%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV434^1 : TPTP v6.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n112.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 13:34:11 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  : SEV434^1 : TPTP v6.1.0. Released v5.2.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n112.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:13:31 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 0x128eea8>, <kernel.DependentProduct object at 0x128e878>) of role type named f
% Using role type
% Declaring f:(Prop->fofType)
% FOF formula (forall (Y:fofType), ((ex Prop) (fun (X:Prop)=> (((eq fofType) (f X)) Y)))) of role axiom named fsurj
% A new axiom: (forall (Y:fofType), ((ex Prop) (fun (X:Prop)=> (((eq fofType) (f X)) Y))))
% FOF formula (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) (((eq fofType) Y) Z))) of role conjecture named less3
% Conjecture to prove = (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) (((eq fofType) Y) Z))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) (((eq fofType) Y) Z)))']
% Parameter fofType:Type.
% Parameter f:(Prop->fofType).
% Axiom fsurj:(forall (Y:fofType), ((ex Prop) (fun (X:Prop)=> (((eq fofType) (f X)) Y)))).
% Trying to prove (forall (X:fofType) (Y:fofType) (Z:fofType), ((or ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) (((eq fofType) Y) Z)))
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 (((eq fofType) Y) Z)):(((eq Prop) (((eq fofType) Y) Z)) (((eq fofType) Y) Z))
% Found (eq_ref0 (((eq fofType) Y) Z)) as proof of (((eq Prop) (((eq fofType) Y) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) Y) Z)) as proof of (((eq Prop) (((eq fofType) Y) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) Y) Z)) as proof of (((eq Prop) (((eq fofType) Y) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) Y) Z)) as proof of (((eq Prop) (((eq fofType) Y) Z)) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) X) Z)):(((eq Prop) (((eq fofType) X) Z)) (((eq fofType) X) Z))
% Found (eq_ref0 (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found eq_ref00:=(eq_ref0 ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))):(((eq Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z)))
% Found (eq_ref0 ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) as proof of (((eq Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) as proof of (((eq Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) as proof of (((eq Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) as proof of (((eq Prop) ((or (((eq fofType) X) Y)) (((eq fofType) X) Z))) b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) X) Z))
% 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) X) Y)):(((eq Prop) (((eq fofType) X) Y)) (((eq fofType) X) Y))
% Found (eq_ref0 (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) X) Z)):(((eq Prop) (((eq fofType) X) Z)) (((eq fofType) X) Z))
% Found (eq_ref0 (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Z)) as proof of (((eq Prop) (((eq fofType) X) Z)) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P Y))):((P Y)->(P Y))
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P Y))):((P Y)->(P Y))
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found classic0:=(classic (((eq fofType) X) Y)):((or (((eq fofType) X) Y)) (not (((eq fofType) X) Y)))
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (or_intror00 (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) X) Y)) a))
% Found ((or_intror0 ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) X) Y)) a))
% Found (((or_intror (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) X) Y)) a))
% Found (((or_intror (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) X) Y)) a))
% Found classic0:=(classic (((eq fofType) X) Y)):((or (((eq fofType) X) Y)) (not (((eq fofType) X) Y)))
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (classic (((eq fofType) X) Y)) as proof of ((or (((eq fofType) X) Y)) a)
% Found (or_intror00 (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)))
% Found ((or_intror0 ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)))
% Found (((or_intror (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)))
% Found (((or_intror (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)) (classic (((eq fofType) X) Y))) as proof of (P ((or (((eq fofType) Y) Z)) ((or (((eq fofType) X) Y)) a)))
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% 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 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) 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 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) X) Y)):(((eq Prop) (((eq fofType) X) Y)) (((eq fofType) X) Y))
% Found (eq_ref0 (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found ((eq_ref Prop) (((eq fofType) X) Y)) as proof of (((eq Prop) (((eq fofType) X) Y)) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P Y))):((P Y)->(P Y))
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P Y))):((P Y)->(P Y))
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P Y))):((P Y)->(P Y))
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found (x0 (fun (x1:fofType)=> (P Y))) as proof of (P0 Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) 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 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_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_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% 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_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) 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 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) 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 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x:(P X)
% Instantiate: b:=X:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% 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_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% 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_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_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_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_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) 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 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) 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 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P Y)->(P Y))
% Found (eq_ref00 P) as proof of (P0 Y)
% Found ((eq_ref0 Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found (((eq_ref fofType) Y) P) as proof of (P0 Y)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found eq_ref000:=(eq_ref00 P):((P X)->(P X))
% Found (eq_ref00 P) as proof of (P0 X)
% Found ((eq_ref0 X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found (((eq_ref fofType) X) P) as proof of (P0 X)
% Found x:(P Y)
% Instantiate: b:=Y:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x:(P Z)
% Instantiate: b:=Z:fofType
% Found x as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref000:=(eq_ref00 P):((P Z)->(P Z))
% Found (eq_ref00 P) as proof of (P0 Z)
% Found ((eq_ref0 Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found (((eq_ref fofType) Z) P) as proof of (P0 Z)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq fofType) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq fofType) (f x)) b)
% Found ((eq_ref fofType) (f x)) as proof of (((eq fofType) (f x)) b)
% Found ((eq_ref fofType) (f x)) as proof of (((eq fofType) (f x)) b)
% Found ((eq_ref fofType) (f x)) as proof of (((eq fofType) (f x)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (f x))
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Y)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Z)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=X:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x00:=(x0 (fun (x1:fofType)=> (P X))):((P X)->(P X))
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found (x0 (fun (x1:fofType)=> (P X))) as proof of (P0 X)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Y:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Y)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found x0:(((eq fofType) (f x)) Y0)
% Instantiate: Y0:=Z:fofType;b:=(f x):fofType
% Found x0 as proof of (((eq fofType) b) Z)
% Found eq_ref00:=(eq_ref0 X):(((eq fofType) X) X)
% Found (eq_ref0 X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found ((eq_ref fofType) X) as proof of (((eq fofType) X) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found eq_ref00:=(eq_ref0 Y):(((eq fofType) Y) Y)
% Found (eq_ref0 Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found ((eq_ref fofType) Y) as proof of (((eq fofType) Y) b0)
% Found eq_ref00:=(eq_ref0 Z):(((eq fofType) Z) Z)
% Found (eq_ref0 Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found ((eq_ref fofType) Z) as proof of (((eq fofType) Z) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) X)
% Found ((eq_ref fofType) b0) as proof of (((eq f
% EOF
%------------------------------------------------------------------------------