TSTP Solution File: NUM806^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM806^5 : TPTP v7.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n062.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:11:48 EST 2018
% Result : Timeout 294.00s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM806^5 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n062.star.cs.uiowa.edu
% 0.02/0.23 % Model : x86_64 x86_64
% 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.23 % Memory : 32218.625MB
% 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.23 % CPULimit : 300
% 0.02/0.23 % DateTime : Fri Jan 5 14:24:04 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.24 Python 2.7.13
% 3.21/3.44 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 3.21/3.44 FOF formula (<kernel.Constant object at 0x2b9d3c35bfc8>, <kernel.Type object at 0x2b9d3ca6d098>) of role type named n_type
% 3.21/3.44 Using role type
% 3.21/3.44 Declaring n:Type
% 3.21/3.44 FOF formula (<kernel.Constant object at 0x2b9d3c35b488>, <kernel.DependentProduct object at 0x2b9d3ca6d2d8>) of role type named c_star
% 3.21/3.44 Using role type
% 3.21/3.44 Declaring c_star:(n->(n->n))
% 3.21/3.44 FOF formula (<kernel.Constant object at 0x2b9d3c35bfc8>, <kernel.DependentProduct object at 0x2b9d3ca6d1b8>) of role type named c_plus
% 3.21/3.44 Using role type
% 3.21/3.44 Declaring c_plus:(n->(n->n))
% 3.21/3.44 FOF formula (<kernel.Constant object at 0x2b9d3c35bfc8>, <kernel.DependentProduct object at 0x2b9d3c3c1998>) of role type named cS
% 3.21/3.44 Using role type
% 3.21/3.44 Declaring cS:(n->n)
% 3.21/3.44 FOF formula (forall (Xx:n) (Xy:n), (((eq n) ((c_star Xx) (cS Xy))) ((c_plus ((c_star Xx) Xy)) Xx))) of role conjecture named cPA_4
% 3.21/3.44 Conjecture to prove = (forall (Xx:n) (Xy:n), (((eq n) ((c_star Xx) (cS Xy))) ((c_plus ((c_star Xx) Xy)) Xx))):Prop
% 3.21/3.44 Parameter n_DUMMY:n.
% 3.21/3.44 We need to prove ['(forall (Xx:n) (Xy:n), (((eq n) ((c_star Xx) (cS Xy))) ((c_plus ((c_star Xx) Xy)) Xx)))']
% 3.21/3.44 Parameter n:Type.
% 3.21/3.44 Parameter c_star:(n->(n->n)).
% 3.21/3.44 Parameter c_plus:(n->(n->n)).
% 3.21/3.44 Parameter cS:(n->n).
% 3.21/3.44 Trying to prove (forall (Xx:n) (Xy:n), (((eq n) ((c_star Xx) (cS Xy))) ((c_plus ((c_star Xx) Xy)) Xx)))
% 3.21/3.44 Found x2:(P ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found (fun (x2:(P ((c_star Xx) (cS Xy))))=> x2) as proof of (P ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found (fun (x2:(P ((c_star Xx) (cS Xy))))=> x2) as proof of (P0 ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 3.21/3.44 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 3.21/3.44 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 3.21/3.44 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 3.21/3.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 3.21/3.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 3.21/3.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found x:(P ((c_star Xx) (cS Xy)))
% 3.21/3.44 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 3.21/3.44 Found x as proof of (P0 b)
% 3.21/3.44 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 3.21/3.44 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 3.21/3.44 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 3.21/3.44 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 5.52/5.76 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 5.52/5.76 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 5.52/5.76 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 5.52/5.76 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 5.52/5.76 Found x:(P0 b)
% 5.52/5.76 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 5.52/5.76 Found (fun (x:(P0 b))=> x) as proof of (P0 ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 ((c_star Xx) (cS Xy))))
% 5.52/5.76 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of (P b)
% 5.52/5.76 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 5.52/5.76 Found x as proof of (P0 b)
% 5.52/5.76 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found x3:(P ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P0 ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 5.52/5.76 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 5.52/5.76 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 5.52/5.76 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 5.52/5.76 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 5.52/5.76 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 5.52/5.76 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 5.52/5.76 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 5.52/5.76 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 5.52/5.76 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 5.52/5.76 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 5.52/5.76 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 5.52/5.76 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 9.11/9.31 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 9.11/9.31 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 9.11/9.31 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 9.11/9.31 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 9.11/9.31 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 9.11/9.31 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 9.11/9.31 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 9.11/9.31 Found x2:(P b)
% 9.11/9.31 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 9.11/9.31 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 9.11/9.31 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 9.11/9.31 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 9.11/9.31 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 9.11/9.31 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 13.91/14.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 13.91/14.15 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 13.91/14.15 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 13.91/14.15 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 13.91/14.15 Found x2:(P ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found (fun (x2:(P ((c_star Xx) (cS Xy))))=> x2) as proof of (P ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found (fun (x2:(P ((c_star Xx) (cS Xy))))=> x2) as proof of (P0 ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 13.91/14.15 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 13.91/14.15 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 13.91/14.15 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 13.91/14.15 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 13.91/14.15 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 13.91/14.15 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found x2:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 13.91/14.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 13.91/14.15 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 13.91/14.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 13.91/14.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 13.91/14.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 13.91/14.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 17.81/18.02 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 17.81/18.02 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 17.81/18.02 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 17.81/18.02 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 17.81/18.02 Found x:(P ((c_star Xx) (cS Xy)))
% 17.81/18.02 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 17.81/18.02 Found x as proof of (P0 b)
% 17.81/18.02 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 17.81/18.02 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 17.81/18.02 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 17.81/18.02 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 17.81/18.02 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 17.81/18.02 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 17.81/18.02 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 17.81/18.02 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 17.81/18.02 Found x:(P0 b)
% 17.81/18.02 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 22.32/22.57 Found (fun (x:(P0 b))=> x) as proof of (P0 ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 ((c_star Xx) (cS Xy))))
% 22.32/22.57 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of (P b)
% 22.32/22.57 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 22.32/22.57 Found x as proof of (P0 b)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found x3:(P ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P0 ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 22.32/22.57 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found x:(P ((c_star Xx) (cS Xy)))
% 22.32/22.57 Instantiate: a:=((c_star Xx) (cS Xy)):n
% 22.32/22.57 Found x as proof of (P0 a)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 22.32/22.57 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 22.32/22.57 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 22.32/22.57 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 22.32/22.57 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 22.32/22.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 22.32/22.57 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 22.32/22.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 22.32/22.57 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 22.32/22.57 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 22.32/22.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 22.32/22.57 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 25.92/26.11 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 25.92/26.11 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found x:(P2 b)
% 25.92/26.11 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 25.92/26.11 Found (fun (x:(P2 b))=> x) as proof of (P2 ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of ((P2 b)->(P2 ((c_star Xx) (cS Xy))))
% 25.92/26.11 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of (P1 b)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 25.92/26.11 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found x:(P2 b)
% 25.92/26.11 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 25.92/26.11 Found (fun (x:(P2 b))=> x) as proof of (P2 ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of ((P2 b)->(P2 ((c_star Xx) (cS Xy))))
% 25.92/26.11 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of (P1 b)
% 25.92/26.11 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 25.92/26.11 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 25.92/26.11 Found x as proof of (P2 b)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 25.92/26.11 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 25.92/26.11 Found x as proof of (P2 b)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 25.92/26.11 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 25.92/26.11 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 25.92/26.11 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 25.92/26.11 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 27.01/27.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 27.01/27.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 27.01/27.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 27.01/27.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 27.01/27.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 27.01/27.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 27.01/27.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 27.01/27.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 27.01/27.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 27.01/27.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 27.01/27.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 27.01/27.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found x2:(P b)
% 32.62/32.83 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 32.62/32.83 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 32.62/32.83 Found x2:(P b)
% 32.62/32.83 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 32.62/32.83 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 32.62/32.83 Found x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found x:(P b)
% 32.62/32.83 Instantiate: b0:=b:n
% 32.62/32.83 Found x as proof of (P0 b0)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 32.62/32.83 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 32.62/32.83 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 32.62/32.83 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 32.62/32.83 Found x as proof of (P0 b)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 32.62/32.83 Found x:(P b)
% 32.62/32.83 Found x as proof of (P0 ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 32.62/32.83 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 32.62/32.83 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 32.62/32.83 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 36.61/36.85 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 36.61/36.85 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 36.61/36.85 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Instantiate: a:=((c_plus ((c_star Xx) Xy)) Xx):n
% 36.61/36.85 Found x as proof of (P0 a)
% 36.61/36.85 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 36.61/36.85 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 36.61/36.85 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 36.61/36.85 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 36.61/36.85 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 36.61/36.85 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 36.61/36.85 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 36.61/36.85 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 36.61/36.85 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 36.61/36.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 36.61/36.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 36.61/36.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 40.21/40.48 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 40.21/40.48 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 40.21/40.48 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 40.21/40.48 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 40.21/40.48 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 40.21/40.48 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 40.21/40.48 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 40.21/40.48 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 40.21/40.48 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 40.21/40.48 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 40.21/40.48 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 40.21/40.48 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 40.21/40.48 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 40.21/40.48 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 45.72/45.92 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 45.72/45.92 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 45.72/45.92 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 45.72/45.92 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 45.72/45.92 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 45.72/45.92 Found x2:(P1 b)
% 45.72/45.92 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 45.72/45.92 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 45.72/45.92 Found x2:(P1 b)
% 45.72/45.92 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 45.72/45.92 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 45.72/45.92 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 45.72/45.92 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 45.72/45.92 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 45.72/45.92 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 45.72/45.92 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 45.72/45.92 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 45.72/45.92 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found x2:(P b)
% 45.72/45.92 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 45.72/45.92 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 45.72/45.92 Found x2:(P b)
% 45.72/45.92 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 45.72/45.92 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 45.72/45.92 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found x:(P0 b0)
% 45.72/45.92 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 45.72/45.92 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 45.72/45.92 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 45.72/45.92 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 45.72/45.92 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 45.72/45.92 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 45.72/45.92 Found x:(P0 b0)
% 45.72/45.92 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 45.72/45.92 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 45.72/45.92 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 49.12/49.35 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 49.12/49.35 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 49.12/49.35 Found x as proof of (P0 b0)
% 49.12/49.35 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 49.12/49.35 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 49.12/49.35 Found x as proof of (P0 b0)
% 49.12/49.35 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 49.12/49.35 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 49.12/49.35 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 49.12/49.35 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 49.12/49.35 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 49.12/49.35 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 49.12/49.35 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 49.12/49.35 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 49.12/49.35 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 49.12/49.35 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 49.12/49.35 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 49.12/49.35 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 49.12/49.35 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 49.12/49.35 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 49.12/49.35 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 53.92/54.15 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 53.92/54.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 53.92/54.15 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 53.92/54.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 53.92/54.16 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 53.92/54.16 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 53.92/54.16 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 53.92/54.16 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 53.92/54.16 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 53.92/54.16 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 53.92/54.16 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 53.92/54.16 Found x2:(P b0)
% 53.92/54.16 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 53.92/54.16 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 60.30/60.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 60.30/60.53 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 60.30/60.53 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found x as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 60.30/60.53 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 60.30/60.53 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 60.30/60.53 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 60.30/60.53 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 60.30/60.53 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 60.30/60.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 60.30/60.53 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 60.30/60.53 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 60.30/60.53 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 60.30/60.53 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 60.30/60.53 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 60.30/60.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 60.30/60.53 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 60.30/60.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 60.30/60.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 60.30/60.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 65.71/65.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 65.71/65.95 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 65.71/65.95 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 65.71/65.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 65.71/65.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 65.71/65.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 65.71/65.95 Found x:(P0 ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found (fun (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P0 b)
% 65.71/65.95 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of ((P0 ((c_star Xx) (cS Xy)))->(P0 b))
% 65.71/65.95 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 65.71/65.95 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 65.71/65.95 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 65.71/65.95 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 65.71/65.95 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 65.71/65.95 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 65.71/65.95 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 65.71/65.95 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 65.71/65.95 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 65.71/65.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 65.71/65.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 65.71/65.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 65.71/65.95 Found x2:(P0 b)
% 67.32/67.55 Found (fun (x2:(P0 b))=> x2) as proof of (P0 b)
% 67.32/67.55 Found (fun (x2:(P0 b))=> x2) as proof of (P1 b)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 67.32/67.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 67.32/67.55 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 67.32/67.55 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 67.32/67.55 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 67.32/67.55 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 67.32/67.55 Found x:(P b)
% 67.32/67.55 Instantiate: b0:=b:n
% 67.32/67.55 Found x as proof of (P0 b0)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 67.32/67.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 67.32/67.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 67.32/67.55 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 67.32/67.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 67.32/67.55 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 67.32/67.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 67.32/67.55 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 67.32/67.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 71.11/71.37 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.11/71.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.11/71.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.11/71.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.11/71.37 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 71.11/71.37 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 71.11/71.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.11/71.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.11/71.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.11/71.37 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 71.11/71.37 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.11/71.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 71.82/72.04 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 71.82/72.04 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 71.82/72.04 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 71.82/72.04 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 71.82/72.04 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 71.82/72.04 Found x:(P0 b0)
% 71.82/72.04 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 71.82/72.04 Found (fun (x:(P0 b0))=> x) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 71.82/72.04 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 ((c_plus ((c_star Xx) Xy)) Xx)))
% 71.82/72.04 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 71.82/72.04 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 71.82/72.04 Found x:(P0 b)
% 71.82/72.04 Instantiate: b0:=b:n
% 71.82/72.04 Found (fun (x:(P0 b))=> x) as proof of (P0 b0)
% 71.82/72.04 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 b0))
% 71.82/72.04 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of (P b0)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 71.82/72.04 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 71.82/72.04 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 71.82/72.04 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 71.82/72.04 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 71.82/72.04 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 71.82/72.04 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 78.21/78.41 Found x2:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found x2:(P b0)
% 78.21/78.41 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 78.21/78.41 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 78.21/78.41 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 78.21/78.41 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 78.21/78.41 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 78.21/78.41 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 78.21/78.41 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 78.21/78.41 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 78.21/78.41 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 78.21/78.41 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 78.21/78.41 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 78.21/78.41 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 78.21/78.41 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 78.21/78.41 Found x:(P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 78.21/78.41 Found (fun (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of ((P0 ((c_plus ((c_star Xx) Xy)) Xx))->(P0 ((c_plus ((c_star Xx) Xy)) Xx)))
% 82.11/82.30 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 82.11/82.30 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 82.11/82.30 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 82.11/82.30 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 82.11/82.30 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 82.11/82.30 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 82.11/82.30 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 82.11/82.30 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 82.11/82.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 82.11/82.30 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 82.11/82.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 82.11/82.30 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 82.11/82.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 82.11/82.30 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 82.11/82.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 82.11/82.30 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 82.11/82.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 82.11/82.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 82.11/82.30 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 82.11/82.30 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 86.70/86.97 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 86.70/86.97 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found x2:(P b0)
% 86.70/86.97 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 86.70/86.97 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 86.70/86.97 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 86.70/86.97 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 86.70/86.97 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 86.70/86.97 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 86.70/86.97 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 86.70/86.97 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found x3:(P b)
% 86.70/86.97 Found (fun (x3:(P b))=> x3) as proof of (P b)
% 86.70/86.97 Found (fun (x3:(P b))=> x3) as proof of (P0 b)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 86.70/86.97 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 86.70/86.97 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 86.70/86.97 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 86.70/86.97 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 86.70/86.97 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 95.32/95.52 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 95.32/95.52 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 95.32/95.52 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 95.32/95.52 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 95.32/95.52 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 95.32/95.52 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 95.32/95.52 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 95.32/95.52 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 95.32/95.52 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 95.32/95.52 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 95.32/95.52 Found x:(P ((c_star Xx) (cS Xy)))
% 95.32/95.52 Instantiate: a:=((c_star Xx) (cS Xy)):n
% 95.32/95.52 Found x as proof of (P0 a)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 95.32/95.52 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 95.32/95.52 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 95.32/95.52 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 95.32/95.52 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 95.32/95.52 Found x:(P2 b)
% 95.32/95.52 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 95.32/95.52 Found (fun (x:(P2 b))=> x) as proof of (P2 ((c_star Xx) (cS Xy)))
% 95.32/95.52 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of ((P2 b)->(P2 ((c_star Xx) (cS Xy))))
% 95.32/95.52 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of (P1 b)
% 95.32/95.52 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found x:(P2 b)
% 99.10/99.37 Instantiate: b:=((c_star Xx) (cS Xy)):n
% 99.10/99.37 Found (fun (x:(P2 b))=> x) as proof of (P2 ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of ((P2 b)->(P2 ((c_star Xx) (cS Xy))))
% 99.10/99.37 Found (fun (P2:(n->Prop)) (x:(P2 b))=> x) as proof of (P1 b)
% 99.10/99.37 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 99.10/99.37 Found x as proof of (P2 b)
% 99.10/99.37 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 99.10/99.37 Found x as proof of (P2 b)
% 99.10/99.37 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 99.10/99.37 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 99.10/99.37 Found (eq_ref0 b00) as proof of (((eq n) b00) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found ((eq_ref n) b00) as proof of (((eq n) b00) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found ((eq_ref n) b00) as proof of (((eq n) b00) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found ((eq_ref n) b00) as proof of (((eq n) b00) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 99.10/99.37 Found (eq_ref0 b) as proof of (((eq n) b) b00)
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) b00)
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) b00)
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) b00)
% 99.10/99.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 99.10/99.37 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 99.10/99.37 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 99.10/99.37 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 99.10/99.37 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 99.10/99.37 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 104.00/104.29 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 104.00/104.29 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 104.00/104.29 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 104.00/104.29 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 104.00/104.29 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.00/104.29 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 104.00/104.29 Found x2:(P b)
% 104.00/104.29 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 104.00/104.29 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 104.00/104.29 Found x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 104.00/104.29 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 104.00/104.29 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 104.00/104.29 Found x:(P b)
% 104.00/104.29 Instantiate: b0:=b:n
% 104.00/104.29 Found x as proof of (P0 b0)
% 104.00/104.29 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.00/104.29 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.00/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.00/104.29 Found x:(P b)
% 104.10/104.29 Instantiate: b0:=b:n
% 104.10/104.29 Found x as proof of (P0 b0)
% 104.10/104.29 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 104.10/104.29 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 104.10/104.29 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 104.10/104.29 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 104.10/104.29 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 104.10/104.29 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 104.10/104.29 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 104.10/104.29 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 110.02/110.21 Found x as proof of (P0 b)
% 110.02/110.21 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 110.02/110.21 Found x:(P b)
% 110.02/110.21 Found x as proof of (P0 ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 110.02/110.21 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 110.02/110.21 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 110.02/110.21 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 110.02/110.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 110.02/110.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 110.02/110.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 110.02/110.21 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 110.02/110.21 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Instantiate: a:=((c_plus ((c_star Xx) Xy)) Xx):n
% 110.02/110.21 Found x as proof of (P0 a)
% 110.02/110.21 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 110.02/110.21 Instantiate: a:=((c_plus ((c_star Xx) Xy)) Xx):n
% 110.02/110.21 Found x as proof of (P0 a)
% 110.02/110.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 110.02/110.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 110.02/110.21 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 110.02/110.21 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 110.02/110.21 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 110.02/110.21 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 110.02/110.21 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 114.82/115.05 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 114.82/115.05 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 114.82/115.05 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 114.82/115.05 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 114.82/115.05 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 114.82/115.05 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 114.82/115.05 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 114.82/115.05 Found x:(P b)
% 114.82/115.05 Found x as proof of (P0 ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 114.82/115.05 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 114.82/115.05 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 118.51/118.78 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 118.51/118.78 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 118.51/118.78 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 118.51/118.78 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 118.51/118.78 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 118.51/118.78 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 118.51/118.78 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 118.51/118.78 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 118.51/118.78 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 118.51/118.78 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 118.51/118.78 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 129.32/129.56 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 129.32/129.56 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found x2:(P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 129.32/129.56 Found x2:(P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 129.32/129.56 Found x2:(P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 129.32/129.56 Found x2:(P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 129.32/129.56 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 129.32/129.56 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 129.32/129.56 Found x as proof of (P2 b)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Instantiate: b:=((c_plus ((c_star Xx) Xy)) Xx):n
% 129.32/129.56 Found x as proof of (P2 b)
% 129.32/129.56 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 129.32/129.56 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b)
% 129.32/129.56 Found x2:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 129.32/129.56 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found x:(P0 b0)
% 135.32/135.55 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 135.32/135.55 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 135.32/135.55 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 135.32/135.55 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 135.32/135.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 135.32/135.55 Found x:(P0 b0)
% 135.32/135.55 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 135.32/135.55 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 135.32/135.55 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 135.32/135.55 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 135.32/135.55 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 135.32/135.55 Found x as proof of (P0 b0)
% 135.32/135.55 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 135.32/135.55 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found x:(P b)
% 135.32/135.55 Instantiate: b0:=b:n
% 135.32/135.55 Found x as proof of (P0 b0)
% 135.32/135.55 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 135.32/135.55 Found x as proof of (P0 b0)
% 135.32/135.55 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 135.32/135.55 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 135.32/135.55 Found x:(P b)
% 135.32/135.55 Instantiate: b0:=b:n
% 135.32/135.55 Found x as proof of (P0 b0)
% 135.32/135.55 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 135.32/135.55 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 135.32/135.55 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 135.32/135.55 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 135.32/135.55 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 135.32/135.55 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 137.80/138.00 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 137.80/138.00 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (fun (x3:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 137.80/138.00 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 137.80/138.00 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b)
% 137.80/138.00 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 137.80/138.00 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 137.80/138.00 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 137.80/138.00 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 137.80/138.00 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 143.32/143.59 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 143.32/143.59 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found x:(P0 b0)
% 143.32/143.59 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 143.32/143.59 Found (fun (x:(P0 b0))=> x) as proof of (P0 ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 ((c_star Xx) (cS Xy))))
% 143.32/143.59 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 143.32/143.59 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 143.32/143.59 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found x:(P0 b0)
% 143.32/143.59 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 143.32/143.59 Found (fun (x:(P0 b0))=> x) as proof of (P0 ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 ((c_star Xx) (cS Xy))))
% 143.32/143.59 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 143.32/143.59 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 143.32/143.59 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 143.32/143.59 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 143.32/143.59 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 143.32/143.59 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 143.32/143.59 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 143.32/143.59 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 143.32/143.59 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 145.62/145.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 145.62/145.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 145.62/145.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 145.62/145.85 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 145.62/145.85 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 145.62/145.85 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 145.62/145.85 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found x2:(P b0)
% 151.00/151.23 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 151.00/151.23 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 151.00/151.23 Found x2:(P b0)
% 151.00/151.23 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 151.00/151.23 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 151.00/151.23 Found x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found x:(P b)
% 151.00/151.23 Found x as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found x:(P b)
% 151.00/151.23 Found x as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 151.00/151.23 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 151.00/151.23 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 151.00/151.23 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 151.00/151.23 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 151.00/151.23 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 161.51/161.79 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 161.51/161.79 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 161.51/161.79 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 161.51/161.79 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 161.51/161.79 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 161.51/161.79 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 161.51/161.79 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 161.51/161.79 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 161.51/161.79 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 161.51/161.79 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 161.51/161.79 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 164.19/164.39 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 164.19/164.39 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 164.19/164.39 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 164.19/164.39 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 164.19/164.39 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found x:(P0 ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found (fun (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P0 b)
% 164.19/164.39 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of ((P0 ((c_star Xx) (cS Xy)))->(P0 b))
% 164.19/164.39 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 164.19/164.39 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 164.19/164.39 Found x:(P0 ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found (fun (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P0 b)
% 164.19/164.39 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of ((P0 ((c_star Xx) (cS Xy)))->(P0 b))
% 164.19/164.39 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P ((c_star Xx) (cS Xy)))
% 164.19/164.39 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found x as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 164.19/164.39 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 164.19/164.39 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 164.19/164.39 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 164.19/164.39 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 172.19/172.47 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 172.19/172.47 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 172.19/172.47 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 172.19/172.47 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 172.19/172.47 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 172.19/172.47 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 172.19/172.47 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 172.19/172.47 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 172.19/172.47 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 172.19/172.47 Found x2:(P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 172.19/172.47 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found x2:(P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 172.19/172.47 Found x2:(P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 172.19/172.47 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found x2:(P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P1 b)
% 172.19/172.47 Found (fun (x2:(P1 b))=> x2) as proof of (P2 b)
% 172.19/172.47 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 172.19/172.47 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 172.19/172.47 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 176.41/176.64 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found x2:(P0 b)
% 176.41/176.64 Found (fun (x2:(P0 b))=> x2) as proof of (P0 b)
% 176.41/176.64 Found (fun (x2:(P0 b))=> x2) as proof of (P1 b)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 176.41/176.64 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 176.41/176.64 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 176.41/176.64 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 176.41/176.64 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 176.41/176.64 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 176.41/176.64 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 176.41/176.64 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 176.41/176.64 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 176.41/176.64 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 176.41/176.64 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 177.60/177.86 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 177.60/177.86 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 177.60/177.86 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 177.60/177.86 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 177.60/177.86 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 177.60/177.86 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 177.60/177.86 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 185.00/185.22 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 185.00/185.22 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 185.00/185.22 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 185.00/185.22 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 185.00/185.22 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 185.00/185.22 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found x:(P0 b0)
% 185.00/185.22 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 185.00/185.22 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 185.00/185.22 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 185.00/185.22 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 185.00/185.22 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 185.00/185.22 Found x:(P0 b0)
% 185.00/185.22 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 185.00/185.22 Found (fun (x:(P0 b0))=> x) as proof of (P0 b)
% 185.00/185.22 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 b))
% 185.00/185.22 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 185.00/185.22 Found x2:(P0 b)
% 185.00/185.22 Found (fun (x2:(P0 b))=> x2) as proof of (P0 b)
% 185.00/185.22 Found (fun (x2:(P0 b))=> x2) as proof of (P1 b)
% 185.00/185.22 Found x:(P b)
% 185.00/185.22 Instantiate: b0:=b:n
% 185.00/185.22 Found x as proof of (P0 b0)
% 185.00/185.22 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 185.00/185.22 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 185.00/185.22 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found x:(P ((c_star Xx) (cS Xy)))
% 189.30/189.57 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 189.30/189.57 Found x as proof of (P0 b0)
% 189.30/189.57 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found x:(P ((c_star Xx) (cS Xy)))
% 189.30/189.57 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 189.30/189.57 Found x as proof of (P0 b0)
% 189.30/189.57 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 189.30/189.57 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 189.30/189.57 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 189.30/189.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 189.30/189.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 189.30/189.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 189.30/189.57 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found x:(P0 ((c_star Xx) (cS Xy)))
% 189.30/189.57 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 189.30/189.57 Found (fun (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P0 b0)
% 189.30/189.57 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of ((P0 ((c_star Xx) (cS Xy)))->(P0 b0))
% 189.30/189.57 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P b0)
% 189.30/189.57 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 189.30/189.57 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 189.30/189.57 Found x:(P0 ((c_star Xx) (cS Xy)))
% 189.30/189.57 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 189.30/189.57 Found (fun (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P0 b0)
% 189.30/189.57 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of ((P0 ((c_star Xx) (cS Xy)))->(P0 b0))
% 189.30/189.57 Found (fun (P0:(n->Prop)) (x:(P0 ((c_star Xx) (cS Xy))))=> x) as proof of (P b0)
% 189.30/189.57 Found x2:(P b)
% 189.30/189.57 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 189.30/189.57 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 189.30/189.57 Found x2:(P b)
% 189.30/189.57 Found (fun (x2:(P b))=> x2) as proof of (P b)
% 196.91/197.15 Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 196.91/197.15 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 196.91/197.15 Found x as proof of (P0 b0)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 196.91/197.15 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found x:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 196.91/197.15 Found x as proof of (P0 b0)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 196.91/197.15 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 196.91/197.15 Found x2:(P b0)
% 196.91/197.15 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 196.91/197.15 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 196.91/197.15 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 196.91/197.15 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found x2:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x2:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 196.91/197.15 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 196.91/197.15 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 196.91/197.15 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 196.91/197.15 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 208.30/208.53 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 208.30/208.53 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 208.30/208.53 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 208.30/208.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 208.30/208.53 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 208.30/208.53 Found x:(P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (fun (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P0 b)
% 208.30/208.53 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of ((P0 ((c_plus ((c_star Xx) Xy)) Xx))->(P0 b))
% 208.30/208.53 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 208.30/208.53 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 208.30/208.53 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 208.30/208.53 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found x:(P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found (fun (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P0 b)
% 217.61/217.90 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of ((P0 ((c_plus ((c_star Xx) Xy)) Xx))->(P0 b))
% 217.61/217.90 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 217.61/217.90 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 217.61/217.90 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 217.61/217.90 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 217.61/217.90 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 217.61/217.90 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 217.61/217.90 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 217.61/217.90 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 217.61/217.90 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 217.61/217.90 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 217.61/217.90 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 217.61/217.90 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 217.61/217.90 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 217.61/217.90 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 217.61/217.90 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 217.61/217.90 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 217.61/217.90 Found x0:(P2 b0)
% 217.61/217.90 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 217.61/217.90 Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% 217.61/217.90 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% 217.61/217.90 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% 217.61/217.90 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 217.61/217.90 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 217.61/217.90 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 217.61/217.90 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 221.80/222.08 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 221.80/222.08 Found (eq_ref0 a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found ((eq_ref n) a) as proof of (((eq n) a) (cS Xy))
% 221.80/222.08 Found x0:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 221.80/222.08 Found x0 as proof of (P2 b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 221.80/222.08 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 221.80/222.08 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 221.80/222.08 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 221.80/222.08 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 221.80/222.08 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 221.80/222.08 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 221.80/222.08 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 221.80/222.08 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 221.80/222.08 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 221.80/222.08 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 221.80/222.08 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 221.80/222.08 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 221.80/222.08 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.48/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 223.48/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.48/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.48/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.48/223.68 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 223.48/223.68 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.48/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.48/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 223.48/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 223.49/223.68 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 223.49/223.68 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 223.49/223.68 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 223.49/223.68 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 223.49/223.68 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.49/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 223.49/223.68 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.49/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 223.49/223.68 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.49/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 223.49/223.68 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 223.49/223.68 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 223.49/223.68 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 223.49/223.68 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 223.49/223.68 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 225.59/225.82 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 225.59/225.82 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 225.59/225.82 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 225.59/225.82 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 225.59/225.82 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 225.59/225.82 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 225.59/225.82 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 225.59/225.82 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 225.59/225.82 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 225.59/225.82 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 225.59/225.82 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 225.59/225.82 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (fun (x2:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x2) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found x2:(P b0)
% 231.01/231.25 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 231.01/231.25 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 231.01/231.25 Found x2:(P b0)
% 231.01/231.25 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 231.01/231.25 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 231.01/231.25 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 231.01/231.25 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 231.01/231.25 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 231.01/231.25 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 231.01/231.25 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 231.01/231.25 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 231.01/231.25 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found x:(P b)
% 234.80/235.01 Instantiate: b0:=b:n
% 234.80/235.01 Found x as proof of (P0 b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 234.80/235.01 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 234.80/235.01 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 234.80/235.01 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 234.80/235.01 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 234.80/235.01 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 234.80/235.01 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 234.80/235.01 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 234.80/235.01 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 234.80/235.01 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 234.80/235.01 Found x:(P0 b0)
% 234.80/235.01 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 234.80/235.01 Found (fun (x:(P0 b0))=> x) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 234.80/235.01 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of ((P0 b0)->(P0 ((c_plus ((c_star Xx) Xy)) Xx)))
% 234.80/235.01 Found (fun (P0:(n->Prop)) (x:(P0 b0))=> x) as proof of (P b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 234.80/235.01 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 234.80/235.01 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 234.80/235.01 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 234.80/235.01 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 234.80/235.01 Found x:(P0 b)
% 234.80/235.01 Instantiate: b0:=b:n
% 234.80/235.01 Found (fun (x:(P0 b))=> x) as proof of (P0 b0)
% 239.40/239.61 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 b0))
% 239.40/239.61 Found (fun (P0:(n->Prop)) (x:(P0 b))=> x) as proof of (P b0)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 239.40/239.61 Found x3:(P ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P0 ((c_star Xx) (cS Xy)))
% 239.40/239.61 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 239.40/239.61 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 239.40/239.61 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found x3:(P ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found (fun (x3:(P ((c_star Xx) (cS Xy))))=> x3) as proof of (P0 ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 246.67/246.88 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 246.67/246.88 Found x:(P1 b)
% 246.67/246.88 Instantiate: b0:=b:n
% 246.67/246.88 Found x as proof of (P2 b0)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found x:(P1 b)
% 246.67/246.88 Instantiate: b0:=b:n
% 246.67/246.88 Found x as proof of (P2 b0)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 246.67/246.88 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 246.67/246.88 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 246.67/246.88 Found (eq_ref0 b0) as proof of (((eq n) b0) b1)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b1)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b1)
% 246.67/246.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) b1)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 246.67/246.88 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 246.67/246.88 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 246.67/246.88 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 246.67/246.88 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 246.67/246.88 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 246.67/246.88 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 246.67/246.88 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 246.67/246.88 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 250.39/250.60 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b00)
% 250.39/250.60 Found x2:(P b0)
% 250.39/250.60 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 250.39/250.60 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 250.39/250.60 Found x3:(P ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found (fun (x3:(P ((c_plus ((c_star Xx) Xy)) Xx)))=> x3) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 250.39/250.60 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.39/250.60 Found x0:(P1 b)
% 250.39/250.60 Instantiate: b0:=b:n
% 250.39/250.60 Found x0 as proof of (P2 b0)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 250.39/250.60 Found x:(P1 b)
% 250.39/250.60 Found x as proof of (P2 ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found x:(P1 b)
% 250.39/250.60 Found x as proof of (P2 ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 250.39/250.60 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 250.39/250.60 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 250.39/250.60 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 250.39/250.60 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 250.39/250.60 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 254.28/254.57 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Instantiate: a:=((c_plus ((c_star Xx) Xy)) Xx):n
% 254.28/254.57 Found x as proof of (P2 a)
% 254.28/254.57 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Instantiate: a:=((c_plus ((c_star Xx) Xy)) Xx):n
% 254.28/254.57 Found x as proof of (P2 a)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 254.28/254.57 Found x0:(P2 b0)
% 254.28/254.57 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 254.28/254.57 Found (fun (x0:(P2 b0))=> x0) as proof of (P2 b)
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 b))
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 254.28/254.57 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 254.28/254.57 Found x0:(P2 b)
% 254.28/254.57 Instantiate: b0:=b:n
% 254.28/254.57 Found (fun (x0:(P2 b))=> x0) as proof of (P2 b0)
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b))=> x0) as proof of ((P2 b)->(P2 b0))
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b))=> x0) as proof of (P1 b0)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 254.28/254.57 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 254.28/254.57 Found x0:(P2 b0)
% 254.28/254.57 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 254.28/254.57 Found (fun (x0:(P2 b0))=> x0) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of ((P2 b0)->(P2 ((c_plus ((c_star Xx) Xy)) Xx)))
% 254.28/254.57 Found (fun (P2:(n->Prop)) (x0:(P2 b0))=> x0) as proof of (P1 b0)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 254.28/254.57 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 254.28/254.57 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 254.28/254.57 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 254.28/254.57 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 254.28/254.57 Found (eq_ref0 b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_star Xx) (cS Xy)))
% 254.28/254.57 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 260.31/260.58 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 260.31/260.58 Found (eq_ref0 a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found ((eq_ref n) a) as proof of (((eq n) a) b)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 260.31/260.58 Found (eq_ref0 b1) as proof of (((eq n) b1) b0)
% 260.31/260.58 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 260.31/260.58 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 260.31/260.58 Found ((eq_ref n) b1) as proof of (((eq n) b1) b0)
% 260.31/260.58 Found x0:(P1 ((c_star Xx) (cS Xy)))
% 260.31/260.58 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 260.31/260.58 Found x0 as proof of (P2 b0)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 260.31/260.58 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 260.31/260.58 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 260.31/260.58 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 260.31/260.58 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found x00:(P1 a)
% 260.31/260.58 Found (fun (x00:(P1 a))=> x00) as proof of (P1 a)
% 260.31/260.58 Found (fun (x00:(P1 a))=> x00) as proof of (P2 a)
% 260.31/260.58 Found x:(P b)
% 260.31/260.58 Instantiate: a:=b:n
% 260.31/260.58 Found x as proof of (P0 a)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 260.31/260.58 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 260.31/260.58 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 260.31/260.58 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 260.31/260.58 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 264.61/264.88 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 264.61/264.88 Found (eq_ref0 a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 264.61/264.88 Found (eq_ref0 a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) b0)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 264.61/264.88 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 264.61/264.88 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 264.61/264.88 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found x:(P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found (fun (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P0 ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of ((P0 ((c_plus ((c_star Xx) Xy)) Xx))->(P0 ((c_plus ((c_star Xx) Xy)) Xx)))
% 264.61/264.88 Found (fun (P0:(n->Prop)) (x:(P0 ((c_plus ((c_star Xx) Xy)) Xx)))=> x) as proof of (P ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 264.61/264.88 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 264.61/264.88 Found x0:(P2 ((c_star Xx) (cS Xy)))
% 264.61/264.88 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 264.61/264.88 Found (fun (x0:(P2 ((c_star Xx) (cS Xy))))=> x0) as proof of (P2 b0)
% 264.61/264.88 Found (fun (P2:(n->Prop)) (x0:(P2 ((c_star Xx) (cS Xy))))=> x0) as proof of ((P2 ((c_star Xx) (cS Xy)))->(P2 b0))
% 264.61/264.88 Found (fun (P2:(n->Prop)) (x0:(P2 ((c_star Xx) (cS Xy))))=> x0) as proof of (P1 b0)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 264.61/264.88 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 264.61/264.88 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 264.61/264.88 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 264.61/264.88 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 271.11/271.32 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 271.11/271.32 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found x:(P b0)
% 271.11/271.32 Instantiate: b1:=b0:n
% 271.11/271.32 Found x as proof of (P0 b1)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b1)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 271.11/271.32 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 271.11/271.32 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 271.11/271.32 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 271.11/271.32 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 271.11/271.32 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 271.11/271.32 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 271.11/271.32 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 271.11/271.32 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 271.11/271.32 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 271.11/271.32 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 273.01/273.22 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 273.01/273.22 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 273.01/273.22 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 274.80/275.06 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 274.80/275.06 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 274.80/275.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 274.80/275.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 274.80/275.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 274.80/275.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 274.80/275.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 279.68/279.95 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 279.68/279.95 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 279.68/279.95 Found x:(P b0)
% 279.68/279.95 Found x as proof of (P0 ((c_star Xx) (cS Xy)))
% 279.68/279.95 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 279.68/279.95 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 279.68/279.95 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 279.68/279.95 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 279.68/279.95 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found x2:(P b0)
% 279.68/279.95 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 279.68/279.95 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 279.68/279.95 Found x2:(P b0)
% 279.68/279.95 Found (fun (x2:(P b0))=> x2) as proof of (P b0)
% 279.68/279.95 Found (fun (x2:(P b0))=> x2) as proof of (P0 b0)
% 279.68/279.95 Found x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found (fun (x00:(P1 ((c_plus ((c_star Xx) Xy)) Xx)))=> x00) as proof of (P2 ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 279.68/279.95 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 279.68/279.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 279.68/279.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 279.68/279.95 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 279.68/279.95 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 279.68/279.95 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 279.68/279.95 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found x:(P2 b0)
% 280.80/281.06 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 280.80/281.06 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 280.80/281.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found x:(P2 b0)
% 280.80/281.06 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 280.80/281.06 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 280.80/281.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found x:(P2 b0)
% 280.80/281.06 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 280.80/281.06 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 280.80/281.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found x:(P2 b0)
% 280.80/281.06 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 280.80/281.06 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 280.80/281.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 280.80/281.06 Found x:(P2 b0)
% 280.80/281.06 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 280.80/281.06 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 280.80/281.06 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 280.80/281.06 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 280.80/281.06 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found x:(P2 b0)
% 284.40/284.61 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 284.40/284.61 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 284.40/284.61 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found x:(P2 b0)
% 284.40/284.61 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 284.40/284.61 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 284.40/284.61 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 284.40/284.61 Found x:(P2 b0)
% 284.40/284.61 Instantiate: b0:=((c_star Xx) (cS Xy)):n
% 284.40/284.61 Found (fun (x:(P2 b0))=> x) as proof of (P2 b)
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of ((P2 b0)->(P2 b))
% 284.40/284.61 Found (fun (P2:(n->Prop)) (x:(P2 b0))=> x) as proof of (P1 b0)
% 284.40/284.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 284.40/284.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 284.40/284.61 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 284.40/284.61 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b1)
% 284.40/284.61 Found eq_ref00:=(eq_ref0 b1):(((eq n) b1) b1)
% 284.40/284.61 Found (eq_ref0 b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found ((eq_ref n) b1) as proof of (((eq n) b1) ((c_plus ((c_star Xx) Xy)) Xx))
% 284.40/284.61 Found eq_ref00:=(eq_ref0 b00):(((eq n) b00) b00)
% 284.40/284.61 Found (eq_ref0 b00) as proof of (((eq n) b00) b)
% 284.40/284.61 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 284.40/284.61 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 284.40/284.61 Found ((eq_ref n) b00) as proof of (((eq n) b00) b)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 294.00/294.24 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 294.00/294.24 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 294.00/294.24 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b00)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P1 ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Instantiate: b0:=((c_plus ((c_star Xx) Xy)) Xx):n
% 294.00/294.24 Found x as proof of (P2 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 294.00/294.24 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 294.00/294.24 Found x:(P0 b)
% 294.00/294.24 Instantiate: b0:=b:n
% 294.00/294.24 Found x as proof of (P1 b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 ((c_star Xx) (cS Xy))):(((eq n) ((c_star Xx) (cS Xy))) ((c_star Xx) (cS Xy)))
% 294.00/294.24 Found (eq_ref0 ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 294.00/294.24 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 294.00/294.24 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 294.00/294.24 Found ((eq_ref n) ((c_star Xx) (cS Xy))) as proof of (((eq n) ((c_star Xx) (cS Xy))) b0)
% 294.00/294.24 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 294.00/294.24 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 294.00/294.24 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 295.67/295.91 Found (eq_ref0 b) as proof of (((eq n) b) b0)
% 295.67/295.91 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 295.67/295.91 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 295.67/295.91 Found ((eq_ref n) b) as proof of (((eq n) b) b0)
% 295.67/295.91 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 295.67/295.91 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 295.67/295.91 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 295.67/295.91 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 295.67/295.91 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_star Xx) (cS Xy)))
% 295.67/295.91 Found eq_ref00:=(eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)):(((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) ((c_plus ((c_star Xx) Xy)) Xx))
% 295.67/295.91 Found (eq_ref0 ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found ((eq_ref n) ((c_plus ((c_star Xx) Xy)) Xx)) as proof of (((eq n) ((c_plus ((c_star Xx) Xy)) Xx)) b0)
% 295.67/295.91 Found x3:(P b)
% 295.67/295.91 Found (fun (x3:(P b))=> x3) as proof of (P b)
% 295.67/295.91 Found (fun (x3:(P b))=> x3) as proof of (P0 b)
% 295.67/295.91 Found eq_re
%------------------------------------------------------------------------------