TSTP Solution File: SEV361^5 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV361^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n099.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 13:34:05 EDT 2014

% Result   : Timeout 300.00s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV361^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n099.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 08:56:56 CDT 2014
% % CPUTime  : 300.00 
% 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 0x1801ab8>, <kernel.Constant object at 0x1801440>) of role type named x
% Using role type
% Declaring x:fofType
% FOF formula (<kernel.Constant object at 0x1c325f0>, <kernel.DependentProduct object at 0x1801d40>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x1801908>, <kernel.DependentProduct object at 0x1801ab8>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1801ea8>, <kernel.DependentProduct object at 0x1801e60>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1801cf8>, <kernel.DependentProduct object at 0x18013b0>) of role type named cGVB_SING_VAL
% Using role type
% Declaring cGVB_SING_VAL:(fofType->Prop)
% FOF formula ((iff (cGVB_SING_VAL x)) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (cGVB_M Xw))->(((and ((cGVB_IN ((cGVB_OP Xu) Xv)) x)) ((cGVB_IN ((cGVB_OP Xu) Xw)) x))->(((eq fofType) Xv) Xw))))) of role conjecture named cGVB_AX_SING_VAL
% Conjecture to prove = ((iff (cGVB_SING_VAL x)) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (cGVB_M Xw))->(((and ((cGVB_IN ((cGVB_OP Xu) Xv)) x)) ((cGVB_IN ((cGVB_OP Xu) Xw)) x))->(((eq fofType) Xv) Xw))))):Prop
% We need to prove ['((iff (cGVB_SING_VAL x)) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (cGVB_M Xw))->(((and ((cGVB_IN ((cGVB_OP Xu) Xv)) x)) ((cGVB_IN ((cGVB_OP Xu) Xw)) x))->(((eq fofType) Xv) Xw)))))']
% Parameter fofType:Type.
% Parameter x:fofType.
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_SING_VAL:(fofType->Prop).
% Trying to prove ((iff (cGVB_SING_VAL x)) (forall (Xu:fofType) (Xv:fofType) (Xw:fofType), (((and ((and (cGVB_M Xu)) (cGVB_M Xv))) (cGVB_M Xw))->(((and ((cGVB_IN ((cGVB_OP Xu) Xv)) x)) ((cGVB_IN ((cGVB_OP Xu) Xw)) x))->(((eq fofType) Xv) Xw)))))
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% 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 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% 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 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found x1:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found x1:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% 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) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found x1:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x1:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x1 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) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 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 eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% 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) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x10:(P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found x3:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found x3:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found x5:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) 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 eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x10:(P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x1:(P0 b))=> x1) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x1:(P0 b))=> x1) as proof of (P b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) 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 x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 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 eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found x3:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x3 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) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) 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 eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x5:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x5 as proof of (P0 b)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found x1:(P Xw)
% Instantiate: b:=Xw:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x5:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) 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) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) 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 eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x10:(P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x30:(P b)
% Found (fun (x30:(P b))=> x30) as proof of (P b)
% Found (fun (x30:(P b))=> x30) as proof of (P0 b)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x3:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x3 as proof of (P0 b)
% Found x50:(P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P Xv)
% Found (fun (x50:(P Xv))=> x50) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found x30:(P Xw)
% Found (fun (x30:(P Xw))=> x30) as proof of (P Xw)
% Found (fun (x30:(P Xw))=> x30) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x1:(P Xv)
% Instantiate: b:=Xv:fofType
% Found x1 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x5:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b)
% Found x10:(P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P Xv)
% Found (fun (x10:(P Xv))=> x10) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x5:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x5:(P0 b))=> x5) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x5:(P0 b))=> x5) as proof of (P b)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) 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 x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% 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 x10:(P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P Xw)
% Found (fun (x10:(P Xw))=> x10) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found x30:(P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P Xv)
% Found (fun (x30:(P Xv))=> x30) as proof of (P0 Xv)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xw)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x30:(P Xw)
% Found (fun (x30:(P Xw))=> x30) as proof of (P Xw)
% Found (fun (x30:(P Xw))=> x30) as proof of (P0 Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xv)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b0)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xv):(((eq fofType) Xv) Xv)
% Found (eq_ref0 Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found ((eq_ref fofType) Xv) as proof of (((eq fofType) Xv) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xw)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found (eq_ref0 Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found ((eq_ref fofType) Xw) as proof of (((eq fofType) Xw) b)
% Found x3:(P0 b)
% Instantiate: b:=Xv:fofType
% Found (fun (x3:(P0 b))=> x3) as proof of (P0 Xv)
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of ((P0 b)->(P0 Xv))
% Found (fun (P0:(fofType->Prop)) (x3:(P0 b))=> x3) as proof of (P b)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) Xv)
% Found eq_ref00:=(eq_ref0 Xw):(((eq fofType) Xw) Xw)
% Found
% EOF
%------------------------------------------------------------------------------