%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV274^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n105.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:59 EDT 2014

% Result   : Timeout 300.08s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV274^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n105.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:41:56 CDT 2014
% % CPUTime  : 300.08 
% 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 0x17085f0>, <kernel.Type object at 0x1708200>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x17083b0>, <kernel.DependentProduct object at 0x16a9cf8>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx)))) of role conjecture named cTHM543_pme
% Conjecture to prove = ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx)))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))']
% Parameter a:Type.
% Parameter cR:(a->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a) (Xy:a), ((or ((cR Xx) Xy)) ((cR Xy) Xx))))
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of (P b)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cR Xy) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xy) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xy) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xy) Xx))
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cR Xx) Xy))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xx) Xy))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xx) Xy))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cR Xx) Xy))
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found ((eq_ref a) b) as proof of (((eq a) b) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of (P a0)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) a0)
% Found (classic ((cR Xx) Xy)) as proof of (P a0)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of (P a0)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) a0)
% Found (classic ((cR Xy) Xx)) as proof of (P a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) a0)):(((eq Prop) ((cR Xy) a0)) ((cR Xy) a0))
% Found (eq_ref0 ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found ((eq_ref Prop) ((cR Xy) a0)) as proof of (((eq Prop) ((cR Xy) a0)) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of (P0 b0)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of (P0 b)
% Found classic0:=(classic ((cR Xy) a0)):((or ((cR Xy) a0)) (not ((cR Xy) a0)))
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of (P0 b)
% Found classic0:=(classic ((cR a0) Xx)):((or ((cR a0) Xx)) (not ((cR a0) Xx)))
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b)
% Found (classic ((cR Xy) Xx)) as proof of (P0 b)
% Found classic0:=(classic ((cR Xy) a0)):((or ((cR Xy) a0)) (not ((cR Xy) a0)))
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of ((or ((cR Xy) a0)) b)
% Found (classic ((cR Xy) a0)) as proof of (P0 b)
% Found classic0:=(classic ((cR a0) Xx)):((or ((cR a0) Xx)) (not ((cR a0) Xx)))
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of ((or ((cR a0) Xx)) b)
% Found (classic ((cR a0) Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xy)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xy)):(((eq Prop) ((cR a0) Xy)) ((cR a0) Xy))
% Found (eq_ref0 ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found ((eq_ref Prop) ((cR a0) Xy)) as proof of (((eq Prop) ((cR a0) Xy)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) a0)):(((eq Prop) ((cR Xx) a0)) ((cR Xx) a0))
% Found (eq_ref0 ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found ((eq_ref Prop) ((cR Xx) a0)) as proof of (((eq Prop) ((cR Xx) a0)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found classic0:=(classic ((cR Xx) a0)):((or ((cR Xx) a0)) (not ((cR Xx) a0)))
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found classic0:=(classic ((cR Xx) a0)):((or ((cR Xx) a0)) (not ((cR Xx) a0)))
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of ((or ((cR Xx) a0)) b)
% Found (classic ((cR Xx) a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found ((eq_ref a) b) as proof of (((eq a) b) b0)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cR a0) Xx)):(((eq Prop) ((cR a0) Xx)) ((cR a0) Xx))
% Found (eq_ref0 ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found ((eq_ref Prop) ((cR a0) Xx)) as proof of (((eq Prop) ((cR a0) Xx)) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq a) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found ((eq_ref a) Xy) as proof of (((eq a) Xy) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b0)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of (P0 b0)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found classic0:=(classic ((cR Xy) Xx)):((or ((cR Xy) Xx)) (not ((cR Xy) Xx)))
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of ((or ((cR Xy) Xx)) b0)
% Found (classic ((cR Xy) Xx)) as proof of (P0 b0)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b)
% Found classic0:=(classic ((cR a0) Xy)):((or ((cR a0) Xy)) (not ((cR a0) Xy)))
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of ((or ((cR a0) Xy)) b)
% Found (classic ((cR a0) Xy)) as proof of (P0 b)
% Found classic0:=(classic ((cR Xx) Xy)):((or ((cR Xx) Xy)) (not ((cR Xx) Xy)))
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of ((or ((cR Xx) Xy)) b)
% Found (classic ((cR Xx) Xy)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xx)
% Found eq_ref00:=(eq_ref0 ((cR Xx) Xy)):(((eq Prop) ((cR Xx) Xy)) ((cR Xx) Xy))
% Found (eq_ref0 ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found ((eq_ref Prop) ((cR Xx) Xy)) as proof of (((eq Prop) ((cR Xx) Xy)) b)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xx) Xy))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xx) Xy))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xx) Xy))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found (eq_sym0000 ((eq_ref Prop) ((cR Xy) Xx))) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((cR Xy) Xx)):(((eq Prop) ((cR Xy) Xx)) ((cR Xy) Xx))
% Found (eq_ref0 ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found ((eq_ref Prop) ((cR Xy) Xx)) as proof of (((eq Prop) ((cR Xy) Xx)) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) Xy)
% Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of ((or b) b0)
% Found (classic b) as proof of (P0 b0)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b0:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b0
% Found (or_introl00 eq_sym) as proof of ((or b0) ((cR Xx) Xy))
% Found ((or_introl0 ((cR Xx) Xy)) eq_sym) as proof of ((or b0) ((cR Xx) Xy))
% Found (((or_introl b0) ((cR Xx) Xy)) eq_sym) as proof of ((or b0) ((cR Xx) Xy))
% Found (((or_introl b0) 
% EOF
%------------------------------------------------------------------------------