TSTP Solution File: SYO041^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO041^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 294.10s 294.44s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SYO041^1 : TPTP v7.5.0. Released v4.0.0.
% 0.10/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n010.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 07:24:22 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'
% 0.13/0.34 Python 2.7.5
% 13.87/14.10 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 13.87/14.10 FOF formula (<kernel.Constant object at 0x1ab5c68>, <kernel.Sort object at 0x2b0b12af2638>) of role type named a
% 13.87/14.10 Using role type
% 13.87/14.10 Declaring a:Prop
% 13.87/14.10 FOF formula (<kernel.Constant object at 0x1ab5ab8>, <kernel.DependentProduct object at 0x1ab5c20>) of role type named f
% 13.87/14.10 Using role type
% 13.87/14.10 Declaring f:(Prop->Prop)
% 13.87/14.10 FOF formula (<kernel.Constant object at 0x1ab5638>, <kernel.DependentProduct object at 0x1ab5d88>) of role type named g
% 13.87/14.10 Using role type
% 13.87/14.10 Declaring g:(Prop->Prop)
% 13.87/14.10 FOF formula (<kernel.Constant object at 0x1ab5c20>, <kernel.Sort object at 0x2b0b12af2638>) of role type named x
% 13.87/14.10 Using role type
% 13.87/14.10 Declaring x:Prop
% 13.87/14.10 FOF formula (<kernel.Constant object at 0x1ab56c8>, <kernel.Sort object at 0x2b0b12af2638>) of role type named y
% 13.87/14.10 Using role type
% 13.87/14.10 Declaring y:Prop
% 13.87/14.10 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)))) of role axiom named 3
% 13.87/14.10 A new axiom: ((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))))
% 13.87/14.10 We need to prove []
% 13.87/14.10 Parameter a:Prop.
% 13.87/14.10 Parameter f:(Prop->Prop).
% 13.87/14.10 Parameter g:(Prop->Prop).
% 13.87/14.10 Parameter x:Prop.
% 13.87/14.10 Parameter y:Prop.
% 13.87/14.10 Axiom 3:((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)))).
% 13.87/14.10 There are no conjectures!
% 13.87/14.10 Adding conjecture False, to look for Unsatisfiability
% 13.87/14.10 Trying to prove False
% 13.87/14.10 Found x04:(((eq Prop) (g x)) y)
% 13.87/14.10 Instantiate: b:=(g x):Prop
% 13.87/14.10 Found x04 as proof of (((eq Prop) b) y)
% 13.87/14.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 13.87/14.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 13.87/14.10 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found x04:(((eq Prop) (g x)) y)
% 13.87/14.10 Instantiate: b:=(g x):Prop
% 13.87/14.10 Found x04 as proof of (((eq Prop) b) y)
% 13.87/14.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 13.87/14.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found x02:(((eq Prop) (g y)) x)
% 13.87/14.10 Instantiate: b:=x:Prop
% 13.87/14.10 Found x02 as proof of (((eq Prop) (g y)) b)
% 13.87/14.10 Found x04:(((eq Prop) (g x)) y)
% 13.87/14.10 Instantiate: b:=(g x):Prop
% 13.87/14.10 Found x04 as proof of (((eq Prop) b) y)
% 13.87/14.10 Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 13.87/14.10 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found x020:=(x02 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 13.87/14.10 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found x020:=(x02 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 13.87/14.10 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 13.87/14.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 13.87/14.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 13.87/14.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 13.87/14.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 13.87/14.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 13.87/14.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 13.87/14.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 13.87/14.10 Found x02:(((eq Prop) (g y)) x)
% 13.87/14.10 Instantiate: b:=x:Prop
% 13.87/14.10 Found x02 as proof of (((eq Prop) (g y)) b)
% 13.87/14.10 Found x04:(((eq Prop) (g x)) y)
% 13.87/14.10 Instantiate: b:=(g x):Prop
% 13.87/14.10 Found x04 as proof of (((eq Prop) b) y)
% 13.87/14.10 Found x02:(((eq Prop) (g y)) x)
% 13.87/14.10 Instantiate: b:=x:Prop
% 13.87/14.10 Found x02 as proof of (((eq Prop) (g y)) b)
% 13.87/14.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 13.87/14.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 13.87/14.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found x02:(((eq Prop) (g y)) x)
% 31.66/31.89 Instantiate: b:=(g y):Prop
% 31.66/31.89 Found x02 as proof of (((eq Prop) b) x)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 31.66/31.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found x020:=(x02 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 31.66/31.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 31.66/31.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 31.66/31.89 Found x020:=(x02 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 31.66/31.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 31.66/31.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.66/31.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 31.66/31.89 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 31.66/31.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 31.66/31.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 31.66/31.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 31.66/31.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 31.66/31.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 31.66/31.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 31.66/31.89 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 31.66/31.89 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.66/31.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found x02:(((eq Prop) (g y)) x)
% 31.66/31.89 Instantiate: b:=x:Prop
% 31.66/31.89 Found x02 as proof of (((eq Prop) (g y)) b)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.66/31.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 31.66/31.89 Found x02:(((eq Prop) (g y)) x)
% 31.66/31.89 Instantiate: b:=(g y):Prop
% 31.66/31.89 Found x02 as proof of (((eq Prop) b) x)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 31.66/31.89 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 31.66/31.89 Found x04:(((eq Prop) (g x)) y)
% 31.66/31.89 Instantiate: b:=y:Prop
% 31.66/31.89 Found x04 as proof of (((eq Prop) (g x)) b)
% 31.66/31.89 Found x02:(((eq Prop) (g y)) x)
% 31.66/31.89 Instantiate: b:=(g y):Prop
% 31.66/31.89 Found x02 as proof of (((eq Prop) b) x)
% 31.66/31.89 Found x02:(((eq Prop) (g y)) x)
% 31.66/31.89 Instantiate: b:=(g y):Prop
% 31.66/31.89 Found x02 as proof of (((eq Prop) b) x)
% 31.66/31.89 Found x04:(((eq Prop) (g x)) y)
% 31.66/31.89 Instantiate: b:=y:Prop
% 31.66/31.89 Found x04 as proof of (((eq Prop) (g x)) b)
% 31.66/31.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 31.66/31.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 31.66/31.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 31.66/31.89 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 31.66/31.89 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 31.66/31.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 31.66/31.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 31.66/31.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 51.45/51.67 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 51.45/51.67 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.45/51.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.45/51.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 51.45/51.67 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 51.45/51.67 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 51.45/51.67 Found x02:(((eq Prop) (g y)) x)
% 51.45/51.67 Instantiate: b:=(g y):Prop
% 51.45/51.67 Found x02 as proof of (((eq Prop) b) x)
% 51.45/51.67 Found x04:(((eq Prop) (g x)) y)
% 51.45/51.67 Instantiate: b:=y:Prop
% 51.45/51.67 Found x04 as proof of (((eq Prop) (g x)) b)
% 51.45/51.67 Found x02:(((eq Prop) (g y)) x)
% 51.45/51.67 Instantiate: b:=(g y):Prop
% 51.45/51.67 Found x02 as proof of (((eq Prop) b) x)
% 51.45/51.67 Found x04:(((eq Prop) (g x)) y)
% 51.45/51.67 Instantiate: b:=y:Prop
% 51.45/51.67 Found x04 as proof of (((eq Prop) (g x)) b)
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 51.45/51.67 Found x04:(((eq Prop) (g x)) y)
% 51.45/51.67 Instantiate: b:=y:Prop
% 51.45/51.67 Found x04 as proof of (((eq Prop) (g x)) b)
% 51.45/51.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.45/51.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found x04:(((eq Prop) (g x)) y)
% 51.45/51.67 Instantiate: b:=y:Prop
% 51.45/51.67 Found x04 as proof of (((eq Prop) (g x)) b)
% 51.45/51.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 51.45/51.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 51.45/51.67 Found x04:(((eq Prop) (g x)) y)
% 51.45/51.67 Instantiate: b:=y:Prop
% 51.45/51.67 Found x04 as proof of (((eq Prop) (g x)) b)
% 51.45/51.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 72.83/73.01 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 72.83/73.01 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 72.83/73.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 72.83/73.01 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 72.83/73.01 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 72.83/73.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 72.83/73.01 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 72.83/73.01 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 72.83/73.01 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 72.83/73.01 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 72.83/73.01 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 101.61/101.82 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=y:Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) (g x)) b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.61/101.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=y:Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) (g x)) b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.61/101.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=y:Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) (g x)) b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.61/101.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g x)))
% 101.61/101.82 Found x02:(((eq Prop) (g y)) x)
% 101.61/101.82 Instantiate: b:=(g y):Prop
% 101.61/101.82 Found x02 as proof of (((eq Prop) b) x)
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=y:Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) (g x)) b)
% 101.61/101.82 Found x02:(((eq Prop) (g y)) x)
% 101.61/101.82 Instantiate: b:=x:Prop
% 101.61/101.82 Found x02 as proof of (((eq Prop) (g y)) b)
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=(g x):Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) b) y)
% 101.61/101.82 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.61/101.82 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 101.61/101.82 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 101.61/101.82 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 101.61/101.82 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 101.61/101.82 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 101.61/101.82 Found x05:(P x)
% 101.61/101.82 Instantiate: b:=x:Prop
% 101.61/101.82 Found x05 as proof of (P0 b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 101.61/101.82 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 101.61/101.82 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 101.61/101.82 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 101.61/101.82 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 101.61/101.82 Found x04:(((eq Prop) (g x)) y)
% 101.61/101.82 Instantiate: b:=(g x):Prop
% 101.61/101.82 Found x04 as proof of (((eq Prop) b) y)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 101.61/101.82 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 101.61/101.82 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.61/101.82 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.61/101.82 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 101.61/101.82 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 101.61/101.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.61/101.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 101.61/101.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 101.61/101.82 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 114.47/114.76 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 114.47/114.76 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 114.47/114.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.47/114.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 114.47/114.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.47/114.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 114.47/114.76 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 114.47/114.76 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 114.47/114.76 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 114.47/114.76 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 114.47/114.76 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 114.47/114.76 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 114.47/114.76 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 114.47/114.76 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 114.47/114.76 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 114.47/114.76 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 114.47/114.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 114.47/114.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 114.47/114.76 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 114.47/114.76 Found x02:(((eq Prop) (g y)) x)
% 114.47/114.76 Instantiate: b:=(g y):Prop
% 114.47/114.76 Found x02 as proof of (((eq Prop) b) x)
% 114.47/114.76 Found x04:(((eq Prop) (g x)) y)
% 114.47/114.76 Instantiate: b:=y:Prop
% 114.47/114.76 Found x04 as proof of (((eq Prop) (g x)) b)
% 114.47/114.76 Found x04:(((eq Prop) (g x)) y)
% 114.47/114.76 Instantiate: b:=y:Prop
% 114.47/114.76 Found x04 as proof of (((eq Prop) (g x)) b)
% 114.47/114.76 Found x02:(((eq Prop) (g y)) x)
% 114.47/114.76 Instantiate: b:=(g y):Prop
% 114.47/114.76 Found x02 as proof of (((eq Prop) b) x)
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found x04:(((eq Prop) (g x)) y)
% 114.47/114.76 Instantiate: b:=(g x):Prop
% 114.47/114.76 Found x04 as proof of (((eq Prop) b) y)
% 114.47/114.76 Found x02:(((eq Prop) (g y)) x)
% 114.47/114.76 Instantiate: b:=x:Prop
% 114.47/114.76 Found x02 as proof of (((eq Prop) (g y)) b)
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 114.47/114.76 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 139.45/139.68 Found x04:(((eq Prop) (g x)) y)
% 139.45/139.68 Instantiate: b:=(g x):Prop
% 139.45/139.68 Found x04 as proof of (((eq Prop) b) y)
% 139.45/139.68 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 139.45/139.68 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 139.45/139.68 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 139.45/139.68 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.45/139.68 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.45/139.68 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 139.45/139.68 Found x02:(((eq Prop) (g y)) x)
% 139.45/139.68 Instantiate: b:=x:Prop
% 139.45/139.68 Found x02 as proof of (((eq Prop) (g y)) b)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.45/139.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found x02:(((eq Prop) (g y)) x)
% 139.45/139.68 Instantiate: b:=x:Prop
% 139.45/139.68 Found x02 as proof of (((eq Prop) (g y)) b)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.45/139.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found x02:(((eq Prop) (g y)) x)
% 139.45/139.68 Instantiate: b:=x:Prop
% 139.45/139.68 Found x02 as proof of (((eq Prop) (g y)) b)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 139.45/139.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 139.45/139.68 Found x05:(P x)
% 139.45/139.68 Instantiate: b:=x:Prop
% 139.45/139.68 Found x05 as proof of (P0 b)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 139.45/139.68 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found x02:(((eq Prop) (g y)) x)
% 139.45/139.68 Instantiate: b:=(g y):Prop
% 139.45/139.68 Found x02 as proof of (P b)
% 139.45/139.68 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 139.45/139.68 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 139.45/139.68 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=(g x):Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) b) y)
% 154.49/154.79 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.49/154.79 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=y:Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) (g x)) b)
% 154.49/154.79 Found x05:(P x)
% 154.49/154.79 Instantiate: b:=x:Prop
% 154.49/154.79 Found x05 as proof of (P0 b)
% 154.49/154.79 Found x050:(P x)
% 154.49/154.79 Instantiate: b:=x:Prop
% 154.49/154.79 Found x050 as proof of (P0 b)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=y:Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) (g x)) b)
% 154.49/154.79 Found x1:(P (g y))
% 154.49/154.79 Instantiate: b:=(g y):Prop
% 154.49/154.79 Found x1 as proof of (P0 b)
% 154.49/154.79 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 154.49/154.79 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=y:Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) (g x)) b)
% 154.49/154.79 Found x05:(P x)
% 154.49/154.79 Instantiate: b:=x:Prop
% 154.49/154.79 Found x05 as proof of (P0 b)
% 154.49/154.79 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 154.49/154.79 Found x02:(((eq Prop) (g y)) x)
% 154.49/154.79 Instantiate: b:=x:Prop
% 154.49/154.79 Found x02 as proof of (((eq Prop) (g y)) b)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=(g x):Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) b) y)
% 154.49/154.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.49/154.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 154.49/154.79 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 154.49/154.79 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 154.49/154.79 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 154.49/154.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.49/154.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 154.49/154.79 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 154.49/154.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 154.49/154.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.49/154.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 154.49/154.79 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 154.49/154.79 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 154.49/154.79 Found x02:(((eq Prop) (g y)) x)
% 154.49/154.79 Instantiate: b:=(g y):Prop
% 154.49/154.79 Found x02 as proof of (((eq Prop) b) x)
% 154.49/154.79 Found x04:(((eq Prop) (g x)) y)
% 154.49/154.79 Instantiate: b:=y:Prop
% 154.49/154.79 Found x04 as proof of (((eq Prop) (g x)) b)
% 154.49/154.79 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 154.49/154.79 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 154.49/154.79 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (P (g x)))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g y))))):((P (g (g y)))->(P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g (g y))))) as proof of (P0 (P (g (g y))))
% 180.64/180.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g x)))):((P (g x))->(P (g x)))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found (x00 (fun (x1:Prop)=> (P (g x)))) as proof of (P0 (g x))
% 180.64/180.89 Found x04:(((eq Prop) (g x)) y)
% 180.64/180.89 Instantiate: b:=(g x):Prop
% 180.64/180.89 Found x04 as proof of (((eq Prop) b) y)
% 180.64/180.89 Found x020:=(x02 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 180.64/180.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 180.64/180.89 Found (x02 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 180.64/180.89 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 180.64/180.89 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 180.64/180.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 180.64/180.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 180.64/180.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 180.64/180.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 180.64/180.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 180.64/180.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 180.64/180.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 180.64/180.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 180.64/180.89 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 180.64/180.89 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 180.64/180.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 180.64/180.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 180.64/180.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 180.64/180.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 180.64/180.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 189.65/189.96 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 189.65/189.96 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 189.65/189.96 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 189.65/189.96 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 189.65/189.96 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 189.65/189.96 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 189.65/189.96 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 189.65/189.96 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 189.65/189.96 Found x02:(((eq Prop) (g y)) x)
% 189.65/189.96 Instantiate: b:=x:Prop
% 189.65/189.96 Found x02 as proof of (((eq Prop) (g y)) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found x02:(((eq Prop) (g y)) x)
% 189.65/189.96 Instantiate: b:=x:Prop
% 189.65/189.96 Found x02 as proof of (((eq Prop) (g y)) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 189.65/189.96 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 189.65/189.96 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found x02:(((eq Prop) (g y)) x)
% 189.65/189.96 Instantiate: b:=x:Prop
% 189.65/189.96 Found x02 as proof of (((eq Prop) (g y)) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 189.65/189.96 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 189.65/189.96 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 189.65/189.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 189.65/189.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 189.65/189.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 208.67/208.97 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.67/208.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 208.67/208.97 Found x02:(((eq Prop) (g y)) x)
% 208.67/208.97 Instantiate: b:=(g y):Prop
% 208.67/208.97 Found x02 as proof of (P b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 208.67/208.97 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found x04:(((eq Prop) (g x)) y)
% 208.67/208.97 Instantiate: b:=y:Prop
% 208.67/208.97 Found x04 as proof of (((eq Prop) (g x)) b)
% 208.67/208.97 Found x05:(P x)
% 208.67/208.97 Instantiate: b:=x:Prop
% 208.67/208.97 Found x05 as proof of (P0 b)
% 208.67/208.97 Found x050:(P x)
% 208.67/208.97 Instantiate: b:=x:Prop
% 208.67/208.97 Found x050 as proof of (P0 b)
% 208.67/208.97 Found x04:(((eq Prop) (g x)) y)
% 208.67/208.97 Instantiate: b:=y:Prop
% 208.67/208.97 Found x04 as proof of (((eq Prop) (g x)) b)
% 208.67/208.97 Found x1:(P (g y))
% 208.67/208.97 Instantiate: b:=(g y):Prop
% 208.67/208.97 Found x1 as proof of (P0 b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 208.67/208.97 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found x05:(P x)
% 208.67/208.97 Instantiate: b:=x:Prop
% 208.67/208.97 Found x05 as proof of (P0 b)
% 208.67/208.97 Found x04:(((eq Prop) (g x)) y)
% 208.67/208.97 Instantiate: b:=y:Prop
% 208.67/208.97 Found x04 as proof of (((eq Prop) (g x)) b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 208.67/208.97 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 208.67/208.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.67/208.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.67/208.97 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 208.67/208.97 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 208.67/208.97 Found x05:(P y)
% 208.67/208.97 Instantiate: b:=y:Prop
% 208.67/208.97 Found x05 as proof of (P0 b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 208.67/208.97 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 208.67/208.97 Found x000:=(x00 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 208.67/208.97 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 208.67/208.97 Found (x00 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 208.67/208.97 Found x02:(((eq Prop) (g y)) x)
% 208.67/208.97 Instantiate: b:=x:Prop
% 208.67/208.97 Found x02 as proof of (((eq Prop) (g y)) b)
% 208.67/208.97 Found x04:(((eq Prop) (g x)) y)
% 208.67/208.97 Instantiate: b:=(g x):Prop
% 208.67/208.97 Found x04 as proof of (((eq Prop) b) y)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 208.67/208.97 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 208.67/208.97 Found (eq_ref0 b) as proof of (((eq Prop) b) (g y))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 208.67/208.97 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g y))
% 208.67/208.97 Found x02:(((eq Prop) (g y)) x)
% 208.67/208.97 Instantiate: b:=(g y):Prop
% 208.67/208.97 Found x02 as proof of (P b)
% 208.67/208.97 Found x04:(((eq Prop) (g x)) y)
% 208.67/208.97 Instantiate: b:=y:Prop
% 208.67/208.97 Found x04 as proof of (((eq Prop) (g x)) b)
% 208.67/208.97 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 208.67/208.97 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 208.67/208.97 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 208.67/208.97 Found x05:(P x)
% 208.67/208.97 Instantiate: b:=x:Prop
% 208.67/208.97 Found x05 as proof of (P0 b)
% 208.67/208.97 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 232.15/232.48 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found x050:(P x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x050 as proof of (P0 b)
% 232.15/232.48 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 232.15/232.48 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=y:Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) (g x)) b)
% 232.15/232.48 Found x1:(P (g y))
% 232.15/232.48 Instantiate: b:=(g y):Prop
% 232.15/232.48 Found x1 as proof of (P0 b)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x05:(P x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x05 as proof of (P0 b)
% 232.15/232.48 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 232.15/232.48 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: a0:=(g y):Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) a0) x)
% 232.15/232.48 Found x1:(P (g y))
% 232.15/232.48 Instantiate: b:=(g y):Prop
% 232.15/232.48 Found x1 as proof of (P0 b)
% 232.15/232.48 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 232.15/232.48 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 232.15/232.48 Found x05:(P (g (g x)))
% 232.15/232.48 Instantiate: b:=(g (g x)):Prop
% 232.15/232.48 Found x05 as proof of (P0 b)
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=y:Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) (g x)) b)
% 232.15/232.48 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 232.15/232.48 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 232.15/232.48 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) (g y)) b)
% 232.15/232.48 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 232.15/232.48 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 232.15/232.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 232.15/232.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 232.15/232.48 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=(g x):Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) b) y)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) (g y)) b)
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=(g x):Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) b) y)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) (g y)) b)
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=(g x):Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) b) y)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) (g y)) b)
% 232.15/232.48 Found x04:(((eq Prop) (g x)) y)
% 232.15/232.48 Instantiate: b:=(g x):Prop
% 232.15/232.48 Found x04 as proof of (((eq Prop) b) y)
% 232.15/232.48 Found x02:(((eq Prop) (g y)) x)
% 232.15/232.48 Instantiate: b:=x:Prop
% 232.15/232.48 Found x02 as proof of (((eq Prop) (g y)) b)
% 253.35/253.66 Found x02:(((eq Prop) (g y)) x)
% 253.35/253.66 Instantiate: b:=(g y):Prop
% 253.35/253.66 Found x02 as proof of (((eq Prop) b) x)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 253.35/253.66 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found x02:(((eq Prop) (g y)) x)
% 253.35/253.66 Instantiate: b:=(g y):Prop
% 253.35/253.66 Found x02 as proof of (((eq Prop) b) x)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 253.35/253.66 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found x02:(((eq Prop) (g y)) x)
% 253.35/253.66 Instantiate: b:=(g y):Prop
% 253.35/253.66 Found x02 as proof of (((eq Prop) b) x)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 253.35/253.66 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.35/253.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 253.35/253.66 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.35/253.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 253.35/253.66 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.35/253.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 253.35/253.66 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 253.35/253.66 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 253.35/253.66 Found (eq_ref00 P) as proof of (P0 x)
% 253.35/253.66 Found ((eq_ref0 x) P) as proof of (P0 x)
% 253.35/253.66 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 253.35/253.66 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 253.35/253.66 Found eq_ref000:=(eq_ref00 P):((P x)->(P x))
% 253.35/253.66 Found (eq_ref00 P) as proof of (P0 x)
% 253.35/253.66 Found ((eq_ref0 x) P) as proof of (P0 x)
% 253.35/253.66 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 253.35/253.66 Found (((eq_ref Prop) x) P) as proof of (P0 x)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 253.35/253.66 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 253.35/253.66 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 253.35/253.66 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 253.35/253.66 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 253.35/253.66 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 266.41/266.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found x040:=(x04 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 266.41/266.71 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found (x04 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 266.41/266.71 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 266.41/266.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 266.41/266.71 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 266.41/266.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 266.41/266.71 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 266.41/266.71 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found x04:(((eq Prop) (g x)) y)
% 266.41/266.71 Instantiate: b0:=(g x):Prop
% 266.41/266.71 Found x04 as proof of (((eq Prop) b0) y)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 266.41/266.71 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 266.41/266.71 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 266.41/266.71 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 266.41/266.71 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found x02:(((eq Prop) (g y)) x)
% 266.41/266.71 Instantiate: b0:=x:Prop
% 266.41/266.71 Found x02 as proof of (((eq Prop) (g y)) b0)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.41/266.71 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 266.41/266.71 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 266.41/266.71 Found x02:(((eq Prop) (g y)) x)
% 266.41/266.71 Instantiate: b:=x:Prop
% 266.41/266.71 Found x02 as proof of (((eq Prop) (g y)) b)
% 266.41/266.71 Found 3__proj20:=(3__proj2 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 266.41/266.71 Found (3__proj2 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 266.41/266.71 Found (3__proj2 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 266.41/266.71 Found (eq_ref0 b) as proof of (((eq Prop) b) (g (g y)))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 266.41/266.71 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g (g y)))
% 266.41/266.71 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 266.41/266.71 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 266.41/266.71 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 266.41/266.71 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 283.51/283.89 Found x05:(P y)
% 283.51/283.89 Instantiate: b:=y:Prop
% 283.51/283.89 Found x05 as proof of (P0 b)
% 283.51/283.89 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 283.51/283.89 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 283.51/283.89 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found x02:(((eq Prop) (g y)) x)
% 283.51/283.89 Instantiate: b:=(g y):Prop
% 283.51/283.89 Found x02 as proof of (P b)
% 283.51/283.89 Found x04:(((eq Prop) (g x)) y)
% 283.51/283.89 Instantiate: b:=y:Prop
% 283.51/283.89 Found x04 as proof of (((eq Prop) (g x)) b)
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found eq_ref00:=(eq_ref0 (g (g x))):(((eq Prop) (g (g x))) (g (g x)))
% 283.51/283.89 Found (eq_ref0 (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g x))) as proof of (((eq Prop) (g (g x))) b)
% 283.51/283.89 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 283.51/283.89 Found (eq_ref0 b) as proof of (((eq Prop) b) (g x))
% 283.51/283.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 283.51/283.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 283.51/283.89 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (g x))
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 283.51/283.89 Found x05:(P x)
% 283.51/283.89 Instantiate: b:=x:Prop
% 283.51/283.89 Found x05 as proof of (P0 b)
% 283.51/283.89 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 283.51/283.89 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 283.51/283.89 Found x050:(P x)
% 283.51/283.89 Instantiate: b:=x:Prop
% 283.51/283.89 Found x050 as proof of (P0 b)
% 283.51/283.89 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 283.51/283.89 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 283.51/283.89 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 283.51/283.89 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 283.51/283.89 Found x04:(((eq Prop) (g x)) y)
% 283.51/283.89 Instantiate: b:=y:Prop
% 294.10/294.44 Found x04 as proof of (((eq Prop) (g x)) b)
% 294.10/294.44 Found x1:(P (g y))
% 294.10/294.44 Instantiate: b:=(g y):Prop
% 294.10/294.44 Found x1 as proof of (P0 b)
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g (g x))))):((P (g (g x)))->(P (g (g x))))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g (g x))))) as proof of (P0 (P (g (g x))))
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (g y))
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P (g y)))):((P (g y))->(P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P (g y)))) as proof of (P0 (P (g y)))
% 294.10/294.44 Found x05:(P x)
% 294.10/294.44 Instantiate: b:=x:Prop
% 294.10/294.44 Found x05 as proof of (P0 b)
% 294.10/294.44 Found eq_ref00:=(eq_ref0 (g (g y))):(((eq Prop) (g (g y))) (g (g y)))
% 294.10/294.44 Found (eq_ref0 (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 294.10/294.44 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 294.10/294.44 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 294.10/294.44 Found ((eq_ref Prop) (g (g y))) as proof of (((eq Prop) (g (g y))) b)
% 294.10/294.44 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 294.10/294.44 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 294.10/294.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 294.10/294.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 294.10/294.44 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 294.10/294.44 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 294.10/294.44 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 294.10/294.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 294.10/294.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 294.10/294.44 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 294.10/294.44 Found x000:=(x00 (fun (x1:Prop)=> (P x))):((P x)->(P x))
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 294.10/294.44 Found (x00 (fun (x1:Prop)=> (P x))) as proof of (P0 x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: a0:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) a0) x)
% 294.10/294.44 Found x02:(((eq Prop) (g y)) x)
% 294.10/294.44 Instantiate: b:=(g y):Prop
% 294.10/294.44 Found x02 as proof of (((eq Prop) b) x)
% 294.10/294.44 Found x040:=(x04 (fun (x1:Prop)=> (P y))):((P y)->(P y))
% 294.10/294.44 Found (x04 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 294.10/294.44 Found (x04 (fun (x1:Prop)=> (P y))) as proof of (P0 y)
% 294.10/294.44 Found eq_ref00:=(eq_ref0 y):(((eq Prop) y) y)
% 294.10/294.44 Found (eq_ref0 y) as proof of (((eq Prop) y) b)
% 294.10/294.44 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 294.10/294.44 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 294.10/294.44 Found ((eq_ref Prop) y) as proof of (((eq Prop) y) b)
% 294.10/294.44 Found x04:(((eq Prop) (g x)) y)
% 294.10/294.44 Instantiate: b:=y:Prop
% 294.10/294.44 Found x04 as proof of (((eq Prop) (g x)) b)
% 294.10/294.44 Found x05:(P (g (g x)))
% 294.10/294.44 Instantiate: b:=(g (g x)):Prop
% 294.10/294.44 Found x05
%------------------------------------------------------------------------------