TSTP Solution File: SYO500^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO500^1 : TPTP v7.5.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:51:57 EDT 2022
% Result : Timeout 300.03s 300.71s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYO500^1 : TPTP v7.5.0. Released v4.0.0.
% 0.03/0.12 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.33 % Computer : n018.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 : Sun Mar 13 12:24:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.20/0.34 Python 2.7.5
% 9.41/9.58 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 9.41/9.58 FOF formula (<kernel.Constant object at 0x2abdccca5cb0>, <kernel.DependentProduct object at 0x15e3fc8>) of role type named f
% 9.41/9.58 Using role type
% 9.41/9.58 Declaring f:(Prop->Prop)
% 9.41/9.58 FOF formula (<kernel.Constant object at 0x2abdccca5a70>, <kernel.Sort object at 0x2abdccc9e638>) of role type named x
% 9.41/9.58 Using role type
% 9.41/9.58 Declaring x:Prop
% 9.41/9.58 FOF formula (((eq Prop) (f (f (f x)))) (f x)) of role conjecture named con
% 9.41/9.58 Conjecture to prove = (((eq Prop) (f (f (f x)))) (f x)):Prop
% 9.41/9.58 We need to prove ['(((eq Prop) (f (f (f x)))) (f x))']
% 9.41/9.58 Parameter f:(Prop->Prop).
% 9.41/9.58 Parameter x:Prop.
% 9.41/9.58 Trying to prove (((eq Prop) (f (f (f x)))) (f x))
% 9.41/9.58 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 9.41/9.58 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 9.41/9.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 9.41/9.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 9.41/9.58 Found x01:(P (f (f (f x))))
% 9.41/9.58 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 9.41/9.58 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 9.41/9.58 Found x01:(P (f (f (f x))))
% 9.41/9.58 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 9.41/9.58 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 9.41/9.58 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 9.41/9.58 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 9.41/9.58 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 9.41/9.58 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 9.41/9.58 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 9.41/9.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 9.41/9.58 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 9.41/9.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 9.41/9.58 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 9.41/9.58 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 9.41/9.58 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 9.41/9.58 Found x01:(P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 9.41/9.58 Found x01:(P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 9.41/9.58 Found x01:(P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 9.41/9.58 Found x01:(P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 9.41/9.58 Found x01:(P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 9.41/9.58 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 9.41/9.58 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 9.41/9.58 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 9.41/9.58 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 9.41/9.58 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 9.41/9.58 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 9.41/9.58 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 9.41/9.58 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 18.76/18.91 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found x0:(P0 (f x))
% 18.76/18.91 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 18.76/18.91 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 18.76/18.91 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.76/18.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 18.76/18.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.76/18.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 18.76/18.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found x01:(P x)
% 18.76/18.91 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 18.76/18.91 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.76/18.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 18.76/18.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.76/18.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 18.76/18.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 18.76/18.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 18.76/18.91 Found x01:(P x)
% 18.76/18.91 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 18.76/18.91 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 18.76/18.91 Found x0:(P (f (f (f x))))
% 18.76/18.91 Instantiate: b:=(f (f (f x))):Prop
% 18.76/18.91 Found x0 as proof of (P0 b)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 18.76/18.91 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 18.76/18.91 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.76/18.91 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.76/18.91 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 18.76/18.91 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 18.76/18.91 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 18.76/18.91 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 26.23/26.43 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 26.23/26.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 26.23/26.43 Found x0:(P (f (f (f x))))
% 26.23/26.43 Instantiate: a:=(f (f x)):Prop
% 26.23/26.43 Found x0 as proof of (P0 (f a))
% 26.23/26.43 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 26.23/26.43 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found x0:(P (f (f (f x))))
% 26.23/26.43 Instantiate: a:=(f (f x)):Prop
% 26.23/26.43 Found x0 as proof of (P0 (P (f a)))
% 26.23/26.43 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 26.23/26.43 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found x0:(P (f (f (f x))))
% 26.23/26.43 Instantiate: a:=(f (f x)):Prop
% 26.23/26.43 Found x0 as proof of (P0 a)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 26.23/26.43 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 26.23/26.43 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found x0:(P (f x))
% 26.23/26.43 Instantiate: b:=(f x):Prop
% 26.23/26.43 Found x0 as proof of (P0 b)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 26.23/26.43 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 26.23/26.43 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 26.23/26.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 26.23/26.43 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 26.23/26.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 26.23/26.43 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 26.23/26.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 26.23/26.43 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 26.23/26.43 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 26.23/26.43 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 26.23/26.43 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 26.23/26.43 Found x0:(P (f (f x)))
% 26.23/26.43 Instantiate: b:=(f (f x)):Prop
% 26.23/26.43 Found x0 as proof of (P0 b)
% 26.23/26.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 26.23/26.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 34.15/34.33 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 34.15/34.33 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 34.15/34.33 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 34.15/34.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.15/34.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 34.15/34.33 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.15/34.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 34.15/34.33 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found x01:(P b)
% 34.15/34.33 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 34.15/34.33 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 34.15/34.33 Found x0:(P (f x))
% 34.15/34.33 Instantiate: a:=x:Prop
% 34.15/34.33 Found x0 as proof of (P0 (P (f a)))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 34.15/34.33 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found x0:(P (f x))
% 34.15/34.33 Instantiate: a:=x:Prop
% 34.15/34.33 Found x0 as proof of (P0 (f a))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 34.15/34.33 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found x0:(P (f x))
% 34.15/34.33 Instantiate: a:=x:Prop
% 34.15/34.33 Found x0 as proof of (P0 a)
% 34.15/34.33 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 34.15/34.33 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.15/34.33 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 34.15/34.33 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 34.15/34.33 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 34.15/34.33 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 34.15/34.33 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 34.15/34.33 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 34.15/34.33 Found x02:(P (f x))
% 34.15/34.33 Found (fun (x02:(P (f x)))=> x02) as proof of (P (f x))
% 34.15/34.33 Found (fun (x02:(P (f x)))=> x02) as proof of (P0 (f x))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.15/34.33 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 34.15/34.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 34.15/34.33 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 34.15/34.33 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 34.15/34.33 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 34.15/34.33 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.60/37.81 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.60/37.81 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.60/37.81 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.60/37.81 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 37.60/37.81 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 37.60/37.81 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 37.60/37.81 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 37.60/37.81 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 37.60/37.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 37.60/37.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 37.60/37.81 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 37.60/37.81 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 37.60/37.81 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 37.60/37.81 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 37.60/37.81 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 37.60/37.81 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 37.60/37.81 Found x0:(P (f (f x)))
% 46.73/46.96 Instantiate: b:=(f (f x)):Prop
% 46.73/46.96 Found x0 as proof of (P0 b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 46.73/46.96 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found x01:(P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 46.73/46.96 Found x01:(P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 46.73/46.96 Found x01:(P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 46.73/46.96 Found x01:(P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 46.73/46.96 Found x01:(P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 46.73/46.96 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 46.73/46.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 46.73/46.96 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 46.73/46.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 46.73/46.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 46.73/46.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 46.73/46.96 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 46.73/46.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 46.73/46.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 46.73/46.96 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 46.73/46.96 Found x0:(P x)
% 46.73/46.96 Instantiate: b:=x:Prop
% 46.73/46.96 Found x0 as proof of (P0 b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 46.73/46.96 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found x0:(P x)
% 46.73/46.96 Instantiate: b:=x:Prop
% 46.73/46.96 Found x0 as proof of (P0 b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 46.73/46.96 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found x01:(P b)
% 46.73/46.96 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 46.73/46.96 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 46.73/46.96 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 46.73/46.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 46.73/46.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 46.73/46.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 46.73/46.96 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 46.73/46.96 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 46.73/46.96 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 46.73/46.96 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.50/64.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.50/64.74 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 64.50/64.74 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 64.50/64.74 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 64.50/64.74 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 64.50/64.74 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 64.50/64.74 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 64.50/64.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 64.50/64.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 64.50/64.74 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.50/64.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.50/64.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 64.50/64.74 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 64.50/64.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 64.50/64.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 64.50/64.74 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 64.50/64.74 Found x0:(P2 (f x))
% 64.50/64.74 Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f x))
% 64.50/64.74 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f x)))
% 64.50/64.74 Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (P1 x)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.50/64.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.50/64.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.50/64.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.50/64.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.50/64.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.50/64.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.50/64.74 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.50/64.74 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.50/64.74 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.50/64.74 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 69.18/69.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 69.18/69.43 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 69.18/69.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 69.18/69.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 69.18/69.43 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 69.18/69.43 Found x01:(P1 x)
% 69.18/69.43 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 69.18/69.43 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 69.18/69.43 Found x0:(P x)
% 69.18/69.43 Instantiate: b:=x:Prop
% 69.18/69.43 Found x0 as proof of (P0 b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 69.18/69.43 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found x0:(P x)
% 69.18/69.43 Instantiate: b:=x:Prop
% 69.18/69.43 Found x0 as proof of (P0 b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 69.18/69.43 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 69.18/69.43 Found x01:(P (f (f x)))
% 69.18/69.43 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P (f (f x)))
% 69.18/69.43 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P0 (f (f x)))
% 69.18/69.43 Found x01:(P (f (f (f x))))
% 69.18/69.43 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 69.18/69.43 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 69.18/69.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.18/69.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 69.18/69.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 69.18/69.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.18/69.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.18/69.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 69.18/69.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.18/69.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 69.18/69.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 69.18/69.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 69.18/69.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 69.18/69.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 71.09/71.30 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 71.09/71.30 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 71.09/71.30 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 71.09/71.30 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 74.01/74.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 74.01/74.28 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found x01:(P (f (f (f x))))
% 74.01/74.28 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 74.01/74.28 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 74.01/74.28 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 74.01/74.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 74.01/74.28 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 74.01/74.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 74.01/74.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 74.01/74.28 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 74.01/74.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 74.01/74.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 74.01/74.28 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 74.01/74.28 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 74.01/74.28 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 74.01/74.28 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 74.01/74.28 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 74.01/74.28 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P (f x))
% 74.01/74.28 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 74.01/74.28 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 74.01/74.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 74.01/74.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 74.01/74.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 74.01/74.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 74.01/74.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 74.01/74.28 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 74.01/74.28 Found x01:(P (f x))
% 74.01/74.28 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 86.60/86.84 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 86.60/86.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 86.60/86.84 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 86.60/86.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 86.60/86.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 86.60/86.84 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 86.60/86.84 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 86.60/86.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 86.60/86.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 86.60/86.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 86.60/86.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 86.60/86.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 86.60/86.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 86.60/86.84 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 86.60/86.84 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 86.60/86.84 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 86.60/86.84 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 86.60/86.84 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 86.60/86.84 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 86.60/86.84 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 86.60/86.84 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 86.60/86.84 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 86.60/86.84 Found x0:(P0 b)
% 86.60/86.84 Instantiate: b:=x:Prop
% 86.60/86.84 Found (fun (x0:(P0 b))=> x0) as proof of (P0 x)
% 86.60/86.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 x))
% 86.60/86.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 86.60/86.84 Found x0:(P (f (f x)))
% 86.60/86.84 Instantiate: b:=(f (f x)):Prop
% 86.60/86.84 Found x0 as proof of (P0 b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 86.60/86.84 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 86.60/86.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 86.60/86.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 86.60/86.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 86.60/86.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 100.30/100.53 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 100.30/100.53 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 100.30/100.53 Found x02:(P x)
% 100.30/100.53 Found (fun (x02:(P x))=> x02) as proof of (P x)
% 100.30/100.53 Found (fun (x02:(P x))=> x02) as proof of (P0 x)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.30/100.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found x02:(P x)
% 100.30/100.53 Found (fun (x02:(P x))=> x02) as proof of (P x)
% 100.30/100.53 Found (fun (x02:(P x))=> x02) as proof of (P0 x)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.30/100.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.30/100.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.30/100.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found x01:(P0 x)
% 100.30/100.53 Found (fun (x01:(P0 x))=> x01) as proof of (P0 x)
% 100.30/100.53 Found (fun (x01:(P0 x))=> x01) as proof of (P1 x)
% 100.30/100.53 Found x01:(P0 x)
% 100.30/100.53 Found (fun (x01:(P0 x))=> x01) as proof of (P0 x)
% 100.30/100.53 Found (fun (x01:(P0 x))=> x01) as proof of (P1 x)
% 100.30/100.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.30/100.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.30/100.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.30/100.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.30/100.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 107.81/108.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 107.81/108.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 107.81/108.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 107.81/108.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 107.81/108.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 107.81/108.10 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 107.81/108.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 107.81/108.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 107.81/108.10 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 107.81/108.10 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 107.81/108.10 Found x01:(P1 x)
% 107.81/108.10 Found (fun (x01:(P1 x))=> x01) as proof of (P1 x)
% 107.81/108.10 Found (fun (x01:(P1 x))=> x01) as proof of (P2 x)
% 107.81/108.10 Found x01:(P (f (f x)))
% 107.81/108.10 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P (f (f x)))
% 107.81/108.10 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P0 (f (f x)))
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 107.81/108.10 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 107.81/108.10 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 107.81/108.10 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 107.81/108.10 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 107.81/108.10 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 107.81/108.10 Found x0:(P0 (f (f (f (f (f x))))))
% 107.81/108.10 Found x0 as proof of (P1 (f (f x)))
% 107.81/108.10 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 107.81/108.10 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 107.81/108.10 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 107.81/108.10 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 107.81/108.10 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 115.38/115.65 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 115.38/115.65 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 115.38/115.65 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 115.38/115.65 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 115.38/115.65 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f x)))
% 115.38/115.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 115.38/115.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 115.38/115.65 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 115.38/115.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 115.38/115.65 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 115.38/115.65 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found x01:(P0 (f (f (f (f (f x))))))
% 115.38/115.65 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 115.38/115.65 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 115.38/115.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 115.38/115.65 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 115.38/115.65 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 115.38/115.65 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 115.38/115.65 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 115.38/115.65 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 115.38/115.65 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 115.38/115.65 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 115.38/115.65 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 115.38/115.65 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 115.38/115.65 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 115.38/115.65 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 124.99/125.23 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 124.99/125.23 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f x)))
% 124.99/125.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 124.99/125.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 124.99/125.23 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 124.99/125.23 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 124.99/125.23 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 124.99/125.23 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 124.99/125.23 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 124.99/125.23 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 (f (f (f (f (f x)))))):(((eq Prop) (f (f (f (f (f x)))))) (f (f (f (f (f x))))))
% 124.99/125.23 Found (eq_ref0 (f (f (f (f (f x)))))) as proof of (((eq Prop) (f (f (f (f (f x)))))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f (f (f (f x)))))) as proof of (((eq Prop) (f (f (f (f (f x)))))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f (f (f (f x)))))) as proof of (((eq Prop) (f (f (f (f (f x)))))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f (f (f (f x)))))) as proof of (((eq Prop) (f (f (f (f (f x)))))) b)
% 124.99/125.23 Found x0:(P0 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0 as proof of (P1 (f (f (f (f x)))))
% 124.99/125.23 Found x0:(P0 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0 as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 124.99/125.23 Found x0:(P0 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0 as proof of (P1 (f (f (f x))))
% 124.99/125.23 Found x0:(P0 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0 as proof of (P1 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0:(P0 (f (f (f (f (f x))))))
% 124.99/125.23 Found x0 as proof of (P1 (f (f x)))
% 124.99/125.23 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 124.99/125.23 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 124.99/125.23 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 124.99/125.23 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 124.99/125.23 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 124.99/125.23 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 124.99/125.23 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found x0:(P0 b)
% 124.99/125.23 Instantiate: b:=x:Prop
% 124.99/125.23 Found (fun (x0:(P0 b))=> x0) as proof of (P0 x)
% 124.99/125.23 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 x))
% 124.99/125.23 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 124.99/125.23 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 124.99/125.23 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 124.99/125.23 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 124.99/125.23 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 124.99/125.23 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 124.99/125.23 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.63/129.92 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 129.63/129.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.63/129.92 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 129.63/129.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.63/129.92 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 129.63/129.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 129.63/129.92 Found x0:(P (f (f x)))
% 129.63/129.92 Instantiate: b:=(f (f x)):Prop
% 129.63/129.92 Found x0 as proof of (P0 b)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 129.63/129.92 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found x01:(P0 (f (f (f (f (f x))))))
% 129.63/129.92 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 129.63/129.92 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 129.63/129.92 Found x01:(P x)
% 129.63/129.92 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 129.63/129.92 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 129.63/129.92 Found x01:(P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 129.63/129.92 Found x01:(P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 129.63/129.92 Found x02:(P x)
% 129.63/129.92 Found (fun (x02:(P x))=> x02) as proof of (P x)
% 129.63/129.92 Found (fun (x02:(P x))=> x02) as proof of (P0 x)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.63/129.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 129.63/129.92 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 129.63/129.92 Found x01:(P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 129.63/129.92 Found x01:(P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 129.63/129.92 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 129.63/129.92 Found x02:(P x)
% 129.63/129.92 Found (fun (x02:(P x))=> x02) as proof of (P x)
% 129.63/129.92 Found (fun (x02:(P x))=> x02) as proof of (P0 x)
% 129.63/129.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 129.63/129.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 129.63/129.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 137.05/137.35 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 137.05/137.35 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 137.05/137.35 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 137.05/137.35 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 137.05/137.35 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 137.05/137.35 Found x01:(P0 (f x))
% 137.05/137.35 Found (fun (x01:(P0 (f x)))=> x01) as proof of (P0 (f x))
% 137.05/137.35 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f x)))=> x01) as proof of ((P0 (f x))->(P0 (f x)))
% 137.05/137.35 Found (fun (P0:(Prop->Prop)) (x01:(P0 (f x)))=> x01) as proof of (P (forall (P0:(Prop->Prop)), ((P0 (f x))->(P0 (f x)))))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 137.05/137.35 Found x01:(P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 137.05/137.35 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 137.05/137.35 Found x01:(P x)
% 137.05/137.35 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 137.05/137.35 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 137.05/137.35 Found x01:(P x)
% 137.05/137.35 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 137.05/137.35 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.05/137.35 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 137.05/137.35 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.05/137.35 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 137.05/137.35 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.05/137.35 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 137.05/137.35 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.05/137.35 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 137.05/137.35 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 137.05/137.35 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 137.05/137.35 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 144.26/144.57 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.26/144.57 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 144.26/144.57 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.26/144.57 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 144.26/144.57 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.26/144.57 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 144.26/144.57 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 144.26/144.57 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 144.26/144.57 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 144.26/144.57 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 144.26/144.57 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 144.26/144.57 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 144.26/144.57 Found x01:(P (f (f (f x))))
% 144.26/144.57 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 144.26/144.57 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 144.26/144.57 Found x01:(P0 (f (f (f (f (f x))))))
% 144.26/144.57 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 144.26/144.57 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 144.26/144.57 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 144.26/144.57 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 144.26/144.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 144.26/144.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 144.26/144.57 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 144.26/144.57 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 144.26/144.57 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 144.26/144.57 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 144.26/144.57 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 144.26/144.57 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 171.51/171.85 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 171.51/171.85 Found (eq_ref0 x) as proof of (((eq Prop) x) b0)
% 171.51/171.85 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 171.51/171.85 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 171.51/171.85 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b0)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 171.51/171.85 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 171.51/171.85 Found x0:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found x0 as proof of (P1 (f (f (f (f x)))))
% 171.51/171.85 Found x0:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found x0 as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 171.51/171.85 Found x0:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found x0 as proof of (P1 (f (f (f x))))
% 171.51/171.85 Found x0:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found x0 as proof of (P1 (f (f (f (f (f x))))))
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.51/171.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 171.51/171.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found x01:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 171.51/171.85 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f x)))
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 171.51/171.85 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f x)))
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.51/171.85 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.51/171.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 171.51/171.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.51/171.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 171.51/171.85 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 171.51/171.85 Found x01:(P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 171.51/171.85 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 171.51/171.85 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 171.51/171.85 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 171.51/171.85 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 179.94/180.25 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found x01:(P0 (f (f (f (f (f x))))))
% 179.94/180.25 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P0 (f (f (f (f (f x))))))
% 179.94/180.25 Found (fun (x01:(P0 (f (f (f (f (f x)))))))=> x01) as proof of (P1 (P0 (f (f (f (f (f x)))))))
% 179.94/180.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.94/180.25 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 179.94/180.25 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.94/180.25 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 179.94/180.25 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.94/180.25 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 179.94/180.25 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 179.94/180.25 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 179.94/180.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.94/180.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.94/180.25 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 179.94/180.25 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 179.94/180.25 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 179.94/180.25 Found x0:(P0 (f x))
% 179.94/180.25 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 179.94/180.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 179.94/180.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 179.94/180.25 Found x01:(P x)
% 179.94/180.25 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 179.94/180.25 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 179.94/180.25 Found x01:(P x)
% 179.94/180.25 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 179.94/180.25 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 179.94/180.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 179.94/180.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 179.94/180.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 179.94/180.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 179.94/180.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 179.94/180.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 179.94/180.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 179.94/180.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.62/186.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 186.62/186.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.62/186.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 186.62/186.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.62/186.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 186.62/186.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 186.62/186.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.62/186.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 186.62/186.91 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 186.62/186.91 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 186.62/186.91 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 186.62/186.91 Found x01:(P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 186.62/186.91 Found x01:(P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 186.62/186.91 Found x01:(P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 186.62/186.91 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 186.62/186.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 186.62/186.91 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 186.62/186.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 186.62/186.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 186.62/186.91 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 186.62/186.91 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 186.62/186.91 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 186.62/186.91 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 230.59/230.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.59/230.92 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 230.59/230.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.59/230.92 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.59/230.92 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 230.59/230.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 230.59/230.92 Found x01:(P (f (f x)))
% 230.59/230.92 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P (f (f x)))
% 230.59/230.92 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P0 (f (f x)))
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 230.59/230.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 230.59/230.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 230.59/230.92 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 230.59/230.92 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 230.59/230.92 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 230.59/230.92 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 230.59/230.92 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 230.59/230.92 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 230.59/230.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 230.59/230.92 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 230.59/230.92 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 230.59/230.92 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 230.59/230.92 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 230.59/230.92 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 239.16/239.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 239.16/239.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 239.16/239.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 239.16/239.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.16/239.53 Found x01:(P x)
% 239.16/239.53 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 239.16/239.53 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 239.16/239.53 Found x01:(P x)
% 239.16/239.53 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 239.16/239.53 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 239.16/239.53 Found x0:(P x)
% 239.16/239.53 Found x0 as proof of (P1 x)
% 239.16/239.53 Found x0:(P x)
% 239.16/239.53 Found x0 as proof of (P1 (P0 x))
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 239.16/239.53 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 239.16/239.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 239.16/239.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 239.16/239.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 239.16/239.53 Found x0:(P (f (f (f x))))
% 239.16/239.53 Instantiate: b:=(f (f (f x))):Prop
% 239.16/239.53 Found x0 as proof of (P0 b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 239.16/239.53 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 239.16/239.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.16/239.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.16/239.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.16/239.53 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 239.16/239.53 Found (eq_ref0 b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) x)
% 239.16/239.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.16/239.53 Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% 239.16/239.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% 257.08/257.43 Found x0:(P x)
% 257.08/257.43 Found x0 as proof of (P1 x)
% 257.08/257.43 Found x0:(P x)
% 257.08/257.43 Found x0 as proof of (P1 (P0 (P x)))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 257.08/257.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 257.08/257.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found x000:(P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P2 x)
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 257.08/257.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 257.08/257.43 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 257.08/257.43 Found x000:(P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P2 x)
% 257.08/257.43 Found x000:(P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P1 x)
% 257.08/257.43 Found (fun (x000:(P1 x))=> x000) as proof of (P2 x)
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f (f (f x))))))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f (f (f x))))))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f (f (f x))))))
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f (f (f x))))))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 257.08/257.43 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 257.08/257.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 257.08/257.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 257.08/257.43 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 257.08/257.43 Found x0:(P0 (f (f (f (f x)))))
% 257.08/257.43 Found x0 as proof of (P1 (f (f x)))
% 257.08/257.43 Found x0:(P0 (f (f (f (f x)))))
% 257.08/257.43 Found x0 as proof of (P1 (f (f (f x))))
% 257.08/257.43 Found x0:(P0 (f (f (f (f x)))))
% 257.08/257.43 Found x0 as proof of (P1 (P0 (f (f (f (f x))))))
% 257.08/257.43 Found x0:(P0 (f (f (f (f x)))))
% 257.08/257.43 Found x0 as proof of (P1 (f (f (f (f x)))))
% 257.08/257.43 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 257.08/257.43 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 257.08/257.43 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 257.08/257.43 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 262.54/262.93 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found x01:(P0 (f (f (f (f x)))))
% 262.54/262.93 Found (fun (x01:(P0 (f (f (f (f x))))))=> x01) as proof of (P0 (f (f (f (f x)))))
% 262.54/262.93 Found (fun (x01:(P0 (f (f (f (f x))))))=> x01) as proof of (P1 (P0 (f (f (f (f x))))))
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 262.54/262.93 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 262.54/262.93 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 262.54/262.93 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 262.54/262.93 Found eq_ref00:=(eq_ref0 (f (f (f (f x))))):(((eq Prop) (f (f (f (f x))))) (f (f (f (f x)))))
% 262.54/262.93 Found (eq_ref0 (f (f (f (f x))))) as proof of (((eq Prop) (f (f (f (f x))))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f (f x))))) as proof of (((eq Prop) (f (f (f (f x))))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f (f x))))) as proof of (((eq Prop) (f (f (f (f x))))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f (f x))))) as proof of (((eq Prop) (f (f (f (f x))))) b)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 262.54/262.93 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 262.54/262.93 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 262.54/262.93 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 262.54/262.93 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 262.54/262.93 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 262.54/262.93 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 273.42/273.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 273.42/273.79 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 273.42/273.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 273.42/273.79 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 273.42/273.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 273.42/273.79 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 273.42/273.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 273.42/273.79 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 273.42/273.79 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 273.42/273.79 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 273.42/273.79 Found x01:(P (f (f x)))
% 273.42/273.79 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P (f (f x)))
% 273.42/273.79 Found (fun (x01:(P (f (f x))))=> x01) as proof of (P0 (f (f x)))
% 273.42/273.79 Found x01:(P0 (f (f (f (f x)))))
% 273.42/273.79 Found (fun (x01:(P0 (f (f (f (f x))))))=> x01) as proof of (P0 (f (f (f (f x)))))
% 273.42/273.79 Found (fun (x01:(P0 (f (f (f (f x))))))=> x01) as proof of (P1 (P0 (f (f (f (f x))))))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 273.42/273.79 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 273.42/273.79 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 273.42/273.79 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 273.42/273.79 Found x0:(P (f (f (f x))))
% 273.42/273.79 Instantiate: a:=(f (f x)):Prop
% 273.42/273.79 Found x0 as proof of (P0 (P (f a)))
% 273.42/273.79 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 273.42/273.79 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 273.42/273.79 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 273.42/273.79 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 273.42/273.79 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 273.42/273.79 Found x0:(P (f (f (f x))))
% 273.42/273.79 Instantiate: a:=(f (f x)):Prop
% 273.42/273.79 Found x0 as proof of (P0 a)
% 273.42/273.79 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a
%------------------------------------------------------------------------------