TSTP Solution File: SYO041^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO041^2 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 290.56s 290.90s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO041^2 : TPTP v7.5.0. Released v4.1.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n012.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 07:20:50 EST 2022
% 0.13/0.33 % 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
% 11.36/11.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 11.36/11.52 FOF formula (<kernel.Constant object at 0x2aaffdc48290>, <kernel.Sort object at 0x2aaffdc24638>) of role type named a
% 11.36/11.52 Using role type
% 11.36/11.52 Declaring a:Prop
% 11.36/11.52 FOF formula (<kernel.Constant object at 0x2aaffdc482d8>, <kernel.DependentProduct object at 0x2aaffdc49200>) of role type named f
% 11.36/11.52 Using role type
% 11.36/11.52 Declaring f:(Prop->Prop)
% 11.36/11.52 FOF formula (<kernel.Constant object at 0x2aaffdc48290>, <kernel.DependentProduct object at 0x2aaffdc496c8>) of role type named g
% 11.36/11.52 Using role type
% 11.36/11.52 Declaring g:(Prop->Prop)
% 11.36/11.52 FOF formula (<kernel.Constant object at 0x2aaffdc482d8>, <kernel.Sort object at 0x2aaffdc24638>) of role type named x
% 11.36/11.52 Using role type
% 11.36/11.52 Declaring x:Prop
% 11.36/11.52 FOF formula (<kernel.Constant object at 0x2aaffdc482d8>, <kernel.Sort object at 0x2aaffdc24638>) of role type named y
% 11.36/11.52 Using role type
% 11.36/11.52 Declaring y:Prop
% 11.36/11.52 FOF formula (((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (((eq Prop) (f (f (f x)))) (g (f x))))->False) of role conjecture named 3
% 11.36/11.52 Conjecture to prove = (((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (((eq Prop) (f (f (f x)))) (g (f x))))->False):Prop
% 11.36/11.52 We need to prove ['(((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (((eq Prop) (f (f (f x)))) (g (f x))))->False)']
% 11.36/11.52 Parameter a:Prop.
% 11.36/11.52 Parameter f:(Prop->Prop).
% 11.36/11.52 Parameter g:(Prop->Prop).
% 11.36/11.52 Parameter x:Prop.
% 11.36/11.52 Parameter y:Prop.
% 11.36/11.52 Trying to prove (((and ((and ((and (not (((eq Prop) x) y))) (((eq Prop) (g x)) y))) (((eq Prop) (g y)) x))) (((eq Prop) (f (f (f x)))) (g (f x))))->False)
% 11.36/11.52 Found x05:(((eq Prop) (g x)) y)
% 11.36/11.52 Instantiate: b:=(g x):Prop
% 11.36/11.52 Found x05 as proof of (((eq Prop) b) y)
% 11.36/11.52 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 11.36/11.52 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found x050:=(x05 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 11.36/11.52 Found (x05 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found (x05 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found x03:(((eq Prop) (g y)) x)
% 11.36/11.52 Instantiate: b:=x:Prop
% 11.36/11.52 Found x03 as proof of (((eq Prop) (g y)) b)
% 11.36/11.52 Found x05:(((eq Prop) (g x)) y)
% 11.36/11.52 Instantiate: b:=(g x):Prop
% 11.36/11.52 Found x05 as proof of (((eq Prop) b) y)
% 11.36/11.52 Found x05:(((eq Prop) (g x)) y)
% 11.36/11.52 Instantiate: b:=(g x):Prop
% 11.36/11.52 Found x05 as proof of (((eq Prop) b) y)
% 11.36/11.52 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 11.36/11.52 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 11.36/11.52 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 11.36/11.52 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 11.36/11.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 11.36/11.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 11.36/11.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 11.36/11.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 11.36/11.52 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 11.36/11.52 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 11.36/11.52 Found x050:=(x05 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 11.36/11.52 Found (x05 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found (x05 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 11.36/11.52 Found x03:(((eq Prop) (g y)) x)
% 11.36/11.52 Instantiate: b:=x:Prop
% 11.36/11.52 Found x03 as proof of (((eq Prop) (g y)) b)
% 11.36/11.52 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 11.36/11.52 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 11.36/11.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 11.36/11.52 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=x:Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) (g y)) b)
% 29.76/29.94 Found x05:(((eq Prop) (g x)) y)
% 29.76/29.94 Instantiate: b:=(g x):Prop
% 29.76/29.94 Found x05 as proof of (((eq Prop) b) y)
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=(g y):Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) b) x)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 29.76/29.94 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 29.76/29.94 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 29.76/29.94 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 29.76/29.94 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 29.76/29.94 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.76/29.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.76/29.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 29.76/29.94 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 29.76/29.94 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 29.76/29.94 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 29.76/29.94 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 29.76/29.94 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=x:Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) (g y)) b)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 29.76/29.94 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 29.76/29.94 Found x05:(((eq Prop) (g x)) y)
% 29.76/29.94 Instantiate: b:=y:Prop
% 29.76/29.94 Found x05 as proof of (((eq Prop) (g x)) b)
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=(g y):Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) b) x)
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=(g y):Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) b) x)
% 29.76/29.94 Found x05:(((eq Prop) (g x)) y)
% 29.76/29.94 Instantiate: b:=y:Prop
% 29.76/29.94 Found x05 as proof of (((eq Prop) (g x)) b)
% 29.76/29.94 Found x03:(((eq Prop) (g y)) x)
% 29.76/29.94 Instantiate: b:=(g y):Prop
% 29.76/29.94 Found x03 as proof of (((eq Prop) b) x)
% 29.76/29.94 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 29.76/29.94 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 29.76/29.94 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 29.76/29.94 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 44.84/45.03 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 44.84/45.03 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 44.84/45.03 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 44.84/45.03 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 44.84/45.03 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 44.84/45.03 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 44.84/45.03 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 44.84/45.03 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 44.84/45.03 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 44.84/45.03 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 44.84/45.03 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 44.84/45.03 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 44.84/45.03 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 44.84/45.03 Found x05:(((eq Prop) (g x)) y)
% 44.84/45.03 Instantiate: b:=y:Prop
% 44.84/45.03 Found x05 as proof of (((eq Prop) (g x)) b)
% 44.84/45.03 Found x03:(((eq Prop) (g y)) x)
% 44.84/45.03 Instantiate: b:=(g y):Prop
% 44.84/45.03 Found x03 as proof of (((eq Prop) b) x)
% 44.84/45.03 Found x05:(((eq Prop) (g x)) y)
% 44.84/45.03 Instantiate: b:=y:Prop
% 44.84/45.03 Found x05 as proof of (((eq Prop) (g x)) b)
% 44.84/45.03 Found x03:(((eq Prop) (g y)) x)
% 44.84/45.03 Instantiate: b:=(g y):Prop
% 44.84/45.03 Found x03 as proof of (((eq Prop) b) x)
% 44.84/45.03 Found x05:(((eq Prop) (g x)) y)
% 44.84/45.03 Instantiate: b:=y:Prop
% 44.84/45.03 Found x05 as proof of (((eq Prop) (g x)) b)
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found x05:(((eq Prop) (g x)) y)
% 44.84/45.03 Instantiate: b:=y:Prop
% 44.84/45.03 Found x05 as proof of (((eq Prop) (g x)) b)
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found x05:(((eq Prop) (g x)) y)
% 44.84/45.03 Instantiate: b:=y:Prop
% 44.84/45.03 Found x05 as proof of (((eq Prop) (g x)) b)
% 44.84/45.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 44.84/45.03 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 44.84/45.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 62.17/62.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 62.17/62.37 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 62.17/62.37 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 62.17/62.37 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 62.17/62.37 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 62.17/62.37 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 62.17/62.37 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 62.17/62.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 62.17/62.37 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 62.17/62.37 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 62.17/62.37 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 91.73/91.92 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 91.73/91.92 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 91.73/91.92 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 91.73/91.92 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=y:Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) (g x)) b)
% 91.73/91.92 Found x03:(((eq Prop) (g y)) x)
% 91.73/91.92 Instantiate: b:=(g y):Prop
% 91.73/91.92 Found x03 as proof of (((eq Prop) b) x)
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=(g x):Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) b) y)
% 91.73/91.92 Found x03:(((eq Prop) (g y)) x)
% 91.73/91.92 Instantiate: b:=x:Prop
% 91.73/91.92 Found x03 as proof of (((eq Prop) (g y)) b)
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=y:Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) (g x)) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=y:Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) (g x)) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=y:Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) (g x)) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 91.73/91.92 Found x06:(P x)
% 91.73/91.92 Instantiate: b:=x:Prop
% 91.73/91.92 Found x06 as proof of (P0 b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 91.73/91.92 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 91.73/91.92 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 91.73/91.92 Found x05:(((eq Prop) (g x)) y)
% 91.73/91.92 Instantiate: b:=(g x):Prop
% 91.73/91.92 Found x05 as proof of (((eq Prop) b) y)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 91.73/91.92 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 91.73/91.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 91.73/91.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 91.73/91.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 91.73/91.92 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 91.73/91.92 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 91.73/91.92 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 91.73/91.92 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 91.73/91.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 91.73/91.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 91.73/91.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 101.41/101.63 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 101.41/101.63 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 101.41/101.63 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.41/101.63 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.41/101.63 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.41/101.63 Found x05:(((eq Prop) (g x)) y)
% 101.41/101.63 Instantiate: b:=y:Prop
% 101.41/101.63 Found x05 as proof of (((eq Prop) (g x)) b)
% 101.41/101.63 Found x03:(((eq Prop) (g y)) x)
% 101.41/101.63 Instantiate: b:=(g y):Prop
% 101.41/101.63 Found x03 as proof of (((eq Prop) b) x)
% 101.41/101.63 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 101.41/101.63 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.41/101.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 101.41/101.63 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.41/101.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.41/101.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.41/101.63 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 101.41/101.63 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 101.41/101.63 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.41/101.63 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 119.63/119.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 119.63/119.88 Found x05:(((eq Prop) (g x)) y)
% 119.63/119.88 Instantiate: b:=(g x):Prop
% 119.63/119.88 Found x05 as proof of (((eq Prop) b) y)
% 119.63/119.88 Found x030:=(x03 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 119.63/119.88 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 119.63/119.88 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 119.63/119.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 119.63/119.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 119.63/119.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 119.63/119.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 119.63/119.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=(g y):Prop
% 119.63/119.88 Found x03 as proof of (((eq Prop) b) x)
% 119.63/119.88 Found x05:(((eq Prop) (g x)) y)
% 119.63/119.88 Instantiate: b:=y:Prop
% 119.63/119.88 Found x05 as proof of (((eq Prop) (g x)) b)
% 119.63/119.88 Found x05:(((eq Prop) (g x)) y)
% 119.63/119.88 Instantiate: b:=(g x):Prop
% 119.63/119.88 Found x05 as proof of (((eq Prop) b) y)
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=x:Prop
% 119.63/119.88 Found x03 as proof of (((eq Prop) (g y)) b)
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=x:Prop
% 119.63/119.88 Found x03 as proof of (((eq Prop) (g y)) b)
% 119.63/119.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.63/119.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=x:Prop
% 119.63/119.88 Found x03 as proof of (((eq Prop) (g y)) b)
% 119.63/119.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.63/119.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=x:Prop
% 119.63/119.88 Found x03 as proof of (((eq Prop) (g y)) b)
% 119.63/119.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 119.63/119.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 119.63/119.88 Found x03:(((eq Prop) (g y)) x)
% 119.63/119.88 Instantiate: b:=(g y):Prop
% 119.63/119.88 Found x03 as proof of (P b)
% 119.63/119.88 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 119.63/119.88 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 119.63/119.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 119.63/119.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 119.63/119.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 119.63/119.88 Found x05:(((eq Prop) (g x)) y)
% 119.63/119.88 Instantiate: b:=y:Prop
% 119.63/119.88 Found x05 as proof of (((eq Prop) (g x)) b)
% 119.63/119.88 Found x060:(P x)
% 149.65/149.89 Instantiate: b:=x:Prop
% 149.65/149.89 Found x060 as proof of (P0 b)
% 149.65/149.89 Found x05:(((eq Prop) (g x)) y)
% 149.65/149.89 Instantiate: b:=y:Prop
% 149.65/149.89 Found x05 as proof of (((eq Prop) (g x)) b)
% 149.65/149.89 Found x06:(P x)
% 149.65/149.89 Instantiate: b:=x:Prop
% 149.65/149.89 Found x06 as proof of (P0 b)
% 149.65/149.89 Found x1:(P (g y))
% 149.65/149.89 Instantiate: b:=(g y):Prop
% 149.65/149.89 Found x1 as proof of (P0 b)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 149.65/149.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found x05:(((eq Prop) (g x)) y)
% 149.65/149.89 Instantiate: b:=y:Prop
% 149.65/149.89 Found x05 as proof of (((eq Prop) (g x)) b)
% 149.65/149.89 Found x06:(P x)
% 149.65/149.89 Instantiate: b:=x:Prop
% 149.65/149.89 Found x06 as proof of (P0 b)
% 149.65/149.89 Found x06:(P x)
% 149.65/149.89 Instantiate: b:=x:Prop
% 149.65/149.89 Found x06 as proof of (P0 b)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 149.65/149.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found x05:(((eq Prop) (g x)) y)
% 149.65/149.89 Instantiate: b:=(g x):Prop
% 149.65/149.89 Found x05 as proof of (((eq Prop) b) y)
% 149.65/149.89 Found x03:(((eq Prop) (g y)) x)
% 149.65/149.89 Instantiate: b:=x:Prop
% 149.65/149.89 Found x03 as proof of (((eq Prop) (g y)) b)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.65/149.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 149.65/149.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 149.65/149.89 Found x05:(((eq Prop) (g x)) y)
% 149.65/149.89 Instantiate: b:=(g x):Prop
% 149.65/149.89 Found x05 as proof of (((eq Prop) b) y)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 149.65/149.89 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 149.65/149.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 149.65/149.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.65/149.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 149.65/149.89 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 149.65/149.89 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.65/149.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 149.65/149.89 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 149.65/149.89 Found x05:(((eq Prop) (g x)) y)
% 149.65/149.89 Instantiate: b:=y:Prop
% 149.65/149.89 Found x05 as proof of (((eq Prop) (g x)) b)
% 149.65/149.89 Found x03:(((eq Prop) (g y)) x)
% 149.65/149.89 Instantiate: b:=(g y):Prop
% 149.65/149.89 Found x03 as proof of (((eq Prop) b) x)
% 149.65/149.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 149.65/149.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 149.65/149.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 154.77/155.06 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found x030:=(x03 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 154.77/155.06 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.77/155.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 154.77/155.06 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.77/155.06 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.77/155.06 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 154.77/155.06 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found x05:(((eq Prop) (g x)) y)
% 154.77/155.06 Instantiate: b:=(g x):Prop
% 154.77/155.06 Found x05 as proof of (((eq Prop) b) y)
% 154.77/155.06 Found x030:=(x03 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 154.77/155.06 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 154.77/155.06 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.77/155.06 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 154.77/155.06 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.77/155.06 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.77/155.06 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.77/155.06 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.13/165.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 165.13/165.37 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 165.13/165.37 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.37 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.37 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.13/165.37 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.37 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 165.13/165.37 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.37 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.13/165.38 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 165.13/165.38 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 165.13/165.38 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 165.13/165.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.13/165.38 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 165.13/165.38 Found x010:=(x01 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found (x01 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 165.13/165.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 165.13/165.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 165.13/165.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 165.13/165.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 165.13/165.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 165.13/165.38 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 165.13/165.38 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 165.13/165.38 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 178.84/179.13 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 178.84/179.13 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 178.84/179.13 Found x06:(P y)
% 178.84/179.13 Instantiate: b:=y:Prop
% 178.84/179.13 Found x06 as proof of (P0 b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 178.84/179.13 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 178.84/179.13 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 178.84/179.13 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 178.84/179.13 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 178.84/179.13 Found x05:(((eq Prop) (g x)) y)
% 178.84/179.13 Instantiate: b:=y:Prop
% 178.84/179.13 Found x05 as proof of (((eq Prop) (g x)) b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: b:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (P b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: b:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (P b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 178.84/179.13 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 178.84/179.13 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 178.84/179.13 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 178.84/179.13 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 178.84/179.13 Found x060:(P x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x060 as proof of (P0 b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 178.84/179.13 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found x06:(P x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x06 as proof of (P0 b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 178.84/179.13 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) (g y)) b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.84/179.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found x1:(P (g y))
% 178.84/179.13 Instantiate: b:=(g y):Prop
% 178.84/179.13 Found x1 as proof of (P0 b)
% 178.84/179.13 Found x05:(((eq Prop) (g x)) y)
% 178.84/179.13 Instantiate: b:=y:Prop
% 178.84/179.13 Found x05 as proof of (((eq Prop) (g x)) b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) (g y)) b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found x06:(P x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x06 as proof of (P0 b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 178.84/179.13 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.84/179.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: a0:=(g y):Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) a0) x)
% 178.84/179.13 Found x03:(((eq Prop) (g y)) x)
% 178.84/179.13 Instantiate: b:=x:Prop
% 178.84/179.13 Found x03 as proof of (((eq Prop) (g y)) b)
% 178.84/179.13 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 178.84/179.13 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 178.84/179.13 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found x06:(P x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x06 as proof of (P0 b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=y:Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) (g x)) b)
% 202.56/202.91 Found x060:(P x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x060 as proof of (P0 b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=y:Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) (g x)) b)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: a0:=(g y):Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) a0) x)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: a0:=(g y):Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) a0) x)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: a0:=(g y):Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) a0) x)
% 202.56/202.91 Found x1:(P (g y))
% 202.56/202.91 Instantiate: b:=(g y):Prop
% 202.56/202.91 Found x1 as proof of (P0 b)
% 202.56/202.91 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 202.56/202.91 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=y:Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) (g x)) b)
% 202.56/202.91 Found x06:(P x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x06 as proof of (P0 b)
% 202.56/202.91 Found x1:(P (g y))
% 202.56/202.91 Instantiate: b:=(g y):Prop
% 202.56/202.91 Found x1 as proof of (P0 b)
% 202.56/202.91 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 202.56/202.91 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 202.56/202.91 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 202.56/202.91 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 202.56/202.91 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=y:Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) (g x)) b)
% 202.56/202.91 Found x06:(P (g (g x)))
% 202.56/202.91 Instantiate: b:=(g (g x)):Prop
% 202.56/202.91 Found x06 as proof of (P0 b)
% 202.56/202.91 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 202.56/202.91 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 202.56/202.91 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=(g x):Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) b) y)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.56/202.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 202.56/202.91 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 202.56/202.91 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 202.56/202.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 202.56/202.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 202.56/202.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 202.56/202.91 Found x010:=(x01 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 202.56/202.91 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 202.56/202.91 Found (x01 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=(g x):Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) b) y)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=(g x):Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) b) y)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=(g x):Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) b) y)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found x03:(((eq Prop) (g y)) x)
% 202.56/202.91 Instantiate: b:=x:Prop
% 202.56/202.91 Found x03 as proof of (((eq Prop) (g y)) b)
% 202.56/202.91 Found x05:(((eq Prop) (g x)) y)
% 202.56/202.91 Instantiate: b:=(g x):Prop
% 202.56/202.91 Found x05 as proof of (((eq Prop) b) y)
% 202.56/202.91 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 231.95/232.29 Found x03:(((eq Prop) (g y)) x)
% 231.95/232.29 Instantiate: b:=(g y):Prop
% 231.95/232.29 Found x03 as proof of (((eq Prop) b) x)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 231.95/232.29 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found x03:(((eq Prop) (g y)) x)
% 231.95/232.29 Instantiate: b:=(g y):Prop
% 231.95/232.29 Found x03 as proof of (((eq Prop) b) x)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 231.95/232.29 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found x03:(((eq Prop) (g y)) x)
% 231.95/232.29 Instantiate: b:=(g y):Prop
% 231.95/232.29 Found x03 as proof of (((eq Prop) b) x)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 231.95/232.29 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found x030:=(x03 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 231.95/232.29 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found x05:(((eq Prop) (g x)) y)
% 231.95/232.29 Instantiate: b0:=(g x):Prop
% 231.95/232.29 Found x05 as proof of (((eq Prop) b0) y)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 231.95/232.29 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 231.95/232.29 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found x03:(((eq Prop) (g y)) x)
% 231.95/232.29 Instantiate: b0:=x:Prop
% 231.95/232.29 Found x03 as proof of (((eq Prop) (g y)) b0)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 231.95/232.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 231.95/232.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 231.95/232.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 231.95/232.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 231.95/232.29 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 231.95/232.29 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found x03:(((eq Prop) (g y)) x)
% 231.95/232.29 Instantiate: b:=x:Prop
% 231.95/232.29 Found x03 as proof of (((eq Prop) (g y)) b)
% 231.95/232.29 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 231.95/232.29 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 231.95/232.29 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 231.95/232.29 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 231.95/232.29 Found x030:=(x03 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 231.95/232.29 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found (x03 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 231.95/232.29 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 231.95/232.29 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 231.95/232.29 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 231.95/232.29 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 231.95/232.29 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 236.53/236.83 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 236.53/236.83 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 236.53/236.83 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 236.53/236.83 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 236.53/236.83 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 236.53/236.83 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 236.53/236.83 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 236.53/236.83 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 236.53/236.83 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 236.53/236.83 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 247.51/247.88 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 247.51/247.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 247.51/247.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 247.51/247.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 247.51/247.88 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 247.51/247.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 247.51/247.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 247.51/247.88 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 247.51/247.88 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 247.51/247.88 Found x03:(((eq Prop) (g y)) x)
% 247.51/247.88 Instantiate: b:=(g y):Prop
% 247.51/247.88 Found x03 as proof of (((eq Prop) b) x)
% 247.51/247.88 Found x050:=(x05 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 247.51/247.88 Found (x05 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 247.51/247.88 Found (x05 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 247.51/247.88 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 247.51/247.88 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 247.51/247.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 247.51/247.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 247.51/247.88 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 247.51/247.88 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 247.51/247.88 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 264.79/265.14 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 264.79/265.14 Found x05:(((eq Prop) (g x)) y)
% 264.79/265.14 Instantiate: b:=(g x):Prop
% 264.79/265.14 Found x05 as proof of (((eq Prop) b) y)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 264.79/265.14 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found x010:=(x01 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 264.79/265.14 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 264.79/265.14 Found x010:=(x01 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 264.79/265.14 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 264.79/265.14 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 264.79/265.14 Found x060:(P y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x060 as proof of (P0 b)
% 264.79/265.14 Found x03:(((eq Prop) (g y)) x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x03 as proof of (((eq Prop) (g y)) b)
% 264.79/265.14 Found x03:(((eq Prop) (g y)) x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x03 as proof of (((eq Prop) (g y)) b)
% 264.79/265.14 Found x06:(P y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x06 as proof of (P0 b)
% 264.79/265.14 Found x06:(P y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x06 as proof of (P0 b)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 264.79/265.14 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found x06:(P (g x))
% 264.79/265.14 Instantiate: b:=(g x):Prop
% 264.79/265.14 Found x06 as proof of (P0 b)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 264.79/265.14 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found x1:(P y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x1 as proof of (P0 b)
% 264.79/265.14 Found x03:(((eq Prop) (g y)) x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x03 as proof of (((eq Prop) (g y)) b)
% 264.79/265.14 Found x06:(P (g x))
% 264.79/265.14 Instantiate: b:=(g x):Prop
% 264.79/265.14 Found x06 as proof of (P0 b)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 264.79/265.14 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 264.79/265.14 Found x03:(((eq Prop) (g y)) x)
% 264.79/265.14 Instantiate: b:=(g y):Prop
% 264.79/265.14 Found x03 as proof of (P b)
% 264.79/265.14 Found x05:(((eq Prop) (g x)) y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x05 as proof of (((eq Prop) (g x)) b)
% 264.79/265.14 Found x1:(P y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x1 as proof of (P0 b)
% 264.79/265.14 Found x03:(((eq Prop) (g y)) x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x03 as proof of (((eq Prop) (g y)) b)
% 264.79/265.14 Found x05:(((eq Prop) (g x)) y)
% 264.79/265.14 Instantiate: b:=y:Prop
% 264.79/265.14 Found x05 as proof of (((eq Prop) (g x)) b)
% 264.79/265.14 Found x06:(P x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x06 as proof of (P0 b)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 264.79/265.14 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found x060:(P x)
% 264.79/265.14 Instantiate: b:=x:Prop
% 264.79/265.14 Found x060 as proof of (P0 b)
% 264.79/265.14 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 264.79/265.14 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 264.79/265.14 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.81/269.18 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 268.81/269.18 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.81/269.18 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 268.81/269.18 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found x1:(P (g y))
% 268.81/269.18 Instantiate: b:=(g y):Prop
% 268.81/269.18 Found x1 as proof of (P0 b)
% 268.81/269.18 Found x05:(((eq Prop) (g x)) y)
% 268.81/269.18 Instantiate: b:=y:Prop
% 268.81/269.18 Found x05 as proof of (((eq Prop) (g x)) b)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x05:(((eq Prop) (g x)) y)
% 268.81/269.18 Instantiate: b:=(g x):Prop
% 268.81/269.18 Found x05 as proof of (((eq Prop) b) y)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: b:=x:Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) (g y)) b)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x1:(P (g y))
% 268.81/269.18 Instantiate: a0:=y:Prop
% 268.81/269.18 Found x1 as proof of (P0 (P (g a0)))
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x1:(P (g y))
% 268.81/269.18 Instantiate: a0:=y:Prop
% 268.81/269.18 Found x1 as proof of (P0 a0)
% 268.81/269.18 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 268.81/269.18 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 268.81/269.18 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 268.81/269.18 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: a0:=(g y):Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) a0) x)
% 268.81/269.18 Found x1:(P (g y))
% 268.81/269.18 Instantiate: a0:=y:Prop
% 268.81/269.18 Found x1 as proof of (P0 (g a0))
% 268.81/269.18 Found x06:(P x)
% 268.81/269.18 Instantiate: b:=x:Prop
% 268.81/269.18 Found x06 as proof of (P0 b)
% 268.81/269.18 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 268.81/269.18 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 268.81/269.18 Found x05:(((eq Prop) (g x)) y)
% 268.81/269.18 Instantiate: b:=(g x):Prop
% 268.81/269.18 Found x05 as proof of (((eq Prop) b) y)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: b:=x:Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) (g y)) b)
% 268.81/269.18 Found x05:(((eq Prop) (g x)) y)
% 268.81/269.18 Instantiate: b:=(g x):Prop
% 268.81/269.18 Found x05 as proof of (((eq Prop) b) y)
% 268.81/269.18 Found x03:(((eq Prop) (g y)) x)
% 268.81/269.18 Instantiate: b:=x:Prop
% 268.81/269.18 Found x03 as proof of (((eq Prop) (g y)) b)
% 268.81/269.18 Found x05:(((eq Prop) (g x)) y)
% 268.81/269.18 Instantiate: b:=(g x):Prop
% 268.81/269.18 Found x05 as proof of (((eq Prop) b) y)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: b:=x:Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) (g y)) b)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.56/290.90 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 290.56/290.90 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 290.56/290.90 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 290.56/290.90 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 290.56/290.90 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 290.56/290.90 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found x06:(P (g (g x)))
% 290.56/290.90 Instantiate: b:=(g (g x)):Prop
% 290.56/290.90 Found x06 as proof of (P0 b)
% 290.56/290.90 Found x05:(((eq Prop) (g x)) y)
% 290.56/290.90 Instantiate: b:=y:Prop
% 290.56/290.90 Found x05 as proof of (((eq Prop) (g x)) b)
% 290.56/290.90 Found x1:(P (g y))
% 290.56/290.90 Instantiate: b:=(g y):Prop
% 290.56/290.90 Found x1 as proof of (P0 b)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 290.56/290.90 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 290.56/290.90 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 290.56/290.90 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 290.56/290.90 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 290.56/290.90 Found x06:(P (g (g x)))
% 290.56/290.90 Instantiate: a0:=(g x):Prop
% 290.56/290.90 Found x06 as proof of (P0 a0)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found x06:(P (g (g x)))
% 290.56/290.90 Instantiate: a0:=(g x):Prop
% 290.56/290.90 Found x06 as proof of (P0 (P (g a0)))
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: a0:=(g y):Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) a0) x)
% 290.56/290.90 Found x06:(P (g (g x)))
% 290.56/290.90 Instantiate: a0:=(g x):Prop
% 290.56/290.90 Found x06 as proof of (P0 (g a0))
% 290.56/290.90 Found x05:(((eq Prop) (g x)) y)
% 290.56/290.90 Instantiate: b:=y:Prop
% 290.56/290.90 Found x05 as proof of (((eq Prop) (g x)) b)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 290.56/290.90 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.56/290.90 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 290.56/290.90 Found x03:(((eq Prop) (g y)) x)
% 290.56/290.90 Instantiate: b:=x:Prop
% 290.56/290.90 Found x03 as proof of (((eq Prop) (g y)) b)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 290.56/290.90 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 290.56/290.90 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 290.56/290.90 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 290.56/290.90 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 290.56/290.90 Found x010:=(x01 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 290.56/290.90 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 290.56/290.90 Found (x01 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 290.56/290.90 Found x1:(P (g y))
% 290.56/290.90 Instantiate: a0:=y:Prop
% 290.56/290.90 Found x1 as proof of (P0 a0)
% 290.56/290.90 Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% 290.56/290.90 Found (eq_ref0 a0) as proof of (((eq Prop) a0) (g y))
% 290.56/290.90 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (g y))
% 290.56/290.90 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (g y))
% 290.56/290.90 Found ((eq_ref Prop) a0) as proof of (((eq Prop) a0) (g y))
% 290.56/290.90 Found x1:(P (g y))
% 290.56/290.90 Instantiate: a0:=y:Prop
% 290.56/290.90 Found x1 as proof of (P0 (P (g a0)))
% 290.56/290.90 Found eq_ref00:=(eq_ref0 a0):(((eq Prop) a0) a0)
% 290.56/290.90 Found (eq_ref0 a0) as proof of ((
%------------------------------------------------------------------------------