%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ALG284^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n180.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 13:18:22 EDT 2014

% Result   : Timeout 300.03s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : ALG284^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n180.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 09:07:41 CDT 2014
% % CPUTime  : 300.03 
% 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 0x20d9cf8>, <kernel.DependentProduct object at 0x1fa1cb0>) of role type named cJ
% Using role type
% Declaring cJ:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0x20d93f8>, <kernel.DependentProduct object at 0x1fa1cb0>) of role type named cP
% Using role type
% Declaring cP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x20d9cf8>, <kernel.Single object at 0x229c518>) of role type named cE
% Using role type
% Declaring cE:fofType
% FOF formula (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType) (Y:fofType), (((eq fofType) (cJ ((cP X) Y))) ((cP (cJ Y)) (cJ X))))) of role conjecture named cTHM18_pme
% Conjecture to prove = (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType) (Y:fofType), (((eq fofType) (cJ ((cP X) Y))) ((cP (cJ Y)) (cJ X))))):Prop
% We need to prove ['(((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType) (Y:fofType), (((eq fofType) (cJ ((cP X) Y))) ((cP (cJ Y)) (cJ X)))))']
% Parameter fofType:Type.
% Parameter cJ:(fofType->fofType).
% Parameter cP:(fofType->(fofType->fofType)).
% Parameter cE:fofType.
% Trying to prove (((and ((and (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz))))) (forall (Xx:fofType), (((eq fofType) ((cP cE) Xx)) Xx)))) (forall (Xy:fofType), (((eq fofType) ((cP (cJ Xy)) Xy)) cE)))->(forall (X:fofType) (Y:fofType), (((eq fofType) (cJ ((cP X) Y))) ((cP (cJ Y)) (cJ X)))))
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found x2:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x0:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% 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 (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x4:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x2:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x2:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found x2:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found x0:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found x4:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x4 as proof of (P0 b)
% Found x30:=(x3 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x30 as proof of (((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) 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 (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x40 as proof of (((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) b)
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found x2:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x2 as proof of (P0 b)
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x40 as proof of (((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% 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 x4:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found x4:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found x4:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found x0:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found x2:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found x2:(P ((cP (cJ Y)) (cJ X)))
% Instantiate: b:=((cP (cJ Y)) (cJ X)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) (cJ X))
% Found eq_ref00:=(eq_ref0 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% 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 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found x30:=(x3 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x30 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found x30:=(x3 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x30 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found x4:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))):(((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X)))))
% Found (eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x40 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x40 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x40 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found x40:=(x4 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP cE) ((cP (cJ Y)) (cJ X)))) ((cP (cJ Y)) (cJ X)))
% Instantiate: a:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x40 as proof of (((eq fofType) a) ((cP (cJ Y)) (cJ X)))
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))):(((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X)))))
% Found (eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found x2:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))):(((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X)))))
% Found (eq_ref0 ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found ((eq_ref fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) as proof of (((eq fofType) ((cP cE) ((cP cE) ((cP (cJ Y)) (cJ X))))) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) ((cP X) Y))
% Found x4:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x4 as proof of (P0 b)
% Found x2000:=(x200 (cJ X)):(((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) ((cP cE) ((cP (cJ Y)) (cJ X))))
% Instantiate: b:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x2000 as proof of (((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref000:=(eq_ref00 P):((P (cJ ((cP X) Y)))->(P (cJ ((cP X) Y))))
% Found (eq_ref00 P) as proof of (P0 (cJ ((cP X) Y)))
% Found ((eq_ref0 (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% Found (((eq_ref fofType) (cJ ((cP X) Y))) P) as proof of (P0 (cJ ((cP X) Y)))
% 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 x3000:=(x300 (cJ X)):(((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) ((cP cE) ((cP (cJ Y)) (cJ X))))
% Instantiate: b:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x3000 as proof of (((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) b)
% Found x0:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x0 as proof of (P0 b)
% Found x3000:=(x300 (cJ X)):(((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) ((cP cE) ((cP (cJ Y)) (cJ X))))
% Instantiate: b:=((cP cE) ((cP (cJ Y)) (cJ X))):fofType
% Found x3000 as proof of (((eq fofType) ((cP ((cP cE) (cJ Y))) (cJ X))) b)
% Found x2:(P (cJ ((cP X) Y)))
% Instantiate: b:=(cJ ((cP X) Y)):fofType
% Found x2 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) b)
% Found ((eq_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 (cJ ((cP X) Y))):(((eq fofType) (cJ ((cP X) Y))) (cJ ((cP X) Y)))
% Found (eq_ref0 (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found ((eq_ref fofType) (cJ ((cP X) Y))) as proof of (((eq fofType) (cJ ((cP X) Y))) b0)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found eq_ref000:=(eq_ref00 P):((P ((cP (cJ Y)) (cJ X)))->(P ((cP (cJ Y)) (cJ X))))
% Found (eq_ref00 P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found ((eq_ref0 ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% Found (((eq_ref fofType) ((cP (cJ Y)) (cJ X))) P) as proof of (P0 ((cP (cJ Y)) (cJ X)))
% 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) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofType) ((cP (cJ Y)) (cJ X))) ((cP (cJ Y)) (cJ X)))
% Found (eq_ref0 ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found ((eq_ref fofType) ((cP (cJ Y)) (cJ X))) as proof of (((eq fofType) ((cP (cJ Y)) (cJ X))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (cJ ((cP X) Y)))
% Found eq_ref00:=(eq_ref0 ((cP (cJ Y)) (cJ X))):(((eq fofT
% EOF
%------------------------------------------------------------------------------