TSTP Solution File: SYO511^1 by cocATP---0.2.0

%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYO511^1 : TPTP v7.5.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 0s
% DateTime : Tue Mar 29 00:51:59 EDT 2022

% Result   : Timeout 285.90s 286.31s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : SYO511^1 : TPTP v7.5.0. Released v4.1.0.
% 0.08/0.12  % Command    : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33  % Computer   : n020.cluster.edu
% 0.12/0.33  % Model      : x86_64 x86_64
% 0.12/0.33  % CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % RAMPerCPU  : 8042.1875MB
% 0.12/0.33  % OS         : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % DateTime   : Sun Mar 13 13:30:41 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.12/0.35  Python 2.7.5
% 17.90/18.09  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 17.90/18.09  FOF formula (<kernel.Constant object at 0x1a329e0>, <kernel.DependentProduct object at 0x1a32ef0>) of role type named eps
% 17.90/18.09  Using role type
% 17.90/18.09  Declaring eps:((fofType->Prop)->fofType)
% 17.90/18.09  FOF formula (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))) of role axiom named epschoice
% 17.90/18.09  A new axiom: (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P))))
% 17.90/18.09  FOF formula (<kernel.Constant object at 0x179ae60>, <kernel.DependentProduct object at 0x1a32fc8>) of role type named eps2
% 17.90/18.09  Using role type
% 17.90/18.09  Declaring eps2:((fofType->Prop)->fofType)
% 17.90/18.09  FOF formula (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps2 P)))) of role axiom named eps2choice
% 17.90/18.09  A new axiom: (forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps2 P))))
% 17.90/18.09  FOF formula (((eq ((fofType->Prop)->fofType)) eps) eps2) of role conjecture named claim
% 17.90/18.09  Conjecture to prove = (((eq ((fofType->Prop)->fofType)) eps) eps2):Prop
% 17.90/18.09  Parameter fofType_DUMMY:fofType.
% 17.90/18.09  We need to prove ['(((eq ((fofType->Prop)->fofType)) eps) eps2)']
% 17.90/18.09  Parameter fofType:Type.
% 17.90/18.09  Parameter eps:((fofType->Prop)->fofType).
% 17.90/18.09  Axiom epschoice:(forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps P)))).
% 17.90/18.09  Parameter eps2:((fofType->Prop)->fofType).
% 17.90/18.09  Axiom eps2choice:(forall (P:(fofType->Prop)), (((ex fofType) (fun (X:fofType)=> (P X)))->(P (eps2 P)))).
% 17.90/18.09  Trying to prove (((eq ((fofType->Prop)->fofType)) eps) eps2)
% 17.90/18.09  Found x2:(P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 17.90/18.09  Found x2:(P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 17.90/18.09  Found x2:(P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 17.90/18.09  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 17.90/18.09  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 17.90/18.09  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 17.90/18.09  Found eta_expansion000:=(eta_expansion00 eps):(((eq ((fofType->Prop)->fofType)) eps) (fun (x:(fofType->Prop))=> (eps x)))
% 17.90/18.09  Found (eta_expansion00 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 17.90/18.09  Found ((eta_expansion0 fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 17.90/18.09  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 17.90/18.09  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 17.90/18.09  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 17.90/18.09  Found x2:(P eps2)
% 17.90/18.09  Found (fun (x2:(P eps2))=> x2) as proof of (P eps2)
% 17.90/18.09  Found (fun (x2:(P eps2))=> x2) as proof of (P0 eps2)
% 17.90/18.09  Found x2:(P eps2)
% 17.90/18.09  Found (fun (x2:(P eps2))=> x2) as proof of (P eps2)
% 17.90/18.09  Found (fun (x2:(P eps2))=> x2) as proof of (P0 eps2)
% 17.90/18.09  Found x01:(P (eps x))
% 17.90/18.09  Found (fun (x01:(P (eps x)))=> x01) as proof of (P (eps x))
% 17.90/18.09  Found (fun (x01:(P (eps x)))=> x01) as proof of (P0 (eps x))
% 17.90/18.09  Found x01:(P (eps x))
% 17.90/18.09  Found (fun (x01:(P (eps x)))=> x01) as proof of (P (eps x))
% 17.90/18.09  Found (fun (x01:(P (eps x)))=> x01) as proof of (P0 (eps x))
% 17.90/18.09  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 17.90/18.09  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 17.90/18.09  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 17.90/18.09  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 40.63/40.81  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 40.63/40.81  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 40.63/40.81  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 40.63/40.81  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 40.63/40.81  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 40.63/40.81  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 40.63/40.81  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 40.63/40.81  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 40.63/40.81  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 40.63/40.81  Found x01:(P (eps2 x))
% 40.63/40.81  Found (fun (x01:(P (eps2 x)))=> x01) as proof of (P (eps2 x))
% 40.63/40.81  Found (fun (x01:(P (eps2 x)))=> x01) as proof of (P0 (eps2 x))
% 40.63/40.81  Found x01:(P (eps2 x))
% 40.63/40.81  Found (fun (x01:(P (eps2 x)))=> x01) as proof of (P (eps2 x))
% 40.63/40.81  Found (fun (x01:(P (eps2 x)))=> x01) as proof of (P0 (eps2 x))
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 40.63/40.81  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 40.63/40.81  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 40.63/40.81  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 40.63/40.81  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 40.63/40.81  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 40.63/40.81  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 40.63/40.81  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 57.74/57.96  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 57.74/57.96  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 57.74/57.96  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 57.74/57.96  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 57.74/57.96  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 57.74/57.96  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 57.74/57.96  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 57.74/57.96  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 57.74/57.96  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 57.74/57.96  Found x:(P eps)
% 57.74/57.96  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 57.74/57.96  Found x as proof of (P0 b)
% 57.74/57.96  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 57.74/57.96  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 57.74/57.96  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 57.74/57.96  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 57.74/57.96  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 57.74/57.96  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 57.74/57.96  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 57.74/57.96  Found (eq_ref0 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) (fun (x:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 57.74/57.96  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))) b)
% 57.74/57.96  Found x:(P eps)
% 57.74/57.96  Instantiate: f:=eps:((fofType->Prop)->fofType)
% 57.74/57.96  Found x as proof of (P0 f)
% 57.74/57.96  Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 57.74/57.96  Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 57.74/57.96  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq fofType) (f x)) (eps2 x)))
% 61.03/61.24  Found x:(P eps)
% 61.03/61.24  Instantiate: f:=eps:((fofType->Prop)->fofType)
% 61.03/61.24  Found x as proof of (P0 f)
% 61.03/61.24  Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 61.03/61.24  Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (eps2 x0))
% 61.03/61.24  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq fofType) (f x)) (eps2 x)))
% 61.03/61.24  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 61.03/61.24  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 61.03/61.24  Found (eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found ((eta_expansion0 Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 61.03/61.24  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 62.81/63.01  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))) b)
% 62.81/63.01  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.81/63.01  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 62.81/63.01  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 62.81/63.01  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 62.81/63.01  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 62.81/63.01  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 62.81/63.01  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 62.81/63.01  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 62.81/63.01  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 62.81/63.01  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 62.81/63.01  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 62.81/63.01  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2))
% 69.93/70.17  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps) eps2)))
% 69.93/70.17  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 69.93/70.17  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 69.93/70.17  Found eta_expansion000:=(eta_expansion00 eps):(((eq ((fofType->Prop)->fofType)) eps) (fun (x:(fofType->Prop))=> (eps x)))
% 69.93/70.17  Found (eta_expansion00 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found ((eta_expansion0 fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 69.93/70.17  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 69.93/70.17  Found x:(P0 b)
% 69.93/70.17  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 69.93/70.17  Found (fun (x:(P0 b))=> x) as proof of (P0 eps)
% 69.93/70.17  Found (fun (P0:(((fofType->Prop)->fofType)->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 eps))
% 69.93/70.17  Found (fun (P0:(((fofType->Prop)->fofType)->Prop)) (x:(P0 b))=> x) as proof of (P b)
% 69.93/70.17  Found x:(P eps2)
% 69.93/70.17  Instantiate: b:=eps2:((fofType->Prop)->fofType)
% 69.93/70.17  Found x as proof of (P0 b)
% 69.93/70.17  Found eq_ref00:=(eq_ref0 eps):(((eq ((fofType->Prop)->fofType)) eps) eps)
% 69.93/70.17  Found (eq_ref0 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found ((eq_ref ((fofType->Prop)->fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 69.93/70.17  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 69.93/70.17  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 69.93/70.17  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 69.93/70.17  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 69.93/70.17  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 72.32/72.57  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 72.32/72.57  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 72.32/72.57  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 72.32/72.57  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2))))
% 72.32/72.57  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps) eps2)))))
% 72.32/72.57  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 72.32/72.57  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 72.32/72.57  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 72.32/72.57  Found x0:(P (eps x))
% 72.32/72.57  Instantiate: b:=(eps x):fofType
% 72.32/72.57  Found x0 as proof of (P0 b)
% 72.32/72.57  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 72.32/72.57  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found x0:(P (eps x))
% 72.32/72.57  Instantiate: b:=(eps x):fofType
% 72.32/72.57  Found x0 as proof of (P0 b)
% 72.32/72.57  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 72.32/72.57  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 72.32/72.57  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 82.32/82.53  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 82.32/82.53  Found x3:(P eps)
% 82.32/82.53  Found (fun (x3:(P eps))=> x3) as proof of (P eps)
% 82.32/82.53  Found (fun (x3:(P eps))=> x3) as proof of (P0 eps)
% 82.32/82.53  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 82.32/82.53  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 82.32/82.53  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 82.32/82.53  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 82.32/82.53  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 82.32/82.53  Found eta_expansion_dep000:=(eta_expansion_dep00 eps):(((eq ((fofType->Prop)->fofType)) eps) (fun (x:(fofType->Prop))=> (eps x)))
% 82.32/82.53  Found (eta_expansion_dep00 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 82.32/82.53  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 82.32/82.53  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 82.32/82.53  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 82.32/82.53  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 82.32/82.53  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) (fun (x:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 82.32/82.53  Found (eta_expansion00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found ((eta_expansion0 Prop) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) (fun (x:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 82.32/82.53  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 82.32/82.53  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))) b)
% 86.93/87.15  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 86.93/87.15  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 86.93/87.15  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 86.93/87.15  Found x:(P eps2)
% 86.93/87.15  Instantiate: f:=eps2:((fofType->Prop)->fofType)
% 86.93/87.15  Found x as proof of (P0 f)
% 86.93/87.15  Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 86.93/87.15  Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq fofType) (f x)) (eps x)))
% 86.93/87.15  Found x:(P eps2)
% 86.93/87.15  Instantiate: f:=eps2:((fofType->Prop)->fofType)
% 86.93/87.15  Found x as proof of (P0 f)
% 86.93/87.15  Found eq_ref00:=(eq_ref0 (f x0)):(((eq fofType) (f x0)) (f x0))
% 86.93/87.15  Found (eq_ref0 (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found ((eq_ref fofType) (f x0)) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (((eq fofType) (f x0)) (eps x0))
% 86.93/87.15  Found (fun (x0:(fofType->Prop))=> ((eq_ref fofType) (f x0))) as proof of (forall (x:(fofType->Prop)), (((eq fofType) (f x)) (eps x)))
% 86.93/87.15  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 86.93/87.16  Found (eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 86.93/87.16  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 86.93/87.16  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 86.93/87.16  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 86.93/87.16  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) (fun (x:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 87.07/87.31  Found (eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) (fun (x:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 87.07/87.31  Found (eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 87.07/87.31  Found (eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 87.07/87.31  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 92.06/92.31  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 92.06/92.31  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))) b)
% 92.06/92.31  Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->fofType)) b0) b0)
% 92.06/92.31  Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps2)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps2)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps2)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps2)
% 92.06/92.31  Found eta_expansion_dep000:=(eta_expansion_dep00 eps):(((eq ((fofType->Prop)->fofType)) eps) (fun (x:(fofType->Prop))=> (eps x)))
% 92.06/92.31  Found (eta_expansion_dep00 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b0)
% 92.06/92.31  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b0)
% 92.06/92.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b0)
% 92.06/92.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b0)
% 92.06/92.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b0)
% 92.06/92.31  Found fofType_DUMMY:fofType
% 92.06/92.31  Found fofType_DUMMY as proof of fofType
% 92.06/92.31  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 92.06/92.31  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found fofType_DUMMY:fofType
% 92.06/92.31  Found fofType_DUMMY as proof of fofType
% 92.06/92.31  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 92.06/92.31  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 92.06/92.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of (P b)
% 92.06/92.31  Found x2:(P1 eps2)
% 92.06/92.31  Found (fun (x2:(P1 eps2))=> x2) as proof of (P1 eps2)
% 92.06/92.31  Found (fun (x2:(P1 eps2))=> x2) as proof of (P2 eps2)
% 92.06/92.31  Found x2:(P1 eps2)
% 92.06/92.31  Found (fun (x2:(P1 eps2))=> x2) as proof of (P1 eps2)
% 96.57/96.83  Found (fun (x2:(P1 eps2))=> x2) as proof of (P2 eps2)
% 96.57/96.83  Found x2:(P1 eps2)
% 96.57/96.83  Found (fun (x2:(P1 eps2))=> x2) as proof of (P1 eps2)
% 96.57/96.83  Found (fun (x2:(P1 eps2))=> x2) as proof of (P2 eps2)
% 96.57/96.83  Found x2:(P1 eps2)
% 96.57/96.83  Found (fun (x2:(P1 eps2))=> x2) as proof of (P1 eps2)
% 96.57/96.83  Found (fun (x2:(P1 eps2))=> x2) as proof of (P2 eps2)
% 96.57/96.83  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) (fun (x0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))
% 96.57/96.83  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x))))
% 96.57/96.83  Found (eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) (fun (x0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))
% 96.57/96.83  Found (eta_expansion00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eta_expansion0 Prop) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) (fun (x0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))
% 96.57/96.83  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 96.57/96.83  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 99.78/100.00  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 99.78/100.00  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 99.78/100.00  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps x)) (eps2 x)))) b)
% 99.78/100.00  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 99.78/100.00  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 99.78/100.00  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 99.78/100.00  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 99.78/100.00  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 99.78/100.00  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 99.78/100.00  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 99.78/100.00  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 99.78/100.00  Found fofType_DUMMY:fofType
% 99.78/100.00  Found fofType_DUMMY as proof of fofType
% 99.78/100.00  Found fofType_DUMMY:fofType
% 99.78/100.00  Found fofType_DUMMY as proof of fofType
% 105.42/105.65  Found x01:(P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P2 (eps x))
% 105.42/105.65  Found x01:(P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P2 (eps x))
% 105.42/105.65  Found x01:(P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P2 (eps x))
% 105.42/105.65  Found x01:(P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P1 (eps x))
% 105.42/105.65  Found (fun (x01:(P1 (eps x)))=> x01) as proof of (P2 (eps x))
% 105.42/105.65  Found x2:(P eps)
% 105.42/105.65  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 105.42/105.65  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 105.42/105.65  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 105.42/105.65  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 105.42/105.65  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 105.42/105.65  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 105.42/105.65  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 105.42/105.65  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 105.42/105.65  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 105.42/105.65  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps))
% 105.42/105.65  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (((eq ((fofType->Prop)->fofType)) eps2) eps)))
% 105.42/105.65  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 105.42/105.65  Found (eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 105.42/105.65  Found ((eta_expansion0 Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 110.85/111.11  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))) b)
% 110.85/111.11  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 110.85/111.11  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 110.85/111.11  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 110.85/111.11  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 110.85/111.11  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.30/111.63  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.30/111.63  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 111.30/111.63  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.92/112.20  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.92/112.20  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.92/112.20  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))
% 111.92/112.20  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))
% 111.92/112.20  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 111.92/112.20  Found (eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found ((eta_expansion0 Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 111.92/112.20  Found (eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 111.92/112.20  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 113.66/113.92  Found (eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 113.66/113.92  Found (eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))) b)
% 113.66/113.92  Found x2:(P eps)
% 113.66/113.92  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 113.66/113.92  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 113.66/113.92  Found x2:(P eps)
% 113.66/113.92  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 113.66/113.92  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 113.66/113.92  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 113.66/113.92  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 113.66/113.92  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 113.66/113.92  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 113.66/113.92  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 119.13/119.41  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 119.13/119.41  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 119.13/119.41  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 119.13/119.41  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 119.13/119.41  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 119.13/119.41  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 119.13/119.41  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 119.13/119.41  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 119.13/119.41  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 119.13/119.41  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 119.13/119.41  Found x0:(P0 b)
% 119.13/119.41  Instantiate: b:=(eps x):fofType
% 119.13/119.41  Found (fun (x0:(P0 b))=> x0) as proof of (P0 (eps x))
% 119.13/119.41  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (eps x)))
% 126.00/126.30  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 126.00/126.30  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 126.00/126.30  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 126.00/126.30  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 126.00/126.30  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 126.00/126.30  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 126.00/126.30  Found x0:(P0 b)
% 126.00/126.30  Instantiate: b:=(eps x):fofType
% 126.00/126.30  Found (fun (x0:(P0 b))=> x0) as proof of (P0 (eps x))
% 126.00/126.30  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (eps x)))
% 126.00/126.30  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 126.00/126.30  Found fofType_DUMMY:fofType
% 126.00/126.30  Found fofType_DUMMY as proof of fofType
% 126.00/126.30  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 126.00/126.30  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.30  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found x0:(P0 (b x))
% 126.00/126.31  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 126.00/126.31  Found (fun (x0:(P0 (b x)))=> x0) as proof of (P0 (eps x))
% 126.00/126.31  Found (fun (P0:(fofType->Prop)) (x0:(P0 (b x)))=> x0) as proof of ((P0 (b x))->(P0 (eps x)))
% 126.00/126.31  Found (fun (P0:(fofType->Prop)) (x0:(P0 (b x)))=> x0) as proof of (P b)
% 126.00/126.31  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 126.00/126.31  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 126.00/126.31  Found x0:(P0 (b x))
% 126.00/126.31  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 126.00/126.31  Found (fun (x0:(P0 (b x)))=> x0) as proof of (P0 (eps x))
% 126.00/126.31  Found (fun (P0:(fofType->Prop)) (x0:(P0 (b x)))=> x0) as proof of ((P0 (b x))->(P0 (eps x)))
% 126.00/126.31  Found (fun (P0:(fofType->Prop)) (x0:(P0 (b x)))=> x0) as proof of (P b)
% 126.00/126.31  Found fofType_DUMMY:fofType
% 126.00/126.31  Found fofType_DUMMY as proof of fofType
% 126.00/126.31  Found x0:(P (eps2 x))
% 126.00/126.31  Instantiate: b:=(eps2 x):fofType
% 126.00/126.31  Found x0 as proof of (P0 b)
% 126.00/126.31  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 126.00/126.31  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found x0:(P (eps2 x))
% 126.00/126.31  Instantiate: b:=(eps2 x):fofType
% 126.00/126.31  Found x0 as proof of (P0 b)
% 126.00/126.31  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 126.00/126.31  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 126.00/126.31  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.00/126.31  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.00/126.31  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.00/126.31  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.00/126.31  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.00/126.31  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 126.72/126.99  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 126.72/126.99  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 126.72/126.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x)))
% 129.71/129.99  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) (((eq fofType) (eps x)) (eps2 x))))
% 129.71/129.99  Found fofType_DUMMY:fofType
% 129.71/129.99  Found fofType_DUMMY as proof of fofType
% 129.71/129.99  Found fofType_DUMMY:fofType
% 129.71/129.99  Found fofType_DUMMY as proof of fofType
% 129.71/129.99  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 129.71/129.99  Found (eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) (fun (x0:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 129.71/129.99  Found (eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found ((eta_expansion0 Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) (fun (x0:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 129.71/129.99  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 129.71/129.99  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) (fun (x0:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 136.41/136.70  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))) b)
% 136.41/136.70  Found x3:(P eps2)
% 136.41/136.70  Found (fun (x3:(P eps2))=> x3) as proof of (P eps2)
% 136.41/136.70  Found (fun (x3:(P eps2))=> x3) as proof of (P0 eps2)
% 136.41/136.70  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 136.41/136.70  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 136.41/136.70  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 136.41/136.70  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 136.41/136.70  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 136.41/136.70  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 136.41/136.70  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 136.41/136.70  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 136.41/136.70  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 136.41/136.70  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 136.41/136.70  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 136.41/136.70  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 136.41/136.70  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 136.41/136.70  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 141.13/141.42  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 141.13/141.42  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 141.13/141.42  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 141.13/141.42  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 141.13/141.42  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 141.13/141.42  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps))))
% 141.13/141.42  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) eps2) eps)))))
% 141.13/141.42  Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 141.13/141.42  Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% 141.13/141.42  Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) x)
% 141.13/141.42  Found x0:(P (eps2 x))
% 141.13/141.42  Instantiate: b:=(eps2 x):fofType
% 141.13/141.42  Found x0 as proof of (P0 b)
% 141.13/141.42  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 141.13/141.42  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 141.13/141.42  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 141.13/141.42  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found x0:(P (eps2 x))
% 146.22/146.51  Instantiate: b:=(eps2 x):fofType
% 146.22/146.51  Found x0 as proof of (P0 b)
% 146.22/146.51  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 146.22/146.51  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 146.22/146.51  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 146.22/146.51  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 146.22/146.51  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 146.22/146.51  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 146.22/146.51  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 146.22/146.51  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.22/146.51  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.22/146.51  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.22/146.51  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.22/146.51  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.22/146.51  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 146.22/146.51  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.22/146.51  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 146.38/146.68  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.38/146.68  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 146.38/146.68  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.38/146.68  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 146.38/146.68  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.38/146.68  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 146.38/146.68  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 146.38/146.68  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 146.38/146.68  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 159.34/159.61  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 159.34/159.61  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 159.34/159.61  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 159.34/159.61  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1))))))
% 159.34/159.61  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps x1)) (eps2 x1)))))))
% 159.34/159.61  Found x02:(P (eps x))
% 159.34/159.61  Found (fun (x02:(P (eps x)))=> x02) as proof of (P (eps x))
% 159.34/159.61  Found (fun (x02:(P (eps x)))=> x02) as proof of (P0 (eps x))
% 159.34/159.61  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 159.34/159.61  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.61  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.61  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.61  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.61  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 159.34/159.61  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.61  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.61  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.61  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.61  Found x02:(P (eps x))
% 159.34/159.62  Found (fun (x02:(P (eps x)))=> x02) as proof of (P (eps x))
% 159.34/159.62  Found (fun (x02:(P (eps x)))=> x02) as proof of (P0 (eps x))
% 159.34/159.62  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 159.34/159.62  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.62  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.62  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.62  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 159.34/159.62  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 159.34/159.62  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.62  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.62  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.62  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps2 x))
% 159.34/159.62  Found x2:(P eps)
% 159.34/159.62  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 159.34/159.62  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 159.34/159.62  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 159.34/159.62  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 175.88/176.22  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 175.88/176.22  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 175.88/176.22  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 175.88/176.22  Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% 175.88/176.22  Found (eq_ref0 x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found (ex_intro000 ((eq_ref fofType) x0)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found ((ex_intro00 (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found x01:(P0 (eps x))
% 175.88/176.22  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 175.88/176.22  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 175.88/176.22  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 175.88/176.22  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 175.88/176.22  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 175.88/176.22  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 175.88/176.22  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 175.88/176.22  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 175.88/176.22  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 175.88/176.22  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 175.88/176.22  Found eq_ref00:=(eq_ref0 x0):(((eq fofType) x0) x0)
% 175.88/176.22  Found (eq_ref0 x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found ((eq_ref fofType) x0) as proof of (((eq fofType) x0) (eps2 x))
% 175.88/176.22  Found (ex_intro000 ((eq_ref fofType) x0)) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found ((ex_intro00 (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 175.88/176.22  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 192.55/192.86  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 192.55/192.86  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x)))) (eps2 x)) ((eq_ref fofType) (eps2 x))) as proof of ((ex fofType) (fun (X:fofType)=> (((eq fofType) X) (eps2 x))))
% 192.55/192.86  Found x01:(P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 192.55/192.86  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 192.55/192.86  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 192.55/192.86  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 192.55/192.86  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 192.55/192.86  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 192.55/192.86  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 192.55/192.86  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 192.55/192.86  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 192.55/192.86  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 192.55/192.86  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps (fun (x10:fofType)=> (((eq fofType) x10) (eps2 x)))))
% 192.55/192.86  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 192.55/192.86  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 192.55/192.86  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 192.55/192.86  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 192.55/192.86  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 192.55/192.86  Found x01:(P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 192.55/192.86  Found x01:(P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 192.55/192.86  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 192.55/192.86  Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->fofType)) b0) b0)
% 192.55/192.86  Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 192.55/192.86  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 200.55/200.89  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 200.55/200.89  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 200.55/200.89  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b0)
% 200.55/200.89  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b0)
% 200.55/200.89  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b0)
% 200.55/200.89  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b0)
% 200.55/200.89  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b0)
% 200.55/200.89  Found x01:(P0 (eps x))
% 200.55/200.89  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 200.55/200.89  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 200.55/200.89  Found x01:(P0 (eps x))
% 200.55/200.89  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P0 (eps x))
% 200.55/200.89  Found (fun (x01:(P0 (eps x)))=> x01) as proof of (P1 (eps x))
% 200.55/200.89  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 200.55/200.89  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 200.55/200.89  Found x2:(P eps)
% 200.55/200.89  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 200.55/200.89  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 200.55/200.89  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 200.55/200.89  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 200.55/200.89  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 200.55/200.89  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 200.55/200.89  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 200.55/200.89  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 200.55/200.89  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 209.00/209.37  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 209.00/209.37  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 209.00/209.37  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 209.00/209.37  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 209.00/209.37  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 209.00/209.37  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 209.00/209.37  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 209.00/209.37  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x)))))
% 209.00/209.37  Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((ex fofType) (fun (X0:fofType)=> (((eq fofType) (eps x)) (eps2 x))))))
% 209.00/209.37  Found x2:(P eps)
% 209.00/209.37  Found (fun (x2:(P eps))=> x2) as proof of (P eps)
% 209.00/209.37  Found (fun (x2:(P eps))=> x2) as proof of (P0 eps)
% 209.00/209.37  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 209.00/209.37  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 209.00/209.37  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 209.00/209.37  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 209.00/209.37  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 209.00/209.37  Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 209.00/209.37  Found (eq_ref0 b0) as proof of (((eq fofType) b0) (eps2 x))
% 209.00/209.37  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 209.52/209.90  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 209.52/209.90  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 209.52/209.90  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) (fun (x:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 209.52/209.90  Found (eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 209.52/209.90  Found (eq_ref0 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) (fun (x:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 209.52/209.90  Found (eta_expansion_dep00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 209.52/209.90  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))):(((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) (fun (x:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 222.21/222.60  Found (eta_expansion00 (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found ((eta_expansion0 Prop) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))) b)
% 222.21/222.60  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 222.21/222.60  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 222.21/222.60  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 222.21/222.60  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 222.21/222.60  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b0)
% 222.21/222.60  Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 222.21/222.60  Found (eq_ref0 b0) as proof of (((eq fofType) b0) (eps2 x))
% 222.21/222.60  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 222.21/222.60  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 222.21/222.60  Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (eps2 x))
% 222.21/222.60  Found x2:(P eps2)
% 222.21/222.60  Found (fun (x2:(P eps2))=> x2) as proof of (P eps2)
% 222.21/222.60  Found (fun (x2:(P eps2))=> x2) as proof of (P0 eps2)
% 222.21/222.60  Found eta_expansion_dep000:=(eta_expansion_dep00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 222.21/222.60  Found (eta_expansion_dep00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 222.21/222.60  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 222.21/222.60  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 233.15/233.49  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 233.15/233.49  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 233.15/233.49  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 233.15/233.49  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps2)
% 233.15/233.49  Found eta_expansion000:=(eta_expansion00 eps):(((eq ((fofType->Prop)->fofType)) eps) (fun (x:(fofType->Prop))=> (eps x)))
% 233.15/233.49  Found (eta_expansion00 eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 233.15/233.49  Found ((eta_expansion0 fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 233.15/233.49  Found (((eta_expansion (fofType->Prop)) fofType) eps) as proof of (((eq ((fofType->Prop)->fofType)) eps) b)
% 233.15/233.49  Found fofType_DUMMY:fofType
% 233.15/233.49  Found fofType_DUMMY as proof of fofType
% 233.15/233.49  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 233.15/233.49  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 233.15/233.49  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 233.15/233.49  Found ((ex_intro01 fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 233.15/233.49  Found (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 233.15/233.49  Found (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 233.15/233.49  Found ((ex_intro00 fofType_DUMMY) (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 233.15/233.49  Found (((ex_intro0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found ((((ex_intro fofType) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) ((((ex_intro fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found ((((ex_intro fofType) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) ((((ex_intro fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found fofType_DUMMY:fofType
% 239.05/239.42  Found fofType_DUMMY as proof of fofType
% 239.05/239.42  Found eq_ref00:=(eq_ref0 b):(((eq ((fofType->Prop)->fofType)) b) b)
% 239.05/239.42  Found (eq_ref0 b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 239.05/239.42  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 239.05/239.42  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 239.05/239.42  Found ((eq_ref ((fofType->Prop)->fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) eps)
% 239.05/239.42  Found ((ex_intro01 fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 239.05/239.42  Found (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 239.05/239.42  Found (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b)) as proof of ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps)))
% 239.05/239.42  Found ((ex_intro00 fofType_DUMMY) (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found (((ex_intro0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) (((ex_intro0 (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found ((((ex_intro fofType) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) ((((ex_intro fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found ((((ex_intro fofType) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))))) fofType_DUMMY) ((((ex_intro fofType) (fun (X0:fofType)=> (((eq ((fofType->Prop)->fofType)) b) eps))) fofType_DUMMY) ((eq_ref ((fofType->Prop)->fofType)) b))) as proof of (P b)
% 239.05/239.42  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 239.05/239.42  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.05/239.42  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.05/239.42  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.05/239.42  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.05/239.42  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 239.74/240.12  Found (eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 239.74/240.12  Found (eta_expansion00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eta_expansion0 Prop) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 239.74/240.12  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 239.74/240.12  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 239.74/240.12  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 242.06/242.44  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 242.06/242.44  Found (eq_ref0 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))):(((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) (fun (x0:fofType)=> (((eq fofType) (eps2 x)) (eps x))))
% 242.06/242.44  Found (eta_expansion_dep00 (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> (((eq fofType) (eps2 x)) (eps x)))) b)
% 242.06/242.44  Found fofType_DUMMY:fofType
% 242.06/242.44  Found fofType_DUMMY as proof of fofType
% 245.47/245.82  Found fofType_DUMMY:fofType
% 245.47/245.82  Found fofType_DUMMY as proof of fofType
% 245.47/245.82  Found fofType_DUMMY:fofType
% 245.47/245.82  Found fofType_DUMMY as proof of fofType
% 245.47/245.82  Found fofType_DUMMY:fofType
% 245.47/245.82  Found fofType_DUMMY as proof of fofType
% 245.47/245.82  Found eq_ref00:=(eq_ref0 b0):(((eq ((fofType->Prop)->fofType)) b0) b0)
% 245.47/245.82  Found (eq_ref0 b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 245.47/245.82  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 245.47/245.82  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 245.47/245.82  Found ((eq_ref ((fofType->Prop)->fofType)) b0) as proof of (((eq ((fofType->Prop)->fofType)) b0) eps)
% 245.47/245.82  Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq ((fofType->Prop)->fofType)) b) (fun (x:(fofType->Prop))=> (b x)))
% 245.47/245.82  Found (eta_expansion_dep00 b) as proof of (((eq ((fofType->Prop)->fofType)) b) b0)
% 245.47/245.82  Found ((eta_expansion_dep0 (fun (x1:(fofType->Prop))=> fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) b0)
% 245.47/245.82  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) b0)
% 245.47/245.82  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) b0)
% 245.47/245.82  Found (((eta_expansion_dep (fofType->Prop)) (fun (x1:(fofType->Prop))=> fofType)) b) as proof of (((eq ((fofType->Prop)->fofType)) b) b0)
% 245.47/245.82  Found eq_ref00:=(eq_ref0 (b x10)):(((eq fofType) (b x10)) (b x10))
% 245.47/245.82  Found (eq_ref0 (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10)))
% 245.47/245.82  Found ((ex_intro00 fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found (((ex_intro0 (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found eq_ref00:=(eq_ref0 (b x10)):(((eq fofType) (b x10)) (b x10))
% 245.47/245.82  Found (eq_ref0 (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10)))
% 245.47/245.82  Found ((ex_intro00 fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found (((ex_intro0 (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 245.47/245.82  Found eq_ref00:=(eq_ref0 (b x10)):(((eq fofType) (b x10)) (b x10))
% 245.47/245.82  Found (eq_ref0 (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 245.47/245.82  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10)))
% 252.00/252.40  Found ((ex_intro00 fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found (((ex_intro0 (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found eq_ref00:=(eq_ref0 (b x10)):(((eq fofType) (b x10)) (b x10))
% 252.00/252.40  Found (eq_ref0 (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found ((eq_ref fofType) (b x10)) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (((eq fofType) (b x10)) (eps x10))
% 252.00/252.40  Found (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10))) as proof of (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10)))
% 252.00/252.40  Found ((ex_intro00 fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found (((ex_intro0 (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found ((((ex_intro fofType) (fun (X:fofType)=> (forall (x10:(fofType->Prop)), (((eq fofType) (b x10)) (eps x10))))) fofType_DUMMY) (fun (x10:(fofType->Prop))=> ((eq_ref fofType) (b x10)))) as proof of (P b)
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found fofType_DUMMY:fofType
% 252.00/252.40  Found fofType_DUMMY as proof of fofType
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found x01:(P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P1 (eps2 x))
% 252.00/252.40  Found (fun (x01:(P1 (eps2 x)))=> x01) as proof of (P2 (eps2 x))
% 252.00/252.40  Found fofType_DUMMY:fofType
% 252.00/252.40  Found fofType_DUMMY as proof of fofType
% 252.00/252.40  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 252.00/252.40  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 252.00/252.40  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 252.00/252.40  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 252.00/252.40  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 270.91/271.32  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 270.91/271.32  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 270.91/271.32  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 270.91/271.32  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 270.91/271.32  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 270.91/271.32  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 270.91/271.32  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 270.91/271.32  Found fofType_DUMMY:fofType
% 270.91/271.32  Found fofType_DUMMY as proof of fofType
% 270.91/271.32  Found fofType_DUMMY:fofType
% 270.91/271.32  Found fofType_DUMMY as proof of fofType
% 270.91/271.32  Found fofType_DUMMY:fofType
% 270.91/271.32  Found fofType_DUMMY as proof of fofType
% 270.91/271.32  Found fofType_DUMMY:fofType
% 270.91/271.32  Found fofType_DUMMY as proof of fofType
% 270.91/271.32  Found x2:(P eps2)
% 270.91/271.32  Found (fun (x2:(P eps2))=> x2) as proof of (P eps2)
% 270.91/271.32  Found (fun (x2:(P eps2))=> x2) as proof of (P0 eps2)
% 270.91/271.32  Found x2:(P eps2)
% 270.91/271.32  Found (fun (x2:(P eps2))=> x2) as proof of (P eps2)
% 270.91/271.32  Found (fun (x2:(P eps2))=> x2) as proof of (P0 eps2)
% 270.91/271.32  Found x2:(P b)
% 270.91/271.32  Found (fun (x2:(P b))=> x2) as proof of (P b)
% 270.91/271.32  Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 270.91/271.32  Found x2:(P b)
% 270.91/271.32  Found (fun (x2:(P b))=> x2) as proof of (P b)
% 270.91/271.32  Found (fun (x2:(P b))=> x2) as proof of (P0 b)
% 270.91/271.32  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 270.91/271.32  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 270.91/271.32  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 270.91/271.32  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 270.91/271.32  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 270.91/271.32  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 270.91/271.32  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 274.07/274.51  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 274.07/274.51  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 274.07/274.51  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 274.07/274.51  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 277.09/277.48  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 277.09/277.48  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 277.09/277.48  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 277.09/277.48  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 279.25/279.69  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found eq_ref00:=(eq_ref0 (eps2 x)):(((eq fofType) (eps2 x)) (eps2 x))
% 279.25/279.69  Found (eq_ref0 (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 279.25/279.69  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 281.17/281.59  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 281.17/281.59  Found ((eq_ref fofType) (eps2 x)) as proof of (((eq fofType) (eps2 x)) b)
% 281.17/281.59  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 281.17/281.59  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 281.17/281.59  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 281.17/281.59  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 281.17/281.59  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 281.17/281.59  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 281.17/281.59  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 281.17/281.59  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 281.17/281.59  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 281.17/281.59  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 281.17/281.59  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 281.17/281.59  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 281.17/281.59  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 281.17/281.59  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 281.17/281.59  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 281.17/281.59  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 284.10/284.52  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 284.10/284.52  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 284.10/284.52  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 284.10/284.52  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 284.10/284.52  Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 284.10/284.52  Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))
% 284.10/284.52  Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))
% 284.10/284.52  Found fofType_DUMMY:fofType
% 284.10/284.52  Found fofType_DUMMY as proof of fofType
% 284.10/284.52  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 284.10/284.52  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 284.10/284.52  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 284.10/284.52  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 284.10/284.52  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 284.10/284.52  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 284.10/284.52  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 284.10/284.52  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 284.10/284.52  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 284.10/284.52  Found x0:(P (eps x))
% 284.10/284.52  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 284.10/284.52  Found x0 as proof of (P0 b)
% 284.10/284.52  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 284.10/284.52  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 284.10/284.52  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 284.10/284.52  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 284.10/284.52  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 284.10/284.52  Found x0:(P (eps x))
% 284.10/284.52  Instantiate: b:=eps:((fofType->Prop)->fofType)
% 284.10/284.52  Found x0 as proof of (P0 b)
% 284.10/284.52  Found eq_ref00:=(eq_ref0 eps2):(((eq ((fofType->Prop)->fofType)) eps2) eps2)
% 284.10/284.52  Found (eq_ref0 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 284.10/284.52  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 285.90/286.31  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 285.90/286.31  Found ((eq_ref ((fofType->Prop)->fofType)) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 285.90/286.31  Found fofType_DUMMY:fofType
% 285.90/286.31  Found fofType_DUMMY as proof of fofType
% 285.90/286.31  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.90/286.31  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found fofType_DUMMY:fofType
% 285.90/286.31  Found fofType_DUMMY as proof of fofType
% 285.90/286.31  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.90/286.31  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found fofType_DUMMY:fofType
% 285.90/286.31  Found fofType_DUMMY as proof of fofType
% 285.90/286.31  Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 285.90/286.31  Found (eq_ref0 b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (eps x))
% 285.90/286.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) b) (eps x)))) fofType_DUMMY) ((eq_ref fofType) b)) as proof of (P b)
% 285.90/286.31  Found fofType_DUMMY:fofType
% 285.90/286.31  Found fofType_DUMMY as proof of fofType
% 285.90/286.31  Found eq_ref00:=(eq_ref0 (b x)):(((eq fofType) (b x)) (b x))
% 285.90/286.31  Found (eq_ref0 (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 285.90/286.31  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 285.90/286.31  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 285.90/286.31  Found fofType_DUMMY:fofType
% 285.90/286.31  Found fofType_DUMMY as proof of fofType
% 285.90/286.31  Found eq_ref00:=(eq_ref0 (b x)):(((eq fofType) (b x)) (b x))
% 285.90/286.31  Found (eq_ref0 (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 285.90/286.31  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found fofType_DUMMY:fofType
% 287.64/288.07  Found fofType_DUMMY as proof of fofType
% 287.64/288.07  Found eq_ref00:=(eq_ref0 (b x)):(((eq fofType) (b x)) (b x))
% 287.64/288.07  Found (eq_ref0 (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found fofType_DUMMY:fofType
% 287.64/288.07  Found fofType_DUMMY as proof of fofType
% 287.64/288.07  Found eq_ref00:=(eq_ref0 (b x)):(((eq fofType) (b x)) (b x))
% 287.64/288.07  Found (eq_ref0 (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((eq_ref fofType) (b x)) as proof of (((eq fofType) (b x)) (eps x))
% 287.64/288.07  Found ((ex_intro00 fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found (((ex_intro0 (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found ((((ex_intro fofType) (fun (X:fofType)=> (((eq fofType) (b x)) (eps x)))) fofType_DUMMY) ((eq_ref fofType) (b x))) as proof of (P b)
% 287.64/288.07  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))))
% 287.64/288.07  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.64/288.07  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.64/288.07  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.64/288.07  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.64/288.07  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found eq_ref00:=(eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))))
% 287.79/288.22  Found (eq_ref0 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found ((eq_ref (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found eta_expansion000:=(eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))))
% 287.79/288.22  Found (eta_expansion00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found ((eta_expansion0 Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found (((eta_expansion fofType) Prop) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 287.79/288.22  Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))):(((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) (fun (x:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1)))))))
% 298.45/298.87  Found (eta_expansion_dep00 (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 298.45/298.87  Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 298.45/298.87  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 298.45/298.87  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 298.45/298.87  Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) as proof of (((eq (fofType->Prop)) (fun (X:fofType)=> ((ex fofType) (fun (X0:fofType)=> (forall (x1:(fofType->Prop)), (((eq fofType) (eps2 x1)) (eps x1))))))) b)
% 298.45/298.87  Found x01:(P b)
% 298.45/298.87  Found (fun (x01:(P b))=> x01) as proof of (P b)
% 298.45/298.87  Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 298.45/298.87  Found x01:(P b)
% 298.45/298.87  Found (fun (x01:(P b))=> x01) as proof of (P b)
% 298.45/298.87  Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 298.45/298.87  Found x01:(P (eps x))
% 298.45/298.87  Found (fun (x01:(P (eps x)))=> x01) as proof of (P (eps x))
% 298.45/298.87  Found (fun (x01:(P (eps x)))=> x01) as proof of (P0 (eps x))
% 298.45/298.87  Found x01:(P (eps x))
% 298.45/298.87  Found (fun (x01:(P (eps x)))=> x01) as proof of (P (eps x))
% 298.45/298.87  Found (fun (x01:(P (eps x)))=> x01) as proof of (P0 (eps x))
% 298.45/298.87  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 298.45/298.87  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found x0:(P0 b)
% 298.45/298.87  Instantiate: b:=(eps2 x):fofType
% 298.45/298.87  Found (fun (x0:(P0 b))=> x0) as proof of (P0 (eps2 x))
% 298.45/298.87  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (eps2 x)))
% 298.45/298.87  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 298.45/298.87  Found eq_ref00:=(eq_ref0 (eps x)):(((eq fofType) (eps x)) (eps x))
% 298.45/298.87  Found (eq_ref0 (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found ((eq_ref fofType) (eps x)) as proof of (((eq fofType) (eps x)) b)
% 298.45/298.87  Found x0:(P0 b)
% 298.45/298.87  Instantiate: b:=(eps2 x):fofType
% 298.45/298.87  Found (fun (x0:(P0 b))=> x0) as proof of (P0 (eps2 x))
% 298.45/298.87  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (eps2 x)))
% 298.45/298.87  Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 298.45/298.87  Found eta_expansion000:=(eta_expansion00 eps2):(((eq ((fofType->Prop)->fofType)) eps2) (fun (x:(fofType->Prop))=> (eps2 x)))
% 298.45/298.87  Found (eta_expansion00 eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 298.45/298.87  Found ((eta_expansion0 fofType) eps2) as proof of (((eq ((fofType->Prop)->fofType)) eps2) b)
% 298.45/298.87  Found (((e
%------------------------------------------------------------------------------