%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV343^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n102.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 13:34:04 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV343^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n102.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 08:53:16 CDT 2014
% % CPUTime  : 300.10 
% 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 0x2293bd8>, <kernel.Constant object at 0x22933f8>) of role type named y
% Using role type
% Declaring y:fofType
% FOF formula (<kernel.Constant object at 0x2293488>, <kernel.Single object at 0x2293a70>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x22935f0>, <kernel.DependentProduct object at 0x223fb90>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x22939e0>, <kernel.DependentProduct object at 0x223f0e0>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula ((forall (Xu:fofType), ((cGVB_M Xu)->((iff ((cGVB_IN Xu) x)) ((cGVB_IN Xu) y))))->(((eq fofType) x) y)) of role conjecture named cGVB_A3
% Conjecture to prove = ((forall (Xu:fofType), ((cGVB_M Xu)->((iff ((cGVB_IN Xu) x)) ((cGVB_IN Xu) y))))->(((eq fofType) x) y)):Prop
% We need to prove ['((forall (Xu:fofType), ((cGVB_M Xu)->((iff ((cGVB_IN Xu) x)) ((cGVB_IN Xu) y))))->(((eq fofType) x) y))']
% Parameter fofType:Type.
% Parameter y:fofType.
% Parameter x:fofType.
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_M:(fofType->Prop).
% Trying to prove ((forall (Xu:fofType), ((cGVB_M Xu)->((iff ((cGVB_IN Xu) x)) ((cGVB_IN Xu) y))))->(((eq fofType) x) y))
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P0 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P0 b))=> x00) as proof of (P0 x)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b))=> x00) as proof of ((P0 b)->(P0 x))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b))=> x00) as proof of (P b)
% Found x00:(P y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x000:(P y)
% Found (fun (x000:(P y))=> x000) as proof of (P y)
% Found (fun (x000:(P y))=> x000) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P0 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P0 b))=> x00) as proof of (P0 x)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b))=> x00) as proof of ((P0 b)->(P0 x))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b))=> x00) as proof of (P b)
% Found x00:(P y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found x00:(P x)
% Instantiate: a:=x:fofType
% Found x00 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P2 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P2 b))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of ((P2 b)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P2 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P2 b))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of ((P2 b)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of (P1 b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x000:(P y)
% Found (fun (x000:(P y))=> x000) as proof of (P y)
% Found (fun (x000:(P y))=> x000) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x000:(P y)
% Found (fun (x000:(P y))=> x000) as proof of (P y)
% Found (fun (x000:(P y))=> x000) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P y)
% Instantiate: a:=y:fofType
% Found x00 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P b)
% Found x1 as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x1:(P y)
% Found x1 as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found x000:(P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P2 b)
% Found x000:(P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P2 b)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P0 x)
% Found (fun (x00:(P0 x))=> x00) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of (P x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x000:(P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 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 x1:(P0 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x000:(P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 y)
% Found (fun (x1:(P0 y))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of ((P0 y)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of (P y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% 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) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found x00:(P x)
% Instantiate: a:=x:fofType
% Found x00 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P2 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P2 b))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of ((P2 b)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P2 b)
% Instantiate: b:=x:fofType
% Found (fun (x00:(P2 b))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of ((P2 b)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b))=> x00) as proof of (P1 b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x00:(P y)
% Instantiate: a:=y:fofType
% Found x00 as proof of (P0 a)
% Found x000:(P y)
% Found (fun (x000:(P y))=> x000) as proof of (P y)
% Found (fun (x000:(P y))=> x000) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x00:(P y)
% Instantiate: a:=y:fofType
% Found x00 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P b)
% Found x1 as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x00:(P1 y)
% Instantiate: b:=y:fofType
% Found x00 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x00:(P b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found x000:(P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P1 y)
% Found (fun (x000:(P1 y))=> x000) as proof of (P2 y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P b)
% Found x1 as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P0 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x00:(P0 b0))=> x00) as proof of (P0 x)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b0))=> x00) as proof of ((P0 b0)->(P0 x))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 b0))=> x00) as proof of (P b0)
% Found x1:(P y)
% Found x1 as proof of (P0 y)
% Found x00:(P b)
% Found x00 as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x000:(P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P0 x)
% Found (fun (x00:(P0 x))=> x00) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of (P x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P0 x)
% Found (fun (x00:(P0 x))=> x00) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of (P x)
% Found x000:(P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P1 b)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x000:(P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P0 b)
% Found (fun (x000:(P0 b))=> x000) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P0 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x1:(P y)
% Instantiate: b0:=y:fofType
% Found x1 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 x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P x)
% Instantiate: b0:=x:fofType
% Found x00 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P y)
% Found x1 as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found x000:(P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P0 x)
% Instantiate: b0:=x:fofType
% Found (fun (x00:(P0 x))=> x00) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of ((P0 x)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x00:(P0 x))=> x00) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 y)
% Found (fun (x1:(P0 y))=> x1) as proof of (P0 b)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of ((P0 y)->(P0 b))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of (P y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 y)
% Found (fun (x1:(P0 y))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of ((P0 y)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of (P y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x000:(P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P2 b)
% Found x000:(P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P1 b)
% Found (fun (x000:(P1 b))=> x000) as proof of (P2 b)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x1:(P0 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P0 b0))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of ((P0 b0)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b0))=> x1) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) as proof of (P0 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P1 y)
% Instantiate: a:=y:fofType
% Found x00 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found x00:(P1 y)
% Instantiate: a:=y:fofType
% Found x00 as proof of (P2 a)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b00)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b00)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b00)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% 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 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 x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 y)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 y))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> 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) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x000:(P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P b0)
% Found (fun (x000:(P b0))=> x000) as proof of (P0 b0)
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 a)
% Found x1:(P1 b)
% Found x1 as proof of (P2 x)
% Found x1:(P1 b)
% Found x1 as proof of (P2 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P b)
% Instantiate: a:=b:fofType
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P0 y)
% Found (fun (x1:(P0 y))=> x1) as proof of (P0 y)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of ((P0 y)->(P0 y))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 y))=> x1) as proof of (P y)
% Found x01:(P1 x)
% Instantiate: b0:=x:fofType
% Found x01 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x01:(P2 x)
% Instantiate: b0:=x:fofType
% Found (fun (x01:(P2 x))=> x01) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x01:(P2 x))=> x01) as proof of ((P2 x)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x01:(P2 x))=> x01) as proof of (P1 b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x10:(P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P b0)
% Found (fun (x10:(P b0))=> x10) as proof of (P0 b0)
% Found x1:(P b0)
% Instantiate: b1:=b0:fofType
% Found x1 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x10:(P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P1 y)
% Found (fun (x10:(P1 y))=> x10) as proof of (P2 y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found x00:(P1 b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P1 b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found x1:(P1 y)
% Instantiate: b0:=y:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x1:(P b0)
% Found x1 as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b00)
% Found x00:(P0 b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) y)
% Found x10:(P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P1 a)
% Found (fun (x10:(P1 a))=> x10) as proof of (P2 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 x10:(P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P2 b0)
% Found x10:(P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P2 b0)
% Found x10:(P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P1 b0)
% Found (fun (x10:(P1 b0))=> x10) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x00:(P2 b0))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of ((P2 b0)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x00:(P2 b0)
% Instantiate: b0:=x:fofType
% Found (fun (x00:(P2 b0))=> x00) as proof of (P2 x)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of ((P2 b0)->(P2 x))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 b0))=> x00) as proof of (P1 b0)
% Found x20:(P1 y)
% Found (fun (x20:(P1 y))=> x20) as proof of (P1 y)
% Found (fun (x20:(P1 y))=> x20) as proof of (P2 y)
% Found x00:(P1 b)
% Found x00 as proof of (P2 y)
% Found x00:(P1 b)
% Found x00 as proof of (P2 y)
% Found x1:(P1 y)
% Found x1 as proof of (P2 y)
% Found x1:(P y)
% Instantiate: a:=y:fofType
% Found x1 as proof of (P0 a)
% Found x1:(P1 y)
% Found x1 as proof of (P2 y)
% Found x1:(P y)
% Instantiate: a:=y:fofType
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) a)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) 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) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% 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) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) y)
% 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 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b0)
% Found x20:(P1 b0)
% Found (fun (x20:(P1 b0))=> x20) as proof of (P1 b0)
% Found (fun (x20:(P1 b0))=> x20) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 x10:(P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P4 y)
% Found x10:(P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P4 y)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found x1:(P0 b1)
% Instantiate: b1:=x:fofType
% Found (fun (x1:(P0 b1))=> x1) as proof of (P0 b0)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b1))=> x1) as proof of ((P0 b1)->(P0 b0))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b1))=> x1) as proof of (P b1)
% Found x000:(P3 b)
% Found (fun (x000:(P3 b))=> x000) as proof of (P3 b)
% Found (fun (x000:(P3 b))=> x000) as proof of (P4 b)
% Found x10:(P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P3 y)
% Found (fun (x10:(P3 y))=> x10) as proof of (P4 y)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P2 x)
% Found (fun (x00:(P2 x))=> x00) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of ((P2 x)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of (P1 x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P2 x)
% Found (fun (x00:(P2 x))=> x00) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of ((P2 x)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of (P1 x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P2 x)
% Found (fun (x00:(P2 x))=> x00) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of ((P2 x)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of (P1 x)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x00:(P2 x)
% Found (fun (x00:(P2 x))=> x00) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of ((P2 x)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x00:(P2 x))=> x00) as proof of (P1 x)
% Found x20:(P1 b0)
% Found (fun (x20:(P1 b0))=> x20) as proof of (P1 b0)
% Found (fun (x20:(P1 b0))=> x20) as proof of (P2 b0)
% Found x1:(P y)
% Instantiate: b1:=y:fofType
% Found x1 as proof of (P0 b1)
% 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 x00:(P b0)
% Instantiate: b1:=b0:fofType
% Found x00 as proof of (P0 b1)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b1)
% Found x000:(P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P3 b)
% Found x000:(P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P2 b)
% Found (fun (x000:(P2 b))=> x000) as proof of (P3 b)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b2)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b2)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b2)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b2)
% Found eq_ref00:=(eq_ref0 b2):(((eq fofType) b2) b2)
% Found (eq_ref0 b2) as proof of (((eq fofType) b2) y)
% Found ((eq_ref fofType) b2) as proof of (((eq fofType) b2) y)
% Found ((eq_ref fofType) b2) as proof of (((eq fofType) b2) y)
% Found ((eq_ref fofType) b2) as proof of (((eq fofType) b2) y)
% Found x010:(P1 x)
% Found (fun (x010:(P1 x))=> x010) as proof of (P1 x)
% Found (fun (x010:(P1 x))=> x010) as proof of (P2 x)
% 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 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x10:(P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P1 b)
% Found (fun (x10:(P1 b))=> x10) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) y)
% 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) 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 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b1)
% 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 x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 y)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 y))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> 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 x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 y)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 y))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b0)
% Found x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 b)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 b))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> 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 x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 y)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 y))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> 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 x1:(P2 b0)
% Instantiate: b0:=y:fofType
% Found (fun (x1:(P2 b0))=> x1) as proof of (P2 y)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of ((P2 b0)->(P2 y))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b0))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 y):(((eq fofType) y) y)
% Found (eq_ref0 y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found ((eq_ref fofType) y) as proof of (((eq fofType) y) b0)
% Found x1:(P2 b)
% Instantiate: b0:=b:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 b0)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 b0))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as
% EOF
%------------------------------------------------------------------------------