TSTP Solution File: NUM827^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM827^5 : TPTP v7.0.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n088.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 13:11:51 EST 2018
% Result : Timeout 292.10s
% 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 : NUM827^5 : TPTP v7.0.0. Bugfixed v5.3.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n088.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 14:34:04 CST 2018
% 0.02/0.23 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 3.59/3.86 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe072463f8>, <kernel.Type object at 0x2afe06e77ef0>) of role type named n_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring n:Type
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe072465a8>, <kernel.Constant object at 0x2afe06e774d0>) of role type named c0_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring c0:n
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe072463f8>, <kernel.DependentProduct object at 0x2afe06e77050>) of role type named cS_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring cS:(n->n)
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe06e7e290>, <kernel.DependentProduct object at 0x2afe06e77440>) of role type named c_plus_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring c_plus:(n->(n->n))
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe072463f8>, <kernel.Sort object at 0x2afe072ce6c8>) of role type named cPA_1_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring cPA_1:Prop
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe072463f8>, <kernel.Sort object at 0x2afe072ce6c8>) of role type named cPA_2_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring cPA_2:Prop
% 3.59/3.86 FOF formula (<kernel.Constant object at 0x2afe06e77098>, <kernel.Sort object at 0x2afe072ce6c8>) of role type named cPA_IND_EQ_type
% 3.59/3.86 Using role type
% 3.59/3.86 Declaring cPA_IND_EQ:Prop
% 3.59/3.86 FOF formula (((eq Prop) cPA_1) (forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx))) of role definition named cPA_1_def
% 3.59/3.86 A new definition: (((eq Prop) cPA_1) (forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx)))
% 3.59/3.86 Defined: cPA_1:=(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx))
% 3.59/3.86 FOF formula (((eq Prop) cPA_2) (forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy))))) of role definition named cPA_2_def
% 3.59/3.86 A new definition: (((eq Prop) cPA_2) (forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy)))))
% 3.59/3.86 Defined: cPA_2:=(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy))))
% 3.59/3.86 FOF formula (((eq Prop) cPA_IND_EQ) (forall (Xp:(n->n)) (Xq:(n->n)), (((and (((eq n) (Xp c0)) (Xq c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) (Xq Xx))->(((eq n) (Xp (cS Xx))) (Xq (cS Xx))))))->(forall (Xx:n), (((eq n) (Xp Xx)) (Xq Xx)))))) of role definition named cPA_IND_EQ_def
% 3.59/3.86 A new definition: (((eq Prop) cPA_IND_EQ) (forall (Xp:(n->n)) (Xq:(n->n)), (((and (((eq n) (Xp c0)) (Xq c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) (Xq Xx))->(((eq n) (Xp (cS Xx))) (Xq (cS Xx))))))->(forall (Xx:n), (((eq n) (Xp Xx)) (Xq Xx))))))
% 3.59/3.86 Defined: cPA_IND_EQ:=(forall (Xp:(n->n)) (Xq:(n->n)), (((and (((eq n) (Xp c0)) (Xq c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) (Xq Xx))->(((eq n) (Xp (cS Xx))) (Xq (cS Xx))))))->(forall (Xx:n), (((eq n) (Xp Xx)) (Xq Xx)))))
% 3.59/3.86 FOF formula (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) ((c_plus c0) Xx)))) of role conjecture named cPA_THM2
% 3.59/3.86 Conjecture to prove = (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) ((c_plus c0) Xx)))):Prop
% 3.59/3.86 We need to prove ['(((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) ((c_plus c0) Xx))))']
% 3.59/3.86 Parameter n:Type.
% 3.59/3.86 Parameter c0:n.
% 3.59/3.86 Parameter cS:(n->n).
% 3.59/3.86 Parameter c_plus:(n->(n->n)).
% 3.59/3.86 Definition cPA_1:=(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx)):Prop.
% 3.59/3.86 Definition cPA_2:=(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy)))):Prop.
% 3.59/3.86 Definition cPA_IND_EQ:=(forall (Xp:(n->n)) (Xq:(n->n)), (((and (((eq n) (Xp c0)) (Xq c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) (Xq Xx))->(((eq n) (Xp (cS Xx))) (Xq (cS Xx))))))->(forall (Xx:n), (((eq n) (Xp Xx)) (Xq Xx))))):Prop.
% 3.59/3.86 Trying to prove (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) ((c_plus c0) Xx))))
% 3.59/3.86 Found x00:(P ((c_plus Xx) c0))
% 3.59/3.86 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P ((c_plus Xx) c0))
% 3.59/3.86 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P0 ((c_plus Xx) c0))
% 3.59/3.86 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 3.59/3.86 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 3.59/3.86 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 16.20/16.42 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found x20:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found x20:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found x20:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 16.20/16.42 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 16.20/16.42 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 16.20/16.42 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 16.20/16.42 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 16.20/16.42 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 16.20/16.42 Found x40:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 16.20/16.42 Found x40:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found x40:(P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 16.20/16.42 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 16.20/16.42 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 16.20/16.42 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 16.20/16.42 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 26.10/26.36 Found x20:(P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 26.10/26.36 Found x20:(P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 26.10/26.36 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found x20:(P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 26.10/26.36 Found x20:(P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 26.10/26.36 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 26.10/26.36 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 26.10/26.36 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 34.93/35.16 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found x0:(P ((c_plus Xx) c0))
% 41.79/41.99 Instantiate: b:=((c_plus Xx) c0):n
% 41.79/41.99 Found x0 as proof of (P0 b)
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found x40:(P ((c_plus c0) Xx))
% 41.79/41.99 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 41.79/41.99 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 41.79/41.99 Found x40:(P ((c_plus c0) Xx))
% 41.79/41.99 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 41.79/41.99 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 41.79/41.99 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 41.79/41.99 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 41.79/41.99 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 41.79/41.99 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 41.79/41.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 55.51/55.73 Found x40:(P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 55.51/55.73 Found x40:(P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 55.51/55.73 Found x40:(P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 55.51/55.73 Found x40:(P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P ((c_plus c0) Xx))
% 55.51/55.73 Found (fun (x40:(P ((c_plus c0) Xx)))=> x40) as proof of (P0 ((c_plus c0) Xx))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 55.51/55.73 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 55.51/55.73 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 55.51/55.73 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 55.51/55.73 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 55.51/55.73 Found x2:(P ((c_plus Xx) c0))
% 55.51/55.73 Instantiate: b:=((c_plus Xx) c0):n
% 55.51/55.73 Found x2 as proof of (P0 b)
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 60.82/61.01 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 60.82/61.01 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 60.82/61.01 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 60.82/61.01 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 60.82/61.01 Found x0:(P0 b)
% 60.82/61.01 Instantiate: b:=((c_plus Xx) c0):n
% 60.82/61.01 Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((c_plus Xx) c0))
% 60.82/61.01 Found (fun (P0:(n->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 60.82/61.01 Found (fun (P0:(n->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 60.82/61.01 Found x0:(P ((c_plus c0) Xx))
% 60.82/61.01 Instantiate: b:=((c_plus c0) Xx):n
% 60.82/61.01 Found x0 as proof of (P0 b)
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 60.82/61.01 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 71.72/71.99 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 71.72/71.99 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 71.72/71.99 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 71.72/71.99 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 71.72/71.99 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 71.72/71.99 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 80.60/80.79 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 80.60/80.79 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 80.60/80.79 Found x00:(P ((c_plus Xx) c0))
% 80.60/80.79 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P ((c_plus Xx) c0))
% 80.60/80.79 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P0 ((c_plus Xx) c0))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 80.60/80.79 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 80.60/80.79 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 80.60/80.79 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 80.60/80.79 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found x2:(P ((c_plus Xx) c0))
% 80.60/80.79 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) c0)):(n->n)
% 80.60/80.79 Found x2 as proof of (P0 (Xp Xx))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found x0:(P ((c_plus Xx) c0))
% 80.60/80.79 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) c0)):(n->n)
% 80.60/80.79 Found x0 as proof of (P0 (Xp Xx))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 80.60/80.79 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 94.29/94.53 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 94.29/94.53 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 94.29/94.53 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 94.29/94.53 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 94.29/94.53 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 94.29/94.53 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 94.29/94.53 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 94.29/94.53 Found (x2 (fun (x3:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 94.29/94.53 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 94.29/94.53 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 94.29/94.53 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 94.29/94.53 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 94.29/94.53 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 94.29/94.53 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 94.29/94.53 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 94.29/94.53 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 94.29/94.53 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 94.29/94.53 Found x2:(P0 b)
% 94.29/94.53 Instantiate: b:=((c_plus Xx) c0):n
% 94.29/94.53 Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((c_plus Xx) c0))
% 98.33/98.54 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 98.33/98.54 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 98.33/98.54 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 108.39/108.67 Found x4:(P ((c_plus Xx) c0))
% 108.39/108.67 Instantiate: b:=((c_plus Xx) c0):n
% 108.39/108.67 Found x4 as proof of (P0 b)
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found x2:(P ((c_plus c0) Xx))
% 108.39/108.67 Instantiate: b:=((c_plus c0) Xx):n
% 108.39/108.67 Found x2 as proof of (P0 b)
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 108.39/108.67 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 108.39/108.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 108.39/108.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 108.39/108.67 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 108.39/108.67 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 108.39/108.67 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 124.20/124.46 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 124.20/124.46 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 124.20/124.46 Found x00:(P b)
% 124.20/124.46 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 124.20/124.46 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 124.20/124.46 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 124.20/124.46 Found x2:(P0 b)
% 124.20/124.46 Instantiate: b:=((c_plus Xx) c0):n
% 124.20/124.46 Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((c_plus Xx) c0))
% 124.20/124.46 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 124.20/124.46 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 124.20/124.46 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus c0) (cS Xx0))):(((eq n) ((c_plus c0) (cS Xx0))) ((c_plus c0) (cS Xx0)))
% 124.20/124.46 Found (eq_ref0 ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 124.20/124.46 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus c0) (cS Xx0))):(((eq n) ((c_plus c0) (cS Xx0))) ((c_plus c0) (cS Xx0)))
% 124.20/124.46 Found (eq_ref0 ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 124.20/124.46 Found x2:(P ((c_plus c0) Xx))
% 124.20/124.46 Instantiate: b:=((c_plus c0) Xx):n
% 124.20/124.46 Found x2 as proof of (P0 b)
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 124.20/124.46 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 124.20/124.46 Found x20:(P ((c_plus Xx) c0))
% 124.20/124.46 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 124.20/124.46 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 124.20/124.46 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 124.20/124.46 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 124.20/124.46 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 125.71/125.94 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 125.71/125.94 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 125.71/125.94 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 125.71/125.94 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 125.71/125.94 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 125.71/125.94 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 125.71/125.94 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 125.71/125.94 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 125.71/125.94 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 125.71/125.94 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 125.71/125.94 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 125.71/125.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 125.71/125.94 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 125.71/125.94 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 125.71/125.94 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 125.71/125.94 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 142.13/142.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 142.13/142.37 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found eq_ref00:=(eq_ref0 ((c_plus c0) (cS Xx0))):(((eq n) ((c_plus c0) (cS Xx0))) ((c_plus c0) (cS Xx0)))
% 142.13/142.37 Found (eq_ref0 ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 142.13/142.37 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 142.13/142.37 Found eq_ref00:=(eq_ref0 ((c_plus c0) (cS Xx0))):(((eq n) ((c_plus c0) (cS Xx0))) ((c_plus c0) (cS Xx0)))
% 142.13/142.37 Found (eq_ref0 ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) (cS Xx0))) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 142.13/142.37 Found x4:(P ((c_plus Xx) c0))
% 142.13/142.37 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) c0)):(n->n)
% 142.13/142.37 Found x4 as proof of (P0 (Xp Xx))
% 142.13/142.37 Found x0:(P ((c_plus Xx) c0))
% 142.13/142.37 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) c0)):(n->n)
% 142.13/142.37 Found x0 as proof of (P0 (Xp Xx))
% 142.13/142.37 Found x00:(P ((c_plus c0) Xx))
% 142.13/142.37 Found (fun (x00:(P ((c_plus c0) Xx)))=> x00) as proof of (P ((c_plus c0) Xx))
% 142.13/142.37 Found (fun (x00:(P ((c_plus c0) Xx)))=> x00) as proof of (P0 ((c_plus c0) Xx))
% 142.13/142.37 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 142.13/142.37 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 142.13/142.37 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 142.13/142.37 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 142.13/142.37 Found x2:(P ((c_plus Xx) c0))
% 142.13/142.37 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) c0)):(n->n)
% 142.13/142.37 Found x2 as proof of (P0 (Xp Xx))
% 142.13/142.37 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 142.13/142.37 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 142.13/142.37 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 142.13/142.37 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 142.13/142.37 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 142.13/142.37 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 142.13/142.37 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 142.13/142.37 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 142.13/142.37 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 142.13/142.37 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 142.13/142.37 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 142.13/142.37 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 142.13/142.37 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 167.09/167.31 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 167.09/167.31 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 167.09/167.31 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 167.09/167.31 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 167.09/167.31 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 167.09/167.31 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 167.09/167.31 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 167.09/167.31 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 167.09/167.31 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 167.09/167.31 Found x2:(P ((c_plus c0) Xx))
% 167.09/167.31 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 167.09/167.31 Found x2 as proof of (P0 (Xp c0))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 167.09/167.31 Found (eq_ref0 a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 167.09/167.31 Found (eq_ref0 a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 167.09/167.31 Found x00:(P ((c_plus Xx) c0))
% 167.09/167.31 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P ((c_plus Xx) c0))
% 167.09/167.31 Found (fun (x00:(P ((c_plus Xx) c0)))=> x00) as proof of (P0 ((c_plus Xx) c0))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 167.09/167.31 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 167.09/167.31 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 167.09/167.31 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 167.09/167.31 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 167.09/167.31 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 167.09/167.31 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 167.09/167.31 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 167.09/167.31 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 167.09/167.31 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 167.09/167.31 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 167.09/167.31 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 167.09/167.31 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 167.09/167.31 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 171.37/171.64 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))):((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) (Xp (cS Xx0))))
% 171.37/171.64 Found (eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found ((eq_substitution000 ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((eq_substitution00 (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found ((((eq_substitution0 n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus c0) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus c0) (cS Xx)))))
% 171.37/171.64 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 171.37/171.64 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 171.37/171.64 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 171.37/171.64 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 171.37/171.64 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 171.37/171.64 Found x4:(P0 b)
% 171.37/171.64 Instantiate: b:=((c_plus Xx) c0):n
% 171.37/171.64 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) c0))
% 171.37/171.64 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 171.37/171.64 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 171.37/171.64 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 171.37/171.64 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 171.37/171.64 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))):((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) (Xp (cS Xx0))))
% 171.37/171.64 Found (eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found ((eq_substitution000 ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((eq_substitution00 (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found ((((eq_substitution0 n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 171.37/171.64 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 188.27/188.52 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of ((((eq n) (Xp Xx0)) ((c_plus c0) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus c0) (cS Xx0))))
% 188.27/188.52 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus c0) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus c0) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus c0) (cS Xx)))))
% 188.27/188.52 Found x20:(P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 188.27/188.52 Found x20:(P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 188.27/188.52 Found x20:(P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 188.27/188.52 Found x20:(P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 188.27/188.52 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 188.27/188.52 Found x2:(P ((c_plus c0) Xx))
% 188.27/188.52 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 188.27/188.52 Found x2 as proof of (P0 (Xp c0))
% 188.27/188.52 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 188.27/188.52 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 188.27/188.52 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 188.27/188.52 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 188.27/188.52 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 188.27/188.52 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 188.27/188.52 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 188.27/188.52 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 188.27/188.52 Found x0:(P ((c_plus c0) Xx))
% 188.27/188.52 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 188.27/188.52 Found x0 as proof of (P0 (Xp c0))
% 188.27/188.52 Found x4:(P ((c_plus c0) Xx))
% 188.27/188.52 Instantiate: b:=((c_plus c0) Xx):n
% 188.27/188.52 Found x4 as proof of (P0 b)
% 188.27/188.52 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 188.27/188.52 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 188.27/188.52 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 188.27/188.52 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 188.27/188.52 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 188.27/188.52 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 198.47/198.74 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 198.47/198.74 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 198.47/198.74 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 198.47/198.74 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 198.47/198.74 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 198.47/198.74 Found x20:(P ((c_plus Xx) c0))
% 198.47/198.74 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 198.47/198.74 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 198.47/198.74 Found x00:(P ((c_plus c0) Xx))
% 198.47/198.74 Found (fun (x00:(P ((c_plus c0) Xx)))=> x00) as proof of (P ((c_plus c0) Xx))
% 198.47/198.74 Found (fun (x00:(P ((c_plus c0) Xx)))=> x00) as proof of (P0 ((c_plus c0) Xx))
% 198.47/198.74 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 198.47/198.74 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 198.47/198.74 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found x4:(P0 b)
% 198.47/198.74 Instantiate: b:=((c_plus Xx) c0):n
% 198.47/198.74 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) c0))
% 198.47/198.74 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 198.47/198.74 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 198.47/198.74 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 198.47/198.74 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 198.47/198.74 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 198.47/198.74 Found x4:(P0 b)
% 198.47/198.74 Instantiate: b:=((c_plus Xx) c0):n
% 198.47/198.74 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) c0))
% 198.47/198.74 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) c0)))
% 218.69/218.94 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 218.69/218.94 Found x20:(P ((c_plus Xx) c0))
% 218.69/218.94 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 218.69/218.94 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 218.69/218.94 Found x4:(P ((c_plus Xx) c0))
% 218.69/218.94 Instantiate: Xp:=(c_plus Xx):(n->n)
% 218.69/218.94 Found x4 as proof of (P0 (Xp c0))
% 218.69/218.94 Found x0:(P ((c_plus Xx) c0))
% 218.69/218.94 Instantiate: Xp:=(c_plus Xx):(n->n)
% 218.69/218.94 Found x0 as proof of (P0 (Xp c0))
% 218.69/218.94 Found x40:(P ((c_plus Xx) c0))
% 218.69/218.94 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 218.69/218.94 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 218.69/218.94 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 218.69/218.94 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 218.69/218.94 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found x2:(P ((c_plus Xx) c0))
% 218.69/218.94 Instantiate: Xp:=(c_plus Xx):(n->n)
% 218.69/218.94 Found x2 as proof of (P0 (Xp c0))
% 218.69/218.94 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 218.69/218.94 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 218.69/218.94 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 218.69/218.94 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 218.69/218.94 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 218.69/218.94 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 218.69/218.94 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 218.69/218.94 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 218.69/218.94 Found x4:(P ((c_plus c0) Xx))
% 218.69/218.94 Instantiate: b:=((c_plus c0) Xx):n
% 218.69/218.94 Found x4 as proof of (P0 b)
% 218.69/218.94 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found x4:(P ((c_plus c0) Xx))
% 218.69/218.94 Instantiate: b:=((c_plus c0) Xx):n
% 218.69/218.94 Found x4 as proof of (P0 b)
% 218.69/218.94 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 218.69/218.94 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 218.69/218.94 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 218.69/218.94 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 218.69/218.94 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 218.69/218.94 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 218.69/218.94 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 218.69/218.94 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 218.69/218.94 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 218.69/218.94 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 218.69/218.94 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found (x4 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 220.50/220.77 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 220.50/220.77 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 220.50/220.77 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 220.50/220.77 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 235.37/235.61 Found x20:(P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 235.37/235.61 Found x20:(P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 235.37/235.61 Found x20:(P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 235.37/235.61 Found x20:(P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P1 ((c_plus c0) Xx))
% 235.37/235.61 Found (fun (x20:(P1 ((c_plus c0) Xx)))=> x20) as proof of (P2 ((c_plus c0) Xx))
% 235.37/235.61 Found x20:(P b)
% 235.37/235.61 Found (fun (x20:(P b))=> x20) as proof of (P b)
% 235.37/235.61 Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% 235.37/235.61 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 235.37/235.61 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 235.37/235.61 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 235.37/235.61 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 235.37/235.61 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 235.37/235.61 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus (cS Xx0)) c0)):(((eq n) ((c_plus (cS Xx0)) c0)) ((c_plus (cS Xx0)) c0))
% 235.37/235.61 Found (eq_ref0 ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 235.37/235.61 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 235.37/235.61 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 235.37/235.61 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 235.37/235.61 Found eq_ref00:=(eq_ref0 ((c_plus (cS Xx0)) c0)):(((eq n) ((c_plus (cS Xx0)) c0)) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found (eq_ref0 ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 249.99/250.28 Found x20:(P ((c_plus c0) Xx))
% 249.99/250.28 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 249.99/250.28 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 249.99/250.28 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 249.99/250.28 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 249.99/250.28 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 249.99/250.28 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 249.99/250.28 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 249.99/250.28 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 249.99/250.28 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 249.99/250.28 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 249.99/250.28 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 249.99/250.28 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 249.99/250.28 Found x20:(P b)
% 249.99/250.28 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) c0))
% 249.99/250.28 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 249.99/250.28 Found x20:(P b)
% 249.99/250.28 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) c0))
% 249.99/250.28 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 249.99/250.28 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 249.99/250.28 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found x300:=(x30 Xx0):(((eq n) ((c_plus c0) (cS Xx0))) (cS ((c_plus c0) Xx0)))
% 249.99/250.28 Found (x30 Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 249.99/250.28 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 249.99/250.28 Found x300:=(x30 Xx0):(((eq n) ((c_plus c0) (cS Xx0))) (cS ((c_plus c0) Xx0)))
% 249.99/250.28 Found (x30 Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 249.99/250.28 Found x20:(P ((c_plus Xx) c0))
% 249.99/250.28 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 249.99/250.28 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 249.99/250.28 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 249.99/250.28 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 249.99/250.28 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 249.99/250.28 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 249.99/250.28 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 249.99/250.28 Found eq_ref00:=(eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))):(((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0)))))
% 254.40/254.69 Found (eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found eq_ref00:=(eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))):(((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0)))))
% 254.40/254.69 Found (eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus c0) Xx)) ((c_plus Xx) c0))->(((eq n) ((c_plus c0) (cS Xx))) ((c_plus (cS Xx)) c0))))) b)
% 254.40/254.69 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 254.40/254.69 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 254.40/254.69 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 254.40/254.69 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 254.40/254.69 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 254.40/254.69 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 254.40/254.69 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 254.40/254.69 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 254.40/254.69 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 254.40/254.69 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 254.40/254.69 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 254.40/254.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 254.40/254.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 254.40/254.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 254.40/254.69 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 261.80/262.05 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 261.80/262.05 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 261.80/262.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 261.80/262.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 261.80/262.05 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus c0) Xx))
% 261.80/262.05 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 261.80/262.05 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 261.80/262.05 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 261.80/262.05 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b0)
% 261.80/262.05 Found eq_ref00:=(eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))):(((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx)))))
% 261.80/262.05 Found (eq_ref0 (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found ((eq_ref Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) as proof of (((eq Prop) (forall (Xx0:n), ((((eq n) ((c_plus Xx) Xx0)) ((c_plus Xx0) Xx))->(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus (cS Xx0)) Xx))))) b)
% 261.80/262.05 Found x0:(P ((c_plus c0) Xx))
% 261.80/262.05 Instantiate: b:=((c_plus c0) Xx):n
% 261.80/262.05 Found x0 as proof of (P0 b)
% 261.80/262.05 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 261.80/262.05 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 261.80/262.05 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 261.80/262.05 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 261.80/262.05 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 261.80/262.05 Found x20:(P ((c_plus Xx) c0))
% 261.80/262.05 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 270.73/270.98 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 270.73/270.98 Found x20:(P ((c_plus Xx) c0))
% 270.73/270.98 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 270.73/270.98 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 270.73/270.98 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 270.73/270.98 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 270.73/270.98 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 270.73/270.98 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 270.73/270.98 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 270.73/270.98 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 270.73/270.98 Found eq_ref00:=(eq_ref0 ((c_plus (cS Xx0)) c0)):(((eq n) ((c_plus (cS Xx0)) c0)) ((c_plus (cS Xx0)) c0))
% 276.76/277.04 Found (eq_ref0 ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 276.76/277.04 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found eq_ref00:=(eq_ref0 ((c_plus (cS Xx0)) c0)):(((eq n) ((c_plus (cS Xx0)) c0)) ((c_plus (cS Xx0)) c0))
% 276.76/277.04 Found (eq_ref0 ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus (cS Xx0)) c0)) as proof of (((eq n) ((c_plus (cS Xx0)) c0)) b)
% 276.76/277.04 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found eq_ref00:=(eq_ref0 ((c_plus c0) c0)):(((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found (eq_ref0 ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) ((c_plus c0) c0)) as proof of (((eq n) ((c_plus c0) c0)) ((c_plus c0) c0))
% 276.76/277.04 Found x20:=(x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found x20:=(x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found x20:=(x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found x20:=(x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))):((P ((c_plus c0) (cS Xx0)))->(P ((c_plus c0) (cS Xx0))))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found (x2 (fun (x5:n)=> (P ((c_plus c0) (cS Xx0))))) as proof of (P0 ((c_plus c0) (cS Xx0)))
% 276.76/277.04 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 276.76/277.04 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 276.76/277.04 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus c0) c0))
% 276.76/277.04 Found x20:(P ((c_plus c0) Xx))
% 276.76/277.04 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P ((c_plus c0) Xx))
% 276.76/277.04 Found (fun (x20:(P ((c_plus c0) Xx)))=> x20) as proof of (P0 ((c_plus c0) Xx))
% 276.76/277.04 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 276.76/277.04 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 276.76/277.04 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) c0))
% 276.76/277.04 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 276.76/277.04 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 276.76/277.04 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 292.10/292.38 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 292.10/292.38 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 292.10/292.38 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 292.10/292.38 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 292.10/292.38 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 292.10/292.38 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) c0))
% 292.10/292.38 Found eq_ref00:=(eq_ref0 ((c_plus c0) Xx)):(((eq n) ((c_plus c0) Xx)) ((c_plus c0) Xx))
% 292.10/292.38 Found (eq_ref0 ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 292.10/292.38 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 292.10/292.38 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 292.10/292.38 Found ((eq_ref n) ((c_plus c0) Xx)) as proof of (((eq n) ((c_plus c0) Xx)) b0)
% 292.10/292.38 Found x4:(P ((c_plus c0) Xx))
% 292.10/292.38 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) Xx)):(n->n)
% 292.10/292.38 Found x4 as proof of (P0 (Xp c0))
% 292.10/292.38 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 292.10/292.38 Found (eq_ref0 a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 292.10/292.38 Found (eq_ref0 a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found ((eq_ref n) a) as proof of (((eq n) a) c0)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 292.10/292.38 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 292.10/292.38 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 292.10/292.38 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 292.10/292.38 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 292.10/292.38 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 292.10/292.38 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 292.10/292.38 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found x300:=(x30 Xx0):(((eq n) ((c_plus c0) (cS Xx0))) (cS ((c_plus c0) Xx0)))
% 292.10/292.38 Found (x30 Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 292.10/292.38 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found x300:=(x30 Xx0):(((eq n) ((c_plus c0) (cS Xx0))) (cS ((c_plus c0) Xx0)))
% 292.10/292.38 Found (x30 Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 292.10/292.38 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) c0))
% 292.10/292.38 Found x300:=(x30 Xx0):(((eq n) ((c_plus c0) (cS Xx0))) (cS ((c_plus c0) Xx0)))
% 292.10/292.38 Found (x30 Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (cS Xx0))) b)
% 292.10/292.38 Found ((x3 c0) Xx0) as proof of (((eq n) ((c_plus c0) (
%------------------------------------------------------------------------------