TSTP Solution File: NUM828^5 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM828^5 : TPTP v7.0.0. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n129.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 290.69s
% 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 : NUM828^5 : TPTP v7.0.0. Bugfixed v5.3.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.23 % Computer : n129.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 14:33:35 CST 2018
% 0.02/0.23 % CPUTime :
% 0.07/0.24 Python 2.7.13
% 3.31/3.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117b518>, <kernel.Type object at 0x2b981117bdd0>) of role type named n_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring n:Type
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b9811181908>, <kernel.Constant object at 0x2b981117b7a0>) of role type named c0_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring c0:n
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117b6c8>, <kernel.DependentProduct object at 0x2b981117b440>) of role type named cS_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring cS:(n->n)
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117b560>, <kernel.DependentProduct object at 0x2b981117b518>) of role type named c_plus_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring c_plus:(n->(n->n))
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117b7a0>, <kernel.Sort object at 0x2b9808dc7320>) of role type named cPA_1_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring cPA_1:Prop
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117be18>, <kernel.Sort object at 0x2b9808dc7320>) of role type named cPA_2_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring cPA_2:Prop
% 3.31/3.52 FOF formula (<kernel.Constant object at 0x2b981117b6c8>, <kernel.Sort object at 0x2b9808dc7320>) of role type named cPA_IND_EQ_type
% 3.31/3.52 Using role type
% 3.31/3.52 Declaring cPA_IND_EQ:Prop
% 3.31/3.52 FOF formula (((eq Prop) cPA_1) (forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx))) of role definition named cPA_1_def
% 3.31/3.52 A new definition: (((eq Prop) cPA_1) (forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx)))
% 3.31/3.52 Defined: cPA_1:=(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx))
% 3.31/3.52 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
% 3.31/3.52 A new definition: (((eq Prop) cPA_2) (forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy)))))
% 3.31/3.52 Defined: cPA_2:=(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy))))
% 3.31/3.52 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
% 3.31/3.52 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))))))
% 3.31/3.52 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)))))
% 3.31/3.52 FOF formula (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) Xy)) ((c_plus Xy) Xx)))) of role conjecture named cPA_THM4
% 3.31/3.52 Conjecture to prove = (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) Xy)) ((c_plus Xy) Xx)))):Prop
% 3.31/3.52 We need to prove ['(((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) Xy)) ((c_plus Xy) Xx))))']
% 3.31/3.53 Parameter n:Type.
% 3.31/3.53 Parameter c0:n.
% 3.31/3.53 Parameter cS:(n->n).
% 3.31/3.53 Parameter c_plus:(n->(n->n)).
% 3.31/3.53 Definition cPA_1:=(forall (Xx:n), (((eq n) ((c_plus Xx) c0)) Xx)):Prop.
% 3.31/3.53 Definition cPA_2:=(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) (cS Xy))) (cS ((c_plus Xx) Xy)))):Prop.
% 3.31/3.53 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.
% 3.31/3.53 Trying to prove (((and ((and cPA_1) cPA_2)) cPA_IND_EQ)->(forall (Xx:n) (Xy:n), (((eq n) ((c_plus Xx) Xy)) ((c_plus Xy) Xx))))
% 3.31/3.53 Found x00:(P ((c_plus Xx) Xy))
% 3.31/3.53 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P ((c_plus Xx) Xy))
% 3.31/3.53 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P0 ((c_plus Xx) Xy))
% 3.31/3.53 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 3.31/3.53 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 3.31/3.53 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 21.45/21.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found x20:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found x20:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found x20:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 21.45/21.67 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 21.45/21.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 21.45/21.67 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 21.45/21.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 21.45/21.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 21.45/21.67 Found x40:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found x40:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found x40:(P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P ((c_plus Xx) Xy))
% 21.45/21.67 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P0 ((c_plus Xx) Xy))
% 21.45/21.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 21.45/21.67 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 21.45/21.67 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 21.45/21.67 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 21.45/21.67 Found x20:(P ((c_plus Xy) Xx))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P ((c_plus Xy) Xx))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P0 ((c_plus Xy) Xx))
% 21.45/21.67 Found x20:(P ((c_plus Xy) Xx))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P ((c_plus Xy) Xx))
% 21.45/21.67 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P0 ((c_plus Xy) Xx))
% 21.45/21.67 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 54.20/54.40 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 54.20/54.40 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found x20:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found x20:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 54.20/54.40 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 54.20/54.40 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found x0:(P ((c_plus Xx) Xy))
% 54.20/54.40 Instantiate: b:=((c_plus Xx) Xy):n
% 54.20/54.40 Found x0 as proof of (P0 b)
% 54.20/54.40 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 54.20/54.40 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 54.20/54.40 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 54.20/54.40 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found x40:(P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P ((c_plus Xy) Xx))
% 54.20/54.40 Found (fun (x40:(P ((c_plus Xy) Xx)))=> x40) as proof of (P0 ((c_plus Xy) Xx))
% 54.20/54.40 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 54.20/54.40 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 81.27/81.48 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 81.27/81.48 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 81.27/81.48 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found x0:(P0 b)
% 81.27/81.48 Instantiate: b:=((c_plus Xx) Xy):n
% 81.27/81.48 Found (fun (x0:(P0 b))=> x0) as proof of (P0 ((c_plus Xx) Xy))
% 81.27/81.48 Found (fun (P0:(n->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 81.27/81.48 Found (fun (P0:(n->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 81.27/81.48 Found x2:(P ((c_plus Xx) Xy))
% 81.27/81.48 Instantiate: b:=((c_plus Xx) Xy):n
% 81.27/81.48 Found x2 as proof of (P0 b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 81.27/81.48 Found x0:(P ((c_plus Xy) Xx))
% 81.27/81.48 Instantiate: b:=((c_plus Xy) Xx):n
% 81.27/81.48 Found x0 as proof of (P0 b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 81.27/81.48 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 81.27/81.48 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 81.27/81.48 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 81.27/81.48 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 112.07/112.30 Found x00:(P ((c_plus Xx) Xy))
% 112.07/112.30 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P ((c_plus Xx) Xy))
% 112.07/112.30 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P0 ((c_plus Xx) Xy))
% 112.07/112.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 112.07/112.30 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 112.07/112.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found x2:(P ((c_plus Xx) Xy))
% 112.07/112.30 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xy)):(n->n)
% 112.07/112.30 Found x2 as proof of (P0 (Xp Xx))
% 112.07/112.30 Found x0:(P ((c_plus Xx) Xy))
% 112.07/112.30 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xy)):(n->n)
% 112.07/112.30 Found x0 as proof of (P0 (Xp Xx))
% 112.07/112.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 112.07/112.30 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 112.07/112.30 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 112.07/112.30 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 112.07/112.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 112.07/112.30 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 112.07/112.30 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 112.07/112.30 Found x2:(P0 b)
% 112.07/112.30 Instantiate: b:=((c_plus Xx) Xy):n
% 112.07/112.30 Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((c_plus Xx) Xy))
% 112.07/112.30 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 112.07/112.30 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 112.07/112.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 112.07/112.30 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 112.07/112.30 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 112.07/112.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 112.07/112.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 112.07/112.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xx) c0)):(((eq n) ((c_plus Xx) c0)) ((c_plus Xx) c0))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) c0)) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 127.14/127.41 Found x4:(P ((c_plus Xx) Xy))
% 127.14/127.41 Instantiate: b:=((c_plus Xx) Xy):n
% 127.14/127.41 Found x4 as proof of (P0 b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found x2:(P ((c_plus Xy) Xx))
% 127.14/127.41 Instantiate: b:=((c_plus Xy) Xx):n
% 127.14/127.41 Found x2 as proof of (P0 b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 127.14/127.41 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 127.14/127.41 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 127.14/127.41 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 127.14/127.41 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 127.14/127.41 Found x00:(P b)
% 127.14/127.41 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 127.14/127.41 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 127.14/127.41 Found x20:(P ((c_plus Xx) c0))
% 127.14/127.41 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 127.14/127.41 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 127.14/127.41 Found x20:(P ((c_plus Xx) c0))
% 127.14/127.41 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P ((c_plus Xx) c0))
% 127.14/127.41 Found (fun (x20:(P ((c_plus Xx) c0)))=> x20) as proof of (P0 ((c_plus Xx) c0))
% 127.14/127.41 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 127.14/127.41 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 140.63/140.90 Found x2:(P0 b)
% 140.63/140.90 Instantiate: b:=((c_plus Xx) Xy):n
% 140.63/140.90 Found (fun (x2:(P0 b))=> x2) as proof of (P0 ((c_plus Xx) Xy))
% 140.63/140.90 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 140.63/140.90 Found (fun (P0:(n->Prop)) (x2:(P0 b))=> x2) as proof of (P b)
% 140.63/140.90 Found x2:(P ((c_plus Xy) Xx))
% 140.63/140.90 Instantiate: b:=((c_plus Xy) Xx):n
% 140.63/140.90 Found x2 as proof of (P0 b)
% 140.63/140.90 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 140.63/140.90 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found eq_ref000:=(eq_ref00 P):((P ((c_plus Xx) (cS Xx0)))->(P ((c_plus Xx) (cS Xx0))))
% 140.63/140.90 Found (eq_ref00 P) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found ((eq_ref0 ((c_plus Xx) (cS Xx0))) P) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found (((eq_ref n) ((c_plus Xx) (cS Xx0))) P) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found (((eq_ref n) ((c_plus Xx) (cS Xx0))) P) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus Xx) (cS Xx0))))):((P ((c_plus Xx) (cS Xx0)))->(P ((c_plus Xx) (cS Xx0))))
% 140.63/140.90 Found (x2 (fun (x3:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found (x2 (fun (x3:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 140.63/140.90 Found x20:(P ((c_plus Xx) Xy))
% 140.63/140.90 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P ((c_plus Xx) Xy))
% 140.63/140.90 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 140.63/140.90 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 140.63/140.90 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 140.63/140.90 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 140.63/140.90 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 140.63/140.90 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 140.63/140.90 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 140.63/140.90 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 140.63/140.90 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 140.63/140.90 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 140.63/140.90 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 140.63/140.90 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)))))
% 140.63/140.90 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)
% 140.63/140.90 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)
% 155.29/155.54 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)
% 155.29/155.54 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)
% 155.29/155.54 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)))))
% 155.29/155.54 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)
% 155.29/155.54 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)
% 155.29/155.54 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)
% 155.29/155.54 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)
% 155.29/155.54 Found x00:(P ((c_plus Xy) Xx))
% 155.29/155.54 Found (fun (x00:(P ((c_plus Xy) Xx)))=> x00) as proof of (P ((c_plus Xy) Xx))
% 155.29/155.54 Found (fun (x00:(P ((c_plus Xy) Xx)))=> x00) as proof of (P0 ((c_plus Xy) Xx))
% 155.29/155.54 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 155.29/155.54 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 155.29/155.54 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 155.29/155.54 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 155.29/155.54 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 155.29/155.54 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 155.29/155.54 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 155.29/155.54 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 155.29/155.54 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 155.29/155.54 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 155.29/155.54 Found x4:(P ((c_plus Xx) Xy))
% 155.29/155.54 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) Xy)):(n->n)
% 187.02/187.30 Found x4 as proof of (P0 (Xp Xx))
% 187.02/187.30 Found x0:(P ((c_plus Xx) Xy))
% 187.02/187.30 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) Xy)):(n->n)
% 187.02/187.30 Found x0 as proof of (P0 (Xp Xx))
% 187.02/187.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 187.02/187.30 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 187.02/187.30 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 187.02/187.30 Found x2:(P ((c_plus Xx) Xy))
% 187.02/187.30 Instantiate: Xp:=(fun (x5:n)=> ((c_plus x5) Xy)):(n->n)
% 187.02/187.30 Found x2 as proof of (P0 (Xp Xx))
% 187.02/187.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 187.02/187.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) (cS Xx0))):(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus Xx) (cS Xx0)))
% 187.02/187.30 Found (eq_ref0 ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 187.02/187.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus (cS Xx0)) Xx))
% 187.02/187.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) (cS Xx0))):(((eq n) ((c_plus Xx) (cS Xx0))) ((c_plus Xx) (cS Xx0)))
% 187.02/187.30 Found (eq_ref0 ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) (cS Xx0))) as proof of (((eq n) ((c_plus Xx) (cS Xx0))) b)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 187.02/187.30 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 187.02/187.30 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 187.02/187.30 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 187.02/187.30 Found x00:(P ((c_plus Xx) Xy))
% 187.02/187.30 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P ((c_plus Xx) Xy))
% 187.02/187.30 Found (fun (x00:(P ((c_plus Xx) Xy)))=> x00) as proof of (P0 ((c_plus Xx) Xy))
% 187.02/187.30 Found x2:(P ((c_plus Xy) Xx))
% 187.02/187.30 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 187.02/187.30 Found x2 as proof of (P0 (Xp Xy))
% 187.02/187.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 187.02/187.30 Found (eq_ref0 a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 187.02/187.30 Found (eq_ref0 a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found ((eq_ref n) a) as proof of (((eq n) a) Xy)
% 187.02/187.30 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 187.02/187.30 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 187.02/187.30 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 196.02/196.27 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 196.02/196.27 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 196.02/196.27 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 196.02/196.27 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 196.02/196.27 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 196.02/196.27 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 196.02/196.27 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 196.02/196.27 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 196.02/196.27 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 196.02/196.27 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 196.02/196.27 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))):((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) (Xp (cS Xx0))))
% 196.02/196.27 Found (eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found ((eq_substitution000 ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found (((eq_substitution00 (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found ((((eq_substitution0 n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 196.02/196.27 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))
% 196.02/196.28 Found ((conj00 ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 196.02/196.28 Found (((conj0 (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 196.02/196.28 Found ((((conj (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 196.02/196.28 Found ((((conj (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 196.02/196.28 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 196.02/196.28 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 196.02/196.28 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 196.02/196.28 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 201.80/202.05 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 201.80/202.05 Found x4:(P0 b)
% 201.80/202.05 Instantiate: b:=((c_plus Xx) Xy):n
% 201.80/202.05 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) Xy))
% 201.80/202.05 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 201.80/202.05 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 201.80/202.05 Found eq_ref00:=(eq_ref0 (Xp c0)):(((eq n) (Xp c0)) (Xp c0))
% 201.80/202.05 Found (eq_ref0 (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 201.80/202.05 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 201.80/202.05 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 201.80/202.05 Found ((eq_ref n) (Xp c0)) as proof of (((eq n) (Xp c0)) ((c_plus Xy) c0))
% 201.80/202.05 Found eq_substitution00000:=(eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))):((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) (Xp (cS Xx0))))
% 201.80/202.05 Found (eq_substitution0000 (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found ((eq_substitution000 ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found (((eq_substitution00 (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found ((((eq_substitution0 n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of ((((eq n) (Xp Xx0)) ((c_plus Xy) Xx0))->(((eq n) (Xp (cS Xx0))) ((c_plus Xy) (cS Xx0))))
% 201.80/202.05 Found (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0))))) as proof of (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))
% 201.80/202.05 Found ((conj00 ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 201.80/202.05 Found (((conj0 (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 201.80/202.05 Found ((((conj (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 201.80/202.05 Found ((((conj (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx)))))) ((eq_ref n) (Xp c0))) (fun (Xx0:n)=> (((((eq_substitution n) n) (Xp Xx0)) ((c_plus Xy) Xx0)) (fun (x5:n)=> (Xp (cS Xx0)))))) as proof of ((and (((eq n) (Xp c0)) ((c_plus Xy) c0))) (forall (Xx:n), ((((eq n) (Xp Xx)) ((c_plus Xy) Xx))->(((eq n) (Xp (cS Xx))) ((c_plus Xy) (cS Xx))))))
% 201.80/202.05 Found x2:(P ((c_plus Xy) Xx))
% 201.80/202.05 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 201.80/202.05 Found x2 as proof of (P0 (Xp Xy))
% 201.80/202.05 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 201.80/202.05 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 208.01/208.26 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 208.01/208.26 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 208.01/208.26 Found x20:(P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 208.01/208.26 Found x20:(P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 208.01/208.26 Found x20:(P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 208.01/208.26 Found x20:(P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 208.01/208.26 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 208.01/208.26 Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 208.01/208.26 Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% 208.01/208.26 Found eq_substitution as proof of b
% 208.01/208.26 Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% 208.01/208.26 Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% 208.01/208.26 Found eq_substitution as proof of b
% 208.01/208.26 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 208.01/208.26 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 208.01/208.26 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 208.01/208.26 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 208.01/208.26 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 208.01/208.26 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 208.01/208.26 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 208.01/208.26 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 208.01/208.26 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found x0:(P ((c_plus Xy) Xx))
% 239.51/239.81 Instantiate: Xp:=(fun (x3:n)=> ((c_plus x3) Xx)):(n->n)
% 239.51/239.81 Found x0 as proof of (P0 (Xp Xy))
% 239.51/239.81 Found x00:(P b)
% 239.51/239.81 Found (fun (x00:(P b))=> x00) as proof of (P b)
% 239.51/239.81 Found (fun (x00:(P b))=> x00) as proof of (P0 b)
% 239.51/239.81 Found x4:(P ((c_plus Xy) Xx))
% 239.51/239.81 Instantiate: b:=((c_plus Xy) Xx):n
% 239.51/239.81 Found x4 as proof of (P0 b)
% 239.51/239.81 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 239.51/239.81 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 239.51/239.81 Found x20:(P b)
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P b)
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% 239.51/239.81 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 239.51/239.81 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 239.51/239.81 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 239.51/239.81 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 239.51/239.81 Found x20:(P ((c_plus Xy) c0))
% 239.51/239.81 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P ((c_plus Xy) c0))
% 239.51/239.81 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P0 ((c_plus Xy) c0))
% 239.51/239.81 Found x20:(P ((c_plus Xy) c0))
% 239.51/239.81 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P ((c_plus Xy) c0))
% 239.51/239.81 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P0 ((c_plus Xy) c0))
% 239.51/239.81 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 239.51/239.81 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found x4:(P0 b)
% 239.51/239.81 Instantiate: b:=((c_plus Xx) Xy):n
% 239.51/239.81 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) Xy))
% 239.51/239.81 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 239.51/239.81 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 239.51/239.81 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 239.51/239.81 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 239.51/239.81 Found x4:(P0 b)
% 239.51/239.81 Instantiate: b:=((c_plus Xx) Xy):n
% 239.51/239.81 Found (fun (x4:(P0 b))=> x4) as proof of (P0 ((c_plus Xx) Xy))
% 239.51/239.81 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of ((P0 b)->(P0 ((c_plus Xx) Xy)))
% 239.51/239.81 Found (fun (P0:(n->Prop)) (x4:(P0 b))=> x4) as proof of (P b)
% 239.51/239.81 Found x20:(P b)
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) Xy))
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 239.51/239.81 Found x20:(P b)
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) Xy))
% 239.51/239.81 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 239.51/239.81 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 239.51/239.81 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 239.51/239.81 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 250.16/250.44 Found (eq_ref0 b0) as proof of (((eq n) b0) b)
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) b)
% 250.16/250.44 Found x40:(P ((c_plus Xx) Xy))
% 250.16/250.44 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P ((c_plus Xx) Xy))
% 250.16/250.44 Found (fun (x40:(P ((c_plus Xx) Xy)))=> x40) as proof of (P0 ((c_plus Xx) Xy))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 250.16/250.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xy) Xx))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 250.16/250.44 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 250.16/250.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 250.16/250.44 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 250.16/250.44 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 250.16/250.44 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 250.16/250.44 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 250.16/250.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 ((c_plus Xy) c0)):(((eq n) ((c_plus Xy) c0)) ((c_plus Xy) c0))
% 250.16/250.44 Found (eq_ref0 ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 250.16/250.44 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 250.16/250.44 Found eq_ref00:=(eq_ref0 ((c_plus Xy) c0)):(((eq n) ((c_plus Xy) c0)) ((c_plus Xy) c0))
% 250.16/250.44 Found (eq_ref0 ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 250.16/250.44 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 258.37/258.69 Found x4:(P ((c_plus Xy) Xx))
% 258.37/258.69 Instantiate: b:=((c_plus Xy) Xx):n
% 258.37/258.69 Found x4 as proof of (P0 b)
% 258.37/258.69 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 258.37/258.69 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found x4:(P ((c_plus Xy) Xx))
% 258.37/258.69 Instantiate: b:=((c_plus Xy) Xx):n
% 258.37/258.69 Found x4 as proof of (P0 b)
% 258.37/258.69 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 258.37/258.69 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 258.37/258.69 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))):((P ((c_plus Xy) (cS Xx0)))->(P ((c_plus Xy) (cS Xx0))))
% 258.37/258.69 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 258.37/258.69 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 258.37/258.69 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))):((P ((c_plus Xy) (cS Xx0)))->(P ((c_plus Xy) (cS Xx0))))
% 258.37/258.69 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 258.37/258.69 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 258.37/258.69 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 258.37/258.69 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 258.37/258.69 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xx))
% 258.37/258.69 Found x20:=(x2 Xx):(((eq n) ((c_plus Xx) c0)) Xx)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found (x2 Xx) as proof of (((eq n) ((c_plus Xx) c0)) b)
% 258.37/258.69 Found x40:(P ((c_plus Xx) c0))
% 258.37/258.69 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 258.37/258.69 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 258.37/258.69 Found x40:(P ((c_plus Xx) c0))
% 258.37/258.69 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 258.37/258.69 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 258.37/258.69 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)))))
% 258.37/258.69 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)
% 258.37/258.69 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)
% 258.37/258.69 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)
% 267.17/267.51 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)
% 267.17/267.51 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)))))
% 267.17/267.51 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)
% 267.17/267.51 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)
% 267.17/267.51 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)
% 267.17/267.51 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)
% 267.17/267.51 Found x20:(P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 267.17/267.51 Found x20:(P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 267.17/267.51 Found x20:(P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 267.17/267.51 Found x20:(P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P1 ((c_plus Xy) Xx))
% 267.17/267.51 Found (fun (x20:(P1 ((c_plus Xy) Xx)))=> x20) as proof of (P2 ((c_plus Xy) Xx))
% 267.17/267.51 Found x20:(P b)
% 267.17/267.51 Found (fun (x20:(P b))=> x20) as proof of (P b)
% 267.17/267.51 Found (fun (x20:(P b))=> x20) as proof of (P0 b)
% 267.17/267.51 Found x20:(P ((c_plus Xy) c0))
% 267.17/267.51 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P ((c_plus Xy) c0))
% 267.17/267.51 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P0 ((c_plus Xy) c0))
% 267.17/267.51 Found x20:(P ((c_plus Xy) c0))
% 267.17/267.51 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P ((c_plus Xy) c0))
% 267.17/267.51 Found (fun (x20:(P ((c_plus Xy) c0)))=> x20) as proof of (P0 ((c_plus Xy) c0))
% 267.17/267.51 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 267.17/267.51 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 267.17/267.51 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 267.17/267.51 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 267.17/267.51 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 267.17/267.51 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 267.17/267.51 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 267.17/267.51 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 267.17/267.51 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 267.17/267.51 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 267.17/267.51 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 290.69/291.03 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 290.69/291.03 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found x20:(P ((c_plus Xy) Xx))
% 290.69/291.03 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P ((c_plus Xy) Xx))
% 290.69/291.03 Found (fun (x20:(P ((c_plus Xy) Xx)))=> x20) as proof of (P0 ((c_plus Xy) Xx))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 290.69/291.03 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus Xx) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 290.69/291.03 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b)
% 290.69/291.03 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 290.69/291.03 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 290.69/291.03 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xx) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 ((c_plus Xy) Xx)):(((eq n) ((c_plus Xy) Xx)) ((c_plus Xy) Xx))
% 290.69/291.03 Found (eq_ref0 ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) Xx)) as proof of (((eq n) ((c_plus Xy) Xx)) b0)
% 290.69/291.03 Found x20:(P b)
% 290.69/291.03 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) Xy))
% 290.69/291.03 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 290.69/291.03 Found x20:(P b)
% 290.69/291.03 Found (fun (x20:(P b))=> x20) as proof of (P ((c_plus Xx) Xy))
% 290.69/291.03 Found (fun (x20:(P b))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 290.69/291.03 Found x20:(P ((c_plus Xx) Xy))
% 290.69/291.03 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P ((c_plus Xx) Xy))
% 290.69/291.03 Found (fun (x20:(P ((c_plus Xx) Xy)))=> x20) as proof of (P0 ((c_plus Xx) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 290.69/291.03 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 ((c_plus Xy) c0)):(((eq n) ((c_plus Xy) c0)) ((c_plus Xy) c0))
% 290.69/291.03 Found (eq_ref0 ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found eq_ref00:=(eq_ref0 b):(((eq n) b) b)
% 290.69/291.03 Found (eq_ref0 b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found ((eq_ref n) b) as proof of (((eq n) b) ((c_plus c0) Xy))
% 290.69/291.03 Found eq_ref00:=(eq_ref0 ((c_plus Xy) c0)):(((eq n) ((c_plus Xy) c0)) ((c_plus Xy) c0))
% 290.69/291.03 Found (eq_ref0 ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found ((eq_ref n) ((c_plus Xy) c0)) as proof of (((eq n) ((c_plus Xy) c0)) b)
% 290.69/291.03 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))):((P ((c_plus Xx) (cS Xx0)))->(P ((c_plus Xx) (cS Xx0))))
% 291.96/292.26 Found (x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 291.96/292.26 Found (x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 291.96/292.26 Found x40:=(x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))):((P ((c_plus Xx) (cS Xx0)))->(P ((c_plus Xx) (cS Xx0))))
% 291.96/292.26 Found (x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 291.96/292.26 Found (x4 (fun (x5:n)=> (P ((c_plus Xx) (cS Xx0))))) as proof of (P0 ((c_plus Xx) (cS Xx0)))
% 291.96/292.26 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 291.96/292.26 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found eq_ref00:=(eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))):(((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy)))))
% 291.96/292.26 Found (eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found eq_ref00:=(eq_ref0 a):(((eq n) a) a)
% 291.96/292.26 Found (eq_ref0 a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found ((eq_ref n) a) as proof of (((eq n) a) Xx)
% 291.96/292.26 Found eq_ref00:=(eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))):(((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy)))))
% 291.96/292.26 Found (eq_ref0 (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 291.96/292.26 Found ((eq_ref Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) as proof of (((eq Prop) (forall (Xx:n), ((((eq n) ((c_plus Xy) Xx)) ((c_plus Xx) Xy))->(((eq n) ((c_plus Xy) (cS Xx))) ((c_plus (cS Xx)) Xy))))) b)
% 299.68/300.00 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 299.68/300.00 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 299.68/300.00 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found x0:(P ((c_plus Xy) Xx))
% 299.68/300.00 Instantiate: b:=((c_plus Xy) Xx):n
% 299.68/300.00 Found x0 as proof of (P0 b)
% 299.68/300.00 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 299.68/300.00 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b)
% 299.68/300.00 Found eq_ref00:=(eq_ref0 b0):(((eq n) b0) b0)
% 299.68/300.00 Found (eq_ref0 b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found ((eq_ref n) b0) as proof of (((eq n) b0) ((c_plus Xy) Xx))
% 299.68/300.00 Found eq_ref00:=(eq_ref0 ((c_plus Xx) Xy)):(((eq n) ((c_plus Xx) Xy)) ((c_plus Xx) Xy))
% 299.68/300.00 Found (eq_ref0 ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found ((eq_ref n) ((c_plus Xx) Xy)) as proof of (((eq n) ((c_plus Xx) Xy)) b0)
% 299.68/300.00 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))):((P ((c_plus Xy) (cS Xx0)))->(P ((c_plus Xy) (cS Xx0))))
% 299.68/300.00 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 299.68/300.00 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 299.68/300.00 Found x20:=(x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))):((P ((c_plus Xy) (cS Xx0)))->(P ((c_plus Xy) (cS Xx0))))
% 299.68/300.00 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 299.68/300.00 Found (x2 (fun (x3:n)=> (P ((c_plus Xy) (cS Xx0))))) as proof of (P0 ((c_plus Xy) (cS Xx0)))
% 299.68/300.00 Found x40:(P ((c_plus Xx) c0))
% 299.68/300.00 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 299.68/300.00 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 299.68/300.00 Found x40:(P ((c_plus Xx) c0))
% 299.68/300.00 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P ((c_plus Xx) c0))
% 299.68/300.00 Found (fun (x40:(P ((c_plus Xx) c0)))=> x40) as proof of (P0 ((c_plus Xx) c0))
% 299.68/300.00 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)))))
% 299.68/300.00 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)
% 299.68/300.00 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)
% 299.68/300.00 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
%------------------------------------------------------------------------------