%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ALG278^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n188.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 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : ALG278^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.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 09:05:26 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 0xf15830>, <kernel.Type object at 0x14217a0>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0x1393170>, <kernel.DependentProduct object at 0x1421200>) of role type named cGROUP2_type
% Using role type
% Declaring cGROUP2:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0xf15830>, <kernel.DependentProduct object at 0x14211b8>) of role type named cGRP_ASSOC_type
% Using role type
% Declaring cGRP_ASSOC:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0xf15c68>, <kernel.DependentProduct object at 0x14216c8>) of role type named cGRP_LEFT_INVERSE_type
% Using role type
% Declaring cGRP_LEFT_INVERSE:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0xf15c68>, <kernel.DependentProduct object at 0x14214d0>) of role type named cGRP_LEFT_UNIT_type
% Using role type
% Declaring cGRP_LEFT_UNIT:((g->(g->g))->(g->Prop))
% FOF formula (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))) of role definition named cGRP_ASSOC_def
% A new definition: (((eq ((g->(g->g))->Prop)) cGRP_ASSOC) (fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))))
% Defined: cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe)))))) of role definition named cGRP_LEFT_INVERSE_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_INVERSE) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))))))
% Defined: cGRP_LEFT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe)))))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))) of role definition named cGRP_LEFT_UNIT_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGRP_LEFT_UNIT) (fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))))
% Defined: cGRP_LEFT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))
% FOF formula (((eq ((g->(g->g))->(g->Prop))) cGROUP2) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe)))) of role definition named cGROUP2_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGROUP2) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe))))
% Defined: cGROUP2:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe)))
% FOF formula (forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP2 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))) of role conjecture named cE12A1
% Conjecture to prove = (forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP2 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa)))):Prop
% Parameter g_DUMMY:g.
% We need to prove ['(forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP2 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))))']
% Parameter g:Type.
% Definition cGROUP2:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_LEFT_UNIT Xf) Xe))) ((cGRP_LEFT_INVERSE Xf) Xe))):((g->(g->g))->(g->Prop)).
% Definition cGRP_ASSOC:=(fun (Xf:(g->(g->g)))=> (forall (Xa:g) (Xb:g) (Xc:g), (((eq g) ((Xf ((Xf Xa) Xb)) Xc)) ((Xf Xa) ((Xf Xb) Xc))))):((g->(g->g))->Prop).
% Definition cGRP_LEFT_INVERSE:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), ((ex g) (fun (Xb:g)=> (((eq g) ((Xf Xb) Xa)) Xe))))):((g->(g->g))->(g->Prop)).
% Definition cGRP_LEFT_UNIT:=(fun (Xf:(g->(g->g))) (Xe:g)=> (forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))):((g->(g->g))->(g->Prop)).
% Trying to prove (forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP2 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xa) Xe)) Xa))))
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Instantiate: b:=((Xf Xa) Xe):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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe))
% Instantiate: b:=((Xf Xa) Xe):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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 x4:(P ((Xf Xa) Xe))
% Instantiate: b:=((Xf Xa) Xe):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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 x00:(P Xa)
% Found (fun (x00:(P Xa))=> x00) as proof of (P Xa)
% Found (fun (x00:(P Xa))=> x00) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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) 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 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x00:(P b)
% Found (fun (x00:(P b))=> x00) as proof of (P b)
% Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) 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 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x4:(P Xa)
% Instantiate: b:=Xa:g
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found x20:(P b)
% Found (fun (x20:(P b))=> x20) as proof of (P b)
% Found (fun (x20:(P b))=> x20) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found x20:(P Xa)
% Found (fun (x20:(P Xa))=> x20) as proof of (P Xa)
% Found (fun (x20:(P Xa))=> x20) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) ((Xf x2) Xa0))):(((eq g) ((Xf Xa) ((Xf x2) Xa0))) ((Xf Xa) ((Xf x2) Xa0)))
% Found (eq_ref0 ((Xf Xa) ((Xf x2) Xa0))) as proof of (((eq g) ((Xf Xa) ((Xf x2) Xa0))) b)
% Found ((eq_ref g) ((Xf Xa) ((Xf x2) Xa0))) as proof of (((eq g) ((Xf Xa) ((Xf x2) Xa0))) b)
% Found ((eq_ref g) ((Xf Xa) ((Xf x2) Xa0))) as proof of (((eq g) ((Xf Xa) ((Xf x2) Xa0))) b)
% Found ((eq_ref g) ((Xf Xa) ((Xf x2) Xa0))) as proof of (((eq g) ((Xf Xa) ((Xf x2) Xa0))) 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 x0:(P Xa)
% Instantiate: b:=Xa:g
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found eq_ref00:=(eq_ref0 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 x20:(P Xa)
% Found (fun (x20:(P Xa))=> x20) as proof of (P Xa)
% Found (fun (x20:(P Xa))=> x20) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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) 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 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% 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 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found eq_ref00:=(eq_ref0 b):(((eq g) b) b)
% Found (eq_ref0 b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 x20:(P Xa)
% Found (fun (x20:(P Xa))=> x20) as proof of (P Xa)
% Found (fun (x20:(P Xa))=> x20) as proof of (P0 Xa)
% Found eq_ref00:=(eq_ref0 b0):(((eq g) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% Found ((eq_ref g) b0) as proof of (((eq g) b0) ((Xf Xa) Xe))
% 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_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:(P b)
% Found (fun (x40:(P b))=> x40) as proof of (P b)
% Found (fun (x40:(P b))=> x40) 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) 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 ((Xf Xa) Xe)):(((eq g) ((Xf Xa) Xe)) ((Xf Xa) Xe))
% Found (eq_ref0 ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) b0)
% Found ((eq_ref g) ((Xf Xa) Xe)) as proof of (((eq g) ((Xf Xa) Xe)) 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 Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% Found ((eq_ref g) b) as proof of (((eq g) b) ((Xf Xa) Xe))
% 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 
% EOF
%------------------------------------------------------------------------------