%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ALG279^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n114.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:18:22 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : ALG279^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n114.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:05:51 CDT 2014
% % CPUTime  : 300.01 
% 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 0x18d5c68>, <kernel.Type object at 0x18d5c20>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0x1ab31b8>, <kernel.DependentProduct object at 0x18d5638>) of role type named cGRP_RIGHT_INVERSE_type
% Using role type
% Declaring cGRP_RIGHT_INVERSE:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0x18d5a70>, <kernel.DependentProduct object at 0x18d55a8>) of role type named cGRP_RIGHT_UNIT_type
% Using role type
% Declaring cGRP_RIGHT_UNIT:((g->(g->g))->(g->Prop))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))) of role definition named cGRP_RIGHT_INVERSE_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))))
% Defined: cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))) of role definition named cGRP_RIGHT_UNIT_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_RIGHT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))))
% Defined: cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))
% FOF formula (forall (Xf:(g->(g->g))) (Xe:g), (((and ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))) of role conjecture named cE13A2A
% Conjecture to prove = (forall (Xf:(g->(g->g))) (Xe:g), (((and ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))):Prop
% Parameter g_DUMMY:g.
% We need to prove ['(forall (Xf:(g->(g->g))) (Xe:g), (((and ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))))']
% Parameter g:Type.
% Definition cGRP_RIGHT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xa) Xb)) Xe))))):((g->(g->g))->(g->Prop)).
% Definition cGRP_RIGHT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))):((g->(g->g))->(g->Prop)).
% Trying to prove (forall (Xf:(g->(g->g))) (Xe:g), (((and ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))))
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found x0:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found x2:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found x0:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x4:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x0:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x2:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found x30:=(x3 Xa):(((eq g) ((Xf Xa) Xe)) Xa)
% Instantiate: b:=Xa:g
% Found x30 as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x4:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found x40:=(x4 Xa):(((eq g) ((Xf Xa) Xe)) Xa)
% Instantiate: b:=Xa:g
% Found x40 as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x0:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found x40:=(x4 Xa):(((eq g) ((Xf Xa) Xe)) Xa)
% Instantiate: b:=Xa:g
% Found x40 as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x2:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf ((Xf Xa0) x2)) Xa)):(((eq g) ((Xf ((Xf Xa0) x2)) Xa)) ((Xf ((Xf Xa0) x2)) Xa))
% Found (eq_ref0 ((Xf ((Xf Xa0) x2)) Xa)) as proof of (((eq g) ((Xf ((Xf Xa0) x2)) Xa)) b)
% Found ((eq_ref g) ((Xf ((Xf Xa0) x2)) Xa)) as proof of (((eq g) ((Xf ((Xf Xa0) x2)) Xa)) b)
% Found ((eq_ref g) ((Xf ((Xf Xa0) x2)) Xa)) as proof of (((eq g) ((Xf ((Xf Xa0) x2)) Xa)) b)
% Found ((eq_ref g) ((Xf ((Xf Xa0) x2)) Xa)) as proof of (((eq g) ((Xf ((Xf Xa0) x2)) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found x30:=(x3 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x30 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xe) Xa))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xa)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (fun (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (P b)
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(P b))
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of ((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->(P b)))
% Found (and_rect10 (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (fun (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))))) as proof of (P b)
% Found (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))))) as proof of (((cGRP_RIGHT_INVERSE Xf) Xe)->(P b))
% Found (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))))) as proof of (((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))->(((cGRP_RIGHT_INVERSE Xf) Xe)->(P b)))
% Found (and_rect00 (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))))) as proof of (P b)
% Found ((and_rect0 (P b)) (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))))) as proof of (P b)
% Found (((fun (P0:Type) (x0:(((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))->(((cGRP_RIGHT_INVERSE Xf) Xe)->P0)))=> (((((and_rect ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)) P0) x0) x)) (P b)) (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))))) as proof of (P b)
% Found (((fun (P0:Type) (x0:(((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))->(((cGRP_RIGHT_INVERSE Xf) Xe)->P0)))=> (((((and_rect ((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)) P0) x0) x)) (P b)) (fun (x0:((and (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe))) (x1:((cGRP_RIGHT_INVERSE Xf) Xe))=> (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))))) as proof of (P b)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (fun (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (P b)
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(P b))
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of ((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->(P b)))
% Found (and_rect10 (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found x30:=(x3 Xe):(((eq g) ((Xf Xe) Xe)) Xe)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (x3 Xe) as proof of (((eq g) ((Xf Xe) b)) b)
% Found (eq_sym010 (x3 Xe)) as proof of (P b)
% Found ((eq_sym01 b) (x3 Xe)) as proof of (P b)
% Found (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)) as proof of (P b)
% Found (fun (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (P b)
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of (((cGRP_RIGHT_UNIT Xf) Xe)->(P b))
% Found (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe))) as proof of ((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->(P b)))
% Found (and_rect10 (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found ((and_rect1 (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found (((fun (P0:Type) (x2:((forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))->(((cGRP_RIGHT_UNIT Xf) Xe)->P0)))=> (((((and_rect (forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) ((cGRP_RIGHT_UNIT Xf) Xe)) P0) x2) x0)) (P b)) (fun (x2:(forall (Xb:g) (Xc:g) (Xa0:g), (((eq g) ((Xf ((Xf Xa0) Xb)) Xc)) ((Xf Xa0) ((Xf Xb) Xc))))) (x3:((cGRP_RIGHT_UNIT Xf) Xe))=> (((eq_sym0 ((Xf Xe) b)) b) (x3 Xe)))) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found (((eq_ref g) b) P) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found x30:=(x3 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x30 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found x30:=(x3 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x30 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found x40:=(x4 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x40 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x0:(P Xa)
% Instantiate: b:=Xa:g
% Found x0 as proof of (P0 b)
% Found x40:=(x4 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x40 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found x40:=(x4 ((Xf Xe) Xa)):(((eq g) ((Xf ((Xf Xe) Xa)) Xe)) ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x40 as proof of (((eq g) ((Xf ((Xf Xe) Xa)) Xe)) b)
% Found x2:(P Xa)
% Instantiate: b:=Xa:g
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) b0)
% Found ((eq_ref g) b) as proof of (((eq g) b) b0)
% Found ((eq_ref g) b) as proof of (((eq g) b) b0)
% Found ((eq_ref g) b) as proof of (((eq g) b) b0)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found ((eq_ref g) b0) as proof of (((eq g) b0) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found x4:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x4 as proof of (P0 b)
% Found x2000:=(x200 Xa):(((eq g) ((Xf ((Xf Xa) Xe)) Xe)) ((Xf Xa) ((Xf Xe) Xe)))
% Found (x200 Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found ((x20 Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x2 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x2 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x2 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found x0:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x0 as proof of (P0 b)
% Found x3000:=(x300 Xa):(((eq g) ((Xf ((Xf Xa) Xe)) Xe)) ((Xf Xa) ((Xf Xe) Xe)))
% Found (x300 Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found ((x30 Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found x2:(P ((Xf Xe) Xa))
% Instantiate: b:=((Xf Xe) Xa):g
% Found x2 as proof of (P0 b)
% Found x3000:=(x300 Xa):(((eq g) ((Xf ((Xf Xa) Xe)) Xe)) ((Xf Xa) ((Xf Xe) Xe)))
% Found (x300 Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found ((x30 Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found (((x3 Xe) Xe) Xa) as proof of (((eq g) ((Xf ((Xf Xa) Xe)) Xe)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found eq_ref000:=(eq_ref00 P):((P Xa)->(P Xa))
% Found (eq_ref00 P) as proof of (P0 Xa)
% Found ((eq_ref0 Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found (((eq_ref g) Xa) P) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 a):(((eq g) a) a)
% Found (eq_ref0 a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found ((eq_ref g) a) as proof of (((eq g) a) Xe)
% Found eq_ref00:=(eq_ref0 ((Xf Xe) Xa)):(((eq g) ((Xf Xe) Xa)) ((Xf Xe) Xa))
% Found (eq_ref0 ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found ((eq_ref g) ((Xf Xe) Xa)) as proof of (((eq g) ((Xf Xe) Xa)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found ((eq_ref g) b) as proof of (((eq g) b) Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xe) Xa))
% Found eq_ref00:=(eq_ref0 Xa):(((eq g) Xa) Xa)
% Found (eq_ref0 Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% Found ((eq_ref g) Xa) as proof of (((eq g) Xa) b)
% F
% EOF
%------------------------------------------------------------------------------