%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU919^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n103.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 13:33:22 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU919^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n103.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 11:42:46 CDT 2014
% % CPUTime  : 300.00 
% 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 0xcd2758>, <kernel.Constant object at 0xcd2c20>) of role type named a
% Using role type
% Declaring a:fofType
% FOF formula (<kernel.Constant object at 0xf105a8>, <kernel.DependentProduct object at 0xcd0488>) of role type named f
% Using role type
% Declaring f:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xcd26c8>, <kernel.DependentProduct object at 0xcd0e18>) of role type named g
% Using role type
% Declaring g:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xcd2638>, <kernel.DependentProduct object at 0xcd0488>) of role type named cP
% Using role type
% Declaring cP:(fofType->Prop)
% FOF formula ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->((cP (f (g a)))->(cP (g (f a))))) of role conjecture named cTHM127_pme
% Conjecture to prove = ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->((cP (f (g a)))->(cP (g (f a))))):Prop
% We need to prove ['((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->((cP (f (g a)))->(cP (g (f a)))))']
% Parameter fofType:Type.
% Parameter a:fofType.
% Parameter f:(fofType->fofType).
% Parameter g:(fofType->fofType).
% Parameter cP:(fofType->Prop).
% Trying to prove ((((eq (fofType->fofType)) (fun (Xx:fofType)=> (f (g Xx)))) (fun (Xx:fofType)=> (g (f Xx))))->((cP (f (g a)))->(cP (g (f a)))))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (cP (f (g a))))):((cP (f (g a)))->(cP (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (cP (f (g a))))) as proof of (P (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (cP (f (g a))))) as proof of (P (f (g a)))
% Found x0:(cP (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (cP (f (g a))))):((cP (f (g a)))->(cP (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (cP (f (g a))))) as proof of (P (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (cP (f (g a))))) as proof of (P (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x0:(cP (f (g a)))
% Instantiate: a0:=(f (g a)):fofType
% Found x0 as proof of (P a0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (g (f a)))
% Instantiate: b:=(g (f a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x0:(P0 (g (f a)))
% Instantiate: b:=(g (f a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (g (f a)))
% Instantiate: b:=(g (f a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x0:(P0 (g (f a)))
% Instantiate: b:=(g (f a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (g a))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found ((eq_ref fofType) b) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x1:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x1 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 a0))):((P0 a0)->(P0 a0))
% Found (x (fun (x1:(fofType->fofType))=> (P0 a0))) as proof of (P1 a0)
% Found (x (fun (x1:(fofType->fofType))=> (P0 a0))) as proof of (P1 a0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Found x0 as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found x0:(P0 b)
% Found x0 as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found x1:(P0 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))):((P1 (g (f a)))->(P1 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))) as proof of (P2 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))) as proof of (P2 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))):((P1 (g (f a)))->(P1 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))) as proof of (P2 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P1 (g (f a))))) as proof of (P2 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: a0:=(g (f a)):fofType
% Found x0 as proof of (P1 a0)
% Found x0:(P0 (g (f a)))
% Instantiate: a0:=(g (f a)):fofType
% Found x0 as proof of (P1 a0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x0:(P2 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P2 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P2 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P2 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found x0:(cP (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq fofType) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found ((eq_ref fofType) b) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found ((eq_ref fofType) (f (g a))) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(cP (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (g a0)):(((eq fofType) (g a0)) (g a0))
% Found (eq_ref0 (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found ((eq_ref fofType) (g a0)) as proof of (((eq fofType) (g a0)) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 (f (g a)))
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 (f (g a)))
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 (f (g a)))
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 (f (g a)))
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 (f (g a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:(P0 (g (f a)))
% Instantiate: b0:=(g (f a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x1:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:(P0 (g (f a)))
% Found x0 as proof of (P1 (g (f a)))
% Found x0:(P0 (g (f a)))
% Found x0 as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found x0:(P0 (f (g a)))
% Instantiate: a0:=(f (g a)):fofType
% Found x0 as proof of (P1 a0)
% Found x0:(P0 (f (g a)))
% Instantiate: a0:=(f (g a)):fofType
% Found x0 as proof of (P1 a0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x1:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x1:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))):((P2 (g (f a)))->(P2 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))) as proof of (P3 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))) as proof of (P3 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))):((P2 (g (f a)))->(P2 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))) as proof of (P3 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (g (f a))))) as proof of (P3 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 b))):((P2 b)->(P2 b))
% Found (x (fun (x0:(fofType->fofType))=> (P2 b))) as proof of (P3 b)
% Found (x (fun (x0:(fofType->fofType))=> (P2 b))) as proof of (P3 b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 b))):((P2 b)->(P2 b))
% Found (x (fun (x0:(fofType->fofType))=> (P2 b))) as proof of (P3 b)
% Found (x (fun (x0:(fofType->fofType))=> (P2 b))) as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a0)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a0)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a0)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))):((P2 (f (g a)))->(P2 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))):((P2 (f (g a)))->(P2 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))):((P2 (f (g a)))->(P2 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))):((P2 (f (g a)))->(P2 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P2 (f (g a))))) as proof of (P3 (f (g a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) 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 x0:(P0 (f (g a)))
% Instantiate: b0:=(f (g a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) 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 x0:(P0 (f (g a)))
% Instantiate: b0:=(f (g a)):fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (P0 (g (f a)))
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 (g (f a)))
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 (g (f a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (P0 (g (f a)))
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 (g (f a)))
% Found ((eq_ref fofType) (g (f a))) as proof of (P0 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found ((eq_ref fofType) b0) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found ((eq_ref fofType) b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P0):((P0 (g (f a)))->(P0 (g (f a))))
% Found (eq_ref00 P0) as proof of (P1 (g (f a)))
% Found ((eq_ref0 (g (f a))) P0) as proof of (P1 (g (f a)))
% Found (((eq_ref fofType) (g (f a))) P0) as proof of (P1 (g (f a)))
% Found (((eq_ref fofType) (g (f a))) P0) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found x0:(P0 (f (g a)))
% Found x0 as proof of (P1 (f (g a)))
% Found x0:(P0 (f (g a)))
% Found x0 as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (f (g a)))
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b0))):((P0 b0)->(P0 b0))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b0))) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 b))):((P0 b)->(P0 b))
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found (x (fun (x0:(fofType->fofType))=> (P0 b))) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found eq_ref00:=(eq_ref0 a1):(((eq fofType) a1) a1)
% Found (eq_ref0 a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found ((eq_ref fofType) a1) as proof of (((eq fofType) a1) a0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b1)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found x0:(P0 (f (g a)))
% Instantiate: b:=(f (g a)):fofType
% Found x0 as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))):((P0 (g (f a)))->(P0 (g (f a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (g (f a))))) as proof of (P1 (g (f a)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found x0:=(x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))):((P0 (f (g a)))->(P0 (f (g a))))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found (x (fun (x0:(fofType->fofType))=> (P0 (f (g a))))) as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x0:(P0 b)
% Instantiate: b0:=b:fofType
% Found x0 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 (g (f a))):(((eq fofType) (g (f a))) (g (f a)))
% Found (eq_ref0 (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found ((eq_ref fofType) (g (f a))) as proof of (((eq fofType) (g (f a))) b0)
% Found x1:=(x (fun (x1:(fofType->fofType))=> (P0 a0))):((P0 a0)->(P0 a0))
% Found (x (fun (x1:(fofType->fofType))=> (P0 a0))) as proof of (P1 a0)
% Found (x (fun (x1:(fofType->fofType))=> (P0 a0))) as proof of (P1 a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) (g (f a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) (f a))
% Found x0:(P0 (g (f a)))
% Instantiate: a0:=(g (f a)):fofType
% Found x0 as proof of (P1 a0)
% Found x0:(P0 (g (f a)))
% Instantiate: a0:=(g (f a)):fofType
% Found x0 as proof of (P1 a0)
% Found x0:(P0 b)
% Found x0 as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found x0:(P0 b)
% Found x0 as proof of (P1 (f (g a)))
% Found eq_ref00:=(eq_ref0 (f (g a))):(((eq fofType) (f (g a))) (f (g a)))
% Found (eq_ref0 (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found ((eq_ref fofType) (f (g a))) as proof of (((eq fofType) (f (g a))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (g (f a)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f (g a)))
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType
% EOF
%------------------------------------------------------------------------------