TSTP Solution File: ALG277^5 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ALG277^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n117.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 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : ALG277^5 : TPTP v6.1.0. Bugfixed v5.3.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n117.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 09:05:11 CDT 2014
% % CPUTime : 300.03
% 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 0xf000e0>, <kernel.Type object at 0xf00cb0>) of role type named g_type
% Using role type
% Declaring g:Type
% FOF formula (<kernel.Constant object at 0x1157ab8>, <kernel.DependentProduct object at 0xf00320>) of role type named cGROUP3_type
% Using role type
% Declaring cGROUP3:((g->(g->g))->(g->Prop))
% FOF formula (<kernel.Constant object at 0xbe55f0>, <kernel.DependentProduct object at 0xf00320>) of role type named cGRP_ASSOC_type
% Using role type
% Declaring cGRP_ASSOC:((g->(g->g))->Prop)
% FOF formula (<kernel.Constant object at 0xf00a28>, <kernel.DependentProduct object at 0xd1f320>) 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 0xf005a8>, <kernel.DependentProduct object at 0xf001b8>) 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))->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_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 (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))) of role definition named cGROUP3_def
% A new definition: (((eq ((g->(g->g))->(g->Prop))) cGROUP3) (fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe))))
% Defined: cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_INVERSE Xf) Xe)))
% FOF formula (forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP3 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa)))) of role conjecture named cE13A2
% Conjecture to prove = (forall (Xf:(g->(g->g))) (Xe:g), (((cGROUP3 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), (((cGROUP3 Xf) Xe)->(forall (Xa:g), (((eq g) ((Xf Xe) Xa)) Xa))))']
% Parameter g:Type.
% Definition cGROUP3:=(fun (Xf:(g->(g->g))) (Xe:g)=> ((and ((and (cGRP_ASSOC Xf)) ((cGRP_RIGHT_UNIT Xf) Xe))) ((cGRP_RIGHT_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_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), (((cGROUP3 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 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_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 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 ((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 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 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_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 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 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 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 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) 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 ((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 ((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 ((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 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)) 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 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 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 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 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 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 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 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 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 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) 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 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 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 ((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 ((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 ((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 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 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) 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_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)) 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_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 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_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 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 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_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 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 ((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 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 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 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 x40:(P Xa)
% Found (fun (x40:(P Xa))=> x40) as proof of (P Xa)
% Found (fun (x40:(P Xa))=> x40) 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 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) 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 ((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 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 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_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 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 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 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 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 x40:(P Xa)
% Found (fun (x40:(P Xa))=> x40) as proof of (P Xa)
% Found (fun (x40:(P Xa))=> x40) 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 x40:(P Xa)
% Found (fun (x40:(P Xa))=> x40) as proof of (P Xa)
% Found (fun (x40:(P Xa))=> x40) 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 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) 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 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
% EOF
%------------------------------------------------------------------------------