TSTP Solution File: SYO473^4 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO473^4 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:50 EDT 2022
% Result : Timeout 300.04s 300.56s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO473^4 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.31 % Computer : n024.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % RAMPerCPU : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % DateTime : Sun Mar 13 07:21:03 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.12/0.32 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.33 Python 2.7.5
% 0.46/0.64 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.46/0.64 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.Type object at 0x2b41019189e0>) of role type named mu_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring mu:Type
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918b90>, <kernel.DependentProduct object at 0x2b4101918bd8>) of role type named meq_ind_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 0.46/0.64 FOF formula (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))) of role definition named meq_ind
% 0.46/0.64 A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% 0.46/0.64 Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.DependentProduct object at 0x2b4101918a70>) of role type named meq_prop_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))) of role definition named meq_prop
% 0.46/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) meq_prop) (fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))))
% 0.46/0.64 Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918b00>, <kernel.DependentProduct object at 0x2b4101918b90>) of role type named mnot_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring mnot:((fofType->Prop)->(fofType->Prop))
% 0.46/0.64 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% 0.46/0.64 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% 0.46/0.64 Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918b90>, <kernel.DependentProduct object at 0x2b41019183f8>) of role type named mor_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))) of role definition named mor
% 0.46/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))))
% 0.46/0.64 Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b41019183f8>, <kernel.DependentProduct object at 0x2b4101918560>) of role type named mand_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))) of role definition named mand
% 0.46/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% 0.46/0.64 Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% 0.46/0.64 FOF formula (<kernel.Constant object at 0x2b4101918560>, <kernel.DependentProduct object at 0x2b4101918488>) of role type named mimplies_type
% 0.46/0.64 Using role type
% 0.46/0.64 Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.46/0.64 FOF formula (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))) of role definition named mimplies
% 0.46/0.64 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% 0.50/0.66 Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b4101918488>, <kernel.DependentProduct object at 0x2b41019187a0>) of role type named mimplied_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.50/0.66 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
% 0.50/0.66 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% 0.50/0.66 Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b41019187a0>, <kernel.DependentProduct object at 0x2b4101918b90>) of role type named mequiv_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.50/0.66 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
% 0.50/0.66 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))))
% 0.50/0.66 Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b4101918b90>, <kernel.DependentProduct object at 0x2b41019183f8>) of role type named mxor_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 0.50/0.66 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
% 0.50/0.66 A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% 0.50/0.66 Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.DependentProduct object at 0x2b41019187a0>) of role type named mforall_ind_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.50/0.66 FOF formula (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))) of role definition named mforall_ind
% 0.50/0.66 A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% 0.50/0.66 Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b41019187a0>, <kernel.DependentProduct object at 0x2b41019189e0>) of role type named mforall_prop_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.50/0.66 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
% 0.50/0.66 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))))
% 0.50/0.66 Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% 0.50/0.66 FOF formula (<kernel.Constant object at 0x2b41019189e0>, <kernel.DependentProduct object at 0x2b4101918368>) of role type named mexists_ind_type
% 0.50/0.66 Using role type
% 0.50/0.66 Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 0.50/0.66 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
% 0.50/0.67 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)))))))
% 0.50/0.67 Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2b41093e9f80>, <kernel.DependentProduct object at 0x2b4101918878>) of role type named mexists_prop_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 0.50/0.67 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
% 0.50/0.67 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)))))))
% 0.50/0.67 Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2b41093e9f80>, <kernel.DependentProduct object at 0x2b4101918878>) of role type named mtrue_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mtrue:(fofType->Prop)
% 0.50/0.67 FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% 0.50/0.67 A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% 0.50/0.67 Defined: mtrue:=(fun (W:fofType)=> True)
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2b41093e93f8>, <kernel.DependentProduct object at 0x2b4101918368>) of role type named mfalse_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mfalse:(fofType->Prop)
% 0.50/0.67 FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% 0.50/0.67 A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% 0.50/0.67 Defined: mfalse:=(mnot mtrue)
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x2b4101918098>, <kernel.DependentProduct object at 0x2b4101918200>) of role type named mbox_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.50/0.67 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
% 0.50/0.67 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)))))
% 0.50/0.67 Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x1420a70>, <kernel.DependentProduct object at 0x1420b90>) of role type named mdia_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 0.50/0.67 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
% 0.50/0.67 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)))))
% 0.50/0.67 Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% 0.50/0.67 FOF formula (<kernel.Constant object at 0x1420950>, <kernel.DependentProduct object at 0x2b4101918200>) of role type named mreflexive_type
% 0.50/0.67 Using role type
% 0.50/0.67 Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% 0.50/0.67 FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% 0.50/0.67 A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% 0.50/0.67 Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x1420638>, <kernel.DependentProduct object at 0x2b4101918170>) of role type named msymmetric_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 0.50/0.69 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
% 0.50/0.69 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)))))
% 0.50/0.69 Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x1420638>, <kernel.DependentProduct object at 0x2b41019189e0>) of role type named mserial_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 0.50/0.69 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
% 0.50/0.69 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))))))
% 0.50/0.69 Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x1420bd8>, <kernel.DependentProduct object at 0x2b4101918368>) of role type named mtransitive_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 0.50/0.69 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
% 0.50/0.69 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)))))
% 0.50/0.69 Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x2b4101918368>, <kernel.DependentProduct object at 0x2b4101918098>) of role type named meuclidean_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 0.50/0.69 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
% 0.50/0.69 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)))))
% 0.50/0.69 Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x2b41019181b8>, <kernel.DependentProduct object at 0x2b4101918098>) of role type named mpartially_functional_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 0.50/0.69 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
% 0.50/0.69 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)))))
% 0.50/0.69 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))))
% 0.50/0.69 FOF formula (<kernel.Constant object at 0x2b41019189e0>, <kernel.DependentProduct object at 0x1446560>) of role type named mfunctional_type
% 0.50/0.69 Using role type
% 0.50/0.69 Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 0.50/0.70 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
% 0.50/0.70 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)))))))))
% 0.50/0.70 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))))))))
% 0.50/0.70 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.DependentProduct object at 0x1446710>) of role type named mweakly_dense_type
% 0.50/0.70 Using role type
% 0.50/0.70 Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 0.50/0.70 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
% 0.50/0.70 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)))))))))
% 0.50/0.70 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))))))))
% 0.50/0.70 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.DependentProduct object at 0x1446560>) of role type named mweakly_connected_type
% 0.50/0.70 Using role type
% 0.50/0.70 Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 0.50/0.70 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
% 0.50/0.70 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))))))
% 0.50/0.70 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)))))
% 0.50/0.70 FOF formula (<kernel.Constant object at 0x2b4101918bd8>, <kernel.DependentProduct object at 0x1446c68>) of role type named mweakly_directed_type
% 0.50/0.70 Using role type
% 0.50/0.70 Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 0.50/0.70 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
% 0.50/0.70 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))))))))
% 0.50/0.70 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)))))))
% 0.50/0.70 FOF formula (<kernel.Constant object at 0x1446638>, <kernel.DependentProduct object at 0x1446cb0>) of role type named mvalid_type
% 0.50/0.70 Using role type
% 0.50/0.70 Declaring mvalid:((fofType->Prop)->Prop)
% 0.50/0.70 FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% 0.50/0.70 A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% 0.50/0.70 Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x1446128>, <kernel.DependentProduct object at 0x2b4101916200>) of role type named minvalid_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring minvalid:((fofType->Prop)->Prop)
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% 0.50/0.71 A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% 0.50/0.71 Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x1446128>, <kernel.DependentProduct object at 0x2b4101916560>) of role type named msatisfiable_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring msatisfiable:((fofType->Prop)->Prop)
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% 0.50/0.71 A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% 0.50/0.71 Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x2b41019163f8>, <kernel.DependentProduct object at 0x2b4101916638>) of role type named mcountersatisfiable_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% 0.50/0.71 A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% 0.50/0.71 Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% 0.50/0.71 Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^4.ax, trying next directory
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x1420b90>, <kernel.DependentProduct object at 0x2b4101918fc8>) of role type named rel_b_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring rel_b:(fofType->(fofType->Prop))
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x14205a8>, <kernel.DependentProduct object at 0x2b4101918fc8>) of role type named mbox_b_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring mbox_b:((fofType->Prop)->(fofType->Prop))
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mbox_b) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_b W) V)->False)) (Phi V))))) of role definition named mbox_b
% 0.50/0.71 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mbox_b) (fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_b W) V)->False)) (Phi V)))))
% 0.50/0.71 Defined: mbox_b:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_b W) V)->False)) (Phi V))))
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x14205a8>, <kernel.DependentProduct object at 0x2b4101918f80>) of role type named mdia_b_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring mdia_b:((fofType->Prop)->(fofType->Prop))
% 0.50/0.71 FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mdia_b) (fun (Phi:(fofType->Prop))=> (mnot (mbox_b (mnot Phi))))) of role definition named mdia_b
% 0.50/0.71 A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mdia_b) (fun (Phi:(fofType->Prop))=> (mnot (mbox_b (mnot Phi)))))
% 0.50/0.71 Defined: mdia_b:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_b (mnot Phi))))
% 0.50/0.71 FOF formula (mreflexive rel_b) of role axiom named a1
% 0.50/0.71 A new axiom: (mreflexive rel_b)
% 0.50/0.71 FOF formula (msymmetric rel_b) of role axiom named a2
% 0.50/0.71 A new axiom: (msymmetric rel_b)
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x14433f8>, <kernel.DependentProduct object at 0x1443128>) of role type named p_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring p:(fofType->Prop)
% 0.50/0.71 FOF formula (<kernel.Constant object at 0x14432d8>, <kernel.DependentProduct object at 0x1443368>) of role type named q_type
% 0.50/0.71 Using role type
% 0.50/0.71 Declaring q:(fofType->Prop)
% 0.50/0.71 FOF formula (mvalid ((mimplies (mbox_b ((mimplies (mbox_b ((mequiv p) q))) (mdia_b q)))) (mbox_b ((mimplies (mbox_b ((mequiv p) q))) q)))) of role conjecture named prove
% 0.50/0.71 Conjecture to prove = (mvalid ((mimplies (mbox_b ((mimplies (mbox_b ((mequiv p) q))) (mdia_b q)))) (mbox_b ((mimplies (mbox_b ((mequiv p) q))) q)))):Prop
% 0.50/0.71 Parameter mu_DUMMY:mu.
% 0.50/0.71 Parameter fofType_DUMMY:fofType.
% 0.50/0.71 We need to prove ['(mvalid ((mimplies (mbox_b ((mimplies (mbox_b ((mequiv p) q))) (mdia_b q)))) (mbox_b ((mimplies (mbox_b ((mequiv p) q))) q))))']
% 0.50/0.71 Parameter mu:Type.
% 0.50/0.71 Parameter fofType:Type.
% 0.50/0.71 Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% 0.50/0.71 Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% 0.50/0.71 Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.50/0.71 Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% 0.50/0.71 Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 0.50/0.71 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)).
% 0.50/0.71 Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% 0.50/0.71 Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 0.50/0.71 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))).
% 0.50/0.71 Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% 0.50/0.71 Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U)))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition mpartially_functional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->(((eq fofType) T) U)))):((fofType->(fofType->Prop))->Prop).
% 0.50/0.71 Definition mfunctional:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((and ((R S) T)) (forall (U:fofType), (((R S) U)->(((eq fofType) T) U)))))))):((fofType->(fofType->Prop))->Prop).
% 5.90/6.13 Definition mweakly_dense:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (fofType->(((R S) T)->((ex fofType) (fun (U:fofType)=> ((and ((R S) U)) ((R U) T)))))))):((fofType->(fofType->Prop))->Prop).
% 5.90/6.13 Definition mweakly_connected:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((or ((or ((R T) U)) (((eq fofType) T) U))) ((R U) T))))):((fofType->(fofType->Prop))->Prop).
% 5.90/6.13 Definition mweakly_directed:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((ex fofType) (fun (V:fofType)=> ((and ((R T) V)) ((R U) V))))))):((fofType->(fofType->Prop))->Prop).
% 5.90/6.13 Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% 5.90/6.13 Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% 5.90/6.13 Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% 5.90/6.13 Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% 5.90/6.13 Parameter rel_b:(fofType->(fofType->Prop)).
% 5.90/6.13 Definition mbox_b:=(fun (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((rel_b W) V)->False)) (Phi V)))):((fofType->Prop)->(fofType->Prop)).
% 5.90/6.13 Definition mdia_b:=(fun (Phi:(fofType->Prop))=> (mnot (mbox_b (mnot Phi)))):((fofType->Prop)->(fofType->Prop)).
% 5.90/6.13 Axiom a1:(mreflexive rel_b).
% 5.90/6.13 Axiom a2:(msymmetric rel_b).
% 5.90/6.13 Parameter p:(fofType->Prop).
% 5.90/6.13 Parameter q:(fofType->Prop).
% 5.90/6.13 Trying to prove (mvalid ((mimplies (mbox_b ((mimplies (mbox_b ((mequiv p) q))) (mdia_b q)))) (mbox_b ((mimplies (mbox_b ((mequiv p) q))) q))))
% 5.90/6.13 Found a10:=(a1 W):((rel_b W) W)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (x1 (a1 W)) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 5.90/6.13 Found a10:=(a1 W):((rel_b W) W)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (x1 (a1 W)) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 5.90/6.13 Found a10:=(a1 S):((rel_b S) S)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (x1 (a1 S)) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 5.90/6.13 Found a10:=(a1 S):((rel_b S) S)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (a1 S) as proof of ((rel_b S) V)
% 5.90/6.13 Found (x1 (a1 S)) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 5.90/6.13 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 5.90/6.13 Found a10:=(a1 W):((rel_b W) W)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (x3 (a1 W)) as proof of False
% 5.90/6.13 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 5.90/6.13 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 5.90/6.13 Found a10:=(a1 W):((rel_b W) W)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V0)
% 5.90/6.13 Found (x3 (a1 W)) as proof of False
% 5.90/6.13 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 5.90/6.13 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 5.90/6.13 Found a10:=(a1 W):((rel_b W) W)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (a1 W) as proof of ((rel_b W) V)
% 5.90/6.13 Found (x1 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (x1 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (x3 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V0)
% 18.00/18.22 Found (x3 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (x1 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (a1 W) as proof of ((rel_b W) V)
% 18.00/18.22 Found (x1 (a1 W)) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 18.00/18.22 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 18.00/18.22 Found a10:=(a1 S):((rel_b S) S)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (x3 (a1 S)) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 18.00/18.22 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 18.00/18.22 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 18.00/18.22 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 18.00/18.22 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 18.00/18.22 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 18.00/18.22 Found a10:=(a1 S):((rel_b S) S)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (a1 S) as proof of ((rel_b S) V0)
% 18.00/18.22 Found (x3 (a1 S)) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 18.00/18.22 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 18.00/18.22 Found a10:=(a1 W):((rel_b W) W)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (x4 (a1 W)) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 34.68/34.92 Found a10:=(a1 W):((rel_b W) W)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (x4 (a1 W)) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 34.68/34.92 Found a10:=(a1 W):((rel_b W) W)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (x4 (a1 W)) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 34.68/34.92 Found a10:=(a1 W):((rel_b W) W)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (a1 W) as proof of ((rel_b W) V0)
% 34.68/34.92 Found (x4 (a1 W)) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 34.68/34.92 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 34.68/34.92 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 34.68/34.92 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 34.68/34.92 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 34.68/34.92 Found a10:=(a1 S):((rel_b S) S)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (x1 (a1 S)) as proof of False
% 34.68/34.92 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 34.68/34.92 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 34.68/34.92 Found a10:=(a1 S):((rel_b S) S)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V)
% 34.68/34.92 Found (x1 (a1 S)) as proof of False
% 34.68/34.92 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 34.68/34.92 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 34.68/34.92 Found a10:=(a1 S):((rel_b S) S)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V0)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V0)
% 34.68/34.92 Found (a1 S) as proof of ((rel_b S) V0)
% 34.68/34.92 Found (x3 (a1 S)) as proof of False
% 34.68/34.92 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 34.68/34.92 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 46.42/46.64 Found a10:=(a1 S):((rel_b S) S)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V0)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V0)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V0)
% 46.42/46.64 Found (x3 (a1 S)) as proof of False
% 46.42/46.64 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 46.42/46.64 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 46.42/46.64 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 46.42/46.64 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 46.42/46.64 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 46.42/46.64 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found a10:=(a1 S):((rel_b S) S)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V)
% 46.42/46.64 Found (a1 S) as proof of ((rel_b S) V)
% 46.42/46.64 Found (x1 (a1 S)) as proof of False
% 46.42/46.64 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 46.42/46.64 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 46.42/46.64 Found a10:=(a1 W):((rel_b W) W)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (x4 (a1 W)) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 46.42/46.64 Found a10:=(a1 W):((rel_b W) W)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (x4 (a1 W)) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 46.42/46.64 Found a10:=(a1 W):((rel_b W) W)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (x4 (a1 W)) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 46.42/46.64 Found a10:=(a1 W):((rel_b W) W)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (a1 W) as proof of ((rel_b W) V0)
% 46.42/46.64 Found (x4 (a1 W)) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 46.42/46.64 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 46.42/46.64 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 46.42/46.64 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 46.42/46.64 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found or_introl00:=(or_introl0 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found (or_introl0 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 65.16/65.42 Found a10:=(a1 S):((rel_b S) S)
% 65.16/65.42 Found (a1 S) as proof of ((rel_b S) V)
% 65.16/65.42 Found (a1 S) as proof of ((rel_b S) V)
% 65.16/65.42 Found (a1 S) as proof of ((rel_b S) V)
% 65.16/65.42 Found (x1 (a1 S)) as proof of False
% 65.16/65.42 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 65.16/65.42 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 65.16/65.42 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) ((mnot q) V0)))
% 65.16/65.42 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 65.16/65.42 Found or_introl10:=(or_introl1 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 65.16/65.42 Found (or_introl1 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 65.16/65.42 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 65.16/65.42 Found a10:=(a1 W):((rel_b W) W)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (x3 (a1 W)) as proof of False
% 65.16/65.42 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.16/65.42 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 65.16/65.42 Found a10:=(a1 W):((rel_b W) W)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (x3 (a1 W)) as proof of False
% 65.16/65.42 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 65.16/65.42 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 65.16/65.42 Found a10:=(a1 W):((rel_b W) W)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (a1 W) as proof of ((rel_b W) V0)
% 65.16/65.42 Found (x3 (a1 W)) as proof of False
% 83.64/83.94 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 83.64/83.94 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 83.64/83.94 Found a10:=(a1 W):((rel_b W) W)
% 83.64/83.94 Found (a1 W) as proof of ((rel_b W) V0)
% 83.64/83.94 Found (a1 W) as proof of ((rel_b W) V0)
% 83.64/83.94 Found (a1 W) as proof of ((rel_b W) V0)
% 83.64/83.94 Found (x3 (a1 W)) as proof of False
% 83.64/83.94 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 83.64/83.94 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 83.64/83.94 Found a10:=(a1 S):((rel_b S) S)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (x4 (a1 S)) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 83.64/83.94 Found a10:=(a1 S):((rel_b S) S)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (x4 (a1 S)) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 83.64/83.94 Found a10:=(a1 S):((rel_b S) S)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (x4 (a1 S)) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 83.64/83.94 Found a10:=(a1 S):((rel_b S) S)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (a1 S) as proof of ((rel_b S) V0)
% 83.64/83.94 Found (x4 (a1 S)) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 83.64/83.94 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 83.64/83.94 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) ((mnot q) V0)))
% 83.64/83.94 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 83.64/83.94 Found or_introl10:=(or_introl1 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found (or_introl1 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 83.64/83.94 Found a10:=(a1 W):((rel_b W) W)
% 83.64/83.94 Found (a1 W) as proof of ((rel_b W) V)
% 83.64/83.94 Found (a1 W) as proof of ((rel_b W) V)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V)
% 123.50/123.75 Found (x1 (a1 W)) as proof of False
% 123.50/123.75 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 123.50/123.75 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (x3 (a1 W)) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (x3 (a1 W)) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 123.50/123.75 Found or_introl00:=(or_introl0 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 123.50/123.75 Found (or_introl0 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 123.50/123.75 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) ((mnot q) V0)))
% 123.50/123.75 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 123.50/123.75 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (x3 (a1 W)) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (x3 (a1 W)) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of False
% 123.50/123.75 Found (fun (x3:(((rel_b W) V0)->False))=> (x3 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 123.50/123.75 Found a10:=(a1 W):((rel_b W) W)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 123.50/123.75 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found a10:=(a1 W):((rel_b W) W)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found a10:=(a1 S):((rel_b S) S)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (x4 (a1 S)) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 130.29/130.55 Found a10:=(a1 S):((rel_b S) S)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (x4 (a1 S)) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 130.29/130.55 Found a10:=(a1 W):((rel_b W) W)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found a10:=(a1 W):((rel_b W) W)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V0)
% 130.29/130.55 Found a10:=(a1 S):((rel_b S) S)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (x4 (a1 S)) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 130.29/130.55 Found a10:=(a1 S):((rel_b S) S)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (a1 S) as proof of ((rel_b S) V0)
% 130.29/130.55 Found (x4 (a1 S)) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of False
% 130.29/130.55 Found (fun (x4:(((rel_b S) V0)->False))=> (x4 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 130.29/130.55 Found a10:=(a1 W):((rel_b W) W)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V)
% 130.29/130.55 Found (a1 W) as proof of ((rel_b W) V)
% 130.29/130.55 Found (x1 (a1 W)) as proof of False
% 130.29/130.55 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of False
% 130.29/130.55 Found (fun (x1:(((rel_b W) V)->False))=> (x1 (a1 W))) as proof of ((((rel_b W) V)->False)->False)
% 130.29/130.55 Found or_introl00:=(or_introl0 ((mnot q) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) ((mnot q) V0)))
% 130.29/130.55 Found (or_introl0 ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 130.29/130.55 Found or_introl00:=(or_introl0 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)):((((rel_b S) V1)->False)->((or (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 130.29/130.55 Found (or_introl0 (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 130.29/130.55 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 178.55/178.83 Found ((or_introl (((rel_b S) V1)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)) as proof of ((((rel_b S) V1)->False)->((or (((rel_b V) V0)->False)) (((mand ((mimplies p) q)) ((mimplies q) p)) V0)))
% 178.55/178.83 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (x5 (a1 W)) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_b W) V1)->False)->False)
% 178.55/178.83 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (x5 (a1 W)) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_b W) V1)->False)->False)
% 178.55/178.83 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (x5 (a1 W)) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_b W) V1)->False)->False)
% 178.55/178.83 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (a1 W) as proof of ((rel_b W) V1)
% 178.55/178.83 Found (x5 (a1 W)) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of False
% 178.55/178.83 Found (fun (x5:(((rel_b W) V1)->False))=> (x5 (a1 W))) as proof of ((((rel_b W) V1)->False)->False)
% 178.55/178.83 Found a10:=(a1 S):((rel_b S) S)
% 178.55/178.83 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.83 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.83 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.83 Found (x3 (a1 S)) as proof of False
% 178.55/178.83 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 178.55/178.83 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 178.55/178.83 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found a10:=(a1 W):((rel_b W) W)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found (a1 W) as proof of ((rel_b W) V0)
% 178.55/178.84 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 178.55/178.84 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 178.55/178.84 Found a10:=(a1 S):((rel_b S) S)
% 178.55/178.84 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.84 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.84 Found (a1 S) as proof of ((rel_b S) V0)
% 178.55/178.84 Found (x3 (a1 S)) as proof of False
% 178.55/178.84 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 178.55/178.84 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 178.55/178.84 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 178.55/178.84 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 178.55/178.84 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 178.55/178.84 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 203.21/203.50 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 203.21/203.50 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 203.21/203.50 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 203.21/203.50 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found a10:=(a1 S):((rel_b S) S)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (x3 (a1 S)) as proof of False
% 203.21/203.50 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 203.21/203.50 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (x4 (a1 W)) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (x4 (a1 W)) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (x4 (a1 W)) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (x4 (a1 W)) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 S):((rel_b S) S)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (a1 S) as proof of ((rel_b S) V0)
% 203.21/203.50 Found (x3 (a1 S)) as proof of False
% 203.21/203.50 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of False
% 203.21/203.50 Found (fun (x3:(((rel_b S) V0)->False))=> (x3 (a1 S))) as proof of ((((rel_b S) V0)->False)->False)
% 203.21/203.50 Found a10:=(a1 W):((rel_b W) W)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (a1 W) as proof of ((rel_b W) V0)
% 203.21/203.50 Found (x4 (a1 W)) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 203.21/203.50 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 209.58/209.87 Found a10:=(a1 W):((rel_b W) W)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (x4 (a1 W)) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 209.58/209.87 Found a10:=(a1 W):((rel_b W) W)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (x4 (a1 W)) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 209.58/209.87 Found a10:=(a1 W):((rel_b W) W)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (a1 W) as proof of ((rel_b W) V0)
% 209.58/209.87 Found (x4 (a1 W)) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of False
% 209.58/209.87 Found (fun (x4:(((rel_b W) V0)->False))=> (x4 (a1 W))) as proof of ((((rel_b W) V0)->False)->False)
% 209.58/209.87 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 209.58/209.87 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 209.58/209.87 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 209.58/209.87 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 209.58/209.87 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found a10:=(a1 W):((rel_b W) W)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found a10:=(a1 W):((rel_b W) W)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 266.75/267.11 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found a10:=(a1 W):((rel_b W) W)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found a10:=(a1 W):((rel_b W) W)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found (a1 W) as proof of ((rel_b W) V0)
% 266.75/267.11 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found a10:=(a1 S):((rel_b S) S)
% 266.75/267.11 Found (a1 S) as proof of ((rel_b S) V)
% 266.75/267.11 Found (a1 S) as proof of ((rel_b S) V)
% 266.75/267.11 Found (a1 S) as proof of ((rel_b S) V)
% 266.75/267.11 Found (x1 (a1 S)) as proof of False
% 266.75/267.11 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of False
% 266.75/267.11 Found (fun (x1:(((rel_b S) V)->False))=> (x1 (a1 S))) as proof of ((((rel_b S) V)->False)->False)
% 266.75/267.11 Found or_introl10:=(or_introl1 ((mnot q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) ((mnot q) V0)))
% 266.75/267.11 Found (or_introl1 ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) ((mnot q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) ((mnot q) V0)))
% 266.75/267.11 Found or_introl10:=(or_introl1 (((mequiv p) q) V0)):((((rel_b W) V1)->False)->((or (((rel_b W) V1)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found (or_introl1 (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->((or (((rel_b V) V0)->False)) (((mequiv p) q) V0)))
% 266.75/267.11 Found ((or_introl (((rel_b W) V1)->False)) (((mequiv p) q) V0)) as proof of ((((rel_b W) V1)->False)->
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