%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : GRP001^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n090.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 13:22:18 EDT 2014

% Result   : Timeout 300.05s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : GRP001^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n090.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 07:24:11 CDT 2014
% % CPUTime  : 300.05 
% 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 0x20f5e18>, <kernel.DependentProduct object at 0x20f5a70>) of role type named cP
% Using role type
% Declaring cP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x252d488>, <kernel.Single object at 0x20f5a28>) of role type named e
% Using role type
% Declaring e:fofType
% FOF formula (((and ((and ((and (forall (Xx:fofType), (((eq fofType) ((cP e) Xx)) Xx))) (forall (Xy:fofType), (((eq fofType) ((cP Xy) e)) Xy)))) (forall (Xz:fofType), (((eq fofType) ((cP Xz) Xz)) e)))) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz)))))->(forall (Xa:fofType) (Xb:fofType), (((eq fofType) ((cP Xa) Xb)) ((cP Xb) Xa)))) of role conjecture named cGRP_COMM2
% Conjecture to prove = (((and ((and ((and (forall (Xx:fofType), (((eq fofType) ((cP e) Xx)) Xx))) (forall (Xy:fofType), (((eq fofType) ((cP Xy) e)) Xy)))) (forall (Xz:fofType), (((eq fofType) ((cP Xz) Xz)) e)))) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz)))))->(forall (Xa:fofType) (Xb:fofType), (((eq fofType) ((cP Xa) Xb)) ((cP Xb) Xa)))):Prop
% We need to prove ['(((and ((and ((and (forall (Xx:fofType), (((eq fofType) ((cP e) Xx)) Xx))) (forall (Xy:fofType), (((eq fofType) ((cP Xy) e)) Xy)))) (forall (Xz:fofType), (((eq fofType) ((cP Xz) Xz)) e)))) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz)))))->(forall (Xa:fofType) (Xb:fofType), (((eq fofType) ((cP Xa) Xb)) ((cP Xb) Xa))))']
% Parameter fofType:Type.
% Parameter cP:(fofType->(fofType->fofType)).
% Parameter e:fofType.
% Trying to prove (((and ((and ((and (forall (Xx:fofType), (((eq fofType) ((cP e) Xx)) Xx))) (forall (Xy:fofType), (((eq fofType) ((cP Xy) e)) Xy)))) (forall (Xz:fofType), (((eq fofType) ((cP Xz) Xz)) e)))) (forall (Xx:fofType) (Xy:fofType) (Xz:fofType), (((eq fofType) ((cP ((cP Xx) Xy)) Xz)) ((cP Xx) ((cP Xy) Xz)))))->(forall (Xa:fofType) (Xb:fofType), (((eq fofType) ((cP Xa) Xb)) ((cP Xb) Xa))))
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found x0:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found x2:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x0:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x0:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) 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 ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x4:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x2:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xb) Xa))->(P ((cP Xb) Xa)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xb) Xa))
% Found ((eq_ref0 ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found x0:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x2:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x2:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found x0:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xb)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xb) Xa))->(P ((cP Xb) Xa)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xb) Xa))
% Found ((eq_ref0 ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% 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 ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xb) Xa))
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xb) Xa))->(P ((cP Xb) Xa)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xb) Xa))
% Found ((eq_ref0 ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% 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 Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x6:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x6 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x0:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x2:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) 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 Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found x4:(P ((cP Xa) Xb))
% Instantiate: b:=((cP Xa) Xb):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xa) Xb))->(P ((cP Xa) Xb)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xa) Xb))
% Found ((eq_ref0 ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found (((eq_ref fofType) ((cP Xa) Xb)) P) as proof of (P0 ((cP Xa) Xb))
% Found eq_ref000:=(eq_ref00 P):((P ((cP Xb) Xa))->(P ((cP Xb) Xa)))
% Found (eq_ref00 P) as proof of (P0 ((cP Xb) Xa))
% Found ((eq_ref0 ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found (((eq_ref fofType) ((cP Xb) Xa)) P) as proof of (P0 ((cP Xb) Xa))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) 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) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found x4:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x4:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x0:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x2:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found x2:(P ((cP Xb) Xa))
% Instantiate: b:=((cP Xb) Xa):fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b)
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 ((cP Xb) Xa)):(((eq fofType) ((cP Xb) Xa)) ((cP Xb) Xa))
% Found (eq_ref0 ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found ((eq_ref fofType) ((cP Xb) Xa)) as proof of (((eq fofType) ((cP Xb) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xa) Xb))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xa)
% Found eq_ref00:=(eq_ref0 ((cP Xa) Xb)):(((eq fofType) ((cP Xa) Xb)) ((cP Xa) Xb))
% Found (eq_ref0 ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found ((eq_ref fofType) ((cP Xa) Xb)) as proof of (((eq fofType) ((cP Xa) Xb)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((cP Xb) Xa))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b
% EOF
%------------------------------------------------------------------------------