%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : ALG298^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n187.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 13:18:23 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  : ALG298^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n187.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 09:10:56 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 0x1f65bd8>, <kernel.Type object at 0x1f64a70>) of role type named c_type
% Using role type
% Declaring c:Type
% FOF formula (<kernel.Constant object at 0x1fc2878>, <kernel.Type object at 0x1f64830>) of role type named b_type
% Using role type
% Declaring b:Type
% FOF formula (<kernel.Constant object at 0x1f65908>, <kernel.Type object at 0x1f64950>) of role type named a_type
% Using role type
% Declaring a:Type
% FOF formula (<kernel.Constant object at 0x1f653b0>, <kernel.DependentProduct object at 0x1f646c8>) of role type named c_starc
% Using role type
% Declaring c_starc:(c->(c->c))
% FOF formula (<kernel.Constant object at 0x1f65908>, <kernel.DependentProduct object at 0x1f64dd0>) of role type named c_starb
% Using role type
% Declaring c_starb:(b->(b->b))
% FOF formula (<kernel.Constant object at 0x1f65bd8>, <kernel.DependentProduct object at 0x1f64a70>) of role type named c_stara
% Using role type
% Declaring c_stara:(a->(a->a))
% FOF formula (forall (Xf:(a->b)) (Xg:(a->c)) (Xh:(b->c)), (((and ((and ((and (forall (Xx:a), (((eq c) (Xh (Xf Xx))) (Xg Xx)))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> (((eq b) (Xf Xx)) Xy)))))) (forall (Xx:a) (Xy:a), (((eq b) (Xf ((c_stara Xx) Xy))) ((c_starb (Xf Xx)) (Xf Xy)))))) (forall (Xx:a) (Xy:a), (((eq c) (Xg ((c_stara Xx) Xy))) ((c_starc (Xg Xx)) (Xg Xy)))))->(forall (Xx:b) (Xy:b), (((eq c) (Xh ((c_starb Xx) Xy))) ((c_starc (Xh Xx)) (Xh Xy)))))) of role conjecture named cTHM270_pme
% Conjecture to prove = (forall (Xf:(a->b)) (Xg:(a->c)) (Xh:(b->c)), (((and ((and ((and (forall (Xx:a), (((eq c) (Xh (Xf Xx))) (Xg Xx)))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> (((eq b) (Xf Xx)) Xy)))))) (forall (Xx:a) (Xy:a), (((eq b) (Xf ((c_stara Xx) Xy))) ((c_starb (Xf Xx)) (Xf Xy)))))) (forall (Xx:a) (Xy:a), (((eq c) (Xg ((c_stara Xx) Xy))) ((c_starc (Xg Xx)) (Xg Xy)))))->(forall (Xx:b) (Xy:b), (((eq c) (Xh ((c_starb Xx) Xy))) ((c_starc (Xh Xx)) (Xh Xy)))))):Prop
% Parameter c_DUMMY:c.
% Parameter b_DUMMY:b.
% Parameter a_DUMMY:a.
% We need to prove ['(forall (Xf:(a->b)) (Xg:(a->c)) (Xh:(b->c)), (((and ((and ((and (forall (Xx:a), (((eq c) (Xh (Xf Xx))) (Xg Xx)))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> (((eq b) (Xf Xx)) Xy)))))) (forall (Xx:a) (Xy:a), (((eq b) (Xf ((c_stara Xx) Xy))) ((c_starb (Xf Xx)) (Xf Xy)))))) (forall (Xx:a) (Xy:a), (((eq c) (Xg ((c_stara Xx) Xy))) ((c_starc (Xg Xx)) (Xg Xy)))))->(forall (Xx:b) (Xy:b), (((eq c) (Xh ((c_starb Xx) Xy))) ((c_starc (Xh Xx)) (Xh Xy))))))']
% Parameter c:Type.
% Parameter b:Type.
% Parameter a:Type.
% Parameter c_starc:(c->(c->c)).
% Parameter c_starb:(b->(b->b)).
% Parameter c_stara:(a->(a->a)).
% Trying to prove (forall (Xf:(a->b)) (Xg:(a->c)) (Xh:(b->c)), (((and ((and ((and (forall (Xx:a), (((eq c) (Xh (Xf Xx))) (Xg Xx)))) (forall (Xy:b), ((ex a) (fun (Xx:a)=> (((eq b) (Xf Xx)) Xy)))))) (forall (Xx:a) (Xy:a), (((eq b) (Xf ((c_stara Xx) Xy))) ((c_starb (Xf Xx)) (Xf Xy)))))) (forall (Xx:a) (Xy:a), (((eq c) (Xg ((c_stara Xx) Xy))) ((c_starc (Xg Xx)) (Xg Xy)))))->(forall (Xx:b) (Xy:b), (((eq c) (Xh ((c_starb Xx) Xy))) ((c_starc (Xh Xx)) (Xh Xy))))))
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found x0:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x0:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x2:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x0:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found x2:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x4:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x0:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x2:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x2:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found x0:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found x4:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq c) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x6:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found x0:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x2:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found x4:(P (Xh ((c_starb Xx) Xy)))
% Instantiate: b0:=(Xh ((c_starb Xx) Xy)):c
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found x4:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x4:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x4 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x0:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found x2:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x2:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x2 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq c) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found ((eq_ref c) a0) as proof of (((eq c) a0) (Xh Xy))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 a0):(((eq b) a0) a0)
% Found (eq_ref0 a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found ((eq_ref b) a0) as proof of (((eq b) a0) ((c_starb Xx) Xy))
% Found eq_ref000:=(eq_ref00 P):((P (Xh ((c_starb Xx) Xy)))->(P (Xh ((c_starb Xx) Xy))))
% Found (eq_ref00 P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref0 (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found (((eq_ref c) (Xh ((c_starb Xx) Xy))) P) as proof of (P0 (Xh ((c_starb Xx) Xy)))
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref000:=(eq_ref00 P):((P b0)->(P b0))
% Found (eq_ref00 P) as proof of (P0 b0)
% Found ((eq_ref0 b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found (((eq_ref c) b0) P) as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b1):(((eq c) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq c) b1) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b1) as proof of (((eq c) b1) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b1) as proof of (((eq c) b1) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b1) as proof of (((eq c) b1) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) b1)
% Found ((eq_ref c) b0) as proof of (((eq c) b0) b1)
% Found ((eq_ref c) b0) as proof of (((eq c) b0) b1)
% Found ((eq_ref c) b0) as proof of (((eq c) b0) b1)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq c) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref000:=(eq_ref00 P):((P ((c_starc (Xh Xx)) (Xh Xy)))->(P ((c_starc (Xh Xx)) (Xh Xy))))
% Found (eq_ref00 P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found (((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) P) as proof of (P0 ((c_starc (Xh Xx)) (Xh Xy)))
% Found x6:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found ((eq_ref c) b0) as proof of (P b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) ((c_starc (Xh Xx)) (Xh Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b1)
% Found eq_ref00:=(eq_ref0 b1):(((eq c) b1) b1)
% Found (eq_ref0 b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found ((eq_ref c) b1) as proof of (((eq c) b1) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))):(((eq c) ((c_starc (Xh Xx)) (Xh Xy))) ((c_starc (Xh Xx)) (Xh Xy)))
% Found (eq_ref0 ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found ((eq_ref c) ((c_starc (Xh Xx)) (Xh Xy))) as proof of (((eq c) ((c_starc (Xh Xx)) (Xh Xy))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq c) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found ((eq_ref c) b0) as proof of (((eq c) b0) (Xh ((c_starb Xx) Xy)))
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b00)
% Found eq_ref00:=(eq_ref0 b00):(((eq c) b00) b00)
% Found (eq_ref0 b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found ((eq_ref c) b00) as proof of (((eq c) b00) ((c_starc (Xh Xx)) (Xh Xy)))
% Found x0:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x0 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x6:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found x6:(P ((c_starc (Xh Xx)) (Xh Xy)))
% Instantiate: b0:=((c_starc (Xh Xx)) (Xh Xy)):c
% Found x6 as proof of (P0 b0)
% Found eq_ref00:=(eq_ref0 (Xh ((c_starb Xx) Xy))):(((eq c) (Xh ((c_starb Xx) Xy))) (Xh ((c_starb Xx) Xy)))
% Found (eq_ref0 (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_starb Xx) Xy))) as proof of (((eq c) (Xh ((c_starb Xx) Xy))) b0)
% Found ((eq_ref c) (Xh ((c_st
% EOF
%------------------------------------------------------------------------------