%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : LCL717^1 : TPTP v6.1.0. Bugfixed v5.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n099.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:26:09 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : LCL717^1 : TPTP v6.1.0. Bugfixed v5.1.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:41:56 CDT 2014
% % CPUTime  : 300.01 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% Failed to open /home/cristobal/cocATP/CASC/TPTP/Axioms/LCL013^0.ax, trying next directory
% FOF formula (<kernel.Constant object at 0x27ac710>, <kernel.Type object at 0x27ac368>) of role type named mu_type
% Using role type
% Declaring mu:Type
% FOF formula (<kernel.Constant object at 0x27ac638>, <kernel.DependentProduct object at 0x27ac710>) of role type named meq_ind_type
% Using role type
% Declaring meq_ind:(mu->(mu->(fofType->Prop)))
% 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
% A new definition: (((eq (mu->(mu->(fofType->Prop)))) meq_ind) (fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)))
% Defined: meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y))
% FOF formula (<kernel.Constant object at 0x27ac710>, <kernel.DependentProduct object at 0x27ac488>) of role type named meq_prop_type
% Using role type
% Declaring meq_prop:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% 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))))
% Defined: meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W)))
% FOF formula (<kernel.Constant object at 0x27ac518>, <kernel.DependentProduct object at 0x27ac638>) of role type named mnot_type
% Using role type
% Declaring mnot:((fofType->Prop)->(fofType->Prop))
% FOF formula (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))) of role definition named mnot
% A new definition: (((eq ((fofType->Prop)->(fofType->Prop))) mnot) (fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)))
% Defined: mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False))
% FOF formula (<kernel.Constant object at 0x27ac638>, <kernel.DependentProduct object at 0x27ac1b8>) of role type named mor_type
% Using role type
% Declaring mor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% 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))))
% Defined: mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W)))
% FOF formula (<kernel.Constant object at 0x27ac1b8>, <kernel.DependentProduct object at 0x27accb0>) of role type named mand_type
% Using role type
% Declaring mand:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mand) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))))
% Defined: mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi))))
% FOF formula (<kernel.Constant object at 0x27accb0>, <kernel.DependentProduct object at 0x27acb48>) of role type named mimplies_type
% Using role type
% Declaring mimplies:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplies) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)))
% Defined: mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi))
% FOF formula (<kernel.Constant object at 0x27acb48>, <kernel.DependentProduct object at 0x27ac050>) of role type named mimplied_type
% Using role type
% Declaring mimplied:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mimplied) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)))
% Defined: mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi))
% FOF formula (<kernel.Constant object at 0x27ac050>, <kernel.DependentProduct object at 0x27ac638>) of role type named mequiv_type
% Using role type
% Declaring mequiv:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% 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))))
% Defined: mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi)))
% FOF formula (<kernel.Constant object at 0x27ac638>, <kernel.DependentProduct object at 0x27ac2d8>) of role type named mxor_type
% Using role type
% Declaring mxor:((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))
% 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
% A new definition: (((eq ((fofType->Prop)->((fofType->Prop)->(fofType->Prop)))) mxor) (fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))))
% Defined: mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi)))
% FOF formula (<kernel.Constant object at 0x27ac710>, <kernel.DependentProduct object at 0x27ace60>) of role type named mforall_ind_type
% Using role type
% Declaring mforall_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 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
% A new definition: (((eq ((mu->(fofType->Prop))->(fofType->Prop))) mforall_ind) (fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))))
% Defined: mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W)))
% FOF formula (<kernel.Constant object at 0x27ace60>, <kernel.DependentProduct object at 0x27ac098>) of role type named mforall_prop_type
% Using role type
% Declaring mforall_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 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
% 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))))
% Defined: mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W)))
% FOF formula (<kernel.Constant object at 0x280bcb0>, <kernel.DependentProduct object at 0x27ac248>) of role type named mexists_ind_type
% Using role type
% Declaring mexists_ind:((mu->(fofType->Prop))->(fofType->Prop))
% 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
% 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)))))))
% Defined: mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X))))))
% FOF formula (<kernel.Constant object at 0x280b0e0>, <kernel.DependentProduct object at 0x27ac908>) of role type named mexists_prop_type
% Using role type
% Declaring mexists_prop:(((fofType->Prop)->(fofType->Prop))->(fofType->Prop))
% 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
% 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)))))))
% Defined: mexists_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop)))=> (mnot (mforall_prop (fun (P:(fofType->Prop))=> (mnot (Phi P))))))
% FOF formula (<kernel.Constant object at 0x280b0e0>, <kernel.DependentProduct object at 0x27ac908>) of role type named mtrue_type
% Using role type
% Declaring mtrue:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True)) of role definition named mtrue
% A new definition: (((eq (fofType->Prop)) mtrue) (fun (W:fofType)=> True))
% Defined: mtrue:=(fun (W:fofType)=> True)
% FOF formula (<kernel.Constant object at 0x280b248>, <kernel.DependentProduct object at 0x27ac128>) of role type named mfalse_type
% Using role type
% Declaring mfalse:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) mfalse) (mnot mtrue)) of role definition named mfalse
% A new definition: (((eq (fofType->Prop)) mfalse) (mnot mtrue))
% Defined: mfalse:=(mnot mtrue)
% FOF formula (<kernel.Constant object at 0x27ac638>, <kernel.DependentProduct object at 0x27ac128>) of role type named mbox_type
% Using role type
% Declaring mbox:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 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
% 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)))))
% Defined: mbox:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop)) (W:fofType)=> (forall (V:fofType), ((or (((R W) V)->False)) (Phi V))))
% FOF formula (<kernel.Constant object at 0x27ac0e0>, <kernel.DependentProduct object at 0x27ac638>) of role type named mdia_type
% Using role type
% Declaring mdia:((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop)))
% 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
% 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)))))
% Defined: mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi))))
% FOF formula (<kernel.Constant object at 0x27ac200>, <kernel.DependentProduct object at 0x27ae5f0>) of role type named mreflexive_type
% Using role type
% Declaring mreflexive:((fofType->(fofType->Prop))->Prop)
% FOF formula (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))) of role definition named mreflexive
% A new definition: (((eq ((fofType->(fofType->Prop))->Prop)) mreflexive) (fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))))
% Defined: mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S)))
% FOF formula (<kernel.Constant object at 0x27ac200>, <kernel.DependentProduct object at 0x27ae680>) of role type named msymmetric_type
% Using role type
% Declaring msymmetric:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))
% Defined: msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S))))
% FOF formula (<kernel.Constant object at 0x27ac638>, <kernel.DependentProduct object at 0x27ae680>) of role type named mserial_type
% Using role type
% Declaring mserial:((fofType->(fofType->Prop))->Prop)
% 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
% 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))))))
% Defined: mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T)))))
% FOF formula (<kernel.Constant object at 0x27aea70>, <kernel.DependentProduct object at 0x23b6758>) of role type named mtransitive_type
% Using role type
% Declaring mtransitive:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))
% Defined: mtransitive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R T) U))->((R S) U))))
% FOF formula (<kernel.Constant object at 0x27ae290>, <kernel.DependentProduct object at 0x23b66c8>) of role type named meuclidean_type
% Using role type
% Declaring meuclidean:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))
% Defined: meuclidean:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType) (U:fofType), (((and ((R S) T)) ((R S) U))->((R T) U))))
% FOF formula (<kernel.Constant object at 0x27ae290>, <kernel.DependentProduct object at 0x23b6758>) of role type named mpartially_functional_type
% Using role type
% Declaring mpartially_functional:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))
% 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))))
% FOF formula (<kernel.Constant object at 0x27ae290>, <kernel.DependentProduct object at 0x23b6a70>) of role type named mfunctional_type
% Using role type
% Declaring mfunctional:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))))))
% 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))))))))
% FOF formula (<kernel.Constant object at 0x23b6a70>, <kernel.DependentProduct object at 0x23b6b00>) of role type named mweakly_dense_type
% Using role type
% Declaring mweakly_dense:((fofType->(fofType->Prop))->Prop)
% 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
% 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)))))))))
% 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))))))))
% FOF formula (<kernel.Constant object at 0x23b6b00>, <kernel.DependentProduct object at 0x23b6758>) of role type named mweakly_connected_type
% Using role type
% Declaring mweakly_connected:((fofType->(fofType->Prop))->Prop)
% 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
% 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))))))
% 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)))))
% FOF formula (<kernel.Constant object at 0x23b6758>, <kernel.DependentProduct object at 0x23b6ef0>) of role type named mweakly_directed_type
% Using role type
% Declaring mweakly_directed:((fofType->(fofType->Prop))->Prop)
% 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
% 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))))))))
% 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)))))))
% FOF formula (<kernel.Constant object at 0x23b6908>, <kernel.DependentProduct object at 0x23b6d88>) of role type named mvalid_type
% Using role type
% Declaring mvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))) of role definition named mvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) mvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))))
% Defined: mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W)))
% FOF formula (<kernel.Constant object at 0x23b6758>, <kernel.DependentProduct object at 0x23b67e8>) of role type named minvalid_type
% Using role type
% Declaring minvalid:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))) of role definition named minvalid
% A new definition: (((eq ((fofType->Prop)->Prop)) minvalid) (fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))))
% Defined: minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False)))
% FOF formula (<kernel.Constant object at 0x23b6d88>, <kernel.DependentProduct object at 0x23b6c68>) of role type named msatisfiable_type
% Using role type
% Declaring msatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))) of role definition named msatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) msatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))))
% Defined: msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W))))
% FOF formula (<kernel.Constant object at 0x23b67e8>, <kernel.DependentProduct object at 0x23b6a70>) of role type named mcountersatisfiable_type
% Using role type
% Declaring mcountersatisfiable:((fofType->Prop)->Prop)
% FOF formula (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))) of role definition named mcountersatisfiable
% A new definition: (((eq ((fofType->Prop)->Prop)) mcountersatisfiable) (fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))))
% Defined: mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False))))
% FOF formula (forall (R:(fofType->(fofType->Prop))), ((mvalid (mforall_prop (fun (A:(fofType->Prop))=> (mforall_prop (fun (B:(fofType->Prop))=> ((mor ((mbox R) ((mimplies ((mand A) ((mbox R) A))) B))) ((mbox R) ((mimplies ((mand B) ((mbox R) B))) A))))))))->(mweakly_connected R))) of role conjecture named conj
% Conjecture to prove = (forall (R:(fofType->(fofType->Prop))), ((mvalid (mforall_prop (fun (A:(fofType->Prop))=> (mforall_prop (fun (B:(fofType->Prop))=> ((mor ((mbox R) ((mimplies ((mand A) ((mbox R) A))) B))) ((mbox R) ((mimplies ((mand B) ((mbox R) B))) A))))))))->(mweakly_connected R))):Prop
% Parameter mu_DUMMY:mu.
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (R:(fofType->(fofType->Prop))), ((mvalid (mforall_prop (fun (A:(fofType->Prop))=> (mforall_prop (fun (B:(fofType->Prop))=> ((mor ((mbox R) ((mimplies ((mand A) ((mbox R) A))) B))) ((mbox R) ((mimplies ((mand B) ((mbox R) B))) A))))))))->(mweakly_connected R)))']
% Parameter mu:Type.
% Parameter fofType:Type.
% Definition meq_ind:=(fun (X:mu) (Y:mu) (W:fofType)=> (((eq mu) X) Y)):(mu->(mu->(fofType->Prop))).
% Definition meq_prop:=(fun (X:(fofType->Prop)) (Y:(fofType->Prop)) (W:fofType)=> (((eq Prop) (X W)) (Y W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mnot:=(fun (Phi:(fofType->Prop)) (W:fofType)=> ((Phi W)->False)):((fofType->Prop)->(fofType->Prop)).
% Definition mor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop)) (W:fofType)=> ((or (Phi W)) (Psi W))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mand:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mor (mnot Phi)) (mnot Psi)))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplies:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Phi)) Psi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mimplied:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mor (mnot Psi)) Phi)):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mequiv:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> ((mand ((mimplies Phi) Psi)) ((mimplies Psi) Phi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mxor:=(fun (Phi:(fofType->Prop)) (Psi:(fofType->Prop))=> (mnot ((mequiv Phi) Psi))):((fofType->Prop)->((fofType->Prop)->(fofType->Prop))).
% Definition mforall_ind:=(fun (Phi:(mu->(fofType->Prop))) (W:fofType)=> (forall (X:mu), ((Phi X) W))):((mu->(fofType->Prop))->(fofType->Prop)).
% Definition mforall_prop:=(fun (Phi:((fofType->Prop)->(fofType->Prop))) (W:fofType)=> (forall (P:(fofType->Prop)), ((Phi P) W))):(((fofType->Prop)->(fofType->Prop))->(fofType->Prop)).
% Definition mexists_ind:=(fun (Phi:(mu->(fofType->Prop)))=> (mnot (mforall_ind (fun (X:mu)=> (mnot (Phi X)))))):((mu->(fofType->Prop))->(fofType->Prop)).
% 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)).
% Definition mtrue:=(fun (W:fofType)=> True):(fofType->Prop).
% Definition mfalse:=(mnot mtrue):(fofType->Prop).
% 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))).
% Definition mdia:=(fun (R:(fofType->(fofType->Prop))) (Phi:(fofType->Prop))=> (mnot ((mbox R) (mnot Phi)))):((fofType->(fofType->Prop))->((fofType->Prop)->(fofType->Prop))).
% Definition mreflexive:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((R S) S))):((fofType->(fofType->Prop))->Prop).
% Definition msymmetric:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType) (T:fofType), (((R S) T)->((R T) S)))):((fofType->(fofType->Prop))->Prop).
% Definition mserial:=(fun (R:(fofType->(fofType->Prop)))=> (forall (S:fofType), ((ex fofType) (fun (T:fofType)=> ((R S) T))))):((fofType->(fofType->Prop))->Prop).
% 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).
% 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).
% 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).
% 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).
% 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).
% 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).
% 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).
% Definition mvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), (Phi W))):((fofType->Prop)->Prop).
% Definition minvalid:=(fun (Phi:(fofType->Prop))=> (forall (W:fofType), ((Phi W)->False))):((fofType->Prop)->Prop).
% Definition msatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> (Phi W)))):((fofType->Prop)->Prop).
% Definition mcountersatisfiable:=(fun (Phi:(fofType->Prop))=> ((ex fofType) (fun (W:fofType)=> ((Phi W)->False)))):((fofType->Prop)->Prop).
% Trying to prove (forall (R:(fofType->(fofType->Prop))), ((mvalid (mforall_prop (fun (A:(fofType->Prop))=> (mforall_prop (fun (B:(fofType->Prop))=> ((mor ((mbox R) ((mimplies ((mand A) ((mbox R) A))) B))) ((mbox R) ((mimplies ((mand B) ((mbox R) B))) A))))))))->(mweakly_connected R)))
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((R T) U)):(((eq Prop) ((R T) U)) ((R T) U))
% Found (eq_ref0 ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x2:((R S) U)
% Instantiate: a:=S:fofType
% Found x2 as proof of ((R a) U)
% Found (or_introl10 x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found ((or_introl1 (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (or_introl00 (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found ((or_introl0 ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found x2:((R S) U)
% Instantiate: a:=S:fofType
% Found x2 as proof of ((R a) U)
% Found (or_introl10 x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found ((or_introl1 (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (or_introl00 (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found ((or_introl0 ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((R T) U)):(((eq Prop) ((R T) U)) ((R T) U))
% Found (eq_ref0 ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 ((R T) U)):(((eq Prop) ((R T) U)) ((R T) U))
% Found (eq_ref0 ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x2:((R S) U)
% Instantiate: a:=S:fofType
% Found x2 as proof of ((R a) U)
% Found (or_introl10 x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found ((or_introl1 (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (or_introl00 (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found ((or_introl0 ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) T)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((R a) U)) (((eq fofType) a) U)))
% Found x2:((R S) U)
% Instantiate: a:=S:fofType
% Found x2 as proof of ((R a) U)
% Found (or_introl10 x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found ((or_introl1 (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (((or_introl ((R a) U)) (((eq fofType) a) U)) x2) as proof of ((or ((R a) U)) (((eq fofType) a) U))
% Found (or_introl00 (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found ((or_introl0 ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found (((or_introl ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)) (((or_introl ((R a) U)) (((eq fofType) a) U)) x2)) as proof of (P ((or ((or ((R a) U)) (((eq fofType) a) U))) ((R U) a)))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found (or_introl10 ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found ((or_introl1 ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 ((R T) U)):(((eq Prop) ((R T) U)) ((R T) U))
% Found (eq_ref0 ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found (or_introl10 ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found ((or_introl1 ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found (or_introl00 ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found ((or_introl0 ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found classic0:=(classic ((or ((R T) U)) (((eq fofType) T) U))):((or ((or ((R T) U)) (((eq fofType) T) U))) (not ((or ((R T) U)) (((eq fofType) T) U))))
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of (P b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of (P b)
% Found classic0:=(classic ((R U) T)):((or ((R U) T)) (not ((R U) T)))
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) a)
% Found (or_introl00 ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found ((or_introl0 ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found (((or_introl (((eq fofType) T) a)) ((R T) a)) ((eq_ref fofType) T)) as proof of (P ((or (((eq fofType) T) a)) ((R T) a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found classic0:=(classic ((or ((R T) U)) (((eq fofType) T) U))):((or ((or ((R T) U)) (((eq fofType) T) U))) (not ((or ((R T) U)) (((eq fofType) T) U))))
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of ((or ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found (classic ((or ((R T) U)) (((eq fofType) T) U))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x3:(P0 b)
% Instantiate: b:=T:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 T)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 T))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x10:(P T)
% Found (fun (x10:(P T))=> x10) as proof of (P T)
% Found (fun (x10:(P T))=> x10) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x3:(P U)
% Instantiate: b:=U:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of (P b)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) b)
% Found (classic ((R T) U)) as proof of (P b)
% Found classic0:=(classic ((R U) T)):((or ((R U) T)) (not ((R U) T)))
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of ((or ((R U) T)) b)
% Found (classic ((R U) T)) as proof of (P b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found classic0:=(classic (((eq fofType) T) U)):((or (((eq fofType) T) U)) (not (((eq fofType) T) U)))
% Found (classic (((eq fofType) T) U)) as proof of ((or (((eq fofType) T) U)) b)
% Found (classic (((eq fofType) T) U)) as proof of ((or (((eq fofType) T) U)) b)
% Found (classic (((eq fofType) T) U)) as proof of ((or (((eq fofType) T) U)) b)
% Found (classic (((eq fofType) T) U)) as proof of (P b)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) T) U))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((or ((R T) U)) (((eq fofType) T) U)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((R T) U)) (((eq fofType) T) U)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((R T) U)) (((eq fofType) T) U)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or ((R T) U)) (((eq fofType) T) U)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) T) U))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) T) U))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) T) U))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) T) U))
% Found x30:(P U)
% Found (fun (x30:(P U))=> x30) as proof of (P U)
% Found (fun (x30:(P U))=> x30) as proof of (P0 U)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x30:(P T)
% Found (fun (x30:(P T))=> x30) as proof of (P T)
% Found (fun (x30:(P T))=> x30) as proof of (P0 T)
% Found x3:(P T)
% Instantiate: b:=T:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found x1:(P T)
% Instantiate: b:=T:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 T):(((eq fofType) T) T)
% Found (eq_ref0 T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found ((eq_ref fofType) T) as proof of (((eq fofType) T) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) U)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((R U) T))
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((R T) U)):(((eq Prop) ((R T) U)) ((R T) U))
% Found (eq_ref0 ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found ((eq_ref Prop) ((R T) U)) as proof of (((eq Prop) ((R T) U)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 ((R U) T)):(((eq Prop) ((R U) T)) ((R U) T))
% Found (eq_ref0 ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found ((eq_ref Prop) ((R U) T)) as proof of (((eq Prop) ((R U) T)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) T)
% Found eq_ref00:=(eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))):(((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) ((or ((R T) U)) (((eq fofType) T) U)))
% Found (eq_ref0 ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found ((eq_ref Prop) ((or ((R T) U)) (((eq fofType) T) U))) as proof of (((eq Prop) ((or ((R T) U)) (((eq fofType) T) U))) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) T) U)):(((eq Prop) (((eq fofType) T) U)) (((eq fofType) T) U))
% Found (eq_ref0 (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found ((eq_ref Prop) (((eq fofType) T) U)) as proof of (((eq Prop) (((eq fofType) T) U)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) T)
% Found eq_ref00:=(eq_ref0 U):(((eq fofType) U) U)
% Found (eq_ref0 U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found ((eq_ref fofType) U) as proof of (((eq fofType) U) b)
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R T) U)) a))
% Found classic0:=(classic ((R T) U)):((or ((R T) U)) (not ((R T) U)))
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (classic ((R T) U)) as proof of ((or ((R T) U)) a)
% Found (or_intror00 (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found ((or_intror0 ((or ((R T) U)) a)) (classic ((R T) U))) as proof of (P ((or ((R U) T)) ((or ((R T) U)) a)))
% Found (((or_intror ((R U) T)) ((or ((R T) U)) a)) (classic (
% EOF
%------------------------------------------------------------------------------