%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : PUZ120^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n093.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:29:00 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : PUZ120^5 : TPTP v6.1.0. Bugfixed v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n093.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:24:31 CDT 2014
% % CPUTime  : 300.09 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0xd354d0>, <kernel.Constant object at 0xd35d40>) of role type named c1_type
% Using role type
% Declaring c1:fofType
% FOF formula (<kernel.Constant object at 0xf8bb00>, <kernel.DependentProduct object at 0xd350e0>) of role type named s_type
% Using role type
% Declaring s:(fofType->fofType)
% FOF formula (<kernel.Constant object at 0xd35c68>, <kernel.DependentProduct object at 0xd35638>) of role type named cCKB6_NUM_type
% Using role type
% Declaring cCKB6_NUM:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) cCKB6_NUM) (fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx))))) of role definition named cCKB6_NUM_def
% A new definition: (((eq (fofType->Prop)) cCKB6_NUM) (fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx)))))
% Defined: cCKB6_NUM:=(fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx))))
% FOF formula (forall (Xx:fofType) (Xy:fofType), (((and ((and (cCKB6_NUM Xx)) (cCKB6_NUM Xy))) (((eq fofType) (s (s (s Xx)))) (s (s (s Xy)))))->(((eq fofType) Xx) Xy))) of role conjecture named cCKB6_L26000
% Conjecture to prove = (forall (Xx:fofType) (Xy:fofType), (((and ((and (cCKB6_NUM Xx)) (cCKB6_NUM Xy))) (((eq fofType) (s (s (s Xx)))) (s (s (s Xy)))))->(((eq fofType) Xx) Xy))):Prop
% We need to prove ['(forall (Xx:fofType) (Xy:fofType), (((and ((and (cCKB6_NUM Xx)) (cCKB6_NUM Xy))) (((eq fofType) (s (s (s Xx)))) (s (s (s Xy)))))->(((eq fofType) Xx) Xy)))']
% Parameter fofType:Type.
% Parameter c1:fofType.
% Parameter s:(fofType->fofType).
% Definition cCKB6_NUM:=(fun (Xx:fofType)=> (forall (Xp:(fofType->Prop)), (((and (Xp c1)) (forall (Xw:fofType), ((Xp Xw)->(Xp (s Xw)))))->(Xp Xx)))):(fofType->Prop).
% Trying to prove (forall (Xx:fofType) (Xy:fofType), (((and ((and (cCKB6_NUM Xx)) (cCKB6_NUM Xy))) (((eq fofType) (s (s (s Xx)))) (s (s (s Xy)))))->(((eq fofType) Xx) Xy)))
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x0:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found x2:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x0:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x0:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found x10:=(x1 (fun (x4:fofType)=> (P c1))):((P c1)->(P c1))
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found x10:=(x1 (fun (x3:fofType)=> (P c1))):((P c1)->(P c1))
% Found (x1 (fun (x3:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found (x1 (fun (x3:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found x10:=(x1 (fun (x4:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x4:(P c1)
% Found x4 as proof of (P c1)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found x3:(P c1)
% Found x3 as proof of (P c1)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref000:=(eq_ref00 P):((P c1)->(P c1))
% Found (eq_ref00 P) as proof of (P0 c1)
% Found ((eq_ref0 c1) P) as proof of (P0 c1)
% Found (((eq_ref fofType) c1) P) as proof of (P0 c1)
% Found (((eq_ref fofType) c1) P) as proof of (P0 c1)
% Found x2:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x4:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x0:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x2:(P Xx)
% Instantiate: b:=Xx:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x10:=(x1 (fun (x3:fofType)=> (P c1))):((P c1)->(P c1))
% Found (x1 (fun (x3:fofType)=> (P c1))) as proof of (P0 c1)
% Found (x1 (fun (x3:fofType)=> (P c1))) as proof of (P0 c1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) c1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x2:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x2 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x10:=(x1 (fun (x5:fofType)=> (P Xw))):((P Xw)->(P Xw))
% Found (x1 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found (x1 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found x0:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x0 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))):(((eq Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy)))))
% Found (eq_ref0 (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) as proof of (((eq Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) as proof of (((eq Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) as proof of (((eq Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) as proof of (((eq Prop) (forall (Xw:fofType), (((cCKB6_NUM Xy)->(((eq fofType) Xw) Xy))->((cCKB6_NUM Xy)->(((eq fofType) (s Xw)) Xy))))) b)
% Found x20:=(x2 (fun (x5:fofType)=> (P Xw))):((P Xw)->(P Xw))
% Found (x2 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found (x2 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x10:=(x1 (fun (x5:fofType)=> (P Xw))):((P Xw)->(P Xw))
% Found (x1 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found (x1 (fun (x5:fofType)=> (P Xw))) as proof of (P0 Xw)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))):(((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy))))
% Found (eq_ref0 (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xw) Xy)->(((eq fofType) (s Xw)) Xy)))) b)
% Found eq_ref000:=(eq_ref00 P):((P Xx)->(P Xx))
% Found (eq_ref00 P) as proof of (P0 Xx)
% Found ((eq_ref0 Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found (((eq_ref fofType) Xx) P) as proof of (P0 Xx)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))):(((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw)))))
% Found (eq_ref0 (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((((eq fofType) Xx) Xw)->(((eq fofType) Xx) (s Xw))))) b)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xy)
% Found x10:=(x1 (fun (x5:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x5:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x5:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x10:=(x1 (fun (x5:fofType)=> (P (s Xw)))):((P (s Xw))->(P (s Xw)))
% Found (x1 (fun (x5:fofType)=> (P (s Xw)))) as proof of (P0 (s Xw))
% Found (x1 (fun (x5:fofType)=> (P (s Xw)))) as proof of (P0 (s Xw))
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))):(((eq Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw))))))
% Found (eq_ref0 (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) as proof of (((eq Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) as proof of (((eq Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) as proof of (((eq Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) as proof of (((eq Prop) (forall (Xw:fofType), (((P Xx)->(P Xw))->((P Xx)->(P (s Xw)))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))):(((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy)))))
% Found (eq_ref0 (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found x10:=(x1 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))):(((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy)))))
% Found (eq_ref0 (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found ((eq_ref Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) as proof of (((eq Prop) (fofType->(((cCKB6_NUM Xy)->(P Xy))->((cCKB6_NUM Xy)->(P Xy))))) b)
% Found x10:=(x1 (fun (x4:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x4:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x10:=(x1 (fun (x4:fofType)=> (P (s Xw)))):((P (s Xw))->(P (s Xw)))
% Found (x1 (fun (x4:fofType)=> (P (s Xw)))) as proof of (P0 (s Xw))
% Found (x1 (fun (x4:fofType)=> (P (s Xw)))) as proof of (P0 (s Xw))
% Found eq_ref000:=(eq_ref00 P):((P b)->(P b))
% Found (eq_ref00 P) as proof of (P0 b)
% Found ((eq_ref0 b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found (((eq_ref fofType) b) P) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found eq_ref00:=(eq_ref0 (fofType->((P Xy)->(P Xy)))):(((eq Prop) (fofType->((P Xy)->(P Xy)))) (fofType->((P Xy)->(P Xy))))
% Found (eq_ref0 (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found x4:(((eq fofType) Xw) Xy)
% Found x4 as proof of (((eq fofType) Xw) Xy)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))):(((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) (forall (Xw:fofType), ((P Xw)->(P (s Xw)))))
% Found (eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->((P Xy)->(P Xy)))):(((eq Prop) (fofType->((P Xy)->(P Xy)))) (fofType->((P Xy)->(P Xy))))
% Found (eq_ref0 (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))):(((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) (forall (Xw:fofType), ((P Xw)->(P (s Xw)))))
% Found (eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found eq_ref00:=(eq_ref0 (fofType->((P Xy)->(P Xy)))):(((eq Prop) (fofType->((P Xy)->(P Xy)))) (fofType->((P Xy)->(P Xy))))
% Found (eq_ref0 (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found ((eq_ref Prop) (fofType->((P Xy)->(P Xy)))) as proof of (((eq Prop) (fofType->((P Xy)->(P Xy)))) b)
% Found eq_ref00:=(eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))):(((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) (forall (Xw:fofType), ((P Xw)->(P (s Xw)))))
% Found (eq_ref0 (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found ((eq_ref Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) as proof of (((eq Prop) (forall (Xw:fofType), ((P Xw)->(P (s Xw))))) b)
% Found eq_ref000:=(eq_ref00 P):((P c1)->(P c1))
% Found (eq_ref00 P) as proof of ((P c1)->(P c1))
% Found ((eq_ref0 c1) P) as proof of ((P c1)->(P c1))
% Found (((eq_ref fofType) c1) P) as proof of ((P c1)->(P c1))
% Found (((eq_ref fofType) c1) P) as proof of ((P c1)->(P c1))
% Found x10:=(x1 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x1 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x1 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 c1):(((eq fofType) c1) c1)
% Found (eq_ref0 c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found ((eq_ref fofType) c1) as proof of (((eq fofType) c1) c1)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 (s Xw)):(((eq fofType) (s Xw)) (s Xw))
% Found (eq_ref0 (s Xw)) as proof of (((eq fofType) (s Xw)) b)
% Found ((eq_ref fofType) (s Xw)) as proof of (((eq fofType) (s Xw)) b)
% Found ((eq_ref fofType) (s Xw)) as proof of (((eq fofType) (s Xw)) b)
% Found ((eq_ref fofType) (s Xw)) as proof of (((eq fofType) (s Xw)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x10:=(x1 (fun (x2:fofType)=> (P b))):((P b)->(P b))
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found (x1 (fun (x2:fofType)=> (P b))) as proof of (P0 b)
% Found eq_ref000:=(eq_ref00 P):((P Xy)->(P Xy))
% Found (eq_ref00 P) as proof of (P0 Xy)
% Found ((eq_ref0 Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found (((eq_ref fofType) Xy) P) as proof of (P0 Xy)
% Found x10:=(x1 (fun (x4:fofType)=> (P c1))):((P c1)->(P c1))
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of (P0 c1)
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of (P0 c1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xy)
% Found x4:(P Xy)
% Instantiate: b:=Xy:fofType
% Found x4 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_sym0:=(eq_sym Prop):(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a)))
% Instantiate: b:=(forall (a:Prop) (b:Prop), ((((eq Prop) a) b)->(((eq Prop) b) a))):Prop
% Found eq_sym0 as proof of b
% Found x4:(((eq fofType) Xx) Xw)
% Found x4 as proof of (((eq fofType) Xx) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found x10:=(x1 (fun (x4:fofType)=> (P c1))):((P c1)->(P c1))
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found (x1 (fun (x4:fofType)=> (P c1))) as proof of ((P c1)->(P c1))
% Found eq_ref000:=(eq_ref00 P):((P c1)->(P c1))
% Found (eq_ref00 P) as proof of ((P c1)->(P c1))
% Found ((eq_ref0 c1) P) as proof of ((P c1)->(P c1))
% Found (((eq_ref fofType) c1) P) as proof of ((P c1)->(P c1))
% Found (((eq_ref fofType) c1) P) as proof of ((P c1)->(P c1))
% Found x10:=(x1 (fun (x2:fofType)=> (P Xx))):((P Xx)->(P Xx))
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found (x1 (fun (x2:fofType)=> (P Xx))) as proof of (P0 Xx)
% Found x10:=(x1 (fun (x2:fofType)=> (P Xy))):((P Xy)->(P Xy))
% Found (x1 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found (x1 (fun (x2:fofType)=> (P Xy))) as proof of (P0 Xy)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 Xy):(((eq fofType) Xy) Xy)
% Found (eq_ref0 Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found ((eq_ref fofType) Xy) as proof of (((eq fofType) Xy) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found classical_choice:=(fun (A:Type) (B:Type) (R:(A->(B->Prop))) (b:B)=> ((fun (C:((forall (x:A), ((ex B) (fun (y:B)=> (((fun (x0:A) (y0:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y0))) x) y))))->((ex (A->B)) (fun (f:(A->B))=> (forall (x:A), (((fun (x0:A) (y:B)=> (((ex B) (fun (z:B)=> ((R x0) z)))->((R x0) y))) x) (f x)))))))=> (C (fun (x:A)=> ((fun (C0:((or ((ex B) (fun (z:B)=> ((R x) z
% EOF
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