%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU930^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n105.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 13:33:23 EDT 2014

% Result   : Timeout 300.07s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU930^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.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 11:43:06 CDT 2014
% % CPUTime  : 300.07 
% 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 0x151a758>, <kernel.DependentProduct object at 0x151a518>) of role type named f
% Using role type
% Declaring f:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x176ab00>, <kernel.DependentProduct object at 0x151a7a0>) of role type named g
% Using role type
% Declaring g:(fofType->fofType)
% FOF formula ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->(forall (Xx:fofType), (((and (((eq fofType) (g Xx)) Xx)) (forall (Xz:fofType), ((((eq fofType) (g Xz)) Xz)->(((eq fofType) Xz) Xx))))->(((eq fofType) (f Xx)) Xx)))) of role conjecture named cTHM171A_pme
% Conjecture to prove = ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->(forall (Xx:fofType), (((and (((eq fofType) (g Xx)) Xx)) (forall (Xz:fofType), ((((eq fofType) (g Xz)) Xz)->(((eq fofType) Xz) Xx))))->(((eq fofType) (f Xx)) Xx)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->(forall (Xx:fofType), (((and (((eq fofType) (g Xx)) Xx)) (forall (Xz:fofType), ((((eq fofType) (g Xz)) Xz)->(((eq fofType) Xz) Xx))))->(((eq fofType) (f Xx)) Xx))))']
% Parameter fofType:Type.
% Parameter f:(fofType->fofType).
% Parameter g:(fofType->fofType).
% Trying to prove ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->(forall (Xx:fofType), (((and (((eq fofType) (g Xx)) Xx)) (forall (Xz:fofType), ((((eq fofType) (g Xz)) Xz)->(((eq fofType) Xz) Xx))))->(((eq fofType) (f Xx)) Xx))))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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 x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (g Xx)))):((P (g Xx))->(P (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x3:=(x (fun (x3:(fofType->fofType))=> (P (g Xx)))):((P (g Xx))->(P (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x1 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 x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:(P (f Xx))
% Instantiate: Xz:=(f Xx):fofType
% Found x3 as proof of (P0 Xz)
% Found x1:(P (f Xx))
% Instantiate: Xz:=(f Xx):fofType
% Found x1 as proof of (P0 Xz)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x2 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (f Xx)))):((P (f Xx))->(P (f Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x10:=(x1 (fun (x3:fofType)=> (P (f Xx)))):((P (f Xx))->(P (f Xx)))
% Found (x1 (fun (x3:fofType)=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found (x1 (fun (x3:fofType)=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x2 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x3:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x3 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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 x1:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x1 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) 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 x1:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) 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) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found x3:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x3 as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:(P (f (g Xx)))
% Instantiate: b:=(f (g Xx)):fofType
% Found x3 as proof of (P0 b)
% Found x3:(P (g (f Xx)))
% Instantiate: b:=(g (f Xx)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x2 as proof of (((eq fofType) (g Xx)) b)
% Found x1:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x2 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x1:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x1:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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 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 x3:(P (g (f Xx)))
% Instantiate: b:=(g (f Xx)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x3:(P (g (f (g Xx))))
% Instantiate: b:=(g (f (g Xx))):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x1:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x1:(fofType->fofType))=> (P Xx))) 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) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 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) 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 x3:=(x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))):((P (g (g Xx)))->(P (g (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))) as proof of (P0 (g (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))) as proof of (P0 (g (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x2 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x10:=(x1 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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) 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 x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))):((P (g (g Xx)))->(P (g (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))) as proof of (P0 (g (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g (g Xx))))) as proof of (P0 (g (g Xx)))
% Found x3:(P (g Xx))
% Instantiate: b:=(g Xx):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x3:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) 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 x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x3:(P (g Xx))
% Instantiate: b:=(g Xx):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) b) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) 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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x2 as proof of (((eq fofType) a) Xx)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x2 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g b)) b)
% Found (eq_sym010 x1) as proof of (P b)
% Found ((eq_sym01 b) x1) as proof of (P b)
% Found (((eq_sym0 (g b)) b) x1) as proof of (P b)
% Found (((eq_sym0 (g b)) b) x1) as proof of (P b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b0)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b0)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b0)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found x3:(P (g Xx))
% Instantiate: b:=(g Xx):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x1:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x1:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))):((P1 (g Xx))->(P1 (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))) as proof of (P2 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))) as proof of (P2 (g Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f 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 x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) 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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) 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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (g Xx))):(((eq fofType) (g (g Xx))) (g (g Xx)))
% Found (eq_ref0 (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found ((eq_ref fofType) (g (g Xx))) as proof of (((eq fofType) (g (g Xx))) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->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 x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:(P (f (g Xx)))
% Instantiate: b:=(f (g Xx)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found x3:(P (f (g Xx)))
% Instantiate: b:=(f (g Xx)):fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) 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 x10:=(x1 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g 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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b0)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b0)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b0)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found x10:=(x1 (fun (x3:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x3:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x3:=(x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))):((P1 (g Xx))->(P1 (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))) as proof of (P2 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (g Xx)))) as proof of (P2 (g Xx))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g b)) b)
% Found (eq_sym010 x1) as proof of (P b)
% Found ((eq_sym01 b) x1) as proof of (P b)
% Found (((eq_sym0 (g b)) b) x1) as proof of (P b)
% Found (((eq_sym0 (g b)) b) x1) as proof of (P 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x3:=(x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))):((P1 (f (g Xx)))->(P1 (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))) as proof of (P2 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))) as proof of (P2 (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))):((P1 (f (g Xx)))->(P1 (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))) as proof of (P2 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P1 (f (g Xx))))) as proof of (P2 (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% 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 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (g Xx)))):((P (g Xx))->(P (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g 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) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x10:=(x1 (fun (x3:fofType)=> (P (f Xx)))):((P (f Xx))->(P (f Xx)))
% Found (x1 (fun (x3:fofType)=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found (x1 (fun (x3:fofType)=> (P (f Xx)))) as proof of (P0 (f Xx))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (g Xx)))):((P (g Xx))->(P (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (g Xx))
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:(P (f (g Xx)))
% Instantiate: b:=(f (g Xx)):fofType
% Found x3 as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% 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 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x2 as proof of (((eq fofType) a) Xx)
% Found x2:(((eq fofType) (g Xx)) Xx)
% Instantiate: a:=(g Xx):fofType
% Found x2 as proof of (((eq fofType) a) 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (g Xx)))):((P (g Xx))->(P (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P (g Xx)))) as proof of (P0 (g Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found x3:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x3 as proof of (P0 b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x3:(fofType->fofType))=> (P b))) 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 x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f 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 x3:=(x (fun (x3:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P b))):((P b)->(P b))
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found (x (fun (x3:(fofType->fofType))=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g b)):(((eq fofType) (g b)) (g b))
% Found (eq_ref0 (g b)) as proof of (((eq fofType) (g b)) b0)
% Found ((eq_ref fofType) (g b)) as proof of (((eq fofType) (g b)) b0)
% Found ((eq_ref fofType) (g b)) as proof of (((eq fofType) (g b)) b0)
% Found ((eq_ref fofType) (g b)) as proof of (((eq fofType) (g 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 x3:(P (f (g Xx)))
% Instantiate: b:=(f (g Xx)):fofType
% Found x3 as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g Xx)))
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (g Xx)))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=(g Xx):fofType
% Found x1 as proof of (((eq fofType) b) Xx)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Found x1 as proof of (((eq fofType) (g Xx)) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g Xx))
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b0)
% Found x3:(P (f Xx))
% Instantiate: b:=(f Xx):fofType
% Found x3 as proof of (P0 b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xx)) b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found eq_ref00:=(eq_ref0 (f Xx)):(((eq fofType) (f Xx)) (f Xx))
% Found (eq_ref0 (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found ((eq_ref fofType) (f Xx)) as proof of (((eq fofType) (f Xx)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 x3:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found x1:(((eq fofType) (g Xx)) Xx)
% Instantiate: Xz:=Xx:fofType
% Found x1 as proof of (((eq fofType) (g Xz)) Xz)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f 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 (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 (g (f (g Xx)))):(((eq fofType) (g (f (g Xx)))) (g (f (g Xx))))
% Found (eq_ref0 (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found ((eq_ref fofType) (g (f (g Xx)))) as proof of (((eq fofType) (g (f (g Xx)))) b)
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found x3:=(x (fun (x3:(fofType->fofType))=> (P Xx))):((P Xx)->(P Xx))
% Found (x (fun (x3:(fofType->fofType))=> (P Xx))) as proof of (P0 Xx)
% Found (x (fun (x3:(fofType->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 x3:=(x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))):((P (f (g Xx)))->(P (f (g Xx))))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found (x (fun (x3:(fofType->fofType))=> (P (f (g Xx))))) as proof of (P0 (f (g Xx)))
% Found x1:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f Xx))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f 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 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f (g Xx))))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g Xx))
% Found eq_ref00:=(eq_ref0 (f (g Xx))):(((eq fofType) (f (g Xx))) (f (g Xx)))
% Found (eq_ref0 (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found ((eq_ref fofType) (f (g Xx))) as proof of (((eq fofType) (f (g Xx))) b)
% Found eq_ref00:=(eq_ref0 (g (f Xx))):(((eq fofType) (g (f Xx))) (g (f Xx)))
% Found (eq_ref0 (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g (f Xx))) as proof of (((eq fofType) (g (f Xx))) b)
% Found ((eq_ref fofType) (g 
% EOF
%------------------------------------------------------------------------------