%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU918^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n092.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:22 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU918^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n092.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 11:42:46 CDT 2014
% % CPUTime  : 300.09 
% 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 0x25dfef0>, <kernel.Constant object at 0x25dfcb0>) of role type named b
% Using role type
% Declaring b:fofType
% FOF formula (<kernel.Constant object at 0x2b42830>, <kernel.Single object at 0x25dfd88>) of role type named a
% Using role type
% Declaring a:fofType
% FOF formula ((not (((eq fofType) a) b))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xf (Xg Xx)))) (fun (Xx:fofType)=> (Xg (Xf Xx)))))->False)) of role conjecture named cTHM197_pme
% Conjecture to prove = ((not (((eq fofType) a) b))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xf (Xg Xx)))) (fun (Xx:fofType)=> (Xg (Xf Xx)))))->False)):Prop
% We need to prove ['((not (((eq fofType) a) b))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xf (Xg Xx)))) (fun (Xx:fofType)=> (Xg (Xf Xx)))))->False))']
% Parameter fofType:Type.
% Parameter b:fofType.
% Parameter a:fofType.
% Trying to prove ((not (((eq fofType) a) b))->((forall (Xf:(fofType->fofType)) (Xg:(fofType->fofType)), (((eq (fofType->fofType)) (fun (Xx:fofType)=> (Xf (Xg Xx)))) (fun (Xx:fofType)=> (Xg (Xf Xx)))))->False))
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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) 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 x1:(P a)
% Instantiate: b0:=a: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 eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 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 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) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 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 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) 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 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 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_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% 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 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) 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P a)
% Instantiate: b0:=a: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 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 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 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) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 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 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 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) 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 x1:(P a)
% Instantiate: b0:=a: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 eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 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 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 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 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P a)
% Instantiate: a0:=a:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 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) 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 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 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 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) 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 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 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 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 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 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 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 x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% Found (eq_ref00 P0) as proof of (P1 b)
% Found ((eq_ref0 b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x1:(P b)
% Instantiate: a0:=b:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found x1:(P b0)
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) 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) 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 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 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) 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 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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 (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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 x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) 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) 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 x1:(P a)
% Instantiate: b0:=a: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 a)
% Instantiate: b0:=a: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 b)
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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) 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 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P 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 eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_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 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 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_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found eq_ref00:=(eq_ref0 b000):(((eq fofType) b000) b000)
% Found (eq_ref0 b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found x1:(P a)
% Instantiate: a0:=a:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 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) 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 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 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) 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 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 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 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 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) 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 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 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 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 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 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% Found (eq_ref00 P0) as proof of (P1 b)
% Found ((eq_ref0 b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x1:(P b)
% Instantiate: a0:=b:fofType
% Found x1 as proof of (P0 a0)
% Found eq_ref00:=(eq_ref0 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found x1:(P b0)
% Found x1 as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) 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) 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 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 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 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 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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 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 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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 (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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) 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P a)
% Instantiate: a0:=a:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found ((eq_ref fofType) b0) as proof of (P1 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found x1:(P b)
% Found x1 as proof of (P0 b)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 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 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 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 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_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 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 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) 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 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P 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 eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% 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 x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% Found (eq_ref00 P0) as proof of (P1 b)
% Found ((eq_ref0 b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found x1:(P b)
% Instantiate: a0:=b:fofType
% Found x1 as proof of (P0 a0)
% Found x1:(P b)
% Instantiate: a0:=b:fofType
% Found x1 as proof of (P0 a0)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found x1:(P b0)
% Found x1 as proof of (P0 a)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 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 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 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 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 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 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 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 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) 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 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found eq_ref00:=(eq_ref0 b000):(((eq fofType) b000) b000)
% Found (eq_ref0 b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 x1:(P1 b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P2 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 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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 (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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 (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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 (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% Found ((eq_ref fofType) b00) as proof of (P b00)
% 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) 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found (((eq_ref fofType) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b)
% Found x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% Found ((eq_ref fofType) a) as proof of (P a)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found x1:(P b0)
% Found x1 as proof of (P0 a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 x1:(P a)
% Instantiate: b0:=a: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 eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b)
% Found x1:(P b)
% Found x1 as proof of (P0 b)
% Found x1:(P b)
% Found x1 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P0):((P0 b)->(P0 b))
% Found (eq_ref00 P0) as proof of (P1 b)
% Found ((eq_ref0 b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found (((eq_ref fofType) b) P0) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b1)
% Found x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 b10):(((eq fofType) b10) b10)
% Found (eq_ref0 b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found ((eq_ref fofType) b10) as proof of (((eq fofType) b10) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b10)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P 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 eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P b1)
% Found ((eq_ref fofType) b1) as proof of (P 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 eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% 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) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% Found ((eq_ref fofType) b0) as proof of (P b00)
% 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) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% 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 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_ref000:=(eq_ref00 P):((P a)->(P a))
% Found (eq_ref00 P) as proof of (P0 a)
% Found ((eq_ref0 a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% Found (((eq_ref fofType) a) P) as proof of (P0 a)
% 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 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 (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found ((eq_ref fofType) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found x1:(P b)
% Instantiate: b1:=b: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 x1:(P b)
% Instantiate: b1:=b: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 eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 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 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% 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) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) b0)
% Found x1:(P b0)
% Instantiate: b00:=b0:fofType
% Found x1 as proof of (P0 b00)
% 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 x1:(P b)
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) 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) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref000:=(eq_ref00 P1):((P1 b0)->(P1 b0))
% Found (eq_ref00 P1) as proof of (P2 b0)
% Found ((eq_ref0 b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found (((eq_ref fofType) b0) P1) as proof of (P2 b0)
% Found eq_ref000:=(eq_ref00 P1):((P1 b)->(P1 b))
% Found (eq_ref00 P1) as proof of (P2 b)
% Found ((eq_ref0 b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found (((eq_ref fofType) b) P1) as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b01)
% Found eq_ref00:=(eq_ref0 b01):(((eq fofType) b01) b01)
% Found (eq_ref0 b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% Found ((eq_ref fofType) b01) as proof of (((eq fofType) b01) b00)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq fofType) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% Found ((eq_ref fofType) b1) as proof of (((eq fofType) b1) b)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found eq_ref00:=(eq_ref0 b000):(((eq fofType) b000) b000)
% Found (eq_ref0 b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found eq_ref00:=(eq_ref0 b00):(((eq fofType) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found ((eq_ref fofType) b00) as proof of (((eq fofType) b00) a)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b000)
% Found eq_ref00:=(eq_ref0 b000):(((eq fofType) b000) b000)
% Found (eq_ref0 b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found ((eq_ref fofType) b000) as proof of (((eq fofType) b000) b0)
% Found x1:(P a)
% Instantiate: a0:=a:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found eq_ref000:=(eq_ref00 P):((P b00)->(P b00))
% Found (eq_ref00 P) as proof of (P0 b00)
% Found ((eq_ref0 b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found (((eq_ref fofType) b00) P) as proof of (P0 b00)
% Found x1:(P a)
% Instantiate: a0:=a:fofType
% Found x1 as proof of (P0 a0)
% 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 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found ((eq_ref fofType) a0) as proof of (((eq fofType) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq fofType) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq fofType) a0) b0)
% EOF
%------------------------------------------------------------------------------