TSTP Solution File: SYO040^2 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SYO040^2 : TPTP v7.5.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 0s
% DateTime : Tue Mar 29 00:50:28 EDT 2022
% Result : Timeout 289.97s 290.38s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SYO040^2 : TPTP v7.5.0. Released v4.1.0.
% 0.11/0.12 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPUModel : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % RAMPerCPU : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % DateTime : Fri Mar 11 07:13:26 EST 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.11/0.34 Python 2.7.5
% 7.76/7.95 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 7.76/7.95 FOF formula (<kernel.Constant object at 0x226fe18>, <kernel.DependentProduct object at 0x2affbcaabcf8>) of role type named f
% 7.76/7.95 Using role type
% 7.76/7.95 Declaring f:(Prop->Prop)
% 7.76/7.95 FOF formula (<kernel.Constant object at 0x226f248>, <kernel.DependentProduct object at 0x2affbcaadb48>) of role type named h
% 7.76/7.95 Using role type
% 7.76/7.95 Declaring h:(Prop->fofType)
% 7.76/7.95 FOF formula (<kernel.Constant object at 0x226f248>, <kernel.Sort object at 0x2affbca895a8>) of role type named x
% 7.76/7.95 Using role type
% 7.76/7.95 Declaring x:Prop
% 7.76/7.95 FOF formula (((eq fofType) (h (f (f (f x))))) (h (f x))) of role conjecture named 2
% 7.76/7.95 Conjecture to prove = (((eq fofType) (h (f (f (f x))))) (h (f x))):Prop
% 7.76/7.95 Parameter fofType_DUMMY:fofType.
% 7.76/7.95 We need to prove ['(((eq fofType) (h (f (f (f x))))) (h (f x)))']
% 7.76/7.95 Parameter f:(Prop->Prop).
% 7.76/7.95 Parameter fofType:Type.
% 7.76/7.95 Parameter h:(Prop->fofType).
% 7.76/7.95 Parameter x:Prop.
% 7.76/7.95 Trying to prove (((eq fofType) (h (f (f (f x))))) (h (f x)))
% 7.76/7.95 Found x01:(P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 7.76/7.95 Found x01:(P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 7.76/7.95 Found x01:(P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 7.76/7.95 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 7.76/7.95 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 7.76/7.95 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 7.76/7.95 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 7.76/7.95 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 7.76/7.95 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 7.76/7.95 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 7.76/7.95 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 7.76/7.95 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 7.76/7.95 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 7.76/7.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 7.76/7.95 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 7.76/7.95 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 7.76/7.95 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 7.76/7.95 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 7.76/7.95 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 7.76/7.95 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 7.76/7.95 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 24.44/24.62 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 24.44/24.62 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 24.44/24.62 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 24.44/24.62 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 24.44/24.62 Found x01:(P (h (f x)))
% 24.44/24.62 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P (h (f x)))
% 24.44/24.62 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P0 (h (f x)))
% 24.44/24.62 Found x01:(P (h (f x)))
% 24.44/24.62 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P (h (f x)))
% 24.44/24.62 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P0 (h (f x)))
% 24.44/24.62 Found x01:(P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 24.44/24.62 Found x01:(P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 24.44/24.62 Found x01:(P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 24.44/24.62 Found x01:(P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 24.44/24.62 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 24.44/24.62 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 24.44/24.62 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.44/24.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.44/24.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 24.44/24.62 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 24.44/24.62 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.44/24.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 24.44/24.62 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 24.44/24.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.44/24.62 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 24.44/24.62 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 24.44/24.62 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 24.44/24.62 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 24.44/24.62 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 24.44/24.62 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 36.12/36.37 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 36.12/36.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 36.12/36.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 36.12/36.37 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 36.12/36.37 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 36.12/36.37 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 36.12/36.37 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 36.12/36.37 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 36.12/36.37 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 ((P (f x))->(P (f x))))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 x)
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (f x))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 36.12/36.37 Found x01:(P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 36.12/36.37 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 54.60/54.82 Found x01:(P (f x))
% 54.60/54.82 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 54.60/54.82 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 54.60/54.82 Found x01:(P (f x))
% 54.60/54.82 Found (fun (x01:(P (f x)))=> x01) as proof of (P (f x))
% 54.60/54.82 Found (fun (x01:(P (f x)))=> x01) as proof of (P0 (P (f x)))
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 54.60/54.82 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 54.60/54.82 Found (eq_ref0 (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found ((eq_ref Prop) (f x)) as proof of (P (((eq Prop) (f x)) (f x)))
% 54.60/54.82 Found x0:(P (h (f (f (f x)))))
% 54.60/54.82 Instantiate: b:=(h (f (f (f x)))):fofType
% 54.60/54.82 Found x0 as proof of (P0 b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 54.60/54.82 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 54.60/54.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 54.60/54.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 54.60/54.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.60/54.82 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 54.60/54.82 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.60/54.82 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 54.60/54.82 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 54.60/54.82 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.60/54.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 54.60/54.82 Found x0:(P0 (f x))
% 54.60/54.82 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 54.60/54.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 54.60/54.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 54.60/54.82 Found x0:(P0 (f x))
% 54.60/54.82 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 54.60/54.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 54.60/54.82 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 54.60/54.82 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 54.60/54.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 54.60/54.82 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 54.60/54.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 64.99/65.25 Found x0:(P0 (f x))
% 64.99/65.25 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 64.99/65.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 64.99/65.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 64.99/65.25 Found x0:(P0 (f x))
% 64.99/65.25 Found (fun (x0:(P0 (f x)))=> x0) as proof of (P0 (f x))
% 64.99/65.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of ((P0 (f x))->(P0 (f x)))
% 64.99/65.25 Found (fun (P0:(Prop->Prop)) (x0:(P0 (f x)))=> x0) as proof of (P x)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found x01:(P x)
% 64.99/65.25 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 64.99/65.25 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 64.99/65.25 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 64.99/65.25 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 64.99/65.25 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 64.99/65.25 Found x0:(P (h (f (f (f x)))))
% 64.99/65.25 Instantiate: a:=(f (f (f x))):Prop
% 64.99/65.25 Found x0 as proof of (P0 (h a))
% 83.27/83.53 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 83.27/83.53 Found (eq_ref0 a) as proof of (((eq Prop) a) (f x))
% 83.27/83.53 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 83.27/83.53 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 83.27/83.53 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f x))
% 83.27/83.53 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 83.27/83.53 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 83.27/83.53 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 83.27/83.53 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 83.27/83.53 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 83.27/83.53 Found x0:(P0 b)
% 83.27/83.53 Instantiate: b:=(h (f (f (f x)))):fofType
% 83.27/83.53 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (h (f (f (f x)))))
% 83.27/83.53 Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (h (f (f (f x))))))
% 83.27/83.53 Found (fun (P0:(fofType->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 83.27/83.53 Found x0:(P (h (f x)))
% 83.27/83.53 Instantiate: b:=(h (f x)):fofType
% 83.27/83.53 Found x0 as proof of (P0 b)
% 83.27/83.53 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 83.27/83.53 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 83.27/83.53 Found x01:(P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 83.27/83.53 Found x01:(P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 83.27/83.53 Found x01:(P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 83.27/83.53 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 83.27/83.53 Found x01:(P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 83.27/83.53 Found x01:(P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 83.27/83.53 Found x01:(P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 83.27/83.53 Found x01:(P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P (f (f (f x))))
% 83.27/83.53 Found (fun (x01:(P (f (f (f x)))))=> x01) as proof of (P0 (P (f (f (f x)))))
% 83.27/83.53 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 83.27/83.53 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 83.27/83.53 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b0)
% 83.27/83.53 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 83.27/83.53 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 83.27/83.53 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f x)))
% 83.27/83.53 Found x02:(P (h (f (f (f x)))))
% 90.43/90.67 Found (fun (x02:(P (h (f (f (f x))))))=> x02) as proof of (P (h (f (f (f x)))))
% 90.43/90.67 Found (fun (x02:(P (h (f (f (f x))))))=> x02) as proof of (P0 (h (f (f (f x)))))
% 90.43/90.67 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 90.43/90.67 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 90.43/90.67 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 90.43/90.67 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 90.43/90.67 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 90.43/90.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 90.43/90.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 90.43/90.67 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 90.43/90.67 Found x0:(P (f (f (f x))))
% 90.43/90.67 Instantiate: b:=(f (f (f x))):Prop
% 90.43/90.67 Found x0 as proof of (P0 b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 90.43/90.67 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 90.43/90.67 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 90.43/90.67 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 90.43/90.67 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found x0:(P (f (f (f x))))
% 90.43/90.67 Instantiate: b:=(f (f (f x))):Prop
% 90.43/90.67 Found x0 as proof of (P0 b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 90.43/90.67 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 90.43/90.67 Found x01:(P x)
% 90.43/90.67 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 90.43/90.67 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 90.43/90.67 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 90.43/90.67 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 90.43/90.67 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.06/100.34 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.06/100.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 100.06/100.34 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 100.06/100.34 Found x01:(P x)
% 100.06/100.34 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 100.06/100.34 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 100.06/100.34 Found x0:(P (f (f (f x))))
% 100.06/100.34 Instantiate: a:=(f (f x)):Prop
% 100.06/100.34 Found x0 as proof of (P0 a)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 100.06/100.34 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found x0:(P (f (f (f x))))
% 100.06/100.34 Instantiate: a:=(f (f x)):Prop
% 100.06/100.34 Found x0 as proof of (P0 (P (f a)))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 100.06/100.34 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found x0:(P (f (f (f x))))
% 100.06/100.34 Instantiate: a:=(f (f x)):Prop
% 100.06/100.34 Found x0 as proof of (P0 (f a))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 100.06/100.34 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 100.06/100.34 Found x01:(P x)
% 100.06/100.34 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 100.06/100.34 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 100.06/100.34 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.06/100.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 100.06/100.34 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.06/100.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 100.06/100.34 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 100.06/100.34 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 100.06/100.34 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 100.06/100.34 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 105.02/105.28 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.02/105.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 105.02/105.28 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.02/105.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found x0:(P (f (f (f x))))
% 105.02/105.28 Instantiate: a:=(f (f x)):Prop
% 105.02/105.28 Found x0 as proof of (P0 a)
% 105.02/105.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 105.02/105.28 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found x0:(P (f (f (f x))))
% 105.02/105.28 Instantiate: a:=(f (f x)):Prop
% 105.02/105.28 Found x0 as proof of (P0 (P (f a)))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 105.02/105.28 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found x0:(P (f (f (f x))))
% 105.02/105.28 Instantiate: a:=(f (f x)):Prop
% 105.02/105.28 Found x0 as proof of (P0 (f a))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 105.02/105.28 Found (eq_ref0 a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) x)
% 105.02/105.28 Found x01:(P x)
% 105.02/105.28 Found (fun (x01:(P x))=> x01) as proof of (P x)
% 105.02/105.28 Found (fun (x01:(P x))=> x01) as proof of (P0 x)
% 105.02/105.28 Found x0:(P (h (f x)))
% 105.02/105.28 Instantiate: a:=(f x):Prop
% 105.02/105.28 Found x0 as proof of (P0 (h a))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 105.02/105.28 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f (f x))))
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 105.02/105.28 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f (f x))))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 105.02/105.28 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 105.02/105.28 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 105.02/105.28 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 105.02/105.28 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 105.02/105.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 105.02/105.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 105.02/105.28 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 105.02/105.28 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 105.02/105.28 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 117.56/117.86 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 117.56/117.86 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 117.56/117.86 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 117.56/117.86 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 117.56/117.86 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 117.56/117.86 Found x01:(P b)
% 117.56/117.86 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 117.56/117.86 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.56/117.86 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 117.56/117.86 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found x01:(P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P2 (h (f x)))
% 117.56/117.86 Found x01:(P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P2 (h (f x)))
% 117.56/117.86 Found x01:(P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P2 (h (f x)))
% 117.56/117.86 Found x01:(P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P1 (h (f x)))
% 117.56/117.86 Found (fun (x01:(P1 (h (f x))))=> x01) as proof of (P2 (h (f x)))
% 117.56/117.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.56/117.86 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 117.56/117.86 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 117.56/117.86 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 117.56/117.86 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 117.56/117.86 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 117.56/117.86 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.54/125.82 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 125.54/125.82 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.54/125.82 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 125.54/125.82 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 125.54/125.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 125.54/125.82 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 125.54/125.82 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 125.54/125.82 Found x0:(P (f x))
% 125.54/125.82 Instantiate: b:=(f x):Prop
% 125.54/125.82 Found x0 as proof of (P0 b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 125.54/125.82 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 125.54/125.82 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 125.54/125.82 Found x02:(P (h (f x)))
% 125.54/125.82 Found (fun (x02:(P (h (f x))))=> x02) as proof of (P (h (f x)))
% 125.54/125.82 Found (fun (x02:(P (h (f x))))=> x02) as proof of (P0 (h (f x)))
% 125.54/125.82 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 125.54/125.82 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.54/125.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.54/125.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.54/125.82 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 125.54/125.82 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.54/125.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.54/125.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.54/125.82 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 125.54/125.82 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 125.54/125.82 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 125.54/125.82 Found x01:(P1 (f (f (f x))))
% 125.54/125.82 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 125.54/125.82 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 125.54/125.82 Found x01:(P1 (f (f (f x))))
% 125.54/125.82 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 137.00/137.29 Found (eq_ref0 b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 137.00/137.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 137.00/137.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 137.00/137.29 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) (h (f (f (f x)))))
% 137.00/137.29 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 137.00/137.29 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 137.00/137.29 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 137.00/137.29 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 137.00/137.29 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 137.00/137.29 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.00/137.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found x0:(P (f x))
% 137.00/137.29 Instantiate: b:=(f x):Prop
% 137.00/137.29 Found x0 as proof of (P0 b)
% 137.00/137.29 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 137.00/137.29 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found x01:(P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P1 (f (f (f x))))
% 137.00/137.29 Found (fun (x01:(P1 (f (f (f x)))))=> x01) as proof of (P2 (P1 (f (f (f x)))))
% 137.00/137.29 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 137.00/137.29 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 137.00/137.29 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 137.00/137.29 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 137.00/137.29 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 137.00/137.29 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 137.00/137.29 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b0)
% 137.00/137.29 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 137.00/137.29 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f x))
% 137.00/137.29 Found x0:(P (f x))
% 137.00/137.29 Instantiate: b:=(f x):Prop
% 159.54/159.88 Found x0 as proof of (P0 b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 159.54/159.88 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 159.54/159.88 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 159.54/159.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 159.54/159.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 159.54/159.88 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 159.54/159.88 Found x0:(P (f x))
% 159.54/159.88 Instantiate: b:=(f x):Prop
% 159.54/159.88 Found x0 as proof of (P0 b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 159.54/159.88 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 159.54/159.88 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 159.54/159.88 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found x01:(P (h (f (f (f x)))))
% 159.54/159.88 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 159.54/159.88 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 159.54/159.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 159.54/159.88 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 159.54/159.88 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found x0:(P (f (f x)))
% 159.54/159.88 Instantiate: b:=(f (f x)):Prop
% 159.54/159.88 Found x0 as proof of (P0 b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 159.54/159.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found x0:(P (f (f x)))
% 159.54/159.88 Instantiate: b:=(f (f x)):Prop
% 159.54/159.88 Found x0 as proof of (P0 b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 159.54/159.88 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 159.54/159.88 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 159.54/159.88 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 159.54/159.88 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 159.54/159.88 Found x01:(P (h (f x)))
% 159.54/159.88 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P (h (f x)))
% 159.54/159.88 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P0 (h (f x)))
% 159.54/159.88 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 159.54/159.88 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 165.30/165.63 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 165.30/165.63 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 165.30/165.63 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 165.30/165.63 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 165.30/165.63 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 165.30/165.63 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 165.30/165.63 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 165.30/165.63 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 168.65/168.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 168.65/168.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 168.65/168.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found x01:(P (h (f (f (f x)))))
% 168.65/168.96 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 168.65/168.96 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 168.65/168.96 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 168.65/168.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 168.65/168.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 168.65/168.96 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 168.65/168.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 168.65/168.96 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 168.65/168.96 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 168.65/168.96 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 168.65/168.96 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 174.33/174.68 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 174.33/174.68 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 174.33/174.68 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 174.33/174.68 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 174.33/174.68 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 174.33/174.68 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found x01:(P (h (f (f (f x)))))
% 174.33/174.68 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P (h (f (f (f x)))))
% 174.33/174.68 Found (fun (x01:(P (h (f (f (f x))))))=> x01) as proof of (P0 (h (f (f (f x)))))
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (h (f (f (f x))))):(((eq fofType) (h (f (f (f x))))) (h (f (f (f x)))))
% 174.33/174.68 Found (eq_ref0 (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 174.33/174.68 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 174.33/174.68 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 174.33/174.68 Found ((eq_ref fofType) (h (f (f (f x))))) as proof of (((eq fofType) (h (f (f (f x))))) b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 174.33/174.68 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f x)))
% 174.33/174.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 174.33/174.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 174.33/174.68 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f x)))
% 174.33/174.68 Found x01:(P b)
% 174.33/174.68 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 174.33/174.68 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 174.33/174.68 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 174.33/174.68 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 174.33/174.68 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 174.33/174.68 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 174.33/174.68 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 174.33/174.68 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.22/181.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.22/181.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 181.22/181.61 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 181.22/181.61 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 181.22/181.61 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 181.22/181.61 Found x01:(P b)
% 181.22/181.61 Found (fun (x01:(P b))=> x01) as proof of (P b)
% 181.22/181.61 Found (fun (x01:(P b))=> x01) as proof of (P0 b)
% 181.22/181.61 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 181.22/181.61 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 181.22/181.61 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 181.22/181.61 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 181.22/181.61 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b0)
% 181.22/181.61 Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% 181.22/181.61 Found (eq_ref0 b0) as proof of (((eq fofType) b0) b)
% 181.22/181.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 181.22/181.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 181.22/181.61 Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) b)
% 181.22/181.61 Found x0:(P (f x))
% 181.22/181.61 Instantiate: a:=x:Prop
% 181.22/181.61 Found x0 as proof of (P0 (P (f a)))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.22/181.61 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found x0:(P (f x))
% 181.22/181.61 Instantiate: a:=x:Prop
% 181.22/181.61 Found x0 as proof of (P0 (f a))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.22/181.61 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found x0:(P (f x))
% 181.22/181.61 Instantiate: a:=x:Prop
% 181.22/181.61 Found x0 as proof of (P0 a)
% 181.22/181.61 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.22/181.61 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found x0:(P (f x))
% 181.22/181.61 Instantiate: a:=x:Prop
% 181.22/181.61 Found x0 as proof of (P0 (P (f a)))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.22/181.61 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found x0:(P (f x))
% 181.22/181.61 Instantiate: a:=x:Prop
% 181.22/181.61 Found x0 as proof of (P0 (f a))
% 181.22/181.61 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 181.22/181.61 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 181.22/181.61 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 a)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.69/191.03 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 190.69/191.03 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.69/191.03 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 190.69/191.03 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 190.69/191.03 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 190.69/191.03 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 (P (f a)))
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found x01:(P1 (f x))
% 190.69/191.03 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 190.69/191.03 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 190.69/191.03 Found x01:(P1 (f x))
% 190.69/191.03 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 190.69/191.03 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 a)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 a)
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 (f a))
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 190.69/191.03 Found x0:(P (f x))
% 190.69/191.03 Instantiate: a:=x:Prop
% 190.69/191.03 Found x0 as proof of (P0 (f a))
% 190.69/191.03 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 190.69/191.03 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found x0:(P (f x))
% 203.18/203.51 Instantiate: a:=x:Prop
% 203.18/203.51 Found x0 as proof of (P0 (P (f a)))
% 203.18/203.51 Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% 203.18/203.51 Found (eq_ref0 a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found ((eq_ref Prop) a) as proof of (((eq Prop) a) (f (f x)))
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.18/203.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 203.18/203.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.18/203.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 203.18/203.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 203.18/203.51 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 203.18/203.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.18/203.51 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.18/203.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 203.18/203.51 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found x01:(P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 203.18/203.51 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 203.18/203.51 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 203.18/203.51 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 203.18/203.51 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 212.86/213.19 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 212.86/213.19 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 212.86/213.19 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 212.86/213.19 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 218.16/218.53 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found x02:(P (f x))
% 218.16/218.53 Found (fun (x02:(P (f x)))=> x02) as proof of (P (f x))
% 218.16/218.53 Found (fun (x02:(P (f x)))=> x02) as proof of (P0 (f x))
% 218.16/218.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.16/218.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 218.16/218.53 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found x02:(P (f x))
% 218.16/218.53 Found (fun (x02:(P (f x)))=> x02) as proof of (P (f x))
% 218.16/218.53 Found (fun (x02:(P (f x)))=> x02) as proof of (P0 (f x))
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 218.16/218.53 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.16/218.53 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 218.16/218.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.16/218.53 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 218.16/218.53 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.16/218.53 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 218.16/218.53 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 218.16/218.53 Found x0:(P (f (f x)))
% 218.16/218.53 Instantiate: b:=(f (f x)):Prop
% 218.16/218.53 Found x0 as proof of (P0 b)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 218.16/218.53 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 218.16/218.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 218.16/218.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 218.16/218.53 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 218.16/218.53 Found x01:(P (h (f x)))
% 218.16/218.53 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P (h (f x)))
% 218.16/218.53 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P0 (h (f x)))
% 218.16/218.53 Found x01:(P (h (f x)))
% 218.16/218.53 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P (h (f x)))
% 218.16/218.53 Found (fun (x01:(P (h (f x))))=> x01) as proof of (P0 (h (f x)))
% 218.16/218.53 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 218.16/218.53 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 218.16/218.53 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 229.70/230.02 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.70/230.02 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 229.70/230.02 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 229.70/230.02 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 229.70/230.02 Found x0:(P0 b)
% 229.70/230.02 Instantiate: b:=(f x):Prop
% 229.70/230.02 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f x))
% 229.70/230.02 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f x)))
% 229.70/230.02 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.70/230.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 229.70/230.02 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 229.70/230.02 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found x02:(P (f x))
% 229.70/230.02 Found (fun (x02:(P (f x)))=> x02) as proof of (P (f x))
% 229.70/230.02 Found (fun (x02:(P (f x)))=> x02) as proof of (P0 (f x))
% 229.70/230.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.70/230.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 229.70/230.02 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found x02:(P (f x))
% 229.70/230.02 Found (fun (x02:(P (f x)))=> x02) as proof of (P (f x))
% 229.70/230.02 Found (fun (x02:(P (f x)))=> x02) as proof of (P0 (f x))
% 229.70/230.02 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 229.70/230.02 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 229.70/230.02 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f (f x))))
% 229.70/230.02 Found x0:(P (f (f x)))
% 229.70/230.02 Instantiate: b:=(f (f x)):Prop
% 229.70/230.02 Found x0 as proof of (P0 b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 229.70/230.02 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 229.70/230.02 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 229.70/230.02 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 229.70/230.02 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 239.50/239.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 239.50/239.84 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 239.50/239.84 Found x0:(P0 b)
% 239.50/239.84 Instantiate: b:=(f x):Prop
% 239.50/239.84 Found (fun (x0:(P0 b))=> x0) as proof of (P0 (f x))
% 239.50/239.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of ((P0 b)->(P0 (f x)))
% 239.50/239.84 Found (fun (P0:(Prop->Prop)) (x0:(P0 b))=> x0) as proof of (P b)
% 239.50/239.84 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 239.50/239.84 Found (eq_ref0 b) as proof of (((eq Prop) b) (f (f x)))
% 239.50/239.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.50/239.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.50/239.84 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f (f x)))
% 239.50/239.84 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 239.50/239.84 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 239.50/239.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.50/239.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.50/239.84 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 239.50/239.84 Found x0:(P (f (f (f x))))
% 239.50/239.84 Instantiate: b:=(f (f (f x))):Prop
% 239.50/239.84 Found x0 as proof of (P0 b)
% 239.50/239.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 239.50/239.84 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 239.50/239.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 239.50/239.84 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 239.50/239.84 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 239.50/239.84 Found x01:(P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 239.50/239.84 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 239.50/239.84 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 244.26/244.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 244.26/244.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 244.26/244.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 244.26/244.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 244.26/244.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 244.26/244.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 244.26/244.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 244.26/244.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 244.26/244.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 244.26/244.64 Found x01:(P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 244.26/244.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 248.98/249.33 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 248.98/249.33 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 248.98/249.33 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 248.98/249.33 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 248.98/249.33 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 248.98/249.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 248.98/249.33 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 248.98/249.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 248.98/249.33 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 248.98/249.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 248.98/249.33 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 248.98/249.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 248.98/249.33 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 248.98/249.33 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 248.98/249.33 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 248.98/249.33 Found x01:(P1 (f x))
% 248.98/249.33 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x0:(P (f (f (f x))))
% 257.27/257.64 Instantiate: b:=(f (f (f x))):Prop
% 257.27/257.64 Found x0 as proof of (P0 b)
% 257.27/257.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 257.27/257.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 257.27/257.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 257.27/257.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 257.27/257.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 257.27/257.64 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 ((P1 (f x))->(P1 (f x))))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 257.27/257.64 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 257.27/257.64 Found (eq_ref0 b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) (f (f (f x))))
% 257.27/257.64 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 257.27/257.64 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 x)
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 257.27/257.64 Found x01:(P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 257.27/257.64 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 270.65/271.09 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 270.65/271.09 Found (eq_ref0 (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (P1 (((eq Prop) (f x)) (f x)))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (f x))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 270.65/271.09 Found x01:(P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P1 (f x))
% 270.65/271.09 Found (fun (x01:(P1 (f x)))=> x01) as proof of (P2 (P1 (f x)))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 270.65/271.09 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 270.65/271.09 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 270.65/271.09 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 270.65/271.09 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 270.65/271.09 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 270.65/271.09 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 270.65/271.09 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.65/271.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 270.65/271.09 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.65/271.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 270.65/271.09 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 270.65/271.09 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 270.65/271.09 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 270.65/271.09 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 270.65/271.09 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 270.65/271.09 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 280.36/280.78 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 280.36/280.78 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 280.36/280.78 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 280.36/280.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.36/280.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.36/280.78 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 x):(((eq Prop) x) x)
% 280.36/280.78 Found (eq_ref0 x) as proof of (((eq Prop) x) b)
% 280.36/280.78 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 280.36/280.78 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 280.36/280.78 Found ((eq_ref Prop) x) as proof of (((eq Prop) x) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 280.36/280.78 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b)
% 280.36/280.78 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 280.36/280.78 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 280.36/280.78 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b)
% 280.36/280.78 Found x0:(P x)
% 280.36/280.78 Instantiate: b:=x:Prop
% 280.36/280.78 Found x0 as proof of (P0 b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 280.36/280.78 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found x0:(P x)
% 280.36/280.78 Instantiate: b:=x:Prop
% 280.36/280.78 Found x0 as proof of (P0 b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 280.36/280.78 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f (f x)))):(((eq Prop) (f (f (f x)))) (f (f (f x))))
% 280.36/280.78 Found (eq_ref0 (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f (f x)))) as proof of (((eq Prop) (f (f (f x)))) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.36/280.78 Found (eq_ref0 b) as proof of (((eq Prop) b) (f x))
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (f x))
% 280.36/280.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.36/280.78 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 280.36/280.78 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.36/280.78 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 280.36/280.78 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 280.36/280.78 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 280.36/280.78 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 280.36/280.78 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 280.36/280.78 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 289.97/290.38 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 289.97/290.38 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% 289.97/290.38 Found (eq_ref0 b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found ((eq_ref fofType) b) as proof of (((eq fofType) b) (h (f (f (f x)))))
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (h (f x))):(((eq fofType) (h (f x))) (h (f x)))
% 289.97/290.38 Found (eq_ref0 (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found ((eq_ref fofType) (h (f x))) as proof of (((eq fofType) (h (f x))) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% 289.97/290.38 Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) b0)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 289.97/290.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.97/290.38 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 289.97/290.38 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% 289.97/290.38 Found (eq_ref0 b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found ((eq_ref Prop) b) as proof of (((eq Prop) b) x)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 289.97/290.38 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% 289.97/290.38 Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq Prop) (f (f x))) (f (f x)))
% 289.97/290.38 Found (eq_ref0 (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 289.97/290.38 Found ((eq_ref Prop) (f (f x))) as proof of (((eq Prop) (f (f x))) b0)
% 289.97/290.38 Found x0:(P x)
% 289.97/290.38 Instantiate: b:=x:Prop
% 289.97/290.38 Found x0 as proof of (P0 b)
% 289.97/290.38 Found eq_ref00:=(eq_ref0 (f (f x))):(((eq P
%------------------------------------------------------------------------------