%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV273^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n107.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:33:58 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV273^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n107.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:41:41 CDT 2014
% % CPUTime  : 300.02 
% 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 0x28ba128>, <kernel.Type object at 0x2864cf8>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x28c5248>, <kernel.DependentProduct object at 0x2864dd0>) of role type named cR
% Using role type
% Declaring cR:(a->(a->Prop))
% FOF formula ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a), ((cR Xx) Xx))) of role conjecture named cTHM542_pme
% Conjecture to prove = ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a), ((cR Xx) Xx))):Prop
% Parameter a_DUMMY:a.
% We need to prove ['((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a), ((cR Xx) Xx)))']
% Parameter a:Type.
% Parameter cR:(a->(a->Prop)).
% Trying to prove ((forall (X:(a->Prop)), (((ex a) (fun (Xz:a)=> (X Xz)))->((ex a) (fun (Xz:a)=> ((and ((and (X Xz)) (forall (Xx:a), ((X Xx)->((cR Xz) Xx))))) (forall (Xy:a), (((and (X Xy)) (forall (Xx:a), ((X Xx)->((cR Xy) Xx))))->(((eq a) Xy) Xz))))))))->(forall (Xx:a), ((cR Xx) 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 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) 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 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 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 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) 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) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% 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 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% 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) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% 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) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% 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 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b0)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% 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) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% 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) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% 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 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found ((eq_ref a) b) as proof of (((eq a) b) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) a0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b0)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b00)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found eq_ref00:=(eq_ref0 a00):(((eq a) a00) a00)
% Found (eq_ref0 a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found ((eq_ref a) a00) as proof of (((eq a) a00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b00):(((eq a) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found ((eq_ref a) b00) as proof of (((eq a) b00) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b)
% Found eq_ref00:=(eq_ref0 a0):(((eq a) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found ((eq_ref a) a0) as proof of (((eq a) a0) b1)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 Xx):(((eq a) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found ((eq_ref a) Xx) as proof of (((eq a) Xx) b2)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% Found (eq_ref0 b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found ((eq_ref a) b) as proof of (((eq a) b) b01)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b0):(((eq a) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found ((eq_ref a) b0) as proof of (((eq a) b0) b2)
% Found eq_ref00:=(eq_ref0 b1):(((eq a) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a) b1) as proof of (((eq a) b1) Xx)
% Found ((eq_ref a
% EOF
%------------------------------------------------------------------------------