TSTP Solution File: SYO569^7 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO569^7 : TPTP v7.5.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:52:07 EDT 2022
% Result : Timeout 292.77s 293.05s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO569^7 : TPTP v7.5.0. Released v5.5.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % RAMPerCPU : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % DateTime : Sun Mar 13 21:31:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.34 Python 2.7.5
% 0.45/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.45/0.62 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^0.ax, trying next directory
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac900441b48>, <kernel.Type object at 0x2ac900441950>) of role type named mu_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring mu:Type
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac900441b00>, <kernel.DependentProduct object at 0x2ac900441b48>) of role type named qmltpeq_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring qmltpeq:(mu->(mu->(fofType->Prop)))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac9004415f0>, <kernel.DependentProduct object at 0x2ac900441320>) of role type named meq_prop_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.45/0.62 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
% 0.45/0.62 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))))
% 0.45/0.62 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac900441638>, <kernel.DependentProduct object at 0x2ac900441560>) of role type named mnot_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.45/0.62 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.45/0.62 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.45/0.62 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac900441560>, <kernel.DependentProduct object at 0x2ac900441368>) of role type named mor_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.45/0.62 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
% 0.45/0.62 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))))
% 0.45/0.62 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac9003f9bd8>, <kernel.DependentProduct object at 0x2ac900441050>) of role type named mbox_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.45/0.62 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
% 0.45/0.62 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)))))
% 0.45/0.62 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.45/0.62 FOF formula (<kernel.Constant object at 0x2ac900441050>, <kernel.DependentProduct object at 0x2ac9004412d8>) of role type named mforall_prop_type
% 0.45/0.62 Using role type
% 0.45/0.62 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.45/0.62 FOF formula (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))) of role definition named mforall_prop
% 0.45/0.62 A new definition: (((eq (((fofType->Prop)->(fofType->Prop))->(fofType->Prop))) mforall_prop) (fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))))
% 0.45/0.62 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ac900441050>, <kernel.DependentProduct object at 0x2ac900441128>) of role type named mtrue_type
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring mtrue:(fofType->Prop)
% 0.45/0.63 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.45/0.63 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.45/0.63 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ac900441128>, <kernel.DependentProduct object at 0x2ac9004414d0>) of role type named mfalse_type
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring mfalse:(fofType->Prop)
% 0.45/0.63 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.45/0.63 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.45/0.63 Defined: mfalse:=(mnot mtrue)
% 0.45/0.63 FOF formula (<kernel.Constant object at 0x2ac9004417e8>, <kernel.DependentProduct object at 0x2ac9004410e0>) of role type named mand_type
% 0.45/0.63 Using role type
% 0.45/0.63 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 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
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.47/0.63 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ac9004410e0>, <kernel.DependentProduct object at 0x2ac9004413f8>) of role type named mimplies_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 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
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.47/0.63 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ac9004413f8>, <kernel.DependentProduct object at 0x2ac900441518>) of role type named mimplied_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 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
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.47/0.63 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ac9004417e8>, <kernel.DependentProduct object at 0x2ac900441128>) of role type named mequiv_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 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
% 0.47/0.63 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))))
% 0.47/0.63 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.47/0.63 FOF formula (<kernel.Constant object at 0x2ac900441518>, <kernel.DependentProduct object at 0xef7cb0>) of role type named mxor_type
% 0.47/0.63 Using role type
% 0.47/0.63 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.63 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
% 0.47/0.63 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.47/0.64 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0x2ac900441518>, <kernel.DependentProduct object at 0xef7998>) of role type named mdia_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.47/0.64 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
% 0.47/0.64 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)))))
% 0.47/0.64 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xef7b48>, <kernel.DependentProduct object at 0xef79e0>) of role type named exists_in_world_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring exists_in_world:(mu->(fofType->Prop))
% 0.47/0.64 FOF formula (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))) of role axiom named nonempty_ax
% 0.47/0.64 A new axiom: (forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xef7b48>, <kernel.DependentProduct object at 0xf1d050>) of role type named mforall_ind_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.47/0.64 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))) of role definition named mforall_ind
% 0.47/0.64 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))))
% 0.47/0.64 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xf1d518>, <kernel.DependentProduct object at 0xf1d638>) of role type named mexists_ind_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.47/0.64 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
% 0.47/0.64 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)))))))
% 0.47/0.64 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xf1d908>, <kernel.DependentProduct object at 0x2ac90043f1b8>) of role type named mexists_prop_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.47/0.64 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
% 0.47/0.64 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)))))))
% 0.47/0.64 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.47/0.64 FOF formula (<kernel.Constant object at 0xf1dcb0>, <kernel.DependentProduct object at 0x2ac90043f368>) of role type named mreflexive_type
% 0.47/0.64 Using role type
% 0.47/0.64 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.47/0.64 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.47/0.64 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.47/0.65 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xf1dcb0>, <kernel.DependentProduct object at 0x2ac90043f440>) of role type named msymmetric_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))) of role definition named msymmetric
% 0.47/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) msymmetric) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))))
% 0.47/0.65 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0xf1dcb0>, <kernel.DependentProduct object at 0x2ac90043f368>) of role type named mserial_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))) of role definition named mserial
% 0.47/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mserial) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))))
% 0.47/0.65 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2ac90043f368>, <kernel.DependentProduct object at 0x2ac90043f2d8>) of role type named mtransitive_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))) of role definition named mtransitive
% 0.47/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mtransitive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))))
% 0.47/0.65 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2ac90043f2d8>, <kernel.DependentProduct object at 0x2ac90043f170>) of role type named meuclidean_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))) of role definition named meuclidean
% 0.47/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) meuclidean) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))))
% 0.47/0.65 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2ac90043f170>, <kernel.DependentProduct object at 0x2ac90043f3b0>) of role type named mpartially_functional_type
% 0.47/0.65 Using role type
% 0.47/0.65 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.65 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))) of role definition named mpartially_functional
% 0.47/0.65 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mpartially_functional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))))
% 0.47/0.65 Defined: mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U))))
% 0.47/0.65 FOF formula (<kernel.Constant object at 0x2ac90043f3b0>, <kernel.DependentProduct object at 0x2ac90043f908>) of role type named mfunctional_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.47/0.66 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))) of role definition named mfunctional
% 0.47/0.66 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mfunctional) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))))
% 0.47/0.66 Defined: mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U))))))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0x2ac90043f908>, <kernel.DependentProduct object at 0x2ac90043f998>) of role type named mweakly_dense_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.47/0.66 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))) of role definition named mweakly_dense
% 0.47/0.66 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_dense) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))))
% 0.47/0.66 Defined: mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T))))))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0x2ac90043f998>, <kernel.DependentProduct object at 0x2ac90043f170>) of role type named mweakly_connected_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.47/0.66 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))) of role definition named mweakly_connected
% 0.47/0.66 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_connected) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))))
% 0.47/0.66 Defined: mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T)))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0x2ac90043f170>, <kernel.DependentProduct object at 0x2ac90043fd88>) of role type named mweakly_directed_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.47/0.66 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))) of role definition named mweakly_directed
% 0.47/0.66 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mweakly_directed) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))))
% 0.47/0.66 Defined: mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V)))))))
% 0.47/0.66 FOF formula (<kernel.Constant object at 0x2ac90043f128>, <kernel.DependentProduct object at 0x2ac90043fc20>) of role type named mvalid_type
% 0.47/0.66 Using role type
% 0.47/0.66 Declaring mvalid:((fofType->Prop)->Prop)
% 0.47/0.66 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.47/0.66 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.47/0.67 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac90043f170>, <kernel.DependentProduct object at 0x2ac90043f8c0>) of role type named msatisfiable_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.47/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.47/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.47/0.67 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac90043fc20>, <kernel.DependentProduct object at 0x2ac90043f9e0>) of role type named mcountersatisfiable_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.47/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.47/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.47/0.67 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac90043f170>, <kernel.DependentProduct object at 0x2ac90043fd40>) of role type named minvalid_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring minvalid:((fofType->Prop)->Prop)
% 0.47/0.67 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.47/0.67 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.47/0.67 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.47/0.67 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^5.ax, trying next directory
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac900441ea8>, <kernel.DependentProduct object at 0x2ac900441cb0>) of role type named rel_s4_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring rel_s4:(fofType->(fofType->Prop))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac900441dd0>, <kernel.DependentProduct object at 0x2ac900441e18>) of role type named mbox_s4_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring mbox_s4:((fofType->Prop)->(fofType->Prop))
% 0.47/0.67 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))) of role definition named mbox_s4
% 0.47/0.67 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_s4) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))))
% 0.47/0.67 Defined: mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V))))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0x2ac900441e18>, <kernel.DependentProduct object at 0x2ac900441a28>) of role type named mdia_s4_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring mdia_s4:((fofType->Prop)->(fofType->Prop))
% 0.47/0.67 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))) of role definition named mdia_s4
% 0.47/0.67 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_s4) (fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))))
% 0.47/0.67 Defined: mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi))))
% 0.47/0.67 FOF formula (mreflexive rel_s4) of role axiom named a1
% 0.47/0.67 A new axiom: (mreflexive rel_s4)
% 0.47/0.67 FOF formula (mtransitive rel_s4) of role axiom named a2
% 0.47/0.67 A new axiom: (mtransitive rel_s4)
% 0.47/0.67 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL015^1.ax, trying next directory
% 0.47/0.67 FOF formula (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))) of role axiom named cumulative_ax
% 0.47/0.67 A new axiom: (forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W)))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xf1a3f8>, <kernel.DependentProduct object at 0x2ac900418e60>) of role type named g_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring g:(mu->(fofType->Prop))
% 0.47/0.67 FOF formula (<kernel.Constant object at 0xf1a290>, <kernel.DependentProduct object at 0x2ac900418c68>) of role type named f_type
% 0.47/0.67 Using role type
% 0.47/0.67 Declaring f:(mu->(fofType->Prop))
% 0.47/0.67 FOF formula (mvalid ((mimplies ((mand (mforall_ind (fun (X:mu)=> (mbox_s4 (mbox_s4 (f X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> (g X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> ((mand (f X)) (g X))))))) of role conjecture named con
% 0.47/0.67 Conjecture to prove = (mvalid ((mimplies ((mand (mforall_ind (fun (X:mu)=> (mbox_s4 (mbox_s4 (f X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> (g X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> ((mand (f X)) (g X))))))):Prop
% 0.47/0.67 Parameter mu_DUMMY:mu.
% 0.47/0.67 Parameter fofType_DUMMY:fofType.
% 0.47/0.67 We need to prove ['(mvalid ((mimplies ((mand (mforall_ind (fun (X:mu)=> (mbox_s4 (mbox_s4 (f X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> (g X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))))))']
% 0.47/0.67 Parameter mu:Type.
% 0.47/0.67 Parameter fofType:Type.
% 0.47/0.67 Parameter qmltpeq:(mu->(mu->(fofType->Prop))).
% 0.47/0.67 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.47/0.67 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.67 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.47/0.67 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.47/0.67 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.47/0.67 Parameter exists_in_world:(mu->(fofType->Prop)).
% 0.47/0.67 Axiom nonempty_ax:(forall (V:fofType), ((ex mu) (fun (X:mu)=> ((exists_in_world X) V)))).
% 0.47/0.67 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), (((exists_in_world X) W)->((Phi X) W)))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.67 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.67 Definition mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P)))))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.47/0.67 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.67 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.47/0.67 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 4.82/4.99 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).
% 4.82/4.99 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).
% 4.82/4.99 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).
% 4.82/4.99 Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% 4.82/4.99 Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% 4.82/4.99 Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% 4.82/4.99 Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% 4.82/4.99 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 4.82/4.99 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 4.82/4.99 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 4.82/4.99 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 4.82/4.99 Parameter rel_s4:(fofType->(fofType->Prop)).
% 4.82/4.99 Definition mbox_s4:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_s4 W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 4.82/4.99 Definition mdia_s4:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_s4 (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 4.82/4.99 Axiom a1:(mreflexive rel_s4).
% 4.82/4.99 Axiom a2:(mtransitive rel_s4).
% 4.82/4.99 Axiom cumulative_ax:(forall (X:mu) (V:fofType) (W:fofType), (((and ((exists_in_world X) V)) ((rel_s4 V) W))->((exists_in_world X) W))).
% 4.82/4.99 Parameter g:(mu->(fofType->Prop)).
% 4.82/4.99 Parameter f:(mu->(fofType->Prop)).
% 4.82/4.99 Trying to prove (mvalid ((mimplies ((mand (mforall_ind (fun (X:mu)=> (mbox_s4 (mbox_s4 (f X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> (g X)))))) (mdia_s4 (mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))))))
% 4.82/4.99 Found a10:=(a1 W):((rel_s4 W) W)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (x1 (a1 W)) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 4.82/4.99 Found a10:=(a1 W):((rel_s4 W) W)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V)
% 4.82/4.99 Found (x1 (a1 W)) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 4.82/4.99 Found a10:=(a1 S):((rel_s4 S) S)
% 4.82/4.99 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.82/4.99 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.82/4.99 Found (a1 S) as proof of ((rel_s4 S) V)
% 4.82/4.99 Found (x1 (a1 S)) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 4.82/4.99 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 4.82/4.99 Found a10:=(a1 W):((rel_s4 W) W)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V0)
% 4.82/4.99 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x3 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x3 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 9.84/10.06 Found a10:=(a1 S):((rel_s4 S) S)
% 9.84/10.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 9.84/10.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 9.84/10.06 Found (a1 S) as proof of ((rel_s4 S) V)
% 9.84/10.06 Found (x1 (a1 S)) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x4 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x4 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x3 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (x1 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (x3 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 9.84/10.06 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V)
% 9.84/10.06 Found (x1 (a1 W)) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 9.84/10.06 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 9.84/10.06 Found a10:=(a1 W):((rel_s4 W) W)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 9.84/10.06 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x3 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x3 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (x1 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V)
% 17.02/17.20 Found (x1 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x4 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x4 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x3 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 17.02/17.20 Found a10:=(a1 W):((rel_s4 W) W)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (a1 W) as proof of ((rel_s4 W) V0)
% 17.02/17.20 Found (x3 (a1 W)) as proof of False
% 17.02/17.20 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 17.02/17.20 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 17.02/17.20 Found a10:=(a1 S):((rel_s4 S) S)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 17.02/17.20 Found (x3 (a1 S)) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 17.02/17.20 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 17.02/17.20 Found a10:=(a1 S):((rel_s4 S) S)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 17.02/17.20 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x3 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x4 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (x1 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x4 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x3 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x3 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V)
% 28.01/28.19 Found (x1 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 28.01/28.19 Found a10:=(a1 W):((rel_s4 W) W)
% 28.01/28.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.01/28.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.01/28.19 Found (a1 W) as proof of ((rel_s4 W) V0)
% 28.01/28.19 Found (x3 (a1 W)) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 28.01/28.19 Found a10:=(a1 S):((rel_s4 S) S)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (a1 S) as proof of ((rel_s4 S) V0)
% 28.01/28.19 Found (x3 (a1 S)) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 28.01/28.19 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x3 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x3 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 S):((rel_s4 S) S)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (x3 (a1 S)) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x3 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 S):((rel_s4 S) S)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V)
% 40.55/40.75 Found (x1 (a1 S)) as proof of False
% 40.55/40.75 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 40.55/40.75 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x4 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x4 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x4 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (a1 W) as proof of ((rel_s4 W) V0)
% 40.55/40.75 Found (x3 (a1 W)) as proof of False
% 40.55/40.75 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 40.55/40.75 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 40.55/40.75 Found a10:=(a1 S):((rel_s4 S) S)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (a1 S) as proof of ((rel_s4 S) V0)
% 40.55/40.75 Found (x4 (a1 S)) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 40.55/40.75 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 40.55/40.75 Found a10:=(a1 W):((rel_s4 W) W)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (x4 (a1 W)) as proof of False
% 43.06/43.27 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 43.06/43.27 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 43.06/43.27 Found a10:=(a1 W):((rel_s4 W) W)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (x3 (a1 W)) as proof of False
% 43.06/43.27 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 43.06/43.27 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 43.06/43.27 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 43.06/43.27 Found a10:=(a1 W):((rel_s4 W) W)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V)
% 43.06/43.27 Found (x1 (a1 W)) as proof of False
% 43.06/43.27 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 43.06/43.27 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 43.06/43.27 Found a10:=(a1 S):((rel_s4 S) S)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (x4 (a1 S)) as proof of False
% 43.06/43.27 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 43.06/43.27 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 43.06/43.27 Found a10:=(a1 W):((rel_s4 W) W)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (x3 (a1 W)) as proof of False
% 43.06/43.27 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 43.06/43.27 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 43.06/43.27 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 43.06/43.27 Found a10:=(a1 S):((rel_s4 S) S)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 43.06/43.27 Found (x3 (a1 S)) as proof of False
% 43.06/43.27 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 43.06/43.27 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 43.06/43.27 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 43.06/43.27 Found a10:=(a1 S):((rel_s4 S) S)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V)
% 43.06/43.27 Found (a1 S) as proof of ((rel_s4 S) V)
% 43.06/43.27 Found (x1 (a1 S)) as proof of False
% 43.06/43.27 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 43.06/43.27 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 43.06/43.27 Found a10:=(a1 W):((rel_s4 W) W)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (a1 W) as proof of ((rel_s4 W) V0)
% 43.06/43.27 Found (x3 (a1 W)) as proof of False
% 43.06/43.27 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 67.39/67.66 Found a10:=(a1 S):((rel_s4 S) S)
% 67.39/67.66 Found (a1 S) as proof of ((rel_s4 S) V0)
% 67.39/67.66 Found (a1 S) as proof of ((rel_s4 S) V0)
% 67.39/67.66 Found (a1 S) as proof of ((rel_s4 S) V0)
% 67.39/67.66 Found (x3 (a1 S)) as proof of False
% 67.39/67.66 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 67.39/67.66 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x4 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x4 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x3 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x3 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x3 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x3 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V)
% 67.39/67.66 Found (x1 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of False
% 67.39/67.66 Found (fun (x1:(((rel_s4 W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_s4 W) V)->False)->False)
% 67.39/67.66 Found a10:=(a1 W):((rel_s4 W) W)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (a1 W) as proof of ((rel_s4 W) V0)
% 67.39/67.66 Found (x4 (a1 W)) as proof of False
% 67.39/67.66 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x4 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x4 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x3 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (x5 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x4 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x3 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V0)
% 78.91/79.14 Found (x3 (a1 W)) as proof of False
% 78.91/79.14 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 78.91/79.14 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 78.91/79.14 Found a10:=(a1 W):((rel_s4 W) W)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (a1 W) as proof of ((rel_s4 W) V1)
% 78.91/79.14 Found (x5 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x5 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (x3 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 110.76/110.98 Found (fun (x3:(((rel_s4 W) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x5 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (x4 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V0)
% 110.76/110.98 Found (x4 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x4:(((rel_s4 W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x6 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x6 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x6 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x6 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 110.76/110.98 Found a10:=(a1 W):((rel_s4 W) W)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (a1 W) as proof of ((rel_s4 W) V1)
% 110.76/110.98 Found (x6 (a1 W)) as proof of False
% 110.76/110.98 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x6 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x5 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x5 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x6 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x6 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x6 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x6 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 119.74/119.99 Found a10:=(a1 W):((rel_s4 W) W)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (a1 W) as proof of ((rel_s4 W) V1)
% 119.74/119.99 Found (x5 (a1 W)) as proof of False
% 119.74/119.99 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 119.74/119.99 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x5 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x5 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x5 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x6 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x6 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (x5 (a1 W)) as proof of False
% 128.04/128.30 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 128.04/128.30 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 128.04/128.30 Found a10:=(a1 W):((rel_s4 W) W)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 128.04/128.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x6 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x6 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x6 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x5 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x5 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x5 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 136.13/136.37 Found (x5 (a1 W)) as proof of False
% 136.13/136.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 136.13/136.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 136.13/136.37 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x6 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x5 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (x5 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x7 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x7 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (x5 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V0)
% 155.80/156.04 Found (x4 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of (((mand (f X)) (g X)) V)
% 155.80/156.04 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->(((mand (f X)) (g X)) V))
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x7 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x7 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 155.80/156.04 Found a10:=(a1 W):((rel_s4 W) W)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (a1 W) as proof of ((rel_s4 W) V1)
% 155.80/156.04 Found (x7 (a1 W)) as proof of False
% 155.80/156.04 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x7 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x7 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x6 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 164.29/164.54 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x6 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 164.29/164.54 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x7 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V0)
% 164.29/164.54 Found (x4 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of (((mand (f X)) (g X)) V)
% 164.29/164.54 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->(((mand (f X)) (g X)) V))
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x7 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 164.29/164.54 Found a10:=(a1 W):((rel_s4 W) W)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (a1 W) as proof of ((rel_s4 W) V1)
% 164.29/164.54 Found (x7 (a1 W)) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 164.29/164.54 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x6 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of False
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x6 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x6 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x6 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of False
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x6 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 169.03/169.30 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 169.03/169.30 Found a10:=(a1 W):((rel_s4 W) W)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (a1 W) as proof of ((rel_s4 W) V1)
% 169.03/169.30 Found (x7 (a1 W)) as proof of False
% 169.03/169.30 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x7 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x6 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x5 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x6 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x6 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x7 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 178.09/178.34 Found a10:=(a1 W):((rel_s4 W) W)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (a1 W) as proof of ((rel_s4 W) V1)
% 178.09/178.34 Found (x6 (a1 W)) as proof of False
% 178.09/178.34 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 178.09/178.34 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 216.00/216.27 Found a10:=(a1 W):((rel_s4 W) W)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (x6 (a1 W)) as proof of False
% 216.00/216.27 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 216.00/216.27 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 216.00/216.27 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 216.00/216.27 Found a10:=(a1 S):((rel_s4 S) S)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (x3 (a1 S)) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 216.00/216.27 Found a10:=(a1 W):((rel_s4 W) W)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (x5 (a1 W)) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 216.00/216.27 Found a10:=(a1 W):((rel_s4 W) W)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (x5 (a1 W)) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 216.00/216.27 Found a10:=(a1 W):((rel_s4 W) W)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (x6 (a1 W)) as proof of False
% 216.00/216.27 Found (fun (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of False
% 216.00/216.27 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 216.00/216.27 Found (fun (x6:(((rel_s4 W) V1)->False)) (x7:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 216.00/216.27 Found a10:=(a1 S):((rel_s4 S) S)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (x3 (a1 S)) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 216.00/216.27 Found a10:=(a1 W):((rel_s4 W) W)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (a1 W) as proof of ((rel_s4 W) V1)
% 216.00/216.27 Found (x5 (a1 W)) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of False
% 216.00/216.27 Found (fun (x5:(((rel_s4 W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 216.00/216.27 Found a10:=(a1 S):((rel_s4 S) S)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (x3 (a1 S)) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 216.00/216.27 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 216.00/216.27 Found a10:=(a1 S):((rel_s4 S) S)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 216.00/216.27 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x3 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 229.20/229.45 Found a10:=(a1 S):((rel_s4 S) S)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x4 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 229.20/229.45 Found a10:=(a1 S):((rel_s4 S) S)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x4 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 229.20/229.45 Found a10:=(a1 W):((rel_s4 W) W)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (x6 (a1 W)) as proof of False
% 229.20/229.45 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 229.20/229.45 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 229.20/229.45 Found a10:=(a1 W):((rel_s4 W) W)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.45 Found (x6 (a1 W)) as proof of False
% 229.20/229.45 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 229.20/229.45 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 229.20/229.45 Found a10:=(a1 S):((rel_s4 S) S)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x4 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 229.20/229.45 Found a10:=(a1 S):((rel_s4 S) S)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x4 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 229.20/229.45 Found a10:=(a1 S):((rel_s4 S) S)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (a1 S) as proof of ((rel_s4 S) V0)
% 229.20/229.45 Found (x3 (a1 S)) as proof of False
% 229.20/229.45 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 229.20/229.45 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 229.20/229.45 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 229.20/229.46 Found a10:=(a1 W):((rel_s4 W) W)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (x6 (a1 W)) as proof of False
% 229.20/229.46 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 229.20/229.46 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 229.20/229.46 Found a10:=(a1 W):((rel_s4 W) W)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (x6 (a1 W)) as proof of False
% 229.20/229.46 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 229.20/229.46 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 229.20/229.46 Found a10:=(a1 W):((rel_s4 W) W)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 229.20/229.46 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x6 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x6 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x5 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 240.11/240.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x5 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 240.11/240.37 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x6 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x6 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 240.11/240.37 Found a10:=(a1 S):((rel_s4 S) S)
% 240.11/240.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 240.11/240.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 240.11/240.37 Found (a1 S) as proof of ((rel_s4 S) V0)
% 240.11/240.37 Found (x3 (a1 S)) as proof of False
% 240.11/240.37 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 240.11/240.37 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 240.11/240.37 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 240.11/240.37 Found a10:=(a1 W):((rel_s4 W) W)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (a1 W) as proof of ((rel_s4 W) V1)
% 240.11/240.37 Found (x6 (a1 W)) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 240.11/240.37 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x6 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x5 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x6 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x6 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x5 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x5 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 246.42/246.71 Found a10:=(a1 W):((rel_s4 W) W)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (a1 W) as proof of ((rel_s4 W) V1)
% 246.42/246.71 Found (x5 (a1 W)) as proof of False
% 246.42/246.71 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 246.42/246.71 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x5 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x6 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x6 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x6 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x5 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x5 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0)
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V0))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V0))
% 256.29/256.56 Found a10:=(a1 W):((rel_s4 W) W)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (a1 W) as proof of ((rel_s4 W) V1)
% 256.29/256.56 Found (x5 (a1 W)) as proof of False
% 256.29/256.56 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 256.29/256.56 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 269.81/270.11 Found a10:=(a1 W):((rel_s4 W) W)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (x5 (a1 W)) as proof of False
% 269.81/270.11 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 269.81/270.11 Found a10:=(a1 W):((rel_s4 W) W)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (x6 (a1 W)) as proof of False
% 269.81/270.11 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of False
% 269.81/270.11 Found (fun (x6:(((rel_s4 W) V1)->False))=> (x6 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 269.81/270.11 Found a10:=(a1 S):((rel_s4 S) S)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (x4 (a1 S)) as proof of False
% 269.81/270.11 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 269.81/270.11 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 269.81/270.11 Found a10:=(a1 W):((rel_s4 W) W)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (x5 (a1 W)) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 269.81/270.11 Found a10:=(a1 S):((rel_s4 S) S)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V)
% 269.81/270.11 Found (x1 (a1 S)) as proof of False
% 269.81/270.11 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of False
% 269.81/270.11 Found (fun (x1:(((rel_s4 S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_s4 S) V)->False)->False)
% 269.81/270.11 Found a10:=(a1 W):((rel_s4 W) W)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V1)
% 269.81/270.11 Found (x5 (a1 W)) as proof of False
% 269.81/270.11 Found (fun (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V)
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V1)->False)) (x6:((mforall_ind (fun (X:mu)=> (mnot ((fun (X:mu)=> ((mand (f X)) (g X))) X)))) V))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->((mexists_ind (fun (X:mu)=> ((mand (f X)) (g X)))) V))
% 269.81/270.11 Found a10:=(a1 S):((rel_s4 S) S)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (x4 (a1 S)) as proof of False
% 269.81/270.11 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of False
% 269.81/270.11 Found (fun (x4:(((rel_s4 S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 269.81/270.11 Found a10:=(a1 W):((rel_s4 W) W)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (a1 W) as proof of ((rel_s4 W) V0)
% 269.81/270.11 Found (x5 (a1 W)) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of False
% 269.81/270.11 Found (fun (x5:(((rel_s4 W) V0)->False))=> (x5 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 269.81/270.11 Found a10:=(a1 S):((rel_s4 S) S)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (a1 S) as proof of ((rel_s4 S) V0)
% 269.81/270.11 Found (x3 (a1 S)) as proof of False
% 269.81/270.11 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W) W)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (x4 (a1 W)) as proof of False
% 292.77/293.05 Found (fun (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of False
% 292.77/293.05 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of (((mand (f X)) (g X)) V)
% 292.77/293.05 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->(((mand (f X)) (g X)) V))
% 292.77/293.05 Found a10:=(a1 S):((rel_s4 S) S)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (x3 (a1 S)) as proof of False
% 292.77/293.05 Found (fun (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V)
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False)) (x4:((mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X))))))) V))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->((mnot (mforall_ind (fun (X:mu)=> (mnot (mnot ((mor (mnot (f X))) (mnot (g X)))))))) V))
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W) W)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (x4 (a1 W)) as proof of False
% 292.77/293.05 Found (fun (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of False
% 292.77/293.05 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of (((mand (f X)) (g X)) V)
% 292.77/293.05 Found (fun (x4:(((rel_s4 W) V0)->False)) (x5:(((mor (mnot (f X))) (mnot (g X))) V))=> (x4 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->(((mand (f X)) (g X)) V))
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W) W)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (x7 (a1 W)) as proof of False
% 292.77/293.05 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 292.77/293.05 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W) W)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V1)
% 292.77/293.05 Found (x7 (a1 W)) as proof of False
% 292.77/293.05 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of False
% 292.77/293.05 Found (fun (x7:(((rel_s4 W) V1)->False))=> (x7 (a1 W))) as proof of ((((rel_s4 W) V1)->False)->False)
% 292.77/293.05 Found a10:=(a1 S):((rel_s4 S) S)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (a1 S) as proof of ((rel_s4 S) V0)
% 292.77/293.05 Found (x3 (a1 S)) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_s4 S) V0)->False)->False)
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W) W)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (a1 W) as proof of ((rel_s4 W) V0)
% 292.77/293.05 Found (x3 (a1 W)) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of False
% 292.77/293.05 Found (fun (x3:(((rel_s4 W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_s4 W) V0)->False)->False)
% 292.77/293.05 Found a10:=(a1 W):((rel_s4 W
%------------------------------------------------------------------------------