%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYO042^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n013.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 00:50:28 EDT 2022

% Result   : Timeout 289.00s 289.32s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SYO042^1 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.12  % Command    : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33  % Computer   : n013.cluster.edu
% 0.13/0.33  % Model      : x86_64 x86_64
% 0.13/0.33  % CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % RAMPerCPU  : 8042.1875MB
% 0.13/0.33  % OS         : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % DateTime   : Fri Mar 11 08:51:37 EST 2022
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35  Python 2.7.5
% 13.96/14.14  Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 13.96/14.14  FOF formula (<kernel.Constant object at 0xc87560>, <kernel.DependentProduct object at 0x2b3142ed76c8>) of role type named g
% 13.96/14.14  Using role type
% 13.96/14.14  Declaring g:(Prop->Prop)
% 13.96/14.14  FOF formula (<kernel.Constant object at 0xc873b0>, <kernel.DependentProduct object at 0x2b3142ed7518>) of role type named p
% 13.96/14.14  Using role type
% 13.96/14.14  Declaring p:((Prop->Prop)->Prop)
% 13.96/14.14  FOF formula (<kernel.Constant object at 0xc87560>, <kernel.Sort object at 0x2b3142eb2638>) of role type named x
% 13.96/14.14  Using role type
% 13.96/14.14  Declaring x:Prop
% 13.96/14.14  FOF formula (<kernel.Constant object at 0xc873b0>, <kernel.Sort object at 0x2b3142eb2638>) of role type named y
% 13.96/14.14  Using role type
% 13.96/14.14  Declaring y:Prop
% 13.96/14.14  FOF formula ((and ((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g))) ((p not)->False)) of role axiom named 4
% 13.96/14.14  A new axiom: ((and ((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g))) ((p not)->False))
% 13.96/14.14  We need to prove []
% 13.96/14.14  Parameter g:(Prop->Prop).
% 13.96/14.14  Parameter p:((Prop->Prop)->Prop).
% 13.96/14.14  Parameter x:Prop.
% 13.96/14.14  Parameter y:Prop.
% 13.96/14.14  Axiom 4:((and ((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g))) ((p not)->False)).
% 13.96/14.14  There are no conjectures!
% 13.96/14.14  Adding conjecture False, to look for Unsatisfiability
% 13.96/14.14  Trying to prove False
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 13.96/14.14  Found (eq_ref00 p) as proof of (P g)
% 13.96/14.14  Found ((eq_ref0 g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 13.96/14.14  Found x000:False
% 13.96/14.14  Found (fun (x02:(p g))=> x000) as proof of False
% 13.96/14.14  Found (fun (x02:(p g))=> x000) as proof of ((p g)->False)
% 13.96/14.14  Found x000:False
% 13.96/14.14  Found (fun (x02:(p g))=> x000) as proof of False
% 13.96/14.14  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x000) as proof of ((p g)->False)
% 13.96/14.14  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x000) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->False))
% 13.96/14.14  Found x000:False
% 13.96/14.14  Found (fun (x04:(((eq Prop) (g y)) x))=> x000) as proof of False
% 13.96/14.14  Found (fun (x04:(((eq Prop) (g y)) x))=> x000) as proof of ((((eq Prop) (g y)) x)->False)
% 13.96/14.14  Found x000:False
% 13.96/14.14  Found (fun (x04:(((eq Prop) (g y)) x))=> x000) as proof of False
% 13.96/14.14  Found (fun (x03:((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (x04:(((eq Prop) (g y)) x))=> x000) as proof of ((((eq Prop) (g y)) x)->False)
% 13.96/14.14  Found (fun (x03:((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (x04:(((eq Prop) (g y)) x))=> x000) as proof of (((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))->((((eq Prop) (g y)) x)->False))
% 13.96/14.14  Found x06:(((eq Prop) (g x)) y)
% 13.96/14.14  Instantiate: b:=(g x):Prop
% 13.96/14.14  Found x06 as proof of (((eq Prop) b) y)
% 13.96/14.14  Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 32.76/32.96  Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 32.76/32.96  Found x000:False
% 32.76/32.96  Found (fun (x06:(((eq Prop) (g x)) y))=> x000) as proof of False
% 32.76/32.96  Found (fun (x06:(((eq Prop) (g x)) y))=> x000) as proof of ((((eq Prop) (g x)) y)->False)
% 32.76/32.96  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 32.76/32.96  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found x000:False
% 32.76/32.96  Found (fun (x06:(((eq Prop) (g x)) y))=> x000) as proof of False
% 32.76/32.96  Found (fun (x05:(not (((eq Prop) x) y))) (x06:(((eq Prop) (g x)) y))=> x000) as proof of ((((eq Prop) (g x)) y)->False)
% 32.76/32.96  Found (fun (x05:(not (((eq Prop) x) y))) (x06:(((eq Prop) (g x)) y))=> x000) as proof of ((not (((eq Prop) x) y))->((((eq Prop) (g x)) y)->False))
% 32.76/32.96  Found x06:(((eq Prop) (g x)) y)
% 32.76/32.96  Instantiate: b:=(g x):Prop
% 32.76/32.96  Found x06 as proof of (((eq Prop) b) y)
% 32.76/32.96  Found x04:(((eq Prop) (g y)) x)
% 32.76/32.96  Instantiate: b:=x:Prop
% 32.76/32.96  Found x04 as proof of (((eq Prop) (g y)) b)
% 32.76/32.96  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 32.76/32.96  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 32.76/32.96  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 32.76/32.96  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 32.76/32.96  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 32.76/32.96  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 32.76/32.96  Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 32.76/32.96  Found x02:(p g)
% 32.76/32.96  Instantiate: b:=g:(Prop->Prop)
% 32.76/32.96  Found x02 as proof of (P b)
% 32.76/32.96  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 32.76/32.96  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 32.76/32.96  Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 32.76/32.96  Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 32.76/32.96  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 32.76/32.96  Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 32.76/32.96  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 32.76/32.96  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 32.76/32.96  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 32.76/32.96  Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 32.76/32.96  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 38.86/39.07  Found x02:(p g)
% 38.86/39.07  Instantiate: b:=g:(Prop->Prop)
% 38.86/39.07  Found x02 as proof of (P b)
% 38.86/39.07  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 38.86/39.07  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 38.86/39.07  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 38.86/39.07  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 38.86/39.07  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 38.86/39.07  Found x02:(p g)
% 38.86/39.07  Instantiate: f:=g:(Prop->Prop)
% 38.86/39.07  Found x02 as proof of (P f)
% 38.86/39.07  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.86/39.07  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 38.86/39.07  Found x02:(p g)
% 38.86/39.07  Instantiate: f:=g:(Prop->Prop)
% 38.86/39.07  Found x02 as proof of (P f)
% 38.86/39.07  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.86/39.07  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 38.86/39.07  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.86/39.07  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 38.86/39.07  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 38.86/39.07  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 38.86/39.07  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 38.86/39.07  Found eta_expansion0000:=(eta_expansion000 p):((p g)->(p (fun (x:Prop)=> (g x))))
% 38.86/39.07  Found (eta_expansion000 p) as proof of ((p g)->(P b))
% 38.86/39.07  Found ((eta_expansion00 g) p) as proof of ((p g)->(P b))
% 38.86/39.07  Found (((eta_expansion0 Prop) g) p) as proof of ((p g)->(P b))
% 38.86/39.07  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 38.86/39.07  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 38.86/39.07  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p)) as proof of ((p g)->(P b))
% 38.86/39.07  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p)) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P b)))
% 38.86/39.07  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 38.86/39.07  Found ((and_rect1 (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 38.86/39.07  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 38.86/39.07  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 46.04/46.21  Found x04:(((eq Prop) (g y)) x)
% 46.04/46.21  Instantiate: b:=x:Prop
% 46.04/46.21  Found x04 as proof of (((eq Prop) (g y)) b)
% 46.04/46.21  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 46.04/46.21  Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 46.04/46.21  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 46.04/46.21  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 46.04/46.21  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 46.04/46.21  Found x02:(p g)
% 46.04/46.21  Instantiate: f:=g:(Prop->Prop)
% 46.04/46.21  Found x02 as proof of (P f)
% 46.04/46.21  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 46.04/46.21  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 46.04/46.21  Found x02:(p g)
% 46.04/46.21  Instantiate: f:=g:(Prop->Prop)
% 46.04/46.21  Found x02 as proof of (P f)
% 46.04/46.21  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 46.04/46.21  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 46.04/46.21  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 46.04/46.21  Found x04:(((eq Prop) (g y)) x)
% 46.04/46.21  Instantiate: b:=(g y):Prop
% 46.04/46.21  Found x04 as proof of (((eq Prop) b) x)
% 46.04/46.21  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 46.04/46.21  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 46.04/46.21  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 46.04/46.21  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 46.04/46.21  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 46.04/46.21  Found x02:(p g)
% 46.04/46.21  Instantiate: b:=g:(Prop->Prop)
% 46.04/46.21  Found x02 as proof of (P b)
% 46.04/46.21  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 46.04/46.21  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 46.04/46.21  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 46.04/46.21  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 46.04/46.21  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 46.04/46.21  Found eta_expansion_dep0000:=(eta_expansion_dep000 p):((p g)->(p (fun (x:Prop)=> (g x))))
% 46.04/46.21  Found (eta_expansion_dep000 p) as proof of ((p g)->(P f))
% 46.04/46.21  Found ((eta_expansion_dep00 g) p) as proof of ((p g)->(P f))
% 46.04/46.21  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) g) p) as proof of ((p g)->(P f))
% 46.04/46.21  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p) as proof of ((p g)->(P f))
% 46.04/46.21  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p) as proof of ((p g)->(P f))
% 46.04/46.21  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p)) as proof of ((p g)->(P f))
% 46.04/46.21  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p)) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P f)))
% 46.04/46.21  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p))) as proof of (P f)
% 46.04/46.21  Found ((and_rect1 (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p))) as proof of (P f)
% 46.04/46.21  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p))) as proof of (P f)
% 48.37/48.59  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) p))) as proof of (P f)
% 48.37/48.59  Found x02:(p g)
% 48.37/48.59  Instantiate: f:=g:(Prop->Prop)
% 48.37/48.59  Found (fun (x02:(p g))=> x02) as proof of (P f)
% 48.37/48.59  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02) as proof of ((p g)->(P f))
% 48.37/48.59  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P f)))
% 48.37/48.59  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02)) as proof of (P f)
% 48.37/48.59  Found ((and_rect1 (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02)) as proof of (P f)
% 48.37/48.59  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02)) as proof of (P f)
% 48.37/48.59  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x02)) as proof of (P f)
% 48.37/48.59  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 48.37/48.59  Found (eq_ref00 p) as proof of (P g)
% 48.37/48.59  Found ((eq_ref0 g) p) as proof of (P g)
% 48.37/48.59  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 48.37/48.59  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 48.37/48.59  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 48.37/48.59  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found eq_ref00:=(eq_ref0 g):(((eq (Prop->Prop)) g) g)
% 48.37/48.59  Found (eq_ref0 g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 48.37/48.59  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 48.37/48.59  Found eq_ref00:=(eq_ref0 g):(((eq (Prop->Prop)) g) g)
% 48.37/48.59  Found (eq_ref0 g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 48.37/48.59  Found eta_expansion0000:=(eta_expansion000 p):((p g)->(p (fun (x:Prop)=> (g x))))
% 48.37/48.59  Found (eta_expansion000 p) as proof of ((p g)->(P b))
% 48.37/48.59  Found ((eta_expansion00 g) p) as proof of ((p g)->(P b))
% 48.37/48.59  Found (((eta_expansion0 Prop) g) p) as proof of ((p g)->(P b))
% 48.37/48.59  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 48.37/48.59  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 55.63/55.80  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p)) as proof of ((p g)->(P b))
% 55.63/55.80  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p)) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P b)))
% 55.63/55.80  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 55.63/55.80  Found ((and_rect1 (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 55.63/55.80  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 55.63/55.80  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P b)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p))) as proof of (P b)
% 55.63/55.80  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 55.63/55.80  Found (eq_ref00 p) as proof of (P g)
% 55.63/55.80  Found ((eq_ref0 g) p) as proof of (P g)
% 55.63/55.80  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 55.63/55.80  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 55.63/55.80  Found x02:(p g)
% 55.63/55.80  Instantiate: f:=g:(Prop->Prop)
% 55.63/55.80  Found x02 as proof of (P f)
% 55.63/55.80  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 55.63/55.80  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 55.63/55.80  Found x02:(p g)
% 55.63/55.80  Instantiate: f:=g:(Prop->Prop)
% 55.63/55.80  Found x02 as proof of (P f)
% 55.63/55.80  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 55.63/55.80  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 55.63/55.80  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 55.63/55.80  Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 55.63/55.80  Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 55.63/55.80  Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 55.63/55.80  Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 55.63/55.80  Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 55.63/55.80  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 55.63/55.80  Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 55.63/55.80  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 55.63/55.80  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 55.63/55.80  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 55.63/55.80  Found eq_ref000:=(eq_ref00 P):((P (g y))->(P (g y)))
% 55.63/55.80  Found (eq_ref00 P) as proof of (P0 (g y))
% 55.63/55.80  Found ((eq_ref0 (g y)) P) as proof of (P0 (g y))
% 55.63/55.80  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (g y))
% 55.63/55.80  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (g y))
% 55.63/55.80  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 55.63/55.80  Found (eq_ref00 p) as proof of (P g)
% 55.63/55.80  Found ((eq_ref0 g) p) as proof of (P g)
% 55.63/55.80  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 55.63/55.80  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 55.63/55.80  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 56.76/56.99  Found (eq_ref00 p) as proof of (P g)
% 56.76/56.99  Found ((eq_ref0 g) p) as proof of (P g)
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 56.76/56.99  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 56.76/56.99  Found (eq_ref00 p) as proof of ((p g)->(P f))
% 56.76/56.99  Found ((eq_ref0 g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p)) as proof of ((p g)->(P f))
% 56.76/56.99  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p)) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P f)))
% 56.76/56.99  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found ((and_rect1 (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 56.76/56.99  Found (eq_ref00 p) as proof of ((p g)->(P f))
% 56.76/56.99  Found ((eq_ref0 g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of ((p g)->(P f))
% 56.76/56.99  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p)) as proof of ((p g)->(P f))
% 56.76/56.99  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p)) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->(P f)))
% 56.76/56.99  Found (and_rect10 (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found ((and_rect1 (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found (((fun (P0:Type) (x1:(((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->P0)))=> (((((and_rect ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (p g)) P0) x1) x0)) (P f)) (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> (((eq_ref (Prop->Prop)) g) p))) as proof of (P f)
% 56.76/56.99  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 56.76/56.99  Found (eq_ref00 p) as proof of (P g)
% 56.76/56.99  Found ((eq_ref0 g) p) as proof of (P g)
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 56.76/56.99  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 56.76/56.99  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 74.55/74.76  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found eq_ref00:=(eq_ref0 g):(((eq (Prop->Prop)) g) g)
% 74.55/74.76  Found (eq_ref0 g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 74.55/74.76  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 74.55/74.76  Found eq_ref00:=(eq_ref0 g):(((eq (Prop->Prop)) g) g)
% 74.55/74.76  Found (eq_ref0 g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found ((eq_ref (Prop->Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 74.55/74.76  Found x02:(p g)
% 74.55/74.76  Instantiate: b:=g:(Prop->Prop)
% 74.55/74.76  Found x02 as proof of (P b)
% 74.55/74.76  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 74.55/74.76  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found x02:(p g)
% 74.55/74.76  Instantiate: b:=g:(Prop->Prop)
% 74.55/74.76  Found x02 as proof of (P b)
% 74.55/74.76  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 74.55/74.76  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found x02:(p g)
% 74.55/74.76  Instantiate: b:=g:(Prop->Prop)
% 74.55/74.76  Found x02 as proof of (P b)
% 74.55/74.76  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 74.55/74.76  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 74.55/74.76  Found x04:(((eq Prop) (g y)) x)
% 74.55/74.76  Instantiate: b:=(g y):Prop
% 74.55/74.76  Found x04 as proof of (((eq Prop) b) x)
% 74.55/74.76  Found x06:(((eq Prop) (g x)) y)
% 74.55/74.76  Instantiate: b:=y:Prop
% 74.55/74.76  Found x06 as proof of (((eq Prop) (g x)) b)
% 74.55/74.76  Found x04:(((eq Prop) (g y)) x)
% 74.55/74.76  Instantiate: b:=(g y):Prop
% 74.55/74.76  Found x04 as proof of (((eq Prop) b) x)
% 74.55/74.76  Found x06:(((eq Prop) (g x)) y)
% 74.55/74.76  Instantiate: b:=y:Prop
% 74.55/74.76  Found x06 as proof of (((eq Prop) (g x)) b)
% 74.55/74.76  Found x02:(p g)
% 74.55/74.76  Instantiate: f:=g:(Prop->Prop)
% 74.55/74.76  Found x02 as proof of (P f)
% 74.55/74.76  Found x02:(p g)
% 74.55/74.76  Instantiate: f:=g:(Prop->Prop)
% 74.55/74.76  Found x02 as proof of (P f)
% 74.55/74.76  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 74.55/74.76  Found (eq_ref00 p) as proof of (P g)
% 74.55/74.76  Found ((eq_ref0 g) p) as proof of (P g)
% 74.55/74.76  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 74.55/74.76  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 74.55/74.76  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 74.55/74.76  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 81.10/81.38  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found x02:(p g)
% 81.10/81.38  Instantiate: b:=g:(Prop->Prop)
% 81.10/81.38  Found x02 as proof of (P b)
% 81.10/81.38  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 81.10/81.38  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 81.10/81.38  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 81.10/81.38  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 81.10/81.38  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 81.10/81.38  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 81.10/81.38  Found x02:(p g)
% 81.10/81.38  Instantiate: f:=g:(Prop->Prop)
% 81.10/81.38  Found x02 as proof of (P f)
% 81.10/81.38  Found x02:(p g)
% 81.10/81.38  Instantiate: f:=g:(Prop->Prop)
% 81.10/81.38  Found x02 as proof of (P f)
% 81.10/81.38  Found x060:=(x06 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 81.10/81.38  Found (x06 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 81.10/81.38  Found (x06 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 81.10/81.38  Found x02:(p g)
% 81.10/81.38  Instantiate: f:=g:(Prop->Prop)
% 81.10/81.38  Found x02 as proof of (P f)
% 81.10/81.38  Found x02:(p g)
% 81.10/81.38  Instantiate: f:=g:(Prop->Prop)
% 81.10/81.38  Found x02 as proof of (P f)
% 81.10/81.38  Found x060:=(x06 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 81.10/81.38  Found (x06 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 81.10/81.38  Found (x06 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 81.10/81.38  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 81.10/81.38  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 81.10/81.38  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 81.10/81.38  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 81.10/81.38  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 81.10/81.38  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 81.10/81.38  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 81.10/81.38  Found (eq_ref00 p) as proof of (P g)
% 81.10/81.38  Found ((eq_ref0 g) p) as proof of (P g)
% 81.10/81.38  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 93.30/93.55  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 93.30/93.55  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 93.30/93.55  Found (eq_ref00 p) as proof of (P g)
% 93.30/93.55  Found ((eq_ref0 g) p) as proof of (P g)
% 93.30/93.55  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 93.30/93.55  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 93.30/93.55  Found x02:(p g)
% 93.30/93.55  Instantiate: b:=g:(Prop->Prop)
% 93.30/93.55  Found x02 as proof of (P b)
% 93.30/93.55  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 93.30/93.55  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 93.30/93.55  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 93.30/93.55  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 93.30/93.55  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 93.30/93.55  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 93.30/93.55  Found eq_ref000:=(eq_ref00 P):((P (g (g x)))->(P (g (g x))))
% 93.30/93.55  Found (eq_ref00 P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found ((eq_ref0 (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found (((eq_ref Prop) (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found (((eq_ref Prop) (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found eq_ref000:=(eq_ref00 P):((P (g y))->(P (g y)))
% 93.30/93.55  Found (eq_ref00 P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found ((eq_ref0 (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found eta_expansion0000:=(eta_expansion000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 93.30/93.55  Found (eta_expansion000 P0) as proof of (P1 not)
% 93.30/93.55  Found ((eta_expansion00 not) P0) as proof of (P1 not)
% 93.30/93.55  Found (((eta_expansion0 Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found eta_expansion0000:=(eta_expansion000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 93.30/93.55  Found (eta_expansion000 P0) as proof of (P1 not)
% 93.30/93.55  Found ((eta_expansion00 not) P0) as proof of (P1 not)
% 93.30/93.55  Found (((eta_expansion0 Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 93.30/93.55  Found eq_ref000:=(eq_ref00 P):((P (g y))->(P (g y)))
% 93.30/93.55  Found (eq_ref00 P) as proof of (P0 (g y))
% 93.30/93.55  Found ((eq_ref0 (g y)) P) as proof of (P0 (g y))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (g y))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (g y))
% 93.30/93.55  Found eq_ref000:=(eq_ref00 P):((P (g y))->(P (g y)))
% 93.30/93.55  Found (eq_ref00 P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found ((eq_ref0 (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found (((eq_ref Prop) (g y)) P) as proof of (P0 (P (g y)))
% 93.30/93.55  Found eq_ref000:=(eq_ref00 P):((P (g (g x)))->(P (g (g x))))
% 93.30/93.55  Found (eq_ref00 P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found ((eq_ref0 (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found (((eq_ref Prop) (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found (((eq_ref Prop) (g (g x))) P) as proof of (P0 (P (g (g x))))
% 93.30/93.55  Found x02:(p g)
% 93.30/93.55  Instantiate: f:=g:(Prop->Prop)
% 93.30/93.55  Found x02 as proof of (P f)
% 93.30/93.55  Found x02:(p g)
% 93.30/93.55  Instantiate: f:=g:(Prop->Prop)
% 93.30/93.55  Found x02 as proof of (P f)
% 93.30/93.55  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 93.30/93.55  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 93.30/93.55  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 93.30/93.55  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 93.30/93.55  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 109.19/109.45  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 109.19/109.45  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 109.19/109.45  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 109.19/109.45  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 109.19/109.45  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 109.19/109.45  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 109.19/109.45  Found x02:(p g)
% 109.19/109.45  Instantiate: f:=g:(Prop->Prop)
% 109.19/109.45  Found x02 as proof of (P f)
% 109.19/109.45  Found x02:(p g)
% 109.19/109.45  Instantiate: f:=g:(Prop->Prop)
% 109.19/109.45  Found x02 as proof of (P f)
% 109.19/109.45  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 109.19/109.45  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 109.19/109.45  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 109.19/109.45  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 109.19/109.45  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 109.19/109.45  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 109.19/109.45  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 109.19/109.45  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 109.19/109.45  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 109.19/109.45  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 109.19/109.45  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 109.19/109.45  Found eta_expansion0000:=(eta_expansion000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 109.19/109.45  Found (eta_expansion000 P0) as proof of (P1 not)
% 109.19/109.45  Found ((eta_expansion00 not) P0) as proof of (P1 not)
% 109.19/109.45  Found (((eta_expansion0 Prop) not) P0) as proof of (P1 not)
% 109.19/109.45  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 109.19/109.45  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 129.48/129.69  Found eta_expansion0000:=(eta_expansion000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 129.48/129.69  Found (eta_expansion000 P0) as proof of (P1 not)
% 129.48/129.69  Found ((eta_expansion00 not) P0) as proof of (P1 not)
% 129.48/129.69  Found (((eta_expansion0 Prop) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion Prop) Prop) not) P0) as proof of (P1 not)
% 129.48/129.69  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 129.48/129.69  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 129.48/129.69  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 129.48/129.69  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 129.48/129.69  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 129.48/129.69  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 129.48/129.69  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 129.48/129.69  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 129.48/129.69  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 129.48/129.69  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 129.48/129.69  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 129.48/129.69  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 129.48/129.69  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 129.48/129.69  Found x06:(((eq Prop) (g x)) y)
% 129.48/129.69  Instantiate: b:=y:Prop
% 129.48/129.69  Found x06 as proof of (((eq Prop) (g x)) b)
% 129.48/129.69  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.48/129.69  Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found x06:(((eq Prop) (g x)) y)
% 129.48/129.69  Instantiate: b:=y:Prop
% 129.48/129.69  Found x06 as proof of (((eq Prop) (g x)) b)
% 129.48/129.69  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.48/129.69  Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found x06:(((eq Prop) (g x)) y)
% 129.48/129.69  Instantiate: b:=y:Prop
% 129.48/129.69  Found x06 as proof of (((eq Prop) (g x)) b)
% 129.48/129.69  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.48/129.69  Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 129.48/129.69  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 129.48/129.69  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 129.48/129.69  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 129.48/129.69  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 129.48/129.69  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 129.48/129.69  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 129.48/129.69  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 129.48/129.69  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 133.30/133.58  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 133.30/133.58  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 133.30/133.58  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 133.30/133.58  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 133.30/133.58  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 133.30/133.58  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 133.30/133.58  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 133.30/133.58  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 133.30/133.58  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 133.30/133.58  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 133.30/133.58  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 147.46/147.72  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 147.46/147.72  Found (eq_ref00 p) as proof of (P g)
% 147.46/147.72  Found ((eq_ref0 g) p) as proof of (P g)
% 147.46/147.72  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 147.46/147.72  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 147.46/147.72  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 147.46/147.72  Found (eq_ref00 P) as proof of (P0 (g x))
% 147.46/147.72  Found ((eq_ref0 (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 147.46/147.72  Found (eq_ref00 P) as proof of (P0 (g x))
% 147.46/147.72  Found ((eq_ref0 (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 147.46/147.72  Found x02:(p g)
% 147.46/147.72  Instantiate: b:=g:(Prop->Prop)
% 147.46/147.72  Found x02 as proof of (P b)
% 147.46/147.72  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 147.46/147.72  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 147.46/147.72  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 147.46/147.72  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 147.46/147.72  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 147.46/147.72  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 147.46/147.72  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 147.46/147.72  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 147.46/147.72  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 147.46/147.72  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 147.46/147.72  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 not)->(P0 (fun (x:Prop)=> (not x))))
% 147.46/147.72  Found (eta_expansion_dep000 P0) as proof of (P1 not)
% 147.46/147.72  Found ((eta_expansion_dep00 not) P0) as proof of (P1 not)
% 147.46/147.72  Found (((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found ((((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) P0) as proof of (P1 not)
% 147.46/147.72  Found x02:(p g)
% 147.46/147.72  Instantiate: b:=g:(Prop->Prop)
% 147.46/147.72  Found x02 as proof of (P b)
% 147.46/147.72  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 147.46/147.72  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found x02:(p g)
% 147.46/147.72  Instantiate: b:=g:(Prop->Prop)
% 147.46/147.72  Found x02 as proof of (P b)
% 147.46/147.72  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 147.46/147.72  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 147.46/147.72  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found x02:(p g)
% 158.50/158.74  Instantiate: b:=g:(Prop->Prop)
% 158.50/158.74  Found x02 as proof of (P b)
% 158.50/158.74  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 158.50/158.74  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 158.50/158.74  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 158.50/158.74  Found (eq_ref00 p) as proof of (P g)
% 158.50/158.74  Found ((eq_ref0 g) p) as proof of (P g)
% 158.50/158.74  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 158.50/158.74  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 158.50/158.74  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 158.50/158.74  Found (eq_ref00 p) as proof of (P g)
% 158.50/158.74  Found ((eq_ref0 g) p) as proof of (P g)
% 158.50/158.74  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 158.50/158.74  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 158.50/158.74  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 158.50/158.74  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 158.50/158.74  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 158.50/158.74  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 158.50/158.74  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 158.50/158.74  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 158.50/158.74  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found eq_ref000:=(eq_ref00 P0):((P0 (g x1))->(P0 (g x1)))
% 158.50/158.74  Found (eq_ref00 P0) as proof of (P1 (g x1))
% 158.50/158.74  Found ((eq_ref0 (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found (((eq_ref Prop) (g x1)) P0) as proof of (P1 (g x1))
% 158.50/158.74  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 158.50/158.74  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 158.50/158.74  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 158.50/158.74  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 158.50/158.74  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 158.50/158.74  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 158.50/158.74  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 158.50/158.74  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 158.50/158.74  Found eq_ref00:=(eq_ref0 (g x1)):(((eq Prop) (g x1)) (g x1))
% 170.54/170.83  Found (eq_ref0 (g x1)) as proof of (((eq Prop) (g x1)) b)
% 170.54/170.83  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 170.54/170.83  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 170.54/170.83  Found ((eq_ref Prop) (g x1)) as proof of (((eq Prop) (g x1)) b)
% 170.54/170.83  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.54/170.83  Found (eq_ref0 b) as proof of (((eq Prop) b) (not x1))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (not x1))
% 170.54/170.83  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.54/170.83  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 170.54/170.83  Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 170.54/170.83  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 170.54/170.83  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 170.54/170.83  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.54/170.83  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 170.54/170.83  Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 170.54/170.83  Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 170.54/170.83  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 170.54/170.83  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 170.54/170.83  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 170.54/170.83  Found (eq_ref00 p) as proof of (P g)
% 170.54/170.83  Found ((eq_ref0 g) p) as proof of (P g)
% 170.54/170.83  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 170.54/170.83  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: b:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P b)
% 170.54/170.83  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 170.54/170.83  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 170.54/170.83  Found x02:(p g)
% 170.54/170.83  Instantiate: f:=g:(Prop->Prop)
% 170.54/170.83  Found x02 as proof of (P f)
% 180.83/181.12  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 180.83/181.12  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 180.83/181.12  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 180.83/181.12  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 180.83/181.12  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 180.83/181.12  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 180.83/181.12  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found x02:(p g)
% 180.83/181.12  Instantiate: f:=g:(Prop->Prop)
% 180.83/181.12  Found x02 as proof of (P f)
% 180.83/181.12  Found x02:(p g)
% 180.83/181.12  Instantiate: f:=g:(Prop->Prop)
% 180.83/181.12  Found x02 as proof of (P f)
% 180.83/181.12  Found x06:(((eq Prop) (g x)) y)
% 180.83/181.12  Instantiate: b:=y:Prop
% 180.83/181.12  Found x06 as proof of (((eq Prop) (g x)) b)
% 180.83/181.12  Found x04:(((eq Prop) (g y)) x)
% 180.83/181.12  Instantiate: b:=(g y):Prop
% 180.83/181.12  Found x04 as proof of (((eq Prop) b) x)
% 180.83/181.12  Found x04:(((eq Prop) (g y)) x)
% 180.83/181.12  Instantiate: b:=x:Prop
% 180.83/181.12  Found x04 as proof of (((eq Prop) (g y)) b)
% 180.83/181.12  Found x06:(((eq Prop) (g x)) y)
% 180.83/181.12  Instantiate: b:=(g x):Prop
% 180.83/181.12  Found x06 as proof of (((eq Prop) b) y)
% 180.83/181.12  Found x02:(p g)
% 180.83/181.12  Instantiate: b:=g:(Prop->Prop)
% 180.83/181.12  Found x02 as proof of (P b)
% 180.83/181.12  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 180.83/181.12  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found x07:(P x)
% 180.83/181.12  Instantiate: b:=x:Prop
% 180.83/181.12  Found x07 as proof of (P0 b)
% 180.83/181.12  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 180.83/181.12  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 180.83/181.12  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 180.83/181.12  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 180.83/181.12  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 180.83/181.12  Found x02:(p g)
% 180.83/181.12  Instantiate: b:=g:(Prop->Prop)
% 180.83/181.12  Found x02 as proof of (P b)
% 180.83/181.12  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 180.83/181.12  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found eta_expansion_dep000:=(eta_expansion_dep00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 180.83/181.12  Found (eta_expansion_dep00 not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found ((eta_expansion_dep0 (fun (x1:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found (((eta_expansion_dep Prop) (fun (x1:Prop)=> Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 180.83/181.12  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 201.72/202.05  Found (eq_ref00 p) as proof of (P g)
% 201.72/202.05  Found ((eq_ref0 g) p) as proof of (P g)
% 201.72/202.05  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 201.72/202.05  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 201.72/202.05  Found eq_ref000:=(eq_ref00 p):((p g)->(p g))
% 201.72/202.05  Found (eq_ref00 p) as proof of (P g)
% 201.72/202.05  Found ((eq_ref0 g) p) as proof of (P g)
% 201.72/202.05  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 201.72/202.05  Found (((eq_ref (Prop->Prop)) g) p) as proof of (P g)
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found x06:(((eq Prop) (g x)) y)
% 201.72/202.05  Instantiate: b:=(g x):Prop
% 201.72/202.05  Found x06 as proof of (((eq Prop) b) y)
% 201.72/202.05  Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 201.72/202.05  Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 201.72/202.05  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 201.72/202.05  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 201.72/202.05  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 201.72/202.05  Found x02:(p g)
% 201.72/202.05  Instantiate: f:=g:(Prop->Prop)
% 201.72/202.05  Found x02 as proof of (P f)
% 201.72/202.05  Found x02:(p g)
% 201.72/202.05  Instantiate: f:=g:(Prop->Prop)
% 201.72/202.05  Found x02 as proof of (P f)
% 201.72/202.05  Found x02:(p g)
% 201.72/202.05  Instantiate: f:=g:(Prop->Prop)
% 201.72/202.05  Found x02 as proof of (P f)
% 201.72/202.05  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 201.72/202.05  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 201.72/202.05  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 213.34/213.67  Found x02:(p g)
% 213.34/213.67  Instantiate: f:=g:(Prop->Prop)
% 213.34/213.67  Found x02 as proof of (P f)
% 213.34/213.67  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 213.34/213.67  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 213.34/213.67  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 213.34/213.67  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 213.34/213.67  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 213.34/213.67  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 213.34/213.67  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 213.34/213.67  Found x02:(p g)
% 213.34/213.67  Instantiate: f:=g:(Prop->Prop)
% 213.34/213.67  Found x02 as proof of (P f)
% 213.34/213.67  Found x02:(p g)
% 213.34/213.67  Instantiate: f:=g:(Prop->Prop)
% 213.34/213.67  Found x02 as proof of (P f)
% 213.34/213.67  Found x000:False
% 213.34/213.67  Found (fun (x02:(p g))=> x000) as proof of False
% 213.34/213.67  Found (fun (x02:(p g))=> x000) as proof of ((p g)->False)
% 213.34/213.67  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 213.34/213.67  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (Prop->Prop)) g) (fun (x:Prop)=> (g x)))
% 213.34/213.67  Found (eta_expansion_dep00 g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 213.34/213.67  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 213.34/213.67  Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (Prop->Prop)) g) (fun (x:Prop)=> (g x)))
% 213.34/213.67  Found (eta_expansion_dep00 g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 213.34/213.67  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 213.34/213.67  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 213.34/213.67  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 213.34/213.67  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 213.34/213.67  Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not x0))
% 213.34/213.67  Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% 221.30/221.62  Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 221.30/221.62  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 221.30/221.62  Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) (not x0))
% 221.30/221.62  Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) (not x0))
% 221.30/221.62  Found (fun (x0:Prop)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found x06:(((eq Prop) (g x)) y)
% 221.30/221.62  Instantiate: b:=(g x):Prop
% 221.30/221.62  Found x06 as proof of (((eq Prop) b) y)
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 221.30/221.62  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 221.30/221.62  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found False_rect00:=(False_rect0 (((eq Prop) x) (g x))):(((eq Prop) x) (g x))
% 221.30/221.62  Found (False_rect0 (((eq Prop) x) (g x))) as proof of (((eq Prop) x) (g x))
% 221.30/221.62  Found ((fun (P:Type)=> ((False_rect P) x000)) (((eq Prop) x) (g x))) as proof of (((eq Prop) x) (g x))
% 221.30/221.62  Found ((fun (P:Type)=> ((False_rect P) x000)) (((eq Prop) x) (g x))) as proof of (((eq Prop) x) (g x))
% 221.30/221.62  Found (x060 ((fun (P:Type)=> ((False_rect P) x000)) (((eq Prop) x) (g x)))) as proof of (((eq Prop) x) y)
% 221.30/221.62  Found ((x06 ((eq Prop) x)) ((fun (P:Type)=> ((False_rect P) x000)) (((eq Prop) x) (g x)))) as proof of (((eq Prop) x) y)
% 221.30/221.62  Found ((x06 ((eq Prop) x)) ((fun (P:Type)=> ((False_rect P) x000)) (((eq Prop) x) (g x)))) as proof of (((eq Prop) x) y)
% 221.30/221.62  Found x06:(((eq Prop) (g x)) y)
% 221.30/221.62  Instantiate: b:=(g x):Prop
% 221.30/221.62  Found x06 as proof of (((eq Prop) b) y)
% 221.30/221.62  Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 221.30/221.62  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 221.30/221.62  Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 221.30/221.62  Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 221.30/221.62  Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 221.30/221.62  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 221.30/221.62  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 221.30/221.62  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 221.30/221.62  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 221.30/221.62  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 221.30/221.62  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 221.30/221.62  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 221.30/221.62  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 237.13/237.47  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 237.13/237.47  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 237.13/237.47  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 237.13/237.47  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 237.13/237.47  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 237.13/237.47  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 237.13/237.47  Found x030:=(x03 (fun (x1:Prop)=> (P0 not))):((P0 not)->(P0 not))
% 237.13/237.47  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 237.13/237.47  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 237.13/237.47  Found x030:=(x03 (fun (x1:Prop)=> (P0 not))):((P0 not)->(P0 not))
% 237.13/237.47  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 237.13/237.47  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 237.13/237.47  Found x02:(p g)
% 237.13/237.47  Instantiate: b:=g:(Prop->Prop)
% 237.13/237.47  Found x02 as proof of (P b)
% 237.13/237.47  Found eq_ref00:=(eq_ref0 not):(((eq (Prop->Prop)) not) not)
% 237.13/237.47  Found (eq_ref0 not) as proof of (((eq (Prop->Prop)) not) b)
% 237.13/237.47  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 237.13/237.47  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 237.13/237.47  Found ((eq_ref (Prop->Prop)) not) as proof of (((eq (Prop->Prop)) not) b)
% 237.13/237.47  Found x000:False
% 237.13/237.47  Found (fun (x02:(p g))=> x000) as proof of False
% 237.13/237.47  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x000) as proof of ((p g)->False)
% 237.13/237.47  Found (fun (x01:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (x02:(p g))=> x000) as proof of (((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))->((p g)->False))
% 237.13/237.47  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 237.13/237.47  Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 237.13/237.47  Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 237.13/237.47  Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 237.13/237.47  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 237.13/237.47  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 237.13/237.47  Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 237.13/237.47  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 237.13/237.47  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 237.13/237.47  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 237.13/237.47  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 237.13/237.47  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 237.13/237.47  Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 237.13/237.47  Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 237.13/237.47  Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 237.13/237.47  Found x04:(((eq Prop) (g y)) x)
% 237.13/237.47  Instantiate: b:=(g y):Prop
% 237.13/237.47  Found x04 as proof of (((eq Prop) b) x)
% 237.13/237.47  Found x06:(((eq Prop) (g x)) y)
% 237.13/237.47  Instantiate: b:=y:Prop
% 237.13/237.47  Found x06 as proof of (((eq Prop) (g x)) b)
% 237.13/237.47  Found eq_ref000:=(eq_ref00 P0):((P0 g)->(P0 g))
% 237.13/237.47  Found (eq_ref00 P0) as proof of (P1 g)
% 237.13/237.47  Found ((eq_ref0 g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found eq_ref000:=(eq_ref00 P0):((P0 g)->(P0 g))
% 237.13/237.47  Found (eq_ref00 P0) as proof of (P1 g)
% 237.13/237.47  Found ((eq_ref0 g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found eq_ref000:=(eq_ref00 P0):((P0 g)->(P0 g))
% 237.13/237.47  Found (eq_ref00 P0) as proof of (P1 g)
% 237.13/237.47  Found ((eq_ref0 g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found eq_ref000:=(eq_ref00 P0):((P0 g)->(P0 g))
% 237.13/237.47  Found (eq_ref00 P0) as proof of (P1 g)
% 237.13/237.47  Found ((eq_ref0 g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found (((eq_ref (Prop->Prop)) g) P0) as proof of (P1 g)
% 237.13/237.47  Found eq_ref000:=(eq_ref00 P):((P y)->(P y))
% 237.13/237.47  Found (eq_ref00 P) as proof of (P0 y)
% 237.13/237.47  Found ((eq_ref0 y) P) as proof of (P0 y)
% 237.13/237.47  Found (((eq_ref Prop) y) P) as proof of (P0 y)
% 256.69/257.05  Found (((eq_ref Prop) y) P) as proof of (P0 y)
% 256.69/257.05  Found x02:(p g)
% 256.69/257.05  Instantiate: b:=g:(Prop->Prop)
% 256.69/257.05  Found x02 as proof of (P b)
% 256.69/257.05  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 256.69/257.05  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 256.69/257.05  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 256.69/257.05  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 256.69/257.05  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 256.69/257.05  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 256.69/257.05  Found x04:(((eq Prop) (g y)) x)
% 256.69/257.05  Instantiate: b:=(g y):Prop
% 256.69/257.05  Found x04 as proof of (P b)
% 256.69/257.05  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 256.69/257.05  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 256.69/257.05  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 256.69/257.05  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 256.69/257.05  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 256.69/257.05  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 256.69/257.05  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 256.69/257.05  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 256.69/257.05  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (Prop->Prop)) g) (fun (x:Prop)=> (g x)))
% 256.69/257.05  Found (eta_expansion_dep00 g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 256.69/257.05  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) not)
% 256.69/257.05  Found eta_expansion_dep000:=(eta_expansion_dep00 g):(((eq (Prop->Prop)) g) (fun (x:Prop)=> (g x)))
% 256.69/257.05  Found (eta_expansion_dep00 g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found ((eta_expansion_dep0 (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found (((eta_expansion_dep Prop) (fun (x2:Prop)=> Prop)) g) as proof of (((eq (Prop->Prop)) g) b)
% 256.69/257.05  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 256.69/257.05  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 256.69/257.05  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 256.69/257.05  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 256.69/257.05  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 256.69/257.05  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found x02:(p g)
% 267.02/267.32  Instantiate: f:=g:(Prop->Prop)
% 267.02/267.32  Found x02 as proof of (P f)
% 267.02/267.32  Found x02:(p g)
% 267.02/267.32  Instantiate: f:=g:(Prop->Prop)
% 267.02/267.32  Found x02 as proof of (P f)
% 267.02/267.32  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 267.02/267.32  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 267.02/267.32  Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% 267.02/267.32  Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (not x1))
% 267.02/267.32  Found (fun (x1:Prop)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:Prop), (((eq Prop) (f x)) (not x)))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (g x))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (g x))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (g x))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (g x))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g (g y)))->(P (g (g y))))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found ((eq_ref0 (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found (((eq_ref Prop) (g (g y))) P) as proof of (P0 (P (g (g y))))
% 267.02/267.32  Found eq_ref000:=(eq_ref00 P):((P (g x))->(P (g x)))
% 267.02/267.32  Found (eq_ref00 P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found ((eq_ref0 (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found (((eq_ref Prop) (g x)) P) as proof of (P0 (P (g x)))
% 267.02/267.32  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 267.02/267.32  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found x07:(P x)
% 289.00/289.32  Instantiate: b:=x:Prop
% 289.00/289.32  Found x07 as proof of (P0 b)
% 289.00/289.32  Found x06:(((eq Prop) (g x)) y)
% 289.00/289.32  Instantiate: b:=y:Prop
% 289.00/289.32  Found x06 as proof of (((eq Prop) (g x)) b)
% 289.00/289.32  Found x070:(P x)
% 289.00/289.32  Instantiate: b:=x:Prop
% 289.00/289.32  Found x070 as proof of (P0 b)
% 289.00/289.32  Found x06:(((eq Prop) (g x)) y)
% 289.00/289.32  Instantiate: b:=y:Prop
% 289.00/289.32  Found x06 as proof of (((eq Prop) (g x)) b)
% 289.00/289.32  Found x1:(P (g y))
% 289.00/289.32  Instantiate: b:=(g y):Prop
% 289.00/289.32  Found x1 as proof of (P0 b)
% 289.00/289.32  Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 289.00/289.32  Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 289.00/289.32  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 289.00/289.32  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 289.00/289.32  Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 289.00/289.32  Found x07:(P x)
% 289.00/289.32  Instantiate: b:=x:Prop
% 289.00/289.32  Found x07 as proof of (P0 b)
% 289.00/289.32  Found x06:(((eq Prop) (g x)) y)
% 289.00/289.32  Instantiate: b:=y:Prop
% 289.00/289.32  Found x06 as proof of (((eq Prop) (g x)) b)
% 289.00/289.32  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 289.00/289.32  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 289.00/289.32  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found eq_ref00:=(eq_ref0 b):(((eq (Prop->Prop)) b) b)
% 289.00/289.32  Found (eq_ref0 b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found ((eq_ref (Prop->Prop)) b) as proof of (((eq (Prop->Prop)) b) g)
% 289.00/289.32  Found eta_expansion000:=(eta_expansion00 not):(((eq (Prop->Prop)) not) (fun (x:Prop)=> (not x)))
% 289.00/289.32  Found (eta_expansion00 not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found ((eta_expansion0 Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found (((eta_expansion Prop) Prop) not) as proof of (((eq (Prop->Prop)) not) b)
% 289.00/289.32  Found x030:=(x03 (fun (x1:Prop)=> (P0 not))):((P0 not)->(P0 not))
% 289.00/289.32  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 289.00/289.32  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 289.00/289.32  Found x030:=(x03 (fun (x1:Prop)=> (P0 not))):((P0 not)->(P0 not))
% 289.00/289.32  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 289.00/289.32  Found (x03 (fun (x1:Prop)=> (P0 not))) as proof of (P1 not)
% 289.00/289.32  Found x04:(((eq Prop) (g y)) x)
% 289.00/289.32  Instantiate: b:=x:Prop
% 289.00/289.32  Found x04 as proof of (((eq Prop) (g y)) b)
% 289.00/289.32  Found x06:(((eq Prop) (g x)) y)
% 289.00/289.32  Instantiate: b:=(g x):Prop
% 289.00/289.32  Found x06 as proof of (((eq Prop) b) y)
% 289.00/289.32  Found x02:(p g)
% 289.00/289.32  Instantiate: f:=g:(Prop->Prop)
% 289.00/289.32  Found x02 as proof of (P f)
% 289.00/289.32  Found x02:(p g)
% 289.00/289.32  Instantiate: f:=g:(Prop->Prop)
% 289.00/289.32  Found x02 as proof of (P f)
% 289.00/289.32  Found eta_expansion0000:=(eta_expansion000 p):((p g)->(p (fun (x:Prop)=> (g x))))
% 289.00/289.32  Found (eta_expansion000 p) as proof of ((p g)->(P b))
% 289.00/289.32  Found ((eta_expansion00 g) p) as proof of ((p g)->(P b))
% 289.00/289.32  Found (((eta_expansion0 Prop) g) p) as proof of ((p g)->(P b))
% 289.00/289.32  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 289.00/289.32  Found ((((eta_expansion Prop) Prop) g) p) as proof of ((p g)->(P b))
% 289.00/289.32  Found (fun (x0:((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x)))=> ((((eta_expansion Prop) Prop) g) p)) as proof of ((p g)->(P b))
% 289.00/289.32  Found (fun (x0:((and ((and (not (((eq Prop) x) y))) (((
%------------------------------------------------------------------------------