TSTP Solution File: SET594^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SET594^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n095.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 13:30:47 EDT 2014

% Result   : Timeout 300.04s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SET594^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n095.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 10:13:36 CDT 2014
% % CPUTime  : 300.04 
% 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 0x14305a8>, <kernel.Type object at 0x14118c0>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), ((((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)->(forall (Xx:a), ((X Xx)->((or (Y Xx)) (Z Xx)))))) of role conjecture named cBOOL_PROP_53_pme
% Conjecture to prove = (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), ((((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)->(forall (Xx:a), ((X Xx)->((or (Y Xx)) (Z Xx)))))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['(forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), ((((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)->(forall (Xx:a), ((X Xx)->((or (Y Xx)) (Z Xx))))))']
% Parameter a:Type.
% Trying to prove (forall (X:(a->Prop)) (Y:(a->Prop)) (Z:(a->Prop)), ((((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)->(forall (Xx:a), ((X Xx)->((or (Y Xx)) (Z Xx))))))
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P b)
% Found (classic (Y Xx)) as proof of (P b)
% Found (classic (Y Xx)) as proof of (P 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P b)
% Found (classic (Z Xx)) as proof of (P b)
% Found (classic (Z Xx)) as proof of (P 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 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) 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 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) (Z Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Z Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Z Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Z Xx))
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P a0)
% Found (classic (Y Xx)) as proof of (P a0)
% Found (classic (Y Xx)) as proof of (P a0)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P a0)
% Found (classic (Y Xx)) as proof of (P a0)
% Found (classic (Y Xx)) as proof of (P a0)
% 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) (Y Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Y Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Y Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Y Xx))
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P a0)
% Found (classic (Z Xx)) as proof of (P a0)
% Found (classic (Z Xx)) as proof of (P a0)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P a0)
% Found (classic (Z Xx)) as proof of (P a0)
% Found (classic (Z Xx)) as proof of (P a0)
% 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) 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) 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) 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 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) 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) 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) 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) 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) 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 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b0)
% Found (classic (Y Xx)) as proof of (P0 b0)
% Found (classic (Y Xx)) 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) 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 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 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found (classic b) 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) 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 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 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 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 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 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 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) 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 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 (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y 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 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) 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y 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 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 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 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 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 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 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y 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) 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 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 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 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 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 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 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 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) 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% 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 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 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 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b0)
% Found (classic (Z Xx)) as proof of (P0 b0)
% Found (classic (Z Xx)) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% 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 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 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 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 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 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) 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 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 or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: b0:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of b0
% Found (or_introl00 or_ind) as proof of (P0 b0)
% Found ((or_introl0 (Y Xx)) or_ind) as proof of (P0 b0)
% Found (((or_introl b0) (Y Xx)) or_ind) as proof of (P0 b0)
% Found (((or_introl b0) (Y Xx)) or_ind) 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z 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 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) 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y 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 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) 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 or_comm_i0:=(or_comm_i (Z Xx)):(forall (B:Prop), (((or (Z Xx)) B)->((or B) (Z Xx))))
% Instantiate: b0:=(forall (B:Prop), (((or (Z Xx)) B)->((or B) (Z Xx)))):Prop
% Found or_comm_i0 as proof of b0
% Found (or_introl00 or_comm_i0) as proof of (P0 b0)
% Found ((or_introl0 (Z Xx)) or_comm_i0) as proof of (P0 b0)
% Found (((or_introl b0) (Z Xx)) or_comm_i0) as proof of (P0 b0)
% Found (((or_introl b0) (Z Xx)) or_comm_i0) 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 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 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 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found (classic b) 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 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y 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) 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 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 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 classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z 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 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 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 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 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found classic0:=(classic b):((or b) (not b))
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found (classic b) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y 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 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 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 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 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y 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 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) 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 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 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 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) 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 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found classic0:=(classic (Z a0)):((or (Z a0)) (not (Z a0)))
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found (classic (Z a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b)
% Found classic0:=(classic (Z Xx)):((or (Z Xx)) (not (Z Xx)))
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found (classic (Z Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Y a0)):(((eq Prop) (Y a0)) (Y a0))
% Found (eq_ref0 (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y a0)) b)
% Found ((eq_ref Prop) (Y a0)) as proof of (((eq Prop) (Y 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 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) 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Y Xx)):(((eq Prop) (Y Xx)) (Y Xx))
% Found (eq_ref0 (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y Xx)) b0)
% Found ((eq_ref Prop) (Y Xx)) as proof of (((eq Prop) (Y 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 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 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 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b0)
% Found (classic (Y Xx)) as proof of (P0 b0)
% Found (classic (Y Xx)) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) 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) 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 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 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 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 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 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 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z 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 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 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 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 (Z a0)):(((eq Prop) (Z a0)) (Z a0))
% Found (eq_ref0 (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found ((eq_ref Prop) (Z a0)) as proof of (((eq Prop) (Z a0)) b)
% Found classic0:=(classic (Y Xx)):((or (Y Xx)) (not (Y Xx)))
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found (classic (Y Xx)) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b)
% Found classic0:=(classic (Y a0)):((or (Y a0)) (not (Y a0)))
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 b)
% Found (classic (Y a0)) as proof of (P0 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 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) 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 x:(((eq (a->Prop)) (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz))))) X)
% Instantiate: b0:=(forall (P:((a->Prop)->Prop)), ((P (fun (Xz:a)=> ((or ((and (X Xz)) (Y Xz))) ((and (X Xz)) (Z Xz)))))->(P X))):Prop
% Found x as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Z Xx)):(((eq Prop) (Z Xx)) (Z Xx))
% Found (eq_ref0 (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% Found ((eq_ref Prop) (Z Xx)) as proof of (((eq Prop) (Z Xx)) b0)
% 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 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) 
% EOF
%------------------------------------------------------------------------------