%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU811^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n108.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 13:33:12 EDT 2014

% Result   : Timeout 300.06s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU811^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n108.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 11:32:16 CDT 2014
% % CPUTime  : 300.06 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x1dc3f38>, <kernel.DependentProduct object at 0x1dc39e0>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x219b248>, <kernel.DependentProduct object at 0x1dc39e0>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1dc3830>, <kernel.Single object at 0x1dc36c8>) of role type named omega_type
% Using role type
% Declaring omega:fofType
% FOF formula (<kernel.Constant object at 0x1dc3d40>, <kernel.Sort object at 0x1ca6d40>) of role type named setadjoinIL_type
% Using role type
% Declaring setadjoinIL:Prop
% FOF formula (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))) of role definition named setadjoinIL
% A new definition: (((eq Prop) setadjoinIL) (forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))))
% Defined: setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x1dc3f38>, <kernel.Sort object at 0x1ca6d40>) of role type named setadjoinE_type
% Using role type
% Declaring setadjoinE:Prop
% FOF formula (((eq Prop) setadjoinE) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi)))))) of role definition named setadjoinE
% A new definition: (((eq Prop) setadjoinE) (forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi))))))
% Defined: setadjoinE:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi)))))
% FOF formula (<kernel.Constant object at 0x1dc3830>, <kernel.Sort object at 0x1ca6d40>) of role type named in__Cong_type
% Using role type
% Declaring in__Cong:Prop
% FOF formula (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))) of role definition named in__Cong
% A new definition: (((eq Prop) in__Cong) (forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))))
% Defined: in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B))))))
% FOF formula (<kernel.Constant object at 0x2071638>, <kernel.Sort object at 0x1ca6d40>) of role type named notinself2_type
% Using role type
% Declaring notinself2:Prop
% FOF formula (((eq Prop) notinself2) (forall (A:fofType) (B:fofType), (((in A) B)->(((in B) A)->False)))) of role definition named notinself2
% A new definition: (((eq Prop) notinself2) (forall (A:fofType) (B:fofType), (((in A) B)->(((in B) A)->False))))
% Defined: notinself2:=(forall (A:fofType) (B:fofType), (((in A) B)->(((in B) A)->False)))
% FOF formula (<kernel.Constant object at 0x21bb8c0>, <kernel.DependentProduct object at 0x1dc3368>) of role type named omegaS_type
% Using role type
% Declaring omegaS:(fofType->fofType)
% FOF formula (((eq (fofType->fofType)) omegaS) (fun (Xx:fofType)=> ((setadjoin Xx) Xx))) of role definition named omegaS
% A new definition: (((eq (fofType->fofType)) omegaS) (fun (Xx:fofType)=> ((setadjoin Xx) Xx)))
% Defined: omegaS:=(fun (Xx:fofType)=> ((setadjoin Xx) Xx))
% FOF formula (setadjoinIL->(setadjoinE->(in__Cong->(notinself2->(forall (Xx:fofType), (((in Xx) omega)->(forall (Xy:fofType), (((in Xy) omega)->((((eq fofType) (omegaS Xx)) (omegaS Xy))->(((eq fofType) Xx) Xy)))))))))) of role conjecture named peanoSinj
% Conjecture to prove = (setadjoinIL->(setadjoinE->(in__Cong->(notinself2->(forall (Xx:fofType), (((in Xx) omega)->(forall (Xy:fofType), (((in Xy) omega)->((((eq fofType) (omegaS Xx)) (omegaS Xy))->(((eq fofType) Xx) Xy)))))))))):Prop
% We need to prove ['(setadjoinIL->(setadjoinE->(in__Cong->(notinself2->(forall (Xx:fofType), (((in Xx) omega)->(forall (Xy:fofType), (((in Xy) omega)->((((eq fofType) (omegaS Xx)) (omegaS Xy))->(((eq fofType) Xx) Xy))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter omega:fofType.
% Definition setadjoinIL:=(forall (Xx:fofType) (Xy:fofType), ((in Xx) ((setadjoin Xx) Xy))):Prop.
% Definition setadjoinE:=(forall (Xx:fofType) (A:fofType) (Xy:fofType), (((in Xy) ((setadjoin Xx) A))->(forall (Xphi:Prop), (((((eq fofType) Xy) Xx)->Xphi)->((((in Xy) A)->Xphi)->Xphi))))):Prop.
% Definition in__Cong:=(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((iff ((in Xx) A)) ((in Xy) B)))))):Prop.
% Definition notinself2:=(forall (A:fofType) (B:fofType), (((in A) B)->(((in B) A)->False))):Prop.
% Definition omegaS:=(fun (Xx:fofType)=> ((setadjoin Xx) Xx)):(fofType->fofType).
% Trying to prove (setadjoinIL->(setadjoinE->(in__Cong->(notinself2->(forall (Xx:fofType), (((in Xx) omega)->(forall (Xy:fofType), (((in Xy) omega)->((((eq fofType) (omegaS Xx)) (omegaS Xy))->(((eq fofType) Xx) Xy))))))))))
% Found x50:=(x5 (fun (x6:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x6:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x6:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 x6:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x5 (fun (x6:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x6:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x6:(P Xx)
% Instantiate: a:=Xx:fofType
% Found x6 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x50:=(x5 (fun (x7:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x6:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x6 as proof of (P0 a)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x6:(P b)
% Found x6 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 x6:(P Xy)
% Found x6 as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x6:(P Xx)
% Instantiate: a:=Xx:fofType
% Found x6 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Found x5 as proof of (((eq fofType) (omegaS Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found ((eq_ref fofType) b) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x50:=(x5 (fun (x7:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x6:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x6 as proof of (P0 a)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x6:(P Xy)
% Instantiate: a:=Xy:fofType
% Found x6 as proof of (P0 a)
% Found x50:=(x5 (fun (x6:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x6:(P b)
% Found x6 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref000:=(eq_ref00 P1):((P1 Xy)->(P1 Xy))
% Found (eq_ref00 P1) as proof of (P2 Xy)
% Found ((eq_ref0 Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found (((eq_ref fofType) Xy) P1) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x6:(P1 Xy)
% Instantiate: b:=Xy:fofType
% Found x6 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xy)
% Found x50:=(x5 (fun (x7:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found x6:(P b)
% Found x6 as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found ((eq_ref fofType) Xx) as proof of (P Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x6:(((eq fofType) Xy0) Xx0)
% Instantiate: Xy0:=Xx:fofType;Xx0:=Xy:fofType
% Found (fun (x6:(((eq fofType) Xy0) Xx0))=> x6) as proof of Xphi
% Found (fun (x6:(((eq fofType) Xy0) Xx0))=> x6) as proof of ((((eq fofType) Xy0) Xx0)->Xphi)
% Found x60:=(x6 A):((in Xy0) ((setadjoin Xy0) A))
% Found (x6 A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 b))):((P1 b)->(P1 b))
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found (x5 (fun (x6:fofType)=> (P1 b))) as proof of (P2 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 x50:=(x5 (fun (x6:fofType)=> (P0 Xy))):((P0 Xy)->(P0 Xy))
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found (x5 (fun (x6:fofType)=> (P0 Xy))) as proof of (P1 Xy)
% Found x6:(P Xy)
% Found x6 as proof of (P0 Xy)
% Found x6:(P b)
% Found x6 as proof of (P0 Xy)
% Found x70:=(x7 A):((in Xy0) ((setadjoin Xy0) A))
% Found (x7 A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P b))):((P b)->(P b))
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found (x5 (fun (x6:fofType)=> (P b))) as proof of (P0 b)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 x6:(P Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P0 b0)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P Xy)
% Found x6 as proof of (P0 Xy)
% Found x6:(((eq fofType) Xy0) Xx0)
% Instantiate: Xy0:=Xy:fofType;Xx0:=Xx:fofType
% Found (fun (x6:(((eq fofType) Xy0) Xx0))=> x6) as proof of Xphi
% Found (fun (x6:(((eq fofType) Xy0) Xx0))=> x6) as proof of ((((eq fofType) Xy0) Xx0)->Xphi)
% Found x60:=(x6 A):((in Xy0) ((setadjoin Xy0) A))
% Found (x6 A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P Xx)
% Instantiate: b0:=Xx:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (P b0)
% Found ((eq_ref fofType) Xx) as proof of (P b0)
% Found ((eq_ref fofType) Xx) as proof of (P b0)
% Found ((eq_ref fofType) Xx) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x70:=(x7 A):((in Xy0) ((setadjoin Xy0) A))
% Found (x7 A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found ((x Xy0) A) as proof of ((in Xy0) ((setadjoin Xx0) A))
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found x50:=(x5 (fun (x6:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x6:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found x7:(P1 Xy)
% Instantiate: b0:=Xy:fofType
% Found x7 as proof of (P2 b0)
% 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 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found x50:=(x5 (fun (x6:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x5 (fun (x6:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) 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 x6:(P b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P0 Xy)
% Instantiate: b0:=Xy:fofType
% Found x6 as proof of (P1 b0)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found ((eq_ref fofType) b) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 x6:(P1 b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x6:(P1 b)
% Instantiate: b0:=b:fofType
% Found x6 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P b0))):((P b0)->(P b0))
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 b0)
% Found (x5 (fun (x6:fofType)=> (P b0))) as proof of (P0 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) 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 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found ((eq_ref fofType) Xy) as proof of (P Xy)
% Found x7:(P1 b)
% Instantiate: b0:=b:fofType
% Found x7 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x6:(P1 Xy)
% Instantiate: a:=Xy:fofType
% Found x6 as proof of (P2 a)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b)
% Found x6:(P1 Xy)
% Instantiate: a:=Xy:fofType
% Found x6 as proof of (P2 a)
% Found x5:(((eq fofType) (omegaS Xx)) (omegaS Xy))
% Instantiate: a:=(omegaS Xx):fofType;b0:=(omegaS Xy):fofType
% Found x5 as proof of (((eq fofType) a) b0)
% Found x6:(P b)
% Instantiate: a:=b:fofType
% Found x6 as proof of (P0 a)
% Found x6:(P1 b)
% Found x6 as proof of (P2 Xx)
% Found x6:(P1 b)
% Found x6 as proof of (P2 Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b1)
% Found x50:=(x5 (fun (x6:fofType)=> (P2 Xy))):((P2 Xy)->(P2 Xy))
% Found (x5 (fun (x6:fofType)=> (P2 Xy))) as proof of (P3 Xy)
% Found (x5 (fun (x6:fofType)=> (P2 Xy))) as proof of (P3 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found x50:=(x5 (fun (x6:fofType)=> (P2 Xy))):((P2 Xy)->(P2 Xy))
% Found (x5 (fun (x6:fofType)=> (P2 Xy))) as proof of (P3 Xy)
% Found (x5 (fun (x6:fofType)=> (P2 Xy))) as proof of (P3 Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P1 b0)
% Found ((eq_ref fofType) b) as proof of (P1 b0)
% Found ((eq_ref fofType) b) as proof of (P1 b0)
% Found ((eq_ref fofType) b) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found x50:=(x5 (fun (x7:fofType)=> (P1 Xy))):((P1 Xy)->(P1 Xy))
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% Found (x5 (fun (x7:fofType)=> (P1 Xy))) as proof of (P2 Xy)
% 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 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Fou
% EOF
%------------------------------------------------------------------------------