TSTP Solution File: SEV342^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV342^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n188.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 13:34:04 EDT 2014

% Result   : Timeout 300.01s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV342^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n188.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 08:53:06 CDT 2014
% % CPUTime  : 300.01 
% 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 0x8c4908>, <kernel.Constant object at 0x8c4ab8>) of role type named y
% Using role type
% Declaring y:fofType
% FOF formula (<kernel.Constant object at 0xcfc098>, <kernel.Single object at 0x8c4e18>) of role type named u
% Using role type
% Declaring u:fofType
% FOF formula (<kernel.Constant object at 0x8c4c20>, <kernel.Single object at 0x8c4bd8>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x8c4908>, <kernel.DependentProduct object at 0x8c47e8>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x8c4998>, <kernel.DependentProduct object at 0x8c4c20>) of role type named cGVB_NOP
% Using role type
% Declaring cGVB_NOP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x8c4dd0>, <kernel.DependentProduct object at 0x8c4908>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula ((iff ((cGVB_IN u) ((cGVB_NOP x) y))) ((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))) of role conjecture named cGVB_A4
% Conjecture to prove = ((iff ((cGVB_IN u) ((cGVB_NOP x) y))) ((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))):Prop
% We need to prove ['((iff ((cGVB_IN u) ((cGVB_NOP x) y))) ((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))']
% Parameter fofType:Type.
% Parameter y:fofType.
% Parameter u:fofType.
% Parameter x:fofType.
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_NOP:(fofType->(fofType->fofType)).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Trying to prove ((iff ((cGVB_IN u) ((cGVB_NOP x) y))) ((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))
% Found eq_ref00:=(eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))):(((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found (eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))):(((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found (eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) u) y)):(((eq Prop) (((eq fofType) u) y)) (((eq fofType) u) y))
% Found (eq_ref0 (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 (((eq fofType) u) y)):(((eq Prop) (((eq fofType) u) y)) (((eq fofType) u) y))
% Found (eq_ref0 (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) u) x)):(((eq Prop) (((eq fofType) u) x)) (((eq fofType) u) x))
% Found (eq_ref0 (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 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 x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType
% Found x02 as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType
% Found x02 as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 (((eq fofType) u) x)):(((eq Prop) (((eq fofType) u) x)) (((eq fofType) u) x))
% Found (eq_ref0 (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found ((eq_ref Prop) (((eq fofType) u) x)) as proof of (((eq Prop) (((eq fofType) u) x)) b)
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) u)):(((eq fofType) ((cGVB_NOP x) u)) ((cGVB_NOP x) u))
% Found (eq_ref0 ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP u) y)):(((eq fofType) ((cGVB_NOP u) y)) ((cGVB_NOP u) y))
% Found (eq_ref0 ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) 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 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType
% Found x02 as proof of (((eq fofType) a) y)
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType
% Found x02 as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP u) y)):(((eq fofType) ((cGVB_NOP u) y)) ((cGVB_NOP u) y))
% Found (eq_ref0 ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP u) y)) as proof of (((eq fofType) ((cGVB_NOP u) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) u)):(((eq fofType) ((cGVB_NOP x) u)) ((cGVB_NOP x) u))
% Found (eq_ref0 ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) u)) as proof of (((eq fofType) ((cGVB_NOP x) u)) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of (P b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 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) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))):(((eq Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y))))
% Found (eq_ref0 (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) as proof of (((eq Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) as proof of (((eq Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) as proof of (((eq Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) b)
% Found ((eq_ref Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) as proof of (((eq Prop) (((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))->((cGVB_IN u) ((cGVB_NOP x) y)))) b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) b)
% Found (classic (((eq fofType) u) x)) as proof of (P b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) u)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))):(((eq Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))))
% Found (eq_ref0 (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) as proof of (((eq Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) b)
% Found ((eq_ref Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) as proof of (((eq Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) b)
% Found ((eq_ref Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) as proof of (((eq Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) b)
% Found ((eq_ref Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) as proof of (((eq Prop) (((cGVB_IN u) ((cGVB_NOP x) y))->((and (cGVB_M u)) ((or (((eq fofType) u) x)) (((eq fofType) u) y))))) b)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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 x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found classic0:=(classic (((eq fofType) u) y)):((or (((eq fofType) u) y)) (not (((eq fofType) u) y)))
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) y))
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType;b:=y:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x02:(((eq fofType) u) x)
% Instantiate: a:=u:fofType;b:=x:fofType
% Found x02 as proof of (((eq fofType) a) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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) 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 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 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 classic0:=(classic (((eq fofType) u) y)):((or (((eq fofType) u) y)) (not (((eq fofType) u) y)))
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) as proof of ((or (((eq fofType) u) y)) b)
% Found (classic (((eq fofType) u) y)) as proof of (P b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))):(((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found (eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType;b:=y:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x02:(((eq fofType) u) x)
% Instantiate: a:=u:fofType;b:=x:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) 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 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:(P u)
% Instantiate: a:=u:fofType
% Found x00 as proof of (P0 a)
% Found x1:(P u)
% Instantiate: a:=u:fofType
% Found x1 as proof of (P0 a)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 ((or (((eq fofType) u) x)) (((eq fofType) u) y))):(((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found (eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))):(((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) ((or (((eq fofType) u) x)) (((eq fofType) u) y)))
% Found (eq_ref0 ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found ((eq_ref Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) as proof of (((eq Prop) ((or (((eq fofType) u) x)) (((eq fofType) u) y))) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType;b:=y:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x02:(((eq fofType) u) x)
% Instantiate: a:=u:fofType;b:=x:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% 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 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (((eq fofType) u) x))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found x1:(P u)
% Instantiate: a:=u:fofType
% Found x1 as proof of (P0 a)
% Found x00:(P u)
% Instantiate: a:=u:fofType
% Found x00 as proof of (P0 a)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) y))
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found or_ind:(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P))))
% Instantiate: a:=(forall (A:Prop) (B:Prop) (P:Prop), ((A->P)->((B->P)->(((or A) B)->P)))):Prop
% Found or_ind as proof of a
% 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) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x02:(((eq fofType) u) x)
% Instantiate: a:=u:fofType;b:=x:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found x02:(((eq fofType) u) y)
% Instantiate: a:=u:fofType;b:=y:fofType
% Found x02 as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 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) 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) u)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) b0)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_NOP x) y)):(((eq fofType) ((cGVB_NOP x) y)) ((cGVB_NOP x) y))
% Found (eq_ref0 ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) y)) b)
% Found ((eq_ref fofType) ((cGVB_NOP x) y)) as proof of (((eq fofType) ((cGVB_NOP x) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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) 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 x1:(P2 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 u)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 u))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 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 x1:(P2 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 u)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 u))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 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 x1:(P2 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 u)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 u))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 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 x1:(P2 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P2 b))=> x1) as proof of (P2 u)
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of ((P2 b)->(P2 u))
% Found (fun (P2:(fofType->Prop)) (x1:(P2 b))=> x1) as proof of (P1 b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) u)
% 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 x000:(P x)
% Found (fun (x000:(P x))=> x000) as proof of (P x)
% Found (fun (x000:(P x))=> x000) as proof of (P0 x)
% Found x10:(P y)
% Found (fun (x10:(P y))=> x10) as proof of (P y)
% Found (fun (x10:(P y))=> x10) 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) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP x) u))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((cGVB_NOP u) y))
% Found x00:(P u)
% Instantiate: b:=u:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P u)
% Instantiate: b:=u:fofType
% Found x1 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found x00:(P b)
% Found x00 as proof of (P0 u)
% Found x1:(P b)
% Found x1 as proof of (P0 u)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of (P a)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x1:(P u)
% Instantiate: a:=u:fofType
% Found x1 as proof of (P0 a)
% Found x00:(P u)
% Instantiate: a:=u:fofType
% Found x00 as proof of (P0 a)
% Found x00:(P x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P0 b)
% Found x1:(P y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P0 b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of (P a)
% 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 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 (((eq fofType) u) y)):(((eq Prop) (((eq fofType) u) y)) (((eq fofType) u) y))
% Found (eq_ref0 (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found ((eq_ref Prop) (((eq fofType) u) y)) as proof of (((eq Prop) (((eq fofType) u) y)) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) y)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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:(P1 x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P2 b)
% Found x1:(P1 y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P2 b)
% Found x00:(P1 x)
% Instantiate: b:=x:fofType
% Found x00 as proof of (P2 b)
% Found x1:(P1 y)
% Instantiate: b:=y:fofType
% Found x1 as proof of (P2 b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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:(P b)
% Instantiate: b0:=b:fofType
% Found x00 as proof of (P0 b0)
% Found x1:(P b)
% Instantiate: b0:=b:fofType
% Found x1 as proof of (P0 b0)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found classic0:=(classic (((eq fofType) u) x)):((or (((eq fofType) u) x)) (not (((eq fofType) u) x)))
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found (classic (((eq fofType) u) x)) as proof of ((or (((eq fofType) u) x)) a)
% Found eq_ref00:=(eq_ref0 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 u):(((eq fofType) u) u)
% Found (eq_ref0 u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) b0)
% Found ((eq_ref fofType) u) as proof of (((eq fofType) u) 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 x10:(P b)
% Found (fun (x10:(P b))=> x10) as proof of (P b)
% Found (fun (x10:(P b))=> x10) as proof of (P0 b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found x000:(P b)
% Found (fun (x000:(P b))=> x000) as proof of (P b)
% Found (fun (x000:(P b))=> x000) as proof of (P0 b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% 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 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 x00:(P x)
% Instantiate: a:=x:fofType
% Found x00 as proof of (P0 a)
% Found x1:(P y)
% Instantiate: a:=y:fofType
% Found x1 as proof of (P0 a)
% 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P 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 x1:(P0 b)
% Instantiate: b:=u:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 u)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 u))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% Found x10:(P u)
% Found (fun (x10:(P u))=> x10) as proof of (P u)
% Found (fun (x10:(P u))=> x10) as proof of (P0 u)
% Found x000:(P u)
% Found (fun (x000:(P u))=> x000) as proof of (P u)
% Found (fun (x000:(P u))=> x000) as proof of (P0 u)
% 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) 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 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a)
% EOF
%------------------------------------------------------------------------------