) as proof of ((rel_s4 S) V0)
% 145.90/146.12 Found a10:=(a1 V):((rel_s4 V) V)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (a1 V) as proof of ((rel_s4 V) V00)
% 145.90/146.12 Found (x2 (a1 V)) as proof of False
% 145.90/146.12 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 145.90/146.12 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 145.90/146.12 Found a10:=(a1 W):((rel_s4 W) W)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found (a1 W) as proof of ((rel_s4 W) V0)
% 145.90/146.12 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 145.90/146.12 Found (or_introl1 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 145.90/146.12 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)))
% 151.59/151.85 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)))
% 151.59/151.85 Found a10:=(a1 W):((rel_s4 W) W)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found a10:=(a1 V):((rel_s4 V) V)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (x1 (a1 V)) as proof of False
% 151.59/151.85 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 151.59/151.85 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 151.59/151.85 Found a10:=(a1 V):((rel_s4 V) V)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V0)
% 151.59/151.85 Found (x1 (a1 V)) as proof of False
% 151.59/151.85 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 151.59/151.85 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 151.59/151.85 Found a10:=(a1 V):((rel_s4 V) V)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (x2 (a1 V)) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 151.59/151.85 Found a10:=(a1 S):((rel_s4 S) S)
% 151.59/151.85 Found (a1 S) as proof of ((rel_s4 S) V0)
% 151.59/151.85 Found (a1 S) as proof of ((rel_s4 S) V0)
% 151.59/151.85 Found (a1 S) as proof of ((rel_s4 S) V0)
% 151.59/151.85 Found a10:=(a1 V):((rel_s4 V) V)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (x2 (a1 V)) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 151.59/151.85 Found a10:=(a1 V):((rel_s4 V) V)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (a1 V) as proof of ((rel_s4 V) V00)
% 151.59/151.85 Found (x2 (a1 V)) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 151.59/151.85 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 151.59/151.85 Found a10:=(a1 W):((rel_s4 W) W)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found (a1 W) as proof of ((rel_s4 W) V0)
% 151.59/151.85 Found or_introl10:=(or_introl1 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found (or_introl1 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 151.59/151.85 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 151.59/151.85 Found (or_introl1 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 151.59/151.85 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)))
% 151.59/151.85 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)))
% 158.40/158.69 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)))
% 158.40/158.69 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)))
% 158.40/158.69 Found a10:=(a1 S):((rel_s4 S) S)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found x3:(((rel_s4 W) V0)->False)
% 158.40/158.69 Instantiate: V0:=V00:fofType;V:=W:fofType
% 158.40/158.69 Found x3 as proof of (((rel_s4 V) V00)->False)
% 158.40/158.69 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 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))
% 158.40/158.69 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)))
% 158.40/158.69 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))
% 158.40/158.69 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))
% 158.40/158.69 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))
% 158.40/158.69 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))
% 158.40/158.69 Found a10:=(a1 V):((rel_s4 V) V)
% 158.40/158.69 Found (a1 V) as proof of ((rel_s4 V) V00)
% 158.40/158.69 Found (a1 V) as proof of ((rel_s4 V) V00)
% 158.40/158.69 Found (a1 V) as proof of ((rel_s4 V) V00)
% 158.40/158.69 Found (x2 (a1 V)) as proof of False
% 158.40/158.69 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 158.40/158.69 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 158.40/158.69 Found a10:=(a1 S):((rel_s4 S) S)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found (a1 S) as proof of ((rel_s4 S) V0)
% 158.40/158.69 Found x3:(((rel_s4 S) V0)->False)
% 158.40/158.69 Instantiate: V0:=V00:fofType;V:=S:fofType
% 158.40/158.69 Found x3 as proof of (((rel_s4 V) V00)->False)
% 158.40/158.69 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found x3:(((rel_s4 W) V0)->False)
% 158.40/158.69 Instantiate: V0:=V00:fofType
% 158.40/158.69 Found x3 as proof of (((rel_s4 V) V00)->False)
% 158.40/158.69 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 158.40/158.69 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))
% 158.40/158.69 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)))
% 158.40/158.69 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))
% 164.93/165.18 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))
% 164.93/165.18 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))
% 164.93/165.18 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))
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found a10:=(a1 S):((rel_s4 S) S)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found a10:=(a1 V):((rel_s4 V) V)
% 164.93/165.18 Found (a1 V) as proof of ((rel_s4 V) V0)
% 164.93/165.18 Found (a1 V) as proof of ((rel_s4 V) V0)
% 164.93/165.18 Found (a1 V) as proof of ((rel_s4 V) V0)
% 164.93/165.18 Found (x1 (a1 V)) as proof of False
% 164.93/165.18 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 164.93/165.18 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 164.93/165.18 Found a10:=(a1 S):((rel_s4 S) S)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found x2:((rel_s4 V) V0)
% 164.93/165.18 Instantiate: V1:=V0:fofType;V:=S:fofType
% 164.93/165.18 Found x2 as proof of ((rel_s4 S) V1)
% 164.93/165.18 Found (x4 x2) as proof of False
% 164.93/165.18 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 164.93/165.18 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found x3:(((rel_s4 S) V0)->False)
% 164.93/165.18 Instantiate: V0:=V00:fofType
% 164.93/165.18 Found x3 as proof of (((rel_s4 V) V00)->False)
% 164.93/165.18 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 164.93/165.18 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 164.93/165.18 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 164.93/165.18 Found x2:((rel_s4 V) V0)
% 164.93/165.18 Instantiate: V1:=V0:fofType;V:=W:fofType
% 164.93/165.18 Found x2 as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found (x4 x2) as proof of False
% 164.93/165.18 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 164.93/165.18 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.93/165.18 Found a10:=(a1 W):((rel_s4 W) W)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.93/165.18 Found a10:=(a1 S):((rel_s4 S) S)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found a10:=(a1 S):((rel_s4 S) S)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 164.93/165.18 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found x2:((rel_s4 V) V0)
% 168.14/168.38 Instantiate: V1:=V0:fofType
% 168.14/168.38 Found x2 as proof of ((rel_s4 S) V1)
% 168.14/168.38 Found (x4 x2) as proof of False
% 168.14/168.38 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 168.14/168.38 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 168.14/168.38 Found a10:=(a1 W):((rel_s4 W) W)
% 168.14/168.38 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.14/168.38 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.14/168.38 Found (a1 W) as proof of ((rel_s4 W) V0)
% 168.14/168.38 Found a10:=(a1 S):((rel_s4 S) S)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found x3:(((rel_s4 S) V0)->False)
% 168.14/168.38 Instantiate: V0:=V00:fofType;V:=S:fofType
% 168.14/168.38 Found x3 as proof of (((rel_s4 V) V00)->False)
% 168.14/168.38 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 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))
% 168.14/168.38 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))
% 168.14/168.38 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))
% 168.14/168.38 Found x3:(((rel_s4 W) V0)->False)
% 168.14/168.38 Instantiate: V0:=V00:fofType;V:=W:fofType
% 168.14/168.38 Found x3 as proof of (((rel_s4 V) V00)->False)
% 168.14/168.38 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 168.14/168.38 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))
% 168.14/168.38 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))
% 168.14/168.38 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))
% 168.14/168.38 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 168.14/168.38 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 168.14/168.38 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)))
% 168.14/168.38 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)))
% 168.14/168.38 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)))
% 168.14/168.38 Found a10:=(a1 S):((rel_s4 S) S)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found (a1 S) as proof of ((rel_s4 S) V0)
% 168.14/168.38 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 168.14/168.38 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 168.14/168.38 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)))
% 168.14/168.38 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)))
% 168.14/168.38 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)))
% 168.14/168.38 Found x2:((rel_s4 V) V0)
% 168.14/168.38 Instantiate: V1:=V0:fofType
% 173.63/173.88 Found x2 as proof of ((rel_s4 W) V1)
% 173.63/173.88 Found (x4 x2) as proof of False
% 173.63/173.88 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of False
% 173.63/173.88 Found (fun (x4:(((rel_s4 W) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 W) V1)->False)->False)
% 173.63/173.88 Found a10:=(a1 S):((rel_s4 S) S)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found a10:=(a1 W):((rel_s4 W) W)
% 173.63/173.88 Found (a1 W) as proof of ((rel_s4 W) V0)
% 173.63/173.88 Found (a1 W) as proof of ((rel_s4 W) V0)
% 173.63/173.88 Found (a1 W) as proof of ((rel_s4 W) V0)
% 173.63/173.88 Found x2:((rel_s4 V) V0)
% 173.63/173.88 Instantiate: V1:=V0:fofType;V:=S:fofType
% 173.63/173.88 Found x2 as proof of ((rel_s4 S) V1)
% 173.63/173.88 Found (x4 x2) as proof of False
% 173.63/173.88 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 173.63/173.88 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 173.63/173.88 Found a10:=(a1 S):((rel_s4 S) S)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found x3:(((rel_s4 S) V0)->False)
% 173.63/173.88 Instantiate: V0:=V00:fofType
% 173.63/173.88 Found x3 as proof of (((rel_s4 V) V00)->False)
% 173.63/173.88 Found (or_intror10 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found ((or_intror1 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 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))
% 173.63/173.88 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))
% 173.63/173.88 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))
% 173.63/173.88 Found x3:(((rel_s4 W) V0)->False)
% 173.63/173.88 Instantiate: V0:=V00:fofType
% 173.63/173.88 Found x3 as proof of (((rel_s4 V) V00)->False)
% 173.63/173.88 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 173.63/173.88 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))
% 173.63/173.88 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))
% 173.63/173.88 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))
% 173.63/173.88 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 173.63/173.88 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 173.63/173.88 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)))
% 173.63/173.88 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)))
% 173.63/173.88 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)))
% 173.63/173.88 Found a10:=(a1 S):((rel_s4 S) S)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found (a1 S) as proof of ((rel_s4 S) V0)
% 173.63/173.88 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 173.63/173.88 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 173.63/173.88 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)))
% 173.63/173.88 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)))
% 180.91/181.16 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)))
% 180.91/181.16 Found a10:=(a1 S):((rel_s4 S) S)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found a10:=(a1 S):((rel_s4 S) S)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 180.91/181.16 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 180.91/181.16 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 Found x2:((rel_s4 V) V0)
% 180.91/181.16 Instantiate: V1:=V0:fofType
% 180.91/181.16 Found x2 as proof of ((rel_s4 S) V1)
% 180.91/181.16 Found (x4 x2) as proof of False
% 180.91/181.16 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 180.91/181.16 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 180.91/181.16 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 180.91/181.16 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 180.91/181.16 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 Found a10:=(a1 S):((rel_s4 S) S)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 180.91/181.16 Found or_intror10:=(or_intror1 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 180.91/181.16 Found (or_intror1 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 180.91/181.16 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found a10:=(a1 W):((rel_s4 W) W)
% 184.80/185.07 Found (a1 W) as proof of ((rel_s4 W) V0)
% 184.80/185.07 Found (a1 W) as proof of ((rel_s4 W) V0)
% 184.80/185.07 Found (a1 W) as proof of ((rel_s4 W) V0)
% 184.80/185.07 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 184.80/185.07 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 184.80/185.07 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 184.80/185.07 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 184.80/185.07 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 184.80/185.07 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 184.80/185.07 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 184.80/185.07 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)))
% 190.64/190.95 Found a10:=(a1 W):((rel_s4 W) W)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found (x3 (a1 W)) as proof of False
% 190.64/190.95 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 190.64/190.95 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 190.64/190.95 Found a10:=(a1 S):((rel_s4 S) S)
% 190.64/190.95 Found (a1 S) as proof of ((rel_s4 S) V0)
% 190.64/190.95 Found (a1 S) as proof of ((rel_s4 S) V0)
% 190.64/190.95 Found (a1 S) as proof of ((rel_s4 S) V0)
% 190.64/190.95 Found a10:=(a1 W):((rel_s4 W) W)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found a10:=(a1 W):((rel_s4 W) W)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V1)
% 190.64/190.95 Found a10:=(a1 W):((rel_s4 W) W)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found (a1 W) as proof of ((rel_s4 W) V0)
% 190.64/190.95 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 190.64/190.95 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 190.64/190.95 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 190.64/190.95 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 Found or_intror00:=(or_intror0 (((rel_s4 W) V2)->False)):((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 W) V2)->False)))
% 190.64/190.95 Found (or_intror0 (((rel_s4 W) V2)->False)) as proof of ((((rel_s4 W) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 190.64/190.95 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 190.64/190.95 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 190.64/190.95 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)))
% 190.64/190.95 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)))
% 195.18/195.43 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)))
% 195.18/195.43 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 195.18/195.43 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found (x3 (a1 W)) as proof of False
% 195.18/195.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 195.18/195.43 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 195.18/195.43 Found a10:=(a1 S):((rel_s4 S) S)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V1)
% 195.18/195.43 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 195.18/195.43 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 Found a10:=(a1 W):((rel_s4 W) W)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 195.18/195.43 Found a10:=(a1 S):((rel_s4 S) S)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V1)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V1)
% 195.18/195.43 Found (a1 S) as proof of ((rel_s4 S) V1)
% 195.18/195.43 Found (x5 (a1 S)) as proof of False
% 195.18/195.43 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 195.18/195.43 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 195.18/195.43 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 195.18/195.43 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 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)))
% 195.18/195.43 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 195.18/195.43 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 195.18/195.43 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 199.62/199.86 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 Found a10:=(a1 W):((rel_s4 W) W)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found a10:=(a1 W):((rel_s4 W) W)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 199.62/199.86 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 199.62/199.86 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 Found or_introl00:=(or_introl0 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 199.62/199.86 Found (or_introl0 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 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)))
% 199.62/199.86 Found a10:=(a1 W):((rel_s4 W) W)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.62/199.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 199.62/199.86 Found a10:=(a1 S):((rel_s4 S) S)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (x5 (a1 S)) as proof of False
% 199.62/199.86 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 199.62/199.86 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 199.62/199.86 Found a10:=(a1 S):((rel_s4 S) S)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (a1 S) as proof of ((rel_s4 S) V1)
% 199.62/199.86 Found (x5 (a1 S)) as proof of False
% 199.62/199.86 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 199.62/199.86 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 199.62/199.86 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 199.62/199.86 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 199.62/199.86 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 202.36/202.66 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 Found or_introl10:=(or_introl1 (p V1)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V1)))
% 202.36/202.66 Found (or_introl1 (p V1)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V0) V1)->False)) (p V1)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 Found x4:((rel_s4 V) V0)
% 202.36/202.66 Instantiate: V2:=V0:fofType;V:=W:fofType
% 202.36/202.66 Found x4 as proof of ((rel_s4 W) V2)
% 202.36/202.66 Found (x6 x4) as proof of False
% 202.36/202.66 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 202.36/202.66 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 202.36/202.66 Found x3:(((rel_s4 W) V0)->False)
% 202.36/202.66 Instantiate: V0:=V00:fofType;V:=W:fofType
% 202.36/202.66 Found x3 as proof of (((rel_s4 V) V00)->False)
% 202.36/202.66 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 202.36/202.66 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 202.36/202.66 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 202.36/202.66 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 202.36/202.66 Found a10:=(a1 V):((rel_s4 V) V)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (x1 (a1 V)) as proof of False
% 202.36/202.66 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 202.36/202.66 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 202.36/202.66 Found a10:=(a1 V):((rel_s4 V) V)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (a1 V) as proof of ((rel_s4 V) V0)
% 202.36/202.66 Found (x1 (a1 V)) as proof of False
% 202.36/202.66 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 202.36/202.66 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 202.36/202.66 Found a10:=(a1 W):((rel_s4 W) W)
% 202.36/202.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 202.36/202.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 202.36/202.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 202.36/202.66 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 202.36/202.66 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 202.36/202.66 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)))
% 206.43/206.70 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)))
% 206.43/206.70 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 206.43/206.70 Found (or_introl0 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 Found a10:=(a1 V):((rel_s4 V) V)
% 206.43/206.70 Found (a1 V) as proof of ((rel_s4 V) V0)
% 206.43/206.70 Found (a1 V) as proof of ((rel_s4 V) V0)
% 206.43/206.70 Found (a1 V) as proof of ((rel_s4 V) V0)
% 206.43/206.70 Found (x1 (a1 V)) as proof of False
% 206.43/206.70 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 206.43/206.70 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 206.43/206.70 Found a10:=(a1 W):((rel_s4 W) W)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found a10:=(a1 W):((rel_s4 W) W)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found (a1 W) as proof of ((rel_s4 W) V1)
% 206.43/206.70 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V00)))
% 206.43/206.70 Found (or_introl1 (p V00)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 S) V2)->False)->((or (((rel_s4 S) V2)->False)) (p V0)))
% 206.43/206.70 Found (or_introl1 (p V0)) as proof of ((((rel_s4 S) V2)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 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)))
% 206.43/206.70 Found a10:=(a1 S):((rel_s4 S) S)
% 206.43/206.70 Found (a1 S) as proof of ((rel_s4 S) V1)
% 206.43/206.70 Found (a1 S) as proof of ((rel_s4 S) V1)
% 206.43/206.70 Found (a1 S) as proof of ((rel_s4 S) V1)
% 206.43/206.70 Found (x5 (a1 S)) as proof of False
% 206.43/206.70 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of False
% 206.43/206.70 Found (fun (x5:(((rel_s4 S) V1)->False))=> (x5 (a1 S))) as proof of ((((rel_s4 S) V1)->False)->False)
% 206.43/206.70 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 206.43/206.70 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 206.43/206.70 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))
% 206.43/206.70 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))
% 206.43/206.70 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)))
% 213.60/213.86 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)
% 213.60/213.86 Found x3:(((rel_s4 W) V0)->False)
% 213.60/213.86 Instantiate: V0:=V00:fofType
% 213.60/213.86 Found x3 as proof of (((rel_s4 V) V00)->False)
% 213.60/213.86 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found x4:((rel_s4 V) V0)
% 213.60/213.86 Instantiate: V2:=V0:fofType
% 213.60/213.86 Found x4 as proof of ((rel_s4 W) V2)
% 213.60/213.86 Found (x6 x4) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 213.60/213.86 Found x4:((rel_s4 V) V0)
% 213.60/213.86 Instantiate: V2:=V0:fofType
% 213.60/213.86 Found x4 as proof of ((rel_s4 W) V2)
% 213.60/213.86 Found (x6 x4) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V0)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found x3:(((rel_s4 W) V0)->False)
% 213.60/213.86 Instantiate: V0:=V00:fofType;V:=W:fofType
% 213.60/213.86 Found x3 as proof of (((rel_s4 V) V00)->False)
% 213.60/213.86 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found False_rect00:=(False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))):((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 Found (False_rect0 ((or (((rel_s4 V) V00)->False)) (p V00))) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 213.60/213.86 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))
% 213.60/213.86 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))
% 213.60/213.86 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)))
% 213.60/213.86 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)
% 213.60/213.86 Found x4:((rel_s4 V) V0)
% 213.60/213.86 Instantiate: V2:=V0:fofType
% 213.60/213.86 Found x4 as proof of ((rel_s4 W) V2)
% 213.60/213.86 Found (x6 x4) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 213.60/213.86 Found x4:((rel_s4 V) V0)
% 213.60/213.86 Instantiate: V2:=V0:fofType;V:=S:fofType
% 213.60/213.86 Found x4 as proof of ((rel_s4 S) V2)
% 213.60/213.86 Found (x6 x4) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 213.60/213.86 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 213.60/213.86 Found a10:=(a1 W):((rel_s4 W) W)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 213.60/213.86 Found (a1 W) as proof of ((rel_s4 W) V1)
% 223.01/223.26 Found a10:=(a1 W):((rel_s4 W) W)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V1)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V1)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V1)
% 223.01/223.26 Found x3:(((rel_s4 W) V0)->False)
% 223.01/223.26 Instantiate: V0:=V00:fofType
% 223.01/223.26 Found x3 as proof of (((rel_s4 V) V00)->False)
% 223.01/223.26 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 223.01/223.26 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 223.01/223.26 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 223.01/223.26 Found a10:=(a1 V):((rel_s4 V) V)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (x1 (a1 V)) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 223.01/223.26 Found a10:=(a1 V):((rel_s4 V) V)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (x1 (a1 V)) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 223.01/223.26 Found a10:=(a1 V):((rel_s4 V) V)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (x1 (a1 V)) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 223.01/223.26 Found a10:=(a1 V):((rel_s4 V) V)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (a1 V) as proof of ((rel_s4 V) V0)
% 223.01/223.26 Found (x1 (a1 V)) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 223.01/223.26 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 223.01/223.26 Found a10:=(a1 W):((rel_s4 W) W)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 223.01/223.26 Found (a1 W) as proof of ((rel_s4 W) V0)
% 223.01/223.26 Found x4:((rel_s4 V) V0)
% 223.01/223.26 Instantiate: V2:=V0:fofType
% 223.01/223.26 Found x4 as proof of ((rel_s4 S) V2)
% 223.01/223.26 Found (x6 x4) as proof of False
% 223.01/223.26 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 223.01/223.26 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 223.01/223.26 Found x4:((rel_s4 V) V0)
% 223.01/223.26 Instantiate: V2:=V0:fofType
% 223.01/223.26 Found x4 as proof of ((rel_s4 S) V2)
% 223.01/223.26 Found (x6 x4) as proof of False
% 223.01/223.26 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 223.01/223.26 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 223.01/223.26 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)))
% 223.01/223.26 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)))
% 223.01/223.26 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)))
% 223.01/223.26 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)))
% 223.01/223.26 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)))
% 223.01/223.26 Found or_introl20:=(or_introl2 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 223.01/223.26 Found (or_introl2 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 223.01/223.26 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 223.01/223.26 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found or_introl00:=(or_introl0 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found (or_introl0 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 231.10/231.39 Found x4:((rel_s4 V) V0)
% 231.10/231.39 Instantiate: V2:=V0:fofType;V:=W:fofType
% 231.10/231.39 Found x4 as proof of ((rel_s4 W) V2)
% 231.10/231.39 Found (x6 x4) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 231.10/231.39 Found a10:=(a1 W):((rel_s4 W) W)
% 231.10/231.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 231.10/231.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 231.10/231.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 231.10/231.39 Found or_introl00:=(or_introl0 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 231.10/231.39 Found (or_introl0 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 231.10/231.39 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)))
% 231.10/231.39 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)))
% 231.10/231.39 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)))
% 231.10/231.39 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)))
% 231.10/231.39 Found x4:((rel_s4 V) V0)
% 231.10/231.39 Instantiate: V2:=V0:fofType
% 231.10/231.39 Found x4 as proof of ((rel_s4 S) V2)
% 231.10/231.39 Found (x6 x4) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 S) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 S) V2)->False)->False)
% 231.10/231.39 Found a10:=(a1 V):((rel_s4 V) V)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (x1 (a1 V)) as proof of False
% 231.10/231.39 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 231.10/231.39 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 231.10/231.39 Found a10:=(a1 V):((rel_s4 V) V)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (a1 V) as proof of ((rel_s4 V) V0)
% 231.10/231.39 Found (x1 (a1 V)) as proof of False
% 231.10/231.39 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of False
% 231.10/231.39 Found (fun (x1:(((rel_s4 V) V0)->False))=> (x1 (a1 V))) as proof of ((((rel_s4 V) V0)->False)->False)
% 231.10/231.39 Found x4:((rel_s4 V) V0)
% 231.10/231.39 Instantiate: V2:=V0:fofType
% 231.10/231.39 Found x4 as proof of ((rel_s4 W) V2)
% 231.10/231.39 Found (x6 x4) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 231.10/231.39 Found x4:((rel_s4 V) V0)
% 231.10/231.39 Instantiate: V2:=V0:fofType
% 231.10/231.39 Found x4 as proof of ((rel_s4 W) V2)
% 231.10/231.39 Found (x6 x4) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 231.10/231.39 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 231.10/231.39 Found or_introl00:=(or_introl0 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 231.10/231.39 Found (or_introl0 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 Found a10:=(a1 S):((rel_s4 S) S)
% 237.16/237.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 237.16/237.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 237.16/237.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 237.16/237.45 Found a10:=(a1 W):((rel_s4 W) W)
% 237.16/237.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 237.16/237.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 237.16/237.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 237.16/237.45 Found a10:=(a1 V):((rel_s4 V) V)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (x2 (a1 V)) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 237.16/237.45 Found a10:=(a1 V):((rel_s4 V) V)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found a10:=(a1 V):((rel_s4 V) V)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (x2 (a1 V)) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 237.16/237.45 Found a10:=(a1 V):((rel_s4 V) V)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (a1 V) as proof of ((rel_s4 V) V00)
% 237.16/237.45 Found (x2 (a1 V)) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 237.16/237.45 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 Found x4:((rel_s4 V) V0)
% 237.16/237.45 Instantiate: V2:=V0:fofType
% 237.16/237.45 Found x4 as proof of ((rel_s4 W) V2)
% 237.16/237.45 Found (x6 x4) as proof of False
% 237.16/237.45 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of False
% 237.16/237.45 Found (fun (x6:(((rel_s4 W) V2)->False))=> (x6 x4)) as proof of ((((rel_s4 W) V2)->False)->False)
% 237.16/237.45 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 S) V3)->False)->((or (((rel_s4 S) V3)->False)) (p V2)))
% 237.16/237.45 Found (or_introl1 (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 237.16/237.45 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)))
% 244.71/245.01 Found a10:=(a1 S):((rel_s4 S) S)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found or_introl20:=(or_introl2 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found (or_introl2 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found or_introl00:=(or_introl0 ((mnot ((mbox rel_s4) p)) V1)):((((rel_s4 V) V00)->False)->((or (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found (or_introl0 ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found ((or_introl (((rel_s4 V) V00)->False)) ((mnot ((mbox rel_s4) p)) V1)) as proof of ((((rel_s4 V) V00)->False)->((or (((rel_s4 V0) V1)->False)) ((mnot ((mbox rel_s4) p)) V1)))
% 244.71/245.01 Found a10:=(a1 W):((rel_s4 W) W)
% 244.71/245.01 Found (a1 W) as proof of ((rel_s4 W) V1)
% 244.71/245.01 Found (a1 W) as proof of ((rel_s4 W) V1)
% 244.71/245.01 Found (a1 W) as proof of ((rel_s4 W) V1)
% 244.71/245.01 Found a10:=(a1 V):((rel_s4 V) V)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (x2 (a1 V)) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 244.71/245.01 Found a10:=(a1 S):((rel_s4 S) S)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found (a1 S) as proof of ((rel_s4 S) V0)
% 244.71/245.01 Found a10:=(a1 V):((rel_s4 V) V)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found a10:=(a1 V):((rel_s4 V) V)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (x2 (a1 V)) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 244.71/245.01 Found a10:=(a1 V):((rel_s4 V) V)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (a1 V) as proof of ((rel_s4 V) V00)
% 244.71/245.01 Found (x2 (a1 V)) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of False
% 244.71/245.01 Found (fun (x2:(((rel_s4 V) V00)->False))=> (x2 (a1 V))) as proof of ((((rel_s4 V) V00)->False)->False)
% 244.71/245.01 Found or_introl10:=(or_introl1 (p V2)):((((rel_s4 S) V3)->False)->((or (((rel_s4 S) V3)->False)) (p V2)))
% 244.71/245.01 Found (or_introl1 (p V2)) as proof of ((((rel_s4 S) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 Found x3:(((rel_s4 S) V0)->False)
% 251.78/252.08 Instantiate: V0:=V00:fofType;V:=S:fofType
% 251.78/252.08 Found x3 as proof of (((rel_s4 V) V00)->False)
% 251.78/252.08 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 251.78/252.08 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 251.78/252.08 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 251.78/252.08 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))
% 251.78/252.08 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)))
% 251.78/252.08 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))
% 251.78/252.08 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))
% 251.78/252.08 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))
% 251.78/252.08 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))
% 251.78/252.08 Found a10:=(a1 W):((rel_s4 W) W)
% 251.78/252.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 251.78/252.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 251.78/252.08 Found (a1 W) as proof of ((rel_s4 W) V1)
% 251.78/252.08 Found a10:=(a1 S):((rel_s4 S) S)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V1)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V1)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V1)
% 251.78/252.08 Found a10:=(a1 S):((rel_s4 S) S)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 251.78/252.08 Found (a1 S) as proof of ((rel_s4 S) V0)
% 251.78/252.08 Found or_introl20:=(or_introl2 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 251.78/252.08 Found (or_introl2 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 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)))
% 251.78/252.08 Found x3:(((rel_s4 S) V0)->False)
% 251.78/252.08 Instantiate: V0:=V00:fofType
% 251.78/252.08 Found x3 as proof of (((rel_s4 V) V00)->False)
% 251.78/252.08 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 251.78/252.08 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 253.70/253.98 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 253.70/253.98 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))
% 253.70/253.98 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)))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 253.70/253.98 Found a10:=(a1 W):((rel_s4 W) W)
% 253.70/253.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 253.70/253.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 253.70/253.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 253.70/253.98 Found a10:=(a1 S):((rel_s4 S) S)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found a10:=(a1 S):((rel_s4 S) S)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V0)
% 253.70/253.98 Found a10:=(a1 S):((rel_s4 S) S)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 253.70/253.98 Found (a1 S) as proof of ((rel_s4 S) V1)
% 253.70/253.98 Found x3:(((rel_s4 W) V0)->False)
% 253.70/253.98 Instantiate: V0:=V00:fofType;V:=W:fofType
% 253.70/253.98 Found x3 as proof of (((rel_s4 V) V00)->False)
% 253.70/253.98 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 253.70/253.98 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 253.70/253.98 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 253.70/253.98 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))
% 253.70/253.98 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)))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 253.70/253.98 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))
% 260.11/260.39 Found x2:((rel_s4 V) V0)
% 260.11/260.39 Instantiate: V1:=V0:fofType;V:=S:fofType
% 260.11/260.39 Found x2 as proof of ((rel_s4 S) V1)
% 260.11/260.39 Found (x4 x2) as proof of False
% 260.11/260.39 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 260.11/260.39 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 260.11/260.39 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 260.11/260.39 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 260.11/260.39 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)))
% 260.11/260.39 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)))
% 260.11/260.39 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)))
% 260.11/260.39 Found a10:=(a1 V):((rel_s4 V) V)
% 260.11/260.39 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.11/260.39 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.11/260.39 Found (a1 V) as proof of ((rel_s4 V) V00)
% 260.11/260.39 Found or_introl20:=(or_introl2 (p V2)):((((rel_s4 W) V3)->False)->((or (((rel_s4 W) V3)->False)) (p V2)))
% 260.11/260.39 Found (or_introl2 (p V2)) as proof of ((((rel_s4 W) V3)->False)->((or (((rel_s4 V1) V2)->False)) (p V2)))
% 260.11/260.39 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)))
% 260.11/260.39 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)))
% 260.11/260.39 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)))
% 260.11/260.39 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)))
% 260.11/260.39 Found a10:=(a1 S):((rel_s4 S) S)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found a10:=(a1 S):((rel_s4 S) S)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found (a1 S) as proof of ((rel_s4 S) V0)
% 260.11/260.39 Found x3:(((rel_s4 S) V0)->False)
% 260.11/260.39 Instantiate: V0:=V00:fofType;V:=S:fofType
% 260.11/260.39 Found x3 as proof of (((rel_s4 V) V00)->False)
% 260.11/260.39 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 260.11/260.39 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 260.11/260.39 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 260.11/260.39 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 260.11/260.39 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))
% 260.11/260.39 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))
% 260.11/260.39 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))
% 260.11/260.39 Found a10:=(a1 W):((rel_s4 W) W)
% 260.11/260.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 260.11/260.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 260.11/260.39 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 260.11/260.39 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of (((mnot (mbox_s4 p)) V1)->((rel_s4 W) V0))
% 260.11/260.39 Found a10:=(a1 W):((rel_s4 W) W)
% 260.11/260.39 Found (a1 W) as proof of ((rel_s4 W) V0)
% 260.11/260.39 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 260.11/260.39 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((((rel_s4 W) V1)->False)->((rel_s4 W) V0))
% 260.11/260.39 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)
% 264.90/265.16 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)
% 264.90/265.16 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)
% 264.90/265.16 Found x3:(((rel_s4 W) V0)->False)
% 264.90/265.16 Instantiate: V0:=V00:fofType
% 264.90/265.16 Found x3 as proof of (((rel_s4 V) V00)->False)
% 264.90/265.16 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 264.90/265.16 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 264.90/265.16 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 264.90/265.16 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))
% 264.90/265.16 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)))
% 264.90/265.16 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))
% 264.90/265.16 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))
% 264.90/265.16 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))
% 264.90/265.16 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))
% 264.90/265.16 Found x2:((rel_s4 V) V0)
% 264.90/265.16 Instantiate: V1:=V0:fofType
% 264.90/265.16 Found x2 as proof of ((rel_s4 S) V1)
% 264.90/265.16 Found (x4 x2) as proof of False
% 264.90/265.16 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of False
% 264.90/265.16 Found (fun (x4:(((rel_s4 S) V1)->False))=> (x4 x2)) as proof of ((((rel_s4 S) V1)->False)->False)
% 264.90/265.16 Found a10:=(a1 S):((rel_s4 S) S)
% 264.90/265.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 264.90/265.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 264.90/265.16 Found (a1 S) as proof of ((rel_s4 S) V0)
% 264.90/265.16 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 264.90/265.16 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 264.90/265.16 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)))
% 264.90/265.16 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)))
% 264.90/265.16 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)))
% 264.90/265.16 Found a10:=(a1 V):((rel_s4 V) V)
% 264.90/265.16 Found (a1 V) as proof of ((rel_s4 V) V00)
% 264.90/265.16 Found (a1 V) as proof of ((rel_s4 V) V00)
% 264.90/265.16 Found (a1 V) as proof of ((rel_s4 V) V00)
% 264.90/265.16 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 264.90/265.16 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 264.90/265.16 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)))
% 264.90/265.16 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)))
% 274.99/275.25 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)))
% 274.99/275.25 Found x3:(((rel_s4 S) V0)->False)
% 274.99/275.25 Instantiate: V0:=V00:fofType
% 274.99/275.25 Found x3 as proof of (((rel_s4 V) V00)->False)
% 274.99/275.25 Found (or_intror00 x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 274.99/275.25 Found ((or_intror0 (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 274.99/275.25 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 274.99/275.25 Found (((or_intror (p V00)) (((rel_s4 V) V00)->False)) x3) as proof of ((or (p V00)) (((rel_s4 V) V00)->False))
% 274.99/275.25 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))
% 274.99/275.25 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))
% 274.99/275.25 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))
% 274.99/275.25 Found a10:=(a1 W):((rel_s4 W) W)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (fun (x5:((mnot (mbox_s4 p)) V1))=> (a1 W)) as proof of (((mnot (mbox_s4 p)) V1)->((rel_s4 W) V0))
% 274.99/275.25 Found a10:=(a1 W):((rel_s4 W) W)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (fun (x5:(((rel_s4 W) V1)->False))=> (a1 W)) as proof of ((((rel_s4 W) V1)->False)->((rel_s4 W) V0))
% 274.99/275.25 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)
% 274.99/275.25 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)
% 274.99/275.25 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)
% 274.99/275.25 Found a10:=(a1 S):((rel_s4 S) S)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 274.99/275.25 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 274.99/275.25 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)))
% 274.99/275.25 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)))
% 274.99/275.25 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)))
% 274.99/275.25 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)))
% 274.99/275.25 Found a10:=(a1 W):((rel_s4 W) W)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (a1 W) as proof of ((rel_s4 W) V0)
% 274.99/275.25 Found (x3 (a1 W)) as proof of False
% 274.99/275.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 274.99/275.25 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 274.99/275.25 Found a10:=(a1 S):((rel_s4 S) S)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found (a1 S) as proof of ((rel_s4 S) V0)
% 274.99/275.25 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 274.99/275.25 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 274.99/275.25 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 278.08/278.37 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 278.08/278.37 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 278.08/278.37 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 Found a10:=(a1 W):((rel_s4 W) W)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found (x3 (a1 W)) as proof of False
% 278.08/278.37 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 278.08/278.37 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 278.08/278.37 Found a10:=(a1 W):((rel_s4 W) W)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found (a1 W) as proof of ((rel_s4 W) V0)
% 278.08/278.37 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 278.08/278.37 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 Found or_intror10:=(or_intror1 (((rel_s4 W) V1)->False)):((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 W) V1)->False)))
% 278.08/278.37 Found (or_intror1 (((rel_s4 W) V1)->False)) as proof of ((((rel_s4 W) V1)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 278.08/278.37 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)))
% 285.49/285.78 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)))
% 285.49/285.78 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 285.49/285.78 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 Found a10:=(a1 W):((rel_s4 W) W)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found a10:=(a1 W):((rel_s4 W) W)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found a10:=(a1 W):((rel_s4 W) W)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 285.49/285.78 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 Found a10:=(a1 S):((rel_s4 S) S)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V0)
% 285.49/285.78 Found or_introl10:=(or_introl1 (p V00)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V00)))
% 285.49/285.78 Found (or_introl1 (p V00)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V00)->False)) (p V00)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 285.49/285.78 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 285.49/285.78 Found a10:=(a1 W):((rel_s4 W) W)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found (a1 W) as proof of ((rel_s4 W) V0)
% 285.49/285.78 Found a10:=(a1 S):((rel_s4 S) S)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found a10:=(a1 S):((rel_s4 S) S)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found (a1 S) as proof of ((rel_s4 S) V1)
% 285.49/285.78 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 285.49/285.78 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 285.49/285.78 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)))
% 285.49/285.78 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)))
% 290.99/291.32 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)))
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V0)
% 290.99/291.32 Found a10:=(a1 S):((rel_s4 S) S)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V0)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V0)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V0)
% 290.99/291.32 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 290.99/291.32 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V2)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V2)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V2)
% 290.99/291.32 Found a10:=(a1 S):((rel_s4 S) S)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found a10:=(a1 S):((rel_s4 S) S)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found a10:=(a1 S):((rel_s4 S) S)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found a10:=(a1 S):((rel_s4 S) S)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found (a1 S) as proof of ((rel_s4 S) V1)
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found a10:=(a1 W):((rel_s4 W) W)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found (a1 W) as proof of ((rel_s4 W) V1)
% 290.99/291.32 Found or_introl10:=(or_introl1 (p V0)):((((rel_s4 W) V1)->False)->((or (((rel_s4 W) V1)->False)) (p V0)))
% 290.99/291.32 Found (or_introl1 (p V0)) as proof of ((((rel_s4 W) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 Found or_intror00:=(or_intror0 (((rel_s4 S) V2)->False)):((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 S) V2)->False)))
% 290.99/291.32 Found (or_intror0 (((rel_s4 S) V2)->False)) as proof of ((((rel_s4 S) V2)->False)->((or (p V0)) (((rel_s4 V) V0)->False)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 290.99/291.32 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)))
% 295.14/295.43 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)))
% 295.14/295.43 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 295.14/295.43 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 295.14/295.43 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)))
% 295.14/295.43 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)))
% 295.14/295.43 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)))
% 295.14/295.43 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)))
% 295.14/295.43 Found a10:=(a1 W):((rel_s4 W) W)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found a10:=(a1 S):((rel_s4 S) S)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found (x3 (a1 S)) as proof of False
% 295.14/295.43 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 295.14/295.43 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 295.14/295.43 Found a10:=(a1 S):((rel_s4 S) S)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found (a1 S) as proof of ((rel_s4 S) V0)
% 295.14/295.43 Found or_introl00:=(or_introl0 (p V0)):((((rel_s4 S) V1)->False)->((or (((rel_s4 S) V1)->False)) (p V0)))
% 295.14/295.43 Found (or_introl0 (p V0)) as proof of ((((rel_s4 S) V1)->False)->((or (((rel_s4 V) V0)->False)) (p V0)))
% 295.14/295.43 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)))
% 295.14/295.43 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)))
% 295.14/295.43 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)))
% 295.14/295.43 Found x3:(((rel_s4 W) V0)->False)
% 295.14/295.43 Instantiate: V0:=V00:fofType;V:=W:fofType
% 295.14/295.43 Found x3 as proof of (((rel_s4 V) V00)->False)
% 295.14/295.43 Found (or_introl10 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found ((or_introl1 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found a10:=(a1 W):((rel_s4 W) W)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found a10:=(a1 W):((rel_s4 W) W)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V2)
% 295.14/295.43 Found x3:(((rel_s4 W) V0)->False)
% 295.14/295.43 Instantiate: V0:=V00:fofType;V:=W:fofType
% 295.14/295.43 Found x3 as proof of (((rel_s4 V) V00)->False)
% 295.14/295.43 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found (((or_introl (((rel_s4 V) V00)->False)) (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found a10:=(a1 W):((rel_s4 W) W)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found a10:=(a1 W):((rel_s4 W) W)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found (a1 W) as proof of ((rel_s4 W) V0)
% 295.14/295.43 Found x3:(((rel_s4 S) V0)->False)
% 295.14/295.43 Instantiate: V0:=V00:fofType;V:=S:fofType
% 295.14/295.43 Found x3 as proof of (((rel_s4 V) V00)->False)
% 295.14/295.43 Found (or_introl00 x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found ((or_introl0 (p V00)) x3) as proof of ((or (((rel_s4 V) V00)->False)) (p V00))
% 295.14/295.43 Found (((or_introl (
%------------------------------------------------------------------------------